diff --git a/buglist b/buglist index 66d1112..19c20b8 100644 --- a/buglist +++ b/buglist @@ -1,6 +1,6 @@ ========================================================================= -bug 7246: +bug 7247: todo 335: wish 1011: meh 5: @@ -12,6 +12,14 @@ dup 50006: nonextend 60077: ========================================================================= +bug 7246: kamke tests missing +kamke1 seems to be missing ode97 +kamke2 missing 104, 105 +kamke6 missing 332 +kamke7 missing 357, 359, 360, 362 and many others +kamke7 repeats 776 with different equations + +========================================================================= bug 7245: v81crcp50-2.6.5.2 and v81crcp50-2.6.5.3 graphs differ from CRC (see ps/v81crcp50-2.6.5.1-3.eps) diff --git a/changelog b/changelog index 898a111..e88dbba 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,22 @@ +20130715 tpd src/axiom-website/patches.html 20130715.01.tpd.patch +20130715 tpd buglist add kamke4, kamke6 missing bug +20130715 tpd src/axiom-website/CATS/index.html updated +20130715 tpd src/axiom-website/CATS/charlwood.input added +20130715 tpd src/axiom-website/CATS/charlwood.input.pdf added +20130715 tpd src/axiom-website/CATS/kamke6.input fixed +20130715 tpd src/axiom-website/CATS/kamke4.input fixed +20130715 tpd src/axiom-website/CATS/kamke0.txt added +20130715 tpd src/axiom-website/CATS/kamke1.txt added +20130715 tpd src/axiom-website/CATS/kamke2.txt added +20130715 tpd src/axiom-website/CATS/kamke3.txt added +20130715 tpd src/axiom-website/CATS/kamke5.txt added +20130715 tpd src/axiom-website/CATS/kamke6.txt added +20130715 tpd src/axiom-website/CATS/kamke7.txt added +20130715 tpd src/input/Makefile add charlwood +20130715 tpd src/input/charlwood.input added +20130714 tpd src/axiom-website/patches.html 20130714.02.tpd.patch +20140714 tpd src/input/Makefile charlwood.input added +20140714 tpd src/input/charlwood.input added 20130714 tpd src/axiom-website/patches.html 20130714.01.tpd.patch 20130714 tpd src/axiom-website/CATS/axiom.sty added 20130714 tpd src/axiom-website/CATS/index.html added @@ -79,7 +98,7 @@ 20130714 tpd src/axiom-website/CATS/richtrig700-799.input.pdf added 20130714 tpd src/axiom-website/CATS/richtrig800-899.input added 20130714 tpd src/axiom-website/CATS/richtrig800-899.input.pdf added -20130714 tpd src/axiom-website/CATS/richtrig900-920.input added +20130714 tpd src/axiom-website/CATS/richtrig900-920.input added 20130714 tpd src/axiom-website/CATS/richtrig900-920.input.pdf added 20130702 tpd src/axiom-website/patches.html 20130702.01.tpd.patch 20130702 tpd books/bookvolbib add Griesmer ref, sort items diff --git a/src/axiom-website/CATS/charlwood.input.pamphlet b/src/axiom-website/CATS/charlwood.input.pamphlet new file mode 100644 index 0000000..ddb9f5d --- /dev/null +++ b/src/axiom-website/CATS/charlwood.input.pamphlet @@ -0,0 +1,6914 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input charlwood.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +Integrals taken from sci.math.symbolic posting of Charlwood, Kevin +``Integration on Computer Algebra Systems'' +Electronic Journal of Mathematics and Technology (2008) +\verb|www.freepatentsonline.com/article/| +\verb|Electronic-journal-Mathematics-Technology/188213666.html| +by Albert Rich at +\verb|www.apmaths.uwo.ca/~arich/CharlwoodIntegrationProblems.pdf| +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f charlwood.output +)spool charlwood.output +)set message auto off +)clear all + +\end{chunk} +\subsection{Problem 1} +\begin{chunk}{*} + +--S 1 of 250 +t0001:= asin(x)*log(x) +--R +--R +--R (1) asin(x)log(x) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 250 +r0001:= -2*sqrt(1-x^2)+atanh(sqrt(1-x^2))-x*asin(x)*(1-log(x))+_ + sqrt(1-x^2)*log(x) +--R +--R +--R (2) +--R +--------+ +--------+ +--R | 2 | 2 +--R atanh(\|- x + 1 ) + (log(x) - 2)\|- x + 1 + x asin(x)log(x) - x asin(x) +--R Type: Expression(Integer) +--E 2 + +--S 3 of 250 +a0001:= integrate(t0001,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R | 2 | 2 +--R log(\|- x + 1 + 1) - log(\|- x + 1 - 1) +--R + +--R +--------+ +--R | 2 +--------+ +--R 2x\|- x + 1 | 2 +--R (- x log(x) + x)atan(-------------) + (2log(x) - 4)\|- x + 1 +--R 2 +--R 2x - 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 250 +m0001:= a0001-r0001 +--R +--R +--R (4) +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R log(\|- x + 1 + 1) - log(\|- x + 1 - 1) - 2atanh(\|- x + 1 ) +--R + +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R (- x log(x) + x)atan(-------------) - 2x asin(x)log(x) + 2x asin(x) +--R 2 +--R 2x - 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 250 +d0001:= D(m0001,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R - log(x)atan(-------------) - 2asin(x)log(x) +--R 2 +--R 2x - 1 +--R (5) -------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 5 + + +\end{chunk} +\subsection{Problem 2} +\begin{chunk}{*} + +--S 6 of 250 +t0002:= x*asin(x)/sqrt(1-x^2) +--R +--R +--R x asin(x) +--R (6) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 250 +r0002:= x-sqrt(1-x^2)*asin(x) +--R +--R +--R +--------+ +--R | 2 +--R (7) - asin(x)\|- x + 1 + x +--R Type: Expression(Integer) +--E 7 + +--S 8 of 250 +a0002:= integrate(t0002,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 2x\|- x + 1 +--R \|- x + 1 atan(-------------) + 2x +--R 2 +--R 2x - 1 +--R (8) ----------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 250 +m0002:= a0002-r0002 +--R +--R +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 2x\|- x + 1 | 2 +--R \|- x + 1 atan(-------------) + 2asin(x)\|- x + 1 +--R 2 +--R 2x - 1 +--R (9) ---------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 250 +d0002:= D(m0002,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R - x atan(-------------) - 2x asin(x) +--R 2 +--R 2x - 1 +--R (10) ------------------------------------ +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 10 + + +\end{chunk} +\subsection{Problem 3} +\begin{chunk}{*} + +--S 11 of 250 +t0003:= asin(sqrt(x+1)-sqrt(x)) +--R +--R +--R +-----+ +-+ +--R (11) asin(\|x + 1 - \|x ) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 250 +r0003:= ((sqrt(x)+3*sqrt(1+x))*sqrt(-x+sqrt(x)*sqrt(1+x)))/(4*sqrt(2))-_ + (3/8+x)*asin(sqrt(x)-sqrt(1+x)) +--R +--R +--R (12) +--R +----------------+ +--R +-----+ +-+ | +-+ +-----+ +-+ +-----+ +-+ +--R (6\|x + 1 + 2\|x )\|\|x \|x + 1 - x + (8x + 3)\|2 asin(\|x + 1 - \|x ) +--R -------------------------------------------------------------------------- +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 250 +a0003:= integrate(t0003,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 13 + +--S 14 of 250 +--m0003:= a0003-r0003 +--E 14 + +--S 15 of 250 +--d0003:= D(m0003,x) +--E 15 + + +\end{chunk} +\subsection{Problem 4} +\begin{chunk}{*} + +--S 16 of 250 +t0004:= log(1+x*sqrt(1+x^2)) +--R +--R +--R +------+ +--R | 2 +--R (13) log(x\|x + 1 + 1) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 250 +r0004:= -2*x+sqrt(2*(1+sqrt(5)))*atan(sqrt(-2+sqrt(5))*(x+sqrt(1+x^2)))-_ + sqrt(2*(-1+sqrt(5)))*atanh(sqrt(2+sqrt(5))*(x+sqrt(1+x^2)))+_ + x*log(1+x*sqrt(1+x^2)) +--R +--R +--R (14) +--R +------+ +---------+ +------+ +--------+ +--R | 2 | +-+ | 2 | +-+ +--R x log(x\|x + 1 + 1) - \|2\|5 - 2 atanh((\|x + 1 + x)\|\|5 + 2 ) +--R + +--R +---------+ +------+ +--------+ +--R | +-+ | 2 | +-+ +--R \|2\|5 + 2 atan((\|x + 1 + x)\|\|5 - 2 ) - 2x +--R Type: Expression(Integer) +--E 17 + +--S 18 of 250 +a0004:= integrate(t0004,x) +--R +--R +--R (15) +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((\|5 + 1)\|x + 1 - x\|5 - x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +--------+ +--------+ +------+ +--R | +-+ | +-+ +-+ +-+ | 2 +--R \|\|5 - 1 log(\|\|5 - 1 + x\|2 ) + 2x\|2 log(x\|x + 1 + 1) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ +-+ +--R - \|\|5 - 1 log(- \|\|5 - 1 + x\|2 ) +--R + +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((- \|5 - 1)\|x + 1 + x\|5 + x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +------+ +--------+ +--R +--------+ +-+ | 2 +-+ | +-+ +--R | +-+ ((\|5 - 1)\|x + 1 - x\|5 + x)\|\|5 + 1 +--R 2\|\|5 + 1 atan(--------------------------------------------) +--R +------+ +--R +-+ | 2 2 +-+ +--R 2x\|2 \|x + 1 + (- 2x - 2)\|2 +--R + +--R +--------+ +--R +--------+ | +-+ +--R | +-+ \|\|5 + 1 +-+ +--R - 2\|\|5 + 1 atan(-----------) - 4x\|2 +--R +-+ +--R x\|2 +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 250 +m0004:= a0004-r0004 +--R +--R +--R (16) +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((\|5 + 1)\|x + 1 - x\|5 - x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ +-+ +--R \|\|5 - 1 log(\|\|5 - 1 + x\|2 ) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ +-+ +--R - \|\|5 - 1 log(- \|\|5 - 1 + x\|2 ) +--R + +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((- \|5 - 1)\|x + 1 + x\|5 + x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +---------+ +------+ +--------+ +--R +-+ | +-+ | 2 | +-+ +--R 2\|2 \|2\|5 - 2 atanh((\|x + 1 + x)\|\|5 + 2 ) +--R + +--R +------+ +--------+ +--R +--------+ +-+ | 2 +-+ | +-+ +--R | +-+ ((\|5 - 1)\|x + 1 - x\|5 + x)\|\|5 + 1 +--R 2\|\|5 + 1 atan(--------------------------------------------) +--R +------+ +--R +-+ | 2 2 +-+ +--R 2x\|2 \|x + 1 + (- 2x - 2)\|2 +--R + +--R +--------+ +--R +--------+ | +-+ +--R | +-+ \|\|5 + 1 +--R - 2\|\|5 + 1 atan(-----------) +--R +-+ +--R x\|2 +--R + +--R +---------+ +------+ +--------+ +--R +-+ | +-+ | 2 | +-+ +--R - 2\|2 \|2\|5 + 2 atan((\|x + 1 + x)\|\|5 - 2 ) +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 250 +d0004:= D(m0004,x) +--R +--R +--R (17) +--R +------+ +--------+ +---------+ +--R +-+ | 2 +-+ | +-+ | +-+ +--R ((- \|5 - 1)\|x + 1 - x\|5 - 3x)\|\|5 - 2 \|2\|5 + 2 +--R + +--R +------+ +--------+ +---------+ +------+ +--R +-+ | 2 +-+ | +-+ | +-+ | 2 +--R ((- \|5 + 1)\|x + 1 - x\|5 + 3x)\|\|5 + 2 \|2\|5 - 2 + 8\|x + 1 +--R + +--R 4x +--R / +--R +------+ +--R | 2 3 +--R 4\|x + 1 + 4x + 4x +--R Type: Expression(Integer) +--E 20 + + +\end{chunk} +\subsection{Problem 5} +\begin{chunk}{*} + +--S 21 of 250 +t0005:= cos(x)^2/sqrt(cos(x)^4+cos(x)^2+1) +--R +--R +--R 2 +--R cos(x) +--R (18) ------------------------ +--R +---------------------+ +--R | 4 2 +--R \|cos(x) + cos(x) + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 250 +r0005:= x/3+1/3*atan((cos(x)*(1+cos(x)^2)*sin(x))/_ + (1+cos(x)^2*sqrt(1+cos(x)^2+cos(x)^4))) +--R +--R +--R 3 +--R (cos(x) + cos(x))sin(x) +--R atan(-----------------------------------) + x +--R +---------------------+ +--R 2 | 4 2 +--R cos(x) \|cos(x) + cos(x) + 1 + 1 +--R (19) --------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 250 +a0005:= integrate(t0005,x) +--R +--R +--R (20) +--R atan +--R 5 4 3 +--R (cos(x) + 2cos(x) + cos(x) )sin(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 6 +--R 4cos(x) - 2 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 250 +m0005:= a0005-r0005 +--R +--R +--R (21) +--R atan +--R 5 4 3 +--R (cos(x) + 2cos(x) + cos(x) )sin(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 6 +--R 4cos(x) - 2 +--R + +--R 3 +--R (cos(x) + cos(x))sin(x) +--R - 2atan(-----------------------------------) - 2x +--R +---------------------+ +--R 2 | 4 2 +--R cos(x) \|cos(x) + cos(x) + 1 + 1 +--R / +--R 6 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 250 +d0005:= D(m0005,x) +--R +--R +--R (22) +--R 26 25 24 23 +--R - 4cos(x) - 8cos(x) - 20cos(x) - 32cos(x) +--R + +--R 22 21 20 19 +--R - 44cos(x) - 56cos(x) - 72cos(x) - 88cos(x) +--R + +--R 18 17 16 15 +--R - 76cos(x) - 64cos(x) - 64cos(x) - 64cos(x) +--R + +--R 14 13 12 10 9 +--R - 36cos(x) - 8cos(x) - 4cos(x) + 12cos(x) + 24cos(x) +--R + +--R 8 7 6 +--R 16cos(x) + 8cos(x) + 4cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 27 26 25 +--R - 8cos(x) - 16cos(x) - 32cos(x) - 48cos(x) +--R + +--R 24 23 22 21 +--R - 72cos(x) - 96cos(x) - 128cos(x) - 160cos(x) +--R + +--R 20 19 18 17 +--R - 176cos(x) - 192cos(x) - 216cos(x) - 240cos(x) +--R + +--R 16 15 14 13 +--R - 209cos(x) - 178cos(x) - 156cos(x) - 134cos(x) +--R + +--R 12 11 10 9 +--R - 94cos(x) - 54cos(x) - 48cos(x) - 42cos(x) +--R + +--R 8 7 6 5 4 +--R - 29cos(x) - 16cos(x) - 11cos(x) - 6cos(x) - cos(x) +--R + +--R 3 2 +--R 4cos(x) + 3cos(x) + 2cos(x) + 1 +--R * +--R 2 +--R sin(x) +--R + +--R 30 29 28 27 26 +--R - 4cos(x) - 8cos(x) - 12cos(x) - 16cos(x) - 32cos(x) +--R + +--R 25 24 23 22 21 +--R - 48cos(x) - 52cos(x) - 56cos(x) - 72cos(x) - 88cos(x) +--R + +--R 20 19 18 17 16 +--R - 56cos(x) - 24cos(x) - 9cos(x) + 6cos(x) + 49cos(x) +--R + +--R 15 14 13 12 11 +--R 92cos(x) + 72cos(x) + 52cos(x) + 46cos(x) + 40cos(x) +--R + +--R 10 9 8 7 6 +--R 11cos(x) - 18cos(x) - 14cos(x) - 10cos(x) - 12cos(x) +--R + +--R 5 4 3 2 +--R - 14cos(x) - 8cos(x) - 2cos(x) - 2cos(x) - 2cos(x) - 1 +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 26 24 22 20 18 +--R 8cos(x) + 40cos(x) + 104cos(x) + 180cos(x) + 236cos(x) +--R + +--R 16 14 12 10 8 +--R 260cos(x) + 248cos(x) + 200cos(x) + 132cos(x) + 76cos(x) +--R + +--R 6 4 +--R 40cos(x) + 12cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 26 24 22 20 +--R 16cos(x) + 64cos(x) + 144cos(x) + 208cos(x) + 272cos(x) +--R + +--R 18 16 14 12 +--R 336cos(x) + 424cos(x) + 436cos(x) + 388cos(x) +--R + +--R 10 8 6 4 2 +--R 296cos(x) + 180cos(x) + 88cos(x) + 16cos(x) + 12cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 30 28 26 24 22 +--R 8cos(x) + 24cos(x) + 48cos(x) + 52cos(x) + 84cos(x) +--R + +--R 20 18 16 14 12 +--R 96cos(x) + 124cos(x) + 48cos(x) - 4cos(x) - 68cos(x) +--R + +--R 10 8 6 4 +--R - 40cos(x) - 28cos(x) - 4cos(x) - 4cos(x) +--R * +--R +---------------------+ +--R | 4 2 +--R \|cos(x) + cos(x) + 1 +--R + +--R 28 27 26 25 24 +--R - 4cos(x) - 8cos(x) - 24cos(x) - 40cos(x) - 68cos(x) +--R + +--R 23 22 21 20 +--R - 96cos(x) - 136cos(x) - 176cos(x) - 180cos(x) +--R + +--R 19 18 17 16 +--R - 184cos(x) - 164cos(x) - 144cos(x) - 80cos(x) +--R + +--R 15 14 13 12 11 +--R - 16cos(x) + 8cos(x) + 32cos(x) + 40cos(x) + 48cos(x) +--R + +--R 10 9 8 +--R 28cos(x) + 8cos(x) + 4cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 30 29 28 27 26 +--R - 8cos(x) - 16cos(x) - 40cos(x) - 64cos(x) - 112cos(x) +--R + +--R 25 24 23 22 +--R - 160cos(x) - 220cos(x) - 280cos(x) - 304cos(x) +--R + +--R 21 20 19 18 +--R - 328cos(x) - 328cos(x) - 328cos(x) - 289cos(x) +--R + +--R 17 16 15 14 +--R - 250cos(x) - 249cos(x) - 248cos(x) - 223cos(x) +--R + +--R 13 12 11 10 +--R - 198cos(x) - 174cos(x) - 150cos(x) - 100cos(x) +--R + +--R 9 8 7 6 5 +--R - 50cos(x) - 27cos(x) - 4cos(x) + 3cos(x) + 10cos(x) +--R + +--R 4 3 2 +--R 6cos(x) + 2cos(x) + cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 31 30 29 28 +--R - 4cos(x) - 8cos(x) - 16cos(x) - 24cos(x) - 48cos(x) +--R + +--R 27 26 25 24 23 +--R - 72cos(x) - 84cos(x) - 96cos(x) - 108cos(x) - 120cos(x) +--R + +--R 22 21 20 19 18 +--R - 84cos(x) - 48cos(x) - 29cos(x) - 10cos(x) + 36cos(x) +--R + +--R 17 16 15 14 13 +--R 82cos(x) + 76cos(x) + 70cos(x) + 78cos(x) + 86cos(x) +--R + +--R 12 11 10 9 8 +--R 53cos(x) + 20cos(x) + 11cos(x) + 2cos(x) - 13cos(x) +--R + +--R 7 6 5 4 3 2 +--R - 28cos(x) - 21cos(x) - 14cos(x) - 11cos(x) - 8cos(x) - 4cos(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 24 22 20 18 16 +--R 16cos(x) + 80cos(x) + 208cos(x) + 360cos(x) + 456cos(x) +--R + +--R 14 12 10 8 6 +--R 456cos(x) + 368cos(x) + 232cos(x) + 104cos(x) + 24cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 26 24 22 20 18 +--R 48cos(x) + 192cos(x) + 448cos(x) + 680cos(x) + 800cos(x) +--R + +--R 16 14 12 10 8 +--R 768cos(x) + 672cos(x) + 528cos(x) + 368cos(x) + 232cos(x) +--R + +--R 6 4 +--R 112cos(x) + 48cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 28 26 24 22 20 +--R 32cos(x) + 96cos(x) + 192cos(x) + 208cos(x) + 176cos(x) +--R + +--R 18 16 14 12 10 +--R 64cos(x) + 16cos(x) - 48cos(x) - 48cos(x) - 64cos(x) +--R + +--R 8 6 +--R - 32cos(x) - 16cos(x) +--R / +--R 26 25 24 23 22 +--R 12cos(x) + 24cos(x) + 60cos(x) + 96cos(x) + 144cos(x) +--R + +--R 21 20 19 18 +--R 192cos(x) + 216cos(x) + 240cos(x) + 228cos(x) +--R + +--R 17 16 15 14 +--R 216cos(x) + 192cos(x) + 168cos(x) + 144cos(x) +--R + +--R 13 12 11 10 9 +--R 120cos(x) + 96cos(x) + 72cos(x) + 48cos(x) + 24cos(x) +--R + +--R 8 +--R 12cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 27 26 25 24 +--R 24cos(x) + 48cos(x) + 96cos(x) + 144cos(x) + 192cos(x) +--R + +--R 23 22 21 20 +--R 240cos(x) + 228cos(x) + 216cos(x) + 240cos(x) +--R + +--R 19 18 17 16 +--R 264cos(x) + 288cos(x) + 312cos(x) + 363cos(x) +--R + +--R 15 14 13 12 +--R 414cos(x) + 336cos(x) + 258cos(x) + 201cos(x) +--R + +--R 11 10 9 8 7 +--R 144cos(x) + 81cos(x) + 18cos(x) + 27cos(x) + 36cos(x) +--R + +--R 6 5 4 3 2 +--R 24cos(x) + 12cos(x) + 9cos(x) + 6cos(x) + 3cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 30 29 28 27 26 +--R 12cos(x) + 24cos(x) + 36cos(x) + 48cos(x) + 60cos(x) +--R + +--R 25 24 23 22 21 +--R 72cos(x) + 48cos(x) + 24cos(x) + 72cos(x) + 120cos(x) +--R + +--R 20 19 18 17 16 +--R 96cos(x) + 72cos(x) + 87cos(x) + 102cos(x) - 27cos(x) +--R + +--R 15 14 13 12 11 +--R - 156cos(x) - 129cos(x) - 102cos(x) - 117cos(x) - 132cos(x) +--R + +--R 10 9 8 7 6 +--R - 45cos(x) + 42cos(x) + 27cos(x) + 12cos(x) + 24cos(x) +--R + +--R 5 4 2 +--R 36cos(x) + 18cos(x) + 3cos(x) + 6cos(x) + 3 +--R * +--R +-------------------------------------------+ +--R | 4 2 +---------------------+ +--R | 16cos(x) + 16cos(x) + 16 | 4 2 +--R |------------------------------------------- \|cos(x) + cos(x) + 1 +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 24 23 22 21 20 +--R 24cos(x) + 48cos(x) + 120cos(x) + 192cos(x) + 288cos(x) +--R + +--R 19 18 17 16 +--R 384cos(x) + 432cos(x) + 480cos(x) + 432cos(x) +--R + +--R 15 14 13 12 +--R 384cos(x) + 288cos(x) + 192cos(x) + 120cos(x) +--R + +--R 11 10 +--R 48cos(x) + 24cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 26 25 24 23 +--R 72cos(x) + 144cos(x) + 288cos(x) + 432cos(x) +--R + +--R 22 21 20 19 +--R 600cos(x) + 768cos(x) + 768cos(x) + 768cos(x) +--R + +--R 18 17 16 15 +--R 672cos(x) + 576cos(x) + 432cos(x) + 288cos(x) +--R + +--R 14 13 12 11 +--R 270cos(x) + 252cos(x) + 216cos(x) + 180cos(x) +--R + +--R 10 9 8 7 6 +--R 162cos(x) + 144cos(x) + 90cos(x) + 36cos(x) + 24cos(x) +--R + +--R 5 4 +--R 12cos(x) + 6cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 28 27 26 25 24 +--R 48cos(x) + 96cos(x) + 144cos(x) + 192cos(x) + 240cos(x) +--R + +--R 23 22 21 20 18 +--R 288cos(x) + 192cos(x) + 96cos(x) + 48cos(x) - 96cos(x) +--R + +--R 17 16 15 14 13 +--R - 192cos(x) - 132cos(x) - 72cos(x) - 108cos(x) - 144cos(x) +--R + +--R 12 11 10 9 7 +--R - 84cos(x) - 24cos(x) - 36cos(x) - 48cos(x) + 48cos(x) +--R + +--R 6 5 4 3 2 +--R 36cos(x) + 24cos(x) + 24cos(x) + 24cos(x) + 12cos(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R Type: Expression(Integer) +--E 25 + + +\end{chunk} +\subsection{Problem 6} +\begin{chunk}{*} + +--S 26 of 250 +t0006:= tan(x)*sqrt(1+tan(x)^4) +--R +--R +--R +-----------+ +--R | 4 +--R (23) tan(x)\|tan(x) + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 250 +r0006:= -1/2*asinh(tan(x)^2)-atanh((1-tan(x)^2)/(sqrt(2)*sqrt(1+tan(x)^4)))/_ + sqrt(2)+1/2*sqrt(1+tan(x)^4) +--R +--R +--R 2 +-----------+ +--R tan(x) - 1 +-+ | 4 +-+ 2 +--R 2atanh(------------------) + \|2 \|tan(x) + 1 - \|2 asinh(tan(x) ) +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R (24) -------------------------------------------------------------------- +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 250 +a0006:= integrate(t0006,x) +--R +--R +--R (25) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-----------------------+ +--R | 4 2 +--R +-+ 4 +-+ 2 |2cos(x) - 2cos(x) + 1 +--R (4\|2 cos(x) - 2\|2 cos(x) ) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 4 2 +--R 8cos(x) - 8cos(x) + 3 +--R + +--R log +--R +-----------------------+ +--R | 4 2 +--R 4 2 |2cos(x) - 2cos(x) + 1 4 +--R (2cos(x) - 2cos(x) ) |----------------------- + 3cos(x) +--R | 4 +--R \| cos(x) +--R + +--R 2 +--R - 4cos(x) + 2 +--R / +--R 4 +--R cos(x) +--R + +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R 2 |----------------------- +--R | 4 +--R \| cos(x) +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 250 +m0006:= a0006-r0006 +--R +--R +--R (26) +--R - +--R 2 +--R * +--R log +--R +-----------------------+ +--R | 4 2 +--R +-+ 4 +-+ 2 |2cos(x) - 2cos(x) + 1 +--R (4\|2 cos(x) - 2\|2 cos(x) ) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 4 2 +--R 8cos(x) - 8cos(x) + 3 +--R + +--R +-+ +--R \|2 +--R * +--R log +--R +-----------------------+ +--R | 4 2 +--R 4 2 |2cos(x) - 2cos(x) + 1 4 +--R (2cos(x) - 2cos(x) ) |----------------------- + 3cos(x) +--R | 4 +--R \| cos(x) +--R + +--R 2 +--R - 4cos(x) + 2 +--R / +--R 4 +--R cos(x) +--R + +--R 2 +-----------+ +--R tan(x) - 1 +-+ | 4 +--R - 4atanh(------------------) - 2\|2 \|tan(x) + 1 +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R + +--R +-----------------------+ +--R | 4 2 +--R +-+ |2cos(x) - 2cos(x) + 1 +-+ 2 +--R 2\|2 |----------------------- + 2\|2 asinh(tan(x) ) +--R | 4 +--R \| cos(x) +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 250 +d0006:= D(m0006,x) +--R +--R +--R (27) +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (8\|2 cos(x) - 12\|2 cos(x) + 8\|2 cos(x) - 2\|2 cos(x) )sin(x) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 8 6 4 2 +--R (16cos(x) - 32cos(x) + 30cos(x) - 14cos(x) + 3)sin(x) +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R + +--R 9 7 5 5 +--R (- 8cos(x) + 8cos(x) - 3cos(x) )tan(x) +--R + +--R 9 7 5 +--R (- 8cos(x) + 8cos(x) - 3cos(x) )tan(x) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 5 +--R (- 8\|2 cos(x) + 12\|2 cos(x) - 8\|2 cos(x) + 2\|2 cos(x) )tan(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R (- 8\|2 cos(x) + 12\|2 cos(x) - 8\|2 cos(x) + 2\|2 cos(x) )tan(x) +--R / +--R +-----------------------+ +--R | 4 2 +--R 9 7 5 |2cos(x) - 2cos(x) + 1 +--R (8cos(x) - 8cos(x) + 3cos(x) ) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R 8\|2 cos(x) - 12\|2 cos(x) + 8\|2 cos(x) - 2\|2 cos(x) +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R Type: Expression(Integer) +--E 30 + + +\end{chunk} +\subsection{Problem 7} +\begin{chunk}{*} + +--S 31 of 250 +t0007:= tan(x)/sqrt(1+sec(x)^3) +--R +--R +--R tan(x) +--R (28) -------------- +--R +-----------+ +--R | 3 +--R \|sec(x) + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 250 +r0007:= -2/3*atanh(sqrt(1+sec(x)^3)) +--R +--R +--R +-----------+ +--R | 3 +--R 2atanh(\|sec(x) + 1 ) +--R (29) - ---------------------- +--R 3 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 250 +a0007:= integrate(t0007,x) +--R +--R +--R (30) +--R - +--R log +--R 6 5 3 2 +--R (- 4cos(x) - 4cos(x) - 2cos(x) - 2cos(x) ) +--R * +--R +----------------------+ +--R | 2 +--R |4cos(x) - 4cos(x) + 4 +--R |---------------------- +--R | 2 +--R \| cos(x) + cos(x) +--R + +--R 6 3 +--R 8cos(x) + 8cos(x) + 1 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 250 +m0007:= a0007-r0007 +--R +--R +--R (31) +--R - +--R log +--R 6 5 3 2 +--R (- 4cos(x) - 4cos(x) - 2cos(x) - 2cos(x) ) +--R * +--R +----------------------+ +--R | 2 +--R |4cos(x) - 4cos(x) + 4 +--R |---------------------- +--R | 2 +--R \| cos(x) + cos(x) +--R + +--R 6 3 +--R 8cos(x) + 8cos(x) + 1 +--R + +--R +-----------+ +--R | 3 +--R 4atanh(\|sec(x) + 1 ) +--R / +--R 6 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 250 +d0007:= D(m0007,x) +--R +--R +--R (32) +--R +----------------------+ +--R +-----------+ | 2 +--R | 3 |4cos(x) - 4cos(x) + 4 +--R - 2sin(x)\|sec(x) + 1 + (- cos(x) - 1)tan(x) |---------------------- +--R | 2 +--R \| cos(x) + cos(x) +--R ----------------------------------------------------------------------- +--R +----------------------+ +--R | 2 +-----------+ +--R |4cos(x) - 4cos(x) + 4 | 3 +--R (cos(x) + 1) |---------------------- \|sec(x) + 1 +--R | 2 +--R \| cos(x) + cos(x) +--R Type: Expression(Integer) +--E 35 + + +\end{chunk} +\subsection{Problem 8} +\begin{chunk}{*} + +--S 36 of 250 +t0008:= sqrt(tan(x)^2+2*tan(x)+2) +--R +--R +--R +---------------------+ +--R | 2 +--R (33) \|tan(x) + 2tan(x) + 2 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 250 +r0008:= asinh(1+tan(x))+sqrt(1/2*(1+sqrt(5)))*_ + atan(((-sqrt(-1+sqrt(5)))+sqrt(1+sqrt(5))*tan(x))/_ + (sqrt(2)*sqrt(2+tan(x)*(2+tan(x)))))-_ + sqrt(1/2*(-1+sqrt(5)))*_ + atanh((sqrt(1+sqrt(5))+sqrt(-1+sqrt(5))*tan(x))/_ + (sqrt(2)*sqrt(2+tan(x)*(2+tan(x))))) +--R +--R +--R (34) +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ \|\|5 + 1 + tan(x)\|\|5 - 1 +--R - \|\|5 - 1 atanh(-------------------------------) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R + +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ tan(x)\|\|5 + 1 - \|\|5 - 1 +-+ +--R \|\|5 + 1 atan(-------------------------------) + \|2 asinh(tan(x) + 1) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 250 +a0008:= integrate(t0008,x) +--R +--R +--R (35) +--R [ +--R 4+-+ atan(2) +--R \|5 cos(-------) +--R 2 +--R * +--R log +--R 4+-+3 9 4+-+3 7 +--R - 38400\|5 cos(x) + 451328\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 169072\|5 cos(x) - 134856\|5 cos(x) +--R + +--R 4+-+3 +--R - 3760\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (- 39040\|5 + 640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (184768\|5 + 266560\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (6952\|5 - 204600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 61356\|5 - 157740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 3074\|5 - 5820\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 211200\|5 cos(x) + 203904\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R 322352\|5 cos(x) - 233648\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 35408\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 94720\|5 - 116480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (19584\|5 + 184320\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (182464\|5 + 208720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 63684\|5 - 247100\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 21759\|5 - 46975\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 9 4+-+3 7 +--R 211200\|5 cos(x) + 11904\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 568096\|5 cos(x) - 103208\|5 cos(x) +--R + +--R 4+-+3 +--R - 80\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (83200\|5 + 505600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (580352\|5 + 604160\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 500976\|5 - 1653200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 239244\|5 - 497740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 7102\|5 - 10480\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 38400\|5 cos(x) + 572672\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R - 276464\|5 cos(x) - 331064\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 13344\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 342400\|5 - 419200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (627136\|5 + 1772480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (244464\|5 - 266640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 459800\|5 - 1168280\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 62635\|5 - 110195\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 9 +--R (79104\|5 + 1228800)cos(x) +--R + +--R 4+-+2 7 +--R (- 1115328\|5 - 1857600)cos(x) +--R + +--R 4+-+2 5 +--R (335640\|5 - 1628200)cos(x) +--R + +--R 4+-+2 3 +--R (639072\|5 + 947080)cos(x) +--R + +--R 4+-+2 +--R (64992\|5 + 147580)cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 10 +--R (483072\|5 + 358400)cos(x) +--R + +--R 4+-+2 8 +--R (- 411840\|5 + 2104000)cos(x) +--R + +--R 4+-+2 6 +--R (- 1076712\|5 - 3359000)cos(x) +--R + +--R 4+-+2 4 +--R (679732\|5 + 91940)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (271292\|5 + 534070)cos(x) + 6656\|5 + 16540 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 246528\|5 - 358400)cos(x) +--R + +--R 4+-+2 7 +--R (- 1667904\|5 - 3089600)cos(x) +--R + +--R 4+-+2 5 +--R (1801320\|5 + 3027400)cos(x) +--R + +--R 4+-+2 3 +--R (1139496\|5 + 2216640)cos(x) +--R + +--R 4+-+2 +--R (61656\|5 + 133640)cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 55936\|5 + 292480)cos(x) +--R + +--R 4+-+2 7 +--R (- 549568\|5 - 1127360)cos(x) +--R + +--R 4+-+2 5 +--R (424480\|5 + 168880)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (409732\|5 + 790380)cos(x) + (41322\|5 + 94610)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 10 +--R (708096\|5 + 1228800)cos(x) +--R + +--R 4+-+2 8 +--R (- 1675520\|5 - 2707200)cos(x) +--R + +--R 4+-+2 6 +--R (- 1078016\|5 - 2334000)cos(x) +--R + +--R 4+-+2 4 +--R (1846276\|5 + 3353220)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (360756\|5 + 738960)cos(x) + 4208\|5 + 9720 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 10 4+-+2 8 +--R (260352\|5 + 368640)cos(x) + (- 468800\|5 - 4800)cos(x) +--R + +--R 4+-+2 6 +--R (- 428592\|5 - 1392000)cos(x) +--R + +--R 4+-+2 4 4+-+2 2 +--R (503512\|5 + 699440)cos(x) + (169147\|5 + 364435)cos(x) +--R + +--R 4+-+2 +--R 4451\|5 + 10610 +--R / +--R 4+-+3 4+-+ 7 +--R (25984\|5 + 55680\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 63008\|5 - 136480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 32640\|5 - 73760\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 952\|5 - 2240\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 8 +--R (30912\|5 + 66240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (20000\|5 + 46240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 60112\|5 - 132640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 8600\|5 - 19840\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 7 +--R (44352\|5 + 95040\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 101984\|5 - 220640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 54000\|5 - 122080\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 1496\|5 - 3520\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 8 +--R (47936\|5 + 102720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (37120\|5 + 85120\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 99536\|5 - 219520\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 14000\|5 - 32320\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 7 4+-+2 5 +--R - 143488\|5 cos(x) + 156480\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 246752\|5 cos(x) + 24736\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 8 4+-+2 6 +--R - 45184\|5 cos(x) - 256768\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 258464\|5 cos(x) + 105024\|5 cos(x) + 2464\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 7 4+-+2 5 +--R - 73984\|5 cos(x) + 71040\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 129536\|5 cos(x) + 12448\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 7 +--R (- 124288\|5 - 180480)cos(x) +--R + +--R 4+-+2 5 +--R (136000\|5 + 192000)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (213952\|5 + 311520)cos(x) + (21456\|5 + 30960)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 8 4+-+2 6 +--R - 14912\|5 cos(x) - 141824\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 131952\|5 cos(x) + 54832\|5 cos(x) + 1152\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 8 +--R (- 39584\|5 - 52640)cos(x) +--R + +--R 4+-+2 6 +--R (- 222208\|5 - 327680)cos(x) +--R + +--R 4+-+2 4 4+-+2 2 +--R (224184\|5 + 324440)cos(x) + (91064\|5 + 132440)cos(x) +--R + +--R 4+-+2 +--R 2144\|5 + 3045 +--R + +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) + 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (- 4\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (- 2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R - +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) - 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (4\|5 cos(x)sin(x) + 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R - 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R 4+-+ atan(2) +--R \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+ 4+-+ 2 atan(2) +--R (- 2\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+ 2 atan(2) +--R - 2\|5 cos(x)cos(-------)sin(x) - 4\|5 cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 4+-+2 2 4+-+2 +--R (2\|5 + 6)cos(x)sin(x) + (\|5 + 3)cos(x) + \|5 + 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 cos(-------) +--R 2 +--R * +--R atan +--R +---------------------------+ +--R | 2 +--R 4+-+ |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x)sin(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (- 2cos(x)sin(x) - cos(x) - 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - cos(x)cos(-------)sin(x) + (2cos(x) - 1)cos(-------) +--R 2 2 +--R / +--R +---------------------------+ +--R | 2 +--R 4+-+ 2 |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) + 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) + (- cos(x) - 1)cos(-------) +--R 2 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 sin(-------) +--R 2 +--R * +--R atan +--R 4+-+3 4+-+ 5 +--R (72\|5 - 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 62\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 36\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 + 76\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 107\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (- 96\|5 - 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 40\|5 + 144\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (8\|5 + 27\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 146\|5 - 362\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (17\|5 + 144\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 +--R - 240\|5 cos(x) + 540\|5 cos(x) +--R + +--R 4+-+2 +--R 202\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R - 320\|5 cos(x) - 120\|5 cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R 476\|5 cos(x) + 30\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (320\|5 cos(x) + 280\|5 cos(x) - 184\|5 cos(x)) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (56\|5 + 440)cos(x) + (78\|5 - 170)cos(x) +--R + +--R 4+-+2 +--R (79\|5 - 110)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 240\|5 cos(x) + 660\|5 cos(x) - 122\|5 cos(x) +--R + +--R 4+-+2 +--R - 50\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 192\|5 - 80)cos(x) + (100\|5 + 480)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (69\|5 - 290)cos(x) + 26\|5 - 10 +--R / +--R 4+-+3 4+-+ 5 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (40\|5 - 204\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 8\|5 - 59\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (- 72\|5 + 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (146\|5 + 34\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 17\|5 - 192\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 822\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 92\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 - 368\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 451\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 +--R - 320\|5 cos(x) - 280\|5 cos(x) +--R + +--R 4+-+2 +--R 184\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R 240\|5 cos(x) - 660\|5 cos(x) + 122\|5 cos(x) +--R + +--R 4+-+2 +--R 50\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R - 240\|5 cos(x) + 540\|5 cos(x) +--R + +--R 4+-+2 +--R 202\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (- 192\|5 - 80)cos(x) + (228\|5 + 920)cos(x) +--R + +--R 4+-+2 +--R (151\|5 + 320)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 320\|5 cos(x) - 120\|5 cos(x) + 476\|5 cos(x) +--R + +--R 4+-+2 +--R 30\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 56\|5 - 440)cos(x) + (- 218\|5 + 30)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (283\|5 + 760)cos(x) + 32\|5 + 50 +--R / +--R 4 +--R , +--R +--R - +--R 4+-+ atan(2) +--R \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+3 4+-+ 3 4+-+3 +--R ((6\|5 - 10\|5 )cos(x) - 2\|5 cos(x))sin(x) +--R + +--R 4+-+3 4+-+ 4 4+-+ 2 +--R (8\|5 + 20\|5 )cos(x) - 10\|5 cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 3 4+-+3 4+-+ +--R ((8\|5 - 20\|5 )cos(x) + (4\|5 + 10\|5 )cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 4 +--R (- 6\|5 - 10\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (10\|5 + 10\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 3 4+-+2 atan(2) +--R (- 12\|5 cos(x) + 12\|5 cos(x))cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 atan(2) +--R (- 16\|5 cos(x) + 4\|5 cos(x) + 4\|5 )cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 atan(2) 2 +--R (24\|5 cos(x) - 24\|5 cos(x))cos(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 +--R - 12\|5 cos(x) + (2\|5 - 30)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 atan(2) 2 +--R (32\|5 cos(x) - 8\|5 cos(x) - 8\|5 )cos(-------) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R - 16\|5 cos(x) + (- \|5 - 15)cos(x) - \|5 - 10 +--R / +--R 4+-+3 4+-+ 3 4+-+3 +--R ((24\|5 + 40\|5 )cos(x) + 8\|5 cos(x))sin(x) +--R + +--R 4+-+3 4+-+ 4 +--R (32\|5 - 80\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 12\|5 + 100\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 3 4+-+3 4+-+ +--R ((32\|5 + 80\|5 )cos(x) + (4\|5 + 20\|5 )cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 4 +--R (- 24\|5 + 40\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (44\|5 + 20\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (- 64\|5 cos(x) + (- 16\|5 - 80)cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 48\|5 cos(x) + (- 72\|5 - 40)cos(x) + 8\|5 +--R + +--R - 40 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 atan(2) 2 +--R (- 32\|5 cos(x) + (- 8\|5 - 40)cos(x))cos(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 +--R (16\|5 - 240)cos(x) + (- 56\|5 - 40)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R (24\|5 cos(x) + (- 36\|5 - 20)cos(x) + 4\|5 - 20) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 +--R (- 12\|5 + 180)cos(x) + (- 12\|5 - 260)cos(x) +--R + +--R 4+-+2 +--R - 17\|5 + 5 +--R + +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) + 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (- 4\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (- 2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R - +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) - 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (4\|5 cos(x)sin(x) + 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R - 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R 4+-+ atan(2) +--R \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+ 4+-+ 2 atan(2) +--R (- 2\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+ 2 atan(2) +--R - 2\|5 cos(x)cos(-------)sin(x) - 4\|5 cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 4+-+2 2 4+-+2 +--R (2\|5 + 6)cos(x)sin(x) + (\|5 + 3)cos(x) + \|5 + 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 cos(-------) +--R 2 +--R * +--R atan +--R +---------------------------+ +--R | 2 +--R 4+-+ |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x)sin(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (- 2cos(x)sin(x) - cos(x) - 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - cos(x)cos(-------)sin(x) + (2cos(x) - 1)cos(-------) +--R 2 2 +--R / +--R +---------------------------+ +--R | 2 +--R 4+-+ 2 |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) + 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) + (- cos(x) - 1)cos(-------) +--R 2 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 cos(-------) +--R 2 +--R * +--R atan +--R 4+-+2 2 atan(2) +--R \|5 cos(x) sin(-------) +--R 2 +--R + +--R 4+-+2 atan(2) +--R - \|5 cos(x)cos(-------)sin(x) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 4+-+ +--R \|5 cos(x)sin(x) - 2\|5 cos(x) + \|5 +--R / +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) )sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) - cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 4+-+ +--R 2\|5 cos(x)sin(x) + \|5 cos(x) + \|5 +--R / +--R 4 +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 38 + +--S 39 of 250 +m0008:= a0008.1-r0008 +--R +--R +--R (36) +--R +-+4+-+ atan(2) +--R \|2 \|5 cos(-------) +--R 2 +--R * +--R log +--R 4+-+3 9 4+-+3 7 +--R - 38400\|5 cos(x) + 451328\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 169072\|5 cos(x) - 134856\|5 cos(x) +--R + +--R 4+-+3 +--R - 3760\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (- 39040\|5 + 640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (184768\|5 + 266560\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (6952\|5 - 204600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 61356\|5 - 157740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 3074\|5 - 5820\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 211200\|5 cos(x) + 203904\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R 322352\|5 cos(x) - 233648\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 35408\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 94720\|5 - 116480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (19584\|5 + 184320\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (182464\|5 + 208720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 63684\|5 - 247100\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 21759\|5 - 46975\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 9 4+-+3 7 +--R 211200\|5 cos(x) + 11904\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 568096\|5 cos(x) - 103208\|5 cos(x) +--R + +--R 4+-+3 +--R - 80\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (83200\|5 + 505600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (580352\|5 + 604160\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 500976\|5 - 1653200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 239244\|5 - 497740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 7102\|5 - 10480\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 38400\|5 cos(x) + 572672\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R - 276464\|5 cos(x) - 331064\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 13344\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 342400\|5 - 419200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (627136\|5 + 1772480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (244464\|5 - 266640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 459800\|5 - 1168280\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 62635\|5 - 110195\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 9 +--R (79104\|5 + 1228800)cos(x) +--R + +--R 4+-+2 7 +--R (- 1115328\|5 - 1857600)cos(x) +--R + +--R 4+-+2 5 +--R (335640\|5 - 1628200)cos(x) +--R + +--R 4+-+2 3 +--R (639072\|5 + 947080)cos(x) +--R + +--R 4+-+2 +--R (64992\|5 + 147580)cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 10 +--R (483072\|5 + 358400)cos(x) +--R + +--R 4+-+2 8 +--R (- 411840\|5 + 2104000)cos(x) +--R + +--R 4+-+2 6 +--R (- 1076712\|5 - 3359000)cos(x) +--R + +--R 4+-+2 4 +--R (679732\|5 + 91940)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (271292\|5 + 534070)cos(x) + 6656\|5 + 16540 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 246528\|5 - 358400)cos(x) +--R + +--R 4+-+2 7 +--R (- 1667904\|5 - 3089600)cos(x) +--R + +--R 4+-+2 5 +--R (1801320\|5 + 3027400)cos(x) +--R + +--R 4+-+2 3 +--R (1139496\|5 + 2216640)cos(x) +--R + +--R 4+-+2 +--R (61656\|5 + 133640)cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 55936\|5 + 292480)cos(x) +--R + +--R 4+-+2 7 +--R (- 549568\|5 - 1127360)cos(x) +--R + +--R 4+-+2 5 +--R (424480\|5 + 168880)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (409732\|5 + 790380)cos(x) + (41322\|5 + 94610)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 10 +--R (708096\|5 + 1228800)cos(x) +--R + +--R 4+-+2 8 +--R (- 1675520\|5 - 2707200)cos(x) +--R + +--R 4+-+2 6 +--R (- 1078016\|5 - 2334000)cos(x) +--R + +--R 4+-+2 4 +--R (1846276\|5 + 3353220)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (360756\|5 + 738960)cos(x) + 4208\|5 + 9720 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 10 4+-+2 8 +--R (260352\|5 + 368640)cos(x) + (- 468800\|5 - 4800)cos(x) +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 428592\|5 - 1392000)cos(x) + (503512\|5 + 699440)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (169147\|5 + 364435)cos(x) + 4451\|5 + 10610 +--R / +--R 4+-+3 4+-+ 7 +--R (25984\|5 + 55680\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 63008\|5 - 136480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 32640\|5 - 73760\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 952\|5 - 2240\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 8 +--R (30912\|5 + 66240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (20000\|5 + 46240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 60112\|5 - 132640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 8600\|5 - 19840\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 7 +--R (44352\|5 + 95040\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 101984\|5 - 220640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 54000\|5 - 122080\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 1496\|5 - 3520\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 8 +--R (47936\|5 + 102720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (37120\|5 + 85120\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 99536\|5 - 219520\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 14000\|5 - 32320\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 7 4+-+2 5 +--R - 143488\|5 cos(x) + 156480\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 246752\|5 cos(x) + 24736\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 8 4+-+2 6 +--R - 45184\|5 cos(x) - 256768\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 258464\|5 cos(x) + 105024\|5 cos(x) + 2464\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 7 4+-+2 5 +--R - 73984\|5 cos(x) + 71040\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 129536\|5 cos(x) + 12448\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 7 +--R (- 124288\|5 - 180480)cos(x) +--R + +--R 4+-+2 5 +--R (136000\|5 + 192000)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (213952\|5 + 311520)cos(x) + (21456\|5 + 30960)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 8 4+-+2 6 +--R - 14912\|5 cos(x) - 141824\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 131952\|5 cos(x) + 54832\|5 cos(x) + 1152\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 8 4+-+2 6 +--R (- 39584\|5 - 52640)cos(x) + (- 222208\|5 - 327680)cos(x) +--R + +--R 4+-+2 4 4+-+2 2 +--R (224184\|5 + 324440)cos(x) + (91064\|5 + 132440)cos(x) +--R + +--R 4+-+2 +--R 2144\|5 + 3045 +--R + +--R +-+ +--R 2\|2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) + 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (- 4\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (- 2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R - +--R +-+ +--R 2\|2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) - 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (4\|5 cos(x)sin(x) + 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R - 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R +-+4+-+ atan(2) +--R \|2 \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+ 4+-+ 2 atan(2) +--R (- 2\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+ 2 atan(2) +--R - 2\|5 cos(x)cos(-------)sin(x) - 4\|5 cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 4+-+2 2 4+-+2 +--R (2\|5 + 6)cos(x)sin(x) + (\|5 + 3)cos(x) + \|5 + 2 +--R + +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ \|\|5 + 1 + tan(x)\|\|5 - 1 +--R 4\|\|5 - 1 atanh(-------------------------------) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R + +--R - +--R +-+4+-+ atan(2) +--R 2\|2 \|5 cos(-------) +--R 2 +--R * +--R atan +--R +---------------------------+ +--R | 2 +--R 4+-+ |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x)sin(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (- 2cos(x)sin(x) - cos(x) - 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - cos(x)cos(-------)sin(x) + (2cos(x) - 1)cos(-------) +--R 2 2 +--R / +--R +---------------------------+ +--R | 2 +--R 4+-+ 2 |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) + 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) + (- cos(x) - 1)cos(-------) +--R 2 2 +--R + +--R - +--R +-+4+-+ atan(2) +--R 2\|2 \|5 sin(-------) +--R 2 +--R * +--R atan +--R 4+-+3 4+-+ 5 +--R (72\|5 - 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 62\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 36\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 + 76\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 107\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (- 96\|5 - 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 4+-+3 4+-+ +--R (- 40\|5 + 144\|5 )cos(x) + (8\|5 + 27\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 146\|5 - 362\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (17\|5 + 144\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (- 240\|5 cos(x) + 540\|5 cos(x) + 202\|5 cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 320\|5 cos(x) - 120\|5 cos(x) + 476\|5 cos(x) +--R + +--R 4+-+2 +--R 30\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (320\|5 cos(x) + 280\|5 cos(x) - 184\|5 cos(x)) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (56\|5 + 440)cos(x) + (78\|5 - 170)cos(x) +--R + +--R 4+-+2 +--R (79\|5 - 110)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 240\|5 cos(x) + 660\|5 cos(x) - 122\|5 cos(x) +--R + +--R 4+-+2 +--R - 50\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 192\|5 - 80)cos(x) + (100\|5 + 480)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (69\|5 - 290)cos(x) + 26\|5 - 10 +--R / +--R 4+-+3 4+-+ 5 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (40\|5 - 204\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 8\|5 - 59\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (- 72\|5 + 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (146\|5 + 34\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 17\|5 - 192\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 822\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 92\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 - 368\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 451\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (- 320\|5 cos(x) - 280\|5 cos(x) + 184\|5 cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R 240\|5 cos(x) - 660\|5 cos(x) + 122\|5 cos(x) +--R + +--R 4+-+2 +--R 50\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (- 240\|5 cos(x) + 540\|5 cos(x) + 202\|5 cos(x)) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (- 192\|5 - 80)cos(x) + (228\|5 + 920)cos(x) +--R + +--R 4+-+2 +--R (151\|5 + 320)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 320\|5 cos(x) - 120\|5 cos(x) + 476\|5 cos(x) +--R + +--R 4+-+2 +--R 30\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 56\|5 - 440)cos(x) + (- 218\|5 + 30)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (283\|5 + 760)cos(x) + 32\|5 + 50 +--R + +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ tan(x)\|\|5 + 1 - \|\|5 - 1 +--R - 4\|\|5 + 1 atan(-------------------------------) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R + +--R +-+ +--R - 4\|2 asinh(tan(x) + 1) +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 250 +--d0008:= D(m0008,x) +--E 40 + + +\end{chunk} +\subsection{Problem 9} +\begin{chunk}{*} + +--S 41 of 250 +t0009:= sin(x)*atan(sqrt(sec(x)-1)) +--R +--R +--R +----------+ +--R (37) sin(x)atan(\|sec(x) - 1 ) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 250 +r0009:= 1/2*atan(sqrt(-1+sec(x)))-atan(sqrt(-1+sec(x)))*cos(x)+_ + 1/2*cos(x)*sqrt(-1+sec(x)) +--R +--R +--R +----------+ +----------+ +--R (- 2cos(x) + 1)atan(\|sec(x) - 1 ) + cos(x)\|sec(x) - 1 +--R (38) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 250 +a0009:= integrate(t0009,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 43 + +--S 44 of 250 +--m0009:= a0009-r0009 +--E 44 + +--S 45 of 250 +--d0009:= D(m0009,x) +--E 45 + + +\end{chunk} +\subsection{Problem 10} +\begin{chunk}{*} + +--S 46 of 250 +t0010:= x^3*%e^asin(x)/sqrt(1-x^2) +--R +--R +--R 3 asin(x) +--R x %e +--R (39) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 250 +r0010:= 1/10*%e^asin(x)*(3*x+x^3-3*sqrt(1-x^2)-3*x^2*sqrt(1-x^2)) +--R +--R +--R +--------+ +--R 2 | 2 3 asin(x) +--R ((- 3x - 3)\|- x + 1 + x + 3x)%e +--R (40) ------------------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 250 +a0010:= integrate(t0010,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R atan(-------------) +--R 2 +--R 2x - 1 +--R +--------+ - ------------------- +--R 2 | 2 3 2 +--R ((- 3x - 3)\|- x + 1 + x + 3x)%e +--R (41) --------------------------------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 250 +m0010:= a0010-r0010 +--R +--R +--R (42) +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R atan(-------------) +--R 2 +--R 2x - 1 +--R +--------+ - ------------------- +--R 2 | 2 3 2 +--R ((- 3x - 3)\|- x + 1 + x + 3x)%e +--R + +--R +--------+ +--R 2 | 2 3 asin(x) +--R ((3x + 3)\|- x + 1 - x - 3x)%e +--R / +--R 10 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 250 +d0010:= D(m0010,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R atan(-------------) +--R 2 +--R 2x - 1 +--R - ------------------- +--R 3 2 3 asin(x) +--R x %e - x %e +--R (43) --------------------------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 50 + + +\end{chunk} +\subsection{Problem 11} +\begin{chunk}{*} + +--S 51 of 250 +t0011:= x*log(1+x^2)*log(x+sqrt(1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +--R 2 | 2 +--R x log(x + 1)log(\|x + 1 + x) +--R (44) ------------------------------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 250 +r0011:= 4*x-2*atan(x)-2*sqrt(1+x^2)*log(x+sqrt(1+x^2))+_ + log(1+x^2)*(-x+sqrt(1+x^2)*log(x+sqrt(1+x^2))) +--R +--R +--R (45) +--R +------+ +------+ +--R 2 | 2 | 2 2 +--R (log(x + 1) - 2)\|x + 1 log(\|x + 1 + x) - x log(x + 1) - 2atan(x) + 4x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 250 +a0011:= integrate(t0011,x) +--R +--R +--R (46) +--R +------+ +--R 2 | 2 2 2 2 +--R ((- x log(x + 1) + 2x)\|x + 1 + (x + 1)log(x + 1) - 2x - 2) +--R * +--R +------+ +--R | 2 +--R log(\|x + 1 + x) +--R + +--R +------+ +--R 2 | 2 2 2 +--R (- x log(x + 1) - 2atan(x) + 4x)\|x + 1 + x log(x + 1) + 2x atan(x) +--R + +--R 2 +--R - 4x +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 250 +m0011:= a0011-r0011 +--R +--R +--R (47) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 250 +d0011:= D(m0011,x) +--R +--R +--R (48) 0 +--R Type: Expression(Integer) +--E 55 + + +\end{chunk} +\subsection{Problem 12} +\begin{chunk}{*} + +--S 56 of 250 +t0012:= atan(x+sqrt(1-x^2)) +--R +--R +--R +--------+ +--R | 2 +--R (49) atan(\|- x + 1 + x) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 250 +r0012:= -asin(x)/2+1/4*sqrt(3)*atan((-1+sqrt(3)*x)/sqrt(1-x^2))+_ + 1/4*sqrt(3)*atan((1+sqrt(3)*x)/sqrt(1-x^2))-_ + 1/4*sqrt(3)*atan((-1+2*x^2)/sqrt(3))+x*atan(x+sqrt(1-x^2))-_ + 1/4*atanh(x*sqrt(1-x^2))-1/8*log(1-x^2+x^4) +--R +--R +--R (50) +--R +--------+ +--------+ +--R | 2 | 2 +--R - 2atanh(x\|- x + 1 ) + 8x atan(\|- x + 1 + x) +--R + +--R +-+ +-+ +--R +-+ x\|3 + 1 +-+ x\|3 - 1 4 2 +--R 2\|3 atan(-----------) + 2\|3 atan(-----------) - log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R - 2\|3 atan(-------------) - 4asin(x) +--R 3 +--R / +--R 8 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 250 +a0012:= integrate(t0012,x) +--R +--R +--R (51) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R - log(2x\|- x + 1 - x + x + 1) + log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--R | 2 2 +-+ +--R \|- x + 1 + x +-+ (2x - 1)\|3 +--R - 8x atan(---------------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x 4 2 +--R 2\|3 atan(-----------------) - 8atan(-----------) - 2log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R 2\|3 atan(-------------) +--R 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 250 +m0012:= a0012-r0012 +--R +--R +--R (52) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R - log(2x\|- x + 1 - x + x + 1) + log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--------+ +--R | 2 | 2 +--R 4atanh(x\|- x + 1 ) - 16x atan(\|- x + 1 + x) +--R + +--R +--------+ +--R | 2 +-+ +--R \|- x + 1 + x +-+ x\|3 + 1 +--R - 8x atan(---------------) - 4\|3 atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 \|- x + 1 +--R + +--R +-+ 2 +-+ +--R +-+ x\|3 - 1 +-+ (2x - 1)\|3 +--R - 4\|3 atan(-----------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x +--R 2\|3 atan(-----------------) - 8atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ 2 +-+ +--R +-+ (2x - 1)\|3 +-+ (2x - 1)\|3 +--R 4\|3 atan(-------------) + 2\|3 atan(-------------) + 8asin(x) +--R 3 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 250 +d0012:= D(m0012,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|- x + 1 + x +--R - 2atan(\|- x + 1 + x) - atan(---------------) +--R +--------+ +--R | 2 +--R x\|- x + 1 +--R (53) ------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 60 + + +\end{chunk} +\subsection{Problem 13} +\begin{chunk}{*} + +--S 61 of 250 +t0013:= x*atan(x+sqrt(1-x^2))/sqrt(1-x^2) +--R +--R +--R +--------+ +--R | 2 +--R x atan(\|- x + 1 + x) +--R (54) ----------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 250 +r0013:= -asin(x)/2+1/4*sqrt(3)*atan((-1+sqrt(3)*x)/sqrt(1-x^2))+_ + 1/4*sqrt(3)*atan((1+sqrt(3)*x)/sqrt(1-x^2))-_ + 1/4*sqrt(3)*atan((-1+2*x^2)/sqrt(3))-sqrt(1-x^2)*atan(x+sqrt(1-x^2))+_ + 1/4*atanh(x*sqrt(1-x^2))+1/8*log(1-x^2+x^4) +--R +--R +--R (55) +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R 2atanh(x\|- x + 1 ) - 8\|- x + 1 atan(\|- x + 1 + x) +--R + +--R +-+ +-+ +--R +-+ x\|3 + 1 +-+ x\|3 - 1 4 2 +--R 2\|3 atan(-----------) + 2\|3 atan(-----------) + log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R - 2\|3 atan(-------------) - 4asin(x) +--R 3 +--R / +--R 8 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 250 +a0013:= integrate(t0013,x) +--R +--R +--R (56) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R log(2x\|- x + 1 - x + x + 1) - log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--R +--------+ | 2 2 +-+ +--R | 2 \|- x + 1 + x +-+ (2x - 1)\|3 +--R 8\|- x + 1 atan(---------------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x 4 2 +--R 2\|3 atan(-----------------) - 8atan(-----------) + 2log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R 2\|3 atan(-------------) +--R 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 250 +m0013:= a0013-r0013 +--R +--R +--R (57) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R log(2x\|- x + 1 - x + x + 1) - log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R - 4atanh(x\|- x + 1 ) + 16\|- x + 1 atan(\|- x + 1 + x) +--R + +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 \|- x + 1 + x +-+ x\|3 + 1 +--R 8\|- x + 1 atan(---------------) - 4\|3 atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 \|- x + 1 +--R + +--R +-+ 2 +-+ +--R +-+ x\|3 - 1 +-+ (2x - 1)\|3 +--R - 4\|3 atan(-----------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x +--R 2\|3 atan(-----------------) - 8atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ 2 +-+ +--R +-+ (2x - 1)\|3 +-+ (2x - 1)\|3 +--R 4\|3 atan(-------------) + 2\|3 atan(-------------) + 8asin(x) +--R 3 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 250 +d0013:= D(m0013,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|- x + 1 + x +--R - 2x atan(\|- x + 1 + x) - x atan(---------------) +--R +--------+ +--R | 2 +--R x\|- x + 1 +--R (58) ---------------------------------------------------- +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 65 + + +\end{chunk} +\subsection{Problem 14} +\begin{chunk}{*} + +--S 66 of 250 +t0014:= asin(x)/(1+sqrt(1-x^2)) +--R +--R +--R asin(x) +--R (59) --------------- +--R +--------+ +--R | 2 +--R \|- x + 1 + 1 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 250 +r0014:= ((-1+sqrt(1-x^2))*asin(x))/x+asin(x)^2/2-log(1+sqrt(1-x^2)) +--R +--R +--R (60) +--R +--------+ +--------+ +--R | 2 | 2 2 +--R - 2x log(\|- x + 1 + 1) + 2asin(x)\|- x + 1 + x asin(x) - 2asin(x) +--R ----------------------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 67 + +--S 68 of 250 +a0014:= integrate(t0014,x) +--R +--R +--R (61) +--R +--------+ +--------+ +--R | 2 | 2 +--R (- 4\|- x + 1 - 4)log(\|- x + 1 + 1) +--R + +--R +--------+ +--------+ +--R | 2 | 2 +--R (4\|- x + 1 + 4)log(\|- x + 1 - 1) +--R + +--R +--------+ 2 +--------+ +--R +--------+ | 2 | 2 +--R | 2 2x\|- x + 1 2x\|- x + 1 +--R (\|- x + 1 + 1)atan(-------------) + 4x atan(-------------) +--R 2 2 +--R 2x - 1 2x - 1 +--R + +--R +--------+ +--R | 2 +--R - 8log(x)\|- x + 1 - 8log(x) +--R / +--R +--------+ +--R | 2 +--R 8\|- x + 1 + 8 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 250 +m0014:= a0014-r0014 +--R +--R +--R (62) +--R +--------+ +--------+ +--R | 2 | 2 +--R (4\|- x + 1 + 4)log(\|- x + 1 + 1) +--R + +--R +--------+ +--------+ +--R | 2 | 2 +--R (4\|- x + 1 + 4)log(\|- x + 1 - 1) +--R + +--R +--------+ 2 +--------+ +--R +--------+ | 2 | 2 +--R | 2 2x\|- x + 1 2x\|- x + 1 +--R (\|- x + 1 + 1)atan(-------------) + 4x atan(-------------) +--R 2 2 +--R 2x - 1 2x - 1 +--R + +--R +--------+ +--R 2 | 2 2 +--R (- 8log(x) - 4asin(x) )\|- x + 1 - 8log(x) - 4asin(x) + 8x asin(x) +--R / +--R +--------+ +--R | 2 +--R 8\|- x + 1 + 8 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 250 +d0014:= D(m0014,x) +--R +--R +--R (63) +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 2 2x\|- x + 1 | 2 +--R (\|- x + 1 - x + 1)atan(-------------) + 2asin(x)\|- x + 1 +--R 2 +--R 2x - 1 +--R + +--R 2 +--R (- 2x + 2)asin(x) +--R / +--R +--------+ +--R 2 | 2 2 +--R (2x - 4)\|- x + 1 + 4x - 4 +--R Type: Expression(Integer) +--E 70 + + +\end{chunk} +\subsection{Problem 15} +\begin{chunk}{*} + +--S 71 of 250 +t0015:= log(x+sqrt(1+x^2))/(1-x^2)^(3/2) +--R +--R +--R +------+ +--R | 2 +--R log(\|x + 1 + x) +--R (64) - ------------------- +--R +--------+ +--R 2 | 2 +--R (x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 250 +r0015:= -1/2*asin(x^2)+x*x*log(x+sqrt(1+x^2))/sqrt(1-x^2) +--R +--R +--R +------+ +--------+ +--R 2 | 2 2 | 2 +--R 2x log(\|x + 1 + x) - asin(x )\|- x + 1 +--R (65) ------------------------------------------- +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 250 +a0015:= integrate(t0015,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 73 + +--S 74 of 250 +--m0015:= a0015-r0015 +--E 74 + +--S 75 of 250 +--d0015:= D(m0015,x) +--E 75 + + +\end{chunk} +\subsection{Problem 16} +\begin{chunk}{*} + +--S 76 of 250 +t0016:= asin(x)/(1+x^2)^(3/2) +--R +--R +--R asin(x) +--R (66) ----------------- +--R +------+ +--R 2 | 2 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 250 +r0016:= x*asin(x)/sqrt(1+x^2)-asin(x^2)/2 +--R +--R +--R +------+ +--R 2 | 2 +--R - asin(x )\|x + 1 + 2x asin(x) +--R (67) -------------------------------- +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 250 +a0016:= integrate(t0016,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 78 + +--S 79 of 250 +--m0016:= a0016-r0016 +--E 79 + +--S 80 of 250 +--d0016:= D(m0016,x) +--E 80 + + +\end{chunk} +\subsection{Problem 17} +\begin{chunk}{*} + +--S 81 of 250 +t0017:= log(x+sqrt(x^2-1))/(1+x^2)^(3/2) +--R +--R +--R +------+ +--R | 2 +--R log(\|x - 1 + x) +--R (68) ------------------ +--R +------+ +--R 2 | 2 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 250 +r0017:= -1/2*acosh(x^2)+x*log(x+sqrt(-1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +------+ +--R | 2 2 | 2 +--R 2x log(\|x - 1 + x) - acosh(x )\|x + 1 +--R (69) ------------------------------------------ +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 250 +a0017:= integrate(t0017,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 83 + +--S 84 of 250 +--m0017:= a0017-r0017 +--E 84 + +--S 85 of 250 +--d0017:= D(m0017,x) +--E 85 + + +\end{chunk} +\subsection{Problem 18} +\begin{chunk}{*} + +--S 86 of 250 +t0018:= log(x)/(x^2*sqrt(x^2-1)) +--R +--R +--R log(x) +--R (70) ----------- +--R +------+ +--R 2 | 2 +--R x \|x - 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 250 +r0018:= sqrt(-1+x^2)/x-atanh(x/sqrt(-1+x^2))+(sqrt(-1+x^2)*log(x))/x +--R +--R +--R +------+ +--R x | 2 +--R - x atanh(---------) + (log(x) + 1)\|x - 1 +--R +------+ +--R | 2 +--R \|x - 1 +--R (71) -------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 87 + +--S 88 of 250 +a0018:= integrate(t0018,x) +--R +--R +--R (72) +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (x\|x - 1 - x )log(\|x - 1 - x) - x log(x)\|x - 1 + (x - 1)log(x) - 1 +--R ---------------------------------------------------------------------------- +--R +------+ +--R | 2 2 +--R x\|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 250 +m0018:= a0018-r0018 +--R +--R +--R +------+ +--R | 2 x +--R (73) log(\|x - 1 - x) + atanh(---------) + 1 +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 250 +d0018:= D(m0018,x) +--R +--R +--R (74) 0 +--R Type: Expression(Integer) +--E 90 + + +\end{chunk} +\subsection{Problem 19} +\begin{chunk}{*} + +--S 91 of 250 +t0019:= sqrt(1+x^3)/x +--R +--R +--R +------+ +--R | 3 +--R \|x + 1 +--R (75) --------- +--R x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 250 +r0019:= 2*sqrt(1+x^3)/3 - 2/3*atanh(sqrt(1+x^3)) +--R +--R +--R +------+ +------+ +--R | 3 | 3 +--R - 2atanh(\|x + 1 ) + 2\|x + 1 +--R (76) -------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 250 +a0019:= integrate(t0019,x) +--R +--R +--R +------+ +------+ +------+ +--R | 3 | 3 | 3 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2\|x + 1 +--R (77) ------------------------------------------------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 250 +m0019:= a0019-r0019 +--R +--R +--R +------+ +------+ +------+ +--R | 3 | 3 | 3 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (78) ------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 250 +d0019:= D(m0019,x) +--R +--R +--R (79) 0 +--R Type: Expression(Integer) +--E 95 + + +\end{chunk} +\subsection{Problem 20} +\begin{chunk}{*} + +--S 96 of 250 +t0020:= x*log(x+sqrt(x^2-1))/sqrt(x^2-1) +--R +--R +--R +------+ +--R | 2 +--R x log(\|x - 1 + x) +--R (80) -------------------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 250 +r0020:= -x+sqrt(-1+x^2)*log(x+sqrt(-1+x^2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (81) \|x - 1 log(\|x - 1 + x) - x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 250 +a0020:= integrate(t0020,x) +--R +--R +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (- x\|x - 1 + x - 1)log(\|x - 1 + x) - x\|x - 1 + x +--R (82) ----------------------------------------------------------- +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 250 +m0020:= a0020-r0020 +--R +--R +--R (83) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 250 +d0020:= D(m0020,x) +--R +--R +--R (84) 0 +--R Type: Expression(Integer) +--E 100 + + +\end{chunk} +\subsection{Problem 21} +\begin{chunk}{*} + +--S 101 of 250 +t0021:= x^3*asin(x)/sqrt(1-x^4) +--R +--R +--R 3 +--R x asin(x) +--R (85) ----------- +--R +--------+ +--R | 4 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 250 +r0021:= 1/4*x*sqrt(1+x^2)-1/2*sqrt(1-x^4)*asin(x)+asinh(x)/4 +--R +--R +--R +------+ +--------+ +--R | 2 | 4 +--R x\|x + 1 - 2asin(x)\|- x + 1 + asinh(x) +--R (86) ------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 250 +a0021:= integrate(t0021,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 103 + +--S 104 of 250 +--m0021:= a0021-r0021 +--E 104 + +--S 105 of 250 +--d0021:= D(m0021,x) +--E 105 + + +\end{chunk} +\subsection{Problem 22} +\begin{chunk}{*} + +--S 106 of 250 +t0022:= x^3*asec(x)/sqrt(x^4-1) +--R +--R +--R 3 +--R x asec(x) +--R (87) --------- +--R +------+ +--R | 4 +--R \|x - 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 250 +r0022:= -sqrt(-1+x^4)/(2*sqrt(1-1/x^2)*x)+1/2*sqrt(-1+x^4)*asec(x)+_ + 1/2*atanh((sqrt(1-1/x^2)*x)/sqrt(-1+x^4)) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 +--R +------+ x |------ +------+ +--R | 2 | 2 | 2 +------+ +--R |x - 1 \| x |x - 1 | 4 +--R x |------ atanh(----------) + (x asec(x) |------ - 1)\|x - 1 +--R | 2 +------+ | 2 +--R \| x | 4 \| x +--R \|x - 1 +--R (88) --------------------------------------------------------------- +--R +------+ +--R | 2 +--R |x - 1 +--R 2x |------ +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 107 + +--S 108 of 250 +a0022:= integrate(t0022,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 108 + +--S 109 of 250 +--m0022:= a0022-r0022 +--E 109 + +--S 110 of 250 +--d0022:= D(m0022,x) +--E 110 + + +\end{chunk} +\subsection{Problem 23} +\begin{chunk}{*} + +--S 111 of 250 +t0023:= x*atan(x)*log(x+sqrt(1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +--R | 2 +--R x atan(x)log(\|x + 1 + x) +--R (89) --------------------------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 250 +r0023:= -x*atan(x)+1/2*log(1+x^2)+_ + sqrt(1+x^2)*atan(x)*log(x+sqrt(1+x^2))-1/2*log(x+sqrt(1+x^2))^2 +--R +--R +--R (90) +--R +------+ 2 +------+ +------+ +--R | 2 | 2 | 2 2 +--R - log(\|x + 1 + x) + 2atan(x)\|x + 1 log(\|x + 1 + x) + log(x + 1) +--R + +--R - 2x atan(x) +--R / +--R 2 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 250 +a0023:= integrate(t0023,x) +--R +--R +--R (91) +--R +------+ +------+ 2 +--R | 2 | 2 +--R (- \|x + 1 + x)log(\|x + 1 + x) +--R + +--R +------+ +------+ +--R 2x | 2 2 2x | 2 +--R (x atan(------)\|x + 1 + (- x - 1)atan(------))log(\|x + 1 + x) +--R 2 2 +--R x - 1 x - 1 +--R + +--R +------+ +--R 2 2x | 2 2 2 2x +--R (log(x + 1) + x atan(------))\|x + 1 - x log(x + 1) - x atan(------) +--R 2 2 +--R x - 1 x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 250 +m0023:= a0023-r0023 +--R +--R +--R (92) +--R +------+ +--R 2x | 2 2 +--R (2x atan(x) + x atan(------))\|x + 1 + (- 2x - 2)atan(x) +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (- x - 1)atan(------) +--R 2 +--R x - 1 +--R * +--R +------+ +--R | 2 +--R log(\|x + 1 + x) +--R + +--R +------+ +--R 2x | 2 2 2 2x +--R (2x atan(x) + x atan(------))\|x + 1 - 2x atan(x) - x atan(------) +--R 2 2 +--R x - 1 x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Expression(Integer) +--E 114 + +--S 115 of 250 +d0023:= D(m0023,x) +--R +--R +--R +------+ +--R 2x | 2 +--R (- 2x atan(x) - x atan(------))log(\|x + 1 + x) +--R 2 +--R x - 1 +--R (93) ------------------------------------------------- +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 115 + + +\end{chunk} +\subsection{Problem 24} +\begin{chunk}{*} + +--S 116 of 250 +t0024:= x*log(1+sqrt(1-x^2))/sqrt(1-x^2) +--R +--R +--R +--------+ +--R | 2 +--R x log(\|- x + 1 + 1) +--R (94) ---------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 250 +r0024:= sqrt(1-x^2)-log(1+sqrt(1-x^2))-sqrt(1-x^2)*log(1+sqrt(1-x^2)) +--R +--R +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R (95) (- \|- x + 1 - 1)log(\|- x + 1 + 1) + \|- x + 1 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 250 +a0024:= integrate(t0024,x) +--R +--R +--R +--------+ +--R 2 | 2 2 +--R x log(\|- x + 1 + 1) - x +--R (96) --------------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 250 +m0024:= a0024-r0024 +--R +--R +--R (97) 1 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 250 +d0024:= D(m0024,x) +--R +--R +--R (98) 0 +--R Type: Expression(Integer) +--E 120 + + +\end{chunk} +\subsection{Problem 25} +\begin{chunk}{*} + +--S 121 of 250 +t0025:= x*log(x+sqrt(1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +--R | 2 +--R x log(\|x + 1 + x) +--R (99) -------------------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 250 +r0025:= -x+sqrt(1+x^2)*log(x+sqrt(1+x^2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (100) \|x + 1 log(\|x + 1 + x) - x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 250 +a0025:= integrate(t0025,x) +--R +--R +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (- x\|x + 1 + x + 1)log(\|x + 1 + x) - x\|x + 1 + x +--R (101) ----------------------------------------------------------- +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 250 +m0025:= a0025-r0025 +--R +--R +--R (102) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 250 +d0025:= D(m0025,x) +--R +--R +--R (103) 0 +--R Type: Expression(Integer) +--E 125 + + +\end{chunk} +\subsection{Problem 26} +\begin{chunk}{*} + +--S 126 of 250 +t0026:= x*log(x+sqrt(1-x^2))/sqrt(1-x^2) +--R +--R +--R +--------+ +--R | 2 +--R x log(\|- x + 1 + x) +--R (104) ---------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 250 +r0026:= sqrt(1-x^2)+atanh(sqrt(2)*x)/sqrt(2)-_ + atanh(sqrt(2)*sqrt(1-x^2))/sqrt(2)-sqrt(1-x^2)*log(x+sqrt(1-x^2)) +--R +--R +--R (105) +--R +--------+ +--------+ +--------+ +--R +-+ | 2 | 2 +-+ | 2 +--R - \|2 \|- x + 1 log(\|- x + 1 + x) - atanh(\|2 \|- x + 1 ) +--R + +--R +--------+ +--R +-+ | 2 +-+ +--R \|2 \|- x + 1 + atanh(x\|2 ) +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 250 +a0026:= integrate(t0026,x) +--R +--R +--R (106) +--R +--------+ +--R 2 +-+ | 2 +--R 2x \|2 log(\|- x + 1 + x) +--R + +--R +--------+ +--R +--------+ | 2 2 +--R +-+ | 2 +-+ (x - 1)\|- x + 1 - x - x + 1 +--R (\|2 \|- x + 1 - \|2 )log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R | 2 +--R (\|- x + 1 - 1) +--R * +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x + 1)\|2 - 2x)\|- x + 1 + (- x - x - 1)\|2 + 2x + 2x +--R log(-------------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x + 1)\|- x + 1 + x - x - 1 +--R + +--R +--------+ +--R | 2 +--R (\|- x + 1 - 1) +--R * +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 1)\|2 - 2x)\|- x + 1 + (x - x + 1)\|2 - 2x + 2x +--R log(-----------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R + +--R +--------+ +--R +--------+ | 2 2 +--R +-+ | 2 +-+ (- x - 1)\|- x + 1 - x + x + 1 +--R (- \|2 \|- x + 1 + \|2 )log(---------------------------------) +--R 2 +--R x +--R + +--R 2 +-+ +--------+ +--R (2x + 1)\|2 + 4x +-+ 2 | 2 +--R (log(------------------) + \|2 log(2x - 1))\|- x + 1 +--R 2 +--R 2x - 1 +--R + +--R 2 +-+ +--R (2x + 1)\|2 + 4x +-+ 2 2 +-+ +--R - log(------------------) - \|2 log(2x - 1) - 2x \|2 +--R 2 +--R 2x - 1 +--R / +--R +--------+ +--R +-+ | 2 +-+ +--R 2\|2 \|- x + 1 - 2\|2 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 250 +m0026:= a0026-r0026 +--R +--R +--R (107) +--R +--------+ +--R +--------+ | 2 2 +--R +-+ | 2 +-+ (x - 1)\|- x + 1 - x - x + 1 +--R - 2\|2 log(\|- x + 1 + x) + \|2 log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x + 1)\|2 - 2x)\|- x + 1 + (- x - x - 1)\|2 + 2x + 2x +--R log(-------------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x + 1)\|- x + 1 + x - x - 1 +--R + +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 1)\|2 - 2x)\|- x + 1 + (x - x + 1)\|2 - 2x + 2x +--R log(-----------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R + +--R +--------+ +--R | 2 2 +--------+ +--R +-+ (- x - 1)\|- x + 1 - x + x + 1 +-+ | 2 +--R - \|2 log(---------------------------------) + 2atanh(\|2 \|- x + 1 ) +--R 2 +--R x +--R + +--R 2 +-+ +--R (2x + 1)\|2 + 4x +-+ 2 +-+ +-+ +--R log(------------------) + \|2 log(2x - 1) - 2atanh(x\|2 ) + 2\|2 +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 250 +d0026:= D(m0026,x) +--R +--R +--R (108) 0 +--R Type: Expression(Integer) +--E 130 + + +\end{chunk} +\subsection{Problem 27} +\begin{chunk}{*} + +--S 131 of 250 +t0027:= log(x)/(x^2*sqrt(1-x^2)) +--R +--R +--R log(x) +--R (109) ------------- +--R +--------+ +--R 2 | 2 +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 250 +r0027:= -sqrt(1-x^2)/x-asin(x)-sqrt(1-x^2)*log(x)/x +--R +--R +--R +--------+ +--R | 2 +--R (- log(x) - 1)\|- x + 1 - x asin(x) +--R (110) ------------------------------------- +--R x +--R Type: Expression(Integer) +--E 132 + +--S 133 of 250 +a0027:= integrate(t0027,x) +--R +--R +--R (111) +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 \|- x + 1 - 1 | 2 +--R (2x\|- x + 1 - 2x)atan(---------------) + (log(x) + 1)\|- x + 1 +--R x +--R + +--R 2 2 +--R (x - 1)log(x) + x - 1 +--R / +--R +--------+ +--R | 2 +--R x\|- x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 250 +m0027:= a0027-r0027 +--R +--R +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R (112) 2atan(---------------) + asin(x) +--R x +--R Type: Expression(Integer) +--E 134 + +--S 135 of 250 +d0027:= D(m0027,x) +--R +--R +--R (113) 0 +--R Type: Expression(Integer) +--E 135 + + +\end{chunk} +\subsection{Problem 28} +\begin{chunk}{*} + +--S 136 of 250 +t0028:= x*atan(x)/sqrt(1+x^2) +--R +--R +--R x atan(x) +--R (114) --------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 250 +r0028:= -asinh(x)+sqrt(1+x^2)*atan(x) +--R +--R +--R +------+ +--R | 2 +--R (115) atan(x)\|x + 1 - asinh(x) +--R Type: Expression(Integer) +--E 137 + +--S 138 of 250 +a0028:= integrate(t0028,x) +--R +--R +--R (116) +--R +------+ +------+ +------+ +--R | 2 | 2 2x | 2 +--R (2\|x + 1 - 2x)log(\|x + 1 - x) + x atan(------)\|x + 1 +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (- x - 1)atan(------) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 250 +m0028:= a0028-r0028 +--R +--R +--R (117) +--R +------+ +------+ +--R | 2 | 2 +--R (2\|x + 1 - 2x)log(\|x + 1 - x) +--R + +--R +------+ +--R 2x | 2 2 +--R (2x atan(x) + x atan(------) + 2asinh(x))\|x + 1 + (- 2x - 2)atan(x) +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (- x - 1)atan(------) - 2x asinh(x) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Expression(Integer) +--E 139 + +--S 140 of 250 +d0028:= D(m0028,x) +--R +--R +--R 2x +--R - 2x atan(x) - x atan(------) +--R 2 +--R x - 1 +--R (118) ----------------------------- +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 140 + + +\end{chunk} +\subsection{Problem 29} +\begin{chunk}{*} + +--S 141 of 250 +t0029:= atan(x)/(x^2*sqrt(1-x^2)) +--R +--R +--R atan(x) +--R (119) ------------- +--R +--------+ +--R 2 | 2 +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 250 +r0029:= -sqrt(1-x^2)*atan(x)/x-atanh(sqrt(1-x^2))+_ + sqrt(2)*atanh(sqrt(1-x^2)/sqrt(2)) +--R +--R +--R (120) +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 +-+ \|- x + 1 | 2 +--R - x atanh(\|- x + 1 ) + x\|2 atanh(-----------) - atan(x)\|- x + 1 +--R +-+ +--R \|2 +--R --------------------------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 142 + +--S 143 of 250 +a0029:= integrate(t0029,x) +--R +--R +--R (121) +--R +--------+ +--------+ +--R | 2 | 2 +--R - x log(\|- x + 1 + 1) + x log(\|- x + 1 - 1) +--R + +--R +--------+ +--R +-+ | 2 2 +--------+ +--R +-+ - 2\|2 \|- x + 1 + x - 3 2x | 2 +--R x\|2 log(---------------------------) + atan(------)\|- x + 1 +--R 2 2 +--R x + 1 x - 1 +--R / +--R 2x +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 250 +m0029:= a0029-r0029 +--R +--R +--R (122) +--R +--------+ +--------+ +--R | 2 | 2 +--R - x log(\|- x + 1 + 1) + x log(\|- x + 1 - 1) +--R + +--R +--------+ +--R +-+ | 2 2 +--------+ +--R +-+ - 2\|2 \|- x + 1 + x - 3 | 2 +--R x\|2 log(---------------------------) + 2x atanh(\|- x + 1 ) +--R 2 +--R x + 1 +--R + +--R +--------+ +--R | 2 +--------+ +--R +-+ \|- x + 1 2x | 2 +--R - 2x\|2 atanh(-----------) + (2atan(x) + atan(------))\|- x + 1 +--R +-+ 2 +--R \|2 x - 1 +--R / +--R 2x +--R Type: Expression(Integer) +--E 144 + +--S 145 of 250 +d0029:= D(m0029,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (123) ------------------------- +--R +--------+ +--R 2 | 2 +--R 2x \|- x + 1 +--R Type: Expression(Integer) +--E 145 + + +\end{chunk} +\subsection{Problem 30} +\begin{chunk}{*} + +--S 146 of 250 +t0030:= x*atan(x)/sqrt(1-x^2) +--R +--R +--R x atan(x) +--R (124) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 250 +r0030:= -asin(x)-sqrt(1-x^2)*atan(x)+sqrt(2)*atan(sqrt(2)*x/sqrt(1-x^2)) +--R +--R +--R +-+ +--------+ +--R +-+ x\|2 | 2 +--R (125) \|2 atan(-----------) - atan(x)\|- x + 1 - asin(x) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 250 +a0030:= integrate(t0030,x) +--R +--R +--R (126) +--R +--------+ +--R +-+ | 2 +--------+ +--R +-+ 2x\|2 \|- x + 1 x 2x | 2 +--R - \|2 atan(-----------------) - 2atan(-----------) + atan(------)\|- x + 1 +--R 2 +--------+ 2 +--R 3x - 1 | 2 x - 1 +--R \|- x + 1 +--R ---------------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 250 +m0030:= a0030-r0030 +--R +--R +--R (127) +--R +--------+ +--R +-+ | 2 +-+ +--R +-+ 2x\|2 \|- x + 1 +-+ x\|2 +--R - \|2 atan(-----------------) - 2\|2 atan(-----------) +--R 2 +--------+ +--R 3x - 1 | 2 +--R \|- x + 1 +--R + +--R +--------+ +--R x 2x | 2 +--R - 2atan(-----------) + (2atan(x) + atan(------))\|- x + 1 + 2asin(x) +--R +--------+ 2 +--R | 2 x - 1 +--R \|- x + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 250 +d0030:= D(m0030,x) +--R +--R +--R 2x +--R - 2x atan(x) - x atan(------) +--R 2 +--R x - 1 +--R (128) ----------------------------- +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 150 + + +\end{chunk} +\subsection{Problem 31} +\begin{chunk}{*} + +--S 151 of 250 +t0031:= atan(x)/(x^2*sqrt(1+x^2)) +--R +--R +--R atan(x) +--R (129) ----------- +--R +------+ +--R 2 | 2 +--R x \|x + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 250 +r0031:= sqrt(1+x^2)*atan(x)/x-atanh(sqrt(1+x^2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R - x atanh(\|x + 1 ) + atan(x)\|x + 1 +--R (130) --------------------------------------- +--R x +--R Type: Expression(Integer) +--E 152 + +--S 153 of 250 +a0031:= integrate(t0031,x) +--R +--R +--R (131) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- 2x\|x + 1 + 2x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 2x | 2 +--R (2x\|x + 1 - 2x )log(\|x + 1 - x - 1) - x atan(------)\|x + 1 +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (x + 1)atan(------) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 2 +--R 2x\|x + 1 - 2x +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 250 +m0031:= a0031-r0031 +--R +--R +--R (132) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- 2x\|x + 1 + 2x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x + 1 - 2x )log(\|x + 1 - x - 1) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x + 1 - 2x )atanh(\|x + 1 ) +--R + +--R +------+ +--R 2x | 2 2 +--R (2x atan(x) - x atan(------))\|x + 1 + (- 2x - 2)atan(x) +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (x + 1)atan(------) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 2 +--R 2x\|x + 1 - 2x +--R Type: Expression(Integer) +--E 154 + +--S 155 of 250 +d0031:= D(m0031,x) +--R +--R +--R 2x +--R 2atan(x) - atan(------) - 4x +--R 2 +--R x - 1 +--R (133) ---------------------------- +--R +------+ +--R 2 | 2 +--R 2x \|x + 1 +--R Type: Expression(Integer) +--E 155 + + +\end{chunk} +\subsection{Problem 32} +\begin{chunk}{*} + +--S 156 of 250 +t0032:= asin(x)/((x^2)*sqrt(1-x^2)) +--R +--R +--R asin(x) +--R (134) ------------- +--R +--------+ +--R 2 | 2 +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 250 +r0032:= -sqrt(1-x^2)*asin(x)/x+log(x) +--R +--R +--R +--------+ +--R | 2 +--R - asin(x)\|- x + 1 + x log(x) +--R (135) ------------------------------- +--R x +--R Type: Expression(Integer) +--E 157 + +--S 158 of 250 +a0032:= integrate(t0032,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 2x\|- x + 1 +--R \|- x + 1 atan(-------------) + 2x log(x) +--R 2 +--R 2x - 1 +--R (136) ------------------------------------------ +--R 2x +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 250 +m0032:= a0032-r0032 +--R +--R +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 2x\|- x + 1 | 2 +--R \|- x + 1 atan(-------------) + 2asin(x)\|- x + 1 +--R 2 +--R 2x - 1 +--R (137) ---------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 159 + +--S 160 of 250 +d0032:= D(m0032,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R - atan(-------------) - 2asin(x) +--R 2 +--R 2x - 1 +--R (138) -------------------------------- +--R +--------+ +--R 2 | 2 +--R 2x \|- x + 1 +--R Type: Expression(Integer) +--E 160 + + +\end{chunk} +\subsection{Problem 33} +\begin{chunk}{*} + +--S 161 of 250 +t0033:= x*log(x)/sqrt(x^2-1) +--R +--R +--R x log(x) +--R (139) --------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 250 +r0033:= -sqrt(x^2-1)+atan(sqrt(x^2-1))+sqrt(x^2-1)*log(x) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (140) atan(\|x - 1 ) + (log(x) - 1)\|x - 1 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 250 +a0033:= integrate(t0033,x) +--R +--R +--R (141) +--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 163 + +--S 164 of 250 +m0033:= a0033-r0033 +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (142) - atan(\|x - 1 ) + 2atan(\|x - 1 - x) +--R Type: Expression(Integer) +--E 164 + +--S 165 of 250 +d0033:= D(m0033,x) +--R +--R +--R (143) 0 +--R Type: Expression(Integer) +--E 165 + + +\end{chunk} +\subsection{Problem 34} +\begin{chunk}{*} + +--S 166 of 250 +t0034:= log(x)/(x^2*sqrt(1+x^2)) +--R +--R +--R log(x) +--R (144) ----------- +--R +------+ +--R 2 | 2 +--R x \|x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 250 +r0034:= -sqrt(1+x^2)/x+asinh(x)-sqrt(1+x^2)*log(x)/x +--R +--R +--R +------+ +--R | 2 +--R (- log(x) - 1)\|x + 1 + x asinh(x) +--R (145) ------------------------------------ +--R x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 250 +a0034:= integrate(t0034,x) +--R +--R +--R (146) +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 +--R (- x\|x + 1 + x )log(\|x + 1 - x) + x log(x)\|x + 1 +--R + +--R 2 +--R (- x - 1)log(x) - 1 +--R / +--R +------+ +--R | 2 2 +--R x\|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 250 +m0034:= a0034-r0034 +--R +--R +--R +------+ +--R | 2 +--R (147) - log(\|x + 1 - x) - asinh(x) - 1 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 250 +d0034:= D(m0034,x) +--R +--R +--R (148) 0 +--R Type: Expression(Integer) +--E 170 + + +\end{chunk} +\subsection{Problem 35} +\begin{chunk}{*} + +--S 171 of 250 +t0035:= x*asec(x)/sqrt(x^2-1) +--R +--R +--R x asec(x) +--R (149) --------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 250 +r0035:= sqrt(x^2-1)*asec(x)-sqrt(1-1/x^2)*x*log(x)/sqrt(x^2-1) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 2 +--R - x log(x) |------ + (x - 1)asec(x) +--R | 2 +--R \| x +--R (150) ------------------------------------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 250 +a0035:= integrate(t0035,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 173 + +--S 174 of 250 +--m0035:= a0035-r0035 +--E 174 + +--S 175 of 250 +--d0035:= D(m0035,x) +--E 175 + + +\end{chunk} +\subsection{Problem 36} +\begin{chunk}{*} + +--S 176 of 250 +t0036:= x*log(x)/sqrt(1+x^2) +--R +--R +--R x log(x) +--R (151) --------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 250 +r0036:= -sqrt(1+x^2)+atanh(sqrt(1+x^2))+sqrt(1+x^2)*log(x) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (152) atanh(\|x + 1 ) + (log(x) - 1)\|x + 1 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 250 +a0036:= integrate(t0036,x) +--R +--R +--R (153) +--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) + (- 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 178 + +--S 179 of 250 +m0036:= a0036-r0036 +--R +--R +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R (154) log(\|x + 1 - x + 1) - log(\|x + 1 - x - 1) - atanh(\|x + 1 ) +--R Type: Expression(Integer) +--E 179 + +--S 180 of 250 +d0036:= D(m0036,x) +--R +--R +--R (155) 0 +--R Type: Expression(Integer) +--E 180 + + +\end{chunk} +\subsection{Problem 37} +\begin{chunk}{*} + +--S 181 of 250 +t0037:= sin(x)/(1+sin(x)^2) +--R +--R +--R sin(x) +--R (156) ----------- +--R 2 +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 250 +r0037:= atanh(cos(x)/sqrt(2))/sqrt(2) +--R +--R +--R cos(x) +--R atanh(------) +--R +-+ +--R \|2 +--R (157) ------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 250 +a0037:= integrate(t0037,x) +--R +--R +--R +-+ 2 +-+ +-+ +--R (- 3\|2 + 4)cos(x) + (- 8\|2 + 12)cos(x) - 6\|2 + 8 +--R log(-------------------------------------------------------) +--R 2 +--R cos(x) - 2 +--R (158) ------------------------------------------------------------ +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 250 +m0037:= a0037-r0037 +--R +--R +--R (159) +--R +-+ 2 +-+ +-+ +--R (- 3\|2 + 4)cos(x) + (- 8\|2 + 12)cos(x) - 6\|2 + 8 cos(x) +--R log(-------------------------------------------------------) - 2atanh(------) +--R 2 +-+ +--R cos(x) - 2 \|2 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 250 +d0037:= D(m0037,x) +--R +--R +--R 2sin(x) +--R (160) - ----------- +--R 2 +--R cos(x) - 2 +--R Type: Expression(Integer) +--E 185 + + +\end{chunk} +\subsection{Problem 38} +\begin{chunk}{*} + +--S 186 of 250 +t0038:= (1+x^2)/((1-x^2)*sqrt(1+x^4)) +--R +--R +--R 2 +--R - x - 1 +--R (161) ----------------- +--R +------+ +--R 2 | 4 +--R (x - 1)\|x + 1 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 250 +r0038:= atanh(sqrt(2)*x/sqrt(1+x^4))/sqrt(2) +--R +--R +--R +-+ +--R x\|2 +--R atanh(---------) +--R +------+ +--R | 4 +--R \|x + 1 +--R (162) ---------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 250 +a0038:= integrate(t0038,x) +--R +--R +--R +------+ +--R +-+ | 4 +--R +-+ \|2 \|x + 1 - 2x +--R \|2 log(------------------) +--R 2 +--R x - 1 +--R (163) - --------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 250 +m0038:= a0038-r0038 +--R +--R +--R +------+ +--R +-+ | 4 +-+ +--R \|2 \|x + 1 - 2x x\|2 +--R - log(------------------) - atanh(---------) +--R 2 +------+ +--R x - 1 | 4 +--R \|x + 1 +--R (164) -------------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 250 +d0038:= D(m0038,x) +--R +--R +--R (165) 0 +--R Type: Expression(Integer) +--E 190 + + +\end{chunk} +\subsection{Problem 39} +\begin{chunk}{*} + +--S 191 of 250 +t0039:= (1-x^2)/((1+x^2)*sqrt(1+x^4)) +--R +--R +--R 2 +--R - x + 1 +--R (166) ----------------- +--R +------+ +--R 2 | 4 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 250 +r0039:= atan(sqrt(2)*x/sqrt(1+x^4))/sqrt(2) +--R +--R +--R +-+ +--R x\|2 +--R atan(---------) +--R +------+ +--R | 4 +--R \|x + 1 +--R (167) --------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 250 +a0039:= integrate(t0039,x) +--R +--R +--R +-+ 2x +--R \|2 atan(-------------) +--R +------+ +--R +-+ | 4 +--R \|2 \|x + 1 +--R (168) ----------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 250 +m0039:= a0039-r0039 +--R +--R +--R +-+ +--R x\|2 2x +--R - atan(---------) + atan(-------------) +--R +------+ +------+ +--R | 4 +-+ | 4 +--R \|x + 1 \|2 \|x + 1 +--R (169) --------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 250 +d0039:= D(m0039,x) +--R +--R +--R (170) 0 +--R Type: Expression(Integer) +--E 195 + + +\end{chunk} +\subsection{Problem 40} +\begin{chunk}{*} + +--S 196 of 250 +t0040:= log(sin(x))/(1+sin(x)) +--R +--R +--R log(sin(x)) +--R (171) ----------- +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 250 +r0040:= -x-atanh(cos(x))-cos(x)*log(sin(x))/(1+sin(x)) +--R +--R +--R - cos(x)log(sin(x)) + (- sin(x) - 1)atanh(cos(x)) - x sin(x) - x +--R (172) ---------------------------------------------------------------- +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 250 +a0040:= integrate(t0040,x) +--R +--R +--R (173) +--R - 2cos(x)log(sin(x)) + (- sin(x) - 1)log(cos(x) + 1) +--R + +--R sin(x) +--R (sin(x) + 1)log(cos(x) - 1) + (2sin(x) + 2)atan(----------) +--R cos(x) - 1 +--R + +--R sin(x) +--R (2sin(x) + 2)atan(----------) - 4x sin(x) - 4x +--R cos(x) + 1 +--R / +--R 2sin(x) + 2 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 250 +m0040:= a0040-r0040 +--R +--R +--R (174) +--R sin(x) +--R - log(cos(x) + 1) + log(cos(x) - 1) + 2atanh(cos(x)) + 2atan(----------) +--R cos(x) - 1 +--R + +--R sin(x) +--R 2atan(----------) - 2x +--R cos(x) + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 250 +d0040:= D(m0040,x) +--R +--R +--R 4 2 2 4 +--R sin(x) + 2cos(x) sin(x) + cos(x) - 1 +--R (175) -------------------------------------------------------- +--R 4 2 2 4 2 +--R sin(x) + (2cos(x) + 2)sin(x) + cos(x) - 2cos(x) + 1 +--R Type: Expression(Integer) +--E 200 + + +\end{chunk} +\subsection{Problem 41} +\begin{chunk}{*} + +--S 201 of 250 +t0041:= log(sin(x))*sqrt(1+sin(x)) +--R +--R +--R +----------+ +--R (176) log(sin(x))\|sin(x) + 1 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 250 +r0041:= 4*cos(x)/sqrt(1+sin(x))-2*cos(x)*log(sin(x))/sqrt(1+sin(x))-_ + 4*atanh(cos(x)/sqrt(1+sin(x))) +--R +--R +--R +----------+ cos(x) +--R - 4\|sin(x) + 1 atanh(-------------) - 2cos(x)log(sin(x)) + 4cos(x) +--R +----------+ +--R \|sin(x) + 1 +--R (177) ------------------------------------------------------------------- +--R +----------+ +--R \|sin(x) + 1 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 250 +a0041:= integrate(t0041,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 203 + +--S 204 of 250 +--m0041:= a0041-r0041 +--E 204 + +--S 205 of 250 +--d0041:= D(m0041,x) +--E 205 + + +\end{chunk} +\subsection{Problem 42} +\begin{chunk}{*} + +--S 206 of 250 +t0042:= sec(x)/sqrt(sec(x)^4-1) +--R +--R +--R sec(x) +--R (178) -------------- +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 250 +r0042:= -atanh(sqrt(sec(x)^4-1)/(sqrt(2)*sec(x)*tan(x)))/sqrt(2) +--R +--R +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R atanh(----------------) +--R +-+ +--R \|2 sec(x)tan(x) +--R (179) - ----------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 250 +a0042:= integrate(t0042,x) +--R +--R +--R (180) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 5 +-+ 4 +-+ 3 +--R - 8\|2 cos(x) - 24\|2 cos(x) - 20\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 4\|2 cos(x) + 12\|2 cos(x) + 4\|2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 3 2 +--R - 32cos(x) - 128cos(x) - 193cos(x) - 128cos(x) - 33 +--R / +--R 6 5 4 2 +--R cos(x) + 4cos(x) + 5cos(x) - 5cos(x) - 4cos(x) - 1 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 250 +m0042:= a0042-r0042 +--R +--R +--R (181) +--R - +--R log +--R +-+ 5 +-+ 4 +-+ 3 +--R - 8\|2 cos(x) - 24\|2 cos(x) - 20\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 4\|2 cos(x) + 12\|2 cos(x) + 4\|2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 3 2 +--R - 32cos(x) - 128cos(x) - 193cos(x) - 128cos(x) - 33 +--R / +--R 6 5 4 2 +--R cos(x) + 4cos(x) + 5cos(x) - 5cos(x) - 4cos(x) - 1 +--R + +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R 2atanh(----------------) +--R +-+ +--R \|2 sec(x)tan(x) +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 250 +d0042:= D(m0042,x) +--R +--R +--R (182) +--R +-+ 5 +-+ 4 +-+ 3 +--R - 32\|2 cos(x) - 128\|2 cos(x) - 194\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 126\|2 cos(x) - 36\|2 cos(x) + 2\|2 +--R * +--R 2 2 +--R sec(x) sin(x)tan(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16\|2 cos(x) + 64\|2 cos(x) + 97\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 63\|2 cos(x) + 18\|2 cos(x) - \|2 +--R * +--R 4 +--R sec(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16\|2 cos(x) - 64\|2 cos(x) - 97\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 63\|2 cos(x) - 18\|2 cos(x) + \|2 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 32cos(x) - 48cos(x) - 80cos(x) + 48cos(x) +--R + +--R - 16cos(x) - 32 +--R * +--R 2 2 +--R sec(x) sin(x)tan(x) +--R + +--R 6 5 4 3 2 +--R 16cos(x) - 16cos(x) + 24cos(x) + 40cos(x) - 24cos(x) +--R + +--R 8cos(x) + 16 +--R * +--R 4 +--R sec(x) +--R + +--R 6 5 4 3 2 +--R - 16cos(x) + 16cos(x) - 24cos(x) - 40cos(x) + 24cos(x) +--R + +--R - 8cos(x) - 16 +--R * +--R sin(x) +--R * +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R + +--R 6 5 4 2 +--R (64cos(x) + 256cos(x) + 322cos(x) - 320cos(x) - 256cos(x) - 66) +--R * +--R 2 +--R sec(x)tan(x) +--R + +--R 6 5 4 2 +--R - 32cos(x) - 128cos(x) - 161cos(x) + 160cos(x) + 128cos(x) +--R + +--R 33 +--R * +--R 5 +--R sec(x) +--R + +--R 6 5 4 2 +--R (32cos(x) + 128cos(x) + 161cos(x) - 160cos(x) - 128cos(x) - 33) +--R * +--R sec(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 64\|2 cos(x) + 64\|2 cos(x) - 32\|2 cos(x) - 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 64\|2 cos(x) - 64\|2 cos(x) + 32\|2 cos(x) + 32\|2 +--R * +--R 2 +--R sec(x)tan(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 +--R * +--R 5 +--R sec(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 +--R * +--R sec(x) +--R / +--R 6 5 4 2 +--R 64cos(x) + 256cos(x) + 322cos(x) - 320cos(x) - 256cos(x) +--R + +--R - 66 +--R * +--R 2 2 +--R sec(x) tan(x) +--R + +--R 6 5 4 2 +--R - 32cos(x) - 128cos(x) - 161cos(x) + 160cos(x) + 128cos(x) +--R + +--R 33 +--R * +--R 4 +--R sec(x) +--R + +--R 6 5 4 2 +--R 32cos(x) + 128cos(x) + 161cos(x) - 160cos(x) - 128cos(x) - 33 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 64\|2 cos(x) + 64\|2 cos(x) - 32\|2 cos(x) - 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 64\|2 cos(x) - 64\|2 cos(x) + 32\|2 cos(x) + 32\|2 +--R * +--R 2 2 +--R sec(x) tan(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 +--R * +--R 4 +--R sec(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 +--R * +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R Type: Expression(Integer) +--E 210 + + +\end{chunk} +\subsection{Problem 43} +\begin{chunk}{*} + +--S 211 of 250 +t0043:= tan(x)/sqrt(1+tan(x)^4) +--R +--R +--R tan(x) +--R (183) -------------- +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 250 +r0043:= -atanh((1-tan(x)^2)/(sqrt(2)*sqrt(1+tan(x)^4)))/(2*sqrt(2)) +--R +--R +--R 2 +--R tan(x) - 1 +--R atanh(------------------) +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R (184) ------------------------- +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 250 +a0043:= integrate(t0043,x) +--R +--R +--R (185) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (- 64\|2 cos(x) + 96\|2 cos(x) - 56\|2 cos(x) + 12\|2 cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 8 6 4 2 +--R 128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 250 +m0043:= a0043-r0043 +--R +--R +--R (186) +--R log +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (- 64\|2 cos(x) + 96\|2 cos(x) - 56\|2 cos(x) + 12\|2 cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 8 6 4 2 +--R 128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17 +--R + +--R 2 +--R tan(x) - 1 +--R - 4atanh(------------------) +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 250 +d0043:= D(m0043,x) +--R +--R +--R (187) +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R (- 64\|2 cos(x) + 96\|2 cos(x) - 56\|2 cos(x) + 12\|2 cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R sin(x) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 9 7 5 3 +--R (128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17cos(x))sin(x) +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R + +--R 10 8 6 4 2 +--R (- 128cos(x) + 256cos(x) - 224cos(x) + 96cos(x) - 17cos(x) )tan(x) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +-+ 4 +--R 128\|2 cos(x) - 320\|2 cos(x) + 368\|2 cos(x) - 232\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 80\|2 cos(x) - 12\|2 +--R * +--R tan(x) +--R / +--R 10 8 6 4 2 +--R (128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +-+ 4 +--R - 128\|2 cos(x) + 320\|2 cos(x) - 368\|2 cos(x) + 232\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 80\|2 cos(x) + 12\|2 +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R Type: Expression(Integer) +--E 215 + + +\end{chunk} +\subsection{Problem 44} +\begin{chunk}{*} + +--S 216 of 250 +t0044:= sin(x)/sqrt(1-sin(x)^6) +--R +--R +--R sin(x) +--R (188) ---------------- +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 250 +r0044:= atanh((sqrt(3)*cos(x)*(1+sin(x)^2))/(2*sqrt(1-sin(x)^6)))/(2*sqrt(3)) +--R +--R +--R +-+ 2 +-+ +--R \|3 cos(x)sin(x) + \|3 cos(x) +--R atanh(------------------------------) +--R +-------------+ +--R | 6 +--R 2\|- sin(x) + 1 +--R (189) ------------------------------------- +--R +-+ +--R 2\|3 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 250 +a0044:= integrate(t0044,x) +--R +--R +--R (190) +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R - \|3 cos(x) - 2\|3 cos(x) + \|3 cos(x) + 4\|3 cos(x) +--R + +--R +-+ +--R 2\|3 +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) - 48cos(x) + 48 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 4 2 +--R 7cos(x) - 24cos(x) + 24 +--R / +--R 4 +--R cos(x) +--R / +--R 12 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 250 +m0044:= a0044-r0044 +--R +--R +--R (191) +--R - +--R log +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R - \|3 cos(x) - 2\|3 cos(x) + \|3 cos(x) + 4\|3 cos(x) +--R + +--R +-+ +--R 2\|3 +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) - 48cos(x) + 48 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 4 2 +--R 7cos(x) - 24cos(x) + 24 +--R / +--R 4 +--R cos(x) +--R + +--R +-+ 2 +-+ +--R \|3 cos(x)sin(x) + \|3 cos(x) +--R - 2atanh(------------------------------) +--R +-------------+ +--R | 6 +--R 2\|- sin(x) + 1 +--R / +--R +-+ +--R 4\|3 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 250 +d0044:= D(m0044,x) +--R +--R +--R (192) +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 16\|3 cos(x) + 32\|3 cos(x) - 16\|3 cos(x) - 64\|3 cos(x) +--R + +--R +-+ +--R - 32\|3 +--R * +--R 7 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 12\|3 cos(x) + 24\|3 cos(x) - 12\|3 cos(x) - 48\|3 cos(x) +--R + +--R +-+ 2 +--R - 24\|3 cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 24\|3 cos(x) + 48\|3 cos(x) - 24\|3 cos(x) - 96\|3 cos(x) +--R + +--R +-+ 2 +--R - 48\|3 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 12\|3 cos(x) + 24\|3 cos(x) - 28\|3 cos(x) - 80\|3 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 8\|3 cos(x) + 64\|3 cos(x) + 32\|3 +--R * +--R sin(x) +--R * +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R + +--R 7 6 5 4 2 +--R 7cos(x) + 14cos(x) - 17cos(x) - 48cos(x) + 48cos(x) +--R + +--R 24cos(x) +--R * +--R 9 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R 7cos(x) + 14cos(x) - 10cos(x) - 34cos(x) - 17cos(x) +--R + +--R 3 2 +--R 24cos(x) + 48cos(x) + 24cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 9 8 7 6 4 +--R 21cos(x) + 42cos(x) - 51cos(x) - 144cos(x) + 144cos(x) +--R + +--R 3 +--R 72cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 6 5 4 2 +--R - 7cos(x) - 14cos(x) + 17cos(x) + 48cos(x) - 48cos(x) +--R + +--R - 24cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R 14cos(x) + 28cos(x) - 41cos(x) - 110cos(x) + 17cos(x) +--R + +--R 4 3 2 +--R 144cos(x) + 48cos(x) - 48cos(x) - 24cos(x) +--R * +--R sin(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) - 48cos(x) + 48 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 4 2 7 +--R (- 112cos(x) + 384cos(x) - 384)sin(x) +--R + +--R 6 4 2 5 +--R (- 84cos(x) + 288cos(x) - 288cos(x) )sin(x) +--R + +--R 6 4 2 3 +--R (- 168cos(x) + 576cos(x) - 576cos(x) )sin(x) +--R + +--R 6 4 2 +--R (- 84cos(x) + 400cos(x) - 672cos(x) + 384)sin(x) +--R * +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ 9 +--R (- 16\|3 cos(x) + 80\|3 cos(x) - 144\|3 cos(x) + 96\|3 cos(x))sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R - 16\|3 cos(x) + 64\|3 cos(x) - 64\|3 cos(x) - 48\|3 cos(x) +--R + +--R +-+ +--R 96\|3 cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R (- 48\|3 cos(x) + 240\|3 cos(x) - 432\|3 cos(x) + 288\|3 cos(x) ) +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ 3 +--R (16\|3 cos(x) - 80\|3 cos(x) + 144\|3 cos(x) - 96\|3 cos(x))sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R - 32\|3 cos(x) + 176\|3 cos(x) - 368\|3 cos(x) + 336\|3 cos(x) +--R + +--R +-+ +--R - 96\|3 cos(x) +--R * +--R sin(x) +--R / +--R 7 6 5 4 2 +--R 28cos(x) + 56cos(x) - 68cos(x) - 192cos(x) + 192cos(x) +--R + +--R 96cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 9 8 7 6 4 +--R 21cos(x) + 42cos(x) - 51cos(x) - 144cos(x) + 144cos(x) +--R + +--R 3 +--R 72cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 9 8 7 6 4 +--R 42cos(x) + 84cos(x) - 102cos(x) - 288cos(x) + 288cos(x) +--R + +--R 3 +--R 144cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R 21cos(x) + 42cos(x) - 79cos(x) - 200cos(x) + 68cos(x) +--R + +--R 4 3 2 +--R 336cos(x) + 72cos(x) - 192cos(x) - 96cos(x) +--R * +--R +-------------------------------------------+ +--R +-------------+ | 4 2 +--R | 6 | 16cos(x) - 48cos(x) + 48 +--R \|- sin(x) + 1 |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 64\|3 cos(x) + 320\|3 cos(x) - 576\|3 cos(x) + 384\|3 cos(x)) +--R * +--R 6 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 48\|3 cos(x) + 240\|3 cos(x) - 432\|3 cos(x) +--R + +--R +-+ 3 +--R 288\|3 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 96\|3 cos(x) + 480\|3 cos(x) - 864\|3 cos(x) +--R + +--R +-+ 3 +--R 576\|3 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R - 48\|3 cos(x) + 304\|3 cos(x) - 752\|3 cos(x) + 864\|3 cos(x) +--R + +--R +-+ +--R - 384\|3 cos(x) +--R * +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R Type: Expression(Integer) +--E 220 + + +\end{chunk} +\subsection{Problem 45} +\begin{chunk}{*} + +--S 221 of 250 +t0045:= sqrt(sqrt(sec(x)+1)-sqrt(sec(x)-1)) +--R +--R +--R +-----------------------------+ +--R | +----------+ +----------+ +--R (193) \|\|sec(x) + 1 - \|sec(x) - 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 250 +r0045:= sqrt(2)*cot(x)*sqrt(-1+sec(x))*sqrt(1+sec(x))*_ + (sqrt(-1+sqrt(2))*_ + atan((sqrt(-2+2*sqrt(2))*(-sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (2*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x)))))-_ + sqrt(1+sqrt(2))*_ + atan((sqrt(2+2*sqrt(2))*(-sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (2*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x)))))-_ + sqrt(1+sqrt(2))*_ + atanh((sqrt(-2+2*sqrt(2))*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))+_ + sqrt(-1+sqrt(2))*_ + atanh((sqrt(2+2*sqrt(2))*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))) +--R +--R +--R (194) +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 - 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R +---------+ +-----------------------------+ +--R | +-+ | +----------+ +----------+ +--R \|2\|2 + 2 \|\|sec(x) + 1 - \|sec(x) - 1 +--R atanh(--------------------------------------------) +--R +----------+ +----------+ +-+ +--R \|sec(x) + 1 - \|sec(x) - 1 + \|2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 + 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R +---------+ +-----------------------------+ +--R | +-+ | +----------+ +----------+ +--R \|2\|2 - 2 \|\|sec(x) + 1 - \|sec(x) - 1 +--R atanh(--------------------------------------------) +--R +----------+ +----------+ +-+ +--R \|sec(x) + 1 - \|sec(x) - 1 + \|2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 + 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R atan +--R +---------+ +---------+ +--R | +-+ +----------+ | +-+ +----------+ +--R \|2\|2 + 2 \|sec(x) + 1 - \|2\|2 + 2 \|sec(x) - 1 +--R + +--R +---------+ +--R +-+ | +-+ +--R - \|2 \|2\|2 + 2 +--R / +--R +-----------------------------+ +--R | +----------+ +----------+ +--R 2\|\|sec(x) + 1 - \|sec(x) - 1 +--R + +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 - 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R atan +--R +---------+ +---------+ +--R | +-+ +----------+ | +-+ +----------+ +--R \|2\|2 - 2 \|sec(x) + 1 - \|2\|2 - 2 \|sec(x) - 1 +--R + +--R +---------+ +--R +-+ | +-+ +--R - \|2 \|2\|2 - 2 +--R / +--R +-----------------------------+ +--R | +----------+ +----------+ +--R 2\|\|sec(x) + 1 - \|sec(x) - 1 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 250 +a0045:= integrate(t0045,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (residue poly has multiple non-linear factors) +--R +--R Continuing to read the file... +--R +--E 223 + +--S 224 of 250 +--m0045:= a0045-r0045 +--E 224 + +--S 225 of 250 +--d0045:= D(m0045,x) +--E 225 + + +\end{chunk} +\subsection{Problem 46} +\begin{chunk}{*} + +--S 226 of 250 +t0046:= x*log(x^2+1)*atan(x)^2 +--R +--R +--R 2 2 +--R (195) x atan(x) log(x + 1) +--R Type: Expression(Integer) +--E 226 + +--S 227 of 250 +r0046:= x*atan(x)*(3-log(1+x^2))-1/4*(6-log(1+x^2))*log(1+x^2)-_ + 1/2*atan(x)^2*(3+x^2-(1+x^2)*log(1+x^2)) +--R +--R +--R (196) +--R 2 2 2 2 2 +--R log(x + 1) + ((2x + 2)atan(x) - 4x atan(x) - 6)log(x + 1) +--R + +--R 2 2 +--R (- 2x - 6)atan(x) + 12x atan(x) +--R / +--R 4 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 250 +a0046:= integrate(t0046,x) +--R +--R +--R (197) +--R 2 2 2 2x 2 2x 2 +--R 2log(x + 1) + ((x + 1)atan(------) + 4x atan(------) - 12)log(x + 1) +--R 2 2 +--R x - 1 x - 1 +--R + +--R 2 2x 2 2x +--R (- x - 3)atan(------) - 12x atan(------) +--R 2 2 +--R x - 1 x - 1 +--R / +--R 8 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 250 +m0046:= a0046-r0046 +--R +--R +--R (198) +--R 2 2 2 2x 2 +--R (- 4x - 4)atan(x) + 8x atan(x) + (x + 1)atan(------) +--R 2 +--R x - 1 +--R + +--R 2x +--R 4x atan(------) +--R 2 +--R x - 1 +--R * +--R 2 +--R log(x + 1) +--R + +--R 2 2 2 2x 2 +--R (4x + 12)atan(x) - 24x atan(x) + (- x - 3)atan(------) +--R 2 +--R x - 1 +--R + +--R 2x +--R - 12x atan(------) +--R 2 +--R x - 1 +--R / +--R 8 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 250 +d0046:= D(m0046,x) +--R +--R +--R 2 2x 2 2 +--R (- 4x atan(x) + x atan(------) )log(x + 1) +--R 2 +--R x - 1 +--R (199) -------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 230 + + +\end{chunk} +\subsection{Problem 47} +\begin{chunk}{*} + +--S 231 of 250 +t0047:= atan(x*sqrt(1+x^2)) +--R +--R +--R +------+ +--R | 2 +--R (200) atan(x\|x + 1 ) +--R Type: Expression(Integer) +--E 231 + +--S 232 of 250 +r0047:= 1/2*atan(sqrt(1+x^2)/x^2)+x*atan(x*sqrt(1+x^2))+_ + 1/2*sqrt(3)*atanh((sqrt(3)*sqrt(1+x^2))/(2+x^2)) +--R +--R +--R +------+ +------+ +--R +-+ | 2 +------+ | 2 +--R +-+ \|3 \|x + 1 | 2 \|x + 1 +--R \|3 atanh(-------------) + 2x atan(x\|x + 1 ) + atan(---------) +--R 2 2 +--R x + 2 x +--R (201) ---------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 250 +a0047:= integrate(t0047,x) +--R +--R +--R (202) +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 2 +--R ((2x + 1)\|3 - 2x - 4x)\|x + 1 + (- 2x - 2x)\|3 + 2x + 5x +--R + +--R 2 +--R + +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 +--R ((- 2x - 1)\|3 - 2x - 4x)\|x + 1 + (2x + 2x)\|3 + 2x +--R + +--R 2 +--R 5x + 2 +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 2x\|x + 1 \|x + 1 - x +--R - 2x atan(-----------) + 2atan(--------------------------------------) +--R 4 2 +------+ +--R x + x - 1 +-+ | 2 +-+ 2 +--R (\|3 - 2x)\|x + 1 - x\|3 + 2x + 2 +--R + +--R +------+ +--R | 2 +--R \|x + 1 - x +--R - 2atan(--------------------------------------) +--R +------+ +--R +-+ | 2 +-+ 2 +--R (\|3 + 2x)\|x + 1 - x\|3 - 2x - 2 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 250 +m0047:= a0047-r0047 +--R +--R +--R (203) +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 2 +--R ((2x + 1)\|3 - 2x - 4x)\|x + 1 + (- 2x - 2x)\|3 + 2x + 5x +--R + +--R 2 +--R + +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 +--R ((- 2x - 1)\|3 - 2x - 4x)\|x + 1 + (2x + 2x)\|3 + 2x +--R + +--R 2 +--R 5x + 2 +--R + +--R +------+ +------+ +--R +-+ | 2 +------+ | 2 +--R +-+ \|3 \|x + 1 | 2 \|x + 1 +--R - 2\|3 atanh(-------------) - 4x atan(x\|x + 1 ) - 2atan(---------) +--R 2 2 +--R x + 2 x +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 2x\|x + 1 \|x + 1 - x +--R - 2x atan(-----------) + 2atan(--------------------------------------) +--R 4 2 +------+ +--R x + x - 1 +-+ | 2 +-+ 2 +--R (\|3 - 2x)\|x + 1 - x\|3 + 2x + 2 +--R + +--R +------+ +--R | 2 +--R \|x + 1 - x +--R - 2atan(--------------------------------------) +--R +------+ +--R +-+ | 2 +-+ 2 +--R (\|3 + 2x)\|x + 1 - x\|3 - 2x - 2 +--R / +--R 4 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 250 +d0047:= D(m0047,x) +--R +--R +--R +------+ +--R +------+ | 2 +--R | 2 2x\|x + 1 +--R - 2atan(x\|x + 1 ) - atan(-----------) +--R 4 2 +--R x + x - 1 +--R (204) --------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 235 + + +\end{chunk} +\subsection{Problem 48} +\begin{chunk}{*} + +--S 236 of 250 +t0048:= atan(sqrt(x+1)-sqrt(x)) +--R +--R +--R +-----+ +-+ +--R (205) atan(\|x + 1 - \|x ) +--R Type: Expression(Integer) +--E 236 + +--S 237 of 250 +r0048:= sqrt(x)/2+(1+x)*atan(sqrt(1+x)-sqrt(x)) +--R +--R +--R +-----+ +-+ +-+ +--R (2x + 2)atan(\|x + 1 - \|x ) + \|x +--R (206) ------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 250 +a0048:= integrate(t0048,x) +--R +--R +--R (207) +--R +-----+ +-+ +--R +-----+ +-+ \|x + 1 - \|x +-+ +-----+ +--R ((x + 1)\|x + 1 + (- x - 1)\|x )atan(----------------) + \|x \|x + 1 - x +--R +-+ +-----+ +--R \|x \|x + 1 - x +--R -------------------------------------------------------------------------- +--R +-----+ +-+ +--R 2\|x + 1 - 2\|x +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 250 +m0048:= a0048-r0048 +--R +--R +--R +-----+ +-+ +--R +-----+ +-+ \|x + 1 - \|x +--R (- 2x - 2)atan(\|x + 1 - \|x ) + (x + 1)atan(----------------) +--R +-+ +-----+ +--R \|x \|x + 1 - x +--I (208) --------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 250 +d0048:= D(m0048,x) +--R +--R +--R +-----+ +-+ +--R +-----+ +-+ \|x + 1 - \|x +--R - 2atan(\|x + 1 - \|x ) + atan(----------------) +--R +-+ +-----+ +--R \|x \|x + 1 - x +--I (209) ------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 240 + + +\end{chunk} +\subsection{Problem 49} +\begin{chunk}{*} + +--S 241 of 250 +t0049:= asin(x/sqrt(1-x^2)) +--R +--R +--R x +--I (210) asin(-----------) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 250 +r0049:= x*asin(x/sqrt(1-x^2))+atan(sqrt(1-2*x^2)) +--R +--R +--R +---------+ +--R | 2 x +--I (211) atan(\|- 2x + 1 ) + x asin(-----------) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 250 +a0049:= integrate(t0049,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 243 + +--S 244 of 250 +--m0049:= a0049-r0049 +--E 244 + +--S 245 of 250 +--d0049:= D(m0049,x) +--E 245 + + +\end{chunk} +\subsection{Problem 50} +\begin{chunk}{*} + +)clear all + +--S 246 of 250 +t0050:= atan(x*sqrt(1-x^2)) +--R +--R +--R +--------+ +--R | 2 +--R (1) atan(x\|- x + 1 ) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 250 +r0050:= x*atan(x*sqrt(1-x^2))-_ + sqrt(1/2*(1+sqrt(5)))*atan(sqrt(1/2*(1+sqrt(5)))*sqrt(1-x^2))+_ + sqrt(1/2*(-1+sqrt(5)))*atanh(sqrt(1/2*(-1+sqrt(5)))*sqrt(1-x^2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--R | +-+ \|- x + 1 \|\|5 - 1 +--R \|\|5 - 1 atanh(----------------------) +--R +-+ +--R \|2 +--R + +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--------+ +--R | +-+ \|- x + 1 \|\|5 + 1 +-+ | 2 +--R - \|\|5 + 1 atan(----------------------) + x\|2 atan(x\|- x + 1 ) +--R +-+ +--R \|2 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 250 +a0050:= integrate(t0050,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--------+ +--R | +-+ +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R \|\|5 - 1 log((\|2 \|5 + \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R +--------+ +--------+ +--R +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R log((- \|2 \|5 - \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 + 2x\|2 \|- x + 1 +--R - 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (2x - 2)\|2 +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 - 2x\|2 \|- x + 1 +--R 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (- 2x + 2)\|2 +--R + +--R +--------+ +--R | 2 +--R +-+ 2x\|- x + 1 +--R 2x\|2 atan(-------------) +--R 4 2 +--R x - x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 250 +m0050:= a0050-r0050 +--R +--R +--R (4) +--R +--------+ +--------+ +--------+ +--R | +-+ +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R \|\|5 - 1 log((\|2 \|5 + \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R +--------+ +--------+ +--R +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R log((- \|2 \|5 - \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--R | +-+ \|- x + 1 \|\|5 - 1 +--R - 4\|\|5 - 1 atanh(----------------------) +--R +-+ +--R \|2 +--R + +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--------+ +--R | +-+ \|- x + 1 \|\|5 + 1 +-+ | 2 +--R 4\|\|5 + 1 atan(----------------------) - 4x\|2 atan(x\|- x + 1 ) +--R +-+ +--R \|2 +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 + 2x\|2 \|- x + 1 +--R - 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (2x - 2)\|2 +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 - 2x\|2 \|- x + 1 +--R 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (- 2x + 2)\|2 +--R + +--R +--------+ +--R | 2 +--R +-+ 2x\|- x + 1 +--R 2x\|2 atan(-------------) +--R 4 2 +--R x - x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 250 +d0050:= D(m0050,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 2x\|- x + 1 +--R - 2atan(x\|- x + 1 ) + atan(-------------) +--R 4 2 +--R x - x + 1 +--R (5) ------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 250 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Charlwood, Kevin +``Integration on Computer Algebra Systems'' +Electronic Journal of Mathematics and Technology (2008) +\verb|www.freepatentsonline.com/article/| +\verb|Electronic-journal-Mathematics-Technology/188213666.html| +\bibitem{2} +Rich, Albert +``Charlwood Integration Problems'' +\verb|www.apmaths.uwo.ca/~arich/CharlwoodIntegrationProblems.pdf| +\end{thebibliography} +\end{document} + + diff --git a/src/axiom-website/CATS/charlwood.input.pdf b/src/axiom-website/CATS/charlwood.input.pdf new file mode 100644 index 0000000..07e52ce Binary files /dev/null and b/src/axiom-website/CATS/charlwood.input.pdf differ diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index d2ad926..f5a42a0 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -129,7 +129,7 @@ Each Axiom result is differenced from the published result and reduced to a constant (usually 0).

- +

Schaums



Schaums 14.59-14.83  source pdf
@@ -233,7 +233,8 @@ and reduced to a constant (usually 0). source pdf
-
+

+

Kamke



This portion of the CATS suite involves Ordinary Differential Equations. This is the Kamke test suite as published by @@ -242,31 +243,47 @@ Where possible we show that the particular solution actually satisfies the original ordinary differential equation.

Kamke0 + txt source pdf
Kamke1 + txt source pdf
Kamke2 + txt source pdf
Kamke3 + txt source pdf
Kamke4 + txt source pdf
Kamke5 + txt source pdf
Kamke6 + txt source pdf
Kamke7 + txt source pdf
-
+

+

Charlwood



+This is the Charlwood test suite

+ Charlwood + source + pdf
+ +

+

Rich



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

diff --git a/src/axiom-website/CATS/kamke0.txt b/src/axiom-website/CATS/kamke0.txt new file mode 100644 index 0000000..94ae57f --- /dev/null +++ b/src/axiom-website/CATS/kamke0.txt @@ -0,0 +1,188 @@ +y:=operator 'y +f := operator 'f +g := operator 'g +ode1 := D(y(x),x) - (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)**(-1/2) +ode1a:=solve(ode1,y,x) + +ode2 := D(y(x),x) + a*y(x) - c*exp(b*x) +ode2a:=solve(ode2,y,x) +yx:=ode2a.particular +ode2expr:=D(yx,x) + a*yx -c*exp(b*x) + +ode3 := D(y(x),x) + a*y(x) - b*sin(c*x) +ode3a:=solve(ode3,y,x) +yx:=ode3a.particular +ode3expr:=D(yx,x) + a*yx - b*sin(c*x) + +ode4 := D(y(x),x) + 2*x*y(x) - x*exp(-x**2) +ode4a:=solve(ode4,y,x) +yx:=ode4a.particular +ode4expr:=D(yx,x) + 2*x*yx - x*exp(-x**2) + +ode5 := D(y(x),x) + y(x)*cos(x) - exp(2*x) +ode5a:=solve(ode5,y,x) + +ode6 := D(y(x),x) + y(x)*cos(x) - sin(2*x)/2 +ode6a:=solve(ode6,y,x) +yx:=ode6a.particular +ode6expr:=D(yx,x) + yx*cos(x) - sin(2*x)/2 + +sin2rule := rule 2*cos(x)*sin(x) == sin(2*x) +sin2rule ode6expr + +ode7 := D(y(x),x) + y(x)*cos(x) - exp(-sin(x)) +ode7a:=solve(ode7,y,x) +yx:=ode7a.particular +ode7expr := D(yx,x) + yx*cos(x) - exp(-sin(x)) + +ode8 := D(y(x),x) + y(x)*tan(x) - sin(2*x) +ode8a:=solve(ode8,y,x) +yx:=ode8a.particular +ode8expr:=D(yx,x) + yx*tan(x) - sin(2*x) + +ode9 := D(y(x),x) - (sin(log(x)) + cos(log(x)) +a)*y(x) +ode9a:=solve(ode9,y,x) +yx:=ode9a.particular +ode9expr:=D(yx,x) - (sin(log(x)) + cos(log(x)) +a)*yx + +ode10 := D(y(x),x) + D(f(x),x)*y(x) - f(x)*D(f(x),x) +ode10a:=solve(ode10,y,x) + +ode11 := D(y(x),x) + f(x)*y(x) - g(x) +ode11a:=solve(ode11,y,x) + +ode12 := D(y(x),x) + y(x)**2 - 1 +yx:=solve(ode12,y,x) +ode12expr:=D(yx,x) + yx**2 - 1 + +ode13 := D(y(x),x) + y(x)**2 - a*x - b +ode13a:=solve(ode13,y,x) + +ode14 := D(y(x),x) + y(x)**2 + a*x**m +ode14a:=solve(ode14,y,x) + +ode15 := D(y(x),x) + y(x)**2 - 2*x**2*y(x) + x**4 -2*x-1 +yx:=solve(ode15,y,x) +ode15expr:=D(yx,x) + yx**2 - 2*x**2*yx + x**4 -2*x-1 + +ode16 := D(y(x),x) + y(x)**2 +(x*y(x)-1)*f(x) +ode16a:=solve(ode16,y,x) + +ode17 := D(y(x),x) - y(x)**2 -3*y(x) + 4 +yx:=solve(ode17,y,x) +ode17expr:=D(yx,x) - yx**2 -3*yx + 4 + +ode18 := D(y(x),x) - y(x)**2 - x*y(x) - x + 1 +yx:=solve(ode18,y,x) +ode18expr:=D(yx,x) - yx**2 - x*yx - x + 1 + +ode19 := D(y(x),x) - (y(x) + x)**2 +yx:=solve(ode19,y,x) +ode19expr := D(yx,x) - (yx + x)**2 + +ode20 := D(y(x),x) - y(x)**2 +(x**2 + 1)*y(x) - 2*x +yx:=solve(ode20,y,x) +ode20expr:=D(yx,x) - yx**2 +(x**2 + 1)*yx - 2*x + +ode21 := D(y(x),x) - y(x)**2 +y(x)*sin(x) - cos(x) +ode21a:=solve(ode21,y,x) + +ode22 := D(y(x),x) - y(x)**2 -y(x)*sin(2*x) - cos(2*x) +ode22a:=solve(ode22,y,x) + +ode23 := D(y(x),x) + a*y(x)**2 - b +yx:=solve(ode23,y,x) +ode23expr := D(yx,x) + a*yx**2 - b + +ode24 := D(y(x),x) + a*y(x)**2 - b*x**nu +ode24a:=solve(ode24,y,x) + +ode25 := D(y(x),x) + a*y(x)**2 - b*x**(2*nu) - c*x**(nu-1) +ode25expr:=solve(ode25,y,x) + +ode26 := D(y(x),x) - (A*y(x) - a)*(B*y(x) - b) +yx:=solve(ode26,y,x) +ode26expr := D(yx,x) - (A*yx - a)*(B*yx - b) + +ode27 := D(y(x),x) + a*y(x)*(y(x)-x) - 1 +ode27a:=solve(ode27,y,x) + +ode28 := D(y(x),x) + x*y(x)**2 -x**3*y(x) - 2*x +ode28a:=solve(ode28,y,x) + +ode29 := D(y(x),x) - x*y(x)**2 - 3*x*y(x) +yx:=solve(ode29,y,x) +ode29expr := D(yx,x) - x*yx**2 - 3*x*yx + +ode30 := D(y(x),x) + x**(-a-1)*y(x)**2 - x**a +ode30a:=solve(ode30,y,x) + +ode31 := D(y(x),x) - a*x**n*(y(x)**2+1) +yx:=solve(ode31,y,x) +ode31expr := D(yx,x) - a*x**n*(yx**2+1) + +ode32 := D(y(x),x) + y(x)**2*sin(x) - 2*sin(x)/cos(x)**2 +yx:=solve(ode32,y,x) + +ode33 := D(y(x),x) - y(x)**2*D(f(x),x)/g(x) + D(g(x),x)/f(x) +ode33a:=solve(ode33,y,x) + +ode34 := D(y(x),x) + f(x)*y(x)**2 + g(x)*y(x) +ode34a:=solve(ode34,y,x) + +ode35 := D(y(x),x) + f(x)*(y(x)**2 + 2*a*y(x) +b) +yx:=solve(ode35,y,x) +ode35expr := D(yx,x) + f(x)*(yx**2 + 2*a*yx +b) + +ode36 := D(y(x),x) + y(x)**3 + a*x*y(x)**2 +ode36a:=solve(ode36,y,x) + +ode37 := D(y(x),x) - y(x)**3 - a*exp(x)*y(x)**2 +ode37a:=solve(ode37,y,x) + +ode38 := D(y(x),x) - a*y(x)**3 - b*x**(3/2) +ode38a:=solve(ode38,y,x) + +ode39 := D(y(x),x) - a3*y(x)**3 - a2*y(x)**2 - a1*y(x) - a0 +yx:=solve(ode39,y,x) + +ode40 := D(y(x),x) + 3*a*y(x)**3 + 6*a*x*y(x)**2 +ode40a:=solve(ode40,y,x) + +ode41 := D(y(x),x) + a*x*y(x)**3 + b*y(x)**2 +ode41a:=solve(ode41,y,x) + +ode42 := D(y(x),x) - x*(x+2)*y(x)**3 - (x+3)*y(x)**2 +ode42a:=solve(ode42,y,x) + +ode43 := D(y(x),x) + (3*a*x**2 + 4*a**2*x + b)*y(x)**3 + 3*x*y(x)**2 +ode43a:=solve(ode43,y,x) + +ode44 := D(y(x),x) + 2*a*x**3*y(x)**3 + 2*x*y(x) +yx:=solve(ode44,y,x) +ode44expr := D(yx,x) + 2*a*x**3*yx**3 + 2*x*yx + +ode45 := D(y(x),x) + 2*(a**2*x**3 - b**2*x)*y(x)**3 + 3*b*y(x)**2 +ode45a:=solve(ode45,y,x) + +ode46 := D(y(x),x) - x**a*y(x)**3 + 3*y(x)**2 - x**(-a)*y(x) _ + -x**(-2*a) + a*x**(-a-1) +ode46a:=solve(ode46,y,x) + +ode47 := D(y(x),x) - a*(x**n - x)*y(x)**3 - y(x)**2 +ode47a:=solve(ode47,y,x) + +ode48 := D(y(x),x) - (a*x**n + b*x)*y(x)**3 - c*y(x)**2 +ode48a:=solve(ode48,y,x) + +ode49 := D(y(x),x) + a*diff(phi(x),x)*y(x)**3 + 6*a*phi(x)*y(x)**2 + _ + (2*a+1)*y(x)*diff(phi(x),x,x)/diff(phi(x),x) +2*(a+1) + +f1 := operator 'f1 +f2 := operator 'f2 +f3 := operator 'f3 +f0 := operator 'f0 + +ode50 := D(y(x),x) - f3(x)*y(x)**3 - f2(x)*y(x)**2 - f1(x)*y(x) - f0(x) +ode50a:=solve(ode50,y,x) + diff --git a/src/axiom-website/CATS/kamke1.txt b/src/axiom-website/CATS/kamke1.txt new file mode 100644 index 0000000..9957e13 --- /dev/null +++ b/src/axiom-website/CATS/kamke1.txt @@ -0,0 +1,186 @@ +y:=operator 'y +f := operator 'f +g := operator 'g +h := operator 'h + +ode51 := D(y(x),x) - (y(x)-f(x))*(y(x)-g(x))*(y(x)-(a*f(x)+b*g(x))/(a+b))*h(x)_ + - D(f(x),x)*(y(x)-g(x))/(f(x)-g(x)) _ + - D(g(x),x)*(y(x)-f(x))/(g(x)-f(x)) +ode51a:=solve(ode51,y,x) + +ode52 := D(y(x),x) - a*y(x)**n - b*x**(n/(1-n)) +ode52a:=solve(ode52,y,x) + +ode53 := D(y(x),x) - f(x)**(1-n)*D(g(x),x)*y(x)**n/(a*g(x)+b)**n _ + - D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x) +ode53a:=solve(ode53,y,x) + +ode54 := D(y(x),x) - a**n*f(x)**(1-n)*D(g(x),x)*y(x)**n - _ + D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x) +ode54a:=solve(ode54,y,x) + +ode55 := D(y(x),x) - f(x)*y(x)**n - g(x)*y(x) - h(x) +ode55a:=solve(ode55,y,x) + +ode56 := D(y(x),x) - f(x)*y(x)**a - g(x)*y(x)**b +ode56a:=solve(ode56,y,x) + +ode57 := D(y(x),x) - sqrt(abs(y(x))) +yx:=solve(ode57,y,x) + +ode57expr := D(yx,x) - sqrt(abs(yx)) + +ode58 := D(y(x),x) - a*sqrt(y(x)) - b*x +ode58a:=solve(ode58,y,x) + +ode59 := D(y(x),x) - a*sqrt(y(x)**2+1) - b + +ode60 := D(y(x),x) - sqrt(y(x)**2-1)/sqrt(x**2-1) +ode60a:=solve(ode60,y,x) + +ode61 := D(y(x),x) - sqrt(x**2-1)/sqrt(y(x)**2-1) +yx:=solve(ode61,y,x) + +ode61expr := D(yx,x) - sqrt(x**2-1)/sqrt(yx**2-1) + +ode62 := D(y(x),x) - (y(x)-x**2*sqrt(x**2-y(x)**2))/_ + (x*y(x)*sqrt(x**2-y(x)**2)+x) +ode62a:=solve(ode62,y,x) + +ode63 := D(y(x),x) - (1+ y(x)**2)/(abs(y(x)+sqrt(1+y(x)))*sqrt(1+x)**3) +ode63a:=solve(ode63,y,x) + +ode64 := D(y(x),x) - sqrt((a*y(x)**2+b*y(x)+c)/(a*x**2+b*x+c)) +yx:=solve(ode64,y,x) +ode64expr := D(yx,x) - sqrt((a*yx**2+b*yx+c)/(a*x**2+b*x+c)); + +ode65 := D(y(x),x) - sqrt((y(x)**3+1)/(x**3+1)) +ode65a:=solve(ode65,y,x) + +ode66 := D(y(x),x) - sqrt(abs(y(x)*(1-y(x))*(1-a*y(x))))/_ + sqrt(abs(x*(1-x)*(1-a*x))) +ode66a:=solve(ode66,y,x) + +ode67 := D(y(x),x) - sqrt(1-y(x)**4)/sqrt(1-x**4) +ode67a:=solve(ode67,y,x) + +ode68 := D(y(x),x) - sqrt((a*y(x)**4+b*y(x)**2+1)/(a*x**4+b*x**2+1)) +ode68a:=solve(ode68,y,x) + +ode69 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)*_ + (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)) +ode69a:=solve(ode69,y,x) + +ode70 := D(y(x),x) - sqrt((a4*x**4+a3*x**3+a2*x**2+a1*x+a0)/_ + (b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)) +ode70a:=solve(ode70,y,x) + +ode71 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)/_ + (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)) +ode71a:=solve(ode71,y,x) + +R1:=operator 'R1 +R2:=operator 'R2 + +ode72 := D(y(x),x) - R1(x,sqrt(a4*x**4+a3*x**3+a2*x**2+a1*x+a0))*_ + R2(y(x),sqrt(b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)) +ode72a:=solve(ode72,y,x) + +ode73 := D(y(x),x) - ((a3*x**3+a2*x**2+a1*x+a0)/_ + (a3*y(x)**3+a2*y(x)**2+a1*y(x)+a0))**(2/3) +ode73a:=solve(ode73,y,x) + +ode74 := D(y(x),x) - f(x)*(y(x)-g(x))*sqrt((y(x)-a)*(y(x)-b)) +ode74a:=solve(ode74,y,x) + +ode75 := D(y(x),x) - exp(x-y(x)) + exp(x) +ode75a:=solve(ode75,y,x) + +ode76 := D(y(x),x) - a*cos(y(x)) + b +yx:=solve(ode76,y,x) +ode76expr := D(yx,x) - a*cos(yx) + b + +ode77 := D(y(x),x) - cos(a*y(x)+b*x) +ode77a:=solve(ode77,y,x) + +ode78 := D(y(x),x) + a*sin(alpha*y(x)+beta*x) + b +ode78a:=solve(ode78,y,x) + +ode79 := D(y(x),x) + f(x)*cos(a*y(x)) + g(x)*sin(a*y(x)) + h(x) +ode79a:=solve(ode79,y,x) + +ode80 := D(y(x),x) + f(x)*sin(y(x)) + (1-D(f(x),x))*cos(y(x)) - D(f(x),x) - 1 +ode80a:=solve(ode80,y,x) + +ode81 := D(y(x),x) + 2*tan(y(x))*tan(x) - 1 +ode81a:=solve(ode81,y,x) + +ode82 := D(y(x),x) - a*(1+tan(y(x))**2) + tan(y(x))*tan(x) +ode82a:=solve(ode82,y,x) + +ode83 := D(y(x),x) - tan(x*y(x)) +ode83a:=solve(ode83,y,x) + +ode84 := D(y(x),x) - f(a*x + b*y(x)) +ode84a:=solve(ode84,y,x) + +ode85 := D(y(x),x) - x**(a-1)*y(x)**(1-b)*f(x**a/a + y(x)**b/b) +ode85a:=solve(ode85,y,x) + +ode86 := D(y(x),x) - (y(x)-x*f(x**2+a*y(x)**2))/(x+a*y(x)*f(x**2+a*y(x)**2)) +ode86a:=solve(ode86,y,x) + +ode87 := D(y(x),x) - (y(x)*a*f(x**c*y(x))+c*x**a*y(x)**b)/_ + (x*b*f(x**c*y(x))-x**a*y(x)**b) +ode87a:=solve(ode87,y,x) + +ode88 := 2*D(y(x),x) - 3*y(x)**2 - 4*a*y(x) - b - c*exp(-2*a*x) +ode88a:=solve(ode88,y,x) + +ode89 := x*D(y(x),x) - sqrt(a**2 - x**2) +ode89a:=solve(ode89,y,x) +yx:=ode89a.particular +ode89expr := x*D(yx,x) - sqrt(a**2 - x**2) + +ode90 := x*D(y(x),x) + y(x) - x*sin(x) +ode90a:=solve(ode90,y,x) +yx:=ode90a.particular +ode90expr := x*D(yx,x) + yx - x*sin(x) + +ode91 := x*D(y(x),x) - y(x) - x/log(x) +ode91a:=solve(ode91,y,x) +yx:=ode91a.particular +ode91expr := x*D(yx,x) - yx - x/log(x) + +ode92 := x*D(y(x),x) - y(x) - x**2*sin(x) +ode92a:=solve(ode92,y,x) +yx:=ode92a.particular +ode92expr := x*D(yx,x) - yx - x**2*sin(x) + +ode93 := x*D(y(x),x) - y(x) - x*cos(log(log(x)))/log(x) +ode93a:=solve(ode93,y,x) +yx:=ode93a.particular +ode93 := x*D(yx,x) - yx - x*cos(log(log(x)))/log(x) + +ode94 := x*D(y(x),x) +a*y(x) + b*x**n +ode94a:=solve(ode94,y,x) +yx:=ode94a.particular +ode94expr := x*D(yx,x) +a*yx + b*x**n +exprule := rule x^n == %e^(n*log(x)) +exprule ode94expr + +ode95 := x*D(y(x),x) + y(x)**2 + x**2 +ode95a:=solve(ode95,y,x) + +ode96 := x*D(y(x),x) - y(x)**2 + 1 +yx:=solve(ode96,y,x) +ode96expr := x*D(yx,x) - yx**2 + 1 + +ode98 := x*D(y(x),x) + a*y(x)**2 - b*y(x) + c*x**(2*b) +ode98a:=solve(ode98,y,x) + +ode99 := x*D(y(x),x) + a*y(x)**2 - b*y(x) - c*x**beta +ode99a:=solve(ode99,y,x) + +ode100 := x*D(y(x),x) + x*y(x)**2 + a +ode100a:=solve(ode100,y,x) diff --git a/src/axiom-website/CATS/kamke2.txt b/src/axiom-website/CATS/kamke2.txt new file mode 100644 index 0000000..14b2afb --- /dev/null +++ b/src/axiom-website/CATS/kamke2.txt @@ -0,0 +1,174 @@ +y:=operator 'y +f:=operator 'f +g:=operator 'g + +ode101 := x*D(y(x),x) + x*y(x)**2 - y(x) +yx:=solve(ode101,y,x) +ode101expr := x*D(yx,x) + x*yx**2 - yx + +ode102 := x*D(y(x),x) + x*y(x)**2 - y(x) - a*x**3 +yx:=solve(ode102,y,x) +ode102expr := x*D(yx,x) + x*yx**2 - yx - a*x**3 + +ode103 := x*D(y(x),x) + x*y(x)**2 - (2*x**2+1)*y(x) - x**3 +yx:=solve(ode103,y,x) +ode103expr := x*D(yx,x) + x*yx**2 - (2*x**2+1)*yx - x**3 + +ode106 := x*D(y(x),x) + x**a*y(x)**2 + (a-b)*y(x)/2 + x**b +yx:=solve(ode106,y,x) + +ode107 := x*D(y(x),x) + a*x**alpha*y(x)**2 + b*y(x) - c*x**beta + +ode108 := x*D(y(x),x) - y(x)**2*log(x) + y(x) +yx:=solve(ode108,y,x) +ode108expr := x*D(yx,x) - yx**2*log(x) + yx + +ode109 := x*D(y(x),x) - y(x)*(2*y(x)*log(x)-1) +yx:=solve(ode109,y,x) +ode109expr := x*D(yx,x) - yx*(2*yx*log(x)-1) + +ode110 := x*D(y(x),x) + f(x)*(y(x)**2-x**2) +yx:=solve(ode110,y,x) + +ode111 := x*D(y(x),x) + y(x)**3 + 3*x*y(x)**2 +yx:=solve(ode111,y,x) + +ode112 := x*D(y(x),x) - sqrt(y(x)**2 + x**2) - y(x) +yx:=solve(ode112,y,x) + +ode113 := x*D(y(x),x) + a*sqrt(y(x)**2 + x**2) - y(x) +yx:=solve(ode113,y,x) + +ode114 := x*D(y(x),x) - x*sqrt(y(x)**2 + x**2) - y(x) +yx:=solve(ode114,y,x) + +ode115 := x*D(y(x),x) - x*(y(x)-x)*sqrt(y(x)**2 + x**2) - y(x) +yx:=solve(ode115,y,x) + +ode116 := x*D(y(x),x) - x*sqrt((y(x)**2 - x**2)*(y(x)**2-4*x**2)) - y(x) +yx:=solve(ode116,y,x) + +ode117 := x*D(y(x),x) - x*exp(y(x)/x) - y(x) - x +yx:=solve(ode117,y,x) + +ode118 := x*D(y(x),x) - y(x)*log(y(x)) +yx:=solve(ode118,y,x) +ode118expr := x*D(yx,x) - yx*log(yx) + +ode119 := x*D(y(x),x) - y(x)*(log(x*y(x))-1) +yx:=solve(ode119,y,x) + +ode120 := x*D(y(x),x) - y(x)*(x*log(x**2/y(x))+2) +yx:=solve(ode120,y,x) + +ode121 := x*D(y(x),x) + sin(y(x)-x) +yx:=solve(ode121,y,x) + +ode122 := x*D(y(x),x) + (sin(y(x))-3*x**2*cos(y(x)))*cos(y(x)) +yx:=solve(ode122,y,x) + +ode123 := x*D(y(x),x) - x*sin(y(x)/x) - y(x) +yx:=solve(ode123,y,x) + +ode124 := x*D(y(x),x) + x*cos(y(x)/x) - y(x) + x +yx:=solve(ode124,y,x) + +ode125 := x*D(y(x),x) + x*tan(y(x)/x) - y(x) +yx:=solve(ode125,y,x) + +ode126 := x*D(y(x),x) - y(x)*f(x*y(x)) +yx:=solve(ode126,y,x) + +ode127 := x*D(y(x),x) - y(x)*f(x**a*y(x)**b) +yx:=solve(ode127,y,x) + +ode128 := x*D(y(x),x) + a*y(x) - f(x)*g(x**a*y(x)) +yx:=solve(ode128,y,x) + +ode129 := (x+1)*D(y(x),x) + y(x)*(y(x)-x) +yx:=solve(ode129,y,x) + +ode130 := 2*x*D(y(x),x) - y(x) -2*x**3 +ode130a:=solve(ode130,y,x) +yx:=ode130a.particular +ode130expr := 2*x*D(yx,x) - yx -2*x**3 + +ode131 := (2*x+1)*D(y(x),x) - 4*exp(-y(x)) + 2 +yx:=solve(ode131,y,x) +ode131expr := (2*x+1)*D(yx,x) - 4*exp(-yx) + 2 + +ode132 := 3*x*D(y(x),x) - 3*x*log(x)*y(x)**4 - y(x) +yx:=solve(ode132,y,x) +ode132expr := 3*x*D(yx,x) - 3*x*log(x)*yx**4 - yx + +ode133 := x**2*D(y(x),x) + y(x) - x +yx:=solve(ode133,y,x) + +ode134 := x**2*D(y(x),x) - y(x) + x**2*exp(x-1/x) +ode134a:=solve(ode134,y,x) +yx:=ode134a.particular +ode134expr := x**2*D(yx,x) - yx + x**2*exp(x-1/x) + +ode135 := x**2*D(y(x),x) - (x-1)*y(x) +ode135a:=solve(ode135,y,x) +yx:=ode135a.particular +ode135expr := x**2*D(yx,x) - (x-1)*yx + +ode136 := x**2*D(y(x),x) + y(x)**2 + x*y(x) + x**2 +yx:=solve(ode136,y,x) +ode136expr := x**2*D(yx,x) + yx**2 + x*yx + x**2 + +ode137 := x**2*D(y(x),x) - y(x)**2 - x*y(x) +yx:=solve(ode137,y,x) +ode137expr := x**2*D(yx,x) - yx**2 - x*yx + +ode138 := x**2*D(y(x),x) - y(x)**2 - x*y(x) - x**2 +yx:=solve(ode138,y,x) +ode138expr := x**2*D(yx,x) - yx**2 - x*yx - x**2 + +ode139 := x**2*(D(y(x),x)+y(x)**2) + a*x**k - b*(b-1) +yx:=solve(ode139,y,x) + +ode140 := x**2*(D(y(x),x)+y(x)**2) + 4*x*y(x) + 2 +yx:=solve(ode140,y,x) +ode140expr := x**2*(D(yx,x)+yx**2) + 4*x*yx + 2 + +ode141 := x**2*(D(y(x),x)+y(x)**2) + a*x*y(x) + b +yx:=solve(ode141,y,x) +ode141expr := x**2*(D(yx,x)+yx**2) + a*x*yx + b + +ode142 := x**2*(D(y(x),x)-y(x)**2) - a*x**2*y(x) + a*x + 2 +yx:=solve(ode142,y,x) +ode142expr := x**2*(D(yx,x)-yx**2) - a*x**2*yx + a*x + 2 + +ode143 := x**2*(D(y(x),x)+a*y(x)**2) - b +yx:=solve(ode143,y,x) +ode143expr := x**2*(D(yx,x)+a*yx**2) - b + +ode144 := x**2*(D(y(x),x)+a*y(x)**2) + b*x**alpha + c +yx:=solve(ode144,y,x) + +ode145 := x**2*D(y(x),x) + a*y(x)**3 - a*x**2*y(x)**2 +yx:=solve(ode145,y,x) + +ode146 := x**2*D(y(x),x) + x*y(x)**3 + a*y(x)**2 +yx:=solve(ode146,y,x) + +ode147 := x**2*D(y(x),x) + a*x**2*y(x)**3 + b*y(x)**2 +yx:=solve(ode147,y,x) + +ode148 := (x**2+1)*D(y(x),x) + x*y(x) - 1 +ode148a:=solve(ode148,y,x) +yx:=ode148a.particular +ode148expr := (x**2+1)*D(yx,x) + x*yx - 1 + +ode149 := (x**2+1)*D(y(x),x) + x*y(x) - x*(x**2+1) +ode149a:=solve(ode149,y,x) +yx:=ode149a.particular +ode149expr := (x**2+1)*D(yx,x) + x*yx - x*(x**2+1) + +ode150 := (x**2+1)*D(y(x),x) + 2*x*y(x) - 2*x**2 +ode150a:=solve(ode150,y,x) +yx:=ode150a.particular +ode150expr := (x**2+1)*D(yx,x) + 2*x*yx - 2*x**2 + diff --git a/src/axiom-website/CATS/kamke3.txt b/src/axiom-website/CATS/kamke3.txt new file mode 100644 index 0000000..d289c38 --- /dev/null +++ b/src/axiom-website/CATS/kamke3.txt @@ -0,0 +1,194 @@ +y:=operator 'y +ode151 := (x**2+1)*D(y(x),x) + (y(x)**2+1)*(2*x*y(x) - 1) +ode151a:=solve(ode151,y,x) + +ode152 := (x**2+1)*D(y(x),x) + x*sin(y(x))*cos(y(x)) - x*(x**2+1)*cos(y(x))**2 +ode152a:=solve(ode152,y,x) + +ode153 := (x**2-1)*D(y(x),x) - x*y(x) + a +ode153a:=solve(ode153,y,x) +yx:=ode153a.particular +ode153expr := (x**2-1)*D(yx,x) - x*yx + a + +ode154 := (x**2-1)*D(y(x),x) + 2*x*y(x) - cos(x) +ode154a:=solve(ode154,y,x) +yx:=ode154a.particular +ode154expr := (x**2-1)*D(yx,x) + 2*x*yx - cos(x) + +ode155 := (x**2-1)*D(y(x),x) + y(x)**2 - 2*x*y(x) + 1 +yx:=solve(ode155,y,x) +ode155expr := (x**2-1)*D(yx,x) + yx**2 - 2*x*yx + 1 + +ode156 := (x**2-1)*D(y(x),x) - y(x)*(y(x)-x) +yx:=solve(ode156,y,x) +ode156expr := (x**2-1)*D(yx,x) - yx*(yx-x) + +ode157 := (x**2-1)*D(y(x),x) + a*(y(x)**2-2*x*y(x)+1) +ode157a:=solve(ode157,y,x) + +ode158 := (x**2-1)*D(y(x),x) + a*x*y(x)**2 + x*y(x) +yx:=solve(ode158,y,x) +ode158expr := (x**2-1)*D(yx,x) + a*x*yx**2 + x*yx + +ode159 := (x**2-1)*D(y(x),x) - 2*x*y(x)*log(y(x)) +yx:=solve(ode159,y,x) +ode159expr := (x**2-1)*D(yx,x) - 2*x*yx*log(yx) + +ode160 := (x**2-4)*D(y(x),x) + (x+2)*y(x)**2 - 4*y(x) +yx:=solve(ode160,y,x) +ode160expr := (x**2-4)*D(yx,x) + (x+2)*yx**2 - 4*yx + +ode161 := (x**2-5*x+6)*D(y(x),x) + 3*x*y(x) - 8*y(x) + x**2 +ode161a:=solve(ode161,y,x) +yx:=ode161a.particular +ode161expr := (x**2-5*x+6)*D(yx,x) + 3*x*yx - 8*yx + x**2 + +ode162 := (x-a)*(x-b)*D(y(x),x) + y(x)**2 + k*(y(x)+x-a)*(y(x)+x-b) +ode162a:=solve(ode162,y,x) + +ode163 := 2*x**2*D(y(x),x) - 2*y(x)**2 - x*y(x) + 2*a**2*x +yx:=solve(ode163,y,x) +ode163expr := 2*x**2*D(yx,x) - 2*yx**2 - x*yx + 2*a**2*x + +ode164 := 2*x**2*D(y(x),x) - 2*y(x)**2 - 3*x*y(x) + 2*a**2*x +yx:=solve(ode164,y,x) +ode164expr := 2*x**2*D(yx,x) - 2*yx**2 - 3*x*yx + 2*a**2*x + +ode165 := x*(2*x-1)*D(y(x),x) + y(x)**2 - (4*x+1)*y(x) + 4*x +yx:=solve(ode165,y,x) +ode165expr := x*(2*x-1)*D(yx,x) + yx**2 - (4*x+1)*yx + 4*x + +ode166 := 2*x*(x-1)*D(y(x),x) + (x-1)*y(x)**2 - x +ode166a:=solve(ode166,y,x) + +ode167 := 3*x**2*D(y(x),x) - 7*y(x)**2 - 3*x*y(x) - x**2 +yx:=solve(ode167,y,x) +ode167expr := 3*x**2*D(yx,x) - 7*yx**2 - 3*x*yx - x**2 + +ode168 := 3*(x**2-4)*D(y(x),x) + y(x)**2 - x*y(x) - 3 +ode168a:=solve(ode168,y,x) + +ode169 := (a*x+b)**2*D(y(x),x) + (a*x+b)*y(x)**3 + c*y(x)**2 +ode169a:=solve(ode169,y,x) + +ode170 := x**3*D(y(x),x) - y(x)**2 - x**4 +yx:=solve(ode170,y,x) +ode170expr := x**3*D(yx,x) - yx**2 - x**4 + +ode171 := x**3*D(y(x),x) - y(x)**2 - x**2*y(x) +yx:=solve(ode171,y,x) +ode171expr := x**3*D(yx,x) - yx**2 - x**2*yx + +ode172 := x**3*D(y(x),x) - x**4*y(x)**2 + x**2*y(x) + 20 +yx:=solve(ode172,y,x) +ode172expr := x**3*D(yx,x) - x**4*yx**2 + x**2*yx + 20 + +ode173 := x**3*D(y(x),x) - x**6*y(x)**2 - (2*x-3)*x**2*y(x) + 3 +yx:=solve(ode173,y,x) +ode173expr := x**3*D(yx,x) - x**6*yx**2 - (2*x-3)*x**2*yx + 3 + +ode174 := x*(x**2+1)*D(y(x),x) + x**2*y(x) +ode174a:=solve(ode174,y,x) +yx:=ode174a.particular +ode174expr := x*(x**2+1)*D(yx,x) + x**2*yx + +ode175 := x*(x**2-1)*D(y(x),x) - (2*x**2-1)*y(x) + a*x**3 +ode175a:=solve(ode175,y,x) +yx:=ode175a.particular +ode175expr := x*(x**2-1)*D(yx,x) - (2*x**2-1)*yx + a*x**3 + +ode176 := x*(x**2-1)*D(y(x),x) + (x**2-1)*y(x)**2 - x**2 +ode176a:=solve(ode176,y,x) + +ode177 := x**2*(x-1)*D(y(x),x) - y(x)**2 - x*(x-2)*y(x) +yx:=solve(ode177,y,x) +ode177expr := x**2*(x-1)*D(yx,x) - yx**2 - x*(x-2)*yx + +ode178 := 2*x*(x**2-1)*D(y(x),x) + 2*(x**2-1)*y(x)**2 _ + - (3*x**2-5)*y(x) + x**2 - 3 +yx:=solve(ode178,y,x) +ode178expr := 2*x*(x**2-1)*D(yx,x) + 2*(x**2-1)*yx**2 _ + - (3*x**2-5)*yx + x**2 - 3 + +ode179 := 3*x*(x**2-1)*D(y(x),x) + x*y(x)**2 - (x**2+1)*y(x) - 3*x +ode179a:=solve(ode179,y,x) + +ode180 := (a*x**2+b*x+c)*(x*D(y(x),x)-y(x)) - y(x)**2 + x**2 +yx:=solve(ode180,y,x) +ode180expr := (a*x**2+b*x+c)*(x*D(yx,x)-yx) - yx**2 + x**2 + +ode181 := x**4*(D(y(x),x)+y(x)**2) + a +yx:=solve(ode181,y,x) +ode181expr := x**4*(D(yx,x)+yx**2) + a + +ode182 := x*(x**3-1)*D(y(x),x) - 2*x*y(x)**2 + y(x) + x**2 + +ode183 := (2*x**4-x)*D(y(x),x) - 2*(x**3-1)*y(x) +ode183a:=solve(ode183,y,x) +yx:=ode183a.particular +ode183expr := (2*x**4-x)*D(yx,x) - 2*(x**3-1)*yx + +ode184 := (a*x**2+b*x+c)**2*(D(y(x),x)+y(x)**2) + A +ode184a:=solve(ode184,y,x) + +ode185 := x**7*D(y(x),x) + 2*(x**2+1)*y(x)**3 + 5*x**3*y(x)**2 +ode185a:=solve(ode185,y,x) + +ode186 := x**n*D(y(x),x) + y(x)**2 -(n-1)*x**(n-1)*y(x) + x**(2*n-2) +ode186a:=solve(ode186,y,x) + +ode187 := x**n*D(y(x),x) - a*y(x)**2 - b*x**(2*n-2) +ode187a:=solve(ode187,y,x) + +ode188 := x**(2*n+1)*D(y(x),x) - a*y(x)**3 - b*x**3*n +ode188a:=solve(ode188,y,x) + +ode189 := x**(m*(n-1)+n)*D(y(x),x) - a*y(x)**n - b*x**(n*(m+1)) +ode189a:=solve(ode189,y,x) + +ode190 := sqrt(x**2-1)*D(y(x),x) - sqrt(y(x)**2-1) +ode190a:=solve(ode190,y,x) + +ode191 := sqrt(1-x**2)*D(y(x),x) - y(x)*sqrt(y(x)**2-1) +ode191a:=solve(ode191,y,x) + +ode192 := sqrt(x**2+a**2)*D(y(x),x) + y(x) - sqrt(x**2+a**2) + x +ode192a:=solve(ode192,y,x) +yx:=ode192a.particular +ode192expr := sqrt(x**2+a**2)*D(yx,x) + yx - sqrt(x**2+a**2) + x + +ode193 := x*D(y(x),x)*log(x) + y(x) - a*x*(log(x)+1) +ode193a:=solve(ode193,y,x) +yx:=ode193a.particular +ode193expr := x*D(yx,x)*log(x) + yx - a*x*(log(x)+1) + +ode194 := x*D(y(x),x)*log(x) - y(x)**2*log(x) - _ + (2*log(x)**2+1)*y(x) - log(x)**3 +ode194a:=solve(ode194,y,x) + +ode195 := sin(x)*D(y(x),x) - y(x)**2*sin(x)**2 + (cos(x) - 3*sin(x))*y(x) + 4 +yx:=solve(ode195,y,x) +ode195expr:=sin(x)*D(yx,x) - yx**2*sin(x)**2 + (cos(x) - 3*sin(x))*yx + 4 + +ode196 := cos(x)*D(y(x),x) + y(x) + (1 + sin(x))*cos(x) +ode196a:=solve(ode196,y,x) +yx:=ode196a.particular +ode196expr := cos(x)*D(yx,x) + yx + (1 + sin(x))*cos(x) + +ode197 := cos(x)*D(y(x),x) - y(x)**4 - y(x)*sin(x) +yx:=solve(ode197,y,x) +ode197expr := cos(x)*D(yx,x) - yx**4 - yx*sin(x) + +ode198 := sin(x)*cos(x)*D(y(x),x) - y(x) - sin(x)**3 +ode198a:=solve(ode198,y,x) +yx:=ode198a.particular +ode198expr := sin(x)*cos(x)*D(yx,x) - yx - sin(x)**3 + +ode199 := sin(2*x)*D(y(x),x) + sin(2*y(x)) +ode199a:=solve(ode199,y,x) + +ode200 := (a*sin(x)**2+b)*D(y(x),x) + a*y(x)*sin(2*x) + A*x*(a*sin(x)**2+c) +ode200a:=solve(ode200,y,x) +yx:=ode200a.particular +ode200expr := (a*sin(x)**2+b)*D(yx,x) + a*yx*sin(2*x) + A*x*(a*sin(x)**2+c) + diff --git a/src/axiom-website/CATS/kamke4.input.pamphlet b/src/axiom-website/CATS/kamke4.input.pamphlet index 57e395d..e4e60bf 100644 --- a/src/axiom-website/CATS/kamke4.input.pamphlet +++ b/src/axiom-website/CATS/kamke4.input.pamphlet @@ -1,1462 +1,178 @@ -\documentclass{article} -\usepackage{axiom} -\begin{document} -\title{\$SPAD/src/input kamke4.input} -\author{Timothy Daly} -\maketitle -\begin{abstract} -This is the 201-250 of the Kamke test suite as published by -E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom -syntax. Where possible we show that the particular solution actually -satisfies the original ordinary differential equation. -\end{abstract} -\eject -\tableofcontents -\eject -<<*>>= -)spool kamke4.output -)set break resume -)set mes auto off -)clear all ---S 1 of 127 y:=operator 'y ---R ---R ---R (1) y ---R Type: BasicOperator ---E 1 - ---S 2 of 127 f:=operator 'f ---R ---R ---R (2) f ---R Type: BasicOperator ---E 2 - ---S 3 of 127 f0:=operator 'f0 ---R ---R ---R (3) f0 ---R Type: BasicOperator ---E 3 - ---S 4 of 127 f1:=operator 'f1 ---R ---R ---R (4) f1 ---R Type: BasicOperator ---E 4 - ---S 5 of 127 f2:=operator 'f2 ---R ---R ---R (5) f2 ---R Type: BasicOperator ---E 5 - ---S 6 of 127 g:=operator 'g ---R ---R ---R (6) g ---R Type: BasicOperator ---E 6 - ---S 7 of 127 tg:=operator 'tg ---R ---R ---R (7) tg ---R Type: BasicOperator ---E 7 - ---S 8 of 127 h:=operator 'h ---R ---R ---R (8) h ---R Type: BasicOperator ---E 8 ---S 9 of 127 ode201 := 2*f(x)*D(y(x),x)+2*f(x)*y(x)**2-D(f(x),x)*y(x)-2*f(x)**2 ---R ---R ---R , , 2 2 ---R (9) 2f(x)y (x) - y(x)f (x) + 2f(x)y(x) - 2f(x) ---R ---R Type: Expression Integer ---E 9 - ---S 10 of 127 solve(ode201,y,x) ---R ---R ---R (10) "failed" ---R Type: Union("failed",...) ---E 10 ---S 11 of 127 ode202 := f(x)*D(y(x),x)+g(x)*tg(y(x))+h(x) ---R ---R ---R , ---R (11) f(x)y (x) + g(x)tg(y(x)) + h(x) ---R ---R Type: Expression Integer ---E 11 - ---S 12 of 127 solve(ode202,y,x) ---R ---R ---R (12) "failed" ---R Type: Union("failed",...) ---E 12 ---S 13 of 127 ode203 := y(x)*D(y(x),x)+y(x)+x**3 ---R ---R ---R , 3 ---R (13) y(x)y (x) + y(x) + x ---R ---R Type: Expression Integer ---E 13 - ---S 14 of 127 solve(ode203,y,x) ---R ---R ---R (14) "failed" ---R Type: Union("failed",...) ---E 14 ---S 15 of 127 ode204 := y(x)*D(y(x),x)+a*y(x)+x ---R ---R ---R , ---R (15) y(x)y (x) + a y(x) + x ---R ---R Type: Expression Integer ---E 15 - ---S 16 of 127 solve(ode204,y,x) ---R ---R ---R (16) "failed" ---R Type: Union("failed",...) ---E 16 ---S 17 of 127 ode205 := y(x)*D(y(x),x)+a*y(x)+(a**2-1)/(4)*x+b*x**n ---R ---R ---R , n 2 ---R 4y(x)y (x) + 4b x + 4a y(x) + (a - 1)x ---R ---R (17) ---------------------------------------- ---R 4 ---R Type: Expression Integer ---E 17 - ---S 18 of 127 solve(ode205,y,x) ---R ---R ---R (18) "failed" ---R Type: Union("failed",...) ---E 18 ---S 19 of 127 ode206 := y(x)*D(y(x),x)+a*y(x)+b*exp(x)-2*a ---R ---R ---R , x ---R (19) y(x)y (x) + b %e + a y(x) - 2a ---R ---R Type: Expression Integer ---E 19 - ---S 20 of 127 solve(ode206,y,x) ---R ---R ---R (20) "failed" ---R Type: Union("failed",...) ---E 20 ---S 21 of 127 ode207 := y(x)*D(y(x),x)+y(x)**2+4*x*(x+1) ---R ---R ---R , 2 2 ---R (21) y(x)y (x) + y(x) + 4x + 4x ---R ---R Type: Expression Integer ---E 21 - ---S 22 of 127 yx:=solve(ode207,y,x) ---R ---R ---R 2 2 2x ---R (y(x) + 4x )%e ---R (22) ----------------- ---R 2 ---R Type: Union(Expression Integer,...) ---E 22 - ---S 23 of 127 ode207expr := yx*D(yx,x)+yx**2+4*x*(x+1) ---R ---R ---R (23) ---R 3 2 2x 2 , ---R (2y(x) + 8x y(x))(%e ) y (x) ---R ---R + ---R 4 2 2 4 3 2x 2 2 ---R (3y(x) + (24x + 8x)y(x) + 48x + 32x )(%e ) + 16x + 16x ---R / ---R 4 ---R Type: Expression Integer ---E 23 ---S 24 of 127 ode208 := y(x)*D(y(x),x)+a*y(x)**2-b*cos(x+c) ---R ---R ---R , 2 ---R (24) y(x)y (x) - b cos(x + c) + a y(x) ---R ---R Type: Expression Integer ---E 24 - ---S 25 of 127 yx:=solve(ode208,y,x) ---R ---R ---R 2a x 2 2 2a x ---R - 2b %e sin(x + c) + (- 4a b cos(x + c) + (4a + 1)y(x) )%e ---R (25) ------------------------------------------------------------------ ---R 2 ---R 8a + 2 ---R Type: Union(Expression Integer,...) ---E 25 - ---S 26 of 127 ode208expr := yx*D(yx,x)+a*yx**2-b*cos(x+c) ---R ---R ---R (26) ---R 2 2a x 2 ---R (- 16a - 4)b y(x)(%e ) sin(x + c) ---R + ---R 3 4 2 3 2a x 2 ---R ((- 32a - 8a)b y(x)cos(x + c) + (32a + 16a + 2)y(x) )(%e ) ---R * ---R , ---R y (x) ---R ---R + ---R 2 2a x 2 2 ---R 4a b (%e ) sin(x + c) ---R + ---R 2 2 3 2 2a x 2 ---R ((32a + 4)b cos(x + c) + (- 32a - 8a)b y(x) )(%e ) sin(x + c) ---R + ---R 3 2 2 4 2 2 ---R (48a + 8a)b cos(x + c) + (- 96a - 32a - 2)b y(x) cos(x + c) ---R + ---R 5 3 4 ---R (48a + 24a + 3a)y(x) ---R * ---R 2a x 2 ---R (%e ) ---R + ---R 4 2 ---R (- 64a - 32a - 4)b cos(x + c) ---R / ---R 4 2 ---R 64a + 32a + 4 ---R Type: Expression Integer ---E 26 ---S 27 of 127 ode209 := y(x)*D(y(x),x)-sqrt(a*y(x)**2+b) ---R ---R ---R +-----------+ ---R , | 2 ---R (27) y(x)y (x) - \|a y(x) + b ---R ---R Type: Expression Integer ---E 27 - ---S 28 of 127 yx:=solve(ode209,y,x) ---R ---R ---R +-----------+ ---R +-+ | 2 2 +-+ ---R - x\|b \|a y(x) + b + y(x) \|b + b x ---R (28) --------------------------------------- ---R +-----------+ ---R +-+ | 2 ---R \|b \|a y(x) + b - b ---R Type: Union(Expression Integer,...) ---E 28 - ---S 29 of 127 ode209expr := yx*D(yx,x)-sqrt(a*yx**2+b) ---R ---R ---R (29) ---R +-----------+ ---R 2 2 | 2 2 4 2 2 +-+ ---R ((- 3a b y(x) - 4b )\|a y(x) + b + (a y(x) + 5a b y(x) + 4b )\|b ) ---R * ---R ROOT ---R +-----------+ ---R 2 +-+ 2 | 2 2 +-+ ---R ((2a x + 2b)\|b + 2a x y(x) )\|a y(x) + b - 2a x y(x) \|b ---R + ---R 4 2 2 2 2 2 ---R - a y(x) + (- a x - a b)y(x) - 2a b x - 2b ---R / ---R +-----------+ ---R +-+ | 2 2 ---R 2\|b \|a y(x) + b - a y(x) - 2b ---R + ---R +-----------+ ---R 3 +-+ 3 | 2 ---R ((a x y(x) + 4b x y(x))\|b + 2b y(x) )\|a y(x) + b ---R + ---R 5 3 +-+ 3 2 ---R (- a y(x) - 2b y(x) )\|b - 3a b x y(x) - 4b x y(x) ---R * ---R , ---R y (x) ---R ---R + ---R +-----------+ ---R 4 2 +-+ 2 2 | 2 ---R ((a y(x) + 2b y(x) )\|b + 3a b x y(x) + 4b x)\|a y(x) + b ---R + ---R 2 4 2 2 +-+ 4 2 2 ---R (- a x y(x) - 5a b x y(x) - 4b x)\|b - 2a b y(x) - 2b y(x) ---R / ---R +-----------+ ---R 2 2 | 2 2 4 2 2 +-+ ---R (3a b y(x) + 4b )\|a y(x) + b + (- a y(x) - 5a b y(x) - 4b )\|b ---R Type: Expression Integer ---E 29 ---S 30 of 127 ode210 := y(x)*D(y(x),x)+x*y(x)**2-4*x ---R ---R ---R , 2 ---R (30) y(x)y (x) + x y(x) - 4x ---R ---R Type: Expression Integer ---E 30 - ---S 31 of 127 yx:=solve(ode210,y,x) ---R ---R ---R 2 ---R 2 x ---R (y(x) - 4)%e ---R (31) --------------- ---R 2 ---R Type: Union(Expression Integer,...) ---E 31 - ---S 32 of 127 ode210expr := yx*D(yx,x)+x*yx**2-4*x ---R ---R ---R (32) ---R 2 2 2 2 ---R 3 x , 4 2 x ---R (2y(x) - 8y(x))(%e ) y (x) + (3x y(x) - 24x y(x) + 48x)(%e ) - 16x ---R ---R ------------------------------------------------------------------------ ---R 4 ---R Type: Expression Integer ---E 32 ---S 33 of 127 ode211 := y(x)*D(y(x),x)-x*exp(x/y(x)) ---R ---R ---R x ---R ---- ---R , y(x) ---R (33) y(x)y (x) - x %e ---R ---R Type: Expression Integer ---E 33 - ---S 34 of 127 solve(ode211,y,x) ---R ---R ---R (34) "failed" ---R Type: Union("failed",...) ---E 34 ---S 35 of 127 ode212 := y(x)*D(y(x),x)+f(x**2+y(x)**2)*g(x)+x ---R ---R ---R , 2 2 ---R (35) y(x)y (x) + g(x)f(y(x) + x ) + x ---R ---R Type: Expression Integer ---E 35 - ---S 36 of 127 solve(ode212,y,x) ---R ---R ---R (36) "failed" ---R Type: Union("failed",...) ---E 36 ---S 37 of 127 ode213 := (y(x)+1)*D(y(x),x)-y(x)-x ---R ---R ---R , ---R (37) (y(x) + 1)y (x) - y(x) - x ---R ---R Type: Expression Integer ---E 37 - ---S 38 of 127 solve(ode213,y,x) ---R ---R ---R (38) "failed" ---R Type: Union("failed",...) ---E 38 ---S 39 of 127 ode214 := (y(x)+x-1)*D(y(x),x)-y(x)+2*x+3 ---R ---R ---R , ---R (39) (y(x) + x - 1)y (x) - y(x) + 2x + 3 ---R ---R Type: Expression Integer ---E 39 - ---S 40 of 127 solve(ode214,y,x) ---R ---R ---R (40) "failed" ---R Type: Union("failed",...) ---E 40 ---S 41 of 127 ode215 := (y(x)+2*x-2)*D(y(x),x)-y(x)+x+1 ---R ---R ---R , ---R (41) (y(x) + 2x - 2)y (x) - y(x) + x + 1 ---R ---R Type: Expression Integer ---E 41 - ---S 42 of 127 solve(ode215,y,x) ---R ---R ---R (42) "failed" ---R Type: Union("failed",...) ---E 42 ---S 43 of 127 ode216 := (y(x)-2*x+1)*D(y(x),x)+y(x)+x ---R ---R ---R , ---R (43) (y(x) - 2x + 1)y (x) + y(x) + x ---R ---R Type: Expression Integer ---E 43 - ---S 44 of 127 solve(ode216,y,x) ---R ---R ---R (44) "failed" ---R Type: Union("failed",...) ---E 44 ---S 45 of 127 ode217 := (y(x)-x**2)*D(y(x),x)-x ---R ---R ---R 2 , ---R (45) (y(x) - x )y (x) - x ---R ---R Type: Expression Integer ---E 45 - ---S 46 of 127 yx:=solve(ode217,y,x) ---R ---R ---R 2 2y(x) ---R (2y(x) - 2x - 1)%e ---R (46) ------------------------ ---R 4 ---R Type: Union(Expression Integer,...) ---E 46 - ---S 47 of 127 ode217expr := (yx-x**2)*D(yx,x)-x ---R ---R ---R (47) ---R 2 2 4 2 2y(x) 2 ---R (2y(x) + (- 4x - 1)y(x) + 2x + x )(%e ) ---R + ---R 2 4 2y(x) ---R (- 4x y(x) + 4x )%e ---R * ---R , ---R y (x) ---R ---R + ---R 3 2y(x) 2 3 2y(x) ---R (- 2x y(x) + 2x + x)(%e ) + 4x %e - 4x ---R / ---R 4 ---R Type: Expression Integer ---E 47 ---S 48 of 127 ode218 := (y(x)-x**2)*D(y(x),x)+4*x*y(x) ---R ---R ---R 2 , ---R (48) (y(x) - x )y (x) + 4x y(x) ---R ---R Type: Expression Integer ---E 48 - ---S 49 of 127 yx:=solve(ode218,y,x) ---R ---R ---R 2 ---R 2y(x) + 2x ---R (49) ----------- ---R +----+ ---R \|y(x) ---R Type: Union(Expression Integer,...) ---E 49 - ---S 50 of 127 ode218expr := (yx-x**2)*D(yx,x)+4*x*yx ---R ---R ---R (50) ---R 2 4 +----+ 2 2 4 , ---R ((2y(x) - 2x )\|y(x) - x y(x) + x y(x))y (x) ---R ---R + ---R 2 3 +----+ 3 3 2 ---R (8x y(x) + 8x y(x))\|y(x) + 8x y(x) + 4x y(x) ---R / ---R 2 +----+ ---R y(x) \|y(x) ---R Type: Expression Integer ---E 50 ---S 51 of 127 ode219 := (y(x)+g(x))*D(y(x),x)-f2(x)*y(x)**2-f1(x)*y(x)-f0(x) ---R ---R ---R , 2 ---R (51) (y(x) + g(x))y (x) - f2(x)y(x) - f1(x)y(x) - f0(x) ---R ---R Type: Expression Integer ---E 51 - ---S 52 of 127 solve(ode219,y,x) ---R ---R ---R (52) "failed" ---R Type: Union("failed",...) ---E 52 ---S 53 of 127 ode220 := 2*y(x)*D(y(x),x)-x*y(x)**2-x**3 ---R ---R ---R , 2 3 ---R (53) 2y(x)y (x) - x y(x) - x ---R ---R Type: Expression Integer ---E 53 - ---S 54 of 127 yx:=solve(ode220,y,x) ---R ---R ---R 2 ---R x ---R - -- ---R 2 2 2 ---R (54) (y(x) + x + 2)%e ---R Type: Union(Expression Integer,...) ---E 54 - ---S 55 of 127 ode220expr := 2*yx*D(yx,x)-x*yx**2-x**3 ---R ---R ---R (55) ---R 2 2 ---R x ---R - -- ---R 3 2 2 , ---R (4y(x) + (4x + 8)y(x))(%e ) y (x) ---R ---R + ---R 2 2 ---R x ---R - -- ---R 4 3 2 5 3 2 3 ---R (- 3x y(x) + (- 6x - 8x)y(x) - 3x - 8x - 4x)(%e ) - x ---R Type: Expression Integer ---E 55 ---S 56 of 127 ode221 := (2*y(x)+x+1)*D(y(x),x)-(2*y(x)+x-1) ---R ---R ---R , ---R (56) (2y(x) + x + 1)y (x) - 2y(x) - x + 1 ---R ---R Type: Expression Integer ---E 56 - ---S 57 of 127 solve(ode221,y,x) ---R ---R ---R (57) "failed" ---R Type: Union("failed",...) ---E 57 ---S 58 of 127 ode222 := (2*y(x)+x+7)*D(y(x),x)-y(x)+2*x+4 ---R ---R ---R , ---R (58) (2y(x) + x + 7)y (x) - y(x) + 2x + 4 ---R ---R Type: Expression Integer ---E 58 - ---S 59 of 127 solve(ode222,y,x) ---R ---R ---R (59) "failed" ---R Type: Union("failed",...) ---E 59 ---S 60 of 127 ode223 := (2*y(x)-x)*D(y(x),x)-y(x)-2*x ---R ---R ---R , ---R (60) (2y(x) - x)y (x) - y(x) - 2x ---R ---R Type: Expression Integer ---E 60 - ---S 61 of 127 yx:=solve(ode223,y,x) ---R ---R ---R 2 2 ---R (61) y(x) - x y(x) - x ---R Type: Union(Expression Integer,...) ---E 61 - ---S 62 of 127 ode223expr := (2*yx-x)*D(yx,x)-yx-2*x ---R ---R ---R (62) ---R 3 2 2 3 2 , 3 ---R (4y(x) - 6x y(x) + (- 2x - 2x)y(x) + 2x + x )y (x) - 2y(x) ---R ---R + ---R 2 2 3 2 ---R (- 2x - 1)y(x) + (6x + 2x)y(x) + 4x + 3x - 2x ---R Type: Expression Integer ---E 62 ---S 63 of 127 ode224 := (2*y(x)-6*x)*D(y(x),x)-y(x)+3*x+2 ---R ---R ---R , ---R (63) (2y(x) - 6x)y (x) - y(x) + 3x + 2 ---R ---R Type: Expression Integer ---E 63 - ---S 64 of 127 solve(ode224,y,x) ---R ---R ---R (64) "failed" ---R Type: Union("failed",...) ---E 64 ---S 65 of 127 ode225 := (4*y(x)+2*x+3)*D(y(x),x)-2*y(x)-x-1 ---R ---R ---R , ---R (65) (4y(x) + 2x + 3)y (x) - 2y(x) - x - 1 ---R ---R Type: Expression Integer ---E 65 - ---S 66 of 127 solve(ode225,y,x) ---R ---R ---R (66) "failed" ---R Type: Union("failed",...) ---E 66 ---S 67 of 127 ode226 := (4*y(x)-2*x-3)*D(y(x),x)+2*y(x)-x-1 ---R ---R ---R , ---R (67) (4y(x) - 2x - 3)y (x) + 2y(x) - x - 1 ---R ---R Type: Expression Integer ---E 67 - ---S 68 of 127 solve(ode226,y,x) ---R ---R ---R (68) "failed" ---R Type: Union("failed",...) ---E 68 ---S 69 of 127 ode227 := (4*y(x)-3*x-5)*D(y(x),x)-3*y(x)+7*x+2 ---R ---R ---R , ---R (69) (4y(x) - 3x - 5)y (x) - 3y(x) + 7x + 2 ---R ---R Type: Expression Integer ---E 69 - ---S 70 of 127 yx:=solve(ode227,y,x) ---R ---R ---R 2 2 ---R 4y(x) + (- 6x - 10)y(x) + 7x + 4x ---R (70) ----------------------------------- ---R 2 ---R Type: Union(Expression Integer,...) ---E 70 - ---S 71 of 127 ode227expr := (4*yx-3*x-5)*D(yx,x)-3*yx+7*x+2 ---R ---R ---R (71) ---R 3 2 2 3 ---R 64y(x) + (- 144x - 240)y(x) + (184x + 280x + 160)y(x) - 84x ---R + ---R 2 ---R - 170x - 20x + 50 ---R * ---R , ---R y (x) ---R ---R + ---R 3 2 2 3 2 ---R - 48y(x) + (184x + 140)y(x) + (- 252x - 340x - 20)y(x) + 196x + 105x ---R + ---R - 48x - 16 ---R / ---R 2 ---R Type: Expression Integer ---E 71 ---S 72 of 127 ode228 := (4*y(x)+11*x-11) *D(y(x),x)-25*y(x)-8*x+62 ---R ---R ---R , ---R (72) (4y(x) + 11x - 11)y (x) - 25y(x) - 8x + 62 ---R ---R Type: Expression Integer ---E 72 - ---S 73 of 127 solve(ode228,y,x) ---R ---R ---R (73) "failed" ---R Type: Union("failed",...) ---E 73 ---S 74 of 127 ode229 := (12*y(x)-5*x-8)*D(y(x),x)-5*y(x)+2*x+3 ---R ---R ---R , ---R (74) (12y(x) - 5x - 8)y (x) - 5y(x) + 2x + 3 ---R ---R Type: Expression Integer ---E 74 - ---S 75 of 127 yx:=solve(ode229,y,x) ---R ---R ---R 2 2 ---R (75) 6y(x) + (- 5x - 8)y(x) + x + 3x ---R Type: Union(Expression Integer,...) ---E 75 - ---S 76 of 127 ode229expr := (12*yx-5*x-8)*D(yx,x)-5*yx+2*x+3 ---R ---R ---R (76) ---R 3 2 2 3 ---R 864y(x) + (- 1080x - 1728)y(x) + (444x + 1332x + 672)y(x) - 60x ---R + ---R 2 ---R - 251x - 208x + 64 ---R * ---R , ---R y (x) ---R ---R + ---R 3 2 2 3 2 ---R - 360y(x) + (444x + 666)y(x) + (- 180x - 502x - 208)y(x) + 24x + 93x ---R + ---R 64x - 21 ---R Type: Expression Integer ---E 76 ---S 77 of 127 ode230 := a*y(x)*D(y(x),x)+b*y(x)**2+f(x) ---R ---R ---R , 2 ---R (77) a y(x)y (x) + b y(x) + f(x) ---R ---R Type: Expression Integer ---E 77 - ---S 78 of 127 solve(ode230,y,x) ---R ---R ---I 2%I b ---R x ----- ---R ++ 2 a ---I (78) | (b y(x) + f(%I))%e d%I ---R ++ ---R Type: Union(Expression Integer,...) ---E 78 ---S 79 of 127 ode231 := (a*y(x)+b*x+c)*D(y(x),x)+alpha*y(x)+beta*x+gamma ---R ---R ---R , ---R (79) (a y(x) + b x + c)y (x) + alpha y(x) + beta x + gamma ---R ---R Type: Expression Integer ---E 79 - ---S 80 of 127 solve(ode231,y,x) ---R ---R ---R (80) "failed" ---R Type: Union("failed",...) ---E 80 ---S 81 of 127 ode232 := x*y(x)*D(y(x),x)+y(x)**2+x**2 ---R ---R ---R , 2 2 ---R (81) x y(x)y (x) + y(x) + x ---R ---R Type: Expression Integer ---E 81 - ---S 82 of 127 yx:=solve(ode232,y,x) ---R ---R ---R 2 2 4 ---R 2x y(x) + x ---R (82) ------------- ---R 4 ---R Type: Union(Expression Integer,...) ---E 82 - ---S 83 of 127 ode232expr := x*yx*D(yx,x)+yx**2+x**2 ---R ---R ---R 5 3 7 , 4 4 6 2 8 2 ---R (8x y(x) + 4x y(x))y (x) + 12x y(x) + 16x y(x) + 5x + 16x ---R ---R (83) -------------------------------------------------------------- ---R 16 ---R Type: Expression Integer ---E 83 ---S 84 of 127 ode233 := x*y(x)*D(y(x),x)-y(x)**2+a*x**3*cos(x) ---R ---R ---R , 3 2 ---R (84) x y(x)y (x) + a x cos(x) - y(x) ---R ---R Type: Expression Integer ---E 84 - ---S 85 of 127 yx:=solve(ode233,y,x) ---R ---R ---R 2 2 ---R 2a x sin(x) + y(x) ---R (85) ------------------- ---R 2 ---R 2x ---R Type: Union(Expression Integer,...) ---E 85 - ---S 86 of 127 ode233expr := x*yx*D(yx,x)-yx**2+a*x**3*cos(x) ---R ---R ---R (86) ---R 3 3 , 2 4 2 ---R (4a x y(x)sin(x) + 2x y(x) )y (x) - 4a x sin(x) ---R ---R + ---R 2 5 2 2 3 2 7 4 ---R (4a x cos(x) - 8a x y(x) )sin(x) + (2a x y(x) + 4a x )cos(x) - 3y(x) ---R / ---R 4 ---R 4x ---R Type: Expression Integer ---E 86 ---S 87 of 127 ode234 := x*y(x)*D(y(x),x)-y(x)**2+x*y(x)+x**3-2*x**2 ---R ---R ---R , 2 3 2 ---R (87) x y(x)y (x) - y(x) + x y(x) + x - 2x ---R ---R Type: Expression Integer ---E 87 - ---S 88 of 127 solve(ode234,y,x) ---R ---R ---R (88) "failed" ---R Type: Union("failed",...) ---E 88 ---S 89 of 127 ode235 := (x*y(x)+a)*D(y(x),x)+b*y(x) ---R ---R ---R , ---R (89) (x y(x) + a)y (x) + b y(x) ---R ---R Type: Expression Integer ---E 89 - ---S 90 of 127 yx:=solve(ode235,y,x) ---R ---R ---R y(x) ---R ---- ---R b y(x) ---R (90) b x %e + a Ei(----) ---R b ---R Type: Union(Expression Integer,...) ---E 90 - ---S 91 of 127 ode235expr := (x*yx+a)*D(yx,x)+b*yx ---R ---R ---R (91) ---R y(x) 2 ---R ---- ---R 3 2 b ---R (b x y(x) + a b x )(%e ) ---R + ---R y(x) ---R ---- ---R 2 2 y(x) 2 b ---R ((a x y(x) + a x)Ei(----) + a x y(x) + a )%e ---R b ---R * ---R , ---R y (x) ---R ---R + ---R y(x) 2 y(x) ---R ---- ---- ---R 2 2 b y(x) 2 b ---R b x y(x)(%e ) + (a b x y(x)Ei(----) + (b x + a b)y(x))%e ---R b ---R + ---R y(x) ---R a b y(x)Ei(----) ---R b ---R / ---R y(x) ---R Type: Expression Integer ---E 91 ---S 92 of 127 ode236 := x*(y(x)+4)*D(y(x),x)-y(x)**2-2*y(x)-2*x ---R ---R ---R , 2 ---R (92) (x y(x) + 4x)y (x) - y(x) - 2y(x) - 2x ---R ---R Type: Expression Integer ---E 92 - ---S 93 of 127 solve(ode236,y,x) ---R ---R ---R (93) "failed" ---R Type: Union("failed",...) ---E 93 ---S 94 of 127 ode237 := x*(y(x)+a)*D(y(x),x)+b*y(x)+c*x ---R ---R ---R , ---R (94) (x y(x) + a x)y (x) + b y(x) + c x ---R ---R Type: Expression Integer ---E 94 - ---S 95 of 127 solve(ode237,y,x) ---R ---R ---R (95) "failed" ---R Type: Union("failed",...) ---E 95 ---S 96 of 127 ode238 := (x*(y(x)+x)+a)*D(y(x),x)-y(x)*(y(x)+x)-b ---R ---R ---R 2 , 2 ---R (96) (x y(x) + x + a)y (x) - y(x) - x y(x) - b ---R ---R Type: Expression Integer ---E 96 - ---S 97 of 127 solve(ode238,y,x) ---R ---R ---R (97) "failed" ---R Type: Union("failed",...) ---E 97 ---S 98 of 127 ode239 := (x*y(x)-x**2)*D(y(x),x)+y(x)**2-3*x*y(x)-2*x**2 ---R ---R ---R 2 , 2 2 ---R (98) (x y(x) - x )y (x) + y(x) - 3x y(x) - 2x ---R ---R Type: Expression Integer ---E 98 - ---S 99 of 127 yx:=solve(ode239,y,x) ---R ---R ---R 2 2 3 4 ---R x y(x) - 2x y(x) - x ---R (99) ---------------------- ---R 2 ---R Type: Union(Expression Integer,...) ---E 99 - ---S 100 of 127 ode239expr := (x*yx-x**2)*D(yx,x)+yx**2-3*x*yx-2*x**2 ---R ---R ---R (100) ---R 5 3 6 2 7 4 8 5 , 4 4 ---R (2x y(x) - 6x y(x) + (2x - 4x )y(x) + 2x + 4x )y (x) + 3x y(x) ---R ---R + ---R 5 3 6 3 2 7 4 8 5 2 ---R - 14x y(x) + (8x - 10x )y(x) + (18x + 24x )y(x) + 5x + 14x - 8x ---R / ---R 4 ---R Type: Expression Integer ---E 100 ---S 101 of 127 ode240 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x ---R ---R ---R , 2 ---R (101) 2x y(x)y (x) - y(x) + a x ---R ---R Type: Expression Integer ---E 101 - ---S 102 of 127 yx:=solve(ode240,y,x) ---R ---R ---R 2 ---R a x log(x) + y(x) ---R (102) ------------------ ---R x ---R Type: Union(Expression Integer,...) ---E 102 - ---S 103 of 127 ode240expr := 2*x*yx*D(yx,x)-yx**2+a*x ---R ---R ---R (103) ---R 2 3 , 2 2 2 ---R (4a x y(x)log(x) + 4x y(x) )y (x) - a x log(x) ---R ---R + ---R 2 2 2 4 2 3 ---R (- 4a x y(x) + 2a x )log(x) - 3y(x) + 2a x y(x) + a x ---R / ---R 2 ---R x ---R Type: Expression Integer ---E 103 ---S 104 of 127 ode241 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x**2 ---R ---R ---R , 2 2 ---R (104) 2x y(x)y (x) - y(x) + a x ---R ---R Type: Expression Integer ---E 104 - ---S 105 of 127 yx:=solve(ode241,y,x) ---R ---R ---R 2 2 ---R y(x) + a x ---R (105) ------------ ---R x ---R Type: Union(Expression Integer,...) ---E 105 - ---S 106 of 127 ode241expr := 2*x*yx*D(yx,x)-yx**2+a*x**2 ---R ---R ---R 3 3 , 4 2 2 2 4 ---R (4x y(x) + 4a x y(x))y (x) - 3y(x) - 2a x y(x) + (a + a)x ---R ---R (106) -------------------------------------------------------------- ---R 2 ---R x ---R Type: Expression Integer ---E 106 ---S 107 of 127 ode242 := 2*x*y(x)*D(y(x),x)+2*y(x)**2+1 ---R ---R ---R , 2 ---R (107) 2x y(x)y (x) + 2y(x) + 1 ---R ---R Type: Expression Integer ---E 107 - ---S 108 of 127 yx:=solve(ode242,y,x) ---R ---R ---R 2 2 2 ---R 2x y(x) + x ---R (108) ------------- ---R 2 ---R Type: Union(Expression Integer,...) ---E 108 - ---S 109 of 127 ode242expr := 2*x*yx*D(yx,x)+2*yx**2+1 ---R ---R ---R 5 3 5 , 4 4 4 2 4 ---R (8x y(x) + 4x y(x))y (x) + 12x y(x) + 12x y(x) + 3x + 2 ---R ---R (109) ----------------------------------------------------------- ---R 2 ---R Type: Expression Integer ---E 109 ---S 110 of 127 ode243 := x*(2*y(x)+x-1)*D(y(x),x)-y(x)*(y(x)+2*x+1) ---R ---R ---R 2 , 2 ---R (110) (2x y(x) + x - x)y (x) - y(x) + (- 2x - 1)y(x) ---R ---R Type: Expression Integer ---E 110 - ---S 111 of 127 solve(ode243,y,x) ---R ---R ---R (111) "failed" ---R Type: Union("failed",...) ---E 111 ---S 112 of 127 ode244 := x*(2*y(x)-x-1)*D(y(x),x)+y(x)*(2*x-y(x)-1) ---R ---R ---R 2 , 2 ---R (112) (2x y(x) - x - x)y (x) - y(x) + (2x - 1)y(x) ---R ---R Type: Expression Integer ---E 112 - ---S 113 of 127 solve(ode244,y,x) ---R ---R ---R (113) "failed" ---R Type: Union("failed",...) ---E 113 ---S 114 of 127 ode245 := (2*x*y(x)+4*x**3)*D(y(x),x)+y(x)**2+112*x**2*y(x) ---R ---R ---R 3 , 2 2 ---R (114) (2x y(x) + 4x )y (x) + y(x) + 112x y(x) ---R ---R Type: Expression Integer ---E 114 - ---S 115 of 127 solve(ode245,y,x) ---R ---R ---R (115) "failed" ---R Type: Union("failed",...) ---E 115 ---S 116 of 127 ode246 := x*(3*y(x)+2*x)*D(y(x),x)+3*(y(x)+x)**2 ---R ---R ---R 2 , 2 2 ---R (116) (3x y(x) + 2x )y (x) + 3y(x) + 6x y(x) + 3x ---R ---R Type: Expression Integer ---E 116 - ---S 117 of 127 yx:=solve(ode246,y,x) ---R ---R ---R 2 2 3 4 ---R 6x y(x) + 8x y(x) + 3x ---R (117) ------------------------ ---R 4 ---R Type: Union(Expression Integer,...) ---E 117 - ---S 118 of 127 ode246expr := x*(3*yx+2*x)*D(yx,x)+3*(yx+x)**2 ---R ---R ---R (118) ---R 5 3 6 2 7 4 8 5 , ---R (216x y(x) + 432x y(x) + (300x + 96x )y(x) + 72x + 64x )y (x) ---R ---R + ---R 4 4 5 3 6 3 2 7 4 ---R 324x y(x) + 1008x y(x) + (1200x + 240x )y(x) + (648x + 384x )y(x) ---R + ---R 8 5 2 ---R 135x + 168x + 48x ---R / ---R 16 ---R Type: Expression Integer ---E 118 ---S 119 of 127 ode247 := (3*x+2)*(y(x)-2*x-1)*D(y(x),x)-y(x)**2+x*y(x)-7*x**2-9*x-3 ---R ---R ---R 2 , 2 2 ---R (119) ((3x + 2)y(x) - 6x - 7x - 2)y (x) - y(x) + x y(x) - 7x - 9x - 3 ---R ---R Type: Expression Integer ---E 119 - ---S 120 of 127 solve(ode247,y,x) ---R ---R ---R (120) "failed" ---R Type: Union("failed",...) ---E 120 ---S 121 of 127 ode248 := (6*x*y(x)+x**2+3)*D(y(x),x)+3*y(x)**2+2*x*y(x)+2*x ---R ---R ---R 2 , 2 ---R (121) (6x y(x) + x + 3)y (x) + 3y(x) + 2x y(x) + 2x ---R ---R Type: Expression Integer ---E 121 - ---S 122 of 127 yx:=solve(ode248,y,x) ---R ---R ---R 2 2 2 ---R (122) 3x y(x) + (x + 3)y(x) + x ---R Type: Union(Expression Integer,...) ---E 122 - ---S 123 of 127 ode248expr := (6*x*yx+x**2+3)*D(yx,x)+3*yx**2+2*x*yx+2*x ---R ---R ---R (123) ---R 3 3 4 2 2 5 4 3 5 ---R 108x y(x) + (54x + 162x )y(x) + (6x + 36x + 42x + 72x)y(x) + 6x ---R + ---R 4 3 2 ---R x + 18x + 6x + 9 ---R * ---R , ---R y (x) ---R ---R + ---R 2 4 3 3 4 3 2 2 ---R 81x y(x) + (72x + 108x)y(x) + (15x + 72x + 63x + 36)y(x) ---R + ---R 4 3 2 4 3 ---R (30x + 4x + 54x + 12x)y(x) + 15x + 4x + 8x ---R Type: Expression Integer ---E 123 ---S 124 of 127 ode249 := (a*x*y(x)+b*x**n)*D(y(x),x)+alpha*y(x)**3+beta*y(x)**2 ---R ---R ---R n , 3 2 ---R (124) (b x + a x y(x))y (x) + alpha y(x) + beta y(x) ---R ---R Type: Expression Integer ---E 124 - ---S 125 of 127 solve(ode249,y,x) ---R ---R ---R (125) "failed" ---R Type: Union("failed",...) ---E 125 ---S 126 of 127 ode250 := (B*x*y(x)+A*x**2+a*x+b*y(x)+c)*D(y(x),x)-B*g(x)**2+_ A*x*y(x)+alpha*x+beta*y(x)+gamma ---R ---R ---R (126) ---R 2 , 2 ---R ((B x + b)y(x) + A x + a x + c)y (x) + (A x + beta)y(x) - B g(x) ---R ---R + ---R alpha x + gamma ---R Type: Expression Integer ---E 126 - ---S 127 of 127 solve(ode250,y,x) ---R ---R ---R (127) "failed" ---R Type: Union("failed",...) ---E 127 - -)spool -)lisp (bye) - -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} -\end{thebibliography} -\end{document} - diff --git a/src/axiom-website/CATS/kamke5.txt b/src/axiom-website/CATS/kamke5.txt new file mode 100644 index 0000000..f704f04 --- /dev/null +++ b/src/axiom-website/CATS/kamke5.txt @@ -0,0 +1,184 @@ +y:=operator 'y +f:=operator 'f +f0:=operator 'f0 +f1:=operator 'f1 +f2:=operator 'f2 +f3:=operator 'f3 +g:=operator 'g +g0:=operator 'g0 +g1:=operator 'g1 +h:=operator 'h + +ode251 := (x**2*y(x)-1)*D(y(x),x)+x*y(x)**2-1 +yx:=solve(ode251,y,x) +ode251expr := (x**2*yx-1)*D(yx,x)+x*yx**2-1 + +ode252 := (x**2*y(x)-1)*D(y(x),x)-(x*y(x)**2-1) +solve(ode252,y,x) + +ode253 := (x**2*y(x)-1)*D(y(x),x)+8*(x*y(x)**2-1) +solve(ode253,y,x) + +ode254 := x*(x*y(x)-2)*D(y(x),x)+x**2*y(x)**3+x*y(x)**2-2*y(x) +solve(ode254,y,x) + +ode255 := x*(x*y(x)-3)*D(y(x),x)+x*y(x)**2-y(x) +solve(ode255,y,x) + +ode256 := x**2*(y(x)-1)*D(y(x),x)+(x-1)*y(x) +solve(ode256,y,x) + +ode257 := x*(x*y(x)+x**4-1)*D(y(x),x)-y(x)*(x*y(x)-x**4-1) +solve(ode257,y,x) + +ode258 := 2*x**2*y(x)*D(y(x),x)+y(x)**2-2*x**3-x**2 +yx:=solve(ode258,y,x) +ode258expr := 2*x**2*yx*D(yx,x)+yx**2-2*x**3-x**2 + +ode259 := 2*x**2*y(x)*D(y(x),x)-y(x)**2-x**2*exp(x-1/x) +yx:=solve(ode259,y,x) +ode259expr := 2*x**2*yx*D(yx,x)-yx**2-x**2*exp(x-1/x) + +ode260 := (2*x**2*y(x)+x)*D(y(x),x)-x**2*y(x)**3+2*x*y(x)**2+y(x) +solve(ode260,y,x) + +ode261 := (2*x**2*y(x)-x)*D(y(x),x)-2*x*y(x)**2-y(x) +solve(ode261,y,x) + +ode262 := (2*x**2*y(x)-x**3)*D(y(x),x)+y(x)**3-4*x*y(x)**2+2*x**3 +solve(ode262,y,x) + +ode263 := 2*x**3+y(x)*D(y(x),x)+3*x**2*y(x)**2+7 +solve(ode263,y,x) + +ode264 := 2*x*(x**3*y(x)+1)*D(y(x),x)+(3*x**3*y(x)-1)*y(x) +solve(ode264,y,x) + +ode265 := (x**(n*(n+1))*y(x)-1)*D(y(x),x)+2*(n+1)**2*x**(n-1)_ + *(x**(n**2)*y(x)**2-1) +solve(ode265,y,x) + +ode266 := (y(x)-x)*sqrt(x**2+1)*D(y(x),x)-a*sqrt((y(x)**2+1)**3) +solve(ode266,y,x) + +ode267 := y(x)*D(y(x),x)*sin(x)**2+y(x)**2*cos(x)*sin(x)-1 +yx:=solve(ode267,y,x) +ode267expr := yx*D(yx,x)*sin(x)**2+yx**2*cos(x)*sin(x)-1 + +ode268 := f(x)*y(x)*D(y(x),x)+g(x)*y(x)**2+h(x) +solve(ode268,y,x) + +ode269 := (g1(x)*y(x)+g0(x))*D(y(x),x)-f1(x)*y(x)-_ + f2(x)*y(x)**2-f3(x)*y(x)**3-f0(x) +solve(ode269,y,x) + +ode270 := (y(x)**2-x)*D(y(x),x)-y(x)+x**2 +yx:=solve(ode270,y,x) +ode270expr := (yx**2-x)*D(yx,x)-yx+x**2 + +ode271 := (y(x)**2+x**2)*D(y(x),x)+2*x*(y(x)+2*x) +yx:=solve(ode271,y,x) +ode271expr := (yx**2+x**2)*D(yx,x)+2*x*(yx+2*x) + +ode272 := (y(x)**2+x**2)*D(y(x),x)-y(x)**2 +solve(ode272,y,x) + +ode273 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x) +yx:=solve(ode273,y,x) +ode273expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx + +ode274 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x)+x**2+b +yx:=solve(ode274,y,x) +ode274expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx+x**2+b + +ode275 := (y(x)**2+x**2+x)*D(y(x),x)-y(x) +solve(ode275,y,x) + +ode276 := (y(x)**2-x**2)*D(y(x),x)+2*x*y(x) +yx:=solve(ode276,y,x) +ode276expr := (yx**2-x**2)*D(yx,x)+2*x*yx + +ode277 := (y(x)**2+x**4)*D(y(x),x)-4*x**3*y(x) +yx:=solve(ode277,y,x) +ode277expr := (yx**2+x**4)*D(yx,x)-4*x**3*yx + +ode278 := (y(x)**2+4*sin(x))*D(y(x),x)-cos(x) +yx:=solve(ode278,y,x) +ode278expr := (yx**2+4*sin(x))*D(yx,x)-cos(x) + +ode279 := (y(x)**2+2*y(x)+x)*D(y(x),x)+(y(x)+x)**2*y(x)**2+y(x)*(y(x)+1) +solve(ode279,y,x) + +ode280 := (y(x)+x)**2*D(y(x),x)-a**2 +solve(ode280,y,x) + +ode281 := (y(x)**2+2*x*y(x)-x**2)*D(y(x),x)-_ + y(x)**2+2*x*y(x)+x**2 +solve(ode281,y,x) + +ode282 := (y(x)+3*x-1)**2*D(y(x),x)-(2*y(x)-1)*(4*y(x)+6*x-3) +solve(ode282,y,x) + +ode283 := 3*(y(x)**2-x**2)*D(y(x),x)+2*y(x)**3-6*x*(x+1)*y(x)-3*exp(x) +yx:=solve(ode283,y,x) +ode283expr := 3*(yx**2-x**2)*D(yx,x)+2*yx**3-6*x*(x+1)*yx-3*exp(x) + +ode284 := (4*y(x)**2+x**2)*D(y(x),x)-x*y(x) +yx:=solve(ode284,y,x) +ode284expr := (4*yx**2+x**2)*D(yx,x)-x*yx + +ode285 := (4*y(x)**2+2*x*y(x)+3*x**2)*D(y(x),x)+y(x)**2+6*x*y(x)+2*x**2 +yx:=solve(ode285,y,x) +ode285expr := (4*yx**2+2*x*yx+3*x**2)*D(yx,x)+yx**2+6*x*yx+2*x**2 + +ode286 := (2*y(x)-3*x+1)**2*D(y(x),x)-(3*y(x)-2*x-4)**2 +solve(ode286,y,x) + +ode287 := (2*y(x)-4*x+1)**2*D(y(x),x)-(y(x)-2*x)**2 +solve(ode287,y,x) + +ode288 := (6*y(x)**2-3*x**2*y(x)+1)*D(y(x),x)-3*x*y(x)**2+x +yx:=solve(ode288,y,x) +ode288expr := (6*yx**2-3*x**2*yx+1)*D(yx,x)-3*x*yx**2+x + +ode289 := (6*y(x)-x)**2*D(y(x),x)-6*y(x)**2+2*x*y(x)+a +yx:=solve(ode289,y,x) +ode289expr := (6*yx-x)**2*D(yx,x)-6*yx**2+2*x*yx+a + +ode290 := (a*y(x)**2+2*b*x*y(x)+c*x**2)*D(y(x),x)+b*y(x)**2+2*c*x*y(x)+d*x**2 +yx:=solve(ode290,y,x) + +ode290expr:=(a*yx**2+2*b*x*yx+c*x**2)*D(yx,x)+b*yx**2+2*c*x*yx+d*x**2 +ode291 := (b*(beta*y(x)+alpha*x)**2-beta*(b*y(x)+a*x))*D(y(x),x)+_ + a*(beta*y(x)+alpha*x)**2-alpha*(b*y(x)+a*x) +solve(ode291,y,x) + +ode292 := (a*y(x)+b*x+c)**2*D(y(x),x)+(alpha*y(x)+beta*x+gamma)**2 +solve(ode292,y,x) + +ode293 := x*(y(x)**2-3*x)*D(y(x),x)+2*y(x)**3-5*x*y(x) +solve(ode293,y,x) + +ode294 := x*(y(x)**2+x**2-a)*D(y(x),x)-y(x)*(y(x)**2+x**2+a) +solve(ode294,y,x) + +ode295 := x*(y(x)**2+x*y(x)-x**2)*D(y(x),x)-y(x)**3+x*y(x)**2+x**2*y(x) +solve(ode295,y,x) + +ode296 := x*(y(x)**2+x**2*y(x)+x**2)*D(y(x),x)-2*y(x)**3-2*x**2*y(x)**2+x**4 +solve(ode296,y,x) + +ode297 := 2*x*(y(x)**2+5*x**2)*D(y(x),x)+y(x)**3-x**2*y(x) +solve(ode297,y,x) + +ode298 := 3*x*y(x)**2*D(y(x),x)+y(x)**3-2*x +yx:=solve(ode298,y,x) +ode298expr := 3*x*yx**2*D(yx,x)+yx**3-2*x + +ode299 := (3*x*y(x)**2-x**2)*D(y(x),x)+y(x)**3-2*x*y(x) +yx:=solve(ode299,y,x) +ode299expr := (3*x*yx**2-x**2)*D(yx,x)+yx**3-2*x*yx + +ode300 := 6*x*y(x)**2*D(y(x),x)+2*y(x)**3+x +yx:=solve(ode300,y,x) +ode300expr := 6*x*yx**2*D(yx,x)+2*yx**3+x diff --git a/src/axiom-website/CATS/kamke6.input.pamphlet b/src/axiom-website/CATS/kamke6.input.pamphlet index ad31cd3..a16be4c 100644 --- a/src/axiom-website/CATS/kamke6.input.pamphlet +++ b/src/axiom-website/CATS/kamke6.input.pamphlet @@ -1,5 +1,6 @@ \documentclass{article} \usepackage{axiom} +\setlength{\textwidth}{400pt} \begin{document} \title{\$SPAD/src/input kamke6.input} \author{Timothy Daly} @@ -13,7 +14,7 @@ satisfies the original ordinary differential equation. \eject \tableofcontents \eject -<<*>>= +\begin{chunk}{*} )spool kamke6.output )set break resume )set mes auto off @@ -28,7 +29,7 @@ y:=operator 'y --E 1 --S 2 of 120 ---Rf:=operator 'f +f:=operator 'f --R --R --R (2) f @@ -36,26 +37,25 @@ y:=operator 'y --E 2 --S 3 of 120 ---Rg:=operator 'g +g:=operator 'g --R --R --R (3) g --R Type: BasicOperator ---R --E 3 --S 4 of 120 ---Rode301 := (6*x*y(x)**2+x**2)*D(y(x),x)-y(x)*(3*y(x)**2-x) +ode301 := (6*x*y(x)**2+x**2)*D(y(x),x)-y(x)*(3*y(x)**2-x) --R --R --R 2 2 , 3 --R (4) (6x y(x) + x )y (x) - 3y(x) + x y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 4 --S 5 of 120 ---Rsolve(ode301,y,x) +solve(ode301,y,x) --R --R --R (5) "failed" @@ -63,17 +63,17 @@ y:=operator 'y --E 5 --S 6 of 120 ---Rode302 := (x**2*y(x)**2+x)*D(y(x),x)+y(x) +ode302 := (x**2*y(x)**2+x)*D(y(x),x)+y(x) --R --R --R 2 2 , --R (6) (x y(x) + x)y (x) + y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 6 --S 7 of 120 ---Rsolve(ode302,y,x) +solve(ode302,y,x) --R --R --R (7) "failed" @@ -81,17 +81,17 @@ y:=operator 'y --E 7 --S 8 of 120 ---Rode303 := (x*y(x)-1)**2*x*D(y(x),x)+(x**2*y(x)**2+1)*y(x) +ode303 := (x*y(x)-1)**2*x*D(y(x),x)+(x**2*y(x)**2+1)*y(x) --R --R --R 3 2 2 , 2 3 --R (8) (x y(x) - 2x y(x) + x)y (x) + x y(x) + y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 8 --S 9 of 120 ---Rsolve(ode303,y,x) +solve(ode303,y,x) --R --R --R (9) "failed" @@ -99,17 +99,17 @@ y:=operator 'y --E 9 --S 10 of 120 ---Rode304 := (10*x**3*y(x)**2+x**2*y(x)+2*x)*D(y(x),x)+5*x**2*y(x)**3+x*y(x)**2 +ode304 := (10*x**3*y(x)**2+x**2*y(x)+2*x)*D(y(x),x)+5*x**2*y(x)**3+x*y(x)**2 --R --R --R 3 2 2 , 2 3 2 --R (10) (10x y(x) + x y(x) + 2x)y (x) + 5x y(x) + x y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 10 --S 11 of 120 ---Rsolve(ode304,y,x) +solve(ode304,y,x) --R --R --R (11) "failed" @@ -117,28 +117,28 @@ y:=operator 'y --E 11 --S 12 of 120 ---Rode305 := (y(x)**3-3*x)*D(y(x),x)-3*y(x)+x**2 +ode305 := (y(x)**3-3*x)*D(y(x),x)-3*y(x)+x**2 --R --R --R 3 , 2 --R (12) (y(x) - 3x)y (x) - 3y(x) + x --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 12 --S 13 of 120 ---Ryx:=solve(ode305,y,x) +yx:=solve(ode305,y,x) --R --R --R 4 3 --R 3y(x) - 36x y(x) + 4x --R (13) ----------------------- --R 12 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 13 --S 14 of 120 ---Rode305expr := (yx**3-3*x)*D(yx,x)-3*yx+x**2 +ode305expr := (yx**3-3*x)*D(yx,x)-3*yx+x**2 --R --R --R (14) @@ -171,32 +171,32 @@ y:=operator 'y --R (- 1920x + 31104x)y(x) + 64x - 6912x + 1728x --R / --R 1728 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 14 --S 15 of 120 ---Rode306 := (y(x)**3-x**3)*D(y(x),x)-x**2*y(x) +ode306 := (y(x)**3-x**3)*D(y(x),x)-x**2*y(x) --R --R --R 3 3 , 2 --R (15) (y(x) - x )y (x) - x y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 15 --S 16 of 120 ---Ryx:=solve(ode306,y,x) +yx:=solve(ode306,y,x) --R --R --R 6 3 3 --R y(x) - 2x y(x) --R (16) ---------------- --R 6 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 16 --S 17 of 120 ---Rode306expr := (yx**3-x**3)*D(yx,x)-x**2*yx +ode306expr := (yx**3-x**3)*D(yx,x)-x**2*yx --R --R --R (17) @@ -214,32 +214,32 @@ y:=operator 'y --R - x y(x) + 6x y(x) - 12x y(x) + 8x y(x) - 36x y(x) + 288x y(x) --R / --R 216 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 17 --S 18 of 120 ---Rode307 := (y(x)**2+x**2+a)*y(x)*D(y(x),x)+(y(x)**2+x**2-a)*x +ode307 := (y(x)**2+x**2+a)*y(x)*D(y(x),x)+(y(x)**2+x**2-a)*x --R --R --R 3 2 , 2 3 --R (18) (y(x) + (x + a)y(x))y (x) + x y(x) + x - a x --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 18 --S 19 of 120 ---Ryx:=solve(ode307,y,x) +yx:=solve(ode307,y,x) --R --R --R 4 2 2 4 2 --R y(x) + (2x + 2a)y(x) + x - 2a x --R (19) ------------------------------------ --R 4 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 19 --S 20 of 120 ---Rode307expr := (yx**2+x**2+a)*yx*D(yx,x)+(yx**2+x**2-a)*x +ode307expr := (yx**2+x**2+a)*yx*D(yx,x)+(yx**2+x**2-a)*x --R --R --R (20) @@ -298,32 +298,32 @@ y:=operator 'y --R - 64a x --R / --R 64 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 20 --S 21 of 120 ---Rode308 := 2*y(x)**3*D(y(x),x)+x*y(x)**2 +ode308 := 2*y(x)**3*D(y(x),x)+x*y(x)**2 --R --R --R 3 , 2 --R (21) 2y(x) y (x) + x y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 21 --S 22 of 120 ---Ryx:=solve(ode308,y,x) +yx:=solve(ode308,y,x) --R --R --R 2 2 --R 2y(x) + x --R (22) ----------- --R 2 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 22 --S 23 of 120 ---Rode308expr := 2*yx**3*D(yx,x)+x*yx**2 +ode308expr := 2*yx**3*D(yx,x)+x*yx**2 --R --R --R (23) @@ -335,32 +335,32 @@ y:=operator 'y --R (12x + 4x)y(x) + (6x + 4x )y(x) + x + x --R / --R 4 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 23 --S 24 of 120 ---Rode309 := (2*y(x)**3+y(x))*D(y(x),x)-2*x**3-x +ode309 := (2*y(x)**3+y(x))*D(y(x),x)-2*x**3-x --R --R --R 3 , 3 --R (24) (2y(x) + y(x))y (x) - 2x - x --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 24 --S 25 of 120 ---Ryx:=solve(ode309,y,x) +yx:=solve(ode309,y,x) --R --R --R 4 2 4 2 --R y(x) + y(x) - x - x --R (25) ----------------------- --R 2 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 25 --S 26 of 120 ---Rode309expr := (2*yx**3+yx)*D(yx,x)-2*x**3-x +ode309expr := (2*yx**3+yx)*D(yx,x)-2*x**3-x --R --R --R (26) @@ -396,32 +396,32 @@ y:=operator 'y --R 5x + 6x - 6x - 4x --R / --R 4 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 26 --S 27 of 120 ---Rode310 := (2*y(x)**3+5*x**2*y(x))*D(y(x),x)+5*x*y(x)**2+x**3 +ode310 := (2*y(x)**3+5*x**2*y(x))*D(y(x),x)+5*x*y(x)**2+x**3 --R --R --R 3 2 , 2 3 --R (27) (2y(x) + 5x y(x))y (x) + 5x y(x) + x --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 27 --S 28 of 120 ---Ryx:=solve(ode310,y,x) +yx:=solve(ode310,y,x) --R --R --R 4 2 2 4 --R 2y(x) + 10x y(x) + x --R (28) ----------------------- --R 4 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 28 --S 29 of 120 ---Rode310expr := (2*yx**3+5*x**2*yx)*D(yx,x)+5*x*yx**2+x**3 +ode310expr := (2*yx**3+5*x**2*yx)*D(yx,x)+5*x*yx**2+x**3 --R --R --R (29) @@ -448,33 +448,33 @@ y:=operator 'y --R x + 50x + 32x --R / --R 32 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 29 --S 30 of 120 ---Rode311 := (20*y(x)**3-3*x*y(x)**2+6*x**2*y(x)+3*x**3)*D(y(x),x)-_ ---R y(x)**3+6*x*y(x)**2+9*x**2*y(x)+4*x**3 +ode311 := (20*y(x)**3-3*x*y(x)**2+6*x**2*y(x)+3*x**3)*D(y(x),x)-_ + y(x)**3+6*x*y(x)**2+9*x**2*y(x)+4*x**3 --R --R --R (30) --R 3 2 2 3 , 3 2 2 3 --R (20y(x) - 3x y(x) + 6x y(x) + 3x )y (x) - y(x) + 6x y(x) + 9x y(x) + 4x --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 30 --S 31 of 120 ---Ryx:=solve(ode311,y,x) +yx:=solve(ode311,y,x) --R --R --R 4 3 2 2 3 4 --R (31) 5y(x) - x y(x) + 3x y(x) + 3x y(x) + x ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 31 --S 32 of 120 ---Rode311expr := (20*yx**3-3*x*yx**2+6*x**2*yx+3*x**3)*D(yx,x)-_ ---R yx**3+6*x*yx**2+9*x**2*yx+4*x**3 +ode311expr := (20*yx**3-3*x*yx**2+6*x**2*yx+3*x**3)*D(yx,x)-_ + yx**3+6*x*yx**2+9*x**2*yx+4*x**3 --R --R --R (32) @@ -529,12 +529,12 @@ y:=operator 'y --R + --R 14 11 8 5 15 12 9 6 3 --R (900x - 108x + 162x + 54x )y(x) + 80x - 13x + 30x + 21x + 4x ---R Type: Expression Integer +--R Type: Expression(Integer) --E 32 --S 33 of 120 ---Rode312 := (y(x)**2/b+x**2/a)*(y(x)*D(y(x),x)+x)+((a-b)/(a+b))*_ ---R (y(x)*D(y(x),x)-x) +ode312 := (y(x)**2/b+x**2/a)*(y(x)*D(y(x),x)+x)+((a-b)/(a+b))*_ + (y(x)*D(y(x),x)-x) --R --R --R (33) @@ -547,11 +547,11 @@ y:=operator 'y --R / --R 2 2 --R a b + a b ---R Type: Expression Integer +--R Type: Expression(Integer) --E 33 --S 34 of 120 ---Rsolve(ode312,y,x) +solve(ode312,y,x) --R --R --R (34) "failed" @@ -559,8 +559,8 @@ y:=operator 'y --E 34 --S 35 of 120 ---Rode313 := (2*a*y(x)**3+3*a*x*y(x)**2-b*x**3+c*x**2)*D(y(x),x)-_ ---R a*y(x)**3+c*y(x)**2+3*b*x**2*y(x)+2*b*x**3 +ode313 := (2*a*y(x)**3+3*a*x*y(x)**2-b*x**3+c*x**2)*D(y(x),x)-_ + a*y(x)**3+c*y(x)**2+3*b*x**2*y(x)+2*b*x**3 --R --R --R (35) @@ -570,11 +570,11 @@ y:=operator 'y --R + --R 3 --R 2b x ---R Type: Expression Integer +--R Type: Expression(Integer) --E 35 --S 36 of 120 ---Rsolve(ode313,y,x) +solve(ode313,y,x) --R --R --R (36) "failed" @@ -582,28 +582,28 @@ y:=operator 'y --E 36 --S 37 of 120 ---Rode314 := x*y(x)**3*D(y(x),x)+y(x)**4-x*sin(x) +ode314 := x*y(x)**3*D(y(x),x)+y(x)**4-x*sin(x) --R --R --R 3 , 4 --R (37) x y(x) y (x) - x sin(x) + y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 37 --S 38 of 120 ---Ryx:=solve(ode314,y,x) +yx:=solve(ode314,y,x) --R --R --R 3 4 2 4 4 --R (- 16x + 96x)sin(x) + (4x - 48x + 96)cos(x) + x y(x) --R (38) -------------------------------------------------------- --R 4 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 38 --S 39 of 120 ---Rode314expr := x*yx**3*D(yx,x)+yx**4-x*sin(x) +ode314expr := x*yx**3*D(yx,x)+yx**4-x*sin(x) --R --R --R (39) @@ -756,21 +756,21 @@ y:=operator 'y --R (64x - 768x + 1536x )y(x) cos(x) + 5x y(x) --R / --R 256 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 39 --S 40 of 120 ---Rode315 := (2*x*y(x)**3-x**4)*D(y(x),x)-y(x)**4+2*x**3*y(x) +ode315 := (2*x*y(x)**3-x**4)*D(y(x),x)-y(x)**4+2*x**3*y(x) --R --R --R 3 4 , 4 3 --R (40) (2x y(x) - x )y (x) - y(x) + 2x y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 40 --S 41 of 120 ---Rsolve(ode315,y,x) +solve(ode315,y,x) --R --R --R (41) "failed" @@ -778,17 +778,17 @@ y:=operator 'y --E 41 --S 42 of 120 ---Rode316 := (2*x*y(x)**3+y(x))*D(y(x),x)+2*y(x)**2 +ode316 := (2*x*y(x)**3+y(x))*D(y(x),x)+2*y(x)**2 --R --R --R 3 , 2 --R (42) (2x y(x) + y(x))y (x) + 2y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 42 --S 43 of 120 ---Ryx:=solve(ode316,y,x) +yx:=solve(ode316,y,x) --R --R --R 2 @@ -799,11 +799,11 @@ y:=operator 'y --R 2 --R (43) ---------------------- --R 2 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 43 --S 44 of 120 ---Rode316expr := (2*x*yx**3+yx)*D(yx,x)+2*yx**2 +ode316expr := (2*x*yx**3+yx)*D(yx,x)+2*yx**2 --R --R --R (44) @@ -854,21 +854,21 @@ y:=operator 'y --R 2 2 2 --R / --R 4y(x) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 44 --S 45 of 120 ---Rode317 := (2*x*y(x)**3+x*y(x)+x**2)*D(y(x),x)+y(x)**2-x*y(x) +ode317 := (2*x*y(x)**3+x*y(x)+x**2)*D(y(x),x)+y(x)**2-x*y(x) --R --R --R 3 2 , 2 --R (45) (2x y(x) + x y(x) + x )y (x) + y(x) - x y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 45 --S 46 of 120 ---Rsolve(ode317,y,x) +solve(ode317,y,x) --R --R --R (46) "failed" @@ -876,17 +876,17 @@ y:=operator 'y --E 46 --S 47 of 120 ---Rode318 := (3*x*y(x)**3-4*x*y(x)+y(x))*D(y(x),x)+y(x)**2*(y(x)**2-2) +ode318 := (3*x*y(x)**3-4*x*y(x)+y(x))*D(y(x),x)+y(x)**2*(y(x)**2-2) --R --R --R 3 , 4 2 --R (47) (3x y(x) + (- 4x + 1)y(x))y (x) + y(x) - 2y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 47 --S 48 of 120 ---Ryx:=solve(ode318,y,x) +yx:=solve(ode318,y,x) --R --R --R (48) @@ -899,11 +899,11 @@ y:=operator 'y --R +---------+ --R | 2 2 --R y(x)\|y(x) - 2 - y(x) + 2 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 48 --S 49 of 120 ---Rode318expr := (3*x*yx**3-4*x*yx+yx)*D(yx,x)+yx**2*(yx**2-2) +ode318expr := (3*x*yx**3-4*x*yx+yx)*D(yx,x)+yx**2*(yx**2-2) --R --R --R (49) @@ -925,32 +925,32 @@ y:=operator 'y --R + --R 3 2 6 2 4 2 --R (52x - 66x + 8x)y(x) + (72x - 38x + 2)y(x) + (44x - 8)y(x) + 8 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 49 --S 50 of 120 ---Rode319 := (7*x*y(x)**3+y(x)-5*x)*D(y(x),x)+y(x)**4-5*y(x) +ode319 := (7*x*y(x)**3+y(x)-5*x)*D(y(x),x)+y(x)**4-5*y(x) --R --R --R 3 , 4 --R (50) (7x y(x) + y(x) - 5x)y (x) + y(x) - 5y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 50 --S 51 of 120 ---Ryx:=solve(ode319,y,x) +yx:=solve(ode319,y,x) --R --R --R 7 5 4 2 --R 10x y(x) + 2y(x) - 100x y(x) - 25y(x) + 250x y(x) --R (51) ----------------------------------------------------- --R 10 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 51 --S 52 of 120 ---Rode319expr := (7*x*yx**3+yx-5*x)*D(yx,x)+yx**4-5*yx +ode319expr := (7*x*yx**3+yx-5*x)*D(yx,x)+yx**4-5*yx --R --R --R (52) @@ -1048,21 +1048,21 @@ y:=operator 'y --R - 2500000x y(x) --R / --R 10000 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 52 --S 53 of 120 ---Rode320 := (x**2*y(x)**3+x*y(x))*D(y(x),x)-1 +ode320 := (x**2*y(x)**3+x*y(x))*D(y(x),x)-1 --R --R --R 2 3 , --R (53) (x y(x) + x y(x))y (x) - 1 --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 53 --S 54 of 120 ---Rsolve(ode320,y,x) +solve(ode320,y,x) --R --R --R (54) "failed" @@ -1070,17 +1070,17 @@ y:=operator 'y --E 54 --S 55 of 120 ---Rode321 := (2*x**2*y(x)**3+x**2*y(x)**2-2*x)*D(y(x),x)-2*y(x)-1 +ode321 := (2*x**2*y(x)**3+x**2*y(x)**2-2*x)*D(y(x),x)-2*y(x)-1 --R --R --R 2 3 2 2 , --R (55) (2x y(x) + x y(x) - 2x)y (x) - 2y(x) - 1 --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 55 --S 56 of 120 ---Rsolve(ode321,y,x) +solve(ode321,y,x) --R --R --R (56) "failed" @@ -1088,28 +1088,28 @@ y:=operator 'y --E 56 --S 57 of 120 ---Rode322 := (10*x**2*y(x)**3-3*y(x)**2-2)*D(y(x),x)+5*x*y(x)**4+x +ode322 := (10*x**2*y(x)**3-3*y(x)**2-2)*D(y(x),x)+5*x*y(x)**4+x --R --R --R 2 3 2 , 4 --R (57) (10x y(x) - 3y(x) - 2)y (x) + 5x y(x) + x --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 57 --S 58 of 120 ---Ryx:=solve(ode322,y,x) +yx:=solve(ode322,y,x) --R --R --R 2 4 3 2 --R 5x y(x) - 2y(x) - 4y(x) + x --R (58) ------------------------------ --R 2 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 58 --S 59 of 120 ---Rode322expr := (10*x**2*yx**3-3*yx**2-2)*D(yx,x)+5*x*yx**4+x +ode322expr := (10*x**2*yx**3-3*yx**2-2)*D(yx,x)+5*x*yx**4+x --R --R --R (59) @@ -1160,21 +1160,21 @@ y:=operator 'y --R (1440x - 192x)y(x) + (- 320x + 96x )y(x) + 25x - 12x - 16x --R / --R 16 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 59 --S 60 of 120 ---Rode323 := (a*x*y(x)**3+c)*x*D(y(x),x)+(b*x**3*y(x)+c)*y(x) +ode323 := (a*x*y(x)**3+c)*x*D(y(x),x)+(b*x**3*y(x)+c)*y(x) --R --R --R 2 3 , 3 2 --R (60) (a x y(x) + c x)y (x) + b x y(x) + c y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 60 --S 61 of 120 ---Rsolve(ode323,y,x) +solve(ode323,y,x) --R --R --R (61) "failed" @@ -1182,17 +1182,17 @@ y:=operator 'y --E 61 --S 62 of 120 ---Rode324 := (2*x**3*y(x)**3-x)*D(y(x),x)+2*x**3*y(x)**3-y(x) +ode324 := (2*x**3*y(x)**3-x)*D(y(x),x)+2*x**3*y(x)**3-y(x) --R --R --R 3 3 , 3 3 --R (62) (2x y(x) - x)y (x) + 2x y(x) - y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 62 --S 63 of 120 ---Rsolve(ode324,y,x) +solve(ode324,y,x) --R --R --R (63) "failed" @@ -1200,17 +1200,17 @@ y:=operator 'y --E 63 --S 64 of 120 ---Rode325 := y(x)*(y(x)**3-2*x**3)*D(y(x),x)+(2*y(x)**3-x**3)*x +ode325 := y(x)*(y(x)**3-2*x**3)*D(y(x),x)+(2*y(x)**3-x**3)*x --R --R --R 4 3 , 3 4 --R (64) (y(x) - 2x y(x))y (x) + 2x y(x) - x --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 64 --S 65 of 120 ---Rsolve(ode325,y,x) +solve(ode325,y,x) --R --R --R (65) "failed" @@ -1218,7 +1218,7 @@ y:=operator 'y --E 65 --S 66 of 120 ---Rode326 := y(x)*((a*y(x)+b*x)**3+b*x**3)*D(y(x),x)+x*((a*y(x)+b*x)**3+a*y(x)**3) +ode326 := y(x)*((a*y(x)+b*x)**3+b*x**3)*D(y(x),x)+x*((a*y(x)+b*x)**3+a*y(x)**3) --R --R --R (66) @@ -1228,11 +1228,11 @@ y:=operator 'y --R + --R 3 3 2 2 2 2 3 3 4 --R (a + a)x y(x) + 3a b x y(x) + 3a b x y(x) + b x ---R Type: Expression Integer +--R Type: Expression(Integer) --E 66 --S 67 of 120 ---Rsolve(ode326,y,x) +solve(ode326,y,x) --R --R --R (67) "failed" @@ -1240,17 +1240,17 @@ y:=operator 'y --E 67 --S 68 of 120 ---Rode327 := (x*y(x)**4+2*x**2*y(x)**3+2*y(x)+x)*D(y(x),x)+y(x)**5+y(x) +ode327 := (x*y(x)**4+2*x**2*y(x)**3+2*y(x)+x)*D(y(x),x)+y(x)**5+y(x) --R --R --R 4 2 3 , 5 --R (68) (x y(x) + 2x y(x) + 2y(x) + x)y (x) + y(x) + y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 68 --S 69 of 120 ---Rsolve(ode327,y,x) +solve(ode327,y,x) --R --R --R (69) "failed" @@ -1258,17 +1258,17 @@ y:=operator 'y --E 69 --S 70 of 120 ---Rode328 := a*x**2*y(x)**n*D(y(x),x)-2*x*D(y(x),x)+y(x) +ode328 := a*x**2*y(x)**n*D(y(x),x)-2*x*D(y(x),x)+y(x) --R --R --R 2 n , --R (70) (a x y(x) - 2x)y (x) + y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 70 --S 71 of 120 ---Rsolve(ode328,y,x) +solve(ode328,y,x) --R --R --R (71) "failed" @@ -1276,17 +1276,17 @@ y:=operator 'y --E 71 --S 72 of 120 ---Rode329 := y(x)**m*x**n*(a*x*D(y(x),x)+b*y(x))+alpha*x*D(y(x),x)+beta*y(x) +ode329 := y(x)**m*x**n*(a*x*D(y(x),x)+b*y(x))+alpha*x*D(y(x),x)+beta*y(x) --R --R --R n m , n m --R (72) (a x x y(x) + alpha x)y (x) + b y(x)x y(x) + beta y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 72 --S 73 of 120 ---Rsolve(ode329,y,x) +solve(ode329,y,x) --R --R --R (73) "failed" @@ -1294,17 +1294,17 @@ y:=operator 'y --E 73 --S 74 of 120 ---Rode330 := (f(x+y(x))+1)*D(y(x),x)+f(x+y(x)) +ode330 := (f(x+y(x))+1)*D(y(x),x)+f(x+y(x)) --R --R --R , --R (74) (f(y(x) + x) + 1)y (x) + f(y(x) + x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 74 --S 75 of 120 ---Rsolve(ode330,y,x) +solve(ode330,y,x) --R --R --R >> Error detected within library code: @@ -1314,28 +1314,28 @@ y:=operator 'y --R --E 75 -@ +\end{chunk} I have no idea what to do with this \begin{verbatim} ode331 := D(y(x),x)*convert([sum(f[nu](x)*y(x)**nu,'nu'=1..p)],`+`)-_ convert([sum(g[nu](x)*y(x)**nu,'nu'=1..q)],`+`) \end{verbatim} -<<*>>= +\begin{chunk}{*} --R --S 76 of 120 ---Rode333 := (2*x**(5/2)*y(x)**(3/2)+x**2*y(x)-x)*D(y(x),x)-_ ---R x**(3/2)*y(x)**(5/2)+x*y(x)**2-y(x) +ode333 := (2*x**(5/2)*y(x)**(3/2)+x**2*y(x)-x)*D(y(x),x)-_ + x**(3/2)*y(x)**(5/2)+x*y(x)**2-y(x) --R --R --R (75) --R 2 +-+ +----+ 2 , 2 +-+ +----+ 2 --R (2x y(x)\|x \|y(x) + x y(x) - x)y (x) - x y(x) \|x \|y(x) + x y(x) - y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 76 --S 77 of 120 ---Rsolve(ode333,y,x) +solve(ode333,y,x) --R --R --R (76) "failed" @@ -1343,17 +1343,17 @@ I have no idea what to do with this --E 77 --S 78 of 120 ---Rode334 := (sqrt(y(x)+x)+1)*D(y(x),x)+1 +ode334 := (sqrt(y(x)+x)+1)*D(y(x),x)+1 --R --R --R +--------+ , --R (77) (\|y(x) + x + 1)y (x) + 1 --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 78 --S 79 of 120 ---Rsolve(ode334,y,x) +solve(ode334,y,x) --R --R --R (78) "failed" @@ -1361,18 +1361,18 @@ I have no idea what to do with this --E 79 --S 80 of 120 ---Rode335 := sqrt(y(x)**2-1)*D(y(x),x)-sqrt(x**2-1) +ode335 := sqrt(y(x)**2-1)*D(y(x),x)-sqrt(x**2-1) --R --R --R +---------+ +------+ --R | 2 , | 2 --R (79) \|y(x) - 1 y (x) - \|x - 1 --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 80 --S 81 of 120 ---Ryx:=solve(ode335,y,x) +yx:=solve(ode335,y,x) --R --R --R (80) @@ -1421,11 +1421,11 @@ I have no idea what to do with this --R +------+ --R 2 | 2 2 2 2 --R (- 8x y(x) + 4x)\|x - 1 + (8x - 4)y(x) - 4x + 2 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 81 --S 82 of 120 ---Rode335expr := sqrt(yx**2-1)*D(yx,x)-sqrt(x**2-1) +ode335expr := sqrt(yx**2-1)*D(yx,x)-sqrt(x**2-1) --R --R --R (81) @@ -1818,22 +1818,22 @@ I have no idea what to do with this --R + --R 5 3 --R (32x - 48x + 16x)y(x) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 82 --S 83 of 120 ---Rode336 := (sqrt(y(x)**2+1)+a*x)*D(y(x),x)+sqrt(x**2+1)+a*y(x) +ode336 := (sqrt(y(x)**2+1)+a*x)*D(y(x),x)+sqrt(x**2+1)+a*y(x) --R --R --R +---------+ +------+ --R | 2 , | 2 --R (82) (\|y(x) + 1 + a x)y (x) + \|x + 1 + a y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 83 --S 84 of 120 ---Ryx:=solve(ode336,y,x) +yx:=solve(ode336,y,x) --R --R --R (83) @@ -1885,11 +1885,11 @@ I have no idea what to do with this --R +------+ --R 2 | 2 2 2 2 --R (- 8x y(x) - 4x)\|x + 1 + (8x + 4)y(x) + 4x + 2 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 84 --S 85 of 120 ---Rode336expr := (sqrt(yx**2+1)+a*x)*D(yx,x)+sqrt(x**2+1)+a*yx +ode336expr := (sqrt(yx**2+1)+a*x)*D(yx,x)+sqrt(x**2+1)+a*yx --R --R --R (84) @@ -2970,22 +2970,22 @@ I have no idea what to do with this --R + --R 7 5 3 3 7 5 3 --R (2432x + 4864x + 2888x + 456x)y(x) + (384x + 768x + 456x + 72x)y(x) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 85 --S 86 of 120 ---Rode337 := (sqrt(y(x)**2+x**2)+x)*D(y(x),x)-y(x) +ode337 := (sqrt(y(x)**2+x**2)+x)*D(y(x),x)-y(x) --R --R --R +----------+ --R | 2 2 , --R (85) (\|y(x) + x + x)y (x) - y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 86 --S 87 of 120 ---Rsolve(ode337,y,x) +solve(ode337,y,x) --R --R --R (86) "failed" @@ -2993,9 +2993,9 @@ I have no idea what to do with this --E 87 --S 88 of 120 ---Rode338 := (y(x)*sqrt(y(x)**2+x**2)+(y(x)**2-x**2)*sin(alpha)-_ ---R 2*x*y(x)*cos(alpha))*D(y(x),x)+x*sqrt(y(x)**2+x**2)+_ ---R 2*x*y(x)*sin(alpha)+(y(x)**2-x**2)*cos(alpha) +ode338 := (y(x)*sqrt(y(x)**2+x**2)+(y(x)**2-x**2)*sin(alpha)-_ + 2*x*y(x)*cos(alpha))*D(y(x),x)+x*sqrt(y(x)**2+x**2)+_ + 2*x*y(x)*sin(alpha)+(y(x)**2-x**2)*cos(alpha) --R --R --R (87) @@ -3007,11 +3007,11 @@ I have no idea what to do with this --R +----------+ --R | 2 2 2 2 --R x\|y(x) + x + 2x y(x)sin(alpha) + (y(x) - x )cos(alpha) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 88 --S 89 of 120 ---Rsolve(ode338,y,x) +solve(ode338,y,x) --R --R --R (88) "failed" @@ -3019,8 +3019,8 @@ I have no idea what to do with this --E 89 --S 90 of 120 ---Rode339 := (x*sqrt(x**2+y(x)**2+1)-y(x)*(x**2+y(x)**2))*D(y(x),x)-_ ---R y(x)*sqrt(x**2+y(x)**2+1)-x*(x**2+y(x)**2) +ode339 := (x*sqrt(x**2+y(x)**2+1)-y(x)*(x**2+y(x)**2))*D(y(x),x)-_ + y(x)*sqrt(x**2+y(x)**2+1)-x*(x**2+y(x)**2) --R --R --R (89) @@ -3031,11 +3031,11 @@ I have no idea what to do with this --R + --R 2 3 --R - x y(x) - x ---R Type: Expression Integer +--R Type: Expression(Integer) --E 90 --S 91 of 120 ---Rsolve(ode339,y,x) +solve(ode339,y,x) --R --R --R (90) "failed" @@ -3043,9 +3043,9 @@ I have no idea what to do with this --E 91 --S 92 of 120 ---Rode340 := (e1*(x+a)/((x+a)**2+y(x)**2)**(3/2)+e2*(x-a)/_ ---R ((x-a)**2+y(x)**2)**(3/2))*D(y(x),x)-y(x)*_ ---R (e1/((x+a)**2+y(x)**2)**(3/2)+e2/((x-a)**2+y(x)**2)**(3/2)) +ode340 := (e1*(x+a)/((x+a)**2+y(x)**2)**(3/2)+e2*(x-a)/_ + ((x-a)**2+y(x)**2)**(3/2))*D(y(x),x)-y(x)*_ + (e1/((x+a)**2+y(x)**2)**(3/2)+e2/((x-a)**2+y(x)**2)**(3/2)) --R --R --R (91) @@ -3082,11 +3082,11 @@ I have no idea what to do with this --R +----------------------+ --R | 2 2 2 --R \|y(x) + x + 2a x + a ---R Type: Expression Integer +--R Type: Expression(Integer) --E 92 --S 93 of 120 ---Rsolve(ode340,y,x) +solve(ode340,y,x) --R --R --R (92) "failed" @@ -3094,26 +3094,26 @@ I have no idea what to do with this --E 93 --S 94 of 120 ---Rode341 := (x*exp(y(x))+exp(x))*D(y(x),x)+exp(y(x))+y(x)*exp(x) +ode341 := (x*exp(y(x))+exp(x))*D(y(x),x)+exp(y(x))+y(x)*exp(x) --R --R --R y(x) x , y(x) x --R (93) (x %e + %e )y (x) + %e + y(x)%e --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 94 --S 95 of 120 ---Ryx:=solve(ode341,y,x) +yx:=solve(ode341,y,x) --R --R --R y(x) x --R (94) x %e + y(x)%e ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 95 --S 96 of 120 ---Rode341expr := (x*exp(yx)+exp(x))*D(yx,x)+exp(yx)+yx*exp(x) +ode341expr := (x*exp(yx)+exp(x))*D(yx,x)+exp(yx)+yx*exp(x) --R --R --R (95) @@ -3125,22 +3125,22 @@ I have no idea what to do with this --R x y(x) x 2 , x y(x) x 2 --R (x %e %e + (%e ) )y (x) + (x + 1)%e %e + 2y(x)(%e ) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 96 --S 97 of 120 ---Rode342 := x*(3*exp(x*y(x))+2*exp(-x*y(x)))*(x*D(y(x),x)+y(x))+1 +ode342 := x*(3*exp(x*y(x))+2*exp(-x*y(x)))*(x*D(y(x),x)+y(x))+1 --R --R --R (96) --R 2 x y(x) 2 - x y(x) , x y(x) - x y(x) --R (3x %e + 2x %e )y (x) + 3x y(x)%e + 2x y(x)%e + 1 --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 97 --S 98 of 120 ---Ryx:=solve(ode342,y,x) +yx:=solve(ode342,y,x) --R --R --R x y(x) 2 x y(x) @@ -3148,11 +3148,11 @@ I have no idea what to do with this --R (97) --------------------------------- --R x y(x) --R %e ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 98 --S 99 of 120 ---Rode342expr := x*(3*exp(x*yx)+2*exp(-x*yx))*(x*D(yx,x)+yx)+1 +ode342expr := x*(3*exp(x*yx)+2*exp(-x*yx))*(x*D(yx,x)+yx)+1 --R --R --R (98) @@ -3189,30 +3189,30 @@ I have no idea what to do with this --R / --R x y(x) --R %e ---R Type: Expression Integer +--R Type: Expression(Integer) --E 99 --S 100 of 120 ---Rode343 := (log(y(x))+x)*D(y(x),x)-1 +ode343 := (log(y(x))+x)*D(y(x),x)-1 --R --R --R , --R (99) (log(y(x)) + x)y (x) - 1 --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 100 --S 101 of 120 ---Ryx:=solve(ode343,y,x) +yx:=solve(ode343,y,x) --R --R --R - y(x) - y(x) --R (100) - %e log(y(x)) - x %e + Ei(- y(x)) ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 101 --S 102 of 120 ---Rode343expr := (log(yx)+x)*D(yx,x)-1 +ode343expr := (log(yx)+x)*D(yx,x)-1 --R --R --R (101) @@ -3226,31 +3226,31 @@ I have no idea what to do with this --R - y(x) 2 - y(x) , - y(x) --R (x %e log(y(x)) + x %e )y (x) - x %e - 1 --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 102 --S 103 of 120 ---Rode344 := (log(y(x))+2*x-1)*D(y(x),x)-2*y(x) +ode344 := (log(y(x))+2*x-1)*D(y(x),x)-2*y(x) --R --R --R , --R (102) (log(y(x)) + 2x - 1)y (x) - 2y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 103 --S 104 of 120 ---Ryx:=solve(ode344,y,x) +yx:=solve(ode344,y,x) --R --R --R - log(y(x)) - 2x --R (103) ---------------- --R y(x) ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 104 --S 105 of 120 ---Rode344expr := (log(yx)+2*x-1)*D(yx,x)-2*yx +ode344expr := (log(yx)+2*x-1)*D(yx,x)-2*yx --R --R --R (104) @@ -3264,21 +3264,21 @@ I have no idea what to do with this --R / --R 2 --R y(x) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 105 --S 106 of 120 ---Rode345 := x*(2*x**2*y(x)*log(y(x))+1)*D(y(x),x)-2*y(x) +ode345 := x*(2*x**2*y(x)*log(y(x))+1)*D(y(x),x)-2*y(x) --R --R --R 3 , --R (105) (2x y(x)log(y(x)) + x)y (x) - 2y(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 106 --S 107 of 120 ---Ryx:=solve(ode345,y,x) +yx:=solve(ode345,y,x) --R --R --R 2 2 2 2 @@ -3286,11 +3286,11 @@ I have no idea what to do with this --R (106) ----------------------------------- --R 2 --R 2x ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 107 --S 108 of 120 ---Rode345expr := x*(2*x**2*yx*log(yx)+1)*D(yx,x)-2*yx +ode345expr := x*(2*x**2*yx*log(yx)+1)*D(yx,x)-2*yx --R --R --R (107) @@ -3318,12 +3318,12 @@ I have no idea what to do with this --R / --R 2 --R x ---R Type: Expression Integer +--R Type: Expression(Integer) --E 108 --S 109 of 120 ---Rode346 := x*(y(x)*log(x*y(x))+y(x)-a*x)*D(y(x),x)-_ ---R y(x)*(a*x*log(x*y(x))-y(x)+a*x) +ode346 := x*(y(x)*log(x*y(x))+y(x)-a*x)*D(y(x),x)-_ + y(x)*(a*x*log(x*y(x))-y(x)+a*x) --R --R --R (108) @@ -3332,11 +3332,11 @@ I have no idea what to do with this --R --R + --R - a x y(x) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 109 --S 110 of 120 ---Rsolve(ode346,y,x) +solve(ode346,y,x) --R --R --R (109) "failed" @@ -3344,17 +3344,17 @@ I have no idea what to do with this --E 110 --S 111 of 120 ---Rode347 := D(y(x),x)*(1+sin(x))*sin(y(x))+cos(x)*(cos(y(x))-1) +ode347 := D(y(x),x)*(1+sin(x))*sin(y(x))+cos(x)*(cos(y(x))-1) --R --R --R , --R (110) (sin(x) + 1)sin(y(x))y (x) + cos(x)cos(y(x)) - cos(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 111 --S 112 of 120 ---Ryx:=solve(ode347,y,x) +yx:=solve(ode347,y,x) --R --R --R (111) @@ -3386,11 +3386,11 @@ I have no idea what to do with this --R + --R 3 2 --R 4cos(x) + 6cos(x) + 4cos(x) + 1 ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 112 --S 113 of 120 ---Rode347expr := D(yx,x)*(1+sin(x))*sin(yx)+cos(x)*(cos(yx)-1) +ode347expr := D(yx,x)*(1+sin(x))*sin(yx)+cos(x)*(cos(yx)-1) --R --R --R (112) @@ -3571,29 +3571,29 @@ I have no idea what to do with this --R + --R 5 4 3 2 --R cos(x) + 5cos(x) + 10cos(x) + 10cos(x) + 5cos(x) + 1 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 113 --S 114 of 120 ---Rode348 := (x*cos(y(x))+sin(x))*D(y(x),x)+y(x)*cos(x)+sin(y(x)) +ode348 := (x*cos(y(x))+sin(x))*D(y(x),x)+y(x)*cos(x)+sin(y(x)) --R --R --R , --R (113) (x cos(y(x)) + sin(x))y (x) + sin(y(x)) + y(x)cos(x) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 114 --S 115 of 120 ---Ryx:=solve(ode348,y,x) +yx:=solve(ode348,y,x) --R --R --R (114) x sin(y(x)) + y(x)sin(x) ---R Type: Union(Expression Integer,...) +--R Type: Union(Expression(Integer),...) --E 115 --S 116 of 120 ---Rode348expr := (x*cos(yx)+sin(x))*D(yx,x)+yx*cos(x)+sin(yx) +ode348expr := (x*cos(yx)+sin(x))*D(yx,x)+yx*cos(x)+sin(yx) --R --R --R (115) @@ -3610,21 +3610,21 @@ I have no idea what to do with this --R --R + --R 2y(x)cos(x)sin(x) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 116 --S 117 of 120 ---Rode349 := x*D(y(x),x)*cot(y(x)/x)+2*x*sin(y(x)/x)-y(x)*cot(y(x)/x) +ode349 := x*D(y(x),x)*cot(y(x)/x)+2*x*sin(y(x)/x)-y(x)*cot(y(x)/x) --R --R --R y(x) , y(x) y(x) --R (116) x cot(----)y (x) + 2x sin(----) - y(x)cot(----) --R x x x ---R Type: Expression Integer +--R Type: Expression(Integer) --E 117 --S 118 of 120 ---Rsolve(ode349,y,x) +solve(ode349,y,x) --R --R --R (117) "failed" @@ -3632,17 +3632,17 @@ I have no idea what to do with this --E 118 --S 119 of 120 ---Rode350 := D(y(x),x)*cos(y(x))-cos(x)*sin(y(x))**2-sin(y(x)) +ode350 := D(y(x),x)*cos(y(x))-cos(x)*sin(y(x))**2-sin(y(x)) --R --R --R , 2 --R (118) cos(y(x))y (x) - cos(x)sin(y(x)) - sin(y(x)) --R ---R Type: Expression Integer +--R Type: Expression(Integer) --E 119 --S 120 of 120 ---Rsolve(ode350,y,x) +solve(ode350,y,x) --R --R --R (119) "failed" @@ -3653,7 +3653,7 @@ I have no idea what to do with this )spool )lisp (bye) -@ +\end{chunk} \eject \begin{thebibliography}{99} \bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} diff --git a/src/axiom-website/CATS/kamke6.txt b/src/axiom-website/CATS/kamke6.txt new file mode 100644 index 0000000..4d58838 --- /dev/null +++ b/src/axiom-website/CATS/kamke6.txt @@ -0,0 +1,182 @@ +y:=operator 'y +f:=operator 'f +g:=operator 'g + +ode301 := (6*x*y(x)**2+x**2)*D(y(x),x)-y(x)*(3*y(x)**2-x) +solve(ode301,y,x) + +ode302 := (x**2*y(x)**2+x)*D(y(x),x)+y(x) +solve(ode302,y,x) + +ode303 := (x*y(x)-1)**2*x*D(y(x),x)+(x**2*y(x)**2+1)*y(x) +solve(ode303,y,x) + +ode304 := (10*x**3*y(x)**2+x**2*y(x)+2*x)*D(y(x),x)+5*x**2*y(x)**3+x*y(x)**2 +solve(ode304,y,x) + +ode305 := (y(x)**3-3*x)*D(y(x),x)-3*y(x)+x**2 +yx:=solve(ode305,y,x) + +ode305expr := (yx**3-3*x)*D(yx,x)-3*yx+x**2 +ode306 := (y(x)**3-x**3)*D(y(x),x)-x**2*y(x) +yx:=solve(ode306,y,x) +ode306expr := (yx**3-x**3)*D(yx,x)-x**2*yx + +ode307 := (y(x)**2+x**2+a)*y(x)*D(y(x),x)+(y(x)**2+x**2-a)*x +yx:=solve(ode307,y,x) +ode307expr := (yx**2+x**2+a)*yx*D(yx,x)+(yx**2+x**2-a)*x + +ode308 := 2*y(x)**3*D(y(x),x)+x*y(x)**2 +yx:=solve(ode308,y,x) +ode308expr := 2*yx**3*D(yx,x)+x*yx**2 + +ode309 := (2*y(x)**3+y(x))*D(y(x),x)-2*x**3-x +yx:=solve(ode309,y,x) +ode309expr := (2*yx**3+yx)*D(yx,x)-2*x**3-x + +ode310 := (2*y(x)**3+5*x**2*y(x))*D(y(x),x)+5*x*y(x)**2+x**3 +yx:=solve(ode310,y,x) +ode310expr := (2*yx**3+5*x**2*yx)*D(yx,x)+5*x*yx**2+x**3 + +ode311 := (20*y(x)**3-3*x*y(x)**2+6*x**2*y(x)+3*x**3)*D(y(x),x)-_ + y(x)**3+6*x*y(x)**2+9*x**2*y(x)+4*x**3 +yx:=solve(ode311,y,x) +ode311expr := (20*yx**3-3*x*yx**2+6*x**2*yx+3*x**3)*D(yx,x)-_ + yx**3+6*x*yx**2+9*x**2*yx+4*x**3 + +ode312 := (y(x)**2/b+x**2/a)*(y(x)*D(y(x),x)+x)+((a-b)/(a+b))*_ + (y(x)*D(y(x),x)-x) +solve(ode312,y,x) + +ode313 := (2*a*y(x)**3+3*a*x*y(x)**2-b*x**3+c*x**2)*D(y(x),x)-_ + a*y(x)**3+c*y(x)**2+3*b*x**2*y(x)+2*b*x**3 +solve(ode313,y,x) + +ode314 := x*y(x)**3*D(y(x),x)+y(x)**4-x*sin(x) +yx:=solve(ode314,y,x) +ode314expr := x*yx**3*D(yx,x)+yx**4-x*sin(x) + +ode315 := (2*x*y(x)**3-x**4)*D(y(x),x)-y(x)**4+2*x**3*y(x) +solve(ode315,y,x) + +ode316 := (2*x*y(x)**3+y(x))*D(y(x),x)+2*y(x)**2 +yx:=solve(ode316,y,x) +ode316expr := (2*x*yx**3+yx)*D(yx,x)+2*yx**2 + +ode317 := (2*x*y(x)**3+x*y(x)+x**2)*D(y(x),x)+y(x)**2-x*y(x) +solve(ode317,y,x) + +ode318 := (3*x*y(x)**3-4*x*y(x)+y(x))*D(y(x),x)+y(x)**2*(y(x)**2-2) +yx:=solve(ode318,y,x) +ode318expr := (3*x*yx**3-4*x*yx+yx)*D(yx,x)+yx**2*(yx**2-2) + +ode319 := (7*x*y(x)**3+y(x)-5*x)*D(y(x),x)+y(x)**4-5*y(x) +yx:=solve(ode319,y,x) +ode319expr := (7*x*yx**3+yx-5*x)*D(yx,x)+yx**4-5*yx + +ode320 := (x**2*y(x)**3+x*y(x))*D(y(x),x)-1 +solve(ode320,y,x) + +ode321 := (2*x**2*y(x)**3+x**2*y(x)**2-2*x)*D(y(x),x)-2*y(x)-1 +solve(ode321,y,x) + +ode322 := (10*x**2*y(x)**3-3*y(x)**2-2)*D(y(x),x)+5*x*y(x)**4+x +yx:=solve(ode322,y,x) +ode322expr := (10*x**2*yx**3-3*yx**2-2)*D(yx,x)+5*x*yx**4+x + +ode323 := (a*x*y(x)**3+c)*x*D(y(x),x)+(b*x**3*y(x)+c)*y(x) +solve(ode323,y,x) + +ode324 := (2*x**3*y(x)**3-x)*D(y(x),x)+2*x**3*y(x)**3-y(x) +solve(ode324,y,x) + +ode325 := y(x)*(y(x)**3-2*x**3)*D(y(x),x)+(2*y(x)**3-x**3)*x +solve(ode325,y,x) + +ode326 := y(x)*((a*y(x)+b*x)**3+b*x**3)*D(y(x),x)+x*((a*y(x)+b*x)**3+a*y(x)**3) +solve(ode326,y,x) + +ode327 := (x*y(x)**4+2*x**2*y(x)**3+2*y(x)+x)*D(y(x),x)+y(x)**5+y(x) +solve(ode327,y,x) + +ode328 := a*x**2*y(x)**n*D(y(x),x)-2*x*D(y(x),x)+y(x) +solve(ode328,y,x) + +ode329 := y(x)**m*x**n*(a*x*D(y(x),x)+b*y(x))+alpha*x*D(y(x),x)+beta*y(x) +solve(ode329,y,x) + +ode330 := (f(x+y(x))+1)*D(y(x),x)+f(x+y(x)) +solve(ode330,y,x) + +ode331 := D(y(x),x)*convert([sum(f[nu](x)*y(x)**nu,'nu'=1..p)],`+`)-_ + convert([sum(g[nu](x)*y(x)**nu,'nu'=1..q)],`+`) + +ode333 := (2*x**(5/2)*y(x)**(3/2)+x**2*y(x)-x)*D(y(x),x)-_ + x**(3/2)*y(x)**(5/2)+x*y(x)**2-y(x) +solve(ode333,y,x) + +ode334 := (sqrt(y(x)+x)+1)*D(y(x),x)+1 +solve(ode334,y,x) + +ode335 := sqrt(y(x)**2-1)*D(y(x),x)-sqrt(x**2-1) +yx:=solve(ode335,y,x) +ode335expr := sqrt(yx**2-1)*D(yx,x)-sqrt(x**2-1) + +ode336 := (sqrt(y(x)**2+1)+a*x)*D(y(x),x)+sqrt(x**2+1)+a*y(x) +yx:=solve(ode336,y,x) +ode336expr := (sqrt(yx**2+1)+a*x)*D(yx,x)+sqrt(x**2+1)+a*yx + +ode337 := (sqrt(y(x)**2+x**2)+x)*D(y(x),x)-y(x) +solve(ode337,y,x) + +ode338 := (y(x)*sqrt(y(x)**2+x**2)+(y(x)**2-x**2)*sin(alpha)-_ + 2*x*y(x)*cos(alpha))*D(y(x),x)+x*sqrt(y(x)**2+x**2)+_ + 2*x*y(x)*sin(alpha)+(y(x)**2-x**2)*cos(alpha) +solve(ode338,y,x) + +ode339 := (x*sqrt(x**2+y(x)**2+1)-y(x)*(x**2+y(x)**2))*D(y(x),x)-_ + y(x)*sqrt(x**2+y(x)**2+1)-x*(x**2+y(x)**2) +solve(ode339,y,x) + +ode340 := (e1*(x+a)/((x+a)**2+y(x)**2)**(3/2)+e2*(x-a)/_ + ((x-a)**2+y(x)**2)**(3/2))*D(y(x),x)-y(x)*_ + (e1/((x+a)**2+y(x)**2)**(3/2)+e2/((x-a)**2+y(x)**2)**(3/2)) +solve(ode340,y,x) + +ode341 := (x*exp(y(x))+exp(x))*D(y(x),x)+exp(y(x))+y(x)*exp(x) +yx:=solve(ode341,y,x) +ode341expr := (x*exp(yx)+exp(x))*D(yx,x)+exp(yx)+yx*exp(x) + +ode342 := x*(3*exp(x*y(x))+2*exp(-x*y(x)))*(x*D(y(x),x)+y(x))+1 +yx:=solve(ode342,y,x) +ode342expr := x*(3*exp(x*yx)+2*exp(-x*yx))*(x*D(yx,x)+yx)+1 + +ode343 := (log(y(x))+x)*D(y(x),x)-1 +yx:=solve(ode343,y,x) +ode343expr := (log(yx)+x)*D(yx,x)-1 + +ode344 := (log(y(x))+2*x-1)*D(y(x),x)-2*y(x) +yx:=solve(ode344,y,x) +ode344expr := (log(yx)+2*x-1)*D(yx,x)-2*yx + +ode345 := x*(2*x**2*y(x)*log(y(x))+1)*D(y(x),x)-2*y(x) +yx:=solve(ode345,y,x) +ode345expr := x*(2*x**2*yx*log(yx)+1)*D(yx,x)-2*yx + +ode346 := x*(y(x)*log(x*y(x))+y(x)-a*x)*D(y(x),x)-_ + y(x)*(a*x*log(x*y(x))-y(x)+a*x) +solve(ode346,y,x) + +ode347 := D(y(x),x)*(1+sin(x))*sin(y(x))+cos(x)*(cos(y(x))-1) +yx:=solve(ode347,y,x) +ode347expr := D(yx,x)*(1+sin(x))*sin(yx)+cos(x)*(cos(yx)-1) + +ode348 := (x*cos(y(x))+sin(x))*D(y(x),x)+y(x)*cos(x)+sin(y(x)) +yx:=solve(ode348,y,x) +ode348expr := (x*cos(yx)+sin(x))*D(yx,x)+yx*cos(x)+sin(yx) + +ode349 := x*D(y(x),x)*cot(y(x)/x)+2*x*sin(y(x)/x)-y(x)*cot(y(x)/x) +solve(ode349,y,x) + +ode350 := D(y(x),x)*cos(y(x))-cos(x)*sin(y(x))**2-sin(y(x)) +solve(ode350,y,x) diff --git a/src/axiom-website/CATS/kamke7.txt b/src/axiom-website/CATS/kamke7.txt new file mode 100644 index 0000000..54929c0 --- /dev/null +++ b/src/axiom-website/CATS/kamke7.txt @@ -0,0 +1,166 @@ + +y:=operator 'y +f:=operator 'f +g:=operator 'g +h:=operator 'h +fa:=operator 'fa +fb:=operator 'fb +fc:=operator 'fc +fd:=operator 'fd +fe:=operator 'fe +ff:=operator 'ff + +ode352 := D(y(x),x)*(cos(y(x))-sin(alpha)*sin(x))*cos(y(x))+(cos(x)-_ + sin(alpha)*sin(y(x)))*cos(x) +yx:=solve(ode352,y,x) +ode352expr := D(yx,x)*(cos(yx)-sin(alpha)*sin(x))*cos(yx)+(cos(x)-_ + sin(alpha)*sin(yx))*cos(x) + +ode353 := x*D(y(x),x)*cos(y(x))+sin(y(x)) +yx:=solve(ode353,y,x) +ode353expr := x*D(yx,x)*cos(yx)+sin(yx) + +ode354 := (x*sin(y(x))-1)*D(y(x),x)+cos(y(x)) +yx:=solve(ode354,y,x) +ode354expr := (x*sin(yx)-1)*D(yx,x)+cos(yx) + +ode355 := (x*cos(y(x))+cos(x))*D(y(x),x)-y(x)*sin(x)+sin(y(x)) +yx:=solve(ode355,y,x) +ode355expr := (x*cos(yx)+cos(x))*D(yx,x)-yx*sin(x)+sin(yx) + +ode356 := (x**2*cos(y(x))+2*y(x)*sin(x))*D(y(x),x)+2*x*sin(y(x))+y(x)**2*cos(x) +yx:=solve(ode356,y,x) +ode356expr:=(x**2*cos(yx)+2*yx*sin(x))*D(yx,x)+2*x*sin(yx)+yx**2*cos(x) + +ode358 := D(y(x),x)*sin(y(x))*cos(x)+cos(y(x))*sin(x) +yx:=solve(ode358,y,x) + +ode358expr := D(yx,x)*sin(yx)*cos(x)+cos(yx)*sin(x) + +ode361 := (x*sin(x*y(x))+cos(x+y(x))-sin(y(x)))*D(y(x),x)+_ + y(x)*sin(x*y(x))+cos(x+y(x))+cos(x) +yx:=solve(ode361,y,x) +ode361expr:=(x*sin(x*yx)+cos(x+yx)-sin(yx))*D(yx,x)+_ + yx*sin(x*yx)+cos(x+yx)+cos(x) + +ode363 := (x*D(y(x),x)-y(x))*cos(y(x)/x)**2+x +yx:=solve(ode363,y,x) +ode363expr := (x*D(yx,x)-yx)*cos(yx/x)**2+x + +ode364 := (y(x)*sin(y(x)/x)-x*cos(y(x)/x))*x*D(y(x),x)-_ + (x*cos(y(x)/x)+y(x)*sin(y(x)/x))*y(x) +yx:=solve(ode364,y,x) +ode364expr := (yx*sin(yx/x)-x*cos(yx/x))*x*D(yx,x)-_ + (x*cos(yx/x)+yx*sin(yx/x))*yx + +ode434 := D(y(x),x)-1 +ode434a:=solve(ode434,y,x) +yx:=ode434a.particular +ode434expr := D(yx,x)-1 + +ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x) +solve(ode683,y,x) + +ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_ + (x-1)/x) +solve(ode703,y,x) + +ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_ + y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x) +solve(ode714,y,x) + +ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x)) +solve(ode719,y,x) + +ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1)) +solve(ode736,y,x) + +ode765 := (D(y(x),x) = y(x)*(-1-log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x*y(x))/x) +solve(ode765,y,x) + +ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x)) +solve(ode766,y,x) +ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_ + log((x**2+1)/x)*x**2*y(x))/x/log(1/x)) +solve(ode776,y,x) + +ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_ + 25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/_ + (-5*y(x)+2*x**3+10*x**(1/2)-5)/x) +solve(ode872,y,x) + +ode555 := sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x) +solve(ode555,y,x) + +ode557 := x*(sqrt(D(y(x),x)**2+1)+D(y(x),x))-y(x) +solve(ode557,y,x) + +ode558 := a*x*sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x) +solve(ode558,y,x) + +ode562 := a*(D(y(x),x)**3+1)**(1/3)+b*x*D(y(x),x)-y(x) +solve(ode562,y,x) + +ode563 := log(D(y(x),x))+x*D(y(x),x)+a*y(x)+b +solve(ode563,y,x) + +ode564 := log(D(y(x),x))+a*(x*D(y(x),x)-y(x)) +solve(ode564,y,x) + +ode571 := a*x**n*f(D(y(x),x))+x*D(y(x),x)-y(x) +solve(ode571,y,x) + +ode573 := f(x*D(y(x),x)**2)+2*x*D(y(x),x)-y(x) +solve(ode573,y,x) + +ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x) +solve(ode683,y,x) + +ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_ + (x-1)/x) +solve(ode703,y,x) + +ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_ + y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x) +solve(ode714,y,x) + +ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x)) +solve(ode719,y,x) + +ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1)) +solve(ode736,y,x) + +ode765 := (D(y(x),x) = y(x)*(-1-log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x*y(x))/x) +solve(ode765,y,x) + +ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x)) +solve(ode766,y,x) +ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_ + log((x**2+1)/x)*x**2*y(x))/x/log(1/x)) +solve(ode776,y,x) + +ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_ + 25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/(-5*y(x)+2*x**3+_ + 10*x**(1/2)-5)/x) +solve(ode872,y,x) + +ode956 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2-x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*log(x)+x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*y(x)+2*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)+x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)**2)/x) +solve(ode956,y,x) + +ode957 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)-x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*log(x)+x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*y(x)+2*x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)+x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)**2)/x) +solve(ode957,y,x) + diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index f15addf..4f4d7eb 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4230,6 +4230,10 @@ src/interp/Makefile make cleanup books/bookvolbib add Griesmer ref, sort items 20130714.01.tpd.patch add rich integral set to CATS test suite +20130714.02.tpd.patch +src/input/charlwood.input added +20130715.01.tpd.patch +CATS updated with txt, charlwood diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 086188b..790ea9e 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -302,7 +302,7 @@ REGRESSTESTS= ackermann.regress \ cachedf.regress calcprob.regress \ calculus2.regress calculus.regress cardinal.regress card.regress \ carten.regress cclass.regress char.regress ch.regress \ - cherry.regress \ + charlwood.regress cherry.regress \ chtheorem.regress classtalk.regress clements.regress \ clifford.regress clif.regress cmds.regress \ coercels.regress collect.regress cohen.regress \ @@ -663,7 +663,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/calcprob.input ${OUT}/calculus.input \ ${OUT}/cardinal.input ${OUT}/card.input ${OUT}/carten.input \ ${OUT}/cclass.input ${OUT}/cdraw.input ${OUT}/char.input \ - ${OUT}/ch.input ${OUT}/cherry.input \ + ${OUT}/ch.input ${OUT}/charlwood.input ${OUT}/cherry.input \ ${OUT}/chtheorem.input ${OUT}/classtalk.input \ ${OUT}/clifford.input ${OUT}/clements.input \ ${OUT}/clif.input ${OUT}/cmds.input \ @@ -955,7 +955,7 @@ DOCFILES= \ ${DOC}/card.input.dvi ${DOC}/carten.input.dvi \ ${DOC}/cclass.input.dvi ${DOC}/cdraw.input.dvi \ ${DOC}/char.input.dvi ${DOC}/ch.input.dvi \ - ${DOC}/cherry.input.dvi \ + ${DOC}/charlwood.input.dvi ${DOC}/cherry.input.dvi \ ${DOC}/chtheorem.input.dvi ${DOC}/classtalk.input.dvi \ ${DOC}/clifford.input.dvi ${DOC}/clements.input.dvi \ ${DOC}/clif.input.dvi ${DOC}/cmds.input.dvi \ diff --git a/src/input/charlwood.input.pamphlet b/src/input/charlwood.input.pamphlet new file mode 100644 index 0000000..ddb9f5d --- /dev/null +++ b/src/input/charlwood.input.pamphlet @@ -0,0 +1,6914 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input charlwood.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +Integrals taken from sci.math.symbolic posting of Charlwood, Kevin +``Integration on Computer Algebra Systems'' +Electronic Journal of Mathematics and Technology (2008) +\verb|www.freepatentsonline.com/article/| +\verb|Electronic-journal-Mathematics-Technology/188213666.html| +by Albert Rich at +\verb|www.apmaths.uwo.ca/~arich/CharlwoodIntegrationProblems.pdf| +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f charlwood.output +)spool charlwood.output +)set message auto off +)clear all + +\end{chunk} +\subsection{Problem 1} +\begin{chunk}{*} + +--S 1 of 250 +t0001:= asin(x)*log(x) +--R +--R +--R (1) asin(x)log(x) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 250 +r0001:= -2*sqrt(1-x^2)+atanh(sqrt(1-x^2))-x*asin(x)*(1-log(x))+_ + sqrt(1-x^2)*log(x) +--R +--R +--R (2) +--R +--------+ +--------+ +--R | 2 | 2 +--R atanh(\|- x + 1 ) + (log(x) - 2)\|- x + 1 + x asin(x)log(x) - x asin(x) +--R Type: Expression(Integer) +--E 2 + +--S 3 of 250 +a0001:= integrate(t0001,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R | 2 | 2 +--R log(\|- x + 1 + 1) - log(\|- x + 1 - 1) +--R + +--R +--------+ +--R | 2 +--------+ +--R 2x\|- x + 1 | 2 +--R (- x log(x) + x)atan(-------------) + (2log(x) - 4)\|- x + 1 +--R 2 +--R 2x - 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 250 +m0001:= a0001-r0001 +--R +--R +--R (4) +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R log(\|- x + 1 + 1) - log(\|- x + 1 - 1) - 2atanh(\|- x + 1 ) +--R + +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R (- x log(x) + x)atan(-------------) - 2x asin(x)log(x) + 2x asin(x) +--R 2 +--R 2x - 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 250 +d0001:= D(m0001,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R - log(x)atan(-------------) - 2asin(x)log(x) +--R 2 +--R 2x - 1 +--R (5) -------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 5 + + +\end{chunk} +\subsection{Problem 2} +\begin{chunk}{*} + +--S 6 of 250 +t0002:= x*asin(x)/sqrt(1-x^2) +--R +--R +--R x asin(x) +--R (6) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 250 +r0002:= x-sqrt(1-x^2)*asin(x) +--R +--R +--R +--------+ +--R | 2 +--R (7) - asin(x)\|- x + 1 + x +--R Type: Expression(Integer) +--E 7 + +--S 8 of 250 +a0002:= integrate(t0002,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 2x\|- x + 1 +--R \|- x + 1 atan(-------------) + 2x +--R 2 +--R 2x - 1 +--R (8) ----------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 250 +m0002:= a0002-r0002 +--R +--R +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 2x\|- x + 1 | 2 +--R \|- x + 1 atan(-------------) + 2asin(x)\|- x + 1 +--R 2 +--R 2x - 1 +--R (9) ---------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 250 +d0002:= D(m0002,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R - x atan(-------------) - 2x asin(x) +--R 2 +--R 2x - 1 +--R (10) ------------------------------------ +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 10 + + +\end{chunk} +\subsection{Problem 3} +\begin{chunk}{*} + +--S 11 of 250 +t0003:= asin(sqrt(x+1)-sqrt(x)) +--R +--R +--R +-----+ +-+ +--R (11) asin(\|x + 1 - \|x ) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 250 +r0003:= ((sqrt(x)+3*sqrt(1+x))*sqrt(-x+sqrt(x)*sqrt(1+x)))/(4*sqrt(2))-_ + (3/8+x)*asin(sqrt(x)-sqrt(1+x)) +--R +--R +--R (12) +--R +----------------+ +--R +-----+ +-+ | +-+ +-----+ +-+ +-----+ +-+ +--R (6\|x + 1 + 2\|x )\|\|x \|x + 1 - x + (8x + 3)\|2 asin(\|x + 1 - \|x ) +--R -------------------------------------------------------------------------- +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 250 +a0003:= integrate(t0003,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 13 + +--S 14 of 250 +--m0003:= a0003-r0003 +--E 14 + +--S 15 of 250 +--d0003:= D(m0003,x) +--E 15 + + +\end{chunk} +\subsection{Problem 4} +\begin{chunk}{*} + +--S 16 of 250 +t0004:= log(1+x*sqrt(1+x^2)) +--R +--R +--R +------+ +--R | 2 +--R (13) log(x\|x + 1 + 1) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 250 +r0004:= -2*x+sqrt(2*(1+sqrt(5)))*atan(sqrt(-2+sqrt(5))*(x+sqrt(1+x^2)))-_ + sqrt(2*(-1+sqrt(5)))*atanh(sqrt(2+sqrt(5))*(x+sqrt(1+x^2)))+_ + x*log(1+x*sqrt(1+x^2)) +--R +--R +--R (14) +--R +------+ +---------+ +------+ +--------+ +--R | 2 | +-+ | 2 | +-+ +--R x log(x\|x + 1 + 1) - \|2\|5 - 2 atanh((\|x + 1 + x)\|\|5 + 2 ) +--R + +--R +---------+ +------+ +--------+ +--R | +-+ | 2 | +-+ +--R \|2\|5 + 2 atan((\|x + 1 + x)\|\|5 - 2 ) - 2x +--R Type: Expression(Integer) +--E 17 + +--S 18 of 250 +a0004:= integrate(t0004,x) +--R +--R +--R (15) +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((\|5 + 1)\|x + 1 - x\|5 - x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +--------+ +--------+ +------+ +--R | +-+ | +-+ +-+ +-+ | 2 +--R \|\|5 - 1 log(\|\|5 - 1 + x\|2 ) + 2x\|2 log(x\|x + 1 + 1) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ +-+ +--R - \|\|5 - 1 log(- \|\|5 - 1 + x\|2 ) +--R + +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((- \|5 - 1)\|x + 1 + x\|5 + x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +------+ +--------+ +--R +--------+ +-+ | 2 +-+ | +-+ +--R | +-+ ((\|5 - 1)\|x + 1 - x\|5 + x)\|\|5 + 1 +--R 2\|\|5 + 1 atan(--------------------------------------------) +--R +------+ +--R +-+ | 2 2 +-+ +--R 2x\|2 \|x + 1 + (- 2x - 2)\|2 +--R + +--R +--------+ +--R +--------+ | +-+ +--R | +-+ \|\|5 + 1 +-+ +--R - 2\|\|5 + 1 atan(-----------) - 4x\|2 +--R +-+ +--R x\|2 +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 250 +m0004:= a0004-r0004 +--R +--R +--R (16) +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((\|5 + 1)\|x + 1 - x\|5 - x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ +-+ +--R \|\|5 - 1 log(\|\|5 - 1 + x\|2 ) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ +-+ +--R - \|\|5 - 1 log(- \|\|5 - 1 + x\|2 ) +--R + +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((- \|5 - 1)\|x + 1 + x\|5 + x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +---------+ +------+ +--------+ +--R +-+ | +-+ | 2 | +-+ +--R 2\|2 \|2\|5 - 2 atanh((\|x + 1 + x)\|\|5 + 2 ) +--R + +--R +------+ +--------+ +--R +--------+ +-+ | 2 +-+ | +-+ +--R | +-+ ((\|5 - 1)\|x + 1 - x\|5 + x)\|\|5 + 1 +--R 2\|\|5 + 1 atan(--------------------------------------------) +--R +------+ +--R +-+ | 2 2 +-+ +--R 2x\|2 \|x + 1 + (- 2x - 2)\|2 +--R + +--R +--------+ +--R +--------+ | +-+ +--R | +-+ \|\|5 + 1 +--R - 2\|\|5 + 1 atan(-----------) +--R +-+ +--R x\|2 +--R + +--R +---------+ +------+ +--------+ +--R +-+ | +-+ | 2 | +-+ +--R - 2\|2 \|2\|5 + 2 atan((\|x + 1 + x)\|\|5 - 2 ) +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 250 +d0004:= D(m0004,x) +--R +--R +--R (17) +--R +------+ +--------+ +---------+ +--R +-+ | 2 +-+ | +-+ | +-+ +--R ((- \|5 - 1)\|x + 1 - x\|5 - 3x)\|\|5 - 2 \|2\|5 + 2 +--R + +--R +------+ +--------+ +---------+ +------+ +--R +-+ | 2 +-+ | +-+ | +-+ | 2 +--R ((- \|5 + 1)\|x + 1 - x\|5 + 3x)\|\|5 + 2 \|2\|5 - 2 + 8\|x + 1 +--R + +--R 4x +--R / +--R +------+ +--R | 2 3 +--R 4\|x + 1 + 4x + 4x +--R Type: Expression(Integer) +--E 20 + + +\end{chunk} +\subsection{Problem 5} +\begin{chunk}{*} + +--S 21 of 250 +t0005:= cos(x)^2/sqrt(cos(x)^4+cos(x)^2+1) +--R +--R +--R 2 +--R cos(x) +--R (18) ------------------------ +--R +---------------------+ +--R | 4 2 +--R \|cos(x) + cos(x) + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 250 +r0005:= x/3+1/3*atan((cos(x)*(1+cos(x)^2)*sin(x))/_ + (1+cos(x)^2*sqrt(1+cos(x)^2+cos(x)^4))) +--R +--R +--R 3 +--R (cos(x) + cos(x))sin(x) +--R atan(-----------------------------------) + x +--R +---------------------+ +--R 2 | 4 2 +--R cos(x) \|cos(x) + cos(x) + 1 + 1 +--R (19) --------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 250 +a0005:= integrate(t0005,x) +--R +--R +--R (20) +--R atan +--R 5 4 3 +--R (cos(x) + 2cos(x) + cos(x) )sin(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 6 +--R 4cos(x) - 2 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 250 +m0005:= a0005-r0005 +--R +--R +--R (21) +--R atan +--R 5 4 3 +--R (cos(x) + 2cos(x) + cos(x) )sin(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 6 +--R 4cos(x) - 2 +--R + +--R 3 +--R (cos(x) + cos(x))sin(x) +--R - 2atan(-----------------------------------) - 2x +--R +---------------------+ +--R 2 | 4 2 +--R cos(x) \|cos(x) + cos(x) + 1 + 1 +--R / +--R 6 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 250 +d0005:= D(m0005,x) +--R +--R +--R (22) +--R 26 25 24 23 +--R - 4cos(x) - 8cos(x) - 20cos(x) - 32cos(x) +--R + +--R 22 21 20 19 +--R - 44cos(x) - 56cos(x) - 72cos(x) - 88cos(x) +--R + +--R 18 17 16 15 +--R - 76cos(x) - 64cos(x) - 64cos(x) - 64cos(x) +--R + +--R 14 13 12 10 9 +--R - 36cos(x) - 8cos(x) - 4cos(x) + 12cos(x) + 24cos(x) +--R + +--R 8 7 6 +--R 16cos(x) + 8cos(x) + 4cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 27 26 25 +--R - 8cos(x) - 16cos(x) - 32cos(x) - 48cos(x) +--R + +--R 24 23 22 21 +--R - 72cos(x) - 96cos(x) - 128cos(x) - 160cos(x) +--R + +--R 20 19 18 17 +--R - 176cos(x) - 192cos(x) - 216cos(x) - 240cos(x) +--R + +--R 16 15 14 13 +--R - 209cos(x) - 178cos(x) - 156cos(x) - 134cos(x) +--R + +--R 12 11 10 9 +--R - 94cos(x) - 54cos(x) - 48cos(x) - 42cos(x) +--R + +--R 8 7 6 5 4 +--R - 29cos(x) - 16cos(x) - 11cos(x) - 6cos(x) - cos(x) +--R + +--R 3 2 +--R 4cos(x) + 3cos(x) + 2cos(x) + 1 +--R * +--R 2 +--R sin(x) +--R + +--R 30 29 28 27 26 +--R - 4cos(x) - 8cos(x) - 12cos(x) - 16cos(x) - 32cos(x) +--R + +--R 25 24 23 22 21 +--R - 48cos(x) - 52cos(x) - 56cos(x) - 72cos(x) - 88cos(x) +--R + +--R 20 19 18 17 16 +--R - 56cos(x) - 24cos(x) - 9cos(x) + 6cos(x) + 49cos(x) +--R + +--R 15 14 13 12 11 +--R 92cos(x) + 72cos(x) + 52cos(x) + 46cos(x) + 40cos(x) +--R + +--R 10 9 8 7 6 +--R 11cos(x) - 18cos(x) - 14cos(x) - 10cos(x) - 12cos(x) +--R + +--R 5 4 3 2 +--R - 14cos(x) - 8cos(x) - 2cos(x) - 2cos(x) - 2cos(x) - 1 +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 26 24 22 20 18 +--R 8cos(x) + 40cos(x) + 104cos(x) + 180cos(x) + 236cos(x) +--R + +--R 16 14 12 10 8 +--R 260cos(x) + 248cos(x) + 200cos(x) + 132cos(x) + 76cos(x) +--R + +--R 6 4 +--R 40cos(x) + 12cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 26 24 22 20 +--R 16cos(x) + 64cos(x) + 144cos(x) + 208cos(x) + 272cos(x) +--R + +--R 18 16 14 12 +--R 336cos(x) + 424cos(x) + 436cos(x) + 388cos(x) +--R + +--R 10 8 6 4 2 +--R 296cos(x) + 180cos(x) + 88cos(x) + 16cos(x) + 12cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 30 28 26 24 22 +--R 8cos(x) + 24cos(x) + 48cos(x) + 52cos(x) + 84cos(x) +--R + +--R 20 18 16 14 12 +--R 96cos(x) + 124cos(x) + 48cos(x) - 4cos(x) - 68cos(x) +--R + +--R 10 8 6 4 +--R - 40cos(x) - 28cos(x) - 4cos(x) - 4cos(x) +--R * +--R +---------------------+ +--R | 4 2 +--R \|cos(x) + cos(x) + 1 +--R + +--R 28 27 26 25 24 +--R - 4cos(x) - 8cos(x) - 24cos(x) - 40cos(x) - 68cos(x) +--R + +--R 23 22 21 20 +--R - 96cos(x) - 136cos(x) - 176cos(x) - 180cos(x) +--R + +--R 19 18 17 16 +--R - 184cos(x) - 164cos(x) - 144cos(x) - 80cos(x) +--R + +--R 15 14 13 12 11 +--R - 16cos(x) + 8cos(x) + 32cos(x) + 40cos(x) + 48cos(x) +--R + +--R 10 9 8 +--R 28cos(x) + 8cos(x) + 4cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 30 29 28 27 26 +--R - 8cos(x) - 16cos(x) - 40cos(x) - 64cos(x) - 112cos(x) +--R + +--R 25 24 23 22 +--R - 160cos(x) - 220cos(x) - 280cos(x) - 304cos(x) +--R + +--R 21 20 19 18 +--R - 328cos(x) - 328cos(x) - 328cos(x) - 289cos(x) +--R + +--R 17 16 15 14 +--R - 250cos(x) - 249cos(x) - 248cos(x) - 223cos(x) +--R + +--R 13 12 11 10 +--R - 198cos(x) - 174cos(x) - 150cos(x) - 100cos(x) +--R + +--R 9 8 7 6 5 +--R - 50cos(x) - 27cos(x) - 4cos(x) + 3cos(x) + 10cos(x) +--R + +--R 4 3 2 +--R 6cos(x) + 2cos(x) + cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 31 30 29 28 +--R - 4cos(x) - 8cos(x) - 16cos(x) - 24cos(x) - 48cos(x) +--R + +--R 27 26 25 24 23 +--R - 72cos(x) - 84cos(x) - 96cos(x) - 108cos(x) - 120cos(x) +--R + +--R 22 21 20 19 18 +--R - 84cos(x) - 48cos(x) - 29cos(x) - 10cos(x) + 36cos(x) +--R + +--R 17 16 15 14 13 +--R 82cos(x) + 76cos(x) + 70cos(x) + 78cos(x) + 86cos(x) +--R + +--R 12 11 10 9 8 +--R 53cos(x) + 20cos(x) + 11cos(x) + 2cos(x) - 13cos(x) +--R + +--R 7 6 5 4 3 2 +--R - 28cos(x) - 21cos(x) - 14cos(x) - 11cos(x) - 8cos(x) - 4cos(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 24 22 20 18 16 +--R 16cos(x) + 80cos(x) + 208cos(x) + 360cos(x) + 456cos(x) +--R + +--R 14 12 10 8 6 +--R 456cos(x) + 368cos(x) + 232cos(x) + 104cos(x) + 24cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 26 24 22 20 18 +--R 48cos(x) + 192cos(x) + 448cos(x) + 680cos(x) + 800cos(x) +--R + +--R 16 14 12 10 8 +--R 768cos(x) + 672cos(x) + 528cos(x) + 368cos(x) + 232cos(x) +--R + +--R 6 4 +--R 112cos(x) + 48cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 28 26 24 22 20 +--R 32cos(x) + 96cos(x) + 192cos(x) + 208cos(x) + 176cos(x) +--R + +--R 18 16 14 12 10 +--R 64cos(x) + 16cos(x) - 48cos(x) - 48cos(x) - 64cos(x) +--R + +--R 8 6 +--R - 32cos(x) - 16cos(x) +--R / +--R 26 25 24 23 22 +--R 12cos(x) + 24cos(x) + 60cos(x) + 96cos(x) + 144cos(x) +--R + +--R 21 20 19 18 +--R 192cos(x) + 216cos(x) + 240cos(x) + 228cos(x) +--R + +--R 17 16 15 14 +--R 216cos(x) + 192cos(x) + 168cos(x) + 144cos(x) +--R + +--R 13 12 11 10 9 +--R 120cos(x) + 96cos(x) + 72cos(x) + 48cos(x) + 24cos(x) +--R + +--R 8 +--R 12cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 27 26 25 24 +--R 24cos(x) + 48cos(x) + 96cos(x) + 144cos(x) + 192cos(x) +--R + +--R 23 22 21 20 +--R 240cos(x) + 228cos(x) + 216cos(x) + 240cos(x) +--R + +--R 19 18 17 16 +--R 264cos(x) + 288cos(x) + 312cos(x) + 363cos(x) +--R + +--R 15 14 13 12 +--R 414cos(x) + 336cos(x) + 258cos(x) + 201cos(x) +--R + +--R 11 10 9 8 7 +--R 144cos(x) + 81cos(x) + 18cos(x) + 27cos(x) + 36cos(x) +--R + +--R 6 5 4 3 2 +--R 24cos(x) + 12cos(x) + 9cos(x) + 6cos(x) + 3cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 30 29 28 27 26 +--R 12cos(x) + 24cos(x) + 36cos(x) + 48cos(x) + 60cos(x) +--R + +--R 25 24 23 22 21 +--R 72cos(x) + 48cos(x) + 24cos(x) + 72cos(x) + 120cos(x) +--R + +--R 20 19 18 17 16 +--R 96cos(x) + 72cos(x) + 87cos(x) + 102cos(x) - 27cos(x) +--R + +--R 15 14 13 12 11 +--R - 156cos(x) - 129cos(x) - 102cos(x) - 117cos(x) - 132cos(x) +--R + +--R 10 9 8 7 6 +--R - 45cos(x) + 42cos(x) + 27cos(x) + 12cos(x) + 24cos(x) +--R + +--R 5 4 2 +--R 36cos(x) + 18cos(x) + 3cos(x) + 6cos(x) + 3 +--R * +--R +-------------------------------------------+ +--R | 4 2 +---------------------+ +--R | 16cos(x) + 16cos(x) + 16 | 4 2 +--R |------------------------------------------- \|cos(x) + cos(x) + 1 +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 24 23 22 21 20 +--R 24cos(x) + 48cos(x) + 120cos(x) + 192cos(x) + 288cos(x) +--R + +--R 19 18 17 16 +--R 384cos(x) + 432cos(x) + 480cos(x) + 432cos(x) +--R + +--R 15 14 13 12 +--R 384cos(x) + 288cos(x) + 192cos(x) + 120cos(x) +--R + +--R 11 10 +--R 48cos(x) + 24cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 26 25 24 23 +--R 72cos(x) + 144cos(x) + 288cos(x) + 432cos(x) +--R + +--R 22 21 20 19 +--R 600cos(x) + 768cos(x) + 768cos(x) + 768cos(x) +--R + +--R 18 17 16 15 +--R 672cos(x) + 576cos(x) + 432cos(x) + 288cos(x) +--R + +--R 14 13 12 11 +--R 270cos(x) + 252cos(x) + 216cos(x) + 180cos(x) +--R + +--R 10 9 8 7 6 +--R 162cos(x) + 144cos(x) + 90cos(x) + 36cos(x) + 24cos(x) +--R + +--R 5 4 +--R 12cos(x) + 6cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 28 27 26 25 24 +--R 48cos(x) + 96cos(x) + 144cos(x) + 192cos(x) + 240cos(x) +--R + +--R 23 22 21 20 18 +--R 288cos(x) + 192cos(x) + 96cos(x) + 48cos(x) - 96cos(x) +--R + +--R 17 16 15 14 13 +--R - 192cos(x) - 132cos(x) - 72cos(x) - 108cos(x) - 144cos(x) +--R + +--R 12 11 10 9 7 +--R - 84cos(x) - 24cos(x) - 36cos(x) - 48cos(x) + 48cos(x) +--R + +--R 6 5 4 3 2 +--R 36cos(x) + 24cos(x) + 24cos(x) + 24cos(x) + 12cos(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R Type: Expression(Integer) +--E 25 + + +\end{chunk} +\subsection{Problem 6} +\begin{chunk}{*} + +--S 26 of 250 +t0006:= tan(x)*sqrt(1+tan(x)^4) +--R +--R +--R +-----------+ +--R | 4 +--R (23) tan(x)\|tan(x) + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 250 +r0006:= -1/2*asinh(tan(x)^2)-atanh((1-tan(x)^2)/(sqrt(2)*sqrt(1+tan(x)^4)))/_ + sqrt(2)+1/2*sqrt(1+tan(x)^4) +--R +--R +--R 2 +-----------+ +--R tan(x) - 1 +-+ | 4 +-+ 2 +--R 2atanh(------------------) + \|2 \|tan(x) + 1 - \|2 asinh(tan(x) ) +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R (24) -------------------------------------------------------------------- +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 250 +a0006:= integrate(t0006,x) +--R +--R +--R (25) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-----------------------+ +--R | 4 2 +--R +-+ 4 +-+ 2 |2cos(x) - 2cos(x) + 1 +--R (4\|2 cos(x) - 2\|2 cos(x) ) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 4 2 +--R 8cos(x) - 8cos(x) + 3 +--R + +--R log +--R +-----------------------+ +--R | 4 2 +--R 4 2 |2cos(x) - 2cos(x) + 1 4 +--R (2cos(x) - 2cos(x) ) |----------------------- + 3cos(x) +--R | 4 +--R \| cos(x) +--R + +--R 2 +--R - 4cos(x) + 2 +--R / +--R 4 +--R cos(x) +--R + +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R 2 |----------------------- +--R | 4 +--R \| cos(x) +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 250 +m0006:= a0006-r0006 +--R +--R +--R (26) +--R - +--R 2 +--R * +--R log +--R +-----------------------+ +--R | 4 2 +--R +-+ 4 +-+ 2 |2cos(x) - 2cos(x) + 1 +--R (4\|2 cos(x) - 2\|2 cos(x) ) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 4 2 +--R 8cos(x) - 8cos(x) + 3 +--R + +--R +-+ +--R \|2 +--R * +--R log +--R +-----------------------+ +--R | 4 2 +--R 4 2 |2cos(x) - 2cos(x) + 1 4 +--R (2cos(x) - 2cos(x) ) |----------------------- + 3cos(x) +--R | 4 +--R \| cos(x) +--R + +--R 2 +--R - 4cos(x) + 2 +--R / +--R 4 +--R cos(x) +--R + +--R 2 +-----------+ +--R tan(x) - 1 +-+ | 4 +--R - 4atanh(------------------) - 2\|2 \|tan(x) + 1 +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R + +--R +-----------------------+ +--R | 4 2 +--R +-+ |2cos(x) - 2cos(x) + 1 +-+ 2 +--R 2\|2 |----------------------- + 2\|2 asinh(tan(x) ) +--R | 4 +--R \| cos(x) +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 250 +d0006:= D(m0006,x) +--R +--R +--R (27) +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (8\|2 cos(x) - 12\|2 cos(x) + 8\|2 cos(x) - 2\|2 cos(x) )sin(x) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 8 6 4 2 +--R (16cos(x) - 32cos(x) + 30cos(x) - 14cos(x) + 3)sin(x) +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R + +--R 9 7 5 5 +--R (- 8cos(x) + 8cos(x) - 3cos(x) )tan(x) +--R + +--R 9 7 5 +--R (- 8cos(x) + 8cos(x) - 3cos(x) )tan(x) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 5 +--R (- 8\|2 cos(x) + 12\|2 cos(x) - 8\|2 cos(x) + 2\|2 cos(x) )tan(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R (- 8\|2 cos(x) + 12\|2 cos(x) - 8\|2 cos(x) + 2\|2 cos(x) )tan(x) +--R / +--R +-----------------------+ +--R | 4 2 +--R 9 7 5 |2cos(x) - 2cos(x) + 1 +--R (8cos(x) - 8cos(x) + 3cos(x) ) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R 8\|2 cos(x) - 12\|2 cos(x) + 8\|2 cos(x) - 2\|2 cos(x) +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R Type: Expression(Integer) +--E 30 + + +\end{chunk} +\subsection{Problem 7} +\begin{chunk}{*} + +--S 31 of 250 +t0007:= tan(x)/sqrt(1+sec(x)^3) +--R +--R +--R tan(x) +--R (28) -------------- +--R +-----------+ +--R | 3 +--R \|sec(x) + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 250 +r0007:= -2/3*atanh(sqrt(1+sec(x)^3)) +--R +--R +--R +-----------+ +--R | 3 +--R 2atanh(\|sec(x) + 1 ) +--R (29) - ---------------------- +--R 3 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 250 +a0007:= integrate(t0007,x) +--R +--R +--R (30) +--R - +--R log +--R 6 5 3 2 +--R (- 4cos(x) - 4cos(x) - 2cos(x) - 2cos(x) ) +--R * +--R +----------------------+ +--R | 2 +--R |4cos(x) - 4cos(x) + 4 +--R |---------------------- +--R | 2 +--R \| cos(x) + cos(x) +--R + +--R 6 3 +--R 8cos(x) + 8cos(x) + 1 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 250 +m0007:= a0007-r0007 +--R +--R +--R (31) +--R - +--R log +--R 6 5 3 2 +--R (- 4cos(x) - 4cos(x) - 2cos(x) - 2cos(x) ) +--R * +--R +----------------------+ +--R | 2 +--R |4cos(x) - 4cos(x) + 4 +--R |---------------------- +--R | 2 +--R \| cos(x) + cos(x) +--R + +--R 6 3 +--R 8cos(x) + 8cos(x) + 1 +--R + +--R +-----------+ +--R | 3 +--R 4atanh(\|sec(x) + 1 ) +--R / +--R 6 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 250 +d0007:= D(m0007,x) +--R +--R +--R (32) +--R +----------------------+ +--R +-----------+ | 2 +--R | 3 |4cos(x) - 4cos(x) + 4 +--R - 2sin(x)\|sec(x) + 1 + (- cos(x) - 1)tan(x) |---------------------- +--R | 2 +--R \| cos(x) + cos(x) +--R ----------------------------------------------------------------------- +--R +----------------------+ +--R | 2 +-----------+ +--R |4cos(x) - 4cos(x) + 4 | 3 +--R (cos(x) + 1) |---------------------- \|sec(x) + 1 +--R | 2 +--R \| cos(x) + cos(x) +--R Type: Expression(Integer) +--E 35 + + +\end{chunk} +\subsection{Problem 8} +\begin{chunk}{*} + +--S 36 of 250 +t0008:= sqrt(tan(x)^2+2*tan(x)+2) +--R +--R +--R +---------------------+ +--R | 2 +--R (33) \|tan(x) + 2tan(x) + 2 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 250 +r0008:= asinh(1+tan(x))+sqrt(1/2*(1+sqrt(5)))*_ + atan(((-sqrt(-1+sqrt(5)))+sqrt(1+sqrt(5))*tan(x))/_ + (sqrt(2)*sqrt(2+tan(x)*(2+tan(x)))))-_ + sqrt(1/2*(-1+sqrt(5)))*_ + atanh((sqrt(1+sqrt(5))+sqrt(-1+sqrt(5))*tan(x))/_ + (sqrt(2)*sqrt(2+tan(x)*(2+tan(x))))) +--R +--R +--R (34) +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ \|\|5 + 1 + tan(x)\|\|5 - 1 +--R - \|\|5 - 1 atanh(-------------------------------) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R + +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ tan(x)\|\|5 + 1 - \|\|5 - 1 +-+ +--R \|\|5 + 1 atan(-------------------------------) + \|2 asinh(tan(x) + 1) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 250 +a0008:= integrate(t0008,x) +--R +--R +--R (35) +--R [ +--R 4+-+ atan(2) +--R \|5 cos(-------) +--R 2 +--R * +--R log +--R 4+-+3 9 4+-+3 7 +--R - 38400\|5 cos(x) + 451328\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 169072\|5 cos(x) - 134856\|5 cos(x) +--R + +--R 4+-+3 +--R - 3760\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (- 39040\|5 + 640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (184768\|5 + 266560\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (6952\|5 - 204600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 61356\|5 - 157740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 3074\|5 - 5820\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 211200\|5 cos(x) + 203904\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R 322352\|5 cos(x) - 233648\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 35408\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 94720\|5 - 116480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (19584\|5 + 184320\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (182464\|5 + 208720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 63684\|5 - 247100\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 21759\|5 - 46975\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 9 4+-+3 7 +--R 211200\|5 cos(x) + 11904\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 568096\|5 cos(x) - 103208\|5 cos(x) +--R + +--R 4+-+3 +--R - 80\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (83200\|5 + 505600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (580352\|5 + 604160\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 500976\|5 - 1653200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 239244\|5 - 497740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 7102\|5 - 10480\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 38400\|5 cos(x) + 572672\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R - 276464\|5 cos(x) - 331064\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 13344\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 342400\|5 - 419200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (627136\|5 + 1772480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (244464\|5 - 266640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 459800\|5 - 1168280\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 62635\|5 - 110195\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 9 +--R (79104\|5 + 1228800)cos(x) +--R + +--R 4+-+2 7 +--R (- 1115328\|5 - 1857600)cos(x) +--R + +--R 4+-+2 5 +--R (335640\|5 - 1628200)cos(x) +--R + +--R 4+-+2 3 +--R (639072\|5 + 947080)cos(x) +--R + +--R 4+-+2 +--R (64992\|5 + 147580)cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 10 +--R (483072\|5 + 358400)cos(x) +--R + +--R 4+-+2 8 +--R (- 411840\|5 + 2104000)cos(x) +--R + +--R 4+-+2 6 +--R (- 1076712\|5 - 3359000)cos(x) +--R + +--R 4+-+2 4 +--R (679732\|5 + 91940)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (271292\|5 + 534070)cos(x) + 6656\|5 + 16540 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 246528\|5 - 358400)cos(x) +--R + +--R 4+-+2 7 +--R (- 1667904\|5 - 3089600)cos(x) +--R + +--R 4+-+2 5 +--R (1801320\|5 + 3027400)cos(x) +--R + +--R 4+-+2 3 +--R (1139496\|5 + 2216640)cos(x) +--R + +--R 4+-+2 +--R (61656\|5 + 133640)cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 55936\|5 + 292480)cos(x) +--R + +--R 4+-+2 7 +--R (- 549568\|5 - 1127360)cos(x) +--R + +--R 4+-+2 5 +--R (424480\|5 + 168880)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (409732\|5 + 790380)cos(x) + (41322\|5 + 94610)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 10 +--R (708096\|5 + 1228800)cos(x) +--R + +--R 4+-+2 8 +--R (- 1675520\|5 - 2707200)cos(x) +--R + +--R 4+-+2 6 +--R (- 1078016\|5 - 2334000)cos(x) +--R + +--R 4+-+2 4 +--R (1846276\|5 + 3353220)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (360756\|5 + 738960)cos(x) + 4208\|5 + 9720 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 10 4+-+2 8 +--R (260352\|5 + 368640)cos(x) + (- 468800\|5 - 4800)cos(x) +--R + +--R 4+-+2 6 +--R (- 428592\|5 - 1392000)cos(x) +--R + +--R 4+-+2 4 4+-+2 2 +--R (503512\|5 + 699440)cos(x) + (169147\|5 + 364435)cos(x) +--R + +--R 4+-+2 +--R 4451\|5 + 10610 +--R / +--R 4+-+3 4+-+ 7 +--R (25984\|5 + 55680\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 63008\|5 - 136480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 32640\|5 - 73760\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 952\|5 - 2240\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 8 +--R (30912\|5 + 66240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (20000\|5 + 46240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 60112\|5 - 132640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 8600\|5 - 19840\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 7 +--R (44352\|5 + 95040\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 101984\|5 - 220640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 54000\|5 - 122080\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 1496\|5 - 3520\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 8 +--R (47936\|5 + 102720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (37120\|5 + 85120\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 99536\|5 - 219520\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 14000\|5 - 32320\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 7 4+-+2 5 +--R - 143488\|5 cos(x) + 156480\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 246752\|5 cos(x) + 24736\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 8 4+-+2 6 +--R - 45184\|5 cos(x) - 256768\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 258464\|5 cos(x) + 105024\|5 cos(x) + 2464\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 7 4+-+2 5 +--R - 73984\|5 cos(x) + 71040\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 129536\|5 cos(x) + 12448\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 7 +--R (- 124288\|5 - 180480)cos(x) +--R + +--R 4+-+2 5 +--R (136000\|5 + 192000)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (213952\|5 + 311520)cos(x) + (21456\|5 + 30960)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 8 4+-+2 6 +--R - 14912\|5 cos(x) - 141824\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 131952\|5 cos(x) + 54832\|5 cos(x) + 1152\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 8 +--R (- 39584\|5 - 52640)cos(x) +--R + +--R 4+-+2 6 +--R (- 222208\|5 - 327680)cos(x) +--R + +--R 4+-+2 4 4+-+2 2 +--R (224184\|5 + 324440)cos(x) + (91064\|5 + 132440)cos(x) +--R + +--R 4+-+2 +--R 2144\|5 + 3045 +--R + +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) + 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (- 4\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (- 2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R - +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) - 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (4\|5 cos(x)sin(x) + 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R - 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R 4+-+ atan(2) +--R \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+ 4+-+ 2 atan(2) +--R (- 2\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+ 2 atan(2) +--R - 2\|5 cos(x)cos(-------)sin(x) - 4\|5 cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 4+-+2 2 4+-+2 +--R (2\|5 + 6)cos(x)sin(x) + (\|5 + 3)cos(x) + \|5 + 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 cos(-------) +--R 2 +--R * +--R atan +--R +---------------------------+ +--R | 2 +--R 4+-+ |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x)sin(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (- 2cos(x)sin(x) - cos(x) - 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - cos(x)cos(-------)sin(x) + (2cos(x) - 1)cos(-------) +--R 2 2 +--R / +--R +---------------------------+ +--R | 2 +--R 4+-+ 2 |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) + 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) + (- cos(x) - 1)cos(-------) +--R 2 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 sin(-------) +--R 2 +--R * +--R atan +--R 4+-+3 4+-+ 5 +--R (72\|5 - 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 62\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 36\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 + 76\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 107\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (- 96\|5 - 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 40\|5 + 144\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (8\|5 + 27\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 146\|5 - 362\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (17\|5 + 144\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 +--R - 240\|5 cos(x) + 540\|5 cos(x) +--R + +--R 4+-+2 +--R 202\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R - 320\|5 cos(x) - 120\|5 cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R 476\|5 cos(x) + 30\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (320\|5 cos(x) + 280\|5 cos(x) - 184\|5 cos(x)) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (56\|5 + 440)cos(x) + (78\|5 - 170)cos(x) +--R + +--R 4+-+2 +--R (79\|5 - 110)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 240\|5 cos(x) + 660\|5 cos(x) - 122\|5 cos(x) +--R + +--R 4+-+2 +--R - 50\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 192\|5 - 80)cos(x) + (100\|5 + 480)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (69\|5 - 290)cos(x) + 26\|5 - 10 +--R / +--R 4+-+3 4+-+ 5 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (40\|5 - 204\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 8\|5 - 59\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (- 72\|5 + 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (146\|5 + 34\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 17\|5 - 192\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 822\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 92\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 - 368\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 451\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 +--R - 320\|5 cos(x) - 280\|5 cos(x) +--R + +--R 4+-+2 +--R 184\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R 240\|5 cos(x) - 660\|5 cos(x) + 122\|5 cos(x) +--R + +--R 4+-+2 +--R 50\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R - 240\|5 cos(x) + 540\|5 cos(x) +--R + +--R 4+-+2 +--R 202\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (- 192\|5 - 80)cos(x) + (228\|5 + 920)cos(x) +--R + +--R 4+-+2 +--R (151\|5 + 320)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 320\|5 cos(x) - 120\|5 cos(x) + 476\|5 cos(x) +--R + +--R 4+-+2 +--R 30\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 56\|5 - 440)cos(x) + (- 218\|5 + 30)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (283\|5 + 760)cos(x) + 32\|5 + 50 +--R / +--R 4 +--R , +--R +--R - +--R 4+-+ atan(2) +--R \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+3 4+-+ 3 4+-+3 +--R ((6\|5 - 10\|5 )cos(x) - 2\|5 cos(x))sin(x) +--R + +--R 4+-+3 4+-+ 4 4+-+ 2 +--R (8\|5 + 20\|5 )cos(x) - 10\|5 cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 3 4+-+3 4+-+ +--R ((8\|5 - 20\|5 )cos(x) + (4\|5 + 10\|5 )cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 4 +--R (- 6\|5 - 10\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (10\|5 + 10\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 3 4+-+2 atan(2) +--R (- 12\|5 cos(x) + 12\|5 cos(x))cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 atan(2) +--R (- 16\|5 cos(x) + 4\|5 cos(x) + 4\|5 )cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 atan(2) 2 +--R (24\|5 cos(x) - 24\|5 cos(x))cos(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 +--R - 12\|5 cos(x) + (2\|5 - 30)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 atan(2) 2 +--R (32\|5 cos(x) - 8\|5 cos(x) - 8\|5 )cos(-------) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R - 16\|5 cos(x) + (- \|5 - 15)cos(x) - \|5 - 10 +--R / +--R 4+-+3 4+-+ 3 4+-+3 +--R ((24\|5 + 40\|5 )cos(x) + 8\|5 cos(x))sin(x) +--R + +--R 4+-+3 4+-+ 4 +--R (32\|5 - 80\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 12\|5 + 100\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 3 4+-+3 4+-+ +--R ((32\|5 + 80\|5 )cos(x) + (4\|5 + 20\|5 )cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 4 +--R (- 24\|5 + 40\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (44\|5 + 20\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (- 64\|5 cos(x) + (- 16\|5 - 80)cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 48\|5 cos(x) + (- 72\|5 - 40)cos(x) + 8\|5 +--R + +--R - 40 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 atan(2) 2 +--R (- 32\|5 cos(x) + (- 8\|5 - 40)cos(x))cos(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 +--R (16\|5 - 240)cos(x) + (- 56\|5 - 40)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R (24\|5 cos(x) + (- 36\|5 - 20)cos(x) + 4\|5 - 20) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 +--R (- 12\|5 + 180)cos(x) + (- 12\|5 - 260)cos(x) +--R + +--R 4+-+2 +--R - 17\|5 + 5 +--R + +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) + 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (- 4\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (- 2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R - +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) - 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (4\|5 cos(x)sin(x) + 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R - 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R 4+-+ atan(2) +--R \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+ 4+-+ 2 atan(2) +--R (- 2\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+ 2 atan(2) +--R - 2\|5 cos(x)cos(-------)sin(x) - 4\|5 cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 4+-+2 2 4+-+2 +--R (2\|5 + 6)cos(x)sin(x) + (\|5 + 3)cos(x) + \|5 + 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 cos(-------) +--R 2 +--R * +--R atan +--R +---------------------------+ +--R | 2 +--R 4+-+ |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x)sin(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (- 2cos(x)sin(x) - cos(x) - 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - cos(x)cos(-------)sin(x) + (2cos(x) - 1)cos(-------) +--R 2 2 +--R / +--R +---------------------------+ +--R | 2 +--R 4+-+ 2 |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) + 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) + (- cos(x) - 1)cos(-------) +--R 2 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 cos(-------) +--R 2 +--R * +--R atan +--R 4+-+2 2 atan(2) +--R \|5 cos(x) sin(-------) +--R 2 +--R + +--R 4+-+2 atan(2) +--R - \|5 cos(x)cos(-------)sin(x) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 4+-+ +--R \|5 cos(x)sin(x) - 2\|5 cos(x) + \|5 +--R / +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) )sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) - cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 4+-+ +--R 2\|5 cos(x)sin(x) + \|5 cos(x) + \|5 +--R / +--R 4 +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 38 + +--S 39 of 250 +m0008:= a0008.1-r0008 +--R +--R +--R (36) +--R +-+4+-+ atan(2) +--R \|2 \|5 cos(-------) +--R 2 +--R * +--R log +--R 4+-+3 9 4+-+3 7 +--R - 38400\|5 cos(x) + 451328\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 169072\|5 cos(x) - 134856\|5 cos(x) +--R + +--R 4+-+3 +--R - 3760\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (- 39040\|5 + 640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (184768\|5 + 266560\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (6952\|5 - 204600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 61356\|5 - 157740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 3074\|5 - 5820\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 211200\|5 cos(x) + 203904\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R 322352\|5 cos(x) - 233648\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 35408\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 94720\|5 - 116480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (19584\|5 + 184320\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (182464\|5 + 208720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 63684\|5 - 247100\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 21759\|5 - 46975\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 9 4+-+3 7 +--R 211200\|5 cos(x) + 11904\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 568096\|5 cos(x) - 103208\|5 cos(x) +--R + +--R 4+-+3 +--R - 80\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (83200\|5 + 505600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (580352\|5 + 604160\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 500976\|5 - 1653200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 239244\|5 - 497740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 7102\|5 - 10480\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 38400\|5 cos(x) + 572672\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R - 276464\|5 cos(x) - 331064\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 13344\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 342400\|5 - 419200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (627136\|5 + 1772480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (244464\|5 - 266640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 459800\|5 - 1168280\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 62635\|5 - 110195\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 9 +--R (79104\|5 + 1228800)cos(x) +--R + +--R 4+-+2 7 +--R (- 1115328\|5 - 1857600)cos(x) +--R + +--R 4+-+2 5 +--R (335640\|5 - 1628200)cos(x) +--R + +--R 4+-+2 3 +--R (639072\|5 + 947080)cos(x) +--R + +--R 4+-+2 +--R (64992\|5 + 147580)cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 10 +--R (483072\|5 + 358400)cos(x) +--R + +--R 4+-+2 8 +--R (- 411840\|5 + 2104000)cos(x) +--R + +--R 4+-+2 6 +--R (- 1076712\|5 - 3359000)cos(x) +--R + +--R 4+-+2 4 +--R (679732\|5 + 91940)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (271292\|5 + 534070)cos(x) + 6656\|5 + 16540 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 246528\|5 - 358400)cos(x) +--R + +--R 4+-+2 7 +--R (- 1667904\|5 - 3089600)cos(x) +--R + +--R 4+-+2 5 +--R (1801320\|5 + 3027400)cos(x) +--R + +--R 4+-+2 3 +--R (1139496\|5 + 2216640)cos(x) +--R + +--R 4+-+2 +--R (61656\|5 + 133640)cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 55936\|5 + 292480)cos(x) +--R + +--R 4+-+2 7 +--R (- 549568\|5 - 1127360)cos(x) +--R + +--R 4+-+2 5 +--R (424480\|5 + 168880)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (409732\|5 + 790380)cos(x) + (41322\|5 + 94610)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 10 +--R (708096\|5 + 1228800)cos(x) +--R + +--R 4+-+2 8 +--R (- 1675520\|5 - 2707200)cos(x) +--R + +--R 4+-+2 6 +--R (- 1078016\|5 - 2334000)cos(x) +--R + +--R 4+-+2 4 +--R (1846276\|5 + 3353220)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (360756\|5 + 738960)cos(x) + 4208\|5 + 9720 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 10 4+-+2 8 +--R (260352\|5 + 368640)cos(x) + (- 468800\|5 - 4800)cos(x) +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 428592\|5 - 1392000)cos(x) + (503512\|5 + 699440)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (169147\|5 + 364435)cos(x) + 4451\|5 + 10610 +--R / +--R 4+-+3 4+-+ 7 +--R (25984\|5 + 55680\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 63008\|5 - 136480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 32640\|5 - 73760\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 952\|5 - 2240\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 8 +--R (30912\|5 + 66240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (20000\|5 + 46240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 60112\|5 - 132640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 8600\|5 - 19840\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 7 +--R (44352\|5 + 95040\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 101984\|5 - 220640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 54000\|5 - 122080\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 1496\|5 - 3520\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 8 +--R (47936\|5 + 102720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (37120\|5 + 85120\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 99536\|5 - 219520\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 14000\|5 - 32320\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 7 4+-+2 5 +--R - 143488\|5 cos(x) + 156480\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 246752\|5 cos(x) + 24736\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 8 4+-+2 6 +--R - 45184\|5 cos(x) - 256768\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 258464\|5 cos(x) + 105024\|5 cos(x) + 2464\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 7 4+-+2 5 +--R - 73984\|5 cos(x) + 71040\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 129536\|5 cos(x) + 12448\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 7 +--R (- 124288\|5 - 180480)cos(x) +--R + +--R 4+-+2 5 +--R (136000\|5 + 192000)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (213952\|5 + 311520)cos(x) + (21456\|5 + 30960)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 8 4+-+2 6 +--R - 14912\|5 cos(x) - 141824\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 131952\|5 cos(x) + 54832\|5 cos(x) + 1152\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 8 4+-+2 6 +--R (- 39584\|5 - 52640)cos(x) + (- 222208\|5 - 327680)cos(x) +--R + +--R 4+-+2 4 4+-+2 2 +--R (224184\|5 + 324440)cos(x) + (91064\|5 + 132440)cos(x) +--R + +--R 4+-+2 +--R 2144\|5 + 3045 +--R + +--R +-+ +--R 2\|2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) + 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (- 4\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (- 2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R - +--R +-+ +--R 2\|2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) - 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (4\|5 cos(x)sin(x) + 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R - 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R +-+4+-+ atan(2) +--R \|2 \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+ 4+-+ 2 atan(2) +--R (- 2\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+ 2 atan(2) +--R - 2\|5 cos(x)cos(-------)sin(x) - 4\|5 cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 4+-+2 2 4+-+2 +--R (2\|5 + 6)cos(x)sin(x) + (\|5 + 3)cos(x) + \|5 + 2 +--R + +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ \|\|5 + 1 + tan(x)\|\|5 - 1 +--R 4\|\|5 - 1 atanh(-------------------------------) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R + +--R - +--R +-+4+-+ atan(2) +--R 2\|2 \|5 cos(-------) +--R 2 +--R * +--R atan +--R +---------------------------+ +--R | 2 +--R 4+-+ |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x)sin(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (- 2cos(x)sin(x) - cos(x) - 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - cos(x)cos(-------)sin(x) + (2cos(x) - 1)cos(-------) +--R 2 2 +--R / +--R +---------------------------+ +--R | 2 +--R 4+-+ 2 |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) + 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) + (- cos(x) - 1)cos(-------) +--R 2 2 +--R + +--R - +--R +-+4+-+ atan(2) +--R 2\|2 \|5 sin(-------) +--R 2 +--R * +--R atan +--R 4+-+3 4+-+ 5 +--R (72\|5 - 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 62\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 36\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 + 76\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 107\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (- 96\|5 - 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 4+-+3 4+-+ +--R (- 40\|5 + 144\|5 )cos(x) + (8\|5 + 27\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 146\|5 - 362\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (17\|5 + 144\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (- 240\|5 cos(x) + 540\|5 cos(x) + 202\|5 cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 320\|5 cos(x) - 120\|5 cos(x) + 476\|5 cos(x) +--R + +--R 4+-+2 +--R 30\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (320\|5 cos(x) + 280\|5 cos(x) - 184\|5 cos(x)) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (56\|5 + 440)cos(x) + (78\|5 - 170)cos(x) +--R + +--R 4+-+2 +--R (79\|5 - 110)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 240\|5 cos(x) + 660\|5 cos(x) - 122\|5 cos(x) +--R + +--R 4+-+2 +--R - 50\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 192\|5 - 80)cos(x) + (100\|5 + 480)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (69\|5 - 290)cos(x) + 26\|5 - 10 +--R / +--R 4+-+3 4+-+ 5 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (40\|5 - 204\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 8\|5 - 59\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (- 72\|5 + 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (146\|5 + 34\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 17\|5 - 192\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 822\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 92\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 - 368\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 451\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (- 320\|5 cos(x) - 280\|5 cos(x) + 184\|5 cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R 240\|5 cos(x) - 660\|5 cos(x) + 122\|5 cos(x) +--R + +--R 4+-+2 +--R 50\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (- 240\|5 cos(x) + 540\|5 cos(x) + 202\|5 cos(x)) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (- 192\|5 - 80)cos(x) + (228\|5 + 920)cos(x) +--R + +--R 4+-+2 +--R (151\|5 + 320)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 320\|5 cos(x) - 120\|5 cos(x) + 476\|5 cos(x) +--R + +--R 4+-+2 +--R 30\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 56\|5 - 440)cos(x) + (- 218\|5 + 30)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (283\|5 + 760)cos(x) + 32\|5 + 50 +--R + +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ tan(x)\|\|5 + 1 - \|\|5 - 1 +--R - 4\|\|5 + 1 atan(-------------------------------) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R + +--R +-+ +--R - 4\|2 asinh(tan(x) + 1) +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 250 +--d0008:= D(m0008,x) +--E 40 + + +\end{chunk} +\subsection{Problem 9} +\begin{chunk}{*} + +--S 41 of 250 +t0009:= sin(x)*atan(sqrt(sec(x)-1)) +--R +--R +--R +----------+ +--R (37) sin(x)atan(\|sec(x) - 1 ) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 250 +r0009:= 1/2*atan(sqrt(-1+sec(x)))-atan(sqrt(-1+sec(x)))*cos(x)+_ + 1/2*cos(x)*sqrt(-1+sec(x)) +--R +--R +--R +----------+ +----------+ +--R (- 2cos(x) + 1)atan(\|sec(x) - 1 ) + cos(x)\|sec(x) - 1 +--R (38) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 250 +a0009:= integrate(t0009,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 43 + +--S 44 of 250 +--m0009:= a0009-r0009 +--E 44 + +--S 45 of 250 +--d0009:= D(m0009,x) +--E 45 + + +\end{chunk} +\subsection{Problem 10} +\begin{chunk}{*} + +--S 46 of 250 +t0010:= x^3*%e^asin(x)/sqrt(1-x^2) +--R +--R +--R 3 asin(x) +--R x %e +--R (39) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 250 +r0010:= 1/10*%e^asin(x)*(3*x+x^3-3*sqrt(1-x^2)-3*x^2*sqrt(1-x^2)) +--R +--R +--R +--------+ +--R 2 | 2 3 asin(x) +--R ((- 3x - 3)\|- x + 1 + x + 3x)%e +--R (40) ------------------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 250 +a0010:= integrate(t0010,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R atan(-------------) +--R 2 +--R 2x - 1 +--R +--------+ - ------------------- +--R 2 | 2 3 2 +--R ((- 3x - 3)\|- x + 1 + x + 3x)%e +--R (41) --------------------------------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 250 +m0010:= a0010-r0010 +--R +--R +--R (42) +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R atan(-------------) +--R 2 +--R 2x - 1 +--R +--------+ - ------------------- +--R 2 | 2 3 2 +--R ((- 3x - 3)\|- x + 1 + x + 3x)%e +--R + +--R +--------+ +--R 2 | 2 3 asin(x) +--R ((3x + 3)\|- x + 1 - x - 3x)%e +--R / +--R 10 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 250 +d0010:= D(m0010,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R atan(-------------) +--R 2 +--R 2x - 1 +--R - ------------------- +--R 3 2 3 asin(x) +--R x %e - x %e +--R (43) --------------------------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 50 + + +\end{chunk} +\subsection{Problem 11} +\begin{chunk}{*} + +--S 51 of 250 +t0011:= x*log(1+x^2)*log(x+sqrt(1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +--R 2 | 2 +--R x log(x + 1)log(\|x + 1 + x) +--R (44) ------------------------------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 250 +r0011:= 4*x-2*atan(x)-2*sqrt(1+x^2)*log(x+sqrt(1+x^2))+_ + log(1+x^2)*(-x+sqrt(1+x^2)*log(x+sqrt(1+x^2))) +--R +--R +--R (45) +--R +------+ +------+ +--R 2 | 2 | 2 2 +--R (log(x + 1) - 2)\|x + 1 log(\|x + 1 + x) - x log(x + 1) - 2atan(x) + 4x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 250 +a0011:= integrate(t0011,x) +--R +--R +--R (46) +--R +------+ +--R 2 | 2 2 2 2 +--R ((- x log(x + 1) + 2x)\|x + 1 + (x + 1)log(x + 1) - 2x - 2) +--R * +--R +------+ +--R | 2 +--R log(\|x + 1 + x) +--R + +--R +------+ +--R 2 | 2 2 2 +--R (- x log(x + 1) - 2atan(x) + 4x)\|x + 1 + x log(x + 1) + 2x atan(x) +--R + +--R 2 +--R - 4x +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 250 +m0011:= a0011-r0011 +--R +--R +--R (47) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 250 +d0011:= D(m0011,x) +--R +--R +--R (48) 0 +--R Type: Expression(Integer) +--E 55 + + +\end{chunk} +\subsection{Problem 12} +\begin{chunk}{*} + +--S 56 of 250 +t0012:= atan(x+sqrt(1-x^2)) +--R +--R +--R +--------+ +--R | 2 +--R (49) atan(\|- x + 1 + x) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 250 +r0012:= -asin(x)/2+1/4*sqrt(3)*atan((-1+sqrt(3)*x)/sqrt(1-x^2))+_ + 1/4*sqrt(3)*atan((1+sqrt(3)*x)/sqrt(1-x^2))-_ + 1/4*sqrt(3)*atan((-1+2*x^2)/sqrt(3))+x*atan(x+sqrt(1-x^2))-_ + 1/4*atanh(x*sqrt(1-x^2))-1/8*log(1-x^2+x^4) +--R +--R +--R (50) +--R +--------+ +--------+ +--R | 2 | 2 +--R - 2atanh(x\|- x + 1 ) + 8x atan(\|- x + 1 + x) +--R + +--R +-+ +-+ +--R +-+ x\|3 + 1 +-+ x\|3 - 1 4 2 +--R 2\|3 atan(-----------) + 2\|3 atan(-----------) - log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R - 2\|3 atan(-------------) - 4asin(x) +--R 3 +--R / +--R 8 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 250 +a0012:= integrate(t0012,x) +--R +--R +--R (51) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R - log(2x\|- x + 1 - x + x + 1) + log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--R | 2 2 +-+ +--R \|- x + 1 + x +-+ (2x - 1)\|3 +--R - 8x atan(---------------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x 4 2 +--R 2\|3 atan(-----------------) - 8atan(-----------) - 2log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R 2\|3 atan(-------------) +--R 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 250 +m0012:= a0012-r0012 +--R +--R +--R (52) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R - log(2x\|- x + 1 - x + x + 1) + log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--------+ +--R | 2 | 2 +--R 4atanh(x\|- x + 1 ) - 16x atan(\|- x + 1 + x) +--R + +--R +--------+ +--R | 2 +-+ +--R \|- x + 1 + x +-+ x\|3 + 1 +--R - 8x atan(---------------) - 4\|3 atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 \|- x + 1 +--R + +--R +-+ 2 +-+ +--R +-+ x\|3 - 1 +-+ (2x - 1)\|3 +--R - 4\|3 atan(-----------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x +--R 2\|3 atan(-----------------) - 8atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ 2 +-+ +--R +-+ (2x - 1)\|3 +-+ (2x - 1)\|3 +--R 4\|3 atan(-------------) + 2\|3 atan(-------------) + 8asin(x) +--R 3 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 250 +d0012:= D(m0012,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|- x + 1 + x +--R - 2atan(\|- x + 1 + x) - atan(---------------) +--R +--------+ +--R | 2 +--R x\|- x + 1 +--R (53) ------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 60 + + +\end{chunk} +\subsection{Problem 13} +\begin{chunk}{*} + +--S 61 of 250 +t0013:= x*atan(x+sqrt(1-x^2))/sqrt(1-x^2) +--R +--R +--R +--------+ +--R | 2 +--R x atan(\|- x + 1 + x) +--R (54) ----------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 250 +r0013:= -asin(x)/2+1/4*sqrt(3)*atan((-1+sqrt(3)*x)/sqrt(1-x^2))+_ + 1/4*sqrt(3)*atan((1+sqrt(3)*x)/sqrt(1-x^2))-_ + 1/4*sqrt(3)*atan((-1+2*x^2)/sqrt(3))-sqrt(1-x^2)*atan(x+sqrt(1-x^2))+_ + 1/4*atanh(x*sqrt(1-x^2))+1/8*log(1-x^2+x^4) +--R +--R +--R (55) +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R 2atanh(x\|- x + 1 ) - 8\|- x + 1 atan(\|- x + 1 + x) +--R + +--R +-+ +-+ +--R +-+ x\|3 + 1 +-+ x\|3 - 1 4 2 +--R 2\|3 atan(-----------) + 2\|3 atan(-----------) + log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R - 2\|3 atan(-------------) - 4asin(x) +--R 3 +--R / +--R 8 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 250 +a0013:= integrate(t0013,x) +--R +--R +--R (56) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R log(2x\|- x + 1 - x + x + 1) - log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--R +--------+ | 2 2 +-+ +--R | 2 \|- x + 1 + x +-+ (2x - 1)\|3 +--R 8\|- x + 1 atan(---------------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x 4 2 +--R 2\|3 atan(-----------------) - 8atan(-----------) + 2log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R 2\|3 atan(-------------) +--R 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 250 +m0013:= a0013-r0013 +--R +--R +--R (57) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R log(2x\|- x + 1 - x + x + 1) - log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R - 4atanh(x\|- x + 1 ) + 16\|- x + 1 atan(\|- x + 1 + x) +--R + +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 \|- x + 1 + x +-+ x\|3 + 1 +--R 8\|- x + 1 atan(---------------) - 4\|3 atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 \|- x + 1 +--R + +--R +-+ 2 +-+ +--R +-+ x\|3 - 1 +-+ (2x - 1)\|3 +--R - 4\|3 atan(-----------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x +--R 2\|3 atan(-----------------) - 8atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ 2 +-+ +--R +-+ (2x - 1)\|3 +-+ (2x - 1)\|3 +--R 4\|3 atan(-------------) + 2\|3 atan(-------------) + 8asin(x) +--R 3 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 250 +d0013:= D(m0013,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|- x + 1 + x +--R - 2x atan(\|- x + 1 + x) - x atan(---------------) +--R +--------+ +--R | 2 +--R x\|- x + 1 +--R (58) ---------------------------------------------------- +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 65 + + +\end{chunk} +\subsection{Problem 14} +\begin{chunk}{*} + +--S 66 of 250 +t0014:= asin(x)/(1+sqrt(1-x^2)) +--R +--R +--R asin(x) +--R (59) --------------- +--R +--------+ +--R | 2 +--R \|- x + 1 + 1 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 250 +r0014:= ((-1+sqrt(1-x^2))*asin(x))/x+asin(x)^2/2-log(1+sqrt(1-x^2)) +--R +--R +--R (60) +--R +--------+ +--------+ +--R | 2 | 2 2 +--R - 2x log(\|- x + 1 + 1) + 2asin(x)\|- x + 1 + x asin(x) - 2asin(x) +--R ----------------------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 67 + +--S 68 of 250 +a0014:= integrate(t0014,x) +--R +--R +--R (61) +--R +--------+ +--------+ +--R | 2 | 2 +--R (- 4\|- x + 1 - 4)log(\|- x + 1 + 1) +--R + +--R +--------+ +--------+ +--R | 2 | 2 +--R (4\|- x + 1 + 4)log(\|- x + 1 - 1) +--R + +--R +--------+ 2 +--------+ +--R +--------+ | 2 | 2 +--R | 2 2x\|- x + 1 2x\|- x + 1 +--R (\|- x + 1 + 1)atan(-------------) + 4x atan(-------------) +--R 2 2 +--R 2x - 1 2x - 1 +--R + +--R +--------+ +--R | 2 +--R - 8log(x)\|- x + 1 - 8log(x) +--R / +--R +--------+ +--R | 2 +--R 8\|- x + 1 + 8 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 250 +m0014:= a0014-r0014 +--R +--R +--R (62) +--R +--------+ +--------+ +--R | 2 | 2 +--R (4\|- x + 1 + 4)log(\|- x + 1 + 1) +--R + +--R +--------+ +--------+ +--R | 2 | 2 +--R (4\|- x + 1 + 4)log(\|- x + 1 - 1) +--R + +--R +--------+ 2 +--------+ +--R +--------+ | 2 | 2 +--R | 2 2x\|- x + 1 2x\|- x + 1 +--R (\|- x + 1 + 1)atan(-------------) + 4x atan(-------------) +--R 2 2 +--R 2x - 1 2x - 1 +--R + +--R +--------+ +--R 2 | 2 2 +--R (- 8log(x) - 4asin(x) )\|- x + 1 - 8log(x) - 4asin(x) + 8x asin(x) +--R / +--R +--------+ +--R | 2 +--R 8\|- x + 1 + 8 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 250 +d0014:= D(m0014,x) +--R +--R +--R (63) +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 2 2x\|- x + 1 | 2 +--R (\|- x + 1 - x + 1)atan(-------------) + 2asin(x)\|- x + 1 +--R 2 +--R 2x - 1 +--R + +--R 2 +--R (- 2x + 2)asin(x) +--R / +--R +--------+ +--R 2 | 2 2 +--R (2x - 4)\|- x + 1 + 4x - 4 +--R Type: Expression(Integer) +--E 70 + + +\end{chunk} +\subsection{Problem 15} +\begin{chunk}{*} + +--S 71 of 250 +t0015:= log(x+sqrt(1+x^2))/(1-x^2)^(3/2) +--R +--R +--R +------+ +--R | 2 +--R log(\|x + 1 + x) +--R (64) - ------------------- +--R +--------+ +--R 2 | 2 +--R (x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 250 +r0015:= -1/2*asin(x^2)+x*x*log(x+sqrt(1+x^2))/sqrt(1-x^2) +--R +--R +--R +------+ +--------+ +--R 2 | 2 2 | 2 +--R 2x log(\|x + 1 + x) - asin(x )\|- x + 1 +--R (65) ------------------------------------------- +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 250 +a0015:= integrate(t0015,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 73 + +--S 74 of 250 +--m0015:= a0015-r0015 +--E 74 + +--S 75 of 250 +--d0015:= D(m0015,x) +--E 75 + + +\end{chunk} +\subsection{Problem 16} +\begin{chunk}{*} + +--S 76 of 250 +t0016:= asin(x)/(1+x^2)^(3/2) +--R +--R +--R asin(x) +--R (66) ----------------- +--R +------+ +--R 2 | 2 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 250 +r0016:= x*asin(x)/sqrt(1+x^2)-asin(x^2)/2 +--R +--R +--R +------+ +--R 2 | 2 +--R - asin(x )\|x + 1 + 2x asin(x) +--R (67) -------------------------------- +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 250 +a0016:= integrate(t0016,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 78 + +--S 79 of 250 +--m0016:= a0016-r0016 +--E 79 + +--S 80 of 250 +--d0016:= D(m0016,x) +--E 80 + + +\end{chunk} +\subsection{Problem 17} +\begin{chunk}{*} + +--S 81 of 250 +t0017:= log(x+sqrt(x^2-1))/(1+x^2)^(3/2) +--R +--R +--R +------+ +--R | 2 +--R log(\|x - 1 + x) +--R (68) ------------------ +--R +------+ +--R 2 | 2 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 250 +r0017:= -1/2*acosh(x^2)+x*log(x+sqrt(-1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +------+ +--R | 2 2 | 2 +--R 2x log(\|x - 1 + x) - acosh(x )\|x + 1 +--R (69) ------------------------------------------ +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 250 +a0017:= integrate(t0017,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 83 + +--S 84 of 250 +--m0017:= a0017-r0017 +--E 84 + +--S 85 of 250 +--d0017:= D(m0017,x) +--E 85 + + +\end{chunk} +\subsection{Problem 18} +\begin{chunk}{*} + +--S 86 of 250 +t0018:= log(x)/(x^2*sqrt(x^2-1)) +--R +--R +--R log(x) +--R (70) ----------- +--R +------+ +--R 2 | 2 +--R x \|x - 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 250 +r0018:= sqrt(-1+x^2)/x-atanh(x/sqrt(-1+x^2))+(sqrt(-1+x^2)*log(x))/x +--R +--R +--R +------+ +--R x | 2 +--R - x atanh(---------) + (log(x) + 1)\|x - 1 +--R +------+ +--R | 2 +--R \|x - 1 +--R (71) -------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 87 + +--S 88 of 250 +a0018:= integrate(t0018,x) +--R +--R +--R (72) +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (x\|x - 1 - x )log(\|x - 1 - x) - x log(x)\|x - 1 + (x - 1)log(x) - 1 +--R ---------------------------------------------------------------------------- +--R +------+ +--R | 2 2 +--R x\|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 250 +m0018:= a0018-r0018 +--R +--R +--R +------+ +--R | 2 x +--R (73) log(\|x - 1 - x) + atanh(---------) + 1 +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 250 +d0018:= D(m0018,x) +--R +--R +--R (74) 0 +--R Type: Expression(Integer) +--E 90 + + +\end{chunk} +\subsection{Problem 19} +\begin{chunk}{*} + +--S 91 of 250 +t0019:= sqrt(1+x^3)/x +--R +--R +--R +------+ +--R | 3 +--R \|x + 1 +--R (75) --------- +--R x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 250 +r0019:= 2*sqrt(1+x^3)/3 - 2/3*atanh(sqrt(1+x^3)) +--R +--R +--R +------+ +------+ +--R | 3 | 3 +--R - 2atanh(\|x + 1 ) + 2\|x + 1 +--R (76) -------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 250 +a0019:= integrate(t0019,x) +--R +--R +--R +------+ +------+ +------+ +--R | 3 | 3 | 3 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2\|x + 1 +--R (77) ------------------------------------------------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 250 +m0019:= a0019-r0019 +--R +--R +--R +------+ +------+ +------+ +--R | 3 | 3 | 3 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (78) ------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 250 +d0019:= D(m0019,x) +--R +--R +--R (79) 0 +--R Type: Expression(Integer) +--E 95 + + +\end{chunk} +\subsection{Problem 20} +\begin{chunk}{*} + +--S 96 of 250 +t0020:= x*log(x+sqrt(x^2-1))/sqrt(x^2-1) +--R +--R +--R +------+ +--R | 2 +--R x log(\|x - 1 + x) +--R (80) -------------------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 250 +r0020:= -x+sqrt(-1+x^2)*log(x+sqrt(-1+x^2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (81) \|x - 1 log(\|x - 1 + x) - x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 250 +a0020:= integrate(t0020,x) +--R +--R +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (- x\|x - 1 + x - 1)log(\|x - 1 + x) - x\|x - 1 + x +--R (82) ----------------------------------------------------------- +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 250 +m0020:= a0020-r0020 +--R +--R +--R (83) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 250 +d0020:= D(m0020,x) +--R +--R +--R (84) 0 +--R Type: Expression(Integer) +--E 100 + + +\end{chunk} +\subsection{Problem 21} +\begin{chunk}{*} + +--S 101 of 250 +t0021:= x^3*asin(x)/sqrt(1-x^4) +--R +--R +--R 3 +--R x asin(x) +--R (85) ----------- +--R +--------+ +--R | 4 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 250 +r0021:= 1/4*x*sqrt(1+x^2)-1/2*sqrt(1-x^4)*asin(x)+asinh(x)/4 +--R +--R +--R +------+ +--------+ +--R | 2 | 4 +--R x\|x + 1 - 2asin(x)\|- x + 1 + asinh(x) +--R (86) ------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 250 +a0021:= integrate(t0021,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 103 + +--S 104 of 250 +--m0021:= a0021-r0021 +--E 104 + +--S 105 of 250 +--d0021:= D(m0021,x) +--E 105 + + +\end{chunk} +\subsection{Problem 22} +\begin{chunk}{*} + +--S 106 of 250 +t0022:= x^3*asec(x)/sqrt(x^4-1) +--R +--R +--R 3 +--R x asec(x) +--R (87) --------- +--R +------+ +--R | 4 +--R \|x - 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 250 +r0022:= -sqrt(-1+x^4)/(2*sqrt(1-1/x^2)*x)+1/2*sqrt(-1+x^4)*asec(x)+_ + 1/2*atanh((sqrt(1-1/x^2)*x)/sqrt(-1+x^4)) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 +--R +------+ x |------ +------+ +--R | 2 | 2 | 2 +------+ +--R |x - 1 \| x |x - 1 | 4 +--R x |------ atanh(----------) + (x asec(x) |------ - 1)\|x - 1 +--R | 2 +------+ | 2 +--R \| x | 4 \| x +--R \|x - 1 +--R (88) --------------------------------------------------------------- +--R +------+ +--R | 2 +--R |x - 1 +--R 2x |------ +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 107 + +--S 108 of 250 +a0022:= integrate(t0022,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 108 + +--S 109 of 250 +--m0022:= a0022-r0022 +--E 109 + +--S 110 of 250 +--d0022:= D(m0022,x) +--E 110 + + +\end{chunk} +\subsection{Problem 23} +\begin{chunk}{*} + +--S 111 of 250 +t0023:= x*atan(x)*log(x+sqrt(1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +--R | 2 +--R x atan(x)log(\|x + 1 + x) +--R (89) --------------------------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 250 +r0023:= -x*atan(x)+1/2*log(1+x^2)+_ + sqrt(1+x^2)*atan(x)*log(x+sqrt(1+x^2))-1/2*log(x+sqrt(1+x^2))^2 +--R +--R +--R (90) +--R +------+ 2 +------+ +------+ +--R | 2 | 2 | 2 2 +--R - log(\|x + 1 + x) + 2atan(x)\|x + 1 log(\|x + 1 + x) + log(x + 1) +--R + +--R - 2x atan(x) +--R / +--R 2 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 250 +a0023:= integrate(t0023,x) +--R +--R +--R (91) +--R +------+ +------+ 2 +--R | 2 | 2 +--R (- \|x + 1 + x)log(\|x + 1 + x) +--R + +--R +------+ +------+ +--R 2x | 2 2 2x | 2 +--R (x atan(------)\|x + 1 + (- x - 1)atan(------))log(\|x + 1 + x) +--R 2 2 +--R x - 1 x - 1 +--R + +--R +------+ +--R 2 2x | 2 2 2 2x +--R (log(x + 1) + x atan(------))\|x + 1 - x log(x + 1) - x atan(------) +--R 2 2 +--R x - 1 x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 250 +m0023:= a0023-r0023 +--R +--R +--R (92) +--R +------+ +--R 2x | 2 2 +--R (2x atan(x) + x atan(------))\|x + 1 + (- 2x - 2)atan(x) +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (- x - 1)atan(------) +--R 2 +--R x - 1 +--R * +--R +------+ +--R | 2 +--R log(\|x + 1 + x) +--R + +--R +------+ +--R 2x | 2 2 2 2x +--R (2x atan(x) + x atan(------))\|x + 1 - 2x atan(x) - x atan(------) +--R 2 2 +--R x - 1 x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Expression(Integer) +--E 114 + +--S 115 of 250 +d0023:= D(m0023,x) +--R +--R +--R +------+ +--R 2x | 2 +--R (- 2x atan(x) - x atan(------))log(\|x + 1 + x) +--R 2 +--R x - 1 +--R (93) ------------------------------------------------- +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 115 + + +\end{chunk} +\subsection{Problem 24} +\begin{chunk}{*} + +--S 116 of 250 +t0024:= x*log(1+sqrt(1-x^2))/sqrt(1-x^2) +--R +--R +--R +--------+ +--R | 2 +--R x log(\|- x + 1 + 1) +--R (94) ---------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 250 +r0024:= sqrt(1-x^2)-log(1+sqrt(1-x^2))-sqrt(1-x^2)*log(1+sqrt(1-x^2)) +--R +--R +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R (95) (- \|- x + 1 - 1)log(\|- x + 1 + 1) + \|- x + 1 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 250 +a0024:= integrate(t0024,x) +--R +--R +--R +--------+ +--R 2 | 2 2 +--R x log(\|- x + 1 + 1) - x +--R (96) --------------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 250 +m0024:= a0024-r0024 +--R +--R +--R (97) 1 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 250 +d0024:= D(m0024,x) +--R +--R +--R (98) 0 +--R Type: Expression(Integer) +--E 120 + + +\end{chunk} +\subsection{Problem 25} +\begin{chunk}{*} + +--S 121 of 250 +t0025:= x*log(x+sqrt(1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +--R | 2 +--R x log(\|x + 1 + x) +--R (99) -------------------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 250 +r0025:= -x+sqrt(1+x^2)*log(x+sqrt(1+x^2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (100) \|x + 1 log(\|x + 1 + x) - x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 250 +a0025:= integrate(t0025,x) +--R +--R +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (- x\|x + 1 + x + 1)log(\|x + 1 + x) - x\|x + 1 + x +--R (101) ----------------------------------------------------------- +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 250 +m0025:= a0025-r0025 +--R +--R +--R (102) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 250 +d0025:= D(m0025,x) +--R +--R +--R (103) 0 +--R Type: Expression(Integer) +--E 125 + + +\end{chunk} +\subsection{Problem 26} +\begin{chunk}{*} + +--S 126 of 250 +t0026:= x*log(x+sqrt(1-x^2))/sqrt(1-x^2) +--R +--R +--R +--------+ +--R | 2 +--R x log(\|- x + 1 + x) +--R (104) ---------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 250 +r0026:= sqrt(1-x^2)+atanh(sqrt(2)*x)/sqrt(2)-_ + atanh(sqrt(2)*sqrt(1-x^2))/sqrt(2)-sqrt(1-x^2)*log(x+sqrt(1-x^2)) +--R +--R +--R (105) +--R +--------+ +--------+ +--------+ +--R +-+ | 2 | 2 +-+ | 2 +--R - \|2 \|- x + 1 log(\|- x + 1 + x) - atanh(\|2 \|- x + 1 ) +--R + +--R +--------+ +--R +-+ | 2 +-+ +--R \|2 \|- x + 1 + atanh(x\|2 ) +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 250 +a0026:= integrate(t0026,x) +--R +--R +--R (106) +--R +--------+ +--R 2 +-+ | 2 +--R 2x \|2 log(\|- x + 1 + x) +--R + +--R +--------+ +--R +--------+ | 2 2 +--R +-+ | 2 +-+ (x - 1)\|- x + 1 - x - x + 1 +--R (\|2 \|- x + 1 - \|2 )log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R | 2 +--R (\|- x + 1 - 1) +--R * +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x + 1)\|2 - 2x)\|- x + 1 + (- x - x - 1)\|2 + 2x + 2x +--R log(-------------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x + 1)\|- x + 1 + x - x - 1 +--R + +--R +--------+ +--R | 2 +--R (\|- x + 1 - 1) +--R * +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 1)\|2 - 2x)\|- x + 1 + (x - x + 1)\|2 - 2x + 2x +--R log(-----------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R + +--R +--------+ +--R +--------+ | 2 2 +--R +-+ | 2 +-+ (- x - 1)\|- x + 1 - x + x + 1 +--R (- \|2 \|- x + 1 + \|2 )log(---------------------------------) +--R 2 +--R x +--R + +--R 2 +-+ +--------+ +--R (2x + 1)\|2 + 4x +-+ 2 | 2 +--R (log(------------------) + \|2 log(2x - 1))\|- x + 1 +--R 2 +--R 2x - 1 +--R + +--R 2 +-+ +--R (2x + 1)\|2 + 4x +-+ 2 2 +-+ +--R - log(------------------) - \|2 log(2x - 1) - 2x \|2 +--R 2 +--R 2x - 1 +--R / +--R +--------+ +--R +-+ | 2 +-+ +--R 2\|2 \|- x + 1 - 2\|2 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 250 +m0026:= a0026-r0026 +--R +--R +--R (107) +--R +--------+ +--R +--------+ | 2 2 +--R +-+ | 2 +-+ (x - 1)\|- x + 1 - x - x + 1 +--R - 2\|2 log(\|- x + 1 + x) + \|2 log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x + 1)\|2 - 2x)\|- x + 1 + (- x - x - 1)\|2 + 2x + 2x +--R log(-------------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x + 1)\|- x + 1 + x - x - 1 +--R + +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 1)\|2 - 2x)\|- x + 1 + (x - x + 1)\|2 - 2x + 2x +--R log(-----------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R + +--R +--------+ +--R | 2 2 +--------+ +--R +-+ (- x - 1)\|- x + 1 - x + x + 1 +-+ | 2 +--R - \|2 log(---------------------------------) + 2atanh(\|2 \|- x + 1 ) +--R 2 +--R x +--R + +--R 2 +-+ +--R (2x + 1)\|2 + 4x +-+ 2 +-+ +-+ +--R log(------------------) + \|2 log(2x - 1) - 2atanh(x\|2 ) + 2\|2 +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 250 +d0026:= D(m0026,x) +--R +--R +--R (108) 0 +--R Type: Expression(Integer) +--E 130 + + +\end{chunk} +\subsection{Problem 27} +\begin{chunk}{*} + +--S 131 of 250 +t0027:= log(x)/(x^2*sqrt(1-x^2)) +--R +--R +--R log(x) +--R (109) ------------- +--R +--------+ +--R 2 | 2 +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 250 +r0027:= -sqrt(1-x^2)/x-asin(x)-sqrt(1-x^2)*log(x)/x +--R +--R +--R +--------+ +--R | 2 +--R (- log(x) - 1)\|- x + 1 - x asin(x) +--R (110) ------------------------------------- +--R x +--R Type: Expression(Integer) +--E 132 + +--S 133 of 250 +a0027:= integrate(t0027,x) +--R +--R +--R (111) +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 \|- x + 1 - 1 | 2 +--R (2x\|- x + 1 - 2x)atan(---------------) + (log(x) + 1)\|- x + 1 +--R x +--R + +--R 2 2 +--R (x - 1)log(x) + x - 1 +--R / +--R +--------+ +--R | 2 +--R x\|- x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 250 +m0027:= a0027-r0027 +--R +--R +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R (112) 2atan(---------------) + asin(x) +--R x +--R Type: Expression(Integer) +--E 134 + +--S 135 of 250 +d0027:= D(m0027,x) +--R +--R +--R (113) 0 +--R Type: Expression(Integer) +--E 135 + + +\end{chunk} +\subsection{Problem 28} +\begin{chunk}{*} + +--S 136 of 250 +t0028:= x*atan(x)/sqrt(1+x^2) +--R +--R +--R x atan(x) +--R (114) --------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 250 +r0028:= -asinh(x)+sqrt(1+x^2)*atan(x) +--R +--R +--R +------+ +--R | 2 +--R (115) atan(x)\|x + 1 - asinh(x) +--R Type: Expression(Integer) +--E 137 + +--S 138 of 250 +a0028:= integrate(t0028,x) +--R +--R +--R (116) +--R +------+ +------+ +------+ +--R | 2 | 2 2x | 2 +--R (2\|x + 1 - 2x)log(\|x + 1 - x) + x atan(------)\|x + 1 +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (- x - 1)atan(------) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 250 +m0028:= a0028-r0028 +--R +--R +--R (117) +--R +------+ +------+ +--R | 2 | 2 +--R (2\|x + 1 - 2x)log(\|x + 1 - x) +--R + +--R +------+ +--R 2x | 2 2 +--R (2x atan(x) + x atan(------) + 2asinh(x))\|x + 1 + (- 2x - 2)atan(x) +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (- x - 1)atan(------) - 2x asinh(x) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Expression(Integer) +--E 139 + +--S 140 of 250 +d0028:= D(m0028,x) +--R +--R +--R 2x +--R - 2x atan(x) - x atan(------) +--R 2 +--R x - 1 +--R (118) ----------------------------- +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 140 + + +\end{chunk} +\subsection{Problem 29} +\begin{chunk}{*} + +--S 141 of 250 +t0029:= atan(x)/(x^2*sqrt(1-x^2)) +--R +--R +--R atan(x) +--R (119) ------------- +--R +--------+ +--R 2 | 2 +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 250 +r0029:= -sqrt(1-x^2)*atan(x)/x-atanh(sqrt(1-x^2))+_ + sqrt(2)*atanh(sqrt(1-x^2)/sqrt(2)) +--R +--R +--R (120) +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 +-+ \|- x + 1 | 2 +--R - x atanh(\|- x + 1 ) + x\|2 atanh(-----------) - atan(x)\|- x + 1 +--R +-+ +--R \|2 +--R --------------------------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 142 + +--S 143 of 250 +a0029:= integrate(t0029,x) +--R +--R +--R (121) +--R +--------+ +--------+ +--R | 2 | 2 +--R - x log(\|- x + 1 + 1) + x log(\|- x + 1 - 1) +--R + +--R +--------+ +--R +-+ | 2 2 +--------+ +--R +-+ - 2\|2 \|- x + 1 + x - 3 2x | 2 +--R x\|2 log(---------------------------) + atan(------)\|- x + 1 +--R 2 2 +--R x + 1 x - 1 +--R / +--R 2x +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 250 +m0029:= a0029-r0029 +--R +--R +--R (122) +--R +--------+ +--------+ +--R | 2 | 2 +--R - x log(\|- x + 1 + 1) + x log(\|- x + 1 - 1) +--R + +--R +--------+ +--R +-+ | 2 2 +--------+ +--R +-+ - 2\|2 \|- x + 1 + x - 3 | 2 +--R x\|2 log(---------------------------) + 2x atanh(\|- x + 1 ) +--R 2 +--R x + 1 +--R + +--R +--------+ +--R | 2 +--------+ +--R +-+ \|- x + 1 2x | 2 +--R - 2x\|2 atanh(-----------) + (2atan(x) + atan(------))\|- x + 1 +--R +-+ 2 +--R \|2 x - 1 +--R / +--R 2x +--R Type: Expression(Integer) +--E 144 + +--S 145 of 250 +d0029:= D(m0029,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (123) ------------------------- +--R +--------+ +--R 2 | 2 +--R 2x \|- x + 1 +--R Type: Expression(Integer) +--E 145 + + +\end{chunk} +\subsection{Problem 30} +\begin{chunk}{*} + +--S 146 of 250 +t0030:= x*atan(x)/sqrt(1-x^2) +--R +--R +--R x atan(x) +--R (124) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 250 +r0030:= -asin(x)-sqrt(1-x^2)*atan(x)+sqrt(2)*atan(sqrt(2)*x/sqrt(1-x^2)) +--R +--R +--R +-+ +--------+ +--R +-+ x\|2 | 2 +--R (125) \|2 atan(-----------) - atan(x)\|- x + 1 - asin(x) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 250 +a0030:= integrate(t0030,x) +--R +--R +--R (126) +--R +--------+ +--R +-+ | 2 +--------+ +--R +-+ 2x\|2 \|- x + 1 x 2x | 2 +--R - \|2 atan(-----------------) - 2atan(-----------) + atan(------)\|- x + 1 +--R 2 +--------+ 2 +--R 3x - 1 | 2 x - 1 +--R \|- x + 1 +--R ---------------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 250 +m0030:= a0030-r0030 +--R +--R +--R (127) +--R +--------+ +--R +-+ | 2 +-+ +--R +-+ 2x\|2 \|- x + 1 +-+ x\|2 +--R - \|2 atan(-----------------) - 2\|2 atan(-----------) +--R 2 +--------+ +--R 3x - 1 | 2 +--R \|- x + 1 +--R + +--R +--------+ +--R x 2x | 2 +--R - 2atan(-----------) + (2atan(x) + atan(------))\|- x + 1 + 2asin(x) +--R +--------+ 2 +--R | 2 x - 1 +--R \|- x + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 250 +d0030:= D(m0030,x) +--R +--R +--R 2x +--R - 2x atan(x) - x atan(------) +--R 2 +--R x - 1 +--R (128) ----------------------------- +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 150 + + +\end{chunk} +\subsection{Problem 31} +\begin{chunk}{*} + +--S 151 of 250 +t0031:= atan(x)/(x^2*sqrt(1+x^2)) +--R +--R +--R atan(x) +--R (129) ----------- +--R +------+ +--R 2 | 2 +--R x \|x + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 250 +r0031:= sqrt(1+x^2)*atan(x)/x-atanh(sqrt(1+x^2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R - x atanh(\|x + 1 ) + atan(x)\|x + 1 +--R (130) --------------------------------------- +--R x +--R Type: Expression(Integer) +--E 152 + +--S 153 of 250 +a0031:= integrate(t0031,x) +--R +--R +--R (131) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- 2x\|x + 1 + 2x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 2x | 2 +--R (2x\|x + 1 - 2x )log(\|x + 1 - x - 1) - x atan(------)\|x + 1 +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (x + 1)atan(------) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 2 +--R 2x\|x + 1 - 2x +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 250 +m0031:= a0031-r0031 +--R +--R +--R (132) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- 2x\|x + 1 + 2x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x + 1 - 2x )log(\|x + 1 - x - 1) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x + 1 - 2x )atanh(\|x + 1 ) +--R + +--R +------+ +--R 2x | 2 2 +--R (2x atan(x) - x atan(------))\|x + 1 + (- 2x - 2)atan(x) +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (x + 1)atan(------) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 2 +--R 2x\|x + 1 - 2x +--R Type: Expression(Integer) +--E 154 + +--S 155 of 250 +d0031:= D(m0031,x) +--R +--R +--R 2x +--R 2atan(x) - atan(------) - 4x +--R 2 +--R x - 1 +--R (133) ---------------------------- +--R +------+ +--R 2 | 2 +--R 2x \|x + 1 +--R Type: Expression(Integer) +--E 155 + + +\end{chunk} +\subsection{Problem 32} +\begin{chunk}{*} + +--S 156 of 250 +t0032:= asin(x)/((x^2)*sqrt(1-x^2)) +--R +--R +--R asin(x) +--R (134) ------------- +--R +--------+ +--R 2 | 2 +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 250 +r0032:= -sqrt(1-x^2)*asin(x)/x+log(x) +--R +--R +--R +--------+ +--R | 2 +--R - asin(x)\|- x + 1 + x log(x) +--R (135) ------------------------------- +--R x +--R Type: Expression(Integer) +--E 157 + +--S 158 of 250 +a0032:= integrate(t0032,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 2x\|- x + 1 +--R \|- x + 1 atan(-------------) + 2x log(x) +--R 2 +--R 2x - 1 +--R (136) ------------------------------------------ +--R 2x +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 250 +m0032:= a0032-r0032 +--R +--R +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 2x\|- x + 1 | 2 +--R \|- x + 1 atan(-------------) + 2asin(x)\|- x + 1 +--R 2 +--R 2x - 1 +--R (137) ---------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 159 + +--S 160 of 250 +d0032:= D(m0032,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R - atan(-------------) - 2asin(x) +--R 2 +--R 2x - 1 +--R (138) -------------------------------- +--R +--------+ +--R 2 | 2 +--R 2x \|- x + 1 +--R Type: Expression(Integer) +--E 160 + + +\end{chunk} +\subsection{Problem 33} +\begin{chunk}{*} + +--S 161 of 250 +t0033:= x*log(x)/sqrt(x^2-1) +--R +--R +--R x log(x) +--R (139) --------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 250 +r0033:= -sqrt(x^2-1)+atan(sqrt(x^2-1))+sqrt(x^2-1)*log(x) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (140) atan(\|x - 1 ) + (log(x) - 1)\|x - 1 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 250 +a0033:= integrate(t0033,x) +--R +--R +--R (141) +--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 163 + +--S 164 of 250 +m0033:= a0033-r0033 +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (142) - atan(\|x - 1 ) + 2atan(\|x - 1 - x) +--R Type: Expression(Integer) +--E 164 + +--S 165 of 250 +d0033:= D(m0033,x) +--R +--R +--R (143) 0 +--R Type: Expression(Integer) +--E 165 + + +\end{chunk} +\subsection{Problem 34} +\begin{chunk}{*} + +--S 166 of 250 +t0034:= log(x)/(x^2*sqrt(1+x^2)) +--R +--R +--R log(x) +--R (144) ----------- +--R +------+ +--R 2 | 2 +--R x \|x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 250 +r0034:= -sqrt(1+x^2)/x+asinh(x)-sqrt(1+x^2)*log(x)/x +--R +--R +--R +------+ +--R | 2 +--R (- log(x) - 1)\|x + 1 + x asinh(x) +--R (145) ------------------------------------ +--R x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 250 +a0034:= integrate(t0034,x) +--R +--R +--R (146) +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 +--R (- x\|x + 1 + x )log(\|x + 1 - x) + x log(x)\|x + 1 +--R + +--R 2 +--R (- x - 1)log(x) - 1 +--R / +--R +------+ +--R | 2 2 +--R x\|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 250 +m0034:= a0034-r0034 +--R +--R +--R +------+ +--R | 2 +--R (147) - log(\|x + 1 - x) - asinh(x) - 1 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 250 +d0034:= D(m0034,x) +--R +--R +--R (148) 0 +--R Type: Expression(Integer) +--E 170 + + +\end{chunk} +\subsection{Problem 35} +\begin{chunk}{*} + +--S 171 of 250 +t0035:= x*asec(x)/sqrt(x^2-1) +--R +--R +--R x asec(x) +--R (149) --------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 250 +r0035:= sqrt(x^2-1)*asec(x)-sqrt(1-1/x^2)*x*log(x)/sqrt(x^2-1) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 2 +--R - x log(x) |------ + (x - 1)asec(x) +--R | 2 +--R \| x +--R (150) ------------------------------------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 250 +a0035:= integrate(t0035,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 173 + +--S 174 of 250 +--m0035:= a0035-r0035 +--E 174 + +--S 175 of 250 +--d0035:= D(m0035,x) +--E 175 + + +\end{chunk} +\subsection{Problem 36} +\begin{chunk}{*} + +--S 176 of 250 +t0036:= x*log(x)/sqrt(1+x^2) +--R +--R +--R x log(x) +--R (151) --------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 250 +r0036:= -sqrt(1+x^2)+atanh(sqrt(1+x^2))+sqrt(1+x^2)*log(x) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (152) atanh(\|x + 1 ) + (log(x) - 1)\|x + 1 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 250 +a0036:= integrate(t0036,x) +--R +--R +--R (153) +--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) + (- 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 178 + +--S 179 of 250 +m0036:= a0036-r0036 +--R +--R +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R (154) log(\|x + 1 - x + 1) - log(\|x + 1 - x - 1) - atanh(\|x + 1 ) +--R Type: Expression(Integer) +--E 179 + +--S 180 of 250 +d0036:= D(m0036,x) +--R +--R +--R (155) 0 +--R Type: Expression(Integer) +--E 180 + + +\end{chunk} +\subsection{Problem 37} +\begin{chunk}{*} + +--S 181 of 250 +t0037:= sin(x)/(1+sin(x)^2) +--R +--R +--R sin(x) +--R (156) ----------- +--R 2 +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 250 +r0037:= atanh(cos(x)/sqrt(2))/sqrt(2) +--R +--R +--R cos(x) +--R atanh(------) +--R +-+ +--R \|2 +--R (157) ------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 250 +a0037:= integrate(t0037,x) +--R +--R +--R +-+ 2 +-+ +-+ +--R (- 3\|2 + 4)cos(x) + (- 8\|2 + 12)cos(x) - 6\|2 + 8 +--R log(-------------------------------------------------------) +--R 2 +--R cos(x) - 2 +--R (158) ------------------------------------------------------------ +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 250 +m0037:= a0037-r0037 +--R +--R +--R (159) +--R +-+ 2 +-+ +-+ +--R (- 3\|2 + 4)cos(x) + (- 8\|2 + 12)cos(x) - 6\|2 + 8 cos(x) +--R log(-------------------------------------------------------) - 2atanh(------) +--R 2 +-+ +--R cos(x) - 2 \|2 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 250 +d0037:= D(m0037,x) +--R +--R +--R 2sin(x) +--R (160) - ----------- +--R 2 +--R cos(x) - 2 +--R Type: Expression(Integer) +--E 185 + + +\end{chunk} +\subsection{Problem 38} +\begin{chunk}{*} + +--S 186 of 250 +t0038:= (1+x^2)/((1-x^2)*sqrt(1+x^4)) +--R +--R +--R 2 +--R - x - 1 +--R (161) ----------------- +--R +------+ +--R 2 | 4 +--R (x - 1)\|x + 1 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 250 +r0038:= atanh(sqrt(2)*x/sqrt(1+x^4))/sqrt(2) +--R +--R +--R +-+ +--R x\|2 +--R atanh(---------) +--R +------+ +--R | 4 +--R \|x + 1 +--R (162) ---------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 250 +a0038:= integrate(t0038,x) +--R +--R +--R +------+ +--R +-+ | 4 +--R +-+ \|2 \|x + 1 - 2x +--R \|2 log(------------------) +--R 2 +--R x - 1 +--R (163) - --------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 250 +m0038:= a0038-r0038 +--R +--R +--R +------+ +--R +-+ | 4 +-+ +--R \|2 \|x + 1 - 2x x\|2 +--R - log(------------------) - atanh(---------) +--R 2 +------+ +--R x - 1 | 4 +--R \|x + 1 +--R (164) -------------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 250 +d0038:= D(m0038,x) +--R +--R +--R (165) 0 +--R Type: Expression(Integer) +--E 190 + + +\end{chunk} +\subsection{Problem 39} +\begin{chunk}{*} + +--S 191 of 250 +t0039:= (1-x^2)/((1+x^2)*sqrt(1+x^4)) +--R +--R +--R 2 +--R - x + 1 +--R (166) ----------------- +--R +------+ +--R 2 | 4 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 250 +r0039:= atan(sqrt(2)*x/sqrt(1+x^4))/sqrt(2) +--R +--R +--R +-+ +--R x\|2 +--R atan(---------) +--R +------+ +--R | 4 +--R \|x + 1 +--R (167) --------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 250 +a0039:= integrate(t0039,x) +--R +--R +--R +-+ 2x +--R \|2 atan(-------------) +--R +------+ +--R +-+ | 4 +--R \|2 \|x + 1 +--R (168) ----------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 250 +m0039:= a0039-r0039 +--R +--R +--R +-+ +--R x\|2 2x +--R - atan(---------) + atan(-------------) +--R +------+ +------+ +--R | 4 +-+ | 4 +--R \|x + 1 \|2 \|x + 1 +--R (169) --------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 250 +d0039:= D(m0039,x) +--R +--R +--R (170) 0 +--R Type: Expression(Integer) +--E 195 + + +\end{chunk} +\subsection{Problem 40} +\begin{chunk}{*} + +--S 196 of 250 +t0040:= log(sin(x))/(1+sin(x)) +--R +--R +--R log(sin(x)) +--R (171) ----------- +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 250 +r0040:= -x-atanh(cos(x))-cos(x)*log(sin(x))/(1+sin(x)) +--R +--R +--R - cos(x)log(sin(x)) + (- sin(x) - 1)atanh(cos(x)) - x sin(x) - x +--R (172) ---------------------------------------------------------------- +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 250 +a0040:= integrate(t0040,x) +--R +--R +--R (173) +--R - 2cos(x)log(sin(x)) + (- sin(x) - 1)log(cos(x) + 1) +--R + +--R sin(x) +--R (sin(x) + 1)log(cos(x) - 1) + (2sin(x) + 2)atan(----------) +--R cos(x) - 1 +--R + +--R sin(x) +--R (2sin(x) + 2)atan(----------) - 4x sin(x) - 4x +--R cos(x) + 1 +--R / +--R 2sin(x) + 2 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 250 +m0040:= a0040-r0040 +--R +--R +--R (174) +--R sin(x) +--R - log(cos(x) + 1) + log(cos(x) - 1) + 2atanh(cos(x)) + 2atan(----------) +--R cos(x) - 1 +--R + +--R sin(x) +--R 2atan(----------) - 2x +--R cos(x) + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 250 +d0040:= D(m0040,x) +--R +--R +--R 4 2 2 4 +--R sin(x) + 2cos(x) sin(x) + cos(x) - 1 +--R (175) -------------------------------------------------------- +--R 4 2 2 4 2 +--R sin(x) + (2cos(x) + 2)sin(x) + cos(x) - 2cos(x) + 1 +--R Type: Expression(Integer) +--E 200 + + +\end{chunk} +\subsection{Problem 41} +\begin{chunk}{*} + +--S 201 of 250 +t0041:= log(sin(x))*sqrt(1+sin(x)) +--R +--R +--R +----------+ +--R (176) log(sin(x))\|sin(x) + 1 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 250 +r0041:= 4*cos(x)/sqrt(1+sin(x))-2*cos(x)*log(sin(x))/sqrt(1+sin(x))-_ + 4*atanh(cos(x)/sqrt(1+sin(x))) +--R +--R +--R +----------+ cos(x) +--R - 4\|sin(x) + 1 atanh(-------------) - 2cos(x)log(sin(x)) + 4cos(x) +--R +----------+ +--R \|sin(x) + 1 +--R (177) ------------------------------------------------------------------- +--R +----------+ +--R \|sin(x) + 1 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 250 +a0041:= integrate(t0041,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 203 + +--S 204 of 250 +--m0041:= a0041-r0041 +--E 204 + +--S 205 of 250 +--d0041:= D(m0041,x) +--E 205 + + +\end{chunk} +\subsection{Problem 42} +\begin{chunk}{*} + +--S 206 of 250 +t0042:= sec(x)/sqrt(sec(x)^4-1) +--R +--R +--R sec(x) +--R (178) -------------- +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 250 +r0042:= -atanh(sqrt(sec(x)^4-1)/(sqrt(2)*sec(x)*tan(x)))/sqrt(2) +--R +--R +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R atanh(----------------) +--R +-+ +--R \|2 sec(x)tan(x) +--R (179) - ----------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 250 +a0042:= integrate(t0042,x) +--R +--R +--R (180) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 5 +-+ 4 +-+ 3 +--R - 8\|2 cos(x) - 24\|2 cos(x) - 20\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 4\|2 cos(x) + 12\|2 cos(x) + 4\|2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 3 2 +--R - 32cos(x) - 128cos(x) - 193cos(x) - 128cos(x) - 33 +--R / +--R 6 5 4 2 +--R cos(x) + 4cos(x) + 5cos(x) - 5cos(x) - 4cos(x) - 1 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 250 +m0042:= a0042-r0042 +--R +--R +--R (181) +--R - +--R log +--R +-+ 5 +-+ 4 +-+ 3 +--R - 8\|2 cos(x) - 24\|2 cos(x) - 20\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 4\|2 cos(x) + 12\|2 cos(x) + 4\|2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 3 2 +--R - 32cos(x) - 128cos(x) - 193cos(x) - 128cos(x) - 33 +--R / +--R 6 5 4 2 +--R cos(x) + 4cos(x) + 5cos(x) - 5cos(x) - 4cos(x) - 1 +--R + +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R 2atanh(----------------) +--R +-+ +--R \|2 sec(x)tan(x) +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 250 +d0042:= D(m0042,x) +--R +--R +--R (182) +--R +-+ 5 +-+ 4 +-+ 3 +--R - 32\|2 cos(x) - 128\|2 cos(x) - 194\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 126\|2 cos(x) - 36\|2 cos(x) + 2\|2 +--R * +--R 2 2 +--R sec(x) sin(x)tan(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16\|2 cos(x) + 64\|2 cos(x) + 97\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 63\|2 cos(x) + 18\|2 cos(x) - \|2 +--R * +--R 4 +--R sec(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16\|2 cos(x) - 64\|2 cos(x) - 97\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 63\|2 cos(x) - 18\|2 cos(x) + \|2 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 32cos(x) - 48cos(x) - 80cos(x) + 48cos(x) +--R + +--R - 16cos(x) - 32 +--R * +--R 2 2 +--R sec(x) sin(x)tan(x) +--R + +--R 6 5 4 3 2 +--R 16cos(x) - 16cos(x) + 24cos(x) + 40cos(x) - 24cos(x) +--R + +--R 8cos(x) + 16 +--R * +--R 4 +--R sec(x) +--R + +--R 6 5 4 3 2 +--R - 16cos(x) + 16cos(x) - 24cos(x) - 40cos(x) + 24cos(x) +--R + +--R - 8cos(x) - 16 +--R * +--R sin(x) +--R * +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R + +--R 6 5 4 2 +--R (64cos(x) + 256cos(x) + 322cos(x) - 320cos(x) - 256cos(x) - 66) +--R * +--R 2 +--R sec(x)tan(x) +--R + +--R 6 5 4 2 +--R - 32cos(x) - 128cos(x) - 161cos(x) + 160cos(x) + 128cos(x) +--R + +--R 33 +--R * +--R 5 +--R sec(x) +--R + +--R 6 5 4 2 +--R (32cos(x) + 128cos(x) + 161cos(x) - 160cos(x) - 128cos(x) - 33) +--R * +--R sec(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 64\|2 cos(x) + 64\|2 cos(x) - 32\|2 cos(x) - 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 64\|2 cos(x) - 64\|2 cos(x) + 32\|2 cos(x) + 32\|2 +--R * +--R 2 +--R sec(x)tan(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 +--R * +--R 5 +--R sec(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 +--R * +--R sec(x) +--R / +--R 6 5 4 2 +--R 64cos(x) + 256cos(x) + 322cos(x) - 320cos(x) - 256cos(x) +--R + +--R - 66 +--R * +--R 2 2 +--R sec(x) tan(x) +--R + +--R 6 5 4 2 +--R - 32cos(x) - 128cos(x) - 161cos(x) + 160cos(x) + 128cos(x) +--R + +--R 33 +--R * +--R 4 +--R sec(x) +--R + +--R 6 5 4 2 +--R 32cos(x) + 128cos(x) + 161cos(x) - 160cos(x) - 128cos(x) - 33 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 64\|2 cos(x) + 64\|2 cos(x) - 32\|2 cos(x) - 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 64\|2 cos(x) - 64\|2 cos(x) + 32\|2 cos(x) + 32\|2 +--R * +--R 2 2 +--R sec(x) tan(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 +--R * +--R 4 +--R sec(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 +--R * +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R Type: Expression(Integer) +--E 210 + + +\end{chunk} +\subsection{Problem 43} +\begin{chunk}{*} + +--S 211 of 250 +t0043:= tan(x)/sqrt(1+tan(x)^4) +--R +--R +--R tan(x) +--R (183) -------------- +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 250 +r0043:= -atanh((1-tan(x)^2)/(sqrt(2)*sqrt(1+tan(x)^4)))/(2*sqrt(2)) +--R +--R +--R 2 +--R tan(x) - 1 +--R atanh(------------------) +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R (184) ------------------------- +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 250 +a0043:= integrate(t0043,x) +--R +--R +--R (185) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (- 64\|2 cos(x) + 96\|2 cos(x) - 56\|2 cos(x) + 12\|2 cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 8 6 4 2 +--R 128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 250 +m0043:= a0043-r0043 +--R +--R +--R (186) +--R log +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (- 64\|2 cos(x) + 96\|2 cos(x) - 56\|2 cos(x) + 12\|2 cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 8 6 4 2 +--R 128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17 +--R + +--R 2 +--R tan(x) - 1 +--R - 4atanh(------------------) +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 250 +d0043:= D(m0043,x) +--R +--R +--R (187) +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R (- 64\|2 cos(x) + 96\|2 cos(x) - 56\|2 cos(x) + 12\|2 cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R sin(x) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 9 7 5 3 +--R (128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17cos(x))sin(x) +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R + +--R 10 8 6 4 2 +--R (- 128cos(x) + 256cos(x) - 224cos(x) + 96cos(x) - 17cos(x) )tan(x) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +-+ 4 +--R 128\|2 cos(x) - 320\|2 cos(x) + 368\|2 cos(x) - 232\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 80\|2 cos(x) - 12\|2 +--R * +--R tan(x) +--R / +--R 10 8 6 4 2 +--R (128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +-+ 4 +--R - 128\|2 cos(x) + 320\|2 cos(x) - 368\|2 cos(x) + 232\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 80\|2 cos(x) + 12\|2 +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R Type: Expression(Integer) +--E 215 + + +\end{chunk} +\subsection{Problem 44} +\begin{chunk}{*} + +--S 216 of 250 +t0044:= sin(x)/sqrt(1-sin(x)^6) +--R +--R +--R sin(x) +--R (188) ---------------- +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 250 +r0044:= atanh((sqrt(3)*cos(x)*(1+sin(x)^2))/(2*sqrt(1-sin(x)^6)))/(2*sqrt(3)) +--R +--R +--R +-+ 2 +-+ +--R \|3 cos(x)sin(x) + \|3 cos(x) +--R atanh(------------------------------) +--R +-------------+ +--R | 6 +--R 2\|- sin(x) + 1 +--R (189) ------------------------------------- +--R +-+ +--R 2\|3 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 250 +a0044:= integrate(t0044,x) +--R +--R +--R (190) +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R - \|3 cos(x) - 2\|3 cos(x) + \|3 cos(x) + 4\|3 cos(x) +--R + +--R +-+ +--R 2\|3 +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) - 48cos(x) + 48 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 4 2 +--R 7cos(x) - 24cos(x) + 24 +--R / +--R 4 +--R cos(x) +--R / +--R 12 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 250 +m0044:= a0044-r0044 +--R +--R +--R (191) +--R - +--R log +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R - \|3 cos(x) - 2\|3 cos(x) + \|3 cos(x) + 4\|3 cos(x) +--R + +--R +-+ +--R 2\|3 +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) - 48cos(x) + 48 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 4 2 +--R 7cos(x) - 24cos(x) + 24 +--R / +--R 4 +--R cos(x) +--R + +--R +-+ 2 +-+ +--R \|3 cos(x)sin(x) + \|3 cos(x) +--R - 2atanh(------------------------------) +--R +-------------+ +--R | 6 +--R 2\|- sin(x) + 1 +--R / +--R +-+ +--R 4\|3 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 250 +d0044:= D(m0044,x) +--R +--R +--R (192) +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 16\|3 cos(x) + 32\|3 cos(x) - 16\|3 cos(x) - 64\|3 cos(x) +--R + +--R +-+ +--R - 32\|3 +--R * +--R 7 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 12\|3 cos(x) + 24\|3 cos(x) - 12\|3 cos(x) - 48\|3 cos(x) +--R + +--R +-+ 2 +--R - 24\|3 cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 24\|3 cos(x) + 48\|3 cos(x) - 24\|3 cos(x) - 96\|3 cos(x) +--R + +--R +-+ 2 +--R - 48\|3 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 12\|3 cos(x) + 24\|3 cos(x) - 28\|3 cos(x) - 80\|3 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 8\|3 cos(x) + 64\|3 cos(x) + 32\|3 +--R * +--R sin(x) +--R * +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R + +--R 7 6 5 4 2 +--R 7cos(x) + 14cos(x) - 17cos(x) - 48cos(x) + 48cos(x) +--R + +--R 24cos(x) +--R * +--R 9 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R 7cos(x) + 14cos(x) - 10cos(x) - 34cos(x) - 17cos(x) +--R + +--R 3 2 +--R 24cos(x) + 48cos(x) + 24cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 9 8 7 6 4 +--R 21cos(x) + 42cos(x) - 51cos(x) - 144cos(x) + 144cos(x) +--R + +--R 3 +--R 72cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 6 5 4 2 +--R - 7cos(x) - 14cos(x) + 17cos(x) + 48cos(x) - 48cos(x) +--R + +--R - 24cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R 14cos(x) + 28cos(x) - 41cos(x) - 110cos(x) + 17cos(x) +--R + +--R 4 3 2 +--R 144cos(x) + 48cos(x) - 48cos(x) - 24cos(x) +--R * +--R sin(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) - 48cos(x) + 48 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 4 2 7 +--R (- 112cos(x) + 384cos(x) - 384)sin(x) +--R + +--R 6 4 2 5 +--R (- 84cos(x) + 288cos(x) - 288cos(x) )sin(x) +--R + +--R 6 4 2 3 +--R (- 168cos(x) + 576cos(x) - 576cos(x) )sin(x) +--R + +--R 6 4 2 +--R (- 84cos(x) + 400cos(x) - 672cos(x) + 384)sin(x) +--R * +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ 9 +--R (- 16\|3 cos(x) + 80\|3 cos(x) - 144\|3 cos(x) + 96\|3 cos(x))sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R - 16\|3 cos(x) + 64\|3 cos(x) - 64\|3 cos(x) - 48\|3 cos(x) +--R + +--R +-+ +--R 96\|3 cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R (- 48\|3 cos(x) + 240\|3 cos(x) - 432\|3 cos(x) + 288\|3 cos(x) ) +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ 3 +--R (16\|3 cos(x) - 80\|3 cos(x) + 144\|3 cos(x) - 96\|3 cos(x))sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R - 32\|3 cos(x) + 176\|3 cos(x) - 368\|3 cos(x) + 336\|3 cos(x) +--R + +--R +-+ +--R - 96\|3 cos(x) +--R * +--R sin(x) +--R / +--R 7 6 5 4 2 +--R 28cos(x) + 56cos(x) - 68cos(x) - 192cos(x) + 192cos(x) +--R + +--R 96cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 9 8 7 6 4 +--R 21cos(x) + 42cos(x) - 51cos(x) - 144cos(x) + 144cos(x) +--R + +--R 3 +--R 72cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 9 8 7 6 4 +--R 42cos(x) + 84cos(x) - 102cos(x) - 288cos(x) + 288cos(x) +--R + +--R 3 +--R 144cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R 21cos(x) + 42cos(x) - 79cos(x) - 200cos(x) + 68cos(x) +--R + +--R 4 3 2 +--R 336cos(x) + 72cos(x) - 192cos(x) - 96cos(x) +--R * +--R +-------------------------------------------+ +--R +-------------+ | 4 2 +--R | 6 | 16cos(x) - 48cos(x) + 48 +--R \|- sin(x) + 1 |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 64\|3 cos(x) + 320\|3 cos(x) - 576\|3 cos(x) + 384\|3 cos(x)) +--R * +--R 6 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 48\|3 cos(x) + 240\|3 cos(x) - 432\|3 cos(x) +--R + +--R +-+ 3 +--R 288\|3 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 96\|3 cos(x) + 480\|3 cos(x) - 864\|3 cos(x) +--R + +--R +-+ 3 +--R 576\|3 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R - 48\|3 cos(x) + 304\|3 cos(x) - 752\|3 cos(x) + 864\|3 cos(x) +--R + +--R +-+ +--R - 384\|3 cos(x) +--R * +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R Type: Expression(Integer) +--E 220 + + +\end{chunk} +\subsection{Problem 45} +\begin{chunk}{*} + +--S 221 of 250 +t0045:= sqrt(sqrt(sec(x)+1)-sqrt(sec(x)-1)) +--R +--R +--R +-----------------------------+ +--R | +----------+ +----------+ +--R (193) \|\|sec(x) + 1 - \|sec(x) - 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 250 +r0045:= sqrt(2)*cot(x)*sqrt(-1+sec(x))*sqrt(1+sec(x))*_ + (sqrt(-1+sqrt(2))*_ + atan((sqrt(-2+2*sqrt(2))*(-sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (2*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x)))))-_ + sqrt(1+sqrt(2))*_ + atan((sqrt(2+2*sqrt(2))*(-sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (2*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x)))))-_ + sqrt(1+sqrt(2))*_ + atanh((sqrt(-2+2*sqrt(2))*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))+_ + sqrt(-1+sqrt(2))*_ + atanh((sqrt(2+2*sqrt(2))*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))) +--R +--R +--R (194) +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 - 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R +---------+ +-----------------------------+ +--R | +-+ | +----------+ +----------+ +--R \|2\|2 + 2 \|\|sec(x) + 1 - \|sec(x) - 1 +--R atanh(--------------------------------------------) +--R +----------+ +----------+ +-+ +--R \|sec(x) + 1 - \|sec(x) - 1 + \|2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 + 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R +---------+ +-----------------------------+ +--R | +-+ | +----------+ +----------+ +--R \|2\|2 - 2 \|\|sec(x) + 1 - \|sec(x) - 1 +--R atanh(--------------------------------------------) +--R +----------+ +----------+ +-+ +--R \|sec(x) + 1 - \|sec(x) - 1 + \|2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 + 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R atan +--R +---------+ +---------+ +--R | +-+ +----------+ | +-+ +----------+ +--R \|2\|2 + 2 \|sec(x) + 1 - \|2\|2 + 2 \|sec(x) - 1 +--R + +--R +---------+ +--R +-+ | +-+ +--R - \|2 \|2\|2 + 2 +--R / +--R +-----------------------------+ +--R | +----------+ +----------+ +--R 2\|\|sec(x) + 1 - \|sec(x) - 1 +--R + +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 - 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R atan +--R +---------+ +---------+ +--R | +-+ +----------+ | +-+ +----------+ +--R \|2\|2 - 2 \|sec(x) + 1 - \|2\|2 - 2 \|sec(x) - 1 +--R + +--R +---------+ +--R +-+ | +-+ +--R - \|2 \|2\|2 - 2 +--R / +--R +-----------------------------+ +--R | +----------+ +----------+ +--R 2\|\|sec(x) + 1 - \|sec(x) - 1 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 250 +a0045:= integrate(t0045,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (residue poly has multiple non-linear factors) +--R +--R Continuing to read the file... +--R +--E 223 + +--S 224 of 250 +--m0045:= a0045-r0045 +--E 224 + +--S 225 of 250 +--d0045:= D(m0045,x) +--E 225 + + +\end{chunk} +\subsection{Problem 46} +\begin{chunk}{*} + +--S 226 of 250 +t0046:= x*log(x^2+1)*atan(x)^2 +--R +--R +--R 2 2 +--R (195) x atan(x) log(x + 1) +--R Type: Expression(Integer) +--E 226 + +--S 227 of 250 +r0046:= x*atan(x)*(3-log(1+x^2))-1/4*(6-log(1+x^2))*log(1+x^2)-_ + 1/2*atan(x)^2*(3+x^2-(1+x^2)*log(1+x^2)) +--R +--R +--R (196) +--R 2 2 2 2 2 +--R log(x + 1) + ((2x + 2)atan(x) - 4x atan(x) - 6)log(x + 1) +--R + +--R 2 2 +--R (- 2x - 6)atan(x) + 12x atan(x) +--R / +--R 4 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 250 +a0046:= integrate(t0046,x) +--R +--R +--R (197) +--R 2 2 2 2x 2 2x 2 +--R 2log(x + 1) + ((x + 1)atan(------) + 4x atan(------) - 12)log(x + 1) +--R 2 2 +--R x - 1 x - 1 +--R + +--R 2 2x 2 2x +--R (- x - 3)atan(------) - 12x atan(------) +--R 2 2 +--R x - 1 x - 1 +--R / +--R 8 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 250 +m0046:= a0046-r0046 +--R +--R +--R (198) +--R 2 2 2 2x 2 +--R (- 4x - 4)atan(x) + 8x atan(x) + (x + 1)atan(------) +--R 2 +--R x - 1 +--R + +--R 2x +--R 4x atan(------) +--R 2 +--R x - 1 +--R * +--R 2 +--R log(x + 1) +--R + +--R 2 2 2 2x 2 +--R (4x + 12)atan(x) - 24x atan(x) + (- x - 3)atan(------) +--R 2 +--R x - 1 +--R + +--R 2x +--R - 12x atan(------) +--R 2 +--R x - 1 +--R / +--R 8 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 250 +d0046:= D(m0046,x) +--R +--R +--R 2 2x 2 2 +--R (- 4x atan(x) + x atan(------) )log(x + 1) +--R 2 +--R x - 1 +--R (199) -------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 230 + + +\end{chunk} +\subsection{Problem 47} +\begin{chunk}{*} + +--S 231 of 250 +t0047:= atan(x*sqrt(1+x^2)) +--R +--R +--R +------+ +--R | 2 +--R (200) atan(x\|x + 1 ) +--R Type: Expression(Integer) +--E 231 + +--S 232 of 250 +r0047:= 1/2*atan(sqrt(1+x^2)/x^2)+x*atan(x*sqrt(1+x^2))+_ + 1/2*sqrt(3)*atanh((sqrt(3)*sqrt(1+x^2))/(2+x^2)) +--R +--R +--R +------+ +------+ +--R +-+ | 2 +------+ | 2 +--R +-+ \|3 \|x + 1 | 2 \|x + 1 +--R \|3 atanh(-------------) + 2x atan(x\|x + 1 ) + atan(---------) +--R 2 2 +--R x + 2 x +--R (201) ---------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 250 +a0047:= integrate(t0047,x) +--R +--R +--R (202) +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 2 +--R ((2x + 1)\|3 - 2x - 4x)\|x + 1 + (- 2x - 2x)\|3 + 2x + 5x +--R + +--R 2 +--R + +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 +--R ((- 2x - 1)\|3 - 2x - 4x)\|x + 1 + (2x + 2x)\|3 + 2x +--R + +--R 2 +--R 5x + 2 +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 2x\|x + 1 \|x + 1 - x +--R - 2x atan(-----------) + 2atan(--------------------------------------) +--R 4 2 +------+ +--R x + x - 1 +-+ | 2 +-+ 2 +--R (\|3 - 2x)\|x + 1 - x\|3 + 2x + 2 +--R + +--R +------+ +--R | 2 +--R \|x + 1 - x +--R - 2atan(--------------------------------------) +--R +------+ +--R +-+ | 2 +-+ 2 +--R (\|3 + 2x)\|x + 1 - x\|3 - 2x - 2 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 250 +m0047:= a0047-r0047 +--R +--R +--R (203) +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 2 +--R ((2x + 1)\|3 - 2x - 4x)\|x + 1 + (- 2x - 2x)\|3 + 2x + 5x +--R + +--R 2 +--R + +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 +--R ((- 2x - 1)\|3 - 2x - 4x)\|x + 1 + (2x + 2x)\|3 + 2x +--R + +--R 2 +--R 5x + 2 +--R + +--R +------+ +------+ +--R +-+ | 2 +------+ | 2 +--R +-+ \|3 \|x + 1 | 2 \|x + 1 +--R - 2\|3 atanh(-------------) - 4x atan(x\|x + 1 ) - 2atan(---------) +--R 2 2 +--R x + 2 x +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 2x\|x + 1 \|x + 1 - x +--R - 2x atan(-----------) + 2atan(--------------------------------------) +--R 4 2 +------+ +--R x + x - 1 +-+ | 2 +-+ 2 +--R (\|3 - 2x)\|x + 1 - x\|3 + 2x + 2 +--R + +--R +------+ +--R | 2 +--R \|x + 1 - x +--R - 2atan(--------------------------------------) +--R +------+ +--R +-+ | 2 +-+ 2 +--R (\|3 + 2x)\|x + 1 - x\|3 - 2x - 2 +--R / +--R 4 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 250 +d0047:= D(m0047,x) +--R +--R +--R +------+ +--R +------+ | 2 +--R | 2 2x\|x + 1 +--R - 2atan(x\|x + 1 ) - atan(-----------) +--R 4 2 +--R x + x - 1 +--R (204) --------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 235 + + +\end{chunk} +\subsection{Problem 48} +\begin{chunk}{*} + +--S 236 of 250 +t0048:= atan(sqrt(x+1)-sqrt(x)) +--R +--R +--R +-----+ +-+ +--R (205) atan(\|x + 1 - \|x ) +--R Type: Expression(Integer) +--E 236 + +--S 237 of 250 +r0048:= sqrt(x)/2+(1+x)*atan(sqrt(1+x)-sqrt(x)) +--R +--R +--R +-----+ +-+ +-+ +--R (2x + 2)atan(\|x + 1 - \|x ) + \|x +--R (206) ------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 250 +a0048:= integrate(t0048,x) +--R +--R +--R (207) +--R +-----+ +-+ +--R +-----+ +-+ \|x + 1 - \|x +-+ +-----+ +--R ((x + 1)\|x + 1 + (- x - 1)\|x )atan(----------------) + \|x \|x + 1 - x +--R +-+ +-----+ +--R \|x \|x + 1 - x +--R -------------------------------------------------------------------------- +--R +-----+ +-+ +--R 2\|x + 1 - 2\|x +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 250 +m0048:= a0048-r0048 +--R +--R +--R +-----+ +-+ +--R +-----+ +-+ \|x + 1 - \|x +--R (- 2x - 2)atan(\|x + 1 - \|x ) + (x + 1)atan(----------------) +--R +-+ +-----+ +--R \|x \|x + 1 - x +--I (208) --------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 250 +d0048:= D(m0048,x) +--R +--R +--R +-----+ +-+ +--R +-----+ +-+ \|x + 1 - \|x +--R - 2atan(\|x + 1 - \|x ) + atan(----------------) +--R +-+ +-----+ +--R \|x \|x + 1 - x +--I (209) ------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 240 + + +\end{chunk} +\subsection{Problem 49} +\begin{chunk}{*} + +--S 241 of 250 +t0049:= asin(x/sqrt(1-x^2)) +--R +--R +--R x +--I (210) asin(-----------) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 250 +r0049:= x*asin(x/sqrt(1-x^2))+atan(sqrt(1-2*x^2)) +--R +--R +--R +---------+ +--R | 2 x +--I (211) atan(\|- 2x + 1 ) + x asin(-----------) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 250 +a0049:= integrate(t0049,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 243 + +--S 244 of 250 +--m0049:= a0049-r0049 +--E 244 + +--S 245 of 250 +--d0049:= D(m0049,x) +--E 245 + + +\end{chunk} +\subsection{Problem 50} +\begin{chunk}{*} + +)clear all + +--S 246 of 250 +t0050:= atan(x*sqrt(1-x^2)) +--R +--R +--R +--------+ +--R | 2 +--R (1) atan(x\|- x + 1 ) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 250 +r0050:= x*atan(x*sqrt(1-x^2))-_ + sqrt(1/2*(1+sqrt(5)))*atan(sqrt(1/2*(1+sqrt(5)))*sqrt(1-x^2))+_ + sqrt(1/2*(-1+sqrt(5)))*atanh(sqrt(1/2*(-1+sqrt(5)))*sqrt(1-x^2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--R | +-+ \|- x + 1 \|\|5 - 1 +--R \|\|5 - 1 atanh(----------------------) +--R +-+ +--R \|2 +--R + +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--------+ +--R | +-+ \|- x + 1 \|\|5 + 1 +-+ | 2 +--R - \|\|5 + 1 atan(----------------------) + x\|2 atan(x\|- x + 1 ) +--R +-+ +--R \|2 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 250 +a0050:= integrate(t0050,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--------+ +--R | +-+ +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R \|\|5 - 1 log((\|2 \|5 + \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R +--------+ +--------+ +--R +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R log((- \|2 \|5 - \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 + 2x\|2 \|- x + 1 +--R - 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (2x - 2)\|2 +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 - 2x\|2 \|- x + 1 +--R 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (- 2x + 2)\|2 +--R + +--R +--------+ +--R | 2 +--R +-+ 2x\|- x + 1 +--R 2x\|2 atan(-------------) +--R 4 2 +--R x - x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 250 +m0050:= a0050-r0050 +--R +--R +--R (4) +--R +--------+ +--------+ +--------+ +--R | +-+ +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R \|\|5 - 1 log((\|2 \|5 + \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R +--------+ +--------+ +--R +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R log((- \|2 \|5 - \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--R | +-+ \|- x + 1 \|\|5 - 1 +--R - 4\|\|5 - 1 atanh(----------------------) +--R +-+ +--R \|2 +--R + +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--------+ +--R | +-+ \|- x + 1 \|\|5 + 1 +-+ | 2 +--R 4\|\|5 + 1 atan(----------------------) - 4x\|2 atan(x\|- x + 1 ) +--R +-+ +--R \|2 +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 + 2x\|2 \|- x + 1 +--R - 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (2x - 2)\|2 +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 - 2x\|2 \|- x + 1 +--R 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (- 2x + 2)\|2 +--R + +--R +--------+ +--R | 2 +--R +-+ 2x\|- x + 1 +--R 2x\|2 atan(-------------) +--R 4 2 +--R x - x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 250 +d0050:= D(m0050,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 2x\|- x + 1 +--R - 2atan(x\|- x + 1 ) + atan(-------------) +--R 4 2 +--R x - x + 1 +--R (5) ------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 250 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Charlwood, Kevin +``Integration on Computer Algebra Systems'' +Electronic Journal of Mathematics and Technology (2008) +\verb|www.freepatentsonline.com/article/| +\verb|Electronic-journal-Mathematics-Technology/188213666.html| +\bibitem{2} +Rich, Albert +``Charlwood Integration Problems'' +\verb|www.apmaths.uwo.ca/~arich/CharlwoodIntegrationProblems.pdf| +\end{thebibliography} +\end{document} + +