diff --git a/changelog b/changelog index e73a059..204b9c7 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100617 tpd src/axiom-website/patches.html 20100617.02.tpd.patch +20100617 tpd src/input/Makefile rule-based log integration +20100617 tpd src/input/richlog100-199.input rule-based log integration 20100617 tpd src/axiom-website/patches.html 20100617.01.tpd.patch 20100617 tpd src/input/Makefile rule-based log integration 20100617 tpd src/input/richlog000-099.input rule-based log integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index d3c497b..3d7dbca 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2910,6 +2910,8 @@ src/input/richhyper800-899.input rule-based hyper integration
src/input/richhyper900-999.input rule-based hyper integration
20100617.01.tpd.patch src/input/richlog000-099.input rule-based log integration
+20100617.02.tpd.patch +src/input/richlog100-199.input rule-based log integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 00909ed..180cd29 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -387,6 +387,7 @@ REGRES= ackermann.regress \ richhyper900-999.regress \ richhyper1000-1098.regress \ richlog000-099.regress \ + richlog100-199.regress \ richrational.regress \ richtrig000-099.regress \ richtrig100-199.regress \ @@ -728,6 +729,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richhyper900-999.input \ ${OUT}/richhyper1000-1098.input \ ${OUT}/richlog000-099.input \ + ${OUT}/richlog100-199.input \ ${OUT}/richrational.input \ ${OUT}/richtrig000-099.input \ ${OUT}/richtrig100-199.input \ @@ -1098,6 +1100,7 @@ DOCFILES= \ ${DOC}/richhyper900-999.input.dvi \ ${DOC}/richhyper1000-1098.input.dvi \ ${DOC}/richlog000-099.input.dvi \ + ${DOC}/richlog100-199.input.dvi \ ${DOC}/richrational.input.dvi \ ${DOC}/richtrig000-099.input.dvi \ ${DOC}/richtrig100-199.input.dvi \ diff --git a/src/input/richlog100-199.input.pamphlet b/src/input/richlog100-199.input.pamphlet new file mode 100644 index 0000000..abf534d --- /dev/null +++ b/src/input/richlog100-199.input.pamphlet @@ -0,0 +1,7844 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richlog100-199.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richlog100-199.output +)spool richlog100-199.output +)set message auto off +)clear all + +--S 1 of 518 +t0100:= (a+b*log(c*x^n))^m +--R +--R +--R n m +--R (1) (b log(c x ) + a) +--R Type: Expression Integer +--E 1 + +--S 2 of 518 +r0100:= x*Gamma(1+m,-(a+b*log(c*x^n))/b/n)*(a+b*log(c*x^n))^m*_ + exp(-a/b/n)*(c*x^n)^(-1/n)*(-(a+b*log(c*x^n))/b/n)^(-m) +--R +--R +--R (2) +--R a 1 +--R - --- - - n - m +--R b n n n - b log(c x ) - a n m +--R x %e (c x ) (-----------------) (b log(c x ) + a) +--R b n +--R * +--R n +--R _ - b log(c x ) - a +--R | (m + 1,-----------------) +--R b n +--R Type: Expression Integer +--E 2 + +--S 3 of 518 +a0100:= integrate(t0100,x) +--R +--R +--R x +--R ++ n m +--R (3) | (b log(c %L ) + a) d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 518 +m0100:= a0100-r0100 +--R +--R +--R (4) +--R x +--R ++ n m +--R | (b log(c %L ) + a) d%L +--R ++ +--R + +--R - +--R a 1 +--R - --- - - n - m +--R b n n n - b log(c x ) - a n m +--R x %e (c x ) (-----------------) (b log(c x ) + a) +--R b n +--R * +--R n +--R _ - b log(c x ) - a +--R | (m + 1,-----------------) +--R b n +--R Type: Expression Integer +--E 4 + +--S 5 of 518 +d0100:= D(m0100,x) +--R +--R +--R (5) +--R a 1 a - n - 1 +--R - --- - - - --- ------- +--R b n n n n b n n - 1 n n n +--R (- %e x (c x ) + c x %e x x (c x ) ) +--R * +--R n - m +--R - b log(c x ) - a +--R (-----------------) +--R b n +--R + +--R a 1 +--R - --- - - n - m - 1 +--R b n n - 1 n n - b log(c x ) - a +--R - m x %e x (c x ) (-----------------) +--R b n +--R * +--R n m +--R (b log(c x ) + a) +--R + +--R - +--R a 1 +--R - --- - - n - m +--R b n n - 1 n n - b log(c x ) - a +--R b m n x %e x (c x ) (-----------------) +--R b n +--R * +--R n m - 1 +--R (b log(c x ) + a) +--R * +--R n +--R _ - b log(c x ) - a +--R | (m + 1,-----------------) +--R b n +--R + +--R - +--R n +--R a 1 b log(c x ) + a +--R - --- - - --------------- n - m +--R b n n - 1 n n b n - b log(c x ) - a +--R x %e x (c x ) %e (-----------------) +--R b n +--R * +--R n m +--R - b log(c x ) - a +--R (-----------------) +--R b n +--R + +--R n +--R x +--R * +--R n m +--R (b log(c x ) + a) +--R / +--R n +--R x +--R Type: Expression Integer +--E 5 + +--S 6 of 518 +t0101:= x^m/(a+b*log(c*x^n)) +--R +--R +--R m +--R x +--R (6) --------------- +--R n +--R b log(c x ) + a +--R Type: Expression Integer +--E 6 + +--S 7 of 518 +r0101:= x^(1+m)*Ei((1+m)*(a+b*log(c*x^n))/b/n)*exp(-a*(1+m)/b/n)*_ + (c*x^n)^(-(1+m)/n)/b/n +--R +--R +--R - a m - a - m - 1 +--R --------- ------- n +--R b n m + 1 n n (b m + b)log(c x ) + a m + a +--R %e x (c x ) Ei(----------------------------) +--R b n +--R (7) -------------------------------------------------------------- +--R b n +--R Type: Expression Integer +--E 7 + +--S 8 of 518 +a0101:= integrate(t0101,x) +--R +--R +--R x m +--R ++ %L +--R (8) | ---------------- d%L +--R ++ n +--R b log(c %L ) + a +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 518 +--m0101:= a0101-r0101 +--E 9 + +--S 10 of 518 +--d0101:= D(m0101,x) +--E 10 + +--S 11 of 518 +t0102:= x^m/(a+b*log(c*x^n))^2 +--R +--R +--R m +--R x +--R (9) ---------------------------------- +--R 2 n 2 n 2 +--R b log(c x ) + 2a b log(c x ) + a +--R Type: Expression Integer +--E 11 + +--S 12 of 518 +r0102:= (1+m)*x^(1+m)*Ei((1+m)*(a+b*log(c*x^n))/b/n)/_ + (exp(1)^(a*(1+m)/b/n))/((c*x^n)^((1+m)/n))/b^2/n^2-x^(1+m)/_ + b/n/(a+b*log(c*x^n)) +--R +--R +--R (10) +--R m + 1 n m + 1 +--R ((b m + b)x log(c x ) + (a m + a)x ) +--R * +--R n +--R (b m + b)log(c x ) + a m + a +--R Ei(----------------------------) +--R b n +--R + +--R a m + a m + 1 +--R ------- ----- +--R b n m + 1 n n +--R - b n %e x (c x ) +--R / +--R a m + a a m + a m + 1 +--R ------- ------- ----- +--R 3 2 b n n 2 2 b n n n +--R (b n %e log(c x ) + a b n %e )(c x ) +--R Type: Expression Integer +--E 12 + +--S 13 of 518 +a0102:= integrate(t0102,x) +--R +--R +--R x m +--R ++ %L +--R (11) | ------------------------------------ d%L +--R ++ 2 n 2 n 2 +--R b log(c %L ) + 2a b log(c %L ) + a +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 518 +--m0102:= a0102-r0102 +--E 14 + +--S 15 of 518 +--d0102:= D(m0102,x) +--E 15 + +--S 16 of 518 +t0103:= x^m*(a+b*log(c*x^n))^p +--R +--R +--R m n p +--R (12) x (b log(c x ) + a) +--R Type: Expression Integer +--E 16 + +--S 17 of 518 +r0103:= x^(1+m)*Gamma(p+1,-(1+m)*(a+b*log(c*x^n))/b/n)*_ + (a+b*log(c*x^n))^p*exp(-a*(1+m)/b/n)*(c*x^n)^(-(1+m)/n)*_ + (-(1+m)*(a+b*log(c*x^n))/b/n)^(-p)/(1+m) +--R +--R +--R (13) +--R - a m - a - m - 1 +--R --------- ------- n - p +--R b n m + 1 n n (- b m - b)log(c x ) - a m - a +--R %e x (c x ) (------------------------------) +--R b n +--R * +--R n +--R n p _ (- b m - b)log(c x ) - a m - a +--R (b log(c x ) + a) | (p + 1,------------------------------) +--R b n +--R / +--R m + 1 +--R Type: Expression Integer +--E 17 + +--S 18 of 518 +a0103:= integrate(t0103,x) +--R +--R +--R x +--R ++ m n p +--R (14) | %L (b log(c %L ) + a) d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 518 +--m0103:= a0103-r0103 +--E 19 + +--S 20 of 518 +--d0103:= D(m0103,x) +--E 20 + +--S 21 of 518 +t0104:= x^4*log(c*(a+b*x)^n) +--R +--R +--R 4 n +--R (15) x log(c (b x + a) ) +--R Type: Expression Integer +--E 21 + +--S 22 of 518 +r0104:= 1/300/b^5*(-60*a^4*n*x*b+30*a^3*n*x^2*b^2-20*a^2*n*x^3*b^3+_ + 15*a*n*x^4*b^4-12*n*x^5*b^5+60*a^5*n*log(a+b*x)+_ + 60*x^5*log(c*(a+b*x)^n)*b^5) +--R +--R +--R (16) +--R 5 5 n 5 5 5 4 4 +--R 60b x log(c (b x + a) ) + 60a n log(b x + a) - 12b n x + 15a b n x +--R + +--R 2 3 3 3 2 2 4 +--R - 20a b n x + 30a b n x - 60a b n x +--R / +--R 5 +--R 300b +--R Type: Expression Integer +--E 22 + +--S 23 of 518 +a0104:= integrate(t0104,x) +--R +--R +--R (17) +--R 5 5 5 5 5 5 5 4 4 +--R (60b n x + 60a n)log(b x + a) + 60b x log(c) - 12b n x + 15a b n x +--R + +--R 2 3 3 3 2 2 4 +--R - 20a b n x + 30a b n x - 60a b n x +--R / +--R 5 +--R 300b +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 518 +m0104:= a0104-r0104 +--R +--R +--R 5 n 5 5 +--R - x log(c (b x + a) ) + n x log(b x + a) + x log(c) +--R (18) --------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 24 + +--S 25 of 518 +d0104:= D(m0104,x) +--R +--R +--R (19) +--R 5 4 n n +--R (- 5b x - 5a x )(b x + a) log(c (b x + a) ) +--R + +--R 5 4 5 4 5 +--R ((5b n x + 5a n x )log(b x + a) + (5b x + 5a x )log(c) + b n x ) +--R * +--R n +--R (b x + a) +--R + +--R 2 6 5 n - 1 +--R (- b n x - a b n x )(b x + a) +--R / +--R n +--R (5b x + 5a)(b x + a) +--R Type: Expression Integer +--E 25 + +--S 26 of 518 +t0105:= x^3*log(c*(a+b*x)^n) +--R +--R +--R 3 n +--R (20) x log(c (b x + a) ) +--R Type: Expression Integer +--E 26 + +--S 27 of 518 +r0105:= -1/48/b^4*(-12*x*a^3*n*b+6*a^2*b^2*n*x^2-4*a*b^3*n*x^3+_ + 3*b^4*n*x^4+12*a^4*n*log(a+b*x)-12*x^4*log(c*(a+b*x)^n)*b^4) +--R +--R +--R (21) +--R 4 4 n 4 4 4 3 3 +--R 12b x log(c (b x + a) ) - 12a n log(b x + a) - 3b n x + 4a b n x +--R + +--R 2 2 2 3 +--R - 6a b n x + 12a b n x +--R / +--R 4 +--R 48b +--R Type: Expression Integer +--E 27 + +--S 28 of 518 +a0105:= integrate(t0105,x) +--R +--R +--R (22) +--R 4 4 4 4 4 4 4 3 3 +--R (12b n x - 12a n)log(b x + a) + 12b x log(c) - 3b n x + 4a b n x +--R + +--R 2 2 2 3 +--R - 6a b n x + 12a b n x +--R / +--R 4 +--R 48b +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 518 +m0105:= a0105-r0105 +--R +--R +--R 4 n 4 4 +--R - x log(c (b x + a) ) + n x log(b x + a) + x log(c) +--R (23) --------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 29 + +--S 30 of 518 +d0105:= D(m0105,x) +--R +--R +--R (24) +--R 4 3 n n +--R (- 4b x - 4a x )(b x + a) log(c (b x + a) ) +--R + +--R 4 3 4 3 4 +--R ((4b n x + 4a n x )log(b x + a) + (4b x + 4a x )log(c) + b n x ) +--R * +--R n +--R (b x + a) +--R + +--R 2 5 4 n - 1 +--R (- b n x - a b n x )(b x + a) +--R / +--R n +--R (4b x + 4a)(b x + a) +--R Type: Expression Integer +--E 30 + +--S 31 of 518 +t0106:= x^2*log(c*(a+b*x)^n) +--R +--R +--R 2 n +--R (25) x log(c (b x + a) ) +--R Type: Expression Integer +--E 31 + +--S 32 of 518 +r0106:= 1/18/b^3*(-6*n*b*x*a^2+3*a*b^2*n*x^2-2*b^3*n*x^3+_ + 6*a^3*n*log(a+b*x)+6*x^3*log(c*(a+b*x)^n)*b^3) +--R +--R +--R (26) +--R 3 3 n 3 3 3 2 2 2 +--R 6b x log(c (b x + a) ) + 6a n log(b x + a) - 2b n x + 3a b n x - 6a b n x +--R --------------------------------------------------------------------------- +--R 3 +--R 18b +--R Type: Expression Integer +--E 32 + +--S 33 of 518 +a0106:= integrate(t0106,x) +--R +--R +--R (27) +--R 3 3 3 3 3 3 3 2 2 2 +--R (6b n x + 6a n)log(b x + a) + 6b x log(c) - 2b n x + 3a b n x - 6a b n x +--R --------------------------------------------------------------------------- +--R 3 +--R 18b +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 518 +m0106:= a0106-r0106 +--R +--R +--R 3 n 3 3 +--R - x log(c (b x + a) ) + n x log(b x + a) + x log(c) +--R (28) --------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 34 + +--S 35 of 518 +d0106:= D(m0106,x) +--R +--R +--R (29) +--R 3 2 n n +--R (- 3b x - 3a x )(b x + a) log(c (b x + a) ) +--R + +--R 3 2 3 2 3 +--R ((3b n x + 3a n x )log(b x + a) + (3b x + 3a x )log(c) + b n x ) +--R * +--R n +--R (b x + a) +--R + +--R 2 4 3 n - 1 +--R (- b n x - a b n x )(b x + a) +--R / +--R n +--R (3b x + 3a)(b x + a) +--R Type: Expression Integer +--E 35 + +--S 36 of 518 +t0107:= log(c*(a+b*x)^n)/x +--R +--R +--R n +--R log(c (b x + a) ) +--R (30) ----------------- +--R x +--R Type: Expression Integer +--E 36 + +--S 37 of 518 +r0107:= log(-b*x/a)*log(c*(a+b*x)^n)+n*polylog(2,1+b*x/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 37 + +--S 38 of 518 +a0107:= integrate(t0107,x) +--R +--R +--R x n +--R ++ log(c (%L b + a) ) +--R (31) | ------------------ d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 518 +--m0107:= a0107-r0107 +--E 39 + +--S 40 of 518 +--d0107:= D(m0107,x) +--E 40 + +--S 41 of 518 +t0108:= log(c*(a+b*x)^n)/x^2 +--R +--R +--R n +--R log(c (b x + a) ) +--R (32) ----------------- +--R 2 +--R x +--R Type: Expression Integer +--E 41 + +--S 42 of 518 +r0108:= b*n*log(x)/a-b*n*log(a+b*x)/a-log(c*(a+b*x)^n)/x +--R +--R +--R n +--R - a log(c (b x + a) ) - b n x log(b x + a) + b n x log(x) +--R (33) --------------------------------------------------------- +--R a x +--R Type: Expression Integer +--E 42 + +--S 43 of 518 +a0108:= integrate(t0108,x) +--R +--R +--R (- b n x - a n)log(b x + a) + b n x log(x) - a log(c) +--R (34) ----------------------------------------------------- +--R a x +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 518 +m0108:= a0108-r0108 +--R +--R +--R n +--R log(c (b x + a) ) - n log(b x + a) - log(c) +--R (35) ------------------------------------------- +--R x +--R Type: Expression Integer +--E 44 + +--S 45 of 518 +d0108:= D(m0108,x) +--R +--R +--R (36) +--R n n +--R (- b x - a)(b x + a) log(c (b x + a) ) +--R + +--R n +--R ((b n x + a n)log(b x + a) + (b x + a)log(c) - b n x)(b x + a) +--R + +--R 2 2 n - 1 +--R (b n x + a b n x)(b x + a) +--R / +--R 3 2 n +--R (b x + a x )(b x + a) +--R Type: Expression Integer +--E 45 + +--S 46 of 518 +t0109:= log(c*(a+b*x)^n)/x^3 +--R +--R +--R n +--R log(c (b x + a) ) +--R (37) ----------------- +--R 3 +--R x +--R Type: Expression Integer +--E 46 + +--S 47 of 518 +r0109:= -1/2/a^2/x^2*(a*b*n*x+b^2*n*log(x)*x^2-b^2*n*log(a+b*x)*x^2+_ + log(c*(a+b*x)^n)*a^2) +--R +--R +--R 2 n 2 2 2 2 +--R - a log(c (b x + a) ) + b n x log(b x + a) - b n x log(x) - a b n x +--R (38) ------------------------------------------------------------------- +--R 2 2 +--R 2a x +--R Type: Expression Integer +--E 47 + +--S 48 of 518 +a0109:= integrate(t0109,x) +--R +--R +--R 2 2 2 2 2 2 +--R (b n x - a n)log(b x + a) - b n x log(x) - a log(c) - a b n x +--R (39) -------------------------------------------------------------- +--R 2 2 +--R 2a x +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 518 +m0109:= a0109-r0109 +--R +--R +--R n +--R log(c (b x + a) ) - n log(b x + a) - log(c) +--R (40) ------------------------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 49 + +--S 50 of 518 +d0109:= D(m0109,x) +--R +--R +--R (41) +--R n n +--R (- 2b x - 2a)(b x + a) log(c (b x + a) ) +--R + +--R n +--R ((2b n x + 2a n)log(b x + a) + (2b x + 2a)log(c) - b n x)(b x + a) +--R + +--R 2 2 n - 1 +--R (b n x + a b n x)(b x + a) +--R / +--R 4 3 n +--R (2b x + 2a x )(b x + a) +--R Type: Expression Integer +--E 50 + +--S 51 of 518 +t0110:= log(c*(a+b*x)^n)/x^4 +--R +--R +--R n +--R log(c (b x + a) ) +--R (42) ----------------- +--R 4 +--R x +--R Type: Expression Integer +--E 51 + +--S 52 of 518 +r0110:= 1/6/a^3/x^3*(-n*b*x*a^2+2*a*b^2*n*x^2+2*b^3*n*log(x)*x^3-_ + 2*b^3*n*log(a+b*x)*x^3-2*log(c*(a+b*x)^n)*a^3) +--R +--R +--R (43) +--R 3 n 3 3 3 3 2 2 +--R - 2a log(c (b x + a) ) - 2b n x log(b x + a) + 2b n x log(x) + 2a b n x +--R + +--R 2 +--R - a b n x +--R / +--R 3 3 +--R 6a x +--R Type: Expression Integer +--E 52 + +--S 53 of 518 +a0110:= integrate(t0110,x) +--R +--R +--R (44) +--R 3 3 3 3 3 3 2 2 +--R (- 2b n x - 2a n)log(b x + a) + 2b n x log(x) - 2a log(c) + 2a b n x +--R + +--R 2 +--R - a b n x +--R / +--R 3 3 +--R 6a x +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 518 +m0110:= a0110-r0110 +--R +--R +--R n +--R log(c (b x + a) ) - n log(b x + a) - log(c) +--R (45) ------------------------------------------- +--R 3 +--R 3x +--R Type: Expression Integer +--E 54 + +--S 55 of 518 +d0110:= D(m0110,x) +--R +--R +--R (46) +--R n n +--R (- 3b x - 3a)(b x + a) log(c (b x + a) ) +--R + +--R n +--R ((3b n x + 3a n)log(b x + a) + (3b x + 3a)log(c) - b n x)(b x + a) +--R + +--R 2 2 n - 1 +--R (b n x + a b n x)(b x + a) +--R / +--R 5 4 n +--R (3b x + 3a x )(b x + a) +--R Type: Expression Integer +--E 55 + +--S 56 of 518 +t0111:= x^4*log(c*(a+b*x^2)^n) +--R +--R +--R 4 2 n +--R (47) x log(c (b x + a) ) +--R Type: Expression Integer +--E 56 + +--S 57 of 518 +r0111:= -2/5*a^2*n*x/b^2+2/15*a*n*x^3/b-2/25*n*x^5+_ + 2/5*a^(5/2)*n*atan(b^(1/2)*x/a^(1/2))/b^(5/2)+_ + 1/5*x^5*log(c*(a+b*x^2)^n) +--R +--R +--R (48) +--R +-+ +--R 2 5 +-+ 2 n 2 +-+ x\|b +--R 15b x \|b log(c (b x + a) ) + 30a n\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 3 2 +-+ +--R (- 6b n x + 10a b n x - 30a n x)\|b +--R / +--R 2 +-+ +--R 75b \|b +--R Type: Expression Integer +--E 57 + +--S 58 of 518 +a0111:= integrate(t0111,x) +--R +--R +--R (49) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 2 | a \| b 2 5 2 +--R 15a n |- - log(---------------------) + 15b n x log(b x + a) +--R \| b 2 +--R b x + a +--R + +--R 2 5 2 5 3 2 +--R 15b x log(c) - 6b n x + 10a b n x - 30a n x +--R / +--R 2 +--R 75b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 2 |a \|b 2 5 2 2 5 2 5 +--R - 30a n |- atan(----) + 15b n x log(b x + a) + 15b x log(c) - 6b n x +--R \|b x +--R + +--R 3 2 +--R 10a b n x - 30a n x +--R / +--R 2 +--R 75b +--R ] +--R Type: Union(List Expression Integer,...) +--E 58 + +--S 59 of 518 +m0111a:= a0111.1-r0111 +--R +--R +--R (50) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 2 | a +-+ \| b 2 5 +-+ 2 n +--R a n |- - \|b log(---------------------) - b x \|b log(c (b x + a) ) +--R \| b 2 +--R b x + a +--R + +--R +-+ +--R 2 +-+ x\|b 2 5 2 2 5 +-+ +--R - 2a n\|a atan(-----) + (b n x log(b x + a) + b x log(c))\|b +--R +-+ +--R \|a +--R / +--R 2 +-+ +--R 5b \|b +--R Type: Expression Integer +--E 59 + +--S 60 of 518 +d0111a:= D(m0111a,x) +--R +--R +--R (51) +--R 6 4 2 n 2 n +--R (- 5b x - 5a x )(b x + a) log(c (b x + a) ) +--R + +--R 6 4 2 6 4 6 +--R ((5b n x + 5a n x )log(b x + a) + (5b x + 5a x )log(c) + 2b n x ) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 8 6 2 n - 1 +--R (- 2b n x - 2a b n x )(b x + a) +--R / +--R 2 2 n +--R (5b x + 5a)(b x + a) +--R Type: Expression Integer +--E 60 + +--S 61 of 518 +m0111b:= a0111.2-r0111 +--R +--R +--R (52) +--R +-+ +--R 2 5 +-+ 2 n 2 +-+ x\|b +--R - b x \|b log(c (b x + a) ) - 2a n\|a atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R |a +--R +-+ |- +--R 2 |a +-+ \|b 2 5 2 2 5 +-+ +--R - 2a n |- \|b atan(----) + (b n x log(b x + a) + b x log(c))\|b +--R \|b x +--R / +--R 2 +-+ +--R 5b \|b +--R Type: Expression Integer +--E 61 + +--S 62 of 518 +d0111b:= D(m0111b,x) +--R +--R +--R (53) +--R 6 4 2 n 2 n +--R (- 5b x - 5a x )(b x + a) log(c (b x + a) ) +--R + +--R 6 4 2 6 4 6 +--R ((5b n x + 5a n x )log(b x + a) + (5b x + 5a x )log(c) + 2b n x ) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 8 6 2 n - 1 +--R (- 2b n x - 2a b n x )(b x + a) +--R / +--R 2 2 n +--R (5b x + 5a)(b x + a) +--R Type: Expression Integer +--E 62 + +--S 63 of 518 +t0112:= x^3*log(c*(a+b*x^2)^n) +--R +--R +--R 3 2 n +--R (54) x log(c (b x + a) ) +--R Type: Expression Integer +--E 63 + +--S 64 of 518 +r0112:= 1/4*a*n*x^2/b-1/8*n*x^4-1/4*a^2*n*log(a+b*x^2)/b^2+_ + 1/4*x^4*log(c*(a+b*x^2)^n) +--R +--R +--R 2 4 2 n 2 2 2 4 2 +--R 2b x log(c (b x + a) ) - 2a n log(b x + a) - b n x + 2a b n x +--R (55) ----------------------------------------------------------------- +--R 2 +--R 8b +--R Type: Expression Integer +--E 64 + +--S 65 of 518 +a0112:= integrate(t0112,x) +--R +--R +--R 2 4 2 2 2 4 2 4 2 +--R (2b n x - 2a n)log(b x + a) + 2b x log(c) - b n x + 2a b n x +--R (56) ---------------------------------------------------------------- +--R 2 +--R 8b +--R Type: Union(Expression Integer,...) +--E 65 + +--S 66 of 518 +m0112:= a0112-r0112 +--R +--R +--R 4 2 n 4 2 4 +--R - x log(c (b x + a) ) + n x log(b x + a) + x log(c) +--R (57) ----------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 66 + +--S 67 of 518 +d0112:= D(m0112,x) +--R +--R +--R (58) +--R 5 3 2 n 2 n +--R (- 2b x - 2a x )(b x + a) log(c (b x + a) ) +--R + +--R 5 3 2 5 3 5 +--R ((2b n x + 2a n x )log(b x + a) + (2b x + 2a x )log(c) + b n x ) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 7 5 2 n - 1 +--R (- b n x - a b n x )(b x + a) +--R / +--R 2 2 n +--R (2b x + 2a)(b x + a) +--R Type: Expression Integer +--E 67 + +--S 68 of 518 +t0113:= x^2*log(c*(a+b*x^2)^n) +--R +--R +--R 2 2 n +--R (59) x log(c (b x + a) ) +--R Type: Expression Integer +--E 68 + +--S 69 of 518 +r0113:= 2/3*a*n*x/b-2/9*n*x^3-2/3*a^(3/2)*n*atan(b^(1/2)*x/a^(1/2))/b^(3/2)+_ + 1/3*x^3*log(c*(a+b*x^2)^n) +--R +--R +--R (60) +--R +-+ +--R 3 +-+ 2 n +-+ x\|b 3 +-+ +--R 3b x \|b log(c (b x + a) ) - 6a n\|a atan(-----) + (- 2b n x + 6a n x)\|b +--R +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +--R 9b\|b +--R Type: Expression Integer +--E 69 + +--S 70 of 518 +a0113:= integrate(t0113,x) +--R +--R +--R (61) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R | a \| b 3 2 +--R 3a n |- - log(-----------------------) + 3b n x log(b x + a) +--R \| b 2 +--R b x + a +--R + +--R 3 3 +--R 3b x log(c) - 2b n x + 6a n x +--R / +--R 9b +--R , +--R +-+ +--R |a +--R +-+ |- +--R |a \|b 3 2 3 3 +--R 6a n |- atan(----) + 3b n x log(b x + a) + 3b x log(c) - 2b n x + 6a n x +--R \|b x +--R --------------------------------------------------------------------------] +--R 9b +--R Type: Union(List Expression Integer,...) +--E 70 + +--S 71 of 518 +m0113a:= a0113.1-r0113 +--R +--R +--R (62) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 3 +-+ 2 n | a +-+ \| b +--R - b x \|b log(c (b x + a) ) + a n |- - \|b log(-----------------------) +--R \| b 2 +--R b x + a +--R + +--R +-+ +--R +-+ x\|b 3 2 3 +-+ +--R 2a n\|a atan(-----) + (b n x log(b x + a) + b x log(c))\|b +--R +-+ +--R \|a +--R / +--R +-+ +--R 3b\|b +--R Type: Expression Integer +--E 71 + +--S 72 of 518 +d0113a:= D(m0113a,x) +--R +--R +--R (63) +--R 4 2 2 n 2 n +--R (- 3b x - 3a x )(b x + a) log(c (b x + a) ) +--R + +--R 4 2 2 4 2 4 +--R ((3b n x + 3a n x )log(b x + a) + (3b x + 3a x )log(c) + 2b n x ) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 6 4 2 n - 1 +--R (- 2b n x - 2a b n x )(b x + a) +--R / +--R 2 2 n +--R (3b x + 3a)(b x + a) +--R Type: Expression Integer +--E 72 + +--S 73 of 518 +m0113b:= a0113.2-r0113 +--R +--R +--R (64) +--R +-+ +--R 3 +-+ 2 n +-+ x\|b +--R - b x \|b log(c (b x + a) ) + 2a n\|a atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R |a +--R +-+ |- +--R |a +-+ \|b 3 2 3 +-+ +--R 2a n |- \|b atan(----) + (b n x log(b x + a) + b x log(c))\|b +--R \|b x +--R / +--R +-+ +--R 3b\|b +--R Type: Expression Integer +--E 73 + +--S 74 of 518 +d0113b:= D(m0113b,x) +--R +--R +--R (65) +--R 4 2 2 n 2 n +--R (- 3b x - 3a x )(b x + a) log(c (b x + a) ) +--R + +--R 4 2 2 4 2 4 +--R ((3b n x + 3a n x )log(b x + a) + (3b x + 3a x )log(c) + 2b n x ) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 6 4 2 n - 1 +--R (- 2b n x - 2a b n x )(b x + a) +--R / +--R 2 2 n +--R (3b x + 3a)(b x + a) +--R Type: Expression Integer +--E 74 + +--S 75 of 518 +t0114:= x*log(c*(a+b*x^2)^n) +--R +--R +--R 2 n +--R (66) x log(c (b x + a) ) +--R Type: Expression Integer +--E 75 + +--S 76 of 518 +r0114:= -1/2*n*x^2+1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)/b +--R +--R +--R 2 2 n 2 +--R (b x + a)log(c (b x + a) ) - b n x +--R (67) ------------------------------------- +--R 2b +--R Type: Expression Integer +--E 76 + +--S 77 of 518 +a0114:= integrate(t0114,x) +--R +--R +--R 2 2 2 2 +--R (b n x + a n)log(b x + a) + b x log(c) - b n x +--R (68) ------------------------------------------------- +--R 2b +--R Type: Union(Expression Integer,...) +--E 77 + +--S 78 of 518 +m0114:= a0114-r0114 +--R +--R +--R (69) +--R 2 2 n 2 2 2 +--R (- b x - a)log(c (b x + a) ) + (b n x + a n)log(b x + a) + b x log(c) +--R ------------------------------------------------------------------------- +--R 2b +--R Type: Expression Integer +--E 78 + +--S 79 of 518 +d0114:= D(m0114,x) +--R +--R +--R (70) +--R 2 n 2 n +--R - x (b x + a) log(c (b x + a) ) +--R + +--R 2 2 n +--R (n x log(b x + a) + x log(c) + n x)(b x + a) +--R + +--R 3 2 n - 1 +--R (- b n x - a n x)(b x + a) +--R / +--R 2 n +--R (b x + a) +--R Type: Expression Integer +--E 79 + +--S 80 of 518 +t0115:= log(c*(a+b*x^2)^n)/x +--R +--R +--R 2 n +--R log(c (b x + a) ) +--R (71) ------------------ +--R x +--R Type: Expression Integer +--E 80 + +--S 81 of 518 +r0115:= 1/2*log(-b*x^2/a)*log(c*(a+b*x^2)^n)+1/2*n*polylog(2,1+b*x^2/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 81 + +--S 82 of 518 +a0115:= integrate(t0115,x) +--R +--R +--R x 2 n +--R ++ log(c (%L b + a) ) +--R (72) | ------------------ d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 82 + +--S 83 of 518 +m0115a:= a0115.1-r0115 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 83 + +--S 84 of 518 +d0115a:= D(m0115a,x) +--R +--R +--R (73) 0 +--R Type: Polynomial Integer +--E 84 + +--S 85 of 518 +m0115b:= a0115.2-r0115 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 85 + +--S 86 of 518 +d0115b:= D(m0115b,x) +--R +--R +--R (74) 0 +--R Type: Polynomial Integer +--E 86 + +--S 87 of 518 +t0116:= log(c*(a+b*x^2)^n)/x^2 +--R +--R +--R 2 n +--R log(c (b x + a) ) +--R (75) ------------------ +--R 2 +--R x +--R Type: Expression Integer +--E 87 + +--S 88 of 518 +r0116:= 2*b^(1/2)*n*atan(b^(1/2)*x/a^(1/2))/a^(1/2)-log(c*(a+b*x^2)^n)/x +--R +--R +--R +-+ +--R +-+ 2 n +-+ x\|b +--R - \|a log(c (b x + a) ) + 2n x\|b atan(-----) +--R +-+ +--R \|a +--R (76) ---------------------------------------------- +--R +-+ +--R x\|a +--R Type: Expression Integer +--E 88 + +--S 89 of 518 +a0116:= integrate(t0116,x) +--R +--R +--R (77) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R | b \| a 2 +--R n x |- - log(---------------------) - n log(b x + a) - log(c) +--R \| a 2 +--R b x + a +--R [--------------------------------------------------------------, +--R x +--R +-+ +--R |b +--R +-+ a |- +--R |b \|a 2 +--R - 2n x |- atan(-----) - n log(b x + a) - log(c) +--R \|a b x +--R ------------------------------------------------] +--R x +--R Type: Union(List Expression Integer,...) +--E 89 + +--S 90 of 518 +m0116a:= a0116.1-r0116 +--R +--R +--R (78) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R | b +-+ \| a +-+ 2 n +--R n x |- - \|a log(---------------------) + \|a log(c (b x + a) ) +--R \| a 2 +--R b x + a +--R + +--R +-+ +--R +-+ x\|b 2 +-+ +--R - 2n x\|b atan(-----) + (- n log(b x + a) - log(c))\|a +--R +-+ +--R \|a +--R / +--R +-+ +--R x\|a +--R Type: Expression Integer +--E 90 + +--S 91 of 518 +d0116a:= D(m0116a,x) +--R +--R +--R (79) +--R 2 2 n 2 n +--R (- b x - a)(b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 2 2 n +--R ((b n x + a n)log(b x + a) + (b x + a)log(c) - 2b n x )(b x + a) +--R + +--R 2 4 2 2 n - 1 +--R (2b n x + 2a b n x )(b x + a) +--R / +--R 4 2 2 n +--R (b x + a x )(b x + a) +--R Type: Expression Integer +--E 91 + +--S 92 of 518 +m0116b:= a0116.2-r0116 +--R +--R +--R (80) +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ 2 n +-+ x\|b +-+ |b \|a +--R \|a log(c (b x + a) ) - 2n x\|b atan(-----) - 2n x\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R + +--R 2 +-+ +--R (- n log(b x + a) - log(c))\|a +--R / +--R +-+ +--R x\|a +--R Type: Expression Integer +--E 92 + +--S 93 of 518 +d0116b:= D(m0116b,x) +--R +--R +--R (81) +--R 2 2 n 2 n +--R (- b x - a)(b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 2 2 n +--R ((b n x + a n)log(b x + a) + (b x + a)log(c) - 2b n x )(b x + a) +--R + +--R 2 4 2 2 n - 1 +--R (2b n x + 2a b n x )(b x + a) +--R / +--R 4 2 2 n +--R (b x + a x )(b x + a) +--R Type: Expression Integer +--E 93 + +--S 94 of 518 +t0117:= log(c*(a+b*x^2)^n)/x^3 +--R +--R +--R 2 n +--R log(c (b x + a) ) +--R (82) ------------------ +--R 3 +--R x +--R Type: Expression Integer +--E 94 + +--S 95 of 518 +r0117:= b*n*log(x)/a-1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)/a/x^2 +--R +--R +--R 2 2 n 2 +--R (- b x - a)log(c (b x + a) ) + 2b n x log(x) +--R (83) ---------------------------------------------- +--R 2 +--R 2a x +--R Type: Expression Integer +--E 95 + +--S 96 of 518 +a0117:= integrate(t0117,x) +--R +--R +--R 2 2 2 +--R (- b n x - a n)log(b x + a) + 2b n x log(x) - a log(c) +--R (84) -------------------------------------------------------- +--R 2 +--R 2a x +--R Type: Union(Expression Integer,...) +--E 96 + +--S 97 of 518 +m0117:= a0117-r0117 +--R +--R +--R (85) +--R 2 2 n 2 2 +--R (b x + a)log(c (b x + a) ) + (- b n x - a n)log(b x + a) - a log(c) +--R ----------------------------------------------------------------------- +--R 2 +--R 2a x +--R Type: Expression Integer +--E 97 + +--S 98 of 518 +d0117:= D(m0117,x) +--R +--R +--R (86) +--R 2 n 2 n +--R - a (b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 n +--R (a n log(b x + a) + a log(c) - b n x )(b x + a) +--R + +--R 2 4 2 2 n - 1 +--R (b n x + a b n x )(b x + a) +--R / +--R 3 2 n +--R a x (b x + a) +--R Type: Expression Integer +--E 98 + +--S 99 of 518 +t0118:= log(c*(a+b*x^2)^n)/x^4 +--R +--R +--R 2 n +--R log(c (b x + a) ) +--R (87) ------------------ +--R 4 +--R x +--R Type: Expression Integer +--E 99 + +--S 100 of 518 +r0118:= -2/3*b*n/a/x-2/3*b^(3/2)*n*atan(b^(1/2)*x/a^(1/2))/a^(3/2)-1/3*log(c*(a+b*x^2)^n)/x^3 +--R +--R +--R +-+ +--R +-+ 2 n 3 +-+ x\|b 2 +-+ +--R - a\|a log(c (b x + a) ) - 2b n x \|b atan(-----) - 2b n x \|a +--R +-+ +--R \|a +--R (88) ---------------------------------------------------------------- +--R 3 +-+ +--R 3a x \|a +--R Type: Expression Integer +--E 100 + +--S 101 of 518 +a0118:= integrate(t0118,x) +--R +--R +--R (89) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 3 | b \| a 2 +--R b n x |- - log(-----------------------) - a n log(b x + a) - a log(c) +--R \| a 2 +--R b x + a +--R + +--R 2 +--R - 2b n x +--R / +--R 3 +--R 3a x +--R , +--R +-+ +--R |b +--R +-+ a |- +--R 3 |b \|a 2 2 +--R 2b n x |- atan(-----) - a n log(b x + a) - a log(c) - 2b n x +--R \|a b x +--R ---------------------------------------------------------------] +--R 3 +--R 3a x +--R Type: Union(List Expression Integer,...) +--E 101 + +--S 102 of 518 +m0118a:= a0118.1-r0118 +--R +--R +--R (90) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R +-+ 2 n 3 | b +-+ \| a +--R a\|a log(c (b x + a) ) + b n x |- - \|a log(-----------------------) +--R \| a 2 +--R b x + a +--R + +--R +-+ +--R 3 +-+ x\|b 2 +-+ +--R 2b n x \|b atan(-----) + (- a n log(b x + a) - a log(c))\|a +--R +-+ +--R \|a +--R / +--R 3 +-+ +--R 3a x \|a +--R Type: Expression Integer +--E 102 + +--S 103 of 518 +d0118a:= D(m0118a,x) +--R +--R +--R (91) +--R 2 2 n 2 n +--R (- 3b x - 3a)(b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 2 2 n +--R ((3b n x + 3a n)log(b x + a) + (3b x + 3a)log(c) - 2b n x )(b x + a) +--R + +--R 2 4 2 2 n - 1 +--R (2b n x + 2a b n x )(b x + a) +--R / +--R 6 4 2 n +--R (3b x + 3a x )(b x + a) +--R Type: Expression Integer +--E 103 + +--S 104 of 518 +m0118b:= a0118.2-r0118 +--R +--R +--R (92) +--R +-+ +--R +-+ 2 n 3 +-+ x\|b +--R a\|a log(c (b x + a) ) + 2b n x \|b atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R |b +--R +-+ a |- +--R 3 +-+ |b \|a 2 +-+ +--R 2b n x \|a |- atan(-----) + (- a n log(b x + a) - a log(c))\|a +--R \|a b x +--R / +--R 3 +-+ +--R 3a x \|a +--R Type: Expression Integer +--E 104 + +--S 105 of 518 +d0118b:= D(m0118b,x) +--R +--R +--R (93) +--R 2 2 n 2 n +--R (- 3b x - 3a)(b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 2 2 n +--R ((3b n x + 3a n)log(b x + a) + (3b x + 3a)log(c) - 2b n x )(b x + a) +--R + +--R 2 4 2 2 n - 1 +--R (2b n x + 2a b n x )(b x + a) +--R / +--R 6 4 2 n +--R (3b x + 3a x )(b x + a) +--R Type: Expression Integer +--E 105 + +--S 106 of 518 +t0119:= x^4*log(c*(a+b*x^3)^n) +--R +--R +--R 4 3 n +--R (94) x log(c (b x + a) ) +--R Type: Expression Integer +--E 106 + +--S 107 of 518 +r0119:= 3/10*a*n*x^2/b-3/25*n*x^5-1/5*3^(1/2)*a^(5/3)*n*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*x*3^(1/2)/a^(1/3))/b^(5/3)+_ + 1/5*a^(5/3)*n*log(a^(1/3)/b^(1/3)+x)/b^(5/3)-_ + 1/10*a^(5/3)*n*log(a^(2/3)/b^(2/3)-a^(1/3)*x/b^(1/3)+x^2)/b^(5/3)+_ + 1/5*x^5*log(c*(a+b*x^3)^n) +--R +--R +--R (95) +--R 5 3+-+2 3 n +--R 10b x \|b log(c (b x + a) ) +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+2 x \|b - x\|a \|b + \|a +--R - 5a n \|a log(---------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R 3+-+2 x\|b + \|a +-+3+-+2 2x\|3 \|b - \|3 \|a +--R 10a n \|a log(------------) - 10a n\|3 \|a atan(---------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R + +--R 5 2 3+-+2 +--R (- 6b n x + 15a n x )\|b +--R / +--R 3+-+2 +--R 50b \|b +--R Type: Expression Integer +--E 107 + +--S 108 of 518 +a0119:= integrate(t0119,x) +--R +--R +--R (96) +--R +--+ +--+2 +--R | 2 | 2 +--R |a |a +--R 10a n |-- log(b |-- + a x) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R |a |a |a 2 +--R - 5a n |-- log(- b x |-- + a |-- + a x ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +--R +--+ b\|3 |-- +--R | 2 3| 2 +--R +-+ |a \|b 5 3 +--R - 10a n\|3 |-- atan(--------------- + 10b n x log(b x + a) +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R b |-- - 2a x +--R 3| 2 +--R \|b +--R + +--R 5 5 2 +--R 10b x log(c) - 6b n x + 15a n x +--R / +--R 50b +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 518 +m0119:= a0119-r0119 +--R +--R +--R (97) +--R +--+ +--+2 +--R | 2 | 2 +--R |a 3+-+2 |a 5 3+-+2 3 n +--R 2a n |-- \|b log(b |-- + a x - 2b x \|b log(c (b x + a) ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 3+-+ 3+-+ +--R 3+-+2 x \|b - x\|a \|b + \|a 3+-+2 x\|b + \|a +--R a n \|a log(---------------------------) - 2a n \|a log(------------) +--R 3+-+2 3+-+ +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R |a 3+-+2 |a |a 2 +--R - a n |-- \|b log(- b x |-- + a |-- + a x ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+2 2x\|3 \|b - \|3 \|a +--R 2a n\|3 \|a atan(---------------------) +--R 3+-+ +--R 3\|a +--R + +--R +--+2 +--R | 2 +--R +-+ |a +--R +--+ b\|3 |-- +--R | 2 3| 2 +--R +-+ |a 3+-+2 \|b +--R - 2a n\|3 |-- \|b atan(---------------) +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R b |-- - 2a x +--R 3| 2 +--R \|b +--R + +--R 5 3 5 3+-+2 +--R (2b n x log(b x + a) + 2b x log(c))\|b +--R / +--R 3+-+2 +--R 10b \|b +--R Type: Expression Integer +--E 109 + +--S 110 of 518 +d0119:= D(m0119,x) +--R +--R +--R (98) +--R 7 4 3 n 3 n +--R (- 5b x - 5a x )(b x + a) log(c (b x + a) ) +--R + +--R 7 4 3 7 4 7 +--R ((5b n x + 5a n x )log(b x + a) + (5b x + 5a x )log(c) + 3b n x ) +--R * +--R 3 n +--R (b x + a) +--R + +--R 2 10 7 3 n - 1 +--R (- 3b n x - 3a b n x )(b x + a) +--R / +--R 3 3 n +--R (5b x + 5a)(b x + a) +--R Type: Expression Integer +--E 110 + +--S 111 of 518 +t0120:= x^3*log(c*(a+b*x^3)^n) +--R +--R +--R 3 3 n +--R (99) x log(c (b x + a) ) +--R Type: Expression Integer +--E 111 + +--S 112 of 518 +r0120:= 3/4*a*n*x/b-3/16*n*x^4-1/4*3^(1/2)*a^(4/3)*n*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*x*3^(1/2)/a^(1/3))/b^(4/3)-_ + 1/4*a^(4/3)*n*log(a^(1/3)/b^(1/3)+x)/b^(4/3)+_ + 1/8*a^(4/3)*n*log(a^(2/3)/b^(2/3)-a^(1/3)*x/b^(1/3)+x^2)/b^(4/3)+_ + 1/4*x^4*log(c*(a+b*x^3)^n) +--R +--R +--R (100) +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 4 3+-+ 3 n 3+-+ x \|b - x\|a \|b + \|a +--R 4b x \|b log(c (b x + a) + 2a n\|a log(---------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R 3+-+ x\|b + \|a +-+3+-+ 2x\|3 \|b - \|3 \|a +--R - 4a n\|a log(------------) - 4a n\|3 \|a atan(---------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R + +--R 4 3+-+ +--R (- 3b n x + 12a n x)\|b +--R / +--R 3+-+ +--R 16b\|b +--R Type: Expression Integer +--E 112 + +--S 113 of 518 +a0120:= integrate(t0120,x) +--R +--R +--R (101) +--R +---+ +---+2 +---+ +---+ +---+ +--R | a | a | a 2 | a | a +--R - 2a n 3|- - log(3|- - + x 3|- - + x + 4a n 3|- - log(- 3|- - + x) +--R \| b \| b \| b \| b \| b +--R + +--R +---+ +--R +-+ | a +--R +---+ \|3 3|- - +--R +-+ | a \| b 4 3 4 +--R 4a n\|3 3|- - atan(----------- + 4b n x log(b x + a) + 4b x log(c) +--R \| b +---+ +--R | a +--R 3|- - + 2x +--R \| b +--R + +--R 4 +--R - 3b n x + 12a n x +--R / +--R 16b +--R Type: Union(Expression Integer,...) +--E 113 + +--S 114 of 518 +m0120:= a0120-r0120 +--R +--R +--R (102) +--R +---+ +---+2 +---+ +--R | a 3+-+ | a | a 2 4 3+-+ 3 n +--R - a n 3|- - \|b log(3|- - + x 3|- - + x - 2b x \|b log(c (b x + a) ) +--R \| b \| b \| b +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 3+-+ 3+-+ +--R 3+-+ x \|b - x\|a \|b + \|a 3+-+ x\|b + \|a +--R - a n\|a log(---------------------------) + 2a n\|a log(------------) +--R 3+-+2 3+-+ +--R \|b \|b +--R + +--R +---+ +---+ +-+3+-+ +-+3+-+ +--R | a 3+-+ | a +-+3+-+ 2x\|3 \|b - \|3 \|a +--R 2a n 3|- - \|b log(- 3|- - + x + 2a n\|3 \|a atan(---------------------) +--R \| b \| b 3+-+ +--R 3\|a +--R + +--R +---+ +--R +-+ | a +--R +---+ \|3 3|- - +--R +-+ | a 3+-+ \| b +--R 2a n\|3 3|- - \|b atan(-----------) +--R \| b +---+ +--R | a +--R 3|- - + 2x +--R \| b +--R + +--R 4 3 4 3+-+ +--R (2b n x log(b x + a) + 2b x log(c))\|b +--R / +--R 3+-+ +--R 8b\|b +--R Type: Expression Integer +--E 114 + +--S 115 of 518 +d0120:= D(m0120,x) +--R +--R +--R (103) +--R 6 3 3 n 3 n +--R (- 4b x - 4a x )(b x + a) log(c (b x + a) ) +--R + +--R 6 3 3 6 3 6 +--R ((4b n x + 4a n x )log(b x + a) + (4b x + 4a x )log(c) + 3b n x ) +--R * +--R 3 n +--R (b x + a) +--R + +--R 2 9 6 3 n - 1 +--R (- 3b n x - 3a b n x )(b x + a) +--R / +--R 3 3 n +--R (4b x + 4a)(b x + a) +--R Type: Expression Integer +--E 115 + +--S 116 of 518 +t0121:= x^2*log(c*(a+b*x^3)^n) +--R +--R +--R 2 3 n +--R (104) x log(c (b x + a) ) +--R Type: Expression Integer +--E 116 + +--S 117 of 518 +r0121:= -1/3*n*x^3+1/3*(a+b*x^3)*log(c*(a+b*x^3)^n)/b +--R +--R +--R 3 3 n 3 +--R (b x + a)log(c (b x + a) ) - b n x +--R (105) ------------------------------------- +--R 3b +--R Type: Expression Integer +--E 117 + +--S 118 of 518 +a0121:= integrate(t0121,x) +--R +--R +--R 3 3 3 3 +--R (b n x + a n)log(b x + a) + b x log(c) - b n x +--R (106) ------------------------------------------------- +--R 3b +--R Type: Union(Expression Integer,...) +--E 118 + +--S 119 of 518 +m0121:= a0121-r0121 +--R +--R +--R (107) +--R 3 3 n 3 3 3 +--R (- b x - a)log(c (b x + a) ) + (b n x + a n)log(b x + a) + b x log(c) +--R ------------------------------------------------------------------------- +--R 3b +--R Type: Expression Integer +--E 119 + +--S 120 of 518 +d0121:= D(m0121,x) +--R +--R +--R (108) +--R 2 3 n 3 n +--R - x (b x + a) log(c (b x + a) ) +--R + +--R 2 3 2 2 3 n +--R (n x log(b x + a) + x log(c) + n x )(b x + a) +--R + +--R 5 2 3 n - 1 +--R (- b n x - a n x )(b x + a) +--R / +--R 3 n +--R (b x + a) +--R Type: Expression Integer +--E 120 + +--S 121 of 518 +t0122:= x*log(c*(a+b*x^3)^n) +--R +--R +--R 3 n +--R (109) x log(c (b x + a) ) +--R Type: Expression Integer +--E 121 + +--S 122 of 518 +r0122:= -3/4*n*x^2+1/2*3^(1/2)*a^(2/3)*n*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*x*3^(1/2)/a^(1/3))/b^(2/3)-_ + 1/2*a^(2/3)*n*log(a^(1/3)/b^(1/3)+x)/b^(2/3)+_ + 1/4*a^(2/3)*n*log(a^(2/3)/b^(2/3)-a^(1/3)*x/b^(1/3)+x^2)/b^(2/3)+_ + 1/2*x^2*log(c*(a+b*x^3)^n) +--R +--R +--R (110) +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 2 3+-+2 3 n 3+-+2 x \|b - x\|a \|b + \|a +--R 2x \|b log(c (b x + a) + n \|a log(---------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R 3+-+2 x\|b + \|a +-+3+-+2 2x\|3 \|b - \|3 \|a +--R - 2n \|a log(------------) + 2n\|3 \|a atan(---------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R + +--R 2 3+-+2 +--R - 3n x \|b +--R / +--R 3+-+2 +--R 4\|b +--R Type: Expression Integer +--E 122 + +--S 123 of 518 +a0122:= integrate(t0122,x) +--R +--R +--R (111) +--R +----+ +----+2 +--R | 2 | 2 +--R | a | a +--R 2n |- -- log(b |- -- + a x) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R | a | a | a 2 +--R - n |- -- log(- b x |- -- - a |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+2 +--R | 2 +--R +-+ | a +--R +----+ b\|3 |- -- +--R | 2 3| 2 +--R +-+ | a \| b 2 3 2 +--R - 2n\|3 |- -- atan(----------------- + 2n x log(b x + a) + 2x log(c) +--R 3| 2 +----+2 +--R \| b | 2 +--R | a +--R b |- -- - 2a x +--R 3| 2 +--R \| b +--R + +--R 2 +--R - 3n x +--R / +--R 4 +--R Type: Union(Expression Integer,...) +--E 123 + +--S 124 of 518 +m0122:= a0122-r0122 +--R +--R +--R (112) +--R +----+ +----+2 +--R | 2 | 2 +--R | a 3+-+2 | a 2 3+-+2 3 n +--R 2n |- -- \|b log(b |- -- + a x - 2x \|b log(c (b x + a) ) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 3+-+ 3+-+ +--R 3+-+2 x \|b - x\|a \|b + \|a 3+-+2 x\|b + \|a +--R - n \|a log(---------------------------) + 2n \|a log(------------) +--R 3+-+2 3+-+ +--R \|b \|b +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R | a 3+-+2 | a | a 2 +--R - n |- -- \|b log(- b x |- -- - a |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+2 2x\|3 \|b - \|3 \|a +--R - 2n\|3 \|a atan(---------------------) +--R 3+-+ +--R 3\|a +--R + +--R +----+2 +--R | 2 +--R +-+ | a +--R +----+ b\|3 |- -- +--R | 2 3| 2 +--R +-+ | a 3+-+2 \| b +--R - 2n\|3 |- -- \|b atan(-----------------) +--R 3| 2 +----+2 +--R \| b | 2 +--R | a +--R b |- -- - 2a x +--R 3| 2 +--R \| b +--R + +--R 2 3 2 3+-+2 +--R (2n x log(b x + a) + 2x log(c))\|b +--R / +--R 3+-+2 +--R 4\|b +--R Type: Expression Integer +--E 124 + +--S 125 of 518 +d0122:= D(m0122,x) +--R +--R +--R (113) +--R 4 3 n 3 n +--R (- 2b x - 2a x)(b x + a) log(c (b x + a) ) +--R + +--R 4 3 4 4 +--R ((2b n x + 2a n x)log(b x + a) + (2b x + 2a x)log(c) + 3b n x ) +--R * +--R 3 n +--R (b x + a) +--R + +--R 2 7 4 3 n - 1 +--R (- 3b n x - 3a b n x )(b x + a) +--R / +--R 3 3 n +--R (2b x + 2a)(b x + a) +--R Type: Expression Integer +--E 125 + +--S 126 of 518 +t0123:= log(c*(a+b*x^3)^n)/x +--R +--R +--R 3 n +--R log(c (b x + a) ) +--R (114) ------------------ +--R x +--R Type: Expression Integer +--E 126 + +--S 127 of 518 +r0123:= 1/3*log(-b*x^3/a)*log(c*(a+b*x^3)^n)+1/3*n*polylog(2,1+b*x^3/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 127 + +--S 128 of 518 +a0123:= integrate(t0123,x) +--R +--R +--R x 3 n +--R ++ log(c (%L b + a) ) +--R (115) | ------------------ d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 128 + +--S 129 of 518 +--m0123:= a0123-r0123 +--E 129 + +--S 130 of 518 +--d0123:= D(m0123,x) +--E 130 + +--S 131 of 518 +t0124:= log(c*(a+b*x^3)^n)/x^2 +--R +--R +--R 3 n +--R log(c (b x + a) ) +--R (116) ------------------ +--R 2 +--R x +--R Type: Expression Integer +--E 131 + +--S 132 of 518 +r0124:= 3^(1/2)*b^(1/3)*n*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*x*3^(1/2)/a^(1/3))/a^(1/3)-_ + b^(1/3)*n*log(a^(1/3)/b^(1/3)+x)/a^(1/3)+_ + 1/2*b^(1/3)*n*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*x/b^(1/3)+x^2)/a^(1/3)-log(c*(a+b*x^3)^n)/x +--R +--R +--R (117) +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ 3 n 3+-+ x \|b - x\|a \|b + \|a +--R - 2\|a log(c (b x + a) ) + n x\|b log(---------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R 3+-+ x\|b + \|a +-+3+-+ 2x\|3 \|b - \|3 \|a +--R - 2n x\|b log(------------) + 2n x\|3 \|b atan(---------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R / +--R 3+-+ +--R 2x\|a +--R Type: Expression Integer +--E 132 + +--S 133 of 518 +a0124:= integrate(t0124,x) +--R +--R +--R (118) +--R +---+ +---+2 +--R | b | b +--R 2n x 3|- - log(a 3|- - + b x) +--R \| a \| a +--R + +--R +---+ +---+2 +---+ +--R | b | b | b 2 +--R - n x 3|- - log(- a x 3|- - - a 3|- - + b x ) +--R \| a \| a \| a +--R + +--R +---+2 +--R +-+ | b +--R +---+ a\|3 3|- - +--R +-+ | b \| a 3 +--R - 2n x\|3 3|- - atan(---------------- - 2n log(b x + a) - 2log(c) +--R \| a +---+2 +--R | b +--R a 3|- - - 2b x +--R \| a +--R / +--R 2x +--R Type: Union(Expression Integer,...) +--E 133 + +--S 134 of 518 +m0124:= a0124-r0124 +--R +--R +--R (119) +--R +---+ +---+2 +--R | b 3+-+ | b 3+-+ 3 n +--R 2n x 3|- - \|a log(a 3|- - + b x + 2\|a log(c (b x + a) ) +--R \| a \| a +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 3+-+ 3+-+ +--R 3+-+ x \|b - x\|a \|b + \|a 3+-+ x\|b + \|a +--R - n x\|b log(---------------------------) + 2n x\|b log(------------) +--R 3+-+2 3+-+ +--R \|b \|b +--R + +--R +---+ +---+2 +---+ +--R | b 3+-+ | b | b 2 +--R - n x 3|- - \|a log(- a x 3|- - - a 3|- - + b x ) +--R \| a \| a \| a +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ 2x\|3 \|b - \|3 \|a +--R - 2n x\|3 \|b atan(---------------------) +--R 3+-+ +--R 3\|a +--R + +--R +---+2 +--R +-+ | b +--R +---+ a\|3 3|- - +--R +-+ | b 3+-+ \| a +--R - 2n x\|3 3|- - \|a atan(----------------) +--R \| a +---+2 +--R | b +--R a 3|- - - 2b x +--R \| a +--R + +--R 3 3+-+ +--R (- 2n log(b x + a) - 2log(c))\|a +--R / +--R 3+-+ +--R 2x\|a +--R Type: Expression Integer +--E 134 + +--S 135 of 518 +d0124:= D(m0124,x) +--R +--R +--R (120) +--R 3 3 n 3 n +--R (- b x - a)(b x + a) log(c (b x + a) ) +--R + +--R 3 3 3 3 3 n +--R ((b n x + a n)log(b x + a) + (b x + a)log(c) - 3b n x )(b x + a) +--R + +--R 2 6 3 3 n - 1 +--R (3b n x + 3a b n x )(b x + a) +--R / +--R 5 2 3 n +--R (b x + a x )(b x + a) +--R Type: Expression Integer +--E 135 + +--S 136 of 518 +t0125:= log(c*(a+b*x^3)^n)/x^3 +--R +--R +--R 3 n +--R log(c (b x + a) ) +--R (121) ------------------ +--R 3 +--R x +--R Type: Expression Integer +--E 136 + +--S 137 of 518 +r0125:= 1/2*3^(1/2)*b^(2/3)*n*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*x*3^(1/2)/a^(1/3))/a^(2/3)+_ + 1/2*b^(2/3)*n*log(a^(1/3)/b^(1/3)+x)/a^(2/3)-_ + 1/4*b^(2/3)*n*log(a^(2/3)/b^(2/3)-a^(1/3)*x/b^(1/3)+x^2)/a^(2/3)-_ + 1/2*log(c*(a+b*x^3)^n)/x^2 +--R +--R +--R (122) +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+2 3 n 2 3+-+2 x \|b - x\|a \|b + \|a +--R - 2\|a log(c (b x + a) ) - n x \|b log(---------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R 2 3+-+2 x\|b + \|a 2 +-+3+-+2 2x\|3 \|b - \|3 \|a +--R 2n x \|b log(------------ + 2n x \|3 \|b atan(---------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R / +--R 2 3+-+2 +--R 4x \|a +--R Type: Expression Integer +--E 137 + +--S 138 of 518 +a0125:= integrate(t0125,x) +--R +--R +--R (123) +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R 2 |b 2 |b |b 2 2 +--R - n x |-- log(a |-- - a b x |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+ +--R | 2 +--R +-+ |b +--R +--+ +--+ +--+ a\|3 |-- +--R | 2 | 2 | 2 3| 2 +--R 2 |b |b 2 +-+ |b \|a +--R 2n x |-- log(a |-- + b x + 2n x \|3 |-- atan(-------------) +--R 3| 2 3| 2 3| 2 +--+ +--R \|a \|a \|a | 2 +--R |b +--R a |-- - 2b x +--R 3| 2 +--R \|a +--R + +--R 3 +--R - 2n log(b x + a) - 2log(c) +--R / +--R 2 +--R 4x +--R Type: Union(Expression Integer,...) +--E 138 + +--S 139 of 518 +m0125:= a0125-r0125 +--R +--R +--R (124) +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R 2 3+-+2 |b 2 |b |b 2 2 +--R - n x \|a |-- log(a |-- - a b x |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+ +--+ +--R | 2 | 2 +--R 2 3+-+2 |b |b 3+-+2 3 n +--R 2n x \|a |-- log(a |-- + b + 2\|a log(c (b x + a) ) +--R 3| 2 3| 2 +--R \|a \|a +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 3+-+ 3+-+ +--R 2 3+-+2 x \|b - x\|a \|b + \|a 2 3+-+2 x\|b + \|a +--R n x \|b log(--------------------------- - 2n x \|b log(------------) +--R 3+-+2 3+-+ +--R \|b \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 2 +-+3+-+2 2x\|3 \|b - \|3 \|a +--R - 2n x \|3 \|b atan(---------------------) +--R 3+-+ +--R 3\|a +--R + +--R +--+ +--R | 2 +--R +-+ |b +--R +--+ a\|3 |-- +--R | 2 3| 2 +--R 2 +-+3+-+2 |b \|a +--R 2n x \|3 \|a |-- atan(-------------) +--R 3| 2 +--+ +--R \|a | 2 +--R |b +--R a |-- - 2b x +--R 3| 2 +--R \|a +--R + +--R 3 3+-+2 +--R (- 2n log(b x + a) - 2log(c))\|a +--R / +--R 2 3+-+2 +--R 4x \|a +--R Type: Expression Integer +--E 139 + +--S 140 of 518 +d0125:= D(m0125,x) +--R +--R +--R (125) +--R 3 3 n 3 n +--R (- 2b x - 2a)(b x + a) log(c (b x + a) ) +--R + +--R 3 3 3 3 3 n +--R ((2b n x + 2a n)log(b x + a) + (2b x + 2a)log(c) - 3b n x )(b x + a) +--R + +--R 2 6 3 3 n - 1 +--R (3b n x + 3a b n x )(b x + a) +--R / +--R 6 3 3 n +--R (2b x + 2a x )(b x + a) +--R Type: Expression Integer +--E 140 + +--S 141 of 518 +t0126:= log(c*(a+b*x^3)^n)/x^4 +--R +--R +--R 3 n +--R log(c (b x + a) ) +--R (126) ------------------ +--R 4 +--R x +--R Type: Expression Integer +--E 141 + +--S 142 of 518 +r0126:= b*n*log(x)/a-1/3*b*n*log(a+b*x^3)/a-1/3*log(c*(a+b*x^3)^n)/x^3 +--R +--R +--R 3 n 3 3 3 +--R - a log(c (b x + a) ) - b n x log(b x + a) + 3b n x log(x) +--R (127) ------------------------------------------------------------ +--R 3 +--R 3a x +--R Type: Expression Integer +--E 142 + +--S 143 of 518 +a0126:= integrate(t0126,x) +--R +--R +--R 3 3 3 +--R (- b n x - a n)log(b x + a) + 3b n x log(x) - a log(c) +--R (128) -------------------------------------------------------- +--R 3 +--R 3a x +--R Type: Union(Expression Integer,...) +--E 143 + +--S 144 of 518 +m0126:= a0126-r0126 +--R +--R +--R 3 n 3 +--R log(c (b x + a) ) - n log(b x + a) - log(c) +--R (129) --------------------------------------------- +--R 3 +--R 3x +--R Type: Expression Integer +--E 144 + +--S 145 of 518 +d0126:= D(m0126,x) +--R +--R +--R (130) +--R 3 3 n 3 n +--R (- b x - a)(b x + a) log(c (b x + a) ) +--R + +--R 3 3 3 3 3 n +--R ((b n x + a n)log(b x + a) + (b x + a)log(c) - b n x )(b x + a) +--R + +--R 2 6 3 3 n - 1 +--R (b n x + a b n x )(b x + a) +--R / +--R 7 4 3 n +--R (b x + a x )(b x + a) +--R Type: Expression Integer +--E 145 + +--S 146 of 518 +t0127:= x^4*log(c*(a+b/x)^n) +--R +--R +--R 4 a x + b n +--R (131) x log(c (-------) ) +--R x +--R Type: Expression Integer +--E 146 + +--S 147 of 518 +r0127:= 1/60/a^5*(-12*b^4*n*x*a+6*b^3*n*x^2*a^2-4*b^2*n*x^3*a^3+_ + 3*b*n*x^4*a^4+12*x^5*log(c*((a*x+b)/x)^n)*a^5+12*b^5*n*log(a*x+b)) +--R +--R +--R (132) +--R 5 5 a x + b n 5 4 4 3 2 3 +--R 12a x log(c (-------) ) + 12b n log(a x + b) + 3a b n x - 4a b n x +--R x +--R + +--R 2 3 2 4 +--R 6a b n x - 12a b n x +--R / +--R 5 +--R 60a +--R Type: Expression Integer +--E 147 + +--S 148 of 518 +a0127:= integrate(t0127,x) +--R +--R +--R (133) +--R 5 5 5 5 5 a x + b 4 4 +--R 12b n log(a x + b) + 12a x log(c) + 12a n x log(-------) + 3a b n x +--R x +--R + +--R 3 2 3 2 3 2 4 +--R - 4a b n x + 6a b n x - 12a b n x +--R / +--R 5 +--R 60a +--R Type: Union(Expression Integer,...) +--E 148 + +--S 149 of 518 +m0127:= a0127-r0127 +--R +--R +--R 5 a x + b n 5 5 a x + b +--R - x log(c (-------) ) + x log(c) + n x log(-------) +--R x x +--R (134) --------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 149 + +--S 150 of 518 +d0127:= D(m0127,x) +--R +--R +--R (135) +--R 5 4 a x + b n a x + b n +--R (- 5a x - 5b x )(-------) log(c (-------) ) +--R x x +--R + +--R 5 4 5 4 a x + b 4 +--R ((5a x + 5b x )log(c) + (5a n x + 5b n x )log(-------) - b n x ) +--R x +--R * +--R a x + b n +--R (-------) +--R x +--R + +--R 4 2 3 a x + b n - 1 +--R (a b n x + b n x )(-------) +--R x +--R / +--R a x + b n +--R (5a x + 5b)(-------) +--R x +--R Type: Expression Integer +--E 150 + +--S 151 of 518 +t0128:= x^3*log(c*(a+b/x)^n) +--R +--R +--R 3 a x + b n +--R (136) x log(c (-------) ) +--R x +--R Type: Expression Integer +--E 151 + +--S 152 of 518 +r0128:= 1/24/a^4*(6*b^3*n*x*a-3*a^2*b^2*n*x^2+2*x^3*n*b*a^3+_ + 6*x^4*log(c*((a*x+b)/x)^n)*a^4-6*b^4*n*log(a*x+b)) +--R +--R +--R (137) +--R 4 4 a x + b n 4 3 3 2 2 2 3 +--R 6a x log(c (-------) ) - 6b n log(a x + b) + 2a b n x - 3a b n x + 6a b n x +--R x +--R ----------------------------------------------------------------------------- +--R 4 +--R 24a +--R Type: Expression Integer +--E 152 + +--S 153 of 518 +a0128:= integrate(t0128,x) +--R +--R +--R (138) +--R 4 4 4 4 4 a x + b 3 3 +--R - 6b n log(a x + b) + 6a x log(c) + 6a n x log(-------) + 2a b n x +--R x +--R + +--R 2 2 2 3 +--R - 3a b n x + 6a b n x +--R / +--R 4 +--R 24a +--R Type: Union(Expression Integer,...) +--E 153 + +--S 154 of 518 +m0128:= a0128-r0128 +--R +--R +--R 4 a x + b n 4 4 a x + b +--R - x log(c (-------) ) + x log(c) + n x log(-------) +--R x x +--R (139) --------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 154 + +--S 155 of 518 +d0128:= D(m0128,x) +--R +--R +--R (140) +--R 4 3 a x + b n a x + b n +--R (- 4a x - 4b x )(-------) log(c (-------) ) +--R x x +--R + +--R 4 3 4 3 a x + b 3 +--R ((4a x + 4b x )log(c) + (4a n x + 4b n x )log(-------) - b n x ) +--R x +--R * +--R a x + b n +--R (-------) +--R x +--R + +--R 3 2 2 a x + b n - 1 +--R (a b n x + b n x )(-------) +--R x +--R / +--R a x + b n +--R (4a x + 4b)(-------) +--R x +--R Type: Expression Integer +--E 155 + +--S 156 of 518 +t0129:= x^2*log(c*(a+b/x)^n) +--R +--R +--R 2 a x + b n +--R (141) x log(c (-------) ) +--R x +--R Type: Expression Integer +--E 156 + +--S 157 of 518 +r0129:= 1/6/a^3*(-2*b^2*n*x*a+x^2*n*b*a^2+2*x^3*log(c*((a*x+b)/x)^n)*a^3+_ + 2*b^3*n*log(a*x+b)) +--R +--R +--R 3 3 a x + b n 3 2 2 2 +--R 2a x log(c (-------) ) + 2b n log(a x + b) + a b n x - 2a b n x +--R x +--R (142) ---------------------------------------------------------------- +--R 3 +--R 6a +--R Type: Expression Integer +--E 157 + +--S 158 of 518 +a0129:= integrate(t0129,x) +--R +--R +--R (143) +--R 3 3 3 3 3 a x + b 2 2 2 +--R 2b n log(a x + b) + 2a x log(c) + 2a n x log(-------) + a b n x - 2a b n x +--R x +--R --------------------------------------------------------------------------- +--R 3 +--R 6a +--R Type: Union(Expression Integer,...) +--E 158 + +--S 159 of 518 +m0129:= a0129-r0129 +--R +--R +--R 3 a x + b n 3 3 a x + b +--R - x log(c (-------) ) + x log(c) + n x log(-------) +--R x x +--R (144) --------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 159 + +--S 160 of 518 +d0129:= D(m0129,x) +--R +--R +--R (145) +--R 3 2 a x + b n a x + b n +--R (- 3a x - 3b x )(-------) log(c (-------) ) +--R x x +--R + +--R 3 2 3 2 a x + b 2 +--R ((3a x + 3b x )log(c) + (3a n x + 3b n x )log(-------) - b n x ) +--R x +--R * +--R a x + b n +--R (-------) +--R x +--R + +--R 2 2 a x + b n - 1 +--R (a b n x + b n x)(-------) +--R x +--R / +--R a x + b n +--R (3a x + 3b)(-------) +--R x +--R Type: Expression Integer +--E 160 + +--S 161 of 518 +t0130:= x*log(c*(a+b/x)^n) +--R +--R +--R a x + b n +--R (146) x log(c (-------) ) +--R x +--R Type: Expression Integer +--E 161 + +--S 162 of 518 +r0130:= 1/2/a^2*(a*b*n*x+x^2*log(c*((a*x+b)/x)^n)*a^2-b^2*n*log(a*x+b)) +--R +--R +--R 2 2 a x + b n 2 +--R a x log(c (-------) ) - b n log(a x + b) + a b n x +--R x +--R (147) -------------------------------------------------- +--R 2 +--R 2a +--R Type: Expression Integer +--E 162 + +--S 163 of 518 +a0130:= integrate(t0130,x) +--R +--R +--R 2 2 2 2 2 a x + b +--R - b n log(a x + b) + a x log(c) + a n x log(-------) + a b n x +--R x +--R (148) -------------------------------------------------------------- +--R 2 +--R 2a +--R Type: Union(Expression Integer,...) +--E 163 + +--S 164 of 518 +m0130:= a0130-r0130 +--R +--R +--R 2 a x + b n 2 2 a x + b +--R - x log(c (-------) ) + x log(c) + n x log(-------) +--R x x +--R (149) --------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 164 + +--S 165 of 518 +d0130:= D(m0130,x) +--R +--R +--R (150) +--R 2 a x + b n a x + b n +--R (- 2a x - 2b x)(-------) log(c (-------) ) +--R x x +--R + +--R 2 2 a x + b a x + b n +--R ((2a x + 2b x)log(c) + (2a n x + 2b n x)log(-------) - b n x)(-------) +--R x x +--R + +--R 2 a x + b n - 1 +--R (a b n x + b n)(-------) +--R x +--R / +--R a x + b n +--R (2a x + 2b)(-------) +--R x +--R Type: Expression Integer +--E 165 + +--S 166 of 518 +t0131:= log(c*(a+b/x)^n)/x +--R +--R +--R a x + b n +--R log(c (-------) ) +--R x +--R (151) ----------------- +--R x +--R Type: Expression Integer +--E 166 + +--S 167 of 518 +r0131:= -log(c*(a+b/x)^n)*log(-b/a/x)-n*polylog(2,1+b/a/x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 167 + +--S 168 of 518 +a0131:= integrate(t0131,x) +--R +--R +--R b + %L a n +--R x log(c (--------) ) +--R ++ %L +--R (152) | ------------------ d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 168 + +--S 169 of 518 +--m0131:= a0131-r0131 +--E 169 + +--S 170 of 518 +--d0131:= D(m0131,x) +--E 170 + +--S 171 of 518 +t0132:= log(c*(a+b/x)^n)/x^2 +--R +--R +--R a x + b n +--R log(c (-------) ) +--R x +--R (153) ----------------- +--R 2 +--R x +--R Type: Expression Integer +--E 171 + +--S 172 of 518 +r0132:= n/x-(a+b/x)*log(c*(a+b/x)^n)/b +--R +--R +--R a x + b n +--R (- a x - b)log(c (-------) ) + b n +--R x +--R (154) ---------------------------------- +--R b x +--R Type: Expression Integer +--E 172 + +--S 173 of 518 +a0132:= integrate(t0132,x) +--R +--R +--R a x + b +--R - b log(c) + (- a n x - b n)log(-------) + b n +--R x +--R (155) ---------------------------------------------- +--R b x +--R Type: Union(Expression Integer,...) +--E 173 + +--S 174 of 518 +m0132:= a0132-r0132 +--R +--R +--R a x + b n a x + b +--R (a x + b)log(c (-------) ) - b log(c) + (- a n x - b n)log(-------) +--R x x +--R (156) ------------------------------------------------------------------- +--R b x +--R Type: Expression Integer +--E 174 + +--S 175 of 518 +d0132:= D(m0132,x) +--R +--R +--R (157) +--R a x + b n a x + b n +--R - x (-------) log(c (-------) ) +--R x x +--R + +--R a x + b a x + b n +--R (x log(c) + n x log(-------) + n x)(-------) +--R x x +--R + +--R a x + b n - 1 +--R (- a n x - b n)(-------) +--R x +--R / +--R 3 a x + b n +--R x (-------) +--R x +--R Type: Expression Integer +--E 175 + +--S 176 of 518 +t0133:= log(c*(a+b/x)^n)/x^3 +--R +--R +--R a x + b n +--R log(c (-------) ) +--R x +--R (158) ----------------- +--R 3 +--R x +--R Type: Expression Integer +--E 176 + +--S 177 of 518 +r0133:= -1/4/b^2/x^2*(-b^2*n+2*a*b*n*x+2*log(c*((a*x+b)/x)^n)*b^2+_ + 2*a^2*n*log(x)*x^2-2*a^2*n*log(a*x+b)*x^2) +--R +--R +--R (159) +--R 2 a x + b n 2 2 2 2 2 +--R - 2b log(c (-------) ) + 2a n x log(a x + b) - 2a n x log(x) - 2a b n x + b n +--R x +--R ----------------------------------------------------------------------------- +--R 2 2 +--R 4b x +--R Type: Expression Integer +--E 177 + +--S 178 of 518 +a0133:= integrate(t0133,x) +--R +--R +--R 2 2 2 2 a x + b 2 +--R - 2b log(c) + (2a n x - 2b n)log(-------) - 2a b n x + b n +--R x +--R (160) ----------------------------------------------------------- +--R 2 2 +--R 4b x +--R Type: Union(Expression Integer,...) +--E 178 + +--S 179 of 518 +m0133:= a0133-r0133 +--R +--R +--R (161) +--R 2 a x + b n 2 2 2 2 2 +--R b log(c (-------) ) - a n x log(a x + b) + a n x log(x) - b log(c) +--R x +--R + +--R 2 2 2 a x + b +--R (a n x - b n)log(-------) +--R x +--R / +--R 2 2 +--R 2b x +--R Type: Expression Integer +--E 179 + +--S 180 of 518 +d0133:= D(m0133,x) +--R +--R +--R (162) +--R 2 a x + b n a x + b n +--R (- 2a x - 2b x)(-------) log(c (-------) ) +--R x x +--R + +--R 2 2 a x + b a x + b n +--R ((2a x + 2b x)log(c) + (2a n x + 2b n x)log(-------) + b n x)(-------) +--R x x +--R + +--R 2 a x + b n - 1 +--R (- a b n x - b n)(-------) +--R x +--R / +--R 5 4 a x + b n +--R (2a x + 2b x )(-------) +--R x +--R Type: Expression Integer +--E 180 + +--S 181 of 518 +t0134:= log(c*(a+b/x)^n)/x^4 +--R +--R +--R a x + b n +--R log(c (-------) ) +--R x +--R (163) ----------------- +--R 4 +--R x +--R Type: Expression Integer +--E 181 + +--S 182 of 518 +r0134:= -1/18/b^3/x^3*(-2*b^3*n+3*b^2*n*x*a-6*x^2*n*b*a^2+_ + 6*log(c*((a*x+b)/x)^n)*b^3-6*a^3*n*log(x)*x^3+6*a^3*n*log(a*x+b)*x^3) +--R +--R +--R (164) +--R 3 a x + b n 3 3 3 3 2 2 +--R - 6b log(c (-------) ) - 6a n x log(a x + b) + 6a n x log(x) + 6a b n x +--R x +--R + +--R 2 3 +--R - 3a b n x + 2b n +--R / +--R 3 3 +--R 18b x +--R Type: Expression Integer +--E 182 + +--S 183 of 518 +a0134:= integrate(t0134,x) +--R +--R +--R (165) +--R 3 3 3 3 a x + b 2 2 2 3 +--R - 6b log(c) + (- 6a n x - 6b n)log(-------) + 6a b n x - 3a b n x + 2b n +--R x +--R -------------------------------------------------------------------------- +--R 3 3 +--R 18b x +--R Type: Union(Expression Integer,...) +--E 183 + +--S 184 of 518 +m0134:= a0134-r0134 +--R +--R +--R (166) +--R 3 a x + b n 3 3 3 3 3 +--R b log(c (-------) ) + a n x log(a x + b) - a n x log(x) - b log(c) +--R x +--R + +--R 3 3 3 a x + b +--R (- a n x - b n)log(-------) +--R x +--R / +--R 3 3 +--R 3b x +--R Type: Expression Integer +--E 184 + +--S 185 of 518 +d0134:= D(m0134,x) +--R +--R +--R (167) +--R 2 a x + b n a x + b n +--R (- 3a x - 3b x)(-------) log(c (-------) ) +--R x x +--R + +--R 2 2 a x + b a x + b n +--R ((3a x + 3b x)log(c) + (3a n x + 3b n x)log(-------) + b n x)(-------) +--R x x +--R + +--R 2 a x + b n - 1 +--R (- a b n x - b n)(-------) +--R x +--R / +--R 6 5 a x + b n +--R (3a x + 3b x )(-------) +--R x +--R Type: Expression Integer +--E 185 + +--S 186 of 518 +t0135:= x^4*log(c*(a+b/x^2)^n) +--R +--R +--R 2 n +--R 4 a x + b +--R (168) x log(c (--------) ) +--R 2 +--R x +--R Type: Expression Integer +--E 186 + +--S 187 of 518 +r0135:= -2/5*b^2*n*x/a^2+2/15*b*n*x^3/a+_ + 2/5*b^(5/2)*n*atan(a^(1/2)*x/b^(1/2))/a^(5/2)+_ + 1/5*x^5*log(c*(a+b/x^2)^n) +--R +--R +--R (169) +--R 2 n +-+ +--R 2 5 +-+ a x + b 2 +-+ x\|a 3 2 +-+ +--R 3a x \|a log(c (--------) ) + 6b n\|b atan(-----) + (2a b n x - 6b n x)\|a +--R 2 +-+ +--R x \|b +--R ---------------------------------------------------------------------------- +--R 2 +-+ +--R 15a \|a +--R Type: Expression Integer +--E 187 + +--S 188 of 518 +a0135:= integrate(t0135,x) +--R +--R +--R (170) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R 2 | b \| a 2 5 +--R 3b n |- - log(---------------------) + 3a x log(c) +--R \| a 2 +--R a x + b +--R + +--R 2 +--R 2 5 a x + b 3 2 +--R 3a n x log(--------) + 2a b n x - 6b n x +--R 2 +--R x +--R / +--R 2 +--R 15a +--R , +--R +--R +-+ +--R |b +--R +-+ |- 2 +--R 2 |b \|a 2 5 2 5 a x + b 3 +--R - 6b n |- atan(----) + 3a x log(c) + 3a n x log(--------) + 2a b n x +--R \|a x 2 +--R x +--R + +--R 2 +--R - 6b n x +--R / +--R 2 +--R 15a +--R ] +--R Type: Union(List Expression Integer,...) +--E 188 + +--S 189 of 518 +m0135a:= a0135.1-r0135 +--R +--R +--R (171) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b 2 n +--R 2 | b +-+ \| a 2 5 +-+ a x + b +--R b n |- - \|a log(---------------------) - a x \|a log(c (--------) ) +--R \| a 2 2 +--R a x + b x +--R + +--R +-+ 2 +--R 2 +-+ x\|a 2 5 2 5 a x + b +-+ +--R - 2b n\|b atan(-----) + (a x log(c) + a n x log(--------))\|a +--R +-+ 2 +--R \|b x +--R / +--R 2 +-+ +--R 5a \|a +--R Type: Expression Integer +--E 189 + +--S 190 of 518 +d0135a:= D(m0135a,x) +--R +--R +--R (172) +--R 2 n 2 n +--R 6 4 a x + b a x + b +--R (- 5a x - 5b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 6 4 6 4 a x + b 4 +--R ((5a x + 5b x )log(c) + (5a n x + 5b n x )log(--------) - 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 4 2 2 a x + b +--R (2a b n x + 2b n x )(--------) +--R 2 +--R x +--R / +--R 2 n +--R 2 a x + b +--R (5a x + 5b)(--------) +--R 2 +--R x +--R Type: Expression Integer +--E 190 + +--S 191 of 518 +m0135b:= a0135.2-r0135 +--R +--R +--R (173) +--R +-+ +--R |b +--R 2 n +-+ |- +--R 2 5 +-+ a x + b 2 +-+ |b \|a +--R - a x \|a log(c (--------) ) - 2b n\|a |- atan(----) +--R 2 \|a x +--R x +--R + +--R +-+ 2 +--R 2 +-+ x\|a 2 5 2 5 a x + b +-+ +--R - 2b n\|b atan(-----) + (a x log(c) + a n x log(--------))\|a +--R +-+ 2 +--R \|b x +--R / +--R 2 +-+ +--R 5a \|a +--R Type: Expression Integer +--E 191 + +--S 192 of 518 +d0135b:= D(m0135b,x) +--R +--R +--R (174) +--R 2 n 2 n +--R 6 4 a x + b a x + b +--R (- 5a x - 5b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 6 4 6 4 a x + b 4 +--R ((5a x + 5b x )log(c) + (5a n x + 5b n x )log(--------) - 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 4 2 2 a x + b +--R (2a b n x + 2b n x )(--------) +--R 2 +--R x +--R / +--R 2 n +--R 2 a x + b +--R (5a x + 5b)(--------) +--R 2 +--R x +--R Type: Expression Integer +--E 192 + +--S 193 of 518 +t0136:= x^3*log(c*(a+b/x^2)^n) +--R +--R +--R 2 n +--R 3 a x + b +--R (175) x log(c (--------) ) +--R 2 +--R x +--R Type: Expression Integer +--E 193 + +--S 194 of 518 +r0136:= 1/4*b*n*x^2/a+1/4*x^4*log(c*(a+b/x^2)^n)-1/4*b^2*n*log(a*x^2+b)/a^2 +--R +--R +--R 2 n +--R 2 4 a x + b 2 2 2 +--R a x log(c (--------) ) - b n log(a x + b) + a b n x +--R 2 +--R x +--R (176) ----------------------------------------------------- +--R 2 +--R 4a +--R Type: Expression Integer +--E 194 + +--S 195 of 518 +a0136:= integrate(t0136,x) +--R +--R +--R 2 +--R 2 2 2 4 2 4 a x + b 2 +--R - b n log(a x + b) + a x log(c) + a n x log(--------) + a b n x +--R 2 +--R x +--R (177) ----------------------------------------------------------------- +--R 2 +--R 4a +--R Type: Union(Expression Integer,...) +--E 195 + +--S 196 of 518 +m0136:= a0136-r0136 +--R +--R +--R 2 n 2 +--R 4 a x + b 4 4 a x + b +--R - x log(c (--------) ) + x log(c) + n x log(--------) +--R 2 2 +--R x x +--R (178) ----------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 196 + +--S 197 of 518 +d0136:= D(m0136,x) +--R +--R +--R (179) +--R 2 n 2 n +--R 5 3 a x + b a x + b +--R (- 2a x - 2b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 5 3 5 3 a x + b 3 +--R ((2a x + 2b x )log(c) + (2a n x + 2b n x )log(--------) - b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 3 2 a x + b +--R (a b n x + b n x)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 2 a x + b +--R (2a x + 2b)(--------) +--R 2 +--R x +--R Type: Expression Integer +--E 197 + +--S 198 of 518 +t0137:= x^2*log(c*(a+b/x^2)^n) +--R +--R +--R 2 n +--R 2 a x + b +--R (180) x log(c (--------) ) +--R 2 +--R x +--R Type: Expression Integer +--E 198 + +--S 199 of 518 +r0137:= 2/3*b*n*x/a-2/3*b^(3/2)*n*atan(a^(1/2)*x/b^(1/2))/a^(3/2)+_ + 1/3*x^3*log(c*(a+b/x^2)^n) +--R +--R +--R 2 n +-+ +--R 3 +-+ a x + b +-+ x\|a +-+ +--R a x \|a log(c (--------) ) - 2b n\|b atan(-----) + 2b n x\|a +--R 2 +-+ +--R x \|b +--R (181) ------------------------------------------------------------- +--R +-+ +--R 3a\|a +--R Type: Expression Integer +--E 199 + +--S 200 of 518 +a0137:= integrate(t0137,x) +--R +--R +--R (182) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R | b \| a 3 +--R b n |- - log(-----------------------) + a x log(c) +--R \| a 2 +--R a x + b +--R + +--R 2 +--R 3 a x + b +--R a n x log(--------) + 2b n x +--R 2 +--R x +--R / +--R 3a +--R , +--R +-+ +--R |b +--R +-+ |- 2 +--R |b \|a 3 3 a x + b +--R 2b n |- atan(----) + a x log(c) + a n x log(--------) + 2b n x +--R \|a x 2 +--R x +--R --------------------------------------------------------------] +--R 3a +--R Type: Union(List Expression Integer,...) +--E 200 + +--S 201 of 518 +m0137a:= a0137.1-r0137 +--R +--R +--R (183) +--R +---+ +--R | b 2 +--R 2 n +---+ - 2a x |- - + a x - b +--R 3 +-+ a x + b | b +-+ \| a +--R - a x \|a log(c (--------) ) + b n |- - \|a log(-----------------------) +--R 2 \| a 2 +--R x a x + b +--R + +--R +-+ 2 +--R +-+ x\|a 3 3 a x + b +-+ +--R 2b n\|b atan(-----) + (a x log(c) + a n x log(--------))\|a +--R +-+ 2 +--R \|b x +--R / +--R +-+ +--R 3a\|a +--R Type: Expression Integer +--E 201 + +--S 202 of 518 +d0137a:= D(m0137a,x) +--R +--R +--R (184) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- 3a x - 3b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((3a x + 3b x )log(c) + (3a n x + 3b n x )log(--------) - 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (2a b n x + 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 2 a x + b +--R (3a x + 3b)(--------) +--R 2 +--R x +--R Type: Expression Integer +--E 202 + +--S 203 of 518 +m0137b:= a0137.2-r0137 +--R +--R +--R (185) +--R +-+ +--R |b +--R 2 n +-+ |- +--R 3 +-+ a x + b +-+ |b \|a +--R - a x \|a log(c (--------) ) + 2b n\|a |- atan(----) +--R 2 \|a x +--R x +--R + +--R +-+ 2 +--R +-+ x\|a 3 3 a x + b +-+ +--R 2b n\|b atan(-----) + (a x log(c) + a n x log(--------))\|a +--R +-+ 2 +--R \|b x +--R / +--R +-+ +--R 3a\|a +--R Type: Expression Integer +--E 203 + +--S 204 of 518 +d0137b:= D(m0137b,x) +--R +--R +--R (186) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- 3a x - 3b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((3a x + 3b x )log(c) + (3a n x + 3b n x )log(--------) - 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (2a b n x + 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 2 a x + b +--R (3a x + 3b)(--------) +--R 2 +--R x +--R Type: Expression Integer +--E 204 + +--S 205 of 518 +t0138:= x*log(c*(a+b/x^2)^n) +--R +--R +--R 2 n +--R a x + b +--R (187) x log(c (--------) ) +--R 2 +--R x +--R Type: Expression Integer +--E 205 + +--S 206 of 518 +r0138:= 1/2*x^2*log(c*(a+b/x^2)^n)+1/2*b*n*log(a*x^2+b)/a +--R +--R +--R 2 n +--R 2 a x + b 2 +--R a x log(c (--------) ) + b n log(a x + b) +--R 2 +--R x +--R (188) ------------------------------------------ +--R 2a +--R Type: Expression Integer +--E 206 + +--S 207 of 518 +a0138:= integrate(t0138,x) +--R +--R +--R 2 +--R 2 2 2 a x + b +--R b n log(a x + b) + a x log(c) + a n x log(--------) +--R 2 +--R x +--R (189) ---------------------------------------------------- +--R 2a +--R Type: Union(Expression Integer,...) +--E 207 + +--S 208 of 518 +m0138:= a0138-r0138 +--R +--R +--R 2 n 2 +--R 2 a x + b 2 2 a x + b +--R - x log(c (--------) ) + x log(c) + n x log(--------) +--R 2 2 +--R x x +--R (190) ----------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 208 + +--S 209 of 518 +d0138:= D(m0138,x) +--R +--R +--R (191) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- a x - b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((a x + b x )log(c) + (a n x + b n x )log(--------) - b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (a b n x + b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 3 a x + b +--R (a x + b x)(--------) +--R 2 +--R x +--R Type: Expression Integer +--E 209 + +--S 210 of 518 +t0139:= log(c*(a+b/x^2)^n)/x +--R +--R +--R 2 n +--R a x + b +--R log(c (--------) ) +--R 2 +--R x +--R (192) ------------------ +--R x +--R Type: Expression Integer +--E 210 + +--S 211 of 518 +r0139:= -1/2*log(c*(a+b/x^2)^n)*log(-b/a/x^2)-1/2*n*polylog(2,1+b/a/x^2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 518 +a0139:= integrate(t0139,x) +--R +--R +--R 2 n +--R b + %L a +--R log(c (--------) ) +--R x 2 +--R ++ %L +--R (193) | ------------------ d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 212 + +--S 213 of 518 +--m0139:= a0139-r0139 +--E 213 + +--S 214 of 518 +--d0139:= D(m0139,x) +--E 214 + +--S 215 of 518 +t0140:= log(c*(a+b/x^2)^n)/x^2 +--R +--R +--R 2 n +--R a x + b +--R log(c (--------) ) +--R 2 +--R x +--R (194) ------------------ +--R 2 +--R x +--R Type: Expression Integer +--E 215 + +--S 216 of 518 +r0140:= 2*n/x+2*a^(1/2)*n*atan(a^(1/2)*x/b^(1/2))/b^(1/2)-log(c*(a+b/x^2)^n)/x +--R +--R +--R 2 n +-+ +--R +-+ a x + b +-+ x\|a +-+ +--R - \|b log(c (--------) ) + 2n x\|a atan(-----) + 2n\|b +--R 2 +-+ +--R x \|b +--R (195) ------------------------------------------------------- +--R +-+ +--R x\|b +--R Type: Expression Integer +--E 216 + +--S 217 of 518 +a0140:= integrate(t0140,x) +--R +--R +--R (196) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b 2 +--R | a \| b a x + b +--R n x |- - log(---------------------) - log(c) - n log(--------) + 2n +--R \| b 2 2 +--R a x + b x +--R [-------------------------------------------------------------------, +--R x +--R +-+ +--R |a +--R +-+ b |- 2 +--R |a \|b a x + b +--R - 2n x |- atan(-----) - log(c) - n log(--------) + 2n +--R \|b a x 2 +--R x +--R -----------------------------------------------------] +--R x +--R Type: Union(List Expression Integer,...) +--E 217 + +--S 218 of 518 +m0140a:= a0140.1-r0140 +--R +--R +--R (197) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b 2 n +--R | a +-+ \| b +-+ a x + b +--R n x |- - \|b log(---------------------) + \|b log(c (--------) ) +--R \| b 2 2 +--R a x + b x +--R + +--R +-+ 2 +--R +-+ x\|a a x + b +-+ +--R - 2n x\|a atan(-----) + (- log(c) - n log(--------))\|b +--R +-+ 2 +--R \|b x +--R / +--R +-+ +--R x\|b +--R Type: Expression Integer +--E 218 + +--S 219 of 518 +d0140a:= D(m0140a,x) +--R +--R +--R (198) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- a x - b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((a x + b x )log(c) + (a n x + b n x )log(--------) + 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (- 2a b n x - 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 6 4 a x + b +--R (a x + b x )(--------) +--R 2 +--R x +--R Type: Expression Integer +--E 219 + +--S 220 of 518 +m0140b:= a0140.2-r0140 +--R +--R +--R (199) +--R +-+ +--R |a +--R 2 n +-+ b |- +-+ +--R +-+ a x + b |a +-+ \|b +-+ x\|a +--R \|b log(c (--------) ) - 2n x |- \|b atan(-----) - 2n x\|a atan(-----) +--R 2 \|b a x +-+ +--R x \|b +--R + +--R 2 +--R a x + b +-+ +--R (- log(c) - n log(--------))\|b +--R 2 +--R x +--R / +--R +-+ +--R x\|b +--R Type: Expression Integer +--E 220 + +--S 221 of 518 +d0140b:= D(m0140b,x) +--R +--R +--R (200) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- a x - b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((a x + b x )log(c) + (a n x + b n x )log(--------) + 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (- 2a b n x - 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 6 4 a x + b +--R (a x + b x )(--------) +--R 2 +--R x +--R Type: Expression Integer +--E 221 + +--S 222 of 518 +t0141:= log(c*(a+b/x^2)^n)/x^3 +--R +--R +--R 2 n +--R a x + b +--R log(c (--------) ) +--R 2 +--R x +--R (201) ------------------ +--R 3 +--R x +--R Type: Expression Integer +--E 222 + +--S 223 of 518 +r0141:= 1/2*n/x^2-1/2*(a+b/x^2)*log(c*(a+b/x^2)^n)/b +--R +--R +--R 2 n +--R 2 a x + b +--R (- a x - b)log(c (--------) ) + b n +--R 2 +--R x +--R (202) ------------------------------------ +--R 2 +--R 2b x +--R Type: Expression Integer +--E 223 + +--S 224 of 518 +a0141:= integrate(t0141,x) +--R +--R +--R 2 +--R 2 a x + b +--R - b log(c) + (- a n x - b n)log(--------) + b n +--R 2 +--R x +--R (203) ------------------------------------------------ +--R 2 +--R 2b x +--R Type: Union(Expression Integer,...) +--E 224 + +--S 225 of 518 +m0141:= a0141-r0141 +--R +--R +--R (204) +--R 2 n 2 +--R 2 a x + b 2 a x + b +--R (a x + b)log(c (--------) ) - b log(c) + (- a n x - b n)log(--------) +--R 2 2 +--R x x +--R ----------------------------------------------------------------------- +--R 2 +--R 2b x +--R Type: Expression Integer +--E 225 + +--S 226 of 518 +d0141:= D(m0141,x) +--R +--R +--R (205) +--R 2 n 2 n +--R 2 a x + b a x + b +--R - x (--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 2 n +--R 2 2 a x + b 2 a x + b +--R (x log(c) + n x log(--------) + n x )(--------) +--R 2 2 +--R x x +--R + +--R 2 n - 1 +--R 2 a x + b +--R (- a n x - b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 5 a x + b +--R x (--------) +--R 2 +--R x +--R Type: Expression Integer +--E 226 + +--S 227 of 518 +t0142:= log(c*(a+b/x^2)^n)/x^4 +--R +--R +--R 2 n +--R a x + b +--R log(c (--------) ) +--R 2 +--R x +--R (206) ------------------ +--R 4 +--R x +--R Type: Expression Integer +--E 227 + +--S 228 of 518 +r0142:= 2/9*n/x^3-2/3*a*n/b/x-2/3*a^(3/2)*n*_ + atan(a^(1/2)*x/b^(1/2))/b^(3/2)-1/3*log(c*(a+b/x^2)^n)/x^3 +--R +--R +--R (207) +--R 2 n +-+ +--R +-+ a x + b 3 +-+ x\|a 2 +-+ +--R - 3b\|b log(c (--------) ) - 6a n x \|a atan(-----) + (- 6a n x + 2b n)\|b +--R 2 +-+ +--R x \|b +--R ---------------------------------------------------------------------------- +--R 3 +-+ +--R 9b x \|b +--R Type: Expression Integer +--E 228 + +--S 229 of 518 +a0142:= integrate(t0142,x) +--R +--R +--R (208) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +--R 3 | a \| b +--R 3a n x |- - log(-----------------------) - 3b log(c) +--R \| b 2 +--R a x + b +--R + +--R 2 +--R a x + b 2 +--R - 3b n log(--------) - 6a n x + 2b n +--R 2 +--R x +--R / +--R 3 +--R 9b x +--R , +--R +-+ +--R |a +--R +-+ b |- 2 +--R 3 |a \|b a x + b 2 +--R 6a n x |- atan(-----) - 3b log(c) - 3b n log(--------) - 6a n x + 2b n +--R \|b a x 2 +--R x +--R ------------------------------------------------------------------------] +--R 3 +--R 9b x +--R Type: Union(List Expression Integer,...) +--E 229 + +--S 230 of 518 +m0142a:= a0142.1-r0142 +--R +--R +--R (209) +--R +---+ +--R | a 2 +--R 2 n +---+ - 2b x |- - + a x - b +--R +-+ a x + b 3 | a +-+ \| b +--R b\|b log(c (--------) ) + a n x |- - \|b log(-----------------------) +--R 2 \| b 2 +--R x a x + b +--R + +--R +-+ 2 +--R 3 +-+ x\|a a x + b +-+ +--R 2a n x \|a atan(-----) + (- b log(c) - b n log(--------))\|b +--R +-+ 2 +--R \|b x +--R / +--R 3 +-+ +--R 3b x \|b +--R Type: Expression Integer +--E 230 + +--S 231 of 518 +d0142a:= D(m0142a,x) +--R +--R +--R (210) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- 3a x - 3b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((3a x + 3b x )log(c) + (3a n x + 3b n x )log(--------) + 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (- 2a b n x - 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 8 6 a x + b +--R (3a x + 3b x )(--------) +--R 2 +--R x +--R Type: Expression Integer +--E 231 + +--S 232 of 518 +m0142b:= a0142.2-r0142 +--R +--R +--R (211) +--R +-+ +--R |a +--R 2 n +-+ b |- +--R +-+ a x + b 3 |a +-+ \|b +--R b\|b log(c (--------) ) + 2a n x |- \|b atan(-----) +--R 2 \|b a x +--R x +--R + +--R +-+ 2 +--R 3 +-+ x\|a a x + b +-+ +--R 2a n x \|a atan(-----) + (- b log(c) - b n log(--------))\|b +--R +-+ 2 +--R \|b x +--R / +--R 3 +-+ +--R 3b x \|b +--R Type: Expression Integer +--E 232 + +--S 233 of 518 +d0142b:= D(m0142b,x) +--R +--R +--R (212) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- 3a x - 3b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((3a x + 3b x )log(c) + (3a n x + 3b n x )log(--------) + 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (- 2a b n x - 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 8 6 a x + b +--R (3a x + 3b x )(--------) +--R 2 +--R x +--R Type: Expression Integer +--E 233 + +--S 234 of 518 +t0143:= x^4*log(c*(a+b*x^(1/2))^n) +--R +--R +--R 4 +-+ n +--R (213) x log(c (b\|x + a) ) +--R Type: Expression Integer +--E 234 + +--S 235 of 518 +r0143:= 1/12600*(2520*a^9*n*x^(1/2)*b-1260*a^8*n*x*b^2+840*a^7*n*_ + x^(3/2)*b^3-630*a^6*n*x^2*b^4+504*a^5*n*x^(5/2)*b^5-420*a^4*n*_ + x^3*b^6+360*a^3*n*x^(7/2)*b^7-315*a^2*n*x^4*b^8+_ + 280*a*n*x^(9/2)*b^9-252*n*x^5*b^10-2520*a^10*n*log(a+b*x^(1/2))+_ + 2520*x^5*log(c*(a+b*x^(1/2))^n)*b^10)/b^10 +--R +--R +--R (214) +--R 10 5 +-+ n 10 +-+ +--R 2520b x log(c (b\|x + a) ) - 2520a n log(b\|x + a) +--R + +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ +--R (280a b n x + 360a b n x + 504a b n x + 840a b n x + 2520a b n)\|x +--R + +--R 10 5 2 8 4 4 6 3 6 4 2 8 2 +--R - 252b n x - 315a b n x - 420a b n x - 630a b n x - 1260a b n x +--R / +--R 10 +--R 12600b +--R Type: Expression Integer +--E 235 + +--S 236 of 518 +a0143:= integrate(t0143,x) +--R +--R +--R (215) +--R 10 5 10 +-+ +--R (2520b n x - 2520a n)log(b\|x + a) +--R + +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ +--R (280a b n x + 360a b n x + 504a b n x + 840a b n x + 2520a b n)\|x +--R + +--R 10 5 10 5 2 8 4 4 6 3 6 4 2 +--R 2520b x log(c) - 252b n x - 315a b n x - 420a b n x - 630a b n x +--R + +--R 8 2 +--R - 1260a b n x +--R / +--R 10 +--R 12600b +--R Type: Union(Expression Integer,...) +--E 236 + +--S 237 of 518 +m0143:= a0143-r0143 +--R +--R +--R 5 +-+ n 5 +-+ 5 +--R - x log(c (b\|x + a) ) + n x log(b\|x + a) + x log(c) +--R (216) ------------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 237 + +--S 238 of 518 +d0143:= D(m0143,x) +--R +--R +--R (217) +--R 4 +-+ 4 +-+ n +-+ n +--R (- 10b x \|x - 10a x )(b\|x + a) log(c (b\|x + a) ) +--R + +--R 4 +-+ 4 +-+ 4 4 +-+ +--R (10b n x \|x + 10a n x )log(b\|x + a) + (10b x log(c) + b n x )\|x +--R + +--R 4 +--R 10a x log(c) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R 4 +-+ 2 5 +-+ n - 1 +--R (- a b n x \|x - b n x )(b\|x + a) +--R / +--R +-+ +-+ n +--R (10b\|x + 10a)(b\|x + a) +--R Type: Expression Integer +--E 238 + +--S 239 of 518 +t0144:= x^3*log(c*(a+b*x^(1/2))^n) +--R +--R +--R 3 +-+ n +--R (218) x log(c (b\|x + a) ) +--R Type: Expression Integer +--E 239 + +--S 240 of 518 +r0144:= 1/3360*(840*a^7*n*x^(1/2)*b-420*a^6*n*x*b^2+280*a^5*n*x^(3/2)*b^3-_ + 210*a^4*n*x^2*b^4+168*a^3*n*x^(5/2)*b^5-140*a^2*n*x^3*b^6+_ + 120*a*n*x^(7/2)*b^7-105*n*x^4*b^8-840*a^8*n*log(a+b*x^(1/2))+_ + 840*x^4*log(c*(a+b*x^(1/2))^n)*b^8)/b^8 +--R +--R +--R (219) +--R 8 4 +-+ n 8 +-+ +--R 840b x log(c (b\|x + a) ) - 840a n log(b\|x + a) +--R + +--R 7 3 3 5 2 5 3 7 +-+ 8 4 +--R (120a b n x + 168a b n x + 280a b n x + 840a b n)\|x - 105b n x +--R + +--R 2 6 3 4 4 2 6 2 +--R - 140a b n x - 210a b n x - 420a b n x +--R / +--R 8 +--R 3360b +--R Type: Expression Integer +--E 240 + +--S 241 of 518 +a0144:= integrate(t0144,x) +--R +--R +--R (220) +--R 8 4 8 +-+ +--R (840b n x - 840a n)log(b\|x + a) +--R + +--R 7 3 3 5 2 5 3 7 +-+ 8 4 +--R (120a b n x + 168a b n x + 280a b n x + 840a b n)\|x + 840b x log(c) +--R + +--R 8 4 2 6 3 4 4 2 6 2 +--R - 105b n x - 140a b n x - 210a b n x - 420a b n x +--R / +--R 8 +--R 3360b +--R Type: Union(Expression Integer,...) +--E 241 + +--S 242 of 518 +m0144:= a0144-r0144 +--R +--R +--R 4 +-+ n 4 +-+ 4 +--R - x log(c (b\|x + a) ) + n x log(b\|x + a) + x log(c) +--R (221) ------------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 242 + +--S 243 of 518 +d0144:= D(m0144,x) +--R +--R +--R (222) +--R 3 +-+ 3 +-+ n +-+ n +--R (- 8b x \|x - 8a x )(b\|x + a) log(c (b\|x + a) ) +--R + +--R 3 +-+ 3 +-+ 3 3 +-+ +--R (8b n x \|x + 8a n x )log(b\|x + a) + (8b x log(c) + b n x )\|x +--R + +--R 3 +--R 8a x log(c) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R 3 +-+ 2 4 +-+ n - 1 +--R (- a b n x \|x - b n x )(b\|x + a) +--R / +--R +-+ +-+ n +--R (8b\|x + 8a)(b\|x + a) +--R Type: Expression Integer +--E 243 + +--S 244 of 518 +t0145:= x^2*log(c*(a+b*x^(1/2))^n) +--R +--R +--R 2 +-+ n +--R (223) x log(c (b\|x + a) ) +--R Type: Expression Integer +--E 244 + +--S 245 of 518 +r0145:= 1/180*(60*a^5*n*x^(1/2)*b-30*a^4*n*x*b^2+20*a^3*n*x^(3/2)*b^3-_ + 15*a^2*n*x^2*b^4+12*a*n*x^(5/2)*b^5-10*n*x^3*b^6-_ + 60*a^6*n*log(a+b*x^(1/2))+60*x^3*log(c*(a+b*x^(1/2))^n)*b^6)/b^6 +--R +--R +--R (224) +--R 6 3 +-+ n 6 +-+ +--R 60b x log(c (b\|x + a) ) - 60a n log(b\|x + a) +--R + +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 +--R (12a b n x + 20a b n x + 60a b n)\|x - 10b n x - 15a b n x - 30a b n x +--R / +--R 6 +--R 180b +--R Type: Expression Integer +--E 245 + +--S 246 of 518 +a0145:= integrate(t0145,x) +--R +--R +--R (225) +--R 6 3 6 +-+ 5 2 3 3 5 +-+ +--R (60b n x - 60a n)log(b\|x + a) + (12a b n x + 20a b n x + 60a b n)\|x +--R + +--R 6 3 6 3 2 4 2 4 2 +--R 60b x log(c) - 10b n x - 15a b n x - 30a b n x +--R / +--R 6 +--R 180b +--R Type: Union(Expression Integer,...) +--E 246 + +--S 247 of 518 +m0145:= a0145-r0145 +--R +--R +--R 3 +-+ n 3 +-+ 3 +--R - x log(c (b\|x + a) ) + n x log(b\|x + a) + x log(c) +--R (226) ------------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 247 + +--S 248 of 518 +d0145:= D(m0145,x) +--R +--R +--R (227) +--R 2 +-+ 2 +-+ n +-+ n +--R (- 6b x \|x - 6a x )(b\|x + a) log(c (b\|x + a) ) +--R + +--R 2 +-+ 2 +-+ 2 2 +-+ +--R (6b n x \|x + 6a n x )log(b\|x + a) + (6b x log(c) + b n x )\|x +--R + +--R 2 +--R 6a x log(c) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R 2 +-+ 2 3 +-+ n - 1 +--R (- a b n x \|x - b n x )(b\|x + a) +--R / +--R +-+ +-+ n +--R (6b\|x + 6a)(b\|x + a) +--R Type: Expression Integer +--E 248 + +--S 249 of 518 +t0146:= x*log(c*(a+b*x^(1/2))^n) +--R +--R +--R +-+ n +--R (228) x log(c (b\|x + a) ) +--R Type: Expression Integer +--E 249 + +--S 250 of 518 +r0146:= 1/24*(12*a^3*n*x^(1/2)*b-6*b^2*n*x*a^2+4*a*n*x^(3/2)*b^3-_ + 3*n*x^2*b^4-12*a^4*n*log(a+b*x^(1/2))+_ + 12*x^2*log(c*(a+b*x^(1/2))^n)*b^4)/b^4 +--R +--R +--R (229) +--R 4 2 +-+ n 4 +-+ +--R 12b x log(c (b\|x + a) ) - 12a n log(b\|x + a) +--R + +--R 3 3 +-+ 4 2 2 2 +--R (4a b n x + 12a b n)\|x - 3b n x - 6a b n x +--R / +--R 4 +--R 24b +--R Type: Expression Integer +--E 250 + +--S 251 of 518 +a0146:= integrate(t0146,x) +--R +--R +--R (230) +--R 4 2 4 +-+ 3 3 +-+ +--R (12b n x - 12a n)log(b\|x + a) + (4a b n x + 12a b n)\|x +--R + +--R 4 2 4 2 2 2 +--R 12b x log(c) - 3b n x - 6a b n x +--R / +--R 4 +--R 24b +--R Type: Union(Expression Integer,...) +--E 251 + +--S 252 of 518 +m0146:= a0146-r0146 +--R +--R +--R 2 +-+ n 2 +-+ 2 +--R - x log(c (b\|x + a) ) + n x log(b\|x + a) + x log(c) +--R (231) ------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 252 + +--S 253 of 518 +d0146:= D(m0146,x) +--R +--R +--R (232) +--R +-+ +-+ n +-+ n +--R (- 4b x\|x - 4a x)(b\|x + a) log(c (b\|x + a) ) +--R + +--R +-+ +-+ +-+ +--R (4b n x\|x + 4a n x)log(b\|x + a) + (4b x log(c) + b n x)\|x +--R + +--R 4a x log(c) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R +-+ 2 2 +-+ n - 1 +--R (- a b n x\|x - b n x )(b\|x + a) +--R / +--R +-+ +-+ n +--R (4b\|x + 4a)(b\|x + a) +--R Type: Expression Integer +--E 253 + +--S 254 of 518 +t0147:= log(c*(a+b*x^(1/2))^n) +--R +--R +--R +-+ n +--R (233) log(c (b\|x + a) ) +--R Type: Expression Integer +--E 254 + +--S 255 of 518 +r0147:= a*n*x^(1/2)/b-1/2*n*x-a^2*n*log(a+b*x^(1/2))/b^2+_ + x*log(c*(a+b*x^(1/2))^n) +--R +--R +--R 2 +-+ n 2 +-+ +-+ 2 +--R 2b x log(c (b\|x + a) ) - 2a n log(b\|x + a) + 2a b n\|x - b n x +--R (234) ------------------------------------------------------------------- +--R 2 +--R 2b +--R Type: Expression Integer +--E 255 + +--S 256 of 518 +a0147:= integrate(t0147,x) +--R +--R +--R 2 2 +-+ +-+ 2 2 +--R (2b n x - 2a n)log(b\|x + a) + 2a b n\|x + 2b x log(c) - b n x +--R (235) ---------------------------------------------------------------- +--R 2 +--R 2b +--R Type: Union(Expression Integer,...) +--E 256 + +--S 257 of 518 +m0147:= a0147-r0147 +--R +--R +--R +-+ n +-+ +--R (236) - x log(c (b\|x + a) ) + n x log(b\|x + a) + x log(c) +--R Type: Expression Integer +--E 257 + +--S 258 of 518 +d0147:= D(m0147,x) +--R +--R +--R (237) +--R +-+ +-+ n +-+ n +--R (- 2b\|x - 2a)(b\|x + a) log(c (b\|x + a) ) +--R + +--R +-+ +-+ +-+ +--R ((2b n\|x + 2a n)log(b\|x + a) + (2b log(c) + b n)\|x + 2a log(c)) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R +-+ 2 +-+ n - 1 +--R (- a b n\|x - b n x)(b\|x + a) +--R / +--R +-+ +-+ n +--R (2b\|x + 2a)(b\|x + a) +--R Type: Expression Integer +--E 258 + +--S 259 of 518 +t0148:= log(c*(a+b*x^(1/2))^n)/x +--R +--R +--R +-+ n +--R log(c (b\|x + a) ) +--R (238) ------------------- +--R x +--R Type: Expression Integer +--E 259 + +--S 260 of 518 +r0148:= 2*log(c*(a+b*x^(1/2))^n)*log(-b*x^(1/2)/a)+2*n*polylog(2,1+b*x^(1/2)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 260 + +--S 261 of 518 +a0148:= integrate(t0148,x) +--R +--R +--R x +--+ n +--R ++ log(c (b\|%L + a) ) +--R (239) | -------------------- d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 261 + +--S 262 of 518 +--m0148:= a0148-r0148 +--E 262 + +--S 263 of 518 +--d0148:= D(m0148,x) +--E 263 + +--S 264 of 518 +t0149:= log(c*(a+b*x^(1/2))^n)/x^2 +--R +--R +--R +-+ n +--R log(c (b\|x + a) ) +--R (240) ------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 264 + +--S 265 of 518 +r0149:= -b*n/a/x^(1/2)+b^2*n*log(a+b*x^(1/2))/a^2-_ + log(c*(a+b*x^(1/2))^n)/x-1/2*b^2*n*log(x)/a^2 +--R +--R +--R (241) +--R 2 +-+ +-+ n 2 +-+ +-+ +--R - 2a \|x log(c (b\|x + a) ) + 2b n x\|x log(b\|x + a) +--R + +--R 2 +-+ +--R - b n x log(x)\|x - 2a b n x +--R / +--R 2 +-+ +--R 2a x\|x +--R Type: Expression Integer +--E 265 + +--S 266 of 518 +a0149:= integrate(t0149,x) +--R +--R +--R 2 2 +-+ 2 +-+ +-+ 2 +--R (b n x - a n)log(b\|x + a) - b n x log(\|x ) - a b n\|x - a log(c) +--R (242) -------------------------------------------------------------------- +--R 2 +--R a x +--R Type: Union(Expression Integer,...) +--E 266 + +--S 267 of 518 +m0149:= a0149-r0149 +--R +--R +--R (243) +--R 2 +-+ n 2 +-+ 2 +-+ +--R 2a log(c (b\|x + a) ) - 2a n log(b\|x + a) - 2b n x log(\|x ) +--R + +--R 2 2 +--R b n x log(x) - 2a log(c) +--R / +--R 2 +--R 2a x +--R Type: Expression Integer +--E 267 + +--S 268 of 518 +d0149:= D(m0149,x) +--R +--R +--R (244) +--R +-+ +-+ n +-+ n +--R (- 2b\|x - 2a)(b\|x + a) log(c (b\|x + a) ) +--R + +--R +-+ +-+ +-+ +--R ((2b n\|x + 2a n)log(b\|x + a) + (2b log(c) - b n)\|x + 2a log(c)) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R +-+ 2 +-+ n - 1 +--R (a b n\|x + b n x)(b\|x + a) +--R / +--R 2 +-+ 2 +-+ n +--R (2b x \|x + 2a x )(b\|x + a) +--R Type: Expression Integer +--E 268 + +--S 269 of 518 +t0150:= log(c*(a+b*x^(1/2))^n)/x^3 +--R +--R +--R +-+ n +--R log(c (b\|x + a) ) +--R (245) ------------------- +--R 3 +--R x +--R Type: Expression Integer +--E 269 + +--S 270 of 518 +r0150:= -1/6*b*n/a/x^(3/2)+1/4*b^2*n/a^2/x-1/2*b^3*n/a^3/x^(1/2)+_ + 1/2*b^4*n*log(a+b*x^(1/2))/a^4-_ + 1/2*log(c*(a+b*x^(1/2))^n)/x^2-1/4*b^4*n*log(x)/a^4 +--R +--R +--R (246) +--R 4 +-+ +-+ n 4 2 +-+ +-+ +--R - 6a \|x log(c (b\|x + a) ) + 6b n x \|x log(b\|x + a) +--R + +--R 4 2 2 2 +-+ 3 2 3 +--R (- 3b n x log(x) + 3a b n x)\|x - 6a b n x - 2a b n x +--R / +--R 4 2 +-+ +--R 12a x \|x +--R Type: Expression Integer +--E 270 + +--S 271 of 518 +a0150:= integrate(t0150,x) +--R +--R +--R (247) +--R 4 2 4 +-+ 4 2 +-+ +--R (6b n x - 6a n)log(b\|x + a) - 6b n x log(\|x ) +--R + +--R 3 3 +-+ 4 2 2 +--R (- 6a b n x - 2a b n)\|x - 6a log(c) + 3a b n x +--R / +--R 4 2 +--R 12a x +--R Type: Union(Expression Integer,...) +--E 271 + +--S 272 of 518 +m0150:= a0150-r0150 +--R +--R +--R (248) +--R 4 +-+ n 4 +-+ 4 2 +-+ +--R 2a log(c (b\|x + a) ) - 2a n log(b\|x + a) - 2b n x log(\|x ) +--R + +--R 4 2 4 +--R b n x log(x) - 2a log(c) +--R / +--R 4 2 +--R 4a x +--R Type: Expression Integer +--E 272 + +--S 273 of 518 +d0150:= D(m0150,x) +--R +--R +--R (249) +--R +-+ +-+ n +-+ n +--R (- 4b\|x - 4a)(b\|x + a) log(c (b\|x + a) ) +--R + +--R +-+ +-+ +-+ +--R ((4b n\|x + 4a n)log(b\|x + a) + (4b log(c) - b n)\|x + 4a log(c)) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R +-+ 2 +-+ n - 1 +--R (a b n\|x + b n x)(b\|x + a) +--R / +--R 3 +-+ 3 +-+ n +--R (4b x \|x + 4a x )(b\|x + a) +--R Type: Expression Integer +--E 273 + +--S 274 of 518 +t0151:= log(c*(a+b*x^(1/2))^n)/x^4 +--R +--R +--R +-+ n +--R log(c (b\|x + a) ) +--R (250) ------------------- +--R 4 +--R x +--R Type: Expression Integer +--E 274 + +--S 275 of 518 +r0151:= -1/180*(12*b*n*a^5*x-15*b^2*n*x^(3/2)*a^4+20*b^3*n*x^2*a^3-_ + 30*b^4*n*x^(5/2)*a^2+60*b^5*n*x^3*a-_ + 60*b^6*n*log(a+b*x^(1/2))*x^(7/2)+_ + 60*log(c*(a+b*x^(1/2))^n)*x^(1/2)*a^6+_ + 30*b^6*n*log(x)*x^(7/2))/x^(7/2)/a^6 +--R +--R +--R (251) +--R 6 +-+ +-+ n 6 3 +-+ +-+ +--R - 60a \|x log(c (b\|x + a) ) + 60b n x \|x log(b\|x + a) +--R + +--R 6 3 2 4 2 4 2 +-+ 5 3 3 3 2 +--R (- 30b n x log(x) + 30a b n x + 15a b n x)\|x - 60a b n x - 20a b n x +--R + +--R 5 +--R - 12a b n x +--R / +--R 6 3 +-+ +--R 180a x \|x +--R Type: Expression Integer +--E 275 + +--S 276 of 518 +a0151:= integrate(t0151,x) +--R +--R +--R (252) +--R 6 3 6 +-+ 6 3 +-+ +--R (60b n x - 60a n)log(b\|x + a) - 60b n x log(\|x ) +--R + +--R 5 2 3 3 5 +-+ 6 2 4 2 +--R (- 60a b n x - 20a b n x - 12a b n)\|x - 60a log(c) + 30a b n x +--R + +--R 4 2 +--R 15a b n x +--R / +--R 6 3 +--R 180a x +--R Type: Union(Expression Integer,...) +--E 276 + +--S 277 of 518 +m0151:= a0151-r0151 +--R +--R +--R (253) +--R 6 +-+ n 6 +-+ 6 3 +-+ +--R 2a log(c (b\|x + a) ) - 2a n log(b\|x + a) - 2b n x log(\|x ) +--R + +--R 6 3 6 +--R b n x log(x) - 2a log(c) +--R / +--R 6 3 +--R 6a x +--R Type: Expression Integer +--E 277 + +--S 278 of 518 +d0151:= D(m0151,x) +--R +--R +--R (254) +--R +-+ +-+ n +-+ n +--R (- 6b\|x - 6a)(b\|x + a) log(c (b\|x + a) ) +--R + +--R +-+ +-+ +-+ +--R ((6b n\|x + 6a n)log(b\|x + a) + (6b log(c) - b n)\|x + 6a log(c)) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R +-+ 2 +-+ n - 1 +--R (a b n\|x + b n x)(b\|x + a) +--R / +--R 4 +-+ 4 +-+ n +--R (6b x \|x + 6a x )(b\|x + a) +--R Type: Expression Integer +--E 278 + +--S 279 of 518 +t0152:= 1/log(a+b*x) +--R +--R +--R 1 +--R (255) ------------ +--R log(b x + a) +--R Type: Expression Integer +--E 279 + +--S 280 of 518 +r0152:= li(a+b*x)/b +--R +--R +--R li(b x + a) +--R (256) ----------- +--R b +--R Type: Expression Integer +--E 280 + +--S 281 of 518 +a0152:= integrate(t0152,x) +--R +--R +--R li(b x + a) +--R (257) ----------- +--R b +--R Type: Union(Expression Integer,...) +--E 281 + +--S 282 of 518 +m0152:= a0152-r0152 +--R +--R +--R (258) 0 +--R Type: Expression Integer +--E 282 + +--S 283 of 518 +d0152:= D(m0152,x) +--R +--R +--R (259) 0 +--R Type: Expression Integer +--E 283 + +--S 284 of 518 +t0153:= log(a+b*x^2)^2 +--R +--R +--R 2 2 +--R (260) log(b x + a) +--R Type: Expression Integer +--E 284 + +--S 285 of 518 +r0153:= 8*x-4*x*log(a+b*x^2)+x*log(a+b*x^2)^2-1/(-b)^(1/2)*a^(1/2)*_ + (log(-a^(1/2)/(-b)^(1/2)+x)^2-log(a^(1/2)/(-b)^(1/2)+x)^2+_ + 4*atanh((-b)^(1/2)*x/a^(1/2))*(log(-a^(1/2)/(-b)^(1/2)+x)+_ + log(a^(1/2)/(-b)^(1/2)+x))-4*log(-(a^(1/2)-(-b)^(1/2)*x)/_ + (a^(1/2)+(-b)^(1/2)*x))+2*log(a^(1/2)/(-b)^(1/2)+x)*_ + log(1/2-1/2*(-b)^(1/2)*x/a^(1/2))-2*log(-a^(1/2)/(-b)^(1/2)+x)*_ + log(1/2+1/2*(-b)^(1/2)*x/a^(1/2))-4*atanh((-b)^(1/2)*x/a^(1/2))*_ + log(a+b*x^2)-2*polylog(2,1/2-1/2*(-b)^(1/2)*x/a^(1/2))+2*_ + polylog(2,1/2+1/2*(-b)^(1/2)*x/a^(1/2))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 285 + +--S 286 of 518 +a0153:= integrate(t0153,x) +--R +--R +--R x +--R ++ 2 2 +--R (261) | log(%L b + a) d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 286 + +--S 287 of 518 +--m0153:= a0153-r0153 +--E 287 + +--S 288 of 518 +--d0153:= D(m0153,x) +--E 288 + +--S 289 of 518 +t0154:= x*log(a+b*x^2)^2 +--R +--R +--R 2 2 +--R (262) x log(b x + a) +--R Type: Expression Integer +--E 289 + +--S 290 of 518 +r0154:= x^2-(a+b*x^2)*log(a+b*x^2)/b+1/2*(a+b*x^2)*log(a+b*x^2)^2/b +--R +--R +--R 2 2 2 2 2 2 +--R (b x + a)log(b x + a) + (- 2b x - 2a)log(b x + a) + 2b x +--R (263) -------------------------------------------------------------- +--R 2b +--R Type: Expression Integer +--E 290 + +--S 291 of 518 +a0154:= integrate(t0154,x) +--R +--R +--R 2 2 2 2 2 2 +--R (b x + a)log(b x + a) + (- 2b x - 2a)log(b x + a) + 2b x +--R (264) -------------------------------------------------------------- +--R 2b +--R Type: Union(Expression Integer,...) +--E 291 + +--S 292 of 518 +m0154:= a0154-r0154 +--R +--R +--R (265) 0 +--R Type: Expression Integer +--E 292 + +--S 293 of 518 +d0154:= D(m0154,x) +--R +--R +--R (266) 0 +--R Type: Expression Integer +--E 293 + +--S 294 of 518 +t0155:= log(a+b*x^2)^2/x +--R +--R +--R 2 2 +--R log(b x + a) +--R (267) -------------- +--R x +--R Type: Expression Integer +--E 294 + +--S 295 of 518 +r0155:= 1/2*log(-b*x^2/a)*log(a+b*x^2)^2+_ + log(a+b*x^2)*polylog(2,1+b*x^2/a)-polylog(3,(a+b*x^2)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 295 + +--S 296 of 518 +a0155:= integrate(t0155,x) +--R +--R +--R x 2 2 +--R ++ log(%L b + a) +--R (268) | -------------- d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 296 + +--S 297 of 518 +--m0155:= a0155-r0155 +--E 297 + +--S 298 of 518 +--d0155:= D(m0155,x) +--E 298 + +--S 299 of 518 +t0156:= log(a+b*x^2)^2/x^3 +--R +--R +--R 2 2 +--R log(b x + a) +--R (269) -------------- +--R 3 +--R x +--R Type: Expression Integer +--E 299 + +--S 300 of 518 +r0156:= b*log(-b*x^2/a)*log(a+b*x^2)/a-_ + 1/2*(a+b*x^2)*log(a+b*x^2)^2/a/x^2+b*polylog(2,1+b*x^2/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 300 + +--S 301 of 518 +a0156:= integrate(t0156,x) +--R +--R +--R x 2 2 +--R ++ log(%L b + a) +--R (270) | -------------- d%L +--R ++ 3 +--R %L +--R Type: Union(Expression Integer,...) +--E 301 + +--S 302 of 518 +--m0156:= a0156-r0156 +--E 302 + +--S 303 of 518 +--d0156:= D(m0156,x) +--E 303 + +--S 304 of 518 +t0157:= x*log(a+b*x^2)^3 +--R +--R +--R 2 3 +--R (271) x log(b x + a) +--R Type: Expression Integer +--E 304 + +--S 305 of 518 +r0157:= -3*x^2+3*(a+b*x^2)*log(a+b*x^2)/b-_ + 3/2*(a+b*x^2)*log(a+b*x^2)^2/b+1/2*(a+b*x^2)*log(a+b*x^2)^3/b +--R +--R +--R (272) +--R 2 2 3 2 2 2 +--R (b x + a)log(b x + a) + (- 3b x - 3a)log(b x + a) +--R + +--R 2 2 2 +--R (6b x + 6a)log(b x + a) - 6b x +--R / +--R 2b +--R Type: Expression Integer +--E 305 + +--S 306 of 518 +a0157:= integrate(t0157,x) +--R +--R +--R (273) +--R 2 2 3 2 2 2 +--R (b x + a)log(b x + a) + (- 3b x - 3a)log(b x + a) +--R + +--R 2 2 2 +--R (6b x + 6a)log(b x + a) - 6b x +--R / +--R 2b +--R Type: Union(Expression Integer,...) +--E 306 + +--S 307 of 518 +m0157:= a0157-r0157 +--R +--R +--R (274) 0 +--R Type: Expression Integer +--E 307 + +--S 308 of 518 +d0157:= D(m0157,x) +--R +--R +--R (275) 0 +--R Type: Expression Integer +--E 308 + +--S 309 of 518 +t0158:= log(a+b*x^2)^3/x +--R +--R +--R 2 3 +--R log(b x + a) +--R (276) -------------- +--R x +--R Type: Expression Integer +--E 309 + +--S 310 of 518 +r0158:= 1/2*log(-b*x^2/a)*log(a+b*x^2)^3+_ + 3/2*log(a+b*x^2)^2*polylog(2,1+b*x^2/a)-_ + 3*log(a+b*x^2)*polylog(3,1+b*x^2/a)+3*polylog(4,(a+b*x^2)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 310 + +--S 311 of 518 +a0158:= integrate(t0158,x) +--R +--R +--R x 2 3 +--R ++ log(%L b + a) +--R (277) | -------------- d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 311 + +--S 312 of 518 +--m0158:= a0158-r0158 +--E 312 + +--S 313 of 518 +--d0158:= D(m0158,x) +--E 313 + +--S 314 of 518 +t0159:= log(a+b*x^2)^3/x^3 +--R +--R +--R 2 3 +--R log(b x + a) +--R (278) -------------- +--R 3 +--R x +--R Type: Expression Integer +--E 314 + +--S 315 of 518 +r0159:= 3/2*b*log(-b*x^2/a)*log(a+b*x^2)^2/a-_ + 1/2*(a+b*x^2)*log(a+b*x^2)^3/a/x^2+_ + 3*b*log(a+b*x^2)*polylog(2,1+b*x^2/a)/a-3*b*polylog(3,(a+b*x^2)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 315 + +--S 316 of 518 +a0159:= integrate(t0159,x) +--R +--R +--R x 2 3 +--R ++ log(%L b + a) +--R (279) | -------------- d%L +--R ++ 3 +--R %L +--R Type: Union(Expression Integer,...) +--E 316 + +--S 317 of 518 +--m0159:= a0159-r0159 +--E 317 + +--S 318 of 518 +--d0159:= D(m0159,x) +--E 318 + +--S 319 of 518 +t0160:= x^3/log(a+b*x^2) +--R +--R +--R 3 +--R x +--R (280) ------------- +--R 2 +--R log(b x + a) +--R Type: Expression Integer +--E 319 + +--S 320 of 518 +r0160:= -1/2*(-Ei(2*log(a+b*x^2))+a*li(a+b*x^2))/b^2 +--R +--R +--R 2 2 +--R Ei(2log(b x + a)) - a li(b x + a) +--R (281) ----------------------------------- +--R 2 +--R 2b +--R Type: Expression Integer +--E 320 + +--S 321 of 518 +a0160:= integrate(t0160,x) +--R +--R +--R x 3 +--R ++ %L +--R (282) | ------------- d%L +--R ++ 2 +--R log(%L b + a) +--R Type: Union(Expression Integer,...) +--E 321 + +--S 322 of 518 +--m0160:= a0160-r0160 +--E 322 + +--S 323 of 518 +--d0160:= D(m0160,x) +--E 323 + +--S 324 of 518 +t0161:= x^3/log(a+b*x^2)^2 +--R +--R +--R 3 +--R x +--R (283) -------------- +--R 2 2 +--R log(b x + a) +--R Type: Expression Integer +--E 324 + +--S 325 of 518 +r0161:= -1/2*(-2*Ei(2*log(a+b*x^2))*log(a+b*x^2)+a*b*x^2+b^2*x^4+_ + a*li(a+b*x^2)*log(a+b*x^2))/b^2/log(a+b*x^2) +--R +--R +--R (284) +--R 2 2 2 2 2 4 +--R 2log(b x + a)Ei(2log(b x + a)) - a li(b x + a)log(b x + a) - b x +--R + +--R 2 +--R - a b x +--R / +--R 2 2 +--R 2b log(b x + a) +--R Type: Expression Integer +--E 325 + +--S 326 of 518 +a0161:= integrate(t0161,x) +--R +--R +--R x 3 +--R ++ %L +--R (285) | -------------- d%L +--R ++ 2 2 +--R log(%L b + a) +--R Type: Union(Expression Integer,...) +--E 326 + +--S 327 of 518 +m0161:= a0161-r0161 +--R +--R +--R (286) +--R x 3 +--R 2 2 ++ %L +--R 2b log(b x + a) | -------------- d%L +--R ++ 2 2 +--R log(%L b + a) +--R + +--R 2 2 2 2 2 4 +--R - 2log(b x + a)Ei(2log(b x + a)) + a li(b x + a)log(b x + a) + b x +--R + +--R 2 +--R a b x +--R / +--R 2 2 +--R 2b log(b x + a) +--R Type: Expression Integer +--E 327 + +--S 328 of 518 +d0161:= D(m0161,x) +--R +--R +--R 2 +--R 2log(b x + a) 2 5 3 2 +--R - 2x %e + 2b x + 4a b x + 2a x +--R (287) ---------------------------------------------- +--R 2 2 2 +--R (b x + a b)log(b x + a) +--R Type: Expression Integer +--E 328 + +--S 329 of 518 +t0162:= x^3/log(a+b*x^2)^3 +--R +--R +--R 3 +--R x +--R (288) -------------- +--R 2 3 +--R log(b x + a) +--R Type: Expression Integer +--E 329 + +--S 330 of 518 +r0162:= -1/4*(-4*Ei(2*log(a+b*x^2))*log(a+b*x^2)^2+a*b*x^2+b^2*x^4+_ + log(a+b*x^2)*a^2+3*log(a+b*x^2)*a*b*x^2+2*log(a+b*x^2)*b^2*x^4+_ + a*li(a+b*x^2)*log(a+b*x^2)^2)/b^2/log(a+b*x^2)^2 +--R +--R +--R (289) +--R 2 2 2 2 2 2 +--R 4log(b x + a) Ei(2log(b x + a)) - a li(b x + a)log(b x + a) +--R + +--R 2 4 2 2 2 2 4 2 +--R (- 2b x - 3a b x - a )log(b x + a) - b x - a b x +--R / +--R 2 2 2 +--R 4b log(b x + a) +--R Type: Expression Integer +--E 330 + +--S 331 of 518 +a0162:= integrate(t0162,x) +--R +--R +--R x 3 +--R ++ %L +--R (290) | -------------- d%L +--R ++ 2 3 +--R log(%L b + a) +--R Type: Union(Expression Integer,...) +--E 331 + +--S 332 of 518 +--m0162:= a0162-r0162 +--E 332 + +--S 333 of 518 +--d0162:= D(m0162,x) +--E 333 + +--S 334 of 518 +t0163:= log(c*(a+b*x^2)^n)^2 +--R +--R +--R 2 n 2 +--R (291) log(c (b x + a) ) +--R Type: Expression Integer +--E 334 + +--S 335 of 518 +r0163:= 8*n^2*x-4*n*x*log(c*(a+b*x^2)^n)+x*log(c*(a+b*x^2)^n)^2-_ + 1/(-b)^(1/2)*a^(1/2)*n*(n*log(-a^(1/2)/(-b)^(1/2)+x)^2-_ + n*log(a^(1/2)/(-b)^(1/2)+x)^2+4*n*atanh((-b)^(1/2)*x/a^(1/2))*_ + (log(-a^(1/2)/(-b)^(1/2)+x)+log(a^(1/2)/(-b)^(1/2)+x))-_ + 4*n*log(-(a^(1/2)-(-b)^(1/2)*x)/(a^(1/2)+(-b)^(1/2)*x))+_ + 2*n*log(a^(1/2)/(-b)^(1/2)+x)*log(1/2-1/2*(-b)^(1/2)*x/a^(1/2))-_ + 2*n*log(-a^(1/2)/(-b)^(1/2)+x)*log(1/2+1/2*(-b)^(1/2)*x/a^(1/2))-_ + 4*atanh((-b)^(1/2)*x/a^(1/2))*log(c*(a+b*x^2)^n)-_ + 2*n*polylog(2,1/2-1/2*(-b)^(1/2)*x/a^(1/2))+_ + 2*n*polylog(2,1/2+1/2*(-b)^(1/2)*x/a^(1/2))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 335 + +--S 336 of 518 +a0163:= integrate(t0163,x) +--R +--R +--R x +--R ++ 2 n 2 +--R (292) | log(c (%L b + a) ) d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 336 + +--S 337 of 518 +--m0163:= a0163-r0163 +--E 337 + +--S 338 of 518 +--d0163:= D(m0163,x) +--E 338 + +--S 339 of 518 +t0164:= x*log(c*(a+b*x^2)^n)^2 +--R +--R +--R 2 n 2 +--R (293) x log(c (b x + a) ) +--R Type: Expression Integer +--E 339 + +--S 340 of 518 +r0164:= n^2*x^2-n*(a+b*x^2)*log(c*(a+b*x^2)^n)/b+_ + 1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)^2/b +--R +--R +--R (294) +--R 2 2 n 2 2 2 n +--R (b x + a)log(c (b x + a) ) + (- 2b n x - 2a n)log(c (b x + a) ) +--R + +--R 2 2 +--R 2b n x +--R / +--R 2b +--R Type: Expression Integer +--E 340 + +--S 341 of 518 +a0164:= integrate(t0164,x) +--R +--R +--R (295) +--R 2 2 2 2 2 +--R (b n x + a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R ((2b n x + 2a n)log(c) - 2b n x - 2a n )log(b x + a) + b x log(c) +--R + +--R 2 2 2 +--R - 2b n x log(c) + 2b n x +--R / +--R 2b +--R Type: Union(Expression Integer,...) +--E 341 + +--S 342 of 518 +m0164:= a0164-r0164 +--R +--R +--R (296) +--R 2 2 n 2 2 2 n +--R (- b x - a)log(c (b x + a) ) + (2b n x + 2a n)log(c (b x + a) ) +--R + +--R 2 2 2 2 2 +--R (b n x + a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R ((2b n x + 2a n)log(c) - 2b n x - 2a n )log(b x + a) + b x log(c) +--R + +--R 2 +--R - 2b n x log(c) +--R / +--R 2b +--R Type: Expression Integer +--E 342 + +--S 343 of 518 +d0164:= D(m0164,x) +--R +--R +--R (297) +--R 2 n 2 n 2 +--R - x (b x + a) log(c (b x + a) ) +--R + +--R 2 n 3 2 n - 1 +--R (2n x (b x + a) + (- 2b n x - 2a n x)(b x + a) ) +--R * +--R 2 n +--R log(c (b x + a) ) +--R + +--R 2 2 2 2 2 2 +--R (n x log(b x + a) + 2n x log(c)log(b x + a) + x log(c) - 2n x) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 3 2 2 n - 1 +--R (2b n x + 2a n x)(b x + a) +--R / +--R 2 n +--R (b x + a) +--R Type: Expression Integer +--E 343 + +--S 344 of 518 +t0165:= x^3*log(c*(a+b*x^2)^n)^2 +--R +--R +--R 3 2 n 2 +--R (298) x log(c (b x + a) ) +--R Type: Expression Integer +--E 344 + +--S 345 of 518 +r0165:= -3/4*a*n^2*x^2/b+1/8*n^2*x^4+1/4*a^2*n^2*log(a+b*x^2)/b^2-_ + 1/4*n*x^4*log(c*(a+b*x^2)^n)+1/2*a*n*(a+b*x^2)*_ + log(c*(a+b*x^2)^n)/b^2-1/4*a^2*log(c*(a+b*x^2)^n)^2/b^2+_ + 1/4*x^4*log(c*(a+b*x^2)^n)^2 +--R +--R +--R (299) +--R 2 4 2 2 n 2 +--R (2b x - 2a )log(c (b x + a) ) +--R + +--R 2 4 2 2 2 n 2 2 2 +--R (- 2b n x + 4a b n x + 4a n)log(c (b x + a) ) + 2a n log(b x + a) +--R + +--R 2 2 4 2 2 +--R b n x - 6a b n x +--R / +--R 2 +--R 8b +--R Type: Expression Integer +--E 345 + +--S 346 of 518 +a0165:= integrate(t0165,x) +--R +--R +--R (300) +--R 2 2 4 2 2 2 2 +--R (2b n x - 2a n )log(b x + a) +--R + +--R 2 4 2 2 2 4 2 2 2 2 2 +--R ((4b n x - 4a n)log(c) - 2b n x + 4a b n x + 6a n )log(b x + a) +--R + +--R 2 4 2 2 4 2 2 2 4 2 2 +--R 2b x log(c) + (- 2b n x + 4a b n x )log(c) + b n x - 6a b n x +--R / +--R 2 +--R 8b +--R Type: Union(Expression Integer,...) +--E 346 + +--S 347 of 518 +m0165:= a0165-r0165 +--R +--R +--R (301) +--R 2 4 2 2 n 2 +--R (- b x + a )log(c (b x + a) ) +--R + +--R 2 4 2 2 2 n +--R (b n x - 2a b n x - 2a n)log(c (b x + a) ) +--R + +--R 2 2 4 2 2 2 2 +--R (b n x - a n )log(b x + a) +--R + +--R 2 4 2 2 2 4 2 2 2 2 2 +--R ((2b n x - 2a n)log(c) - b n x + 2a b n x + 2a n )log(b x + a) +--R + +--R 2 4 2 2 4 2 +--R b x log(c) + (- b n x + 2a b n x )log(c) +--R / +--R 2 +--R 4b +--R Type: Expression Integer +--E 347 + +--S 348 of 518 +d0165:= D(m0165,x) +--R +--R +--R (302) +--R 2 5 3 2 n 2 n 2 +--R (- 2b x - 2a b x )(b x + a) log(c (b x + a) ) +--R + +--R 2 5 2 2 n +--R (2b n x - 2a n x)(b x + a) +--R + +--R 3 7 2 5 2 3 3 2 n - 1 +--R (- 2b n x - 2a b n x + 2a b n x + 2a n x)(b x + a) +--R * +--R 2 n +--R log(c (b x + a) ) +--R + +--R 2 2 5 2 3 2 2 +--R (2b n x + 2a b n x )log(b x + a) +--R + +--R 2 5 3 2 2 5 3 2 +--R (4b n x + 4a b n x )log(c)log(b x + a) + (2b x + 2a b x )log(c) +--R + +--R 2 2 5 2 3 2 2 +--R - b n x + 2a b n x + 2a n x +--R * +--R 2 n +--R (b x + a) +--R + +--R 3 2 7 2 2 5 2 2 3 3 2 2 n - 1 +--R (b n x - a b n x - 4a b n x - 2a n x)(b x + a) +--R / +--R 2 2 2 n +--R (2b x + 2a b)(b x + a) +--R Type: Expression Integer +--E 348 + +--S 349 of 518 +t0166:= log(c*(a+b*x^2)^n)^2/x +--R +--R +--R 2 n 2 +--R log(c (b x + a) ) +--R (303) ------------------- +--R x +--R Type: Expression Integer +--E 349 + +--S 350 of 518 +r0166:= 1/2*log(-b*x^2/a)*log(c*(a+b*x^2)^n)^2+_ + n*log(c*(a+b*x^2)^n)*polylog(2,1+b*x^2/a)-n^2*polylog(3,(a+b*x^2)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 350 + +--S 351 of 518 +a0166:= integrate(t0166,x) +--R +--R +--R x 2 n 2 +--R ++ log(c (%L b + a) ) +--R (304) | ------------------- d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 351 + +--S 352 of 518 +--m0166:= a0166-r0166 +--E 352 + +--S 353 of 518 +--d0166:= D(m0166,x) +--E 353 + +--S 354 of 518 +t0167:= log(c*(a+b*x^2)^n)^2/x^3 +--R +--R +--R 2 n 2 +--R log(c (b x + a) ) +--R (305) ------------------- +--R 3 +--R x +--R Type: Expression Integer +--E 354 + +--S 355 of 518 +r0167:= b*n*log(-b*x^2/a)*log(c*(a+b*x^2)^n)/a-_ + 1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)^2/a/x^2+b*n^2*polylog(2,1+b*x^2/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 355 + +--S 356 of 518 +a0167:= integrate(t0167,x) +--R +--R +--R x 2 n 2 +--R ++ log(c (%L b + a) ) +--R (306) | ------------------- d%L +--R ++ 3 +--R %L +--R Type: Union(Expression Integer,...) +--E 356 + +--S 357 of 518 +--m0167:= a0167-r0167 +--E 357 + +--S 358 of 518 +--d0167:= D(m0167,x) +--E 358 + +--S 359 of 518 +t0168:= x*log(c*(a+b*x^2)^n)^3 +--R +--R +--R 2 n 3 +--R (307) x log(c (b x + a) ) +--R Type: Expression Integer +--E 359 + +--S 360 of 518 +r0168:= -3*n^3*x^2+3*n^2*(a+b*x^2)*log(c*(a+b*x^2)^n)/b-_ + 3/2*n*(a+b*x^2)*log(c*(a+b*x^2)^n)^2/b+_ + 1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)^3/b +--R +--R +--R (308) +--R 2 2 n 3 2 2 n 2 +--R (b x + a)log(c (b x + a) ) + (- 3b n x - 3a n)log(c (b x + a) ) +--R + +--R 2 2 2 2 n 3 2 +--R (6b n x + 6a n )log(c (b x + a) ) - 6b n x +--R / +--R 2b +--R Type: Expression Integer +--E 360 + +--S 361 of 518 +a0168:= integrate(t0168,x) +--R +--R +--R (309) +--R 3 2 3 2 3 +--R (b n x + a n )log(b x + a) +--R + +--R 2 2 2 3 2 3 2 2 +--R ((3b n x + 3a n )log(c) - 3b n x - 3a n )log(b x + a) +--R + +--R 2 2 2 2 2 3 2 3 +--R ((3b n x + 3a n)log(c) + (- 6b n x - 6a n )log(c) + 6b n x + 6a n ) +--R * +--R 2 +--R log(b x + a) +--R + +--R 2 3 2 2 2 2 3 2 +--R b x log(c) - 3b n x log(c) + 6b n x log(c) - 6b n x +--R / +--R 2b +--R Type: Union(Expression Integer,...) +--E 361 + +--S 362 of 518 +m0168:= a0168-r0168 +--R +--R +--R (310) +--R 2 2 n 3 2 2 n 2 +--R (- b x - a)log(c (b x + a) ) + (3b n x + 3a n)log(c (b x + a) ) +--R + +--R 2 2 2 2 n 3 2 3 2 3 +--R (- 6b n x - 6a n )log(c (b x + a) ) + (b n x + a n )log(b x + a) +--R + +--R 2 2 2 3 2 3 2 2 +--R ((3b n x + 3a n )log(c) - 3b n x - 3a n )log(b x + a) +--R + +--R 2 2 2 2 2 3 2 3 +--R ((3b n x + 3a n)log(c) + (- 6b n x - 6a n )log(c) + 6b n x + 6a n ) +--R * +--R 2 +--R log(b x + a) +--R + +--R 2 3 2 2 2 2 +--R b x log(c) - 3b n x log(c) + 6b n x log(c) +--R / +--R 2b +--R Type: Expression Integer +--E 362 + +--S 363 of 518 +d0168:= D(m0168,x) +--R +--R +--R (311) +--R 2 n 2 n 3 +--R - x (b x + a) log(c (b x + a) ) +--R + +--R 2 n 3 2 n - 1 +--R (3n x (b x + a) + (- 3b n x - 3a n x)(b x + a) ) +--R * +--R 2 n 2 +--R log(c (b x + a) ) +--R + +--R 2 2 n 2 3 2 2 n - 1 +--R (- 6n x (b x + a) + (6b n x + 6a n x)(b x + a) ) +--R * +--R 2 n +--R log(c (b x + a) ) +--R + +--R 3 2 3 2 2 2 +--R n x log(b x + a) + 3n x log(c)log(b x + a) +--R + +--R 2 2 3 3 +--R 3n x log(c) log(b x + a) + x log(c) + 6n x +--R * +--R 2 n +--R (b x + a) +--R + +--R 3 3 3 2 n - 1 +--R (- 6b n x - 6a n x)(b x + a) +--R / +--R 2 n +--R (b x + a) +--R Type: Expression Integer +--E 363 + +--S 364 of 518 +t0169:= x^3*log(c*(a+b*x^2)^n)^3 +--R +--R +--R 3 2 n 3 +--R (312) x log(c (b x + a) ) +--R Type: Expression Integer +--E 364 + +--S 365 of 518 +r0169:= 21/8*a*n^3*x^2/b-3/16*n^3*x^4-3/8*a^2*n^3*log(a+b*x^2)/b^2+_ + 3/8*n^2*x^4*log(c*(a+b*x^2)^n)-9/4*a*n^2*(a+b*x^2)*_ + log(c*(a+b*x^2)^n)/b^2-3/8*n*x^4*log(c*(a+b*x^2)^n)^2+_ + 9/8*a*n*(a+2/3*b*x^2)*log(c*(a+b*x^2)^n)^2/b^2-_ + 1/4*a^2*log(c*(a+b*x^2)^n)^3/b^2+1/4*x^4*log(c*(a+b*x^2)^n)^3 +--R +--R +--R (313) +--R 2 4 2 2 n 3 +--R (4b x - 4a )log(c (b x + a) ) +--R + +--R 2 4 2 2 2 n 2 +--R (- 6b n x + 12a b n x + 18a n)log(c (b x + a) ) +--R + +--R 2 2 4 2 2 2 2 2 n 2 3 2 +--R (6b n x - 36a b n x - 36a n )log(c (b x + a) ) - 6a n log(b x + a) +--R + +--R 2 3 4 3 2 +--R - 3b n x + 42a b n x +--R / +--R 2 +--R 16b +--R Type: Expression Integer +--E 365 + +--S 366 of 518 +a0169:= integrate(t0169,x) +--R +--R +--R (314) +--R 2 3 4 2 3 2 3 +--R (4b n x - 4a n )log(b x + a) +--R + +--R 2 2 4 2 2 2 3 4 3 2 2 3 2 2 +--R ((12b n x - 12a n )log(c) - 6b n x + 12a b n x + 18a n )log(b x + a) +--R + +--R 2 4 2 2 2 2 4 2 2 2 2 +--R (12b n x - 12a n)log(c) + (- 12b n x + 24a b n x + 36a n )log(c) +--R + +--R 2 3 4 3 2 2 3 +--R 6b n x - 36a b n x - 42a n +--R * +--R 2 +--R log(b x + a) +--R + +--R 2 4 3 2 4 2 2 +--R 4b x log(c) + (- 6b n x + 12a b n x )log(c) +--R + +--R 2 2 4 2 2 2 3 4 3 2 +--R (6b n x - 36a b n x )log(c) - 3b n x + 42a b n x +--R / +--R 2 +--R 16b +--R Type: Union(Expression Integer,...) +--E 366 + +--S 367 of 518 +m0169:= a0169-r0169 +--R +--R +--R (315) +--R 2 4 2 2 n 3 +--R (- 2b x + 2a )log(c (b x + a) ) +--R + +--R 2 4 2 2 2 n 2 +--R (3b n x - 6a b n x - 9a n)log(c (b x + a) ) +--R + +--R 2 2 4 2 2 2 2 2 n +--R (- 3b n x + 18a b n x + 18a n )log(c (b x + a) ) +--R + +--R 2 3 4 2 3 2 3 +--R (2b n x - 2a n )log(b x + a) +--R + +--R 2 2 4 2 2 2 3 4 3 2 2 3 2 2 +--R ((6b n x - 6a n )log(c) - 3b n x + 6a b n x + 9a n )log(b x + a) +--R + +--R 2 4 2 2 2 2 4 2 2 2 2 +--R (6b n x - 6a n)log(c) + (- 6b n x + 12a b n x + 18a n )log(c) +--R + +--R 2 3 4 3 2 2 3 +--R 3b n x - 18a b n x - 18a n +--R * +--R 2 +--R log(b x + a) +--R + +--R 2 4 3 2 4 2 2 +--R 2b x log(c) + (- 3b n x + 6a b n x )log(c) +--R + +--R 2 2 4 2 2 +--R (3b n x - 18a b n x )log(c) +--R / +--R 2 +--R 8b +--R Type: Expression Integer +--E 367 + +--S 368 of 518 +d0169:= D(m0169,x) +--R +--R +--R (316) +--R 2 5 3 2 n 2 n 3 +--R (- 4b x - 4a b x )(b x + a) log(c (b x + a) ) +--R + +--R 2 5 2 2 n +--R (6b n x - 6a n x)(b x + a) +--R + +--R 3 7 2 5 2 3 3 2 n - 1 +--R (- 6b n x - 6a b n x + 6a b n x + 6a n x)(b x + a) +--R * +--R 2 n 2 +--R log(c (b x + a) ) +--R + +--R 2 2 5 2 3 2 2 2 n +--R (- 6b n x + 12a b n x + 18a n x)(b x + a) +--R + +--R 3 2 7 2 2 5 2 2 3 3 2 2 n - 1 +--R (6b n x - 6a b n x - 30a b n x - 18a n x)(b x + a) +--R * +--R 2 n +--R log(c (b x + a) ) +--R + +--R 2 3 5 3 3 2 3 +--R (4b n x + 4a b n x )log(b x + a) +--R + +--R 2 2 5 2 3 2 2 +--R (12b n x + 12a b n x )log(c)log(b x + a) +--R + +--R 2 5 3 2 2 +--R (12b n x + 12a b n x )log(c) log(b x + a) +--R + +--R 2 5 3 3 2 3 5 3 3 2 3 +--R (4b x + 4a b x )log(c) + 3b n x - 18a b n x - 18a n x +--R * +--R 2 n +--R (b x + a) +--R + +--R 3 3 7 2 3 5 2 3 3 3 3 2 n - 1 +--R (- 3b n x + 15a b n x + 36a b n x + 18a n x)(b x + a) +--R / +--R 2 2 2 n +--R (4b x + 4a b)(b x + a) +--R Type: Expression Integer +--E 368 + +--S 369 of 518 +t0170:= log(c*(a+b*x^2)^n)^3/x +--R +--R +--R 2 n 3 +--R log(c (b x + a) ) +--R (317) ------------------- +--R x +--R Type: Expression Integer +--E 369 + +--S 370 of 518 +r0170:= 1/2*log(-b*x^2/a)*log(c*(a+b*x^2)^n)^3+_ + 3/2*n*log(c*(a+b*x^2)^n)^2*polylog(2,1+b*x^2/a)-_ + 3*n^2*log(c*(a+b*x^2)^n)*polylog(3,1+b*x^2/a)+_ + 3*n^3*polylog(4,(a+b*x^2)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 370 + +--S 371 of 518 +a0170:= integrate(t0170,x) +--R +--R +--R x 2 n 3 +--R ++ log(c (%L b + a) ) +--R (318) | ------------------- d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 371 + +--S 372 of 518 +--m0170:= a0170-r0170 +--E 372 + +--S 373 of 518 +--d0170:= D(m0170,x) +--E 373 + +--S 374 of 518 +t0171:= log(c*(a+b*x^2)^n)^3/x^3 +--R +--R +--R 2 n 3 +--R log(c (b x + a) ) +--R (319) ------------------- +--R 3 +--R x +--R Type: Expression Integer +--E 374 + +--S 375 of 518 +r0171:= 3/2*b*n*log(-b*x^2/a)*log(c*(a+b*x^2)^n)^2/a-_ + 1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)^3/a/x^2+_ + 3*b*n^2*log(c*(a+b*x^2)^n)*polylog(2,1+b*x^2/a)/a-_ + 3*b*n^3*polylog(3,(a+b*x^2)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 375 + +--S 376 of 518 +a0171:= integrate(t0171,x) +--R +--R +--R x 2 n 3 +--R ++ log(c (%L b + a) ) +--R (320) | ------------------- d%L +--R ++ 3 +--R %L +--R Type: Union(Expression Integer,...) +--E 376 + +--S 377 of 518 +--m0171:= a0171-r0171 +--E 377 + +--S 378 of 518 +--d0171:= D(m0171,x) +--E 378 + +--S 379 of 518 +t0172:= x/log(c*(a+b*x^2)^n) +--R +--R +--R x +--R (321) ------------------ +--R 2 n +--R log(c (b x + a) ) +--R Type: Expression Integer +--E 379 + +--S 380 of 518 +r0172:= 1/2*(a+b*x^2)*Ei(log(c*(a+b*x^2)^n)/n)/b/n/((c*(a+b*x^2)^n)^(1/n)) +--R +--R +--R 2 n +--R 2 log(c (b x + a) ) +--R (b x + a)Ei(------------------) +--R n +--R (322) -------------------------------- +--R 1 +--R - +--R 2 n n +--R 2b n (c (b x + a) ) +--R Type: Expression Integer +--E 380 + +--S 381 of 518 +a0172:= integrate(t0172,x) +--R +--R +--R x +--R ++ %L +--R (323) | ------------------ d%L +--R ++ 2 n +--R log(c (%L b + a) ) +--R Type: Union(Expression Integer,...) +--E 381 + +--S 382 of 518 +--m0172:= a0172-r0172 +--E 382 + +--S 383 of 518 +--d0172:= D(m0172,x) +--E 383 + +--S 384 of 518 +t0173:= x^3/log(c*(a+b*x^2)^n) +--R +--R +--R 3 +--R x +--R (324) ------------------ +--R 2 n +--R log(c (b x + a) ) +--R Type: Expression Integer +--E 384 + +--S 385 of 518 +r0173:= -1/2*a*(a+b*x^2)*Ei(log(c*(a+b*x^2)^n)/n)/_ + ((c*(a+b*x^2)^n)^(1/n))/b^2/n+1/2*(a+b*x^2)^2*_ + Ei(2*log(c*(a+b*x^2)^n)/n)/((c*(a+b*x^2)^n)^(2/n))/b^2/n +--R +--R +--R (325) +--R 1 +--R - 2 n +--R 2 4 2 2 2 n n 2log(c (b x + a) ) +--R (b x + 2a b x + a )(c (b x + a) ) Ei(-------------------) +--R n +--R + +--R 2 +--R - 2 n +--R 2 2 2 n n log(c (b x + a) ) +--R (- a b x - a )(c (b x + a) ) Ei(------------------) +--R n +--R / +--R 1 2 +--R - - +--R 2 2 n n 2 n n +--R 2b n (c (b x + a) ) (c (b x + a) ) +--R Type: Expression Integer +--E 385 + +--S 386 of 518 +a0173:= integrate(t0173,x) +--R +--R +--R x 3 +--R ++ %L +--R (326) | ------------------ d%L +--R ++ 2 n +--R log(c (%L b + a) ) +--R Type: Union(Expression Integer,...) +--E 386 + +--S 387 of 518 +--m0173:= a0173-r0173 +--E 387 + +--S 388 of 518 +--d0173:= D(m0173,x) +--E 388 + +--S 389 of 518 +t0174:= x/log(c*(a+b*x^2)^n)^2 +--R +--R +--R x +--R (327) ------------------- +--R 2 n 2 +--R log(c (b x + a) ) +--R Type: Expression Integer +--E 389 + +--S 390 of 518 +r0174:= 1/2*(a+b*x^2)*(Ei(log(c*(a+b*x^2)^n)/n)*_ + (c*(a+b*x^2)^n)^(-1/n)*log(c*(a+b*x^2)^n)-n)/n^2/b/log(c*(a+b*x^2)^n) +--R +--R +--R (328) +--R 1 +--R - - 2 n +--R 2 2 n 2 n n log(c (b x + a) ) +--R (b x + a)log(c (b x + a) )(c (b x + a) ) Ei(------------------) +--R n +--R + +--R 2 +--R - b n x - a n +--R / +--R 2 2 n +--R 2b n log(c (b x + a) ) +--R Type: Expression Integer +--E 390 + +--S 391 of 518 +a0174:= integrate(t0174,x) +--R +--R +--R x +--R ++ %L +--R (329) | ------------------- d%L +--R ++ 2 n 2 +--R log(c (%L b + a) ) +--R Type: Union(Expression Integer,...) +--E 391 + +--S 392 of 518 +--m0174:= a0174-r0174 +--E 392 + +--S 393 of 518 +--d0174:= D(m0174,x) +--E 393 + +--S 394 of 518 +t0175:= x^3/log(c*(a+b*x^2)^n)^2 +--R +--R +--R 3 +--R x +--R (330) ------------------- +--R 2 n 2 +--R log(c (b x + a) ) +--R Type: Expression Integer +--E 394 + +--S 395 of 518 +r0175:= -1/2*a*(a+b*x^2)*Ei(log(c*(a+b*x^2)^n)/n)/_ + ((c*(a+b*x^2)^n)^(1/n))/b^2/n^2+(a+b*x^2)^2*_ + Ei(2*log(c*(a+b*x^2)^n)/n)/((c*(a+b*x^2)^n)^(2/n))/b^2/n^2+_ + 1/2*a*(a+b*x^2)/b^2/n/log(c*(a+b*x^2)^n)-_ + 1/2*(a+b*x^2)^2/b^2/n/log(c*(a+b*x^2)^n) +--R +--R +--R (331) +--R 1 +--R - +--R 2 4 2 2 2 n 2 n n +--R (2b x + 4a b x + 2a )log(c (b x + a) )(c (b x + a) ) +--R * +--R 2 n +--R 2log(c (b x + a) ) +--R Ei(-------------------) +--R n +--R + +--R 2 +--R - 2 n +--R 2 2 2 n 2 n n log(c (b x + a) ) +--R (- a b x - a )log(c (b x + a) )(c (b x + a) ) Ei(------------------) +--R n +--R + +--R 1 2 +--R - - +--R 2 4 2 2 n n 2 n n +--R (- b n x - a b n x )(c (b x + a) ) (c (b x + a) ) +--R / +--R 1 2 +--R - - +--R 2 2 2 n 2 n n 2 n n +--R 2b n log(c (b x + a) )(c (b x + a) ) (c (b x + a) ) +--R Type: Expression Integer +--E 395 + +--S 396 of 518 +a0175:= integrate(t0175,x) +--R +--R +--R x 3 +--R ++ %L +--R (332) | ------------------- d%L +--R ++ 2 n 2 +--R log(c (%L b + a) ) +--R Type: Union(Expression Integer,...) +--E 396 + +--S 397 of 518 +--m0175:= a0175-r0175 +--E 397 + +--S 398 of 518 +--d0175:= D(m0175,x) +--E 398 + +--S 399 of 518 +t0176:= x/log(c*(a+b*x^2)^n)^3 +--R +--R +--R x +--R (333) ------------------- +--R 2 n 3 +--R log(c (b x + a) ) +--R Type: Expression Integer +--E 399 + +--S 400 of 518 +r0176:= 1/4*(a+b*x^2)*(Ei(log(c*(a+b*x^2)^n)/n)*_ + (c*(a+b*x^2)^n)^(-1/n)*log(c*(a+b*x^2)^n)^2-_ + n^2-n*log(c*(a+b*x^2)^n))/n^3/b/log(c*(a+b*x^2)^n)^2 +--R +--R +--R (334) +--R 1 +--R - - 2 n +--R 2 2 n 2 2 n n log(c (b x + a) ) +--R (b x + a)log(c (b x + a) ) (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 2 2 n 2 2 2 +--R (- b n x - a n)log(c (b x + a) ) - b n x - a n +--R / +--R 3 2 n 2 +--R 4b n log(c (b x + a) ) +--R Type: Expression Integer +--E 400 + +--S 401 of 518 +a0176:= integrate(t0176,x) +--R +--R +--R x +--R ++ %L +--R (335) | ------------------- d%L +--R ++ 2 n 3 +--R log(c (%L b + a) ) +--R Type: Union(Expression Integer,...) +--E 401 + +--S 402 of 518 +--m0176:= a0176-r0176 +--E 402 + +--S 403 of 518 +--d0176:= D(m0176,x) +--E 403 + +--S 404 of 518 +t0177:= x^3/log(c*(a+b*x^2)^n)^3 +--R +--R +--R 3 +--R x +--R (336) ------------------- +--R 2 n 3 +--R log(c (b x + a) ) +--R Type: Expression Integer +--E 404 + +--S 405 of 518 +r0177:= 1/4*(a+b*x^2)*(-Ei(log(c*(a+b*x^2)^n)/n)*(c*(a+b*x^2)^n)^(-1/n)*_ + log(c*(a+b*x^2)^n)^2*a+4*Ei(2*log(c*(a+b*x^2)^n)/n)*_ + (c*(a+b*x^2)^n)^(-2/n)*log(c*(a+b*x^2)^n)^2*a+_ + 4*Ei(2*log(c*(a+b*x^2)^n)/n)*(c*(a+b*x^2)^n)^(-2/n)*_ + log(c*(a+b*x^2)^n)^2*b*x^2-n^2*x^2*b-n*log(c*(a+b*x^2)^n)*a-_ + 2*n*log(c*(a+b*x^2)^n)*b*x^2)/n^3/b^2/log(c*(a+b*x^2)^n)^2 +--R +--R +--R (337) +--R 2 +--R - - +--R 2 4 2 2 2 n 2 2 n n +--R (4b x + 8a b x + 4a )log(c (b x + a) ) (c (b x + a) ) +--R * +--R 2 n +--R 2log(c (b x + a) ) +--R Ei(-------------------) +--R n +--R + +--R 1 +--R - - +--R 2 2 2 n 2 2 n n +--R (- a b x - a )log(c (b x + a) ) (c (b x + a) ) +--R * +--R 2 n +--R log(c (b x + a) ) +--R Ei(------------------) +--R n +--R + +--R 2 4 2 2 2 n 2 2 4 2 2 +--R (- 2b n x - 3a b n x - a n)log(c (b x + a) ) - b n x - a b n x +--R / +--R 2 3 2 n 2 +--R 4b n log(c (b x + a) ) +--R Type: Expression Integer +--E 405 + +--S 406 of 518 +a0177:= integrate(t0177,x) +--R +--R +--R x 3 +--R ++ %L +--R (338) | ------------------- d%L +--R ++ 2 n 3 +--R log(c (%L b + a) ) +--R Type: Union(Expression Integer,...) +--E 406 + +--S 407 of 518 +--m0177:= a0177-r0177 +--E 407 + +--S 408 of 518 +--d0177:= D(m0177,x) +--E 408 + +--S 409 of 518 +t0178:= log(c*(a*x+b)/x) +--R +--R +--R a c x + b c +--R (339) log(-----------) +--R x +--R Type: Expression Integer +--E 409 + +--S 410 of 518 +r0178:= b*log(a*x+b)/a+x*log(c*(a*x+b)/x) +--R +--R +--R a c x + b c +--R b log(a x + b) + a x log(-----------) +--R x +--R (340) ------------------------------------- +--R a +--R Type: Expression Integer +--E 410 + +--S 411 of 518 +a0178:= integrate(t0178,x) +--R +--R +--R a c x + b c +--R b log(a x + b) + a x log(-----------) +--R x +--R (341) ------------------------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 411 + +--S 412 of 518 +m0178:= a0178-r0178 +--R +--R +--R (342) 0 +--R Type: Expression Integer +--E 412 + +--S 413 of 518 +d0178:= D(m0178,x) +--R +--R +--R (343) 0 +--R Type: Expression Integer +--E 413 + +--S 414 of 518 +t0179:= log(c*(a*x+b)/x)^2 +--R +--R +--R a c x + b c 2 +--R (344) log(-----------) +--R x +--R Type: Expression Integer +--E 414 + +--S 415 of 518 +r0179:= (a*x+b)*log(a*c+b*c/x)^2/a-2*b*log(a*c+b*c/x)*log(-b/a/x)/a-_ + 2*b*polylog(2,1+b/a/x)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 415 + +--S 416 of 518 +a0179:= integrate(t0179,x) +--R +--R +--R x +--R ++ (b + %L a)c 2 +--R (345) | log(-----------) d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 416 + +--S 417 of 518 +--m0179:= a0179-r0179 +--E 417 + +--S 418 of 518 +--d0179:= D(m0179,x) +--E 418 + +--S 419 of 518 +t0180:= log(c*(a*x+b)/x)^3 +--R +--R +--R a c x + b c 3 +--R (346) log(-----------) +--R x +--R Type: Expression Integer +--E 419 + +--S 420 of 518 +r0180:= (a*x+b)*log(a*c+b*c/x)^3/a-3*b*log(a*c+b*c/x)^2*log(-b/a/x)/a-_ + 6*b*log(a*c+b*c/x)*polylog(2,1+b/a/x)/a+6*b*polylog(3,(a+b/x)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 420 + +--S 421 of 518 +a0180:= integrate(t0180,x) +--R +--R +--R x +--R ++ (b + %L a)c 3 +--R (347) | log(-----------) d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 421 + +--S 422 of 518 +--m0180:= a0180-r0180 +--E 422 + +--S 423 of 518 +--d0180:= D(m0180,x) +--E 423 + +--S 424 of 518 +t0181:= log(c*x/(a*x+b))^2 +--R +--R +--R c x 2 +--R (348) log(-------) +--R a x + b +--R Type: Expression Integer +--E 424 + +--S 425 of 518 +r0181:= (2*b*log(b/(a*x+b))*log(c*x/(a*x+b))+x*log(c*x/(a*x+b))^2*a+_ + 2*b*polylog(2,a*x/(a*x+b)))/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 425 + +--S 426 of 518 +a0181:= integrate(t0181,x) +--R +--R +--R x +--R ++ %L c 2 +--R (349) | log(--------) d%L +--R ++ b + %L a +--R Type: Union(Expression Integer,...) +--E 426 + +--S 427 of 518 +--m0181:= a0181-r0181 +--E 427 + +--S 428 of 518 +--d0181:= D(m0181,x) +--E 428 + +--S 429 of 518 +t0182:= log(c*x/(a*x+b))^3 +--R +--R +--R c x 3 +--R (350) log(-------) +--R a x + b +--R Type: Expression Integer +--E 429 + +--S 430 of 518 +r0182:= (3*b*log(b/(a*x+b))*log(c*x/(a*x+b))^2+x*log(c*x/(a*x+b))^3*a+_ + 6*b*log(c*x/(a*x+b))*polylog(2,a*x/(a*x+b))-_ + 6*b*polylog(3,a*x/(a*x+b)))/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 430 + +--S 431 of 518 +a0182:= integrate(t0182,x) +--R +--R +--R x +--R ++ %L c 3 +--R (351) | log(--------) d%L +--R ++ b + %L a +--R Type: Union(Expression Integer,...) +--E 431 + +--S 432 of 518 +--m0182:= a0182-r0182 +--E 432 + +--S 433 of 518 +--d0182:= D(m0182,x) +--E 433 + +--S 434 of 518 +t0183:= log(c*(a*x+b)^2/x^2) +--R +--R +--R 2 2 2 +--R a c x + 2a b c x + b c +--R (352) log(-----------------------) +--R 2 +--R x +--R Type: Expression Integer +--E 434 + +--S 435 of 518 +r0183:= 2*b*log(a*x+b)/a+x*log(c*(a*x+b)^2/x^2) +--R +--R +--R 2 2 2 +--R a c x + 2a b c x + b c +--R 2b log(a x + b) + a x log(-----------------------) +--R 2 +--R x +--R (353) -------------------------------------------------- +--R a +--R Type: Expression Integer +--E 435 + +--S 436 of 518 +a0183:= integrate(t0183,x) +--R +--R +--R 2 2 2 +--R a c x + 2a b c x + b c +--R 2b log(a x + b) + a x log(-----------------------) +--R 2 +--R x +--R (354) -------------------------------------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 436 + +--S 437 of 518 +m0183:= a0183-r0183 +--R +--R +--R (355) 0 +--R Type: Expression Integer +--E 437 + +--S 438 of 518 +d0183:= D(m0183,x) +--R +--R +--R (356) 0 +--R Type: Expression Integer +--E 438 + +--S 439 of 518 +t0184:= log(c*(a*x+b)^2/x^2)^2 +--R +--R +--R 2 2 2 2 +--R a c x + 2a b c x + b c +--R (357) log(-----------------------) +--R 2 +--R x +--R Type: Expression Integer +--E 439 + +--S 440 of 518 +r0184:= (a*x+b)*log(c*(a+b/x)^2)^2/a-4*b*log(c*(a+b/x)^2)*log(-b/a/x)/a-_ + 8*b*polylog(2,1+b/a/x)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 440 + +--S 441 of 518 +a0184:= integrate(t0184,x) +--R +--R +--R x 2 2 2 2 +--R ++ (b + 2%L a b + %L a )c +--R (358) | log(-----------------------) d%L +--R ++ 2 +--R %L +--R Type: Union(Expression Integer,...) +--E 441 + +--S 442 of 518 +--m0184:= a0184-r0184 +--E 442 + +--S 443 of 518 +--d0184:= D(m0184,x) +--E 443 + +--S 444 of 518 +t0185:= log(c*(a*x+b)^2/x^2)^3 +--R +--R +--R 2 2 2 3 +--R a c x + 2a b c x + b c +--R (359) log(-----------------------) +--R 2 +--R x +--R Type: Expression Integer +--E 444 + +--S 445 of 518 +r0185:= (a*x+b)*log(c*(a+b/x)^2)^3/a-6*b*log(c*(a+b/x)^2)^2*log(-b/a/x)/a-_ + 24*b*log(c*(a+b/x)^2)*polylog(2,1+b/a/x)/a+48*b*polylog(3,(a+b/x)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 445 + +--S 446 of 518 +a0185:= integrate(t0185,x) +--R +--R +--R x 2 2 2 3 +--R ++ (b + 2%L a b + %L a )c +--R (360) | log(-----------------------) d%L +--R ++ 2 +--R %L +--R Type: Union(Expression Integer,...) +--E 446 + +--S 447 of 518 +--m0185:= a0185-r0185 +--E 447 + +--S 448 of 518 +--d0185:= D(m0185,x) +--E 448 + +--S 449 of 518 +t0186:= log(c*x^2/(a*x+b)^2) +--R +--R +--R 2 +--R c x +--R (361) log(------------------) +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression Integer +--E 449 + +--S 450 of 518 +r0186:= x*log(c*x^2/(a*x+b)^2)-2*b*log(a*x+b)/a +--R +--R +--R 2 +--R c x +--R - 2b log(a x + b) + a x log(------------------) +--R 2 2 2 +--R a x + 2a b x + b +--R (362) ----------------------------------------------- +--R a +--R Type: Expression Integer +--E 450 + +--S 451 of 518 +a0186:= integrate(t0186,x) +--R +--R +--R 2 +--R c x +--R - 2b log(a x + b) + a x log(------------------) +--R 2 2 2 +--R a x + 2a b x + b +--R (363) ----------------------------------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 451 + +--S 452 of 518 +m0186:= a0186-r0186 +--R +--R +--R (364) 0 +--R Type: Expression Integer +--E 452 + +--S 453 of 518 +d0186:= D(m0186,x) +--R +--R +--R (365) 0 +--R Type: Expression Integer +--E 453 + +--S 454 of 518 +t0187:= log(c*x^2/(a*x+b)^2)^2 +--R +--R +--R 2 2 +--R c x +--R (366) log(------------------) +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression Integer +--E 454 + +--S 455 of 518 +r0187:= (a*x+b)*log(c/(a+b/x)^2)^2/a+4*b*log(c/(a+b/x)^2)*log(-b/a/x)/a-_ + 8*b*polylog(2,1+b/a/x)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 455 + +--S 456 of 518 +a0187:= integrate(t0187,x) +--R +--R +--R x 2 2 +--R ++ %L c +--R (367) | log(--------------------) d%L +--R ++ 2 2 2 +--R b + 2%L a b + %L a +--R Type: Union(Expression Integer,...) +--E 456 + +--S 457 of 518 +--m0187:= a0187-r0187 +--E 457 + +--S 458 of 518 +--d0187:= D(m0187,x) +--E 458 + +--S 459 of 518 +t0188:= log(c*x^2/(a*x+b)^2)^3 +--R +--R +--R 2 3 +--R c x +--R (368) log(------------------) +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression Integer +--E 459 + +--S 460 of 518 +r0188:= (a*x+b)*log(c/(a+b/x)^2)^3/a+6*b*log(c/(a+b/x)^2)^2*log(-b/a/x)/a-_ + 24*b*log(c/(a+b/x)^2)*polylog(2,1+b/a/x)/a-48*b*polylog(3,(a+b/x)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 460 + +--S 461 of 518 +a0188:= integrate(t0188,x) +--R +--R +--R x 2 3 +--R ++ %L c +--R (369) | log(--------------------) d%L +--R ++ 2 2 2 +--R b + 2%L a b + %L a +--R Type: Union(Expression Integer,...) +--E 461 + +--S 462 of 518 +--m0188:= a0188-r0188 +--E 462 + +--S 463 of 518 +--d0188:= D(m0188,x) +--E 463 + +--S 464 of 518 +t0189:= log(c*(a+b/x)^n)^2 +--R +--R +--R a x + b n 2 +--R (370) log(c (-------) ) +--R x +--R Type: Expression Integer +--E 464 + +--S 465 of 518 +r0189:= (a*x+b)*log(c*(a+b/x)^n)^2/a-2*b*n*log(c*(a+b/x)^n)*log(-b/a/x)/a-_ + 2*b*n^2*polylog(2,1+b/a/x)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 465 + +--S 466 of 518 +a0189:= integrate(t0189,x) +--R +--R +--R x +--R ++ b + %L a n 2 +--R (371) | log(c (--------) ) d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 466 + +--S 467 of 518 +--m0189:= a0189-r0189 +--E 467 + +--S 468 of 518 +--d0189:= D(m0189,x) +--E 468 + +--S 469 of 518 +t0190:= log(c*(a+b/x)^n)^3 +--R +--R +--R a x + b n 3 +--R (372) log(c (-------) ) +--R x +--R Type: Expression Integer +--E 469 + +--S 470 of 518 +r0190:= (a*x+b)*log(c*(a+b/x)^n)^3/a-3*b*n*log(c*(a+b/x)^n)^2*log(-b/a/x)/a-_ + 6*b*n^2*log(c*(a+b/x)^n)*polylog(2,1+b/a/x)/a+_ + 6*b*n^3*polylog(3,(a+b/x)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 470 + +--S 471 of 518 +a0190:= integrate(t0190,x) +--R +--R +--R x +--R ++ b + %L a n 3 +--R (373) | log(c (--------) ) d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 471 + +--S 472 of 518 +--m0190:= a0190-r0190 +--E 472 + +--S 473 of 518 +--d0190:= D(m0190,x) +--E 473 + +--S 474 of 518 +t0191:= log(a+b*x^(1/2))/x^(1/2) +--R +--R +--R +-+ +--R log(b\|x + a) +--R (374) -------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 474 + +--S 475 of 518 +r0191:= -2*x^(1/2)+2*(a+b*x^(1/2))*log(a+b*x^(1/2))/b +--R +--R +--R +-+ +-+ +-+ +--R (2b\|x + 2a)log(b\|x + a) - 2b\|x +--R (375) ------------------------------------ +--R b +--R Type: Expression Integer +--E 475 + +--S 476 of 518 +a0191:= integrate(t0191,x) +--R +--R +--R +-+ +-+ +-+ +--R (2b\|x + 2a)log(b\|x + a) - 2b\|x +--R (376) ------------------------------------ +--R b +--R Type: Union(Expression Integer,...) +--E 476 + +--S 477 of 518 +m0191:= a0191-r0191 +--R +--R +--R (377) 0 +--R Type: Expression Integer +--E 477 + +--S 478 of 518 +d0191:= D(m0191,x) +--R +--R +--R (378) 0 +--R Type: Expression Integer +--E 478 + +--S 479 of 518 +t0192:= log(2+b*x^m)/x +--R +--R +--R m +--R log(b x + 2) +--R (379) ------------- +--R x +--R Type: Expression Integer +--E 479 + +--S 480 of 518 +r0192:= 1/m*(log(2)*log(x^m)-polylog(2,-1/2*b*x^m)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 480 + +--S 481 of 518 +a0192:= integrate(t0192,x) +--R +--R +--R x m +--R ++ log(b %L + 2) +--R (380) | -------------- d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 481 + +--S 482 of 518 +--m0192:= a0192-r0192 +--E 482 + +--S 483 of 518 +--d0192:= D(m0192,x) +--E 483 + +--S 484 of 518 +t0193:= log(c*(a+b*x^m)^n)/x +--R +--R +--R m n +--R log(c (b x + a) ) +--R (381) ------------------ +--R x +--R Type: Expression Integer +--E 484 + +--S 485 of 518 +r0193:= 1/m*(log(-b*x^m/a)*log(c*(a+b*x^m)^n)+n*polylog(2,(a+b*x^m)/a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 485 + +--S 486 of 518 +a0193:= integrate(t0193,x) +--R +--R +--R x m n +--R ++ log(c (b %L + a) ) +--R (382) | ------------------- d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 486 + +--S 487 of 518 +--m0193:= a0193-r0193 +--E 487 + +--S 488 of 518 +--d0193:= D(m0193,x) +--E 488 + +--S 489 of 518 +t0194:= log(c*(a+b*x^m)^n)^2/x +--R +--R +--R m n 2 +--R log(c (b x + a) ) +--R (383) ------------------- +--R x +--R Type: Expression Integer +--E 489 + +--S 490 of 518 +r0194:= -1/m*(-log(-b*x^m/a)*log(c*(a+b*x^m)^n)^2-_ + 2*n*log(c*(a+b*x^m)^n)*polylog(2,(a+b*x^m)/a)+_ + 2*n^2*polylog(3,(a+b*x^m)/a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 490 + +--S 491 of 518 +a0194:= integrate(t0194,x) +--R +--R +--R x m n 2 +--R ++ log(c (b %L + a) ) +--R (384) | -------------------- d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 491 + +--S 492 of 518 +--m0194:= a0194-r0194 +--E 492 + +--S 493 of 518 +--d0194:= D(m0194,x) +--E 493 + +--S 494 of 518 +t0195:= log(c*(a+b*x^m)^n)^3/x +--R +--R +--R m n 3 +--R log(c (b x + a) ) +--R (385) ------------------- +--R x +--R Type: Expression Integer +--E 494 + +--S 495 of 518 +r0195:= 1/m*(log(-b*x^m/a)*log(c*(a+b*x^m)^n)^3+_ + 3*n*log(c*(a+b*x^m)^n)^2*polylog(2,(a+b*x^m)/a)-_ + 6*n^2*log(c*(a+b*x^m)^n)*polylog(3,(a+b*x^m)/a)+_ + 6*n^3*polylog(4,(a+b*x^m)/a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 495 + +--S 496 of 518 +a0195:= integrate(t0195,x) +--R +--R +--R x m n 3 +--R ++ log(c (b %L + a) ) +--R (386) | -------------------- d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 496 + +--S 497 of 518 +--m0195:= a0195-r0195 +--E 497 + +--S 498 of 518 +--d0195:= D(m0195,x) +--E 498 + +--S 499 of 518 +t0196:= x^2*log(c*(a+b*x)^n)^2 +--R +--R +--R 2 n 2 +--R (387) x log(c (b x + a) ) +--R Type: Expression Integer +--E 499 + +--S 500 of 518 +r0196:= 11/9*a^2*n^2*x/b^2-5/18*a*n^2*x^2/b+2/27*n^2*x^3-_ + 5/9*a^3*n^2*log(a+b*x)/b^3+1/3*a*n*x^2*log(c*(a+b*x)^n)/b-_ + 2/9*n*x^3*log(c*(a+b*x)^n)-2/3*a^2*n*(a+b*x)*log(c*(a+b*x)^n)/b^3+_ + 1/3*a^3*log(c*(a+b*x)^n)^2/b^3+1/3*x^3*log(c*(a+b*x)^n)^2 +--R +--R +--R (388) +--R 3 3 3 n 2 +--R (18b x + 18a )log(c (b x + a) ) +--R + +--R 3 3 2 2 2 3 n +--R (- 12b n x + 18a b n x - 36a b n x - 36a n)log(c (b x + a) ) +--R + +--R 3 2 3 2 3 2 2 2 2 2 +--R - 30a n log(b x + a) + 4b n x - 15a b n x + 66a b n x +--R / +--R 3 +--R 54b +--R Type: Expression Integer +--E 500 + +--S 501 of 518 +a0196:= integrate(t0196,x) +--R +--R +--R (389) +--R 3 2 3 3 2 2 +--R (18b n x + 18a n )log(b x + a) +--R + +--R 3 3 3 3 2 3 2 2 2 2 2 3 2 +--R ((36b n x + 36a n)log(c) - 12b n x + 18a b n x - 36a b n x - 66a n ) +--R * +--R log(b x + a) +--R + +--R 3 3 2 3 3 2 2 2 3 2 3 +--R 18b x log(c) + (- 12b n x + 18a b n x - 36a b n x)log(c) + 4b n x +--R + +--R 2 2 2 2 2 +--R - 15a b n x + 66a b n x +--R / +--R 3 +--R 54b +--R Type: Union(Expression Integer,...) +--E 501 + +--S 502 of 518 +m0196:= a0196-r0196 +--R +--R +--R (390) +--R 3 3 3 n 2 +--R (- 3b x - 3a )log(c (b x + a) ) +--R + +--R 3 3 2 2 2 3 n +--R (2b n x - 3a b n x + 6a b n x + 6a n)log(c (b x + a) ) +--R + +--R 3 2 3 3 2 2 +--R (3b n x + 3a n )log(b x + a) +--R + +--R 3 3 3 3 2 3 2 2 2 2 2 3 2 +--R ((6b n x + 6a n)log(c) - 2b n x + 3a b n x - 6a b n x - 6a n ) +--R * +--R log(b x + a) +--R + +--R 3 3 2 3 3 2 2 2 +--R 3b x log(c) + (- 2b n x + 3a b n x - 6a b n x)log(c) +--R / +--R 3 +--R 9b +--R Type: Expression Integer +--E 502 + +--S 503 of 518 +d0196:= D(m0196,x) +--R +--R +--R (391) +--R 3 3 2 2 n n 2 +--R (- 9b x - 9a b x )(b x + a) log(c (b x + a) ) +--R + +--R 3 3 3 n +--R (6b n x + 6a n)(b x + a) +--R + +--R 4 4 3 3 3 4 n - 1 +--R (- 6b n x - 6a b n x - 6a b n x - 6a n)(b x + a) +--R * +--R n +--R log(c (b x + a) ) +--R + +--R 3 2 3 2 2 2 2 +--R (9b n x + 9a b n x )log(b x + a) +--R + +--R 3 3 2 2 3 3 2 2 2 +--R (18b n x + 18a b n x )log(c)log(b x + a) + (9b x + 9a b x )log(c) +--R + +--R 3 2 3 2 2 2 2 2 3 2 +--R - 2b n x + 3a b n x - 6a b n x - 6a n +--R * +--R n +--R (b x + a) +--R + +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 n - 1 +--R (2b n x - a b n x + 3a b n x + 12a b n x + 6a n )(b x + a) +--R / +--R 3 2 n +--R (9b x + 9a b )(b x + a) +--R Type: Expression Integer +--E 503 + +--S 504 of 518 +t0197:= x*log(c*(a+b*x)^n)^2 +--R +--R +--R n 2 +--R (392) x log(c (b x + a) ) +--R Type: Expression Integer +--E 504 + +--S 505 of 518 +r0197:= -3/2*a*n^2*x/b+1/4*n^2*x^2+1/2*a^2*n^2*log(a+b*x)/b^2-1/2*n*x^2*_ + log(c*(a+b*x)^n)+a*n*(a+b*x)*log(c*(a+b*x)^n)/b^2-_ + 1/2*a^2*log(c*(a+b*x)^n)^2/b^2+1/2*x^2*log(c*(a+b*x)^n)^2 +--R +--R +--R (393) +--R 2 2 2 n 2 +--R (2b x - 2a )log(c (b x + a) ) +--R + +--R 2 2 2 n 2 2 +--R (- 2b n x + 4a b n x + 4a n)log(c (b x + a) ) + 2a n log(b x + a) +--R + +--R 2 2 2 2 +--R b n x - 6a b n x +--R / +--R 2 +--R 4b +--R Type: Expression Integer +--E 505 + +--S 506 of 518 +a0197:= integrate(t0197,x) +--R +--R +--R (394) +--R 2 2 2 2 2 2 +--R (2b n x - 2a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((4b n x - 4a n)log(c) - 2b n x + 4a b n x + 6a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R 2b x log(c) + (- 2b n x + 4a b n x)log(c) + b n x - 6a b n x +--R / +--R 2 +--R 4b +--R Type: Union(Expression Integer,...) +--E 506 + +--S 507 of 518 +m0197:= a0197-r0197 +--R +--R +--R (395) +--R 2 2 2 n 2 +--R (- b x + a )log(c (b x + a) ) +--R + +--R 2 2 2 n +--R (b n x - 2a b n x - 2a n)log(c (b x + a) ) +--R + +--R 2 2 2 2 2 2 +--R (b n x - a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((2b n x - 2a n)log(c) - b n x + 2a b n x + 2a n )log(b x + a) +--R + +--R 2 2 2 2 2 +--R b x log(c) + (- b n x + 2a b n x)log(c) +--R / +--R 2 +--R 2b +--R Type: Expression Integer +--E 507 + +--S 508 of 518 +d0197:= D(m0197,x) +--R +--R +--R (396) +--R 2 2 n n 2 +--R (- 2b x - 2a b x)(b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 n +--R (2b n x - 2a n)(b x + a) +--R + +--R 3 3 2 2 2 3 n - 1 +--R (- 2b n x - 2a b n x + 2a b n x + 2a n)(b x + a) +--R * +--R n +--R log(c (b x + a) ) +--R + +--R 2 2 2 2 2 +--R (2b n x + 2a b n x)log(b x + a) +--R + +--R 2 2 2 2 2 +--R (4b n x + 4a b n x)log(c)log(b x + a) + (2b x + 2a b x)log(c) +--R + +--R 2 2 2 2 2 2 +--R - b n x + 2a b n x + 2a n +--R * +--R n +--R (b x + a) +--R + +--R 3 2 3 2 2 2 2 2 3 2 n - 1 +--R (b n x - a b n x - 4a b n x - 2a n )(b x + a) +--R / +--R 2 n +--R (2b x + 2a b)(b x + a) +--R Type: Expression Integer +--E 508 + +--S 509 of 518 +t0198:= log(c*(a+b*x)^n)^2 +--R +--R +--R n 2 +--R (397) log(c (b x + a) ) +--R Type: Expression Integer +--E 509 + +--S 510 of 518 +r0198:= 2*n^2*x-2*n*(a+b*x)*log(c*(a+b*x)^n)/b+(a+b*x)*log(c*(a+b*x)^n)^2/b +--R +--R +--R (398) +--R n 2 n 2 +--R (b x + a)log(c (b x + a) ) + (- 2b n x - 2a n)log(c (b x + a) ) + 2b n x +--R ------------------------------------------------------------------------- +--R b +--R Type: Expression Integer +--E 510 + +--S 511 of 518 +a0198:= integrate(t0198,x) +--R +--R +--R (399) +--R 2 2 2 +--R (b n x + a n )log(b x + a) +--R + +--R 2 2 2 +--R ((2b n x + 2a n)log(c) - 2b n x - 2a n )log(b x + a) + b x log(c) +--R + +--R 2 +--R - 2b n x log(c) + 2b n x +--R / +--R b +--R Type: Union(Expression Integer,...) +--E 511 + +--S 512 of 518 +m0198:= a0198-r0198 +--R +--R +--R (400) +--R n 2 n +--R (- b x - a)log(c (b x + a) ) + (2b n x + 2a n)log(c (b x + a) ) +--R + +--R 2 2 2 +--R (b n x + a n )log(b x + a) +--R + +--R 2 2 2 +--R ((2b n x + 2a n)log(c) - 2b n x - 2a n )log(b x + a) + b x log(c) +--R + +--R - 2b n x log(c) +--R / +--R b +--R Type: Expression Integer +--E 512 + +--S 513 of 518 +d0198:= D(m0198,x) +--R +--R +--R (401) +--R n n 2 +--R - (b x + a) log(c (b x + a) ) +--R + +--R n n - 1 n +--R (2n (b x + a) + (- 2b n x - 2a n)(b x + a) )log(c (b x + a) ) +--R + +--R 2 2 2 2 n +--R (n log(b x + a) + 2n log(c)log(b x + a) + log(c) - 2n )(b x + a) +--R + +--R 2 2 n - 1 +--R (2b n x + 2a n )(b x + a) +--R / +--R n +--R (b x + a) +--R Type: Expression Integer +--E 513 + +--S 514 of 518 +t0199:= log(c*(a+b*x)^n)^2/x +--R +--R +--R n 2 +--R log(c (b x + a) ) +--R (402) ------------------ +--R x +--R Type: Expression Integer +--E 514 + +--S 515 of 518 +r0199:= log(-b*x/a)*log(c*(a+b*x)^n)^2+2*n*log(c*(a+b*x)^n)*_ + polylog(2,1+b*x/a)-2*n^2*polylog(3,(a+b*x)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 515 + +--S 516 of 518 +a0199:= integrate(t0199,x) +--R +--R +--R x n 2 +--R ++ log(c (%L b + a) ) +--R (403) | ------------------- d%L +--R ++ %L +--R Type: Union(Expression Integer,...) +--E 516 + +--S 517 of 518 +--m0199:= a0199-r0199 +--E 517 + +--S 518 of 518 +--d0199:= D(m0199,x) +--E 518 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}