diff --git a/changelog b/changelog index 6da6082..964e533 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20100629 rhx src/axiom-website/patches.html 20100629.01.tpd.patch +20100629 tpd src/input/richhyper100-199,input rule-based hyper integration 20100623 rhx src/axiom-website/patches.html 20100623.01.rhx.patch 20100623 rhx books/axbook.tgz rewrite section 8.3.2 for current output 20100623 rhx books/bookvol0 rewrite section 8.3.2 for current output diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 3fed920..c6e78ae 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2938,6 +2938,8 @@ src/input/richspecfunc000-022.input special function integration
src/input/richtrig000-099, richtrig100-199 remove useless derivatives
20100623.01.rhx.patch books/bookvol0 rewrite section 8.3.2 for current output
+20100629.01.tpd.patch +src/input/richhyper100-199,input rule-based hyper integration
diff --git a/src/input/richhyper100-199,input.pamphlet b/src/input/richhyper100-199,input.pamphlet new file mode 100644 index 0000000..ef971e6 --- /dev/null +++ b/src/input/richhyper100-199,input.pamphlet @@ -0,0 +1,7879 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richinvhyper100-199.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richinvhyper100-199.output +)spool richinvhyper100-199.output +)set message auto off +)clear all + +--S 1 OF 506 +t0100:= atanh(x^(1/2)) +--R +--R +--R +-+ +--R (1) atanh(\|x ) +--R Type: Expression Integer +--E 1 + +--S 2 OF 506 +r0100:= x^(1/2)-atanh(x^(1/2))+x*atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (2) (x - 1)atanh(\|x ) + \|x +--R Type: Expression Integer +--E 2 + +--S 3 OF 506 +a0100:= integrate(t0100,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R (x - 1)log(----------) + 2\|x +--R +-+ +--R \|x - 1 +--R (3) ------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 OF 506 +m0100:= a0100-r0100 +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (4) ---------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 4 + +--S 5 OF 506 +d0100:= D(m0100,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (5) ------------------------------ +--R 2 +--R Type: Expression Integer +--E 5 + +--S 6 OF 506 +t0101:= x*atanh(x^(1/2)) +--R +--R +--R +-+ +--R (6) x atanh(\|x ) +--R Type: Expression Integer +--E 6 + +--S 7 OF 506 +r0101:= 1/2*x^(1/2)+1/6*x^(3/2)-1/2*atanh(x^(1/2))+1/2*x^2*atanh(x^(1/2)) +--R +--R +--R 2 +-+ +-+ +--R (3x - 3)atanh(\|x ) + (x + 3)\|x +--R (7) ---------------------------------- +--R 6 +--R Type: Expression Integer +--E 7 + +--S 8 OF 506 +a0101:= integrate(t0101,x) +--R +--R +--R +-+ +--R 2 - \|x - 1 +-+ +--R (3x - 3)log(----------) + (2x + 6)\|x +--R +-+ +--R \|x - 1 +--R (8) --------------------------------------- +--R 12 +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 OF 506 +m0101:= a0101-r0101 +--R +--R +--R +-+ +--R 2 - \|x - 1 2 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (9) ------------------------------------------------ +--R 4 +--R Type: Expression Integer +--E 9 + +--S 10 OF 506 +d0101:= D(m0101,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R x log(----------) - 2x atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (10) ---------------------------------- +--R 2 +--R Type: Expression Integer +--E 10 + +--S 11 OF 506 +t0102:= atanh(x^(1/2))/x^2 +--R +--R +--R +-+ +--R atanh(\|x ) +--R (11) ----------- +--R 2 +--R x +--R Type: Expression Integer +--E 11 + +--S 12 OF 506 +r0102:= -1/x^(1/2)+atanh(x^(1/2))-atanh(x^(1/2))/x +--R +--R +--R +-+ +-+ +--R (x - 1)\|x atanh(\|x ) - x +--R (12) -------------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 12 + +--S 13 OF 506 +a0102:= integrate(t0102,x) +--R +--R +--R +-+ +--R +-+ - \|x - 1 +--R (x - 1)\|x log(----------) - 2x +--R +-+ +--R \|x - 1 +--R (13) ------------------------------- +--R +-+ +--R 2x\|x +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 OF 506 +m0102:= a0102-r0102 +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (14) ---------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 14 + +--S 15 OF 506 +d0102:= D(m0102,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (15) ------------------------------ +--R 2 +--R 2x +--R Type: Expression Integer +--E 15 + +--S 16 OF 506 +t0103:= atanh(x^(1/2))/x^3 +--R +--R +--R +-+ +--R atanh(\|x ) +--R (16) ----------- +--R 3 +--R x +--R Type: Expression Integer +--E 16 + +--S 17 OF 506 +r0103:= -1/6/x^(3/2)-1/2/x^(1/2)+1/2*atanh(x^(1/2))-1/2*atanh(x^(1/2))/x^2 +--R +--R +--R 2 +-+ +-+ 2 +--R (3x - 3)\|x atanh(\|x ) - 3x - x +--R (17) ---------------------------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression Integer +--E 17 + +--S 18 OF 506 +a0103:= integrate(t0103,x) +--R +--R +--R +-+ +--R 2 +-+ - \|x - 1 2 +--R (3x - 3)\|x log(----------) - 6x - 2x +--R +-+ +--R \|x - 1 +--R (18) --------------------------------------- +--R 2 +-+ +--R 12x \|x +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 OF 506 +m0103:= a0103-r0103 +--R +--R +--R +-+ +--R 2 - \|x - 1 2 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (19) ------------------------------------------------ +--R 2 +--R 4x +--R Type: Expression Integer +--E 19 + +--S 20 OF 506 +d0103:= D(m0103,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (20) ------------------------------ +--R 3 +--R 2x +--R Type: Expression Integer +--E 20 + +--S 21 OF 506 +t0104:= x^(1/2)*atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (21) \|x atanh(\|x ) +--R Type: Expression Integer +--E 21 + +--S 22 OF 506 +r0104:= 1/3*x+2/3*x^(3/2)*atanh(x^(1/2))+1/3*log(1-x) +--R +--R +--R +-+ +-+ +--R 2x\|x atanh(\|x ) + log(- x + 1) + x +--R (22) ------------------------------------ +--R 3 +--R Type: Expression Integer +--E 22 + +--S 23 OF 506 +a0104:= integrate(t0104,x) +--R +--R +--R +-+ +--R +-+ - \|x - 1 +--R x\|x log(----------) + log(x - 1) + x +--R +-+ +--R \|x - 1 +--R (23) ------------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 OF 506 +m0104:= a0104-r0104 +--R +--R +--R +-+ +--R +-+ - \|x - 1 +-+ +-+ +--R x\|x log(----------) - 2x\|x atanh(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R (24) -------------------------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 24 + +--S 25 OF 506 +d0104:= D(m0104,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R x log(----------) - 2x atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (25) ---------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression Integer +--E 25 + +--S 26 OF 506 +t0105:= x^(3/2)*atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (26) x\|x atanh(\|x ) +--R Type: Expression Integer +--E 26 + +--S 27 OF 506 +r0105:= 1/5*x+1/10*x^2+2/5*x^(5/2)*atanh(x^(1/2))+1/5*log(1-x) +--R +--R +--R 2 +-+ +-+ 2 +--R 4x \|x atanh(\|x ) + 2log(- x + 1) + x + 2x +--R (27) -------------------------------------------- +--R 10 +--R Type: Expression Integer +--E 27 + +--S 28 OF 506 +a0105:= integrate(t0105,x) +--R +--R +--R +-+ +--R 2 +-+ - \|x - 1 2 +--R 2x \|x log(----------) + 2log(x - 1) + x + 2x +--R +-+ +--R \|x - 1 +--R (28) ---------------------------------------------- +--R 10 +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 OF 506 +m0105:= a0105-r0105 +--R +--R +--R (29) +--R +-+ +--R 2 +-+ - \|x - 1 2 +-+ +-+ +--R x \|x log(----------) - 2x \|x atanh(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R ---------------------------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 29 + +--S 30 OF 506 +d0105:= D(m0105,x) +--R +--R +--R +-+ +--R 2 - \|x - 1 2 +-+ +--R x log(----------) - 2x atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (30) ---------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression Integer +--E 30 + +--S 31 OF 506 +t0106:= atanh(x^(1/2))/x^(3/2) +--R +--R +--R +-+ +--R atanh(\|x ) +--R (31) ----------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 31 + +--S 32 OF 506 +r0106:= 2*atanh(-1+2*x)-2*atanh(x^(1/2))/x^(1/2) +--R +--R +--R +-+ +-+ +--R - 2atanh(\|x ) + 2atanh(2x - 1)\|x +--R (32) ----------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 32 + +--S 33 OF 506 +a0106:= integrate(t0106,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R - log(----------) + (log(x) - log(x - 1))\|x +--R +-+ +--R \|x - 1 +--R (33) --------------------------------------------- +--R +-+ +--R \|x +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 OF 506 +m0106:= a0106-r0106 +--R +--R +--R (34) +--R +-+ +--R - \|x - 1 +-+ +-+ +--R - log(----------) + 2atanh(\|x ) + (log(x) - log(x - 1) - 2atanh(2x - 1))\|x +--R +-+ +--R \|x - 1 +--R ----------------------------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 34 + +--S 35 OF 506 +d0106:= D(m0106,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (35) ------------------------------ +--R +-+ +--R 2x\|x +--R Type: Expression Integer +--E 35 + +--S 36 OF 506 +t0107:= x*acoth(a*x) +--R +--R +--R (36) x acoth(a x) +--R Type: Expression Integer +--E 36 + +--S 37 OF 506 +r0107:= 1/2*(a*x+x^2*acoth(a*x)*a^2-atanh(a*x))/a^2 +--R +--R +--R 2 2 +--R - atanh(a x) + a x acoth(a x) + a x +--R (37) ----------------------------------- +--R 2 +--R 2a +--R Type: Expression Integer +--E 37 + +--S 38 OF 506 +a0107:= integrate(t0107,x) +--R +--R +--R 2 2 a x + 1 +--R (a x - 1)log(-------) + 2a x +--R a x - 1 +--R (38) ----------------------------- +--R 2 +--R 4a +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 OF 506 +m0107:= a0107-r0107 +--R +--R +--R 2 2 a x + 1 2 2 +--R (a x - 1)log(-------) + 2atanh(a x) - 2a x acoth(a x) +--R a x - 1 +--R (39) ------------------------------------------------------ +--R 2 +--R 4a +--R Type: Expression Integer +--E 39 + +--S 40 OF 506 +d0107:= D(m0107,x) +--R +--R +--R a x + 1 +--R x log(-------) - 2x acoth(a x) +--R a x - 1 +--R (40) ------------------------------ +--R 2 +--R Type: Expression Integer +--E 40 + +--S 41 OF 506 +t0108:= acoth(a*x)/x +--R +--R +--R acoth(a x) +--R (41) ---------- +--R x +--R Type: Expression Integer +--E 41 + +--S 42 OF 506 +r0108:= 1/2*polylog(2,-1/a/x)-1/2*polylog(2,1/a/x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 42 + +--S 43 OF 506 +a0108:= integrate(t0108,x) +--R +--R +--R x +--R ++ acoth(%Q a) +--R (42) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 OF 506 +--m0108:= a0108-r0108 +--E 44 + +--S 45 OF 506 +--d0108:= D(m0108,x) +--E 45 + +--S 46 OF 506 +t0109:= acoth(a*x)/x^3 +--R +--R +--R acoth(a x) +--R (43) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 46 + +--S 47 OF 506 +r0109:= -1/2*(a*x+acoth(a*x)-a^2*atanh(a*x)*x^2)/x^2 +--R +--R +--R 2 2 +--R a x atanh(a x) - acoth(a x) - a x +--R (44) --------------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 47 + +--S 48 OF 506 +a0109:= integrate(t0109,x) +--R +--R +--R 2 2 a x + 1 +--R (a x - 1)log(-------) - 2a x +--R a x - 1 +--R (45) ----------------------------- +--R 2 +--R 4x +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 OF 506 +m0109:= a0109-r0109 +--R +--R +--R 2 2 a x + 1 2 2 +--R (a x - 1)log(-------) - 2a x atanh(a x) + 2acoth(a x) +--R a x - 1 +--R (46) ------------------------------------------------------ +--R 2 +--R 4x +--R Type: Expression Integer +--E 49 + +--S 50 OF 506 +d0109:= D(m0109,x) +--R +--R +--R a x + 1 +--R log(-------) - 2acoth(a x) +--R a x - 1 +--R (47) -------------------------- +--R 3 +--R 2x +--R Type: Expression Integer +--E 50 + +--S 51 OF 506 +t0110:= (a+b*x)*acoth(a+b*x) +--R +--R +--R (48) (b x + a)acoth(b x + a) +--R Type: Expression Integer +--E 51 + +--S 52 OF 506 +r0110:= 1/2/b*(a+b*x)+1/2*(a+b*x)^2*acoth(a+b*x)/b-1/2*atanh(a+b*x)/b +--R +--R +--R 2 2 2 +--R - atanh(b x + a) + (b x + 2a b x + a )acoth(b x + a) + b x + a +--R (49) --------------------------------------------------------------- +--R 2b +--R Type: Expression Integer +--E 52 + +--S 53 OF 506 +a0110:= integrate(t0110,x) +--R +--R +--R 2 2 2 b x + a + 1 +--R (b x + 2a b x + a - 1)log(-----------) + 2b x +--R b x + a - 1 +--R (50) ----------------------------------------------- +--R 4b +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 OF 506 +m0110:= a0110-r0110 +--R +--R +--R (51) +--R 2 2 2 b x + a + 1 +--R (b x + 2a b x + a - 1)log(-----------) + 2atanh(b x + a) +--R b x + a - 1 +--R + +--R 2 2 2 +--R (- 2b x - 4a b x - 2a )acoth(b x + a) - 2a +--R / +--R 4b +--R Type: Expression Integer +--E 54 + +--S 55 OF 506 +d0110:= D(m0110,x) +--R +--R +--R b x + a + 1 +--R (b x + a)log(-----------) + (- 2b x - 2a)acoth(b x + a) +--R b x + a - 1 +--R (52) ------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 55 + +--S 56 OF 506 +t0111:= (a+b*x)^2*acoth(a+b*x) +--R +--R +--R 2 2 2 +--R (53) (b x + 2a b x + a )acoth(b x + a) +--R Type: Expression Integer +--E 56 + +--S 57 OF 506 +r0111:= 1/6*(a+b*x)^2/b+1/3*(a+b*x)^3*acoth(a+b*x)/b+1/6*log(1-(a+b*x)^2)/b +--R +--R +--R (54) +--R 2 2 2 +--R log(- b x - 2a b x - a + 1) +--R + +--R 3 3 2 2 2 3 2 2 2 +--R (2b x + 6a b x + 6a b x + 2a )acoth(b x + a) + b x + 2a b x + a +--R / +--R 6b +--R Type: Expression Integer +--E 57 + +--S 58 OF 506 +a0111:= integrate(t0111,x) +--R +--R +--R (55) +--R 3 3 +--R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) +--R + +--R 3 3 2 2 2 b x + a + 1 2 2 +--R (b x + 3a b x + 3a b x)log(-----------) + b x + 2a b x +--R b x + a - 1 +--R / +--R 6b +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 OF 506 +m0111:= a0111-r0111 +--R +--R +--R (56) +--R 3 3 +--R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) +--R + +--R 3 3 2 2 2 b x + a + 1 2 2 2 +--R (b x + 3a b x + 3a b x)log(-----------) - log(- b x - 2a b x - a + 1) +--R b x + a - 1 +--R + +--R 3 3 2 2 2 3 2 +--R (- 2b x - 6a b x - 6a b x - 2a )acoth(b x + a) - a +--R / +--R 6b +--R Type: Expression Integer +--E 59 + +--S 60 OF 506 +d0111:= D(m0111,x) +--R +--R +--R (57) +--R 2 2 2 b x + a + 1 2 2 2 +--R (b x + 2a b x + a )log(-----------) + (- 2b x - 4a b x - 2a )acoth(b x + a) +--R b x + a - 1 +--R ----------------------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 60 + +--S 61 OF 506 +t0112:= acoth(1+x)/(2+2*x) +--R +--R +--R acoth(x + 1) +--R (58) ------------ +--R 2x + 2 +--R Type: Expression Integer +--E 61 + +--S 62 OF 506 +r0112:= 1/4*polylog(2,-1/(1+x))-1/4*polylog(2,1/(1+x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 OF 506 +a0112:= integrate(t0112,x) +--R +--R +--R x +--R ++ acoth(%Q + 1) +--R (59) | ------------- d%Q +--R ++ 2%Q + 2 +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 OF 506 +--m0112:= a0112-r0112 +--E 64 + +--S 65 OF 506 +--d0112:= D(m0112,x) +--E 65 + +--S 66 OF 506 +t0113:= acoth(a+b*x)/(a+b*x) +--R +--R +--R acoth(b x + a) +--R (60) -------------- +--R b x + a +--R Type: Expression Integer +--E 66 + +--S 67 OF 506 +r0113:= 1/2*(polylog(2,-1/(a+b*x))-polylog(2,1/(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 OF 506 +a0113:= integrate(t0113,x) +--R +--R +--R x +--R ++ acoth(%Q b + a) +--R (61) | --------------- d%Q +--R ++ %Q b + a +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 OF 506 +--m0113:= a0113-r0113 +--E 69 + +--S 70 OF 506 +--d0113:= D(m0113,x) +--E 70 + +--S 71 OF 506 +t0114:= 1/(1-x^2)/acoth(x) +--R +--R +--R 1 +--R (62) - ---------------- +--R 2 +--R (x - 1)acoth(x) +--R Type: Expression Integer +--E 71 + +--S 72 OF 506 +r0114:= log(acoth(x)) +--R +--R +--R (63) log(acoth(x)) +--R Type: Expression Integer +--E 72 + +--S 73 OF 506 +a0114:= integrate(t0114,x) +--R +--R +--R x + 1 +--R (64) log(log(-----)) +--R x - 1 +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 OF 506 +m0114:= a0114-r0114 +--R +--R +--R x + 1 +--R (65) log(log(-----)) - log(acoth(x)) +--R x - 1 +--R Type: Expression Integer +--E 74 + +--S 75 OF 506 +d0114:= D(m0114,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (66) -------------------------- +--R 2 x + 1 +--R (x - 1)acoth(x)log(-----) +--R x - 1 +--R Type: Expression Integer +--E 75 + +--S 76 OF 506 +t0115:= acoth(x)^n/(1-x^2) +--R +--R +--R n +--R acoth(x) +--R (67) - --------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 76 + +--S 77 OF 506 +r0115:= acoth(x)^(1+n)/(1+n) +--R +--R +--R n + 1 +--R acoth(x) +--R (68) ------------- +--R n + 1 +--R Type: Expression Integer +--E 77 + +--S 78 OF 506 +a0115:= integrate(t0115,x) +--R +--R +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x + 1 x - 1 x + 1 x - 1 +--R log(-----)sinh(n log(----------)) + log(-----)cosh(n log(----------)) +--R x - 1 2 x - 1 2 +--R (69) --------------------------------------------------------------------- +--R 2n + 2 +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 OF 506 +m0115:= a0115-r0115 +--R +--R +--R (70) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x + 1 x - 1 x + 1 x - 1 +--R log(-----)sinh(n log(----------)) + log(-----)cosh(n log(----------)) +--R x - 1 2 x - 1 2 +--R + +--R n + 1 +--R - 2acoth(x) +--R / +--R 2n + 2 +--R Type: Expression Integer +--E 79 + +--S 80 OF 506 +d0115:= D(m0115,x) +--R +--R +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 n +--R - sinh(n log(----------)) - cosh(n log(----------)) + acoth(x) +--R 2 2 +--R (71) --------------------------------------------------------------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 80 + +--S 81 OF 506 +t0116:= acoth(x)/(1-x^2)^2 +--R +--R +--R acoth(x) +--R (72) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 81 + +--S 82 OF 506 +r0116:= 1/(-4+4*x^2)-x*acoth(x)/(-2+2*x^2)+1/4*acoth(x)^2 +--R +--R +--R 2 2 +--R (x - 1)acoth(x) - 2x acoth(x) + 1 +--R (73) ----------------------------------- +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 82 + +--S 83 OF 506 +a0116:= integrate(t0116,x) +--R +--R +--R 2 x + 1 2 x + 1 +--R (x - 1)log(-----) - 4x log(-----) + 4 +--R x - 1 x - 1 +--R (74) --------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 OF 506 +m0116:= a0116-r0116 +--R +--R +--R (75) +--R 2 x + 1 2 x + 1 2 2 +--R (x - 1)log(-----) - 4x log(-----) + (- 4x + 4)acoth(x) + 8x acoth(x) +--R x - 1 x - 1 +--R ------------------------------------------------------------------------ +--R 2 +--R 16x - 16 +--R Type: Expression Integer +--E 84 + +--S 85 OF 506 +d0116:= D(m0116,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (76) ---------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression Integer +--E 85 + +--S 86 OF 506 +t0117:= acoth(x)^2/(1-x^2)^2 +--R +--R +--R 2 +--R acoth(x) +--R (77) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 86 + +--S 87 OF 506 +r0117:= 1/12*(-3*x+3*acoth(x)+3*x^2*acoth(x)-6*x*acoth(x)^2-2*acoth(x)^3+_ + 2*acoth(x)^3*x^2)/(-1+x^2) +--R +--R +--R 2 3 2 2 +--R (2x - 2)acoth(x) - 6x acoth(x) + (3x + 3)acoth(x) - 3x +--R (78) ---------------------------------------------------------- +--R 2 +--R 12x - 12 +--R Type: Expression Integer +--E 87 + +--S 88 OF 506 +a0117:= integrate(t0117,x) +--R +--R +--R 2 x + 1 3 x + 1 2 2 x + 1 +--R (x - 1)log(-----) - 6x log(-----) + (6x + 6)log(-----) - 12x +--R x - 1 x - 1 x - 1 +--R (79) ---------------------------------------------------------------- +--R 2 +--R 48x - 48 +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 OF 506 +m0117:= a0117-r0117 +--R +--R +--R (80) +--R 2 x + 1 3 x + 1 2 2 x + 1 +--R (x - 1)log(-----) - 6x log(-----) + (6x + 6)log(-----) +--R x - 1 x - 1 x - 1 +--R + +--R 2 3 2 2 +--R (- 8x + 8)acoth(x) + 24x acoth(x) + (- 12x - 12)acoth(x) +--R / +--R 2 +--R 48x - 48 +--R Type: Expression Integer +--E 89 + +--S 90 OF 506 +d0117:= D(m0117,x) +--R +--R +--R x + 1 2 2 +--R log(-----) - 4acoth(x) +--R x - 1 +--R (81) ------------------------ +--R 4 2 +--R 4x - 8x + 4 +--R Type: Expression Integer +--E 90 + +--S 91 OF 506 +t0118:= 1/(a-a*x^2)/(b-2*b*acoth(x)) +--R +--R +--R 1 +--R (82) --------------------------------------- +--R 2 2 +--R (2a b x - 2a b)acoth(x) - a b x + a b +--R Type: Expression Integer +--E 91 + +--S 92 OF 506 +r0118:= -1/2*log(1-2*acoth(x))/a/b +--R +--R +--R log(- 2acoth(x) + 1) +--R (83) - -------------------- +--R 2a b +--R Type: Expression Integer +--E 92 + +--S 93 OF 506 +a0118:= integrate(t0118,x) +--R +--R +--R x + 1 +--R log(log(-----) - 1) +--R x - 1 +--R (84) - ------------------- +--R 2a b +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 OF 506 +m0118:= a0118-r0118 +--R +--R +--R x + 1 +--R - log(log(-----) - 1) + log(- 2acoth(x) + 1) +--R x - 1 +--R (85) -------------------------------------------- +--R 2a b +--R Type: Expression Integer +--E 94 + +--S 95 OF 506 +d0118:= D(m0118,x) +--R +--R +--R (86) +--R x + 1 +--R - log(-----) + 2acoth(x) +--R x - 1 +--R / +--R 2 2 x + 1 +--R ((2a b x - 2a b)acoth(x) - a b x + a b)log(-----) +--R x - 1 +--R + +--R 2 2 +--R (- 2a b x + 2a b)acoth(x) + a b x - a b +--R Type: Expression Integer +--E 95 + +--S 96 OF 506 +t0119:= x*acoth(x)/(1-x^2) +--R +--R +--R x acoth(x) +--R (87) - ---------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 96 + +--S 97 OF 506 +r0119:= -1/2*acoth(x)^2+acoth(x)*log(2/(1-x))+1/2*polylog(2,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 OF 506 +a0119:= integrate(t0119,x) +--R +--R +--R x +--R ++ %Q acoth(%Q) +--R (88) | - ------------ d%Q +--R ++ 2 +--R %Q - 1 +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 OF 506 +--m0119:= a0119-r0119 +--E 99 + +--S 100 OF 506 +--d0119:= D(m0119,x) +--E 100 + +--S 101 OF 506 +t0120:= x*acoth(x)/(1-x^2)^2 +--R +--R +--R x acoth(x) +--R (89) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 101 + +--S 102 OF 506 +r0120:= -1/4*(-x+acoth(x)+x^2*acoth(x))/(-1+x^2) +--R +--R +--R 2 +--R (- x - 1)acoth(x) + x +--R (90) ---------------------- +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 102 + +--S 103 OF 506 +a0120:= integrate(t0120,x) +--R +--R +--R 2 x + 1 +--R (- x - 1)log(-----) + 2x +--R x - 1 +--R (91) ------------------------- +--R 2 +--R 8x - 8 +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 OF 506 +m0120:= a0120-r0120 +--R +--R +--R 2 x + 1 2 +--R (- x - 1)log(-----) + (2x + 2)acoth(x) +--R x - 1 +--R (92) ---------------------------------------- +--R 2 +--R 8x - 8 +--R Type: Expression Integer +--E 104 + +--S 105 OF 506 +d0120:= D(m0120,x) +--R +--R +--R x + 1 +--R x log(-----) - 2x acoth(x) +--R x - 1 +--R (93) -------------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression Integer +--E 105 + +--S 106 OF 506 +t0121:= x*acoth(x)/(1-x^2)^3 +--R +--R +--R x acoth(x) +--R (94) - ------------------ +--R 6 4 2 +--R x - 3x + 3x - 1 +--R Type: Expression Integer +--E 106 + +--S 107 OF 506 +r0121:= -1/32*(5*x-3*x^3-5*acoth(x)+3*acoth(x)*x^4-6*x^2*acoth(x))/(-1+x^2)^2 +--R +--R +--R 4 2 3 +--R (- 3x + 6x + 5)acoth(x) + 3x - 5x +--R (95) ------------------------------------ +--R 4 2 +--R 32x - 64x + 32 +--R Type: Expression Integer +--E 107 + +--S 108 OF 506 +a0121:= integrate(t0121,x) +--R +--R +--R 4 2 x + 1 3 +--R (- 3x + 6x + 5)log(-----) + 6x - 10x +--R x - 1 +--R (96) --------------------------------------- +--R 4 2 +--R 64x - 128x + 64 +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 OF 506 +m0121:= a0121-r0121 +--R +--R +--R 4 2 x + 1 4 2 +--R (- 3x + 6x + 5)log(-----) + (6x - 12x - 10)acoth(x) +--R x - 1 +--R (97) ------------------------------------------------------- +--R 4 2 +--R 64x - 128x + 64 +--R Type: Expression Integer +--E 109 + +--S 110 OF 506 +d0121:= D(m0121,x) +--R +--R +--R x + 1 +--R - x log(-----) + 2x acoth(x) +--R x - 1 +--R (98) ---------------------------- +--R 6 4 2 +--R 2x - 6x + 6x - 2 +--R Type: Expression Integer +--E 110 + +--S 111 OF 506 +t0122:= acoth(x)/(a+b*x^2)^(3/2) +--R +--R +--R acoth(x) +--R (99) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression Integer +--E 111 + +--S 112 OF 506 +r0122:= x*acoth(x)/a/(a+b*x^2)^(1/2)-_ + atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a/(a+b)^(1/2) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-----+ +--R - \|b x + a atanh(-----------) + x acoth(x)\|b + a +--R +-----+ +--R \|b + a +--R (100) ---------------------------------------------------- +--R +--------+ +--R +-----+ | 2 +--R a\|b + a \|b x + a +--R Type: Expression Integer +--E 112 + +--S 113 OF 506 +a0122:= integrate(t0122,x) +--R +--R +--R (101) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R +--------+ +--R x + 1 +-----+ | 2 x + 1 +-+ +-----+ +--R - x log(-----)\|b + a \|b x + a + x log(-----)\|a \|b + a +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-+ +-----+ | 2 2 2 +-----+ +--R 2a\|a \|b + a \|b x + a + (- 2a b x - 2a )\|b + a +--R , +--R +--R +--------+ +--R +-+ | 2 2 +--R (- 2\|a \|b x + a + 2b x + 2a) +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R +--------+ +--R x + 1 +-------+ | 2 x + 1 +-------+ +-+ +--R - x log(-----)\|- b - a \|b x + a + x log(-----)\|- b - a \|a +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-------+ +-+ | 2 2 2 +-------+ +--R 2a\|- b - a \|a \|b x + a + (- 2a b x - 2a )\|- b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 113 + +--S 114 OF 506 +m0122a:= a0122.1-r0122 +--R +--R +--R (102) +--R +--------+ +--R 2 | 2 2 +-+ +--R ((b x + a)\|b x + a + (- b x - a)\|a ) +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 2 +-+ \|b x + a +--R ((2b x + 2a)\|b x + a + (- 2b x - 2a)\|a )atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +--------+ +--R x + 1 +-+ +-----+ | 2 +--R (- x log(-----) + 2x acoth(x))\|a \|b + a \|b x + a +--R x - 1 +--R + +--R 3 x + 1 3 +-----+ +--R ((b x + a x)log(-----) + (- 2b x - 2a x)acoth(x))\|b + a +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-----+ | 2 2 2 +-+ +-----+ +--R (2a b x + 2a )\|b + a \|b x + a + (- 2a b x - 2a )\|a \|b + a +--R Type: Expression Integer +--E 114 + +--S 115 OF 506 +d0122a:= D(m0122a,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (103) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 115 + +--S 116 OF 506 +m0122b:= a0122.2-r0122 +--R +--R +--R (104) +--R +--------+ +--R 2 +-------+ | 2 2 +-------+ +-+ +--R ((2b x + 2a)\|- b - a \|b x + a + (- 2b x - 2a)\|- b - a \|a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +--------+ +--R 2 +-----+ | 2 2 +-+ +-----+ +--R ((- 2b x - 2a)\|b + a \|b x + a + (2b x + 2a)\|a \|b + a ) +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R +--------+ +--R x + 1 +-------+ +-+ +-----+ | 2 +--R (- x log(-----) + 2x acoth(x))\|- b - a \|a \|b + a \|b x + a +--R x - 1 +--R + +--R 3 x + 1 3 +-------+ +-----+ +--R ((b x + a x)log(-----) + (- 2b x - 2a x)acoth(x))\|- b - a \|b + a +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ +-----+ | 2 +--R (2a b x + 2a )\|- b - a \|b + a \|b x + a +--R + +--R 2 2 +-------+ +-+ +-----+ +--R (- 2a b x - 2a )\|- b - a \|a \|b + a +--R Type: Expression Integer +--E 116 + +--S 117 OF 506 +d0122b:= D(m0122b,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (105) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 117 + +--S 118 OF 506 +t0123:= acoth(x)/(a+b*x^2)^(5/2) +--R +--R +--R acoth(x) +--R (106) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression Integer +--E 118 + +--S 119 OF 506 +r0123:= 1/3/a/(a+b)/(a+b*x^2)^(1/2)+_ + 1/3*x*(3*a+2*b*x^2)*acoth(x)/a^2/(a+b*x^2)^(3/2)-_ + 1/3*(3*a+2*b)*atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^2/(a+b)^(3/2) +--R +--R +--R (107) +--R +--------+ +--R +--------+ | 2 +--R 2 2 2 | 2 \|b x + a +--R ((- 2b - 3a b)x - 2a b - 3a )\|b x + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 2 2 +-----+ +--R (((2b + 2a b)x + (3a b + 3a )x)acoth(x) + a b x + a )\|b + a +--R / +--R +--------+ +--R 2 2 3 2 3 4 +-----+ | 2 +--R ((3a b + 3a b)x + 3a b + 3a )\|b + a \|b x + a +--R Type: Expression Integer +--E 119 + +--S 120 OF 506 +a0123:= integrate(t0123,x) +--R +--R +--R (108) +--R [ +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b + 12a b )x + (32a b + 48a b )x + (40a b + 60a b)x +--R + +--R 3 4 +--R 16a b + 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (- 2b - 3a b )x + (- 20a b - 30a b )x + (- 50a b - 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (- 48a b - 72a b)x - 16a b - 24a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b - 2a b )x + (- 19a b - 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b - 40a b)x + (- 24a b - 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b + 8a b )x + (36a b + 36a b )x + (52a b + 52a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b + 24a b )x + (96a b + 96a b )x + (120a b + 120a b)x +--R + +--R 5 6 +--R 48a b + 48a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b - 6a b )x + (- 60a b - 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b - 150a b )x + (- 144a b - 144a b)x - 48a b - 48a +--R * +--R +-----+ +--R \|b + a +--R , +--R +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (4b + 6a b )x + (40a b + 60a b )x + (100a b + 150a b )x +--R + +--R 3 2 4 2 4 5 +--R (96a b + 144a b)x + 32a b + 48a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b - 2a b )x + (- 19a b - 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b - 40a b)x + (- 24a b - 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b + 8a b )x + (36a b + 36a b )x + (52a b + 52a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b + 24a b )x + (96a b + 96a b )x + (120a b + 120a b)x +--R + +--R 5 6 +--R 48a b + 48a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b - a \|a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b - 6a b )x + (- 60a b - 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b - 150a b )x + (- 144a b - 144a b)x - 48a b - 48a +--R * +--R +-------+ +--R \|- b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 120 + +--S 121 OF 506 +m0123a:= a0123.1-r0123 +--R +--R +--R (109) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (2b + 3a b )x + (18a b + 27a b )x + (32a b + 48a b)x +--R + +--R 3 4 +--R 16a b + 24a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 8b - 12a b )x + (- 32a b - 48a b )x + (- 40a b - 60a b)x +--R + +--R 3 4 +--R - 16a b - 24a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b + 6a b )x + (36a b + 54a b )x + (64a b + 96a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b - 8a b )x + (- 28a b - 28a b)x + (- 24a b - 24a )x) +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b + 16a b )x + (56a b + 56a b)x + (48a b + 48a )x)acoth(x) +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b + 2a b )x + (19a b + 19a b )x + (40a b + 40a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b - 4a b )x + (- 38a b - 38a b )x + (- 80a b - 80a b)x +--R + +--R 3 4 +--R (- 48a b - 48a )x +--R * +--R acoth(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-----+ +--R \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b + 6a b )x + (54a b + 54a b )x + (96a b + 96a b)x + 48a b +--R + +--R 6 +--R 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b - 24a b )x + (- 96a b - 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b - 120a b)x - 48a b - 48a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression Integer +--E 121 + +--S 122 OF 506 +d0123a:= D(m0123a,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (110) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 122 + +--S 123 OF 506 +m0123b:= a0123.2-r0123 +--R +--R +--R (111) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b + 6a b )x + (36a b + 54a b )x + (64a b + 96a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 4b - 6a b )x + (- 36a b - 54a b )x + (- 64a b - 96a b)x +--R + +--R 3 4 +--R - 32a b - 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (16b + 24a b )x + (64a b + 96a b )x + (80a b + 120a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b - 8a b )x + (- 28a b - 28a b)x + (- 24a b - 24a )x) +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b + 16a b )x + (56a b + 56a b)x + (48a b + 48a )x)acoth(x) +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b - a \|a \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b + 2a b )x + (19a b + 19a b )x + (40a b + 40a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b - 4a b )x + (- 38a b - 38a b )x + (- 80a b - 80a b)x +--R + +--R 3 4 +--R (- 48a b - 48a )x +--R * +--R acoth(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-------+ +-----+ +--R \|- b - a \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b + 6a b )x + (54a b + 54a b )x + (96a b + 96a b)x + 48a b +--R + +--R 6 +--R 48a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b - a \|b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b - 24a b )x + (- 96a b - 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b - 120a b)x - 48a b - 48a +--R * +--R +-------+ +-+ +-----+ +--R \|- b - a \|a \|b + a +--R Type: Expression Integer +--E 123 + +--S 124 OF 506 +d0123b:= D(m0123b,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (112) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 124 + +--S 125 OF 506 +t0124:= acoth(x)/(a+b*x^2)^(7/2) +--R +--R +--R acoth(x) +--R (113) ------------------------------------------ +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression Integer +--E 125 + +--S 126 OF 506 +r0124:= 1/15/a/(a+b)/(a+b*x^2)^(3/2)+_ + 1/15*(7*a+4*b)/a^2/(a+b)^2/(a+b*x^2)^(1/2)+_ + 1/15*x*(8*(a+b*x^2)^2+a*(7*a+4*b*x^2))*acoth(x)/a^3/(a+b*x^2)^(5/2)-_ + 1/15*(15*a^2+20*a*b+8*b^2)*_ + atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^3/(a+b)^(5/2) +--R +--R +--R (114) +--R 4 3 2 2 4 3 2 2 3 2 2 2 +--R (- 8b - 20a b - 15a b )x + (- 16a b - 40a b - 30a b)x - 8a b +--R + +--R 3 4 +--R - 20a b - 15a +--R * +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +--R \|b x + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 3 2 2 5 3 2 2 3 3 +--R (8b + 16a b + 8a b )x + (20a b + 40a b + 20a b)x +--R + +--R 2 2 3 4 +--R (15a b + 30a b + 15a )x +--R * +--R acoth(x) +--R + +--R 3 2 2 4 2 2 3 2 3 4 +--R (4a b + 7a b )x + (9a b + 15a b)x + 5a b + 8a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 5 2 +--R (15a b + 30a b + 15a b )x + (30a b + 60a b + 30a b)x + 15a b +--R + +--R 6 7 +--R 30a b + 15a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R Type: Expression Integer +--E 126 + +--S 127 OF 506 +a0124:= integrate(t0124,x) +--R +--R +--R (115) +--R [ +--R 8 7 2 6 12 +--R (64b + 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b + 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b + 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b + 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b + 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b + 11520a b + 8640a b)x + 1024a b + 2560a b + 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (- 8b - 20a b - 15a b )x + (- 280a b - 700a b - 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (- 2072a b - 5180a b - 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (- 6664a b - 16660a b - 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (- 11264a b - 28160a b - 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (- 10496a b - 26240a b - 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (- 5120a b - 12800a b - 9600a b)x - 1024a b - 2560a b - 1920a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 8 7 2 6 13 +--R (- 8b - 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b - 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b - 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b - 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b - 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b - 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b + 114a b )x + (766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b + 4080a b )x + (4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b + 4608a b )x + (896a b + 1280a b)x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b + 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b + 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b + 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b + 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b + 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b + 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b - 16a b )x + (- 286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b - 2672a b )x + (- 4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b - 8480a b )x + (- 3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b - 1280a b)x +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b + 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b + 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b + 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b + 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b + 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b + 34560a b + 17280a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b - 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b - 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b - 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b - 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b - 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b - 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b - 38400a b - 19200a b)x - 3840a b - 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-----+ +--R \|b + a +--R , +--R +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b +--R + +--R 8 +--R - 3840a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (16b + 40a b + 30a b )x + (560a b + 1400a b + 1050a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (4144a b + 10360a b + 7770a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (13328a b + 33320a b + 24990a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (22528a b + 56320a b + 42240a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (20992a b + 52480a b + 39360a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (10240a b + 25600a b + 19200a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 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+--R (9320a b + 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b + 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b + 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b - 16a b )x + (- 286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b - 2672a b )x + (- 4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b - 8480a b )x + (- 3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b - 1280a b)x +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b + 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b + 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b + 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b + 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b + 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b + 34560a b + 17280a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b - a \|a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b - 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b - 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b - 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b - 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b - 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b - 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b - 38400a b - 19200a b)x - 3840a b - 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-------+ +--R \|- b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 127 + +--S 128 OF 506 +m0124a:= a0124.1-r0124 +--R +--R +--R (116) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (8b + 20a b + 15a b )x + (272a b + 680a b + 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (1800a b + 4500a b + 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (4864a b + 12160a b + 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (6400a b + 16000a b + 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4096a b + 10240a b + 7680a b)x + 1024a b + 2560a b + 1920a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 64b - 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b - 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b - 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b - 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b - 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4608a b - 11520a b - 8640a b)x - 1024a b - 2560a b - 1920a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b + 40a b + 30a b )x + (544a b + 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b + 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b + 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b + 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b + 20480a b + 15360a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b - 3840a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 7 6 2 5 11 +--R (- 64b - 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b - 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b - 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b - 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b - 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b + 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b + 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b + 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b + 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b + 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b + 7680a b + 3840a )x +--R * +--R acoth(x) +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b + 16a b )x + (340a b + 544a b )x + (2250a b + 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b + 9728a b )x + (8000a b + 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b + 8192a b)x + 1280a b + 2048a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b + 16a b + 8a b )x + (276a b + 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b + 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b + 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b + 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b + 12800a b + 6400a b)x + (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b - 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b - 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b - 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b - 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b - 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b - 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b - 7680a b - 3840a )x +--R * +--R acoth(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b - 128a b )x + (- 1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b - 7296a b )x + (- 9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b - 16640a b )x + (- 5760a b - 9216a b)x - 1280a b +--R + +--R 8 +--R - 2048a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b + 60a b + 30a b )x + (1020a b + 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b + 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b + 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b + 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b + 30720a b + 15360a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b - 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b - 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b - 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b - 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b - 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b - 34560a b - 17280a b)x - 3840a b - 7680a b - 3840a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression Integer +--E 128 + +--S 129 OF 506 +d0124a:= D(m0124a,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (117) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 129 + +--S 130 OF 506 +m0124b:= a0124.2-r0124 +--R +--R +--R (118) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b + 40a b + 30a b )x + (544a b + 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b + 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b + 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b + 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b + 20480a b + 15360a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b - 3840a +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 8 7 2 6 12 +--R (- 16b - 40a b - 30a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 544a b - 1360a b - 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3600a b - 9000a b - 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 9728a b - 24320a b - 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 12800a b - 32000a b - 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 8192a b - 20480a b - 15360a b)x - 2048a b - 5120a b - 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 8 7 2 6 12 +--R (128b + 320a b + 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (1664a b + 4160a b + 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (7296a b + 18240a b + 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (15232a b + 38080a b + 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (16640a b + 41600a b + 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (9216a b + 23040a b + 17280a b)x + 2048a b + 5120a b + 3840a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 7 6 2 5 11 +--R (- 64b - 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b - 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b - 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b - 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b - 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b + 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b + 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b + 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b + 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b + 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b + 7680a b + 3840a )x +--R * +--R acoth(x) +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b + 16a b )x + (340a b + 544a b )x + (2250a b + 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b + 9728a b )x + (8000a b + 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b + 8192a b)x + 1280a b + 2048a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b - a \|a \|b + a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b + 16a b + 8a b )x + (276a b + 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b + 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b + 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b + 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b + 12800a b + 6400a b)x + (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b - 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b - 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b - 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b - 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b - 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b - 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b - 7680a b - 3840a )x +--R * +--R acoth(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b - 128a b )x + (- 1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b - 7296a b )x + (- 9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b - 16640a b )x + (- 5760a b - 9216a b)x - 1280a b +--R + +--R 8 +--R - 2048a +--R * +--R +-------+ +-----+ +--R \|- b - a \|b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b + 60a b + 30a b )x + (1020a b + 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b + 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b + 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b + 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b + 30720a b + 15360a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b - a \|b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b - 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b - 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b - 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b - 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b - 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b - 34560a b - 17280a b)x - 3840a b - 7680a b - 3840a +--R * +--R +-------+ +-+ +-----+ +--R \|- b - a \|a \|b + a +--R Type: Expression Integer +--E 130 + +--S 131 OF 506 +d0124b:= D(m0124b,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (119) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 131 + +--S 132 OF 506 +t0125:= acoth(x)*(a-a*x^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (120) acoth(x)\|- a x + a +--R Type: Expression Integer +--E 132 + +--S 133 OF 506 +r0125:= 1/2/(1-1/x^2)^(1/2)/x*(a*(1-x^2))^(1/2)*((1-1/x^2)^(1/2)*x+_ + (1-1/x^2)^(1/2)*x^2*acoth(x)-2*acoth(x)*atanh(exp(1)^acoth(x))-_ + polylog(2,-exp(1)^acoth(x))+polylog(2,exp(1)^acoth(x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 133 + +--S 134 OF 506 +a0125:= integrate(t0125,x) +--R +--R +--R x +------------+ +--R ++ | 2 +--R (121) | acoth(%Q)\|(- %Q + 1)a d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 134 + +--S 135 OF 506 +--m0125:= a0125-r0125 +--E 135 + +--S 136 OF 506 +--d0125:= D(m0125,x) +--E 136 + +--S 137 OF 506 +t0126:= acoth(x)/(a-a*x^2)^(1/2) +--R +--R +--R acoth(x) +--R (122) ------------- +--R +----------+ +--R | 2 +--R \|- a x + a +--R Type: Expression Integer +--E 137 + +--S 138 OF 506 +r0126:= (1-1/x^2)^(1/2)*x*(2*acoth(x)*atanh(exp(1)^acoth(x))+_ + polylog(2,-exp(1)^acoth(x))-_ + polylog(2,exp(1)^acoth(x)))/(a*(1-x^2))^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 138 + +--S 139 OF 506 +a0126:= integrate(t0126,x) +--R +--R +--R x +--R ++ acoth(%Q) +--R (123) | --------------- d%Q +--R ++ +------------+ +--R | 2 +--R \|(- %Q + 1)a +--R Type: Union(Expression Integer,...) +--E 139 + +--S 140 OF 506 +--m0126:= a0126-r0126 +--E 140 + +--S 141 OF 506 +--d0126:= D(m0126,x) +--E 141 + +--S 142 OF 506 +t0127:= acoth(x)/(a-a*x^2)^(3/2) +--R +--R +--R acoth(x) +--R (124) - ----------------------- +--R +----------+ +--R 2 | 2 +--R (a x - a)\|- a x + a +--R Type: Expression Integer +--E 142 + +--S 143 OF 506 +r0127:= (x*acoth(x)-1)/a/(-a*(-1+x^2))^(1/2) +--R +--R +--R x acoth(x) - 1 +--R (125) -------------- +--R +----------+ +--R | 2 +--R a\|- a x + a +--R Type: Expression Integer +--E 143 + +--S 144 OF 506 +a0127:= integrate(t0127,x) +--R +--R +--R +----------+ +--R x + 1 2 +-+ x + 1 | 2 +--R (x log(-----) - 2x )\|a - x log(-----)\|- a x + a +--R x - 1 x - 1 +--R (126) ---------------------------------------------------- +--R +----------+ +--R | 2 +-+ 2 2 2 +--R 2a\|- a x + a \|a + 2a x - 2a +--R Type: Union(Expression Integer,...) +--E 144 + +--S 145 OF 506 +m0127:= a0127-r0127 +--R +--R +--R (127) +--R +----------+ +--R x + 1 2 | 2 +-+ +--R (- x log(-----) + 2x acoth(x) + 2x - 2)\|- a x + a \|a +--R x - 1 +--R + +--R 3 x + 1 3 2 +--R (- a x + a x)log(-----) + (2a x - 2a x)acoth(x) - 2a x + 2a +--R x - 1 +--R / +--R +----------+ +--R 2 2 2 +-+ 2 2 2 | 2 +--R (2a x - 2a )\|a + (- 2a x + 2a )\|- a x + a +--R Type: Expression Integer +--E 145 + +--S 146 OF 506 +d0127:= D(m0127,x) +--R +--R +--R x + 1 +--R - log(-----) + 2acoth(x) +--R x - 1 +--R (128) ------------------------- +--R +----------+ +--R 2 | 2 +--R (2a x - 2a)\|- a x + a +--R Type: Expression Integer +--E 146 + +--S 147 OF 506 +t0128:= acoth(x)/(a-a*x^2)^(5/2) +--R +--R +--R acoth(x) +--R (129) -------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (a x - 2a x + a )\|- a x + a +--R Type: Expression Integer +--E 147 + +--S 148 OF 506 +r0128:= 1/9*(6*acoth(x)*x^3-6*x^2-_ + 9*x*acoth(x)+7)/a^2/(-1+x^2)/(-a*(-1+x^2))^(1/2) +--R +--R +--R 3 2 +--R (6x - 9x)acoth(x) - 6x + 7 +--R (130) ---------------------------- +--R +----------+ +--R 2 2 2 | 2 +--R (9a x - 9a )\|- a x + a +--R Type: Expression Integer +--E 148 + +--S 149 OF 506 +a0128:= integrate(t0128,x) +--R +--R +--R (131) +--R 5 3 x + 1 6 4 2 +-+ +--R ((18x - 51x + 36x)log(-----) - 14x + 48x - 36x )\|a +--R x - 1 +--R + +--R +----------+ +--R 5 3 x + 1 4 2 | 2 +--R ((- 6x + 33x - 36x)log(-----) - 30x + 36x )\|- a x + a +--R x - 1 +--R / +--R +----------+ +--R 2 4 2 2 2 | 2 +-+ 3 6 3 4 3 2 +--R (54a x - 126a x + 72a )\|- a x + a \|a + 18a x - 108a x + 162a x +--R + +--R 3 +--R - 72a +--R Type: Union(Expression Integer,...) +--E 149 + +--S 150 OF 506 +m0128:= a0128-r0128 +--R +--R +--R (132) +--R 5 3 x + 1 5 3 6 +--R (- 18x + 51x - 36x)log(-----) + (36x - 102x + 72x)acoth(x) + 14x +--R x - 1 +--R + +--R 4 2 +--R - 84x + 126x - 56 +--R * +--R +----------+ +--R | 2 +-+ +--R \|- a x + a \|a +--R + +--R 7 5 3 x + 1 +--R (- 6a x + 39a x - 69a x + 36a x)log(-----) +--R x - 1 +--R + +--R 7 5 3 6 4 2 +--R (12a x - 78a x + 138a x - 72a x)acoth(x) - 42a x + 140a x - 154a x +--R + +--R 56a +--R / +--R 3 6 3 4 3 2 3 +-+ +--R (54a x - 180a x + 198a x - 72a )\|a +--R + +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (- 18a x + 108a x - 162a x + 72a )\|- a x + a +--R Type: Expression Integer +--E 150 + +--S 151 OF 506 +d0128:= D(m0128,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (133) ---------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (2a x - 4a x + 2a )\|- a x + a +--R Type: Expression Integer +--E 151 + +--S 152 OF 506 +t0129:= acoth(x)/(a-a*x^2)^(7/2) +--R +--R +--R acoth(x) +--R (134) - ---------------------------------------- +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (a x - 3a x + 3a x - a )\|- a x + a +--R Type: Expression Integer +--E 152 + +--S 153 OF 506 +r0129:= 1/225*(120*acoth(x)*x^5-120*x^4-_ + 300*acoth(x)*x^3+260*x^2+225*x*_ + acoth(x)-149)/a^3/(-1+x^2)^2/(-a*(-1+x^2))^(1/2) +--R +--R +--R 5 3 4 2 +--R (120x - 300x + 225x)acoth(x) - 120x + 260x - 149 +--R (135) ---------------------------------------------------- +--R +----------+ +--R 3 4 3 2 3 | 2 +--R (225a x - 450a x + 225a )\|- a x + a +--R Type: Expression Integer +--E 153 + +--S 154 OF 506 +a0129:= integrate(t0129,x) +--R +--R +--R (136) +--R 9 7 5 3 x + 1 10 +--R (600x - 3900x + 9045x - 9300x + 3600x)log(-----) - 298x +--R x - 1 +--R + +--R 8 6 4 2 +--R 3270x - 8990x + 9600x - 3600x +--R * +--R +-+ +--R \|a +--R + +--R 9 7 5 3 x + 1 8 +--R (- 120x + 1740x - 5745x + 7500x - 3600x)log(-----) - 1250x +--R x - 1 +--R + +--R 6 4 2 +--R 5540x - 7800x + 3600x +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R / +--R +----------+ +--R 3 8 3 6 3 4 3 2 3 | 2 +-+ +--R (2250a x - 13500a x + 27450a x - 23400a x + 7200a )\|- a x + a \|a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R 450a x - 6750a x + 24750a x - 38250a x + 27000a x - 7200a +--R Type: Union(Expression Integer,...) +--E 154 + +--S 155 OF 506 +m0129:= a0129-r0129 +--R +--R +--R (137) +--R 9 7 5 3 x + 1 +--R (- 600x + 3900x - 9045x + 9300x - 3600x)log(-----) +--R x - 1 +--R + +--R 9 7 5 3 10 +--R (1200x - 7800x + 18090x - 18600x + 7200x)acoth(x) + 298x +--R + +--R 8 6 4 2 +--R - 4470x + 16390x - 25330x + 17880x - 4768 +--R * +--R +----------+ +--R | 2 +-+ +--R \|- a x + a \|a +--R + +--R 11 9 7 5 3 +--R (- 120a x + 1860a x - 7485a x + 13245a x - 11100a x + 3600a x) +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 11 9 7 5 3 +--R (240a x - 3720a x + 14970a x - 26490a x + 22200a x - 7200a x) +--R * +--R acoth(x) +--R + +--R 10 8 6 4 2 +--R - 1490a x + 10430a x - 27118a x + 33674a x - 20264a x + 4768a +--R / +--R 4 10 4 8 4 6 4 4 4 2 4 +-+ +--R (2250a x - 15750a x + 40950a x - 50850a x + 30600a x - 7200a )\|a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R (- 450a x + 6750a x - 24750a x + 38250a x - 27000a x + 7200a ) +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R Type: Expression Integer +--E 155 + +--S 156 OF 506 +d0129:= D(m0129,x) +--R +--R +--R x + 1 +--R - log(-----) + 2acoth(x) +--R x - 1 +--R (138) ------------------------------------------ +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (2a x - 6a x + 6a x - 2a )\|- a x + a +--R Type: Expression Integer +--E 156 + +--S 157 OF 506 +t0130:= acoth(x^(1/2)) +--R +--R +--R +-+ +--R (139) acoth(\|x ) +--R Type: Expression Integer +--E 157 + +--S 158 OF 506 +r0130:= x^(1/2)+x*acoth(x^(1/2))-atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R (140) - atanh(\|x ) + x acoth(\|x ) + \|x +--R Type: Expression Integer +--E 158 + +--S 159 OF 506 +a0130:= integrate(t0130,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R (x - 1)log(--------) + 2\|x +--R +-+ +--R \|x - 1 +--R (141) ---------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 159 + +--S 160 OF 506 +m0130:= a0130-r0130 +--R +--R +--R +-+ +--R \|x + 1 +-+ +-+ +--R (x - 1)log(--------) + 2atanh(\|x ) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (142) ---------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 160 + +--S 161 OF 506 +d0130:= D(m0130,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (143) ---------------------------- +--R 2 +--R Type: Expression Integer +--E 161 + +--S 162 OF 506 +t0131:= x*acoth(x^(1/2)) +--R +--R +--R +-+ +--R (144) x acoth(\|x ) +--R Type: Expression Integer +--E 162 + +--S 163 OF 506 +r0131:= 1/2*x^(1/2)+1/6*x^(3/2)+1/2*x^2*acoth(x^(1/2))-1/2*atanh(x^(1/2)) +--R +--R +--R +-+ 2 +-+ +-+ +--R - 3atanh(\|x ) + 3x acoth(\|x ) + (x + 3)\|x +--R (145) --------------------------------------------- +--R 6 +--R Type: Expression Integer +--E 163 + +--S 164 OF 506 +a0131:= integrate(t0131,x) +--R +--R +--R +-+ +--R 2 \|x + 1 +-+ +--R (3x - 3)log(--------) + (2x + 6)\|x +--R +-+ +--R \|x - 1 +--R (146) ------------------------------------- +--R 12 +--R Type: Union(Expression Integer,...) +--E 164 + +--S 165 OF 506 +m0131:= a0131-r0131 +--R +--R +--R +-+ +--R 2 \|x + 1 +-+ 2 +-+ +--R (x - 1)log(--------) + 2atanh(\|x ) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (147) ----------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 165 + +--S 166 OF 506 +d0131:= D(m0131,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R x log(--------) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (148) -------------------------------- +--R 2 +--R Type: Expression Integer +--E 166 + +--S 167 OF 506 +t0132:= acoth(x^(1/2))/x +--R +--R +--R +-+ +--R acoth(\|x ) +--R (149) ----------- +--R x +--R Type: Expression Integer +--E 167 + +--S 168 OF 506 +r0132:= polylog(2,-1/x^(1/2))-polylog(2,1/x^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 168 + +--S 169 OF 506 +a0132:= integrate(t0132,x) +--R +--R +--R x +--+ +--R ++ acoth(\|%Q ) +--R (150) | ------------ d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 169 + +--S 170 OF 506 +--m0132:= a0132-r0132 +--E 170 + +--S 171 OF 506 +--d0132:= D(m0132,x) +--E 171 + +--S 172 OF 506 +t0133:= acoth(x^(1/2))/x^2 +--R +--R +--R +-+ +--R acoth(\|x ) +--R (151) ----------- +--R 2 +--R x +--R Type: Expression Integer +--E 172 + +--S 173 OF 506 +r0133:= -1/x^(1/2)-acoth(x^(1/2))/x+atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +-+ +-+ +--R x\|x atanh(\|x ) - \|x acoth(\|x ) - x +--R (152) -------------------------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 173 + +--S 174 OF 506 +a0133:= integrate(t0133,x) +--R +--R +--R +-+ +--R +-+ \|x + 1 +--R (x - 1)\|x log(--------) - 2x +--R +-+ +--R \|x - 1 +--R (153) ----------------------------- +--R +-+ +--R 2x\|x +--R Type: Union(Expression Integer,...) +--E 174 + +--S 175 OF 506 +m0133:= a0133-r0133 +--R +--R +--R +-+ +--R \|x + 1 +-+ +-+ +--R (x - 1)log(--------) - 2x atanh(\|x ) + 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (154) ---------------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 175 + +--S 176 OF 506 +d0133:= D(m0133,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (155) ---------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 176 + +--S 177 OF 506 +t0134:= acoth(x^(1/2))/x^3 +--R +--R +--R +-+ +--R acoth(\|x ) +--R (156) ----------- +--R 3 +--R x +--R Type: Expression Integer +--E 177 + +--S 178 OF 506 +r0134:= -1/6/x^(3/2)-1/2/x^(1/2)-1/2*acoth(x^(1/2))/x^2+1/2*atanh(x^(1/2)) +--R +--R +--R 2 +-+ +-+ +-+ +-+ 2 +--R 3x \|x atanh(\|x ) - 3\|x acoth(\|x ) - 3x - x +--R (157) ----------------------------------------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression Integer +--E 178 + +--S 179 OF 506 +a0134:= integrate(t0134,x) +--R +--R +--R +-+ +--R 2 +-+ \|x + 1 2 +--R (3x - 3)\|x log(--------) - 6x - 2x +--R +-+ +--R \|x - 1 +--R (158) ------------------------------------- +--R 2 +-+ +--R 12x \|x +--R Type: Union(Expression Integer,...) +--E 179 + +--S 180 OF 506 +m0134:= a0134-r0134 +--R +--R +--R +-+ +--R 2 \|x + 1 2 +-+ +-+ +--R (x - 1)log(--------) - 2x atanh(\|x ) + 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (159) ----------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 180 + +--S 181 OF 506 +d0134:= D(m0134,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (160) ---------------------------- +--R 3 +--R 2x +--R Type: Expression Integer +--E 181 + +--S 182 OF 506 +t0135:= x^(1/2)*acoth(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (161) \|x acoth(\|x ) +--R Type: Expression Integer +--E 182 + +--S 183 OF 506 +r0135:= 1/3*x+2/3*x^(3/2)*acoth(x^(1/2))+1/3*log(1-x) +--R +--R +--R +-+ +-+ +--R 2x\|x acoth(\|x ) + log(- x + 1) + x +--R (162) ------------------------------------ +--R 3 +--R Type: Expression Integer +--E 183 + +--S 184 OF 506 +a0135:= integrate(t0135,x) +--R +--R +--R +-+ +--R +-+ \|x + 1 +--R x\|x log(--------) + log(x - 1) + x +--R +-+ +--R \|x - 1 +--R (163) ----------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 184 + +--S 185 OF 506 +m0135:= a0135-r0135 +--R +--R +--R +-+ +--R +-+ \|x + 1 +-+ +-+ +--R x\|x log(--------) - 2x\|x acoth(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R (164) ------------------------------------------------------------------ +--R 3 +--R Type: Expression Integer +--E 185 + +--S 186 OF 506 +d0135:= D(m0135,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R x log(--------) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (165) -------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression Integer +--E 186 + +--S 187 OF 506 +t0136:= x^(3/2)*acoth(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (166) x\|x acoth(\|x ) +--R Type: Expression Integer +--E 187 + +--S 188 OF 506 +r0136:= 1/5*x+1/10*x^2+2/5*x^(5/2)*acoth(x^(1/2))+1/5*log(1-x) +--R +--R +--R 2 +-+ +-+ 2 +--R 4x \|x acoth(\|x ) + 2log(- x + 1) + x + 2x +--R (167) -------------------------------------------- +--R 10 +--R Type: Expression Integer +--E 188 + +--S 189 OF 506 +a0136:= integrate(t0136,x) +--R +--R +--R +-+ +--R 2 +-+ \|x + 1 2 +--R 2x \|x log(--------) + 2log(x - 1) + x + 2x +--R +-+ +--R \|x - 1 +--R (168) -------------------------------------------- +--R 10 +--R Type: Union(Expression Integer,...) +--E 189 + +--S 190 OF 506 +m0136:= a0136-r0136 +--R +--R +--R +-+ +--R 2 +-+ \|x + 1 2 +-+ +-+ +--R x \|x log(--------) - 2x \|x acoth(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R (169) -------------------------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 190 + +--S 191 OF 506 +d0136:= D(m0136,x) +--R +--R +--R +-+ +--R 2 \|x + 1 2 +-+ +--R x log(--------) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (170) -------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression Integer +--E 191 + +--S 192 OF 506 +t0137:= acoth(x^(1/2))/x^(3/2) +--R +--R +--R +-+ +--R acoth(\|x ) +--R (171) ----------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 192 + +--S 193 OF 506 +r0137:= -2*acoth(x^(1/2))/x^(1/2)+2*atanh(-1+2*x) +--R +--R +--R +-+ +-+ +--R - 2acoth(\|x ) + 2atanh(2x - 1)\|x +--R (172) ----------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 193 + +--S 194 OF 506 +a0137:= integrate(t0137,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R - log(--------) + (log(x) - log(x - 1))\|x +--R +-+ +--R \|x - 1 +--R (173) ------------------------------------------- +--R +-+ +--R \|x +--R Type: Union(Expression Integer,...) +--E 194 + +--S 195 OF 506 +m0137:= a0137-r0137 +--R +--R +--R (174) +--R +-+ +--R \|x + 1 +-+ +-+ +--R - log(--------) + 2acoth(\|x ) + (log(x) - log(x - 1) - 2atanh(2x - 1))\|x +--R +-+ +--R \|x - 1 +--R --------------------------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 195 + +--S 196 OF 506 +d0137:= D(m0137,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (175) ---------------------------- +--R +-+ +--R 2x\|x +--R Type: Expression Integer +--E 196 + +--S 197 OF 506 +t0138:= x^3*asech(a*x) +--R +--R +--R 3 +--R (176) x asech(a x) +--R Type: Expression Integer +--E 197 + +--S 198 OF 506 +r0138:= -1/16*((1-a*x)/(1+a*x))^(1/2)*(1+a*x)^3/a^4-_ + 1/24*((1-a*x)/(1+a*x))^(3/2)*(1+a*x)^3/a^4-_ + 1/16*((1-a*x)/(1+a*x))^(5/2)*(1+a*x)^3/a^4+1/4*x^4*asech(a*x) +--R +--R +--R +---------+ +--R 3 3 2 2 |- a x + 1 4 4 +--R (- a x - a x - 2a x - 2) |--------- + 3a x asech(a x) +--R \| a x + 1 +--R (177) -------------------------------------------------------- +--R 4 +--R 12a +--R Type: Expression Integer +--E 198 + +--S 199 OF 506 +a0138:= integrate(t0138,x) +--R +--R +--R (178) +--R +----------+ +--R +----------+ | 2 2 +--R 2 6 4 | 2 2 2 6 4 \|- a x + 1 + 1 +--R ((3a x - 12x )\|- a x + 1 - 9a x + 12x )log(-----------------) +--R a x +--R + +--R +----------+ +--R 4 | 2 2 2 6 4 +--R 3x \|- a x + 1 + a x - 3x +--R / +--R +----------+ +--R 2 2 | 2 2 2 2 +--R (12a x - 48)\|- a x + 1 - 36a x + 48 +--R Type: Union(Expression Integer,...) +--E 199 + +--S 200 OF 506 +m0138:= a0138-r0138 +--R +--R +--R (179) +--R +----------+ +--R +----------+ | 2 2 +--R 6 6 4 4 | 2 2 6 6 4 4 \|- a x + 1 + 1 +--R ((3a x - 12a x )\|- a x + 1 - 9a x + 12a x )log(-----------------) +--R a x +--R + +--R +----------+ +--R 5 5 4 4 3 3 2 2 | 2 2 5 5 4 4 +--R (a x + a x - 2a x - 2a x - 8a x - 8)\|- a x + 1 - 3a x - 3a x +--R + +--R 3 3 2 2 +--R - 2a x - 2a x + 8a x + 8 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 6 6 4 4 4 4 | 2 2 +--R ((- 3a x + 12a x )asech(a x) + 3a x )\|- a x + 1 +--R + +--R 6 6 4 4 6 6 4 4 +--R (9a x - 12a x )asech(a x) + a x - 3a x +--R / +--R +----------+ +--R 6 2 4 | 2 2 6 2 4 +--R (12a x - 48a )\|- a x + 1 - 36a x + 48a +--R Type: Expression Integer +--E 200 + +--S 201 OF 506 +d0138:= D(m0138,x) +--R +--R +--R (180) +--R 7 10 6 9 5 8 4 7 3 6 2 5 4 +--R 4a x + 4a x - 72a x - 72a x + 192a x + 192a x - 128a x +--R + +--R 3 +--R - 128x +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 4 +--R - 24a x - 24a x + 152a x + 152a x - 256a x - 256a x + 128a x +--R + +--R 3 +--R 128x +--R * +--R +----------+ +--R +---------+ | 2 2 +--R |- a x + 1 \|- a x + 1 + 1 +--R |--------- log(-----------------) +--R \| a x + 1 a x +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 +--R - 4a x - 4a x + 72a x + 72a x - 192a x - 192a x +--R + +--R 4 3 +--R 128a x + 128x +--R * +--R asech(a x) +--R + +--R 5 8 4 7 3 6 2 5 4 3 +--R 6a x + 6a x - 32a x - 32a x + 32a x + 32x +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 +--R 24a x + 24a x - 152a x - 152a x + 256a x + 256a x +--R + +--R 4 3 +--R - 128a x - 128x +--R * +--R asech(a x) +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 4 3 +--R a x + a x - 18a x - 18a x + 48a x + 48a x - 32a x - 32x +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 6 9 4 7 2 5 3 | 2 2 6 9 4 7 2 5 +--R (- a x + 18a x - 48a x + 32x )\|- a x + 1 + 6a x - 38a x + 64a x +--R + +--R 3 +--R - 32x +--R / +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R (4a x + 4a x - 72a x - 72a x + 192a x + 192a x - 128a x - 128) +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - 24a x - 24a x + 152a x + 152a x - 256a x - 256a x + 128a x + 128 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R Type: Expression Integer +--E 201 + +--S 202 OF 506 +t0139:= asech(a*x)/x +--R +--R +--R asech(a x) +--R (181) ---------- +--R x +--R Type: Expression Integer +--E 202 + +--S 203 OF 506 +r0139:= -1/2*asech(a*x)^2-asech(a*x)*log(1+exp(1)^(-2*asech(a*x)))+_ + 1/2*polylog(2,-exp(1)^(-2*asech(a*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 203 + +--S 204 OF 506 +a0139:= integrate(t0139,x) +--R +--R +--R x +--R ++ asech(%Q a) +--R (182) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 204 + +--S 205 OF 506 +--m0139:= a0139-r0139 +--E 205 + +--S 206 OF 506 +--d0139:= D(m0139,x) +--E 206 + +--S 207 OF 506 +t0140:= asech(a*x)/x^3 +--R +--R +--R asech(a x) +--R (183) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 207 + +--S 208 OF 506 +r0140:= 1/4*((-(-1+a*x)/(1+a*x))^(1/2)*a*x+(-(-1+a*x)/(1+a*x))^(1/2)-_ + 2*asech(a*x)+2*a^2*atanh((-(-1+a*x)/(1+a*x))^(1/2))*x^2)/x^2 +--R +--R +--R +---------+ +---------+ +--R 2 2 |- a x + 1 |- a x + 1 +--R 2a x atanh( |--------- ) + (a x + 1) |--------- - 2asech(a x) +--R \| a x + 1 \| a x + 1 +--R (184) -------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 208 + +--S 209 OF 506 +a0140:= integrate(t0140,x) +--R +--R +--R (185) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 4 4 2 2 \|- a x + 1 + 1 +--R ((2a x - 4)\|- a x + 1 + a x - 4a x + 4)log(-----------------) +--R a x +--R + +--R +----------+ +--R 2 2 | 2 2 2 2 +--R (a x - 2)\|- a x + 1 - 2a x + 2 +--R / +--R +----------+ +--R 2 | 2 2 2 4 2 +--R 8x \|- a x + 1 + 4a x - 8x +--R Type: Union(Expression Integer,...) +--E 209 + +--S 210 OF 506 +m0140:= a0140-r0140 +--R +--R +--R (186) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 4 4 2 2 \|- a x + 1 + 1 +--R ((2a x - 4)\|- a x + 1 + a x - 4a x + 4)log(-----------------) +--R a x +--R + +--R +----------+ +---------+ +--R 2 2 | 2 2 4 4 2 2 |- a x + 1 +--R (- 4a x \|- a x + 1 - 2a x + 4a x )atanh( |--------- ) +--R \| a x + 1 +--R + +--R +----------+ +---------+ +--R | 2 2 3 3 2 2 |- a x + 1 +--R ((- 2a x - 2)\|- a x + 1 - a x - a x + 2a x + 2) |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 2 2 | 2 2 2 2 2 2 +--R (4asech(a x) + a x - 2)\|- a x + 1 + (2a x - 4)asech(a x) - 2a x + 2 +--R / +--R +----------+ +--R 2 | 2 2 2 4 2 +--R 8x \|- a x + 1 + 4a x - 8x +--R Type: Expression Integer +--E 210 + +--S 211 OF 506 +d0140:= D(m0140,x) +--R +--R +--R (187) +--R +----------+ +--R 5 5 4 4 3 3 2 2 | 2 2 5 5 +--R (2a x + 2a x - 16a x - 16a x + 16a x + 16)\|- a x + 1 - 8a x +--R + +--R 4 4 3 3 2 2 +--R - 8a x + 24a x + 24a x - 16a x - 16 +--R * +--R +----------+ +--R +---------+ | 2 2 +--R |- a x + 1 \|- a x + 1 + 1 +--R |--------- log(-----------------) +--R \| a x + 1 a x +--R + +--R 5 5 4 4 3 3 2 2 +--R (- 2a x - 2a x + 16a x + 16a x - 16a x - 16)asech(a x) +--R + +--R 3 3 2 2 +--R - 4a x - 4a x + 8a x + 8 +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 5 5 4 4 3 3 2 2 5 5 +--R (8a x + 8a x - 24a x - 24a x + 16a x + 16)asech(a x) - a x +--R + +--R 4 4 3 3 2 2 +--R - a x + 8a x + 8a x - 8a x - 8 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 4 4 2 2 | 2 2 4 4 2 2 +--R (a x - 8a x + 8)\|- a x + 1 - 4a x + 12a x - 8 +--R / +--R +----------+ +--R 5 8 4 7 3 6 2 5 4 3 | 2 2 5 8 +--R (2a x + 2a x - 16a x - 16a x + 16a x + 16x )\|- a x + 1 - 8a x +--R + +--R 4 7 3 6 2 5 4 3 +--R - 8a x + 24a x + 24a x - 16a x - 16x +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R Type: Expression Integer +--E 211 + +--S 212 OF 506 +t0141:= asech(a*x)/x^4 +--R +--R +--R asech(a x) +--R (188) ---------- +--R 4 +--R x +--R Type: Expression Integer +--E 212 + +--S 213 OF 506 +r0141:= 1/12*((1-a*x)/(1+a*x))^(1/2)*(1+a*x)^3/x^3-_ + 1/18*((1-a*x)/(1+a*x))^(3/2)*(1+a*x)^3/x^3+_ + 1/12*((1-a*x)/(1+a*x))^(5/2)*(1+a*x)^3/x^3-1/3*asech(a*x)/x^3 +--R +--R +--R +---------+ +--R 3 3 2 2 |- a x + 1 +--R (2a x + 2a x + a x + 1) |--------- - 3asech(a x) +--R \| a x + 1 +--R (189) --------------------------------------------------- +--R 3 +--R 9x +--R Type: Expression Integer +--E 213 + +--S 214 OF 506 +a0141:= integrate(t0141,x) +--R +--R +--R (190) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 2 2 \|- a x + 1 + 1 +--R ((- 3a x + 12)\|- a x + 1 + 9a x - 12)log(-----------------) +--R a x +--R + +--R +----------+ +--R 4 4 2 2 | 2 2 6 6 4 4 2 2 +--R (- 6a x + 5a x + 4)\|- a x + 1 - 2a x + 9a x - 3a x - 4 +--R / +--R +----------+ +--R 2 5 3 | 2 2 2 5 3 +--R (9a x - 36x )\|- a x + 1 - 27a x + 36x +--R Type: Union(Expression Integer,...) +--E 214 + +--S 215 OF 506 +m0141:= a0141-r0141 +--R +--R +--R (191) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 2 2 \|- a x + 1 + 1 +--R ((- 3a x + 12)\|- a x + 1 + 9a x - 12)log(-----------------) +--R a x +--R + +--R +----------+ +--R 5 5 4 4 3 3 2 2 | 2 2 5 5 +--R (- 2a x - 2a x + 7a x + 7a x + 4a x + 4)\|- a x + 1 + 6a x +--R + +--R 4 4 3 3 2 2 +--R 6a x - 5a x - 5a x - 4a x - 4 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 2 2 4 4 2 2 | 2 2 +--R ((3a x - 12)asech(a x) - 6a x + 5a x + 4)\|- a x + 1 +--R + +--R 2 2 6 6 4 4 2 2 +--R (- 9a x + 12)asech(a x) - 2a x + 9a x - 3a x - 4 +--R / +--R +----------+ +--R 2 5 3 | 2 2 2 5 3 +--R (9a x - 36x )\|- a x + 1 - 27a x + 36x +--R Type: Expression Integer +--E 215 + +--S 216 OF 506 +d0141:= D(m0141,x) +--R +--R +--R (192) +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R (3a x + 3a x - 54a x - 54a x + 144a x + 144a x - 96a x - 96) +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - 18a x - 18a x + 114a x + 114a x - 192a x - 192a x + 96a x + 96 +--R * +--R +----------+ +--R +---------+ | 2 2 +--R |- a x + 1 \|- a x + 1 + 1 +--R |--------- log(-----------------) +--R \| a x + 1 a x +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - 3a x - 3a x + 54a x + 54a x - 144a x - 144a x + 96a x +--R + +--R 96 +--R * +--R asech(a x) +--R + +--R 5 5 4 4 3 3 2 2 +--R - 6a x - 6a x + 32a x + 32a x - 32a x - 32 +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R 18a x + 18a x - 114a x - 114a x + 192a x + 192a x - 96a x +--R + +--R - 96 +--R * +--R asech(a x) +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - a x - a x + 18a x + 18a x - 48a x - 48a x + 32a x + 32 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 6 6 4 4 2 2 | 2 2 6 6 4 4 2 2 +--R (a x - 18a x + 48a x - 32)\|- a x + 1 - 6a x + 38a x - 64a x + 32 +--R / +--R 7 11 6 10 5 9 4 8 3 7 2 6 5 +--R 3a x + 3a x - 54a x - 54a x + 144a x + 144a x - 96a x +--R + +--R 4 +--R - 96x +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 11 6 10 5 9 4 8 3 7 2 6 5 +--R - 18a x - 18a x + 114a x + 114a x - 192a x - 192a x + 96a x +--R + +--R 4 +--R 96x +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R Type: Expression Integer +--E 216 + +--S 217 OF 506 +t0142:= x*asech(x^(1/2)) +--R +--R +--R +-+ +--R (193) x asech(\|x ) +--R Type: Expression Integer +--E 217 + +--S 218 OF 506 +r0142:= -1/8*((1-x^(1/2))/(1+x^(1/2)))^(1/2)*(1+x^(1/2))^3-_ + 1/12*((1-x^(1/2))/(1+x^(1/2)))^(3/2)*(1+x^(1/2))^3-_ + 1/8*((1-x^(1/2))/(1+x^(1/2)))^(5/2)*(1+x^(1/2))^3+_ + 1/2*x^2*asech(x^(1/2)) +--R +--R +--R (194) +--R +----------+ +--R | +-+ +--R 2 +-+ 3 2 |- \|x + 1 +--R ((- 4x - 12x - 8)\|x - x - 8x - 13x - 2) |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R 3 2 +-+ 3 2 +-+ +--R ((3x + 9x )\|x + 9x + 3x )asech(\|x ) +--R / +--R +-+ +--R (6x + 18)\|x + 18x + 6 +--R Type: Expression Integer +--E 218 + +--S 219 OF 506 +a0142:= integrate(t0142,x) +--R +--R +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +-------+ +--R 2 \| x |- x + 1 +-+ +--R 3x log(------------------) + (- x - 2) |------- \|x +--R +-+ \| x +--R \|x +--R (195) ---------------------------------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 219 + +--S 220 OF 506 +m0142:= a0142-r0142 +--R +--R +--R (196) +--R +----------+ +--R | +-+ +--R 2 +-+ 3 2 |- \|x + 1 +--R ((4x + 12x + 8)\|x + x + 8x + 13x + 2) |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R 3 2 +-+ 3 2 \| x +--R ((3x + 9x )\|x + 9x + 3x )log(------------------) +--R +-+ +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+ +--R ((- 3x - 9x )\|x - 9x - 3x )asech(\|x ) +--R + +--R +-------+ +-------+ +--R 2 |- x + 1 +-+ 3 2 |- x + 1 +--R (- 3x - 7x - 2) |------- \|x + (- x - 5x - 6x) |------- +--R \| x \| x +--R / +--R +-+ +--R (6x + 18)\|x + 18x + 6 +--R Type: Expression Integer +--E 220 + +--S 221 OF 506 +d0142:= D(m0142,x) +--R +--R +--R (197) +--R 7 6 5 4 3 2 +-------+ +--R (4x + 220x + 1320x + 1848x + 660x + 44x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (44x + 660x + 1848x + 1320x + 220x + 4x)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (44x + 660x + 1848x + 1320x + 220x + 4x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (4x + 220x + 1320x + 1848x + 660x + 44x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R \| x +--R log(------------------) +--R +-+ +--R \|x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (- 4x - 220x - 1320x - 1848x - 660x - 44x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (- 44x - 660x - 1848x - 1320x - 220x - 4x)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (- 44x - 660x - 1848x - 1320x - 220x - 4x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (- 4x - 220x - 1320x - 1848x - 660x - 44x )\|- x + 1 +--R * +--R +-+ +--R asech(\|x ) +--R + +--R +-------+ +--R 7 6 5 4 3 2 |- x + 1 6 +--R (x + 55x + 330x + 462x + 165x + 11x ) |------- + 11x +--R \| x +--R + +--R 5 4 3 2 +--R 165x + 462x + 330x + 55x + x +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 7 6 5 4 3 2 |- x + 1 7 6 +--R (11x + 165x + 462x + 330x + 55x + x ) |------- + x + 55x +--R \| x +--R + +--R 5 4 3 2 +--R 330x + 462x + 165x + 11x +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R 6 5 4 3 2 +-------+ |- x + 1 +--R (- 10x - 120x - 252x - 120x - 10x )\|- x + 1 |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (- x - 45x - 210x - 210x - 45x - x)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 7 6 5 4 3 2 +-------+ |- x + 1 +--R (- x - 45x - 210x - 210x - 45x - x )\|- x + 1 |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (- 10x - 120x - 252x - 120x - 10x )\|- x + 1 +--R / +--R +-------+ +--R 6 5 4 3 2 +-------+ |- x + 1 +--R (4x + 220x + 1320x + 1848x + 660x + 44x)\|- x + 1 |------- +--R \| x +--R + +--R 5 4 3 2 +-------+ +--R (44x + 660x + 1848x + 1320x + 220x + 4)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 6 5 4 3 2 +-------+ |- x + 1 +--R (44x + 660x + 1848x + 1320x + 220x + 4x)\|- x + 1 |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (4x + 220x + 1320x + 1848x + 660x + 44x)\|- x + 1 +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R Type: Expression Integer +--E 221 + +--S 222 OF 506 +t0143:= x^2*asech(x^(1/2)) +--R +--R +--R 2 +-+ +--R (198) x asech(\|x ) +--R Type: Expression Integer +--E 222 + +--S 223 OF 506 +r0143:= -8/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)+1/3*x^3*asech(x^(1/2))-_ + 8/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(1/2)-_ + 4/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x-_ + 4/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(3/2)-_ + 1/15*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^2-_ + 1/15*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(5/2) +--R +--R +--R +----------+ +--R | +-+ +--R 2 +-+ 2 |- \|x + 1 3 +-+ +--R ((- 3x - 4x - 8)\|x - 3x - 4x - 8) |---------- + 15x asech(\|x ) +--R | +-+ +--R \| \|x + 1 +--R (199) -------------------------------------------------------------------- +--R 45 +--R Type: Expression Integer +--E 223 + +--S 224 OF 506 +a0143:= integrate(t0143,x) +--R +--R +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +-------+ +--R 3 \| x 2 |- x + 1 +-+ +--R 15x log(------------------) + (- 3x - 4x - 8) |------- \|x +--R +-+ \| x +--R \|x +--R (200) ------------------------------------------------------------ +--R 45 +--R Type: Union(Expression Integer,...) +--E 224 + +--S 225 OF 506 +m0143:= a0143-r0143 +--R +--R +--R (201) +--R +----------+ +--R | +-+ +--R 2 +-+ 2 |- \|x + 1 +--R ((3x + 4x + 8)\|x + 3x + 4x + 8) |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R 3 \| x 3 +-+ +--R 15x log(------------------) - 15x asech(\|x ) +--R +-+ +--R \|x +--R + +--R +-------+ +--R 2 |- x + 1 +-+ +--R (- 3x - 4x - 8) |------- \|x +--R \| x +--R / +--R 45 +--R Type: Expression Integer +--E 225 + +--S 226 OF 506 +d0143:= D(m0143,x) +--R +--R +--R (202) +--R +-------+ +--R 3 2 +-------+ |- x + 1 3 2 +-------+ +-+ +--R ((18x + 6x )\|- x + 1 |------- + (6x + 18x )\|- x + 1 )\|x +--R \| x +--R + +--R +-------+ +--R 4 3 +-------+ |- x + 1 3 2 +-------+ +--R (6x + 18x )\|- x + 1 |------- + (18x + 6x )\|- x + 1 +--R \| x +--R * +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R \| x +--R log(------------------) +--R +-+ +--R \|x +--R + +--R +-------+ +--R 3 2 +-------+ |- x + 1 3 2 +-------+ +--R ((- 18x - 6x )\|- x + 1 |------- + (- 6x - 18x )\|- x + 1 ) +--R \| x +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 4 3 +-------+ |- x + 1 3 2 +-------+ +--R (- 6x - 18x )\|- x + 1 |------- + (- 18x - 6x )\|- x + 1 +--R \| x +--R * +--R +-+ +--R asech(\|x ) +--R + +--R +-------+ +-------+ +--R 3 2 |- x + 1 3 2 +-+ 4 3 |- x + 1 3 2 +--R ((3x + x ) |------- + x + 3x )\|x + (x + 3x ) |------- + 3x + x +--R \| x \| x +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R 3 2 +-------+ |- x + 1 2 +-------+ +-+ +--R ((- x - x )\|- x + 1 |------- - 2x \|- x + 1 )\|x +--R \| x +--R + +--R +-------+ +--R 3 +-------+ |- x + 1 3 2 +-------+ +--R - 2x \|- x + 1 |------- + (- x - x )\|- x + 1 +--R \| x +--R / +--R +-------+ +--R +-------+ |- x + 1 +-------+ +-+ +--R ((18x + 6)\|- x + 1 |------- + (6x + 18)\|- x + 1 )\|x +--R \| x +--R + +--R +-------+ +--R 2 +-------+ |- x + 1 +-------+ +--R (6x + 18x)\|- x + 1 |------- + (18x + 6)\|- x + 1 +--R \| x +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R Type: Expression Integer +--E 226 + +--S 227 OF 506 +t0144:= asech(x^(1/2))/x +--R +--R +--R +-+ +--R asech(\|x ) +--R (203) ----------- +--R x +--R Type: Expression Integer +--E 227 + +--S 228 OF 506 +r0144:= -asech(x^(1/2))^2-2*asech(x^(1/2))*_ + log(1+exp(1)^(-2*asech(x^(1/2))))+_ + polylog(2,-exp(1)^(-2*asech(x^(1/2)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 228 + +--S 229 OF 506 +a0144:= integrate(t0144,x) +--R +--R +--R x +--+ +--R ++ asech(\|%Q ) +--R (204) | ------------ d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 229 + +--S 230 OF 506 +--m0144:= a0144-r0144 +--E 230 + +--S 231 OF 506 +--d0144:= D(m0144,x) +--E 231 + +--S 232 OF 506 +t0145:= asech(x^(1/2))/x^3 +--R +--R +--R +-+ +--R asech(\|x ) +--R (205) ----------- +--R 3 +--R x +--R Type: Expression Integer +--E 232 + +--S 233 OF 506 +r0145:= 1/16*(2*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x+_ + 3*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^2+_ + 3*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(3/2)+_ + 2*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(1/2)+_ + 6*atanh((-(-1+x^(1/2))/(1+x^(1/2)))^(1/2))*x^(5/2)-_ + 8*asech(x^(1/2))*x^(1/2))/x^(5/2) +--R +--R +--R (206) +--R +----------+ +----------+ +--R | +-+ | +-+ +--R 2 +-+ |- \|x + 1 +-+ 2 |- \|x + 1 +--R 6x \|x atanh( |---------- ) + ((3x + 2)\|x + 3x + 2x) |---------- +--R | +-+ | +-+ +--R \| \|x + 1 \| \|x + 1 +--R + +--R +-+ +-+ +--R - 8\|x asech(\|x ) +--R / +--R 2 +-+ +--R 16x \|x +--R Type: Expression Integer +--E 233 + +--S 234 OF 506 +a0145:= integrate(t0145,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 234 + +--S 235 OF 506 +--m0145:= a0145-r0145 +--E 235 + +--S 236 OF 506 +--d0145:= D(m0145,x) +--E 236 + +--S 237 OF 506 +t0146:= x^2*acsch(a*x) +--R +--R +--R 2 +--R (207) x acsch(a x) +--R Type: Expression Integer +--E 237 + +--S 238 OF 506 +r0146:= 1/6*(1+1/a^2/x^2)^(1/2)*x^2/a+1/3*x^3*acsch(a*x)-_ + 1/6*atanh((1+1/a^2/x^2)^(1/2))/a^3 +--R +--R +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R |a x + 1 2 2 |a x + 1 3 3 +--R - atanh( |-------- ) + a x |-------- + 2a x acsch(a x) +--R | 2 2 | 2 2 +--R \| a x \| a x +--R (208) -------------------------------------------------------- +--R 3 +--R 6a +--R Type: Expression Integer +--E 238 + +--S 239 OF 506 +a0146:= integrate(t0146,x) +--R +--R +--R (209) +--R +--------+ +--------+ +--R | 2 2 2 2 | 2 2 +--R (2a x\|a x + 1 - 2a x - 1)log(\|a x + 1 - a x) +--R + +--R +--------+ +--R +--------+ | 2 2 +--R 4 4 | 2 2 5 5 3 3 \|a x + 1 + 1 +--R (4a x \|a x + 1 - 4a x - 2a x )log(---------------) +--R a x +--R + +--R +--------+ +--R 3 3 | 2 2 4 4 2 2 +--R (- 2a x - a x)\|a x + 1 + 2a x + 2a x +--R / +--R +--------+ +--R 4 | 2 2 5 2 3 +--R 12a x\|a x + 1 - 12a x - 6a +--R Type: Union(Expression Integer,...) +--E 239 + +--S 240 OF 506 +m0146:= a0146-r0146 +--R +--R +--R (210) +--R +--------+ +--------+ +--R | 2 2 2 2 | 2 2 +--R (2a x\|a x + 1 - 2a x - 1)log(\|a x + 1 - a x) +--R + +--R +--------+ +--R +--------+ | 2 2 +--R 4 4 | 2 2 5 5 3 3 \|a x + 1 + 1 +--R (4a x \|a x + 1 - 4a x - 2a x )log(---------------) +--R a x +--R + +--R +--------+ +--R +--------+ | 2 2 +--R | 2 2 2 2 |a x + 1 +--R (2a x\|a x + 1 - 2a x - 1)atanh( |-------- ) +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--------+ +--R 3 3 |a x + 1 4 4 3 3 | 2 2 +--R (- 2a x |-------- - 4a x acsch(a x) - 2a x - a x)\|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 4 4 2 2 |a x + 1 5 5 3 3 4 4 2 2 +--R (2a x + a x ) |-------- + (4a x + 2a x )acsch(a x) + 2a x + 2a x +--R | 2 2 +--R \| a x +--R / +--R +--------+ +--R 4 | 2 2 5 2 3 +--R 12a x\|a x + 1 - 12a x - 6a +--R Type: Expression Integer +--E 240 + +--S 241 OF 506 +d0146:= D(m0146,x) +--R +--R +--R (211) +--R +--------+ +--R | 2 2 +--------+ +--R 5 6 3 4 2 |a x + 1 | 2 2 +--R (24a x + 24a x + 3a x ) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 7 4 5 2 3 |a x + 1 +--R (- 24a x - 36a x - 12a x ) |-------- +--R | 2 2 +--R \| a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 + 1 +--R log(---------------) +--R a x +--R + +--R +--------+ +--R | 2 2 +--R 5 6 3 4 2 4 5 2 3 |a x + 1 +--R ((- 24a x - 24a x - 3a x )acsch(a x) - 8a x - 4a x ) |-------- +--R | 2 2 +--R \| a x +--R + +--R 4 5 2 3 +--R - 8a x - 8a x - x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 +--R + +--R +--------+ +--R | 2 2 +--R 6 7 4 5 2 3 5 6 3 4 2 |a x + 1 +--R ((24a x + 36a x + 12a x )acsch(a x) + 8a x + 8a x + a x ) |-------- +--R | 2 2 +--R \| a x +--R + +--R 5 6 3 4 2 +--R 8a x + 12a x + 4a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R 5 4 3 2 |a x + 1 | 2 2 +--R (24a x + 24a x + 3a) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 5 4 3 2 |a x + 1 +--R (- 24a x - 36a x - 12a x) |-------- +--R | 2 2 +--R \| a x +--R Type: Expression Integer +--E 241 + +--S 242 OF 506 +t0147:= acsch(a*x)/x +--R +--R +--R acsch(a x) +--R (212) ---------- +--R x +--R Type: Expression Integer +--E 242 + +--S 243 OF 506 +r0147:= -1/2*acsch(a*x)^2-acsch(a*x)*log(1-exp(1)^(-2*acsch(a*x)))+_ + 1/2*polylog(2,exp(1)^(-2*acsch(a*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 243 + +--S 244 OF 506 +a0147:= integrate(t0147,x) +--R +--R +--R x +--R ++ acsch(%Q a) +--R (213) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 244 + +--S 245 OF 506 +--m0147:= a0147-r0147 +--E 245 + +--S 246 OF 506 +--d0147:= D(m0147,x) +--E 246 + +--S 247 OF 506 +t0148:= acsch(a*x)/x^3 +--R +--R +--R acsch(a x) +--R (214) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 247 + +--S 248 OF 506 +r0148:= 1/4*a*(1+1/a^2/x^2)^(1/2)/x-1/2*acsch(a*x)/x^2-1/4*a^2*asinh(1/a/x) +--R +--R +--R +--------+ +--R | 2 2 +--R |a x + 1 2 2 1 +--R a x |-------- - a x asinh(---) - 2acsch(a x) +--R | 2 2 a x +--R \| a x +--R (215) --------------------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 248 + +--S 249 OF 506 +a0148:= integrate(t0148,x) +--R +--R +--R (216) +--R +--------+ +--R +--------+ | 2 2 +--R 3 3 | 2 2 4 4 2 2 \|a x + 1 + 1 +--R ((- 2a x - 4a x)\|a x + 1 + 2a x + 5a x + 2)log(---------------) +--R a x +--R + +--R +--------+ +--R 2 2 | 2 2 3 3 +--R (- 2a x - 1)\|a x + 1 + 2a x + 2a x +--R / +--R +--------+ +--R 3 | 2 2 2 4 2 +--R 8a x \|a x + 1 - 8a x - 4x +--R Type: Union(Expression Integer,...) +--E 249 + +--S 250 OF 506 +m0148:= a0148-r0148 +--R +--R +--R (217) +--R +--------+ +--R +--------+ | 2 2 +--R 3 3 | 2 2 4 4 2 2 \|a x + 1 + 1 +--R ((- 2a x - 4a x)\|a x + 1 + 2a x + 5a x + 2)log(---------------) +--R a x +--R + +--R +--------+ +--R | 2 2 +--R 2 2 |a x + 1 3 3 1 2 2 +--R (- 2a x |-------- + 2a x asinh(---) + 4a x acsch(a x) - 2a x - 1) +--R | 2 2 a x +--R \| a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 +--R + +--R +--------+ +--R | 2 2 +--R 3 3 |a x + 1 4 4 2 2 1 +--R (2a x + a x) |-------- + (- 2a x - a x )asinh(---) +--R | 2 2 a x +--R \| a x +--R + +--R 2 2 3 3 +--R (- 4a x - 2)acsch(a x) + 2a x + 2a x +--R / +--R +--------+ +--R 3 | 2 2 2 4 2 +--R 8a x \|a x + 1 - 8a x - 4x +--R Type: Expression Integer +--E 250 + +--S 251 OF 506 +d0148:= D(m0148,x) +--R +--R +--R (218) +--R +--------+ +--R | 2 2 +--------+ +--R 5 5 3 3 |a x + 1 | 2 2 +--R (16a x + 16a x + 2a x) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 6 4 4 2 2 |a x + 1 +--R (- 16a x - 24a x - 8a x ) |-------- +--R | 2 2 +--R \| a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 + 1 +--R log(---------------) +--R a x +--R + +--R +--------+ +--R | 2 2 +--R 5 5 3 3 4 4 2 2 |a x + 1 +--R ((- 16a x - 16a x - 2a x)acsch(a x) + 8a x + 4a x ) |-------- +--R | 2 2 +--R \| a x +--R + +--R 4 4 2 2 +--R 8a x + 8a x + 1 +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 +--R + +--R +--------+ +--R | 2 2 +--R 6 6 4 4 2 2 5 5 3 3 |a x + 1 +--R ((16a x + 24a x + 8a x )acsch(a x) - 8a x - 8a x - a x) |-------- +--R | 2 2 +--R \| a x +--R + +--R 5 5 3 3 +--R - 8a x - 12a x - 4a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R 5 8 3 6 4 |a x + 1 | 2 2 +--R (16a x + 16a x + 2a x ) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 9 4 7 2 5 |a x + 1 +--R (- 16a x - 24a x - 8a x ) |-------- +--R | 2 2 +--R \| a x +--R Type: Expression Integer +--E 251 + +--S 252 OF 506 +t0149:= acsch(x^(1/2))/x +--R +--R +--R +-+ +--R acsch(\|x ) +--R (219) ----------- +--R x +--R Type: Expression Integer +--E 252 + +--S 253 OF 506 +r0149:= -acsch(x^(1/2))^2-2*acsch(x^(1/2))*_ + log(1-exp(1)^(-2*acsch(x^(1/2))))+_ + polylog(2,exp(1)^(-2*acsch(x^(1/2)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 253 + +--S 254 OF 506 +a0149:= integrate(t0149,x) +--R +--R +--R x +--+ +--R ++ acsch(\|%Q ) +--R (220) | ------------ d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 254 + +--S 255 OF 506 +--m0149:= a0149-r0149 +--E 255 + +--S 256 OF 506 +--d0149:= D(m0149,x) +--E 256 + +--S 257 OF 506 +t0150:= acsch(x^(1/2))/x^2 +--R +--R +--R +-+ +--R acsch(\|x ) +--R (221) ----------- +--R 2 +--R x +--R Type: Expression Integer +--E 257 + +--S 258 OF 506 +r0150:= 1/2*(1/x+1)^(1/2)/x^(1/2)-1/2*acsch(x^(1/2))-acsch(x^(1/2))/x +--R +--R +--R +-----+ +--R +-+ +-+ |x + 1 +--R (- x - 2)\|x acsch(\|x ) + x |----- +--R \| x +--R (222) ------------------------------------ +--R +-+ +--R 2x\|x +--R Type: Expression Integer +--E 258 + +--S 259 OF 506 +a0150:= integrate(t0150,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 259 + +--S 260 OF 506 +--m0150:= a0150-r0150 +--E 260 + +--S 261 OF 506 +--d0150:= D(m0150,x) +--E 261 + +--S 262 OF 506 +t0151:= acosh(1/x) +--R +--R +--R 1 +--R (223) acosh(-) +--R x +--R Type: Expression Integer +--E 262 + +--S 263 OF 506 +r0151:= x*asech(x)-2*atan((-(-1+x)/(1+x))^(1/2)) +--R +--R +--R +-------+ +--R |- x + 1 +--R (224) - 2atan( |------- ) + x asech(x) +--R \| x + 1 +--R Type: Expression Integer +--E 263 + +--S 264 OF 506 +a0151:= integrate(t0151,x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 + 1 \|- x + 1 - 1 +--R (225) x log(---------------) - 2atan(---------------) +--R x x +--R Type: Union(Expression Integer,...) +--E 264 + +--S 265 OF 506 +m0151:= a0151-r0151 +--R +--R +--R (226) +--R +--------+ +--------+ +--R | 2 +-------+ | 2 +--R \|- x + 1 + 1 |- x + 1 \|- x + 1 - 1 +--R x log(---------------) + 2atan( |------- ) - 2atan(---------------) +--R x \| x + 1 x +--R + +--R - x asech(x) +--R Type: Expression Integer +--E 265 + +--S 266 OF 506 +d0151:= D(m0151,x) +--R +--R +--R (227) +--R +--------+ +--R +--------+ +-------+ | 2 +--R | 2 |- x + 1 \|- x + 1 + 1 +--R (x + 1)\|- x + 1 |------- log(---------------) +--R \| x + 1 x +--R + +--R +--------+ +-------+ +--------+ +--R | 2 |- x + 1 | 2 +--R ((- x - 1)asech(x)\|- x + 1 + x + 1) |------- - \|- x + 1 +--R \| x + 1 +--R / +--R +--------+ +-------+ +--R | 2 |- x + 1 +--R (x + 1)\|- x + 1 |------- +--R \| x + 1 +--R Type: Expression Integer +--E 266 + +--S 267 OF 506 +t0152:= atanh(1/x) +--R +--R +--R 1 +--R (228) atanh(-) +--R x +--R Type: Expression Integer +--E 267 + +--S 268 OF 506 +r0152:= x*acoth(x)+1/2*log(1-x^2) +--R +--R +--R 2 +--R log(- x + 1) + 2x acoth(x) +--R (229) --------------------------- +--R 2 +--R Type: Expression Integer +--E 268 + +--S 269 OF 506 +a0152:= integrate(t0152,x) +--R +--R +--R 2 x + 1 +--R log(x - 1) + x log(-----) +--R x - 1 +--R (230) -------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 269 + +--S 270 OF 506 +m0152:= a0152-r0152 +--R +--R +--R 2 x + 1 2 +--R log(x - 1) + x log(-----) - log(- x + 1) - 2x acoth(x) +--R x - 1 +--R (231) -------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 270 + +--S 271 OF 506 +d0152:= D(m0152,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (232) ---------------------- +--R 2 +--R Type: Expression Integer +--E 271 + +--S 272 OF 506 +t0153:= acoth(1/x) +--R +--R +--R 1 +--R (233) acoth(-) +--R x +--R Type: Expression Integer +--E 272 + +--S 273 OF 506 +r0153:= x*atanh(x)+1/2*log(1-x^2) +--R +--R +--R 2 +--R log(- x + 1) + 2x atanh(x) +--R (234) --------------------------- +--R 2 +--R Type: Expression Integer +--E 273 + +--S 274 OF 506 +a0153:= integrate(t0153,x) +--R +--R +--R 2 - x - 1 +--R log(x - 1) + x log(-------) +--R x - 1 +--R (235) ---------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 274 + +--S 275 OF 506 +m0153:= a0153-r0153 +--R +--R +--R 2 - x - 1 2 +--R log(x - 1) + x log(-------) - log(- x + 1) - 2x atanh(x) +--R x - 1 +--R (236) ---------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 275 + +--S 276 OF 506 +d0153:= D(m0153,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (237) ------------------------ +--R 2 +--R Type: Expression Integer +--E 276 + +--S 277 OF 506 +t0154:= atanh(a+b*x)/x +--R +--R +--R atanh(b x + a) +--R (238) -------------- +--R x +--R Type: Expression Integer +--E 277 + +--S 278 OF 506 +r0154:= -1/2*log(b*x/(1-a))*log(1-a-b*x)+1/2*log(-b*x/(1+a))*log(a+1+b*x)-_ + 1/2*polylog(2,1-b*x/(1-a))+1/2*polylog(2,1+b*x/(1+a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 278 + +--S 279 OF 506 +a0154:= integrate(t0154,x) +--R +--R +--R x +--R ++ atanh(%Q b + a) +--R (239) | --------------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 279 + +--S 280 OF 506 +--m0154:= a0154-r0154 +--E 280 + +--S 281 OF 506 +--d0154:= D(m0154,x) +--E 281 + +--S 282 OF 506 +t0155:= acoth(a+b*x)/x +--R +--R +--R acoth(b x + a) +--R (240) -------------- +--R x +--R Type: Expression Integer +--E 282 + +--S 283 OF 506 +r0155:= 1/2*log(x)*log((a+b*x-1)/(-1+a))-_ + 1/2*log(x)*log((a+1+b*x)/(1+a))-_ + 1/2*log(x)*log((a+b*x-1)/(a+b*x))+_ + 1/2*log(x)*log((a+1+b*x)/(a+b*x))+_ + 1/2*polylog(2,-b*x/(-1+a))-_ + 1/2*polylog(2,-b*x/(1+a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 283 + +--S 284 OF 506 +a0155:= integrate(t0155,x) +--R +--R +--R x +--R ++ acoth(%Q b + a) +--R (241) | --------------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 284 + +--S 285 OF 506 +--m0155:= a0155-r0155 +--E 285 + +--S 286 OF 506 +--d0155:= D(m0155,x) +--E 286 + +--S 287 OF 506 +t0156:= asinh(a+b*x)/(a*d/b+d*x) +--R +--R +--R b asinh(b x + a) +--R (242) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 287 + +--S 288 OF 506 +r0156:= 1/2*asinh(a+b*x)^2/d+asinh(a+b*x)*_ + log(1-exp(1)^(-2*asinh(a+b*x)))/d-1/2*_ + polylog(2,exp(1)^(-2*asinh(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 288 + +--S 289 OF 506 +a0156:= integrate(t0156,x) +--R +--R +--R x +--R ++ b asinh(%Q b + a) +--R (243) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 289 + +--S 290 OF 506 +--m0156:= a0156-r0156 +--E 290 + +--S 291 OF 506 +--d0156:= D(m0156,x) +--E 291 + +--S 292 OF 506 +t0157:= acosh(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acosh(b x + a) +--R (244) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 292 + +--S 293 OF 506 +r0157:= 1/2*acosh(a+b*x)^2/d+acosh(a+b*x)*_ + log(1+exp(1)^(-2*acosh(a+b*x)))/d-_ + 1/2*polylog(2,-exp(1)^(-2*acosh(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 293 + +--S 294 OF 506 +a0157:= integrate(t0157,x) +--R +--R +--R x +--R ++ b acosh(%Q b + a) +--R (245) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 294 + +--S 295 OF 506 +--m0157:= a0157-r0157 +--E 295 + +--S 296 OF 506 +--d0157:= D(m0157,x) +--E 296 + +--S 297 OF 506 +t0158:= atanh(a+b*x)/(a*d/b+d*x) +--R +--R +--R b atanh(b x + a) +--R (246) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 297 + +--S 298 OF 506 +r0158:= -1/2*(polylog(2,-a-b*x)-polylog(2,a+b*x))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 298 + +--S 299 OF 506 +a0158:= integrate(t0158,x) +--R +--R +--R x +--R ++ b atanh(%Q b + a) +--R (247) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 299 + +--S 300 OF 506 +--m0158:= a0158-r0158 +--E 300 + +--S 301 OF 506 +--d0158:= D(m0158,x) +--E 301 + +--S 302 OF 506 +t0159:= acoth(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acoth(b x + a) +--R (248) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 302 + +--S 303 OF 506 +r0159:= 1/2*(polylog(2,-1/(a+b*x))-polylog(2,1/(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 303 + +--S 304 OF 506 +a0159:= integrate(t0159,x) +--R +--R +--R x +--R ++ b acoth(%Q b + a) +--R (249) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 304 + +--S 305 OF 506 +--m0159:= a0159-r0159 +--E 305 + +--S 306 OF 506 +--d0159:= D(m0159,x) +--E 306 + +--S 307 OF 506 +t0160:= asech(a+b*x)/(a*d/b+d*x) +--R +--R +--R b asech(b x + a) +--R (250) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 307 + +--S 308 OF 506 +r0160:= -1/2*asech(a+b*x)^2/d-asech(a+b*x)*log(1+exp(1)^(-2*asech(a+b*x)))/d+_ + 1/2*polylog(2,-exp(1)^(-2*asech(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 308 + +--S 309 OF 506 +a0160:= integrate(t0160,x) +--R +--R +--R x +--R ++ b asech(%Q b + a) +--R (251) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 309 + +--S 310 OF 506 +--m0160:= a0160-r0160 +--E 310 + +--S 311 OF 506 +--d0160:= D(m0160,x) +--E 311 + +--S 312 OF 506 +t0161:= acsch(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acsch(b x + a) +--R (252) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 312 + +--S 313 OF 506 +r0161:= -1/2*acsch(a+b*x)^2/d-acsch(a+b*x)*log(1-exp(1)^(-2*acsch(a+b*x)))/d+_ + 1/2*polylog(2,exp(1)^(-2*acsch(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 313 + +--S 314 OF 506 +a0161:= integrate(t0161,x) +--R +--R +--R x +--R ++ b acsch(%Q b + a) +--R (253) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 314 + +--S 315 OF 506 +--m0161:= a0161-r0161 +--E 315 + +--S 316 OF 506 +--d0161:= D(m0161,x) +--E 316 + +--S 317 OF 506 +t0162:= x/(1+x^2)^(1/2)/asinh(x) +--R +--R +--R x +--R (254) ----------------- +--R +------+ +--R | 2 +--R asinh(x)\|x + 1 +--R Type: Expression Integer +--E 317 + +--S 318 OF 506 +r0162:= Shi(asinh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 318 + +--S 319 OF 506 +a0162:= integrate(t0162,x) +--R +--R +--R x +--R ++ %Q +--R (255) | ------------------- d%Q +--R ++ +-------+ +--R | 2 +--R asinh(%Q)\|%Q + 1 +--R Type: Union(Expression Integer,...) +--E 319 + +--S 320 OF 506 +--m0162:= a0162-r0162 +--E 320 + +--S 321 OF 506 +--d0162:= D(m0162,x) +--E 321 + +--S 322 OF 506 +t0163:= x/(-1+x)^(1/2)/(1+x)^(1/2)/acosh(x) +--R +--R +--R x +--R (256) ------------------------ +--R +-----+ +-----+ +--R acosh(x)\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 322 + +--S 323 OF 506 +r0163:= Chi(acosh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 323 + +--S 324 OF 506 +a0163:= integrate(t0163,x) +--R +--R +--R x +--R ++ %Q +--R (257) | --------------------------- d%Q +--R ++ +------+ +------+ +--R acosh(%Q)\|%Q - 1 \|%Q + 1 +--R Type: Union(Expression Integer,...) +--E 324 + +--S 325 OF 506 +--m0163:= a0163-r0163 +--E 325 + +--S 326 OF 506 +--d0163:= D(m0163,x) +--E 326 + +--S 327 OF 506 +t0164:= asinh(a*x^n)/x +--R +--R +--R n +--R asinh(a x ) +--R (258) ----------- +--R x +--R Type: Expression Integer +--E 327 + +--S 328 OF 506 +r0164:= 1/2*asinh(a*x^n)^2/n+asinh(a*x^n)*log(1-exp(1)^(-2*asinh(a*x^n)))/n-_ + 1/2*polylog(2,exp(1)^(-2*asinh(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 328 + +--S 329 OF 506 +a0164:= integrate(t0164,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 329 + +--S 330 OF 506 +--m0164:= a0164-r0164 +--E 330 + +--S 331 OF 506 +--d0164:= D(m0164,x) +--E 331 + +--S 332 OF 506 +t0165:= acosh(a*x^n)/x +--R +--R +--R n +--R acosh(a x ) +--R (259) ----------- +--R x +--R Type: Expression Integer +--E 332 + +--S 333 OF 506 +r0165:= 1/2*acosh(a*x^n)^2/n+acosh(a*x^n)*log(1+exp(1)^(-2*acosh(a*x^n)))/n-_ + 1/2*polylog(2,-exp(1)^(-2*acosh(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 333 + +--S 334 OF 506 +a0165:= integrate(t0165,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 334 + +--S 335 OF 506 +--m0165:= a0165-r0165 +--E 335 + +--S 336 OF 506 +--d0165:= D(m0165,x) +--E 336 + +--S 337 OF 506 +t0166:= atanh(a*x^n)/x +--R +--R +--R n +--R atanh(a x ) +--R (260) ----------- +--R x +--R Type: Expression Integer +--E 337 + +--S 338 OF 506 +r0166:= -1/2/n*(polylog(2,-a*x^n)-polylog(2,a*x^n)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 338 + +--S 339 OF 506 +a0166:= integrate(t0166,x) +--R +--R +--R x n +--R ++ atanh(a %Q ) +--R (261) | ------------ d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 339 + +--S 340 OF 506 +--m0166:= a0166-r0166 +--E 340 + +--S 341 OF 506 +--d0166:= D(m0166,x) +--E 341 + +--S 342 OF 506 +t0167:= acoth(a*x^n)/x +--R +--R +--R n +--R acoth(a x ) +--R (262) ----------- +--R x +--R Type: Expression Integer +--E 342 + +--S 343 OF 506 +r0167:= 1/2/n*(polylog(2,-1/a*x^(-n))-polylog(2,1/a*x^(-n))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 343 + +--S 344 OF 506 +a0167:= integrate(t0167,x) +--R +--R +--R x n +--R ++ acoth(a %Q ) +--R (263) | ------------ d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 344 + +--S 345 OF 506 +--m0167:= a0167-r0167 +--E 345 + +--S 346 OF 506 +--d0167:= D(m0167,x) +--E 346 + +--S 347 OF 506 +t0168:= asech(a*x^n)/x +--R +--R +--R n +--R asech(a x ) +--R (264) ----------- +--R x +--R Type: Expression Integer +--E 347 + +--S 348 OF 506 +r0168:= -1/2*asech(a*x^n)^2/n-asech(a*x^n)*_ + log(1+exp(1)^(-2*asech(a*x^n)))/n+_ + 1/2*polylog(2,-exp(1)^(-2*asech(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 348 + +--S 349 OF 506 +a0168:= integrate(t0168,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 349 + +--S 350 OF 506 +--m0168:= a0168-r0168 +--E 350 + +--S 351 OF 506 +--d0168:= D(m0168,x) +--E 351 + +--S 352 OF 506 +t0169:= acsch(a*x^n)/x +--R +--R +--R n +--R acsch(a x ) +--R (265) ----------- +--R x +--R Type: Expression Integer +--E 352 + +--S 353 OF 506 +r0169:= -1/2*acsch(a*x^n)^2/n-acsch(a*x^n)*_ + log(1-exp(1)^(-2*acsch(a*x^n)))/n+_ + 1/2*polylog(2,exp(1)^(-2*acsch(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 353 + +--S 354 OF 506 +a0169:= integrate(t0169,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 354 + +--S 355 OF 506 +--m0169:= a0169-r0169 +--E 355 + +--S 356 OF 506 +--d0169:= D(m0169,x) +--E 356 + +--S 357 OF 506 +t0170:= x^3*acsch(a+b*x^4) +--R +--R +--R 3 4 +--R (266) x acsch(b x + a) +--R Type: Expression Integer +--E 357 + +--S 358 OF 506 +r0170:= 1/4*(a+b*x^4)*acsch(a+b*x^4)/b+1/4*atanh((1+1/(a+b*x^4)^2)^(1/2))/b +--R +--R +--R +-----------------------+ +--R | 2 8 4 2 +--R |b x + 2a b x + a + 1 4 4 +--R atanh( |----------------------- ) + (b x + a)acsch(b x + a) +--R | 2 8 4 2 +--R \| b x + 2a b x + a +--R (267) ------------------------------------------------------------- +--R 4b +--R Type: Expression Integer +--E 358 + +--S 359 OF 506 +a0170:= integrate(t0170,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 359 + +--S 360 OF 506 +--m0170:= a0170-r0170 +--E 360 + +--S 361 OF 506 +--d0170:= D(m0170,x) +--E 361 + +--S 362 OF 506 +t0171:= x^(-1+n)*asinh(a+b*x^n) +--R +--R +--R n - 1 n +--R (268) x asinh(b x + a) +--R Type: Expression Integer +--E 362 + +--S 363 OF 506 +r0171:= -(1+(a+b*x^n)^2)^(1/2)/b/n+(a+b*x^n)*asinh(a+b*x^n)/b/n +--R +--R +--R +--------------------------+ +--R | 2 n 2 n 2 n n +--R - \|b (x ) + 2a b x + a + 1 + (b x + a)asinh(b x + a) +--R (269) ----------------------------------------------------------- +--R b n +--R Type: Expression Integer +--E 363 + +--S 364 OF 506 +a0171:= integrate(t0171,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 364 + +--S 365 OF 506 +--m0171:= a0171-r0171 +--E 365 + +--S 366 OF 506 +--d0171:= D(m0171,x) +--E 366 + +--S 367 OF 506 +t0172:= x^(-1+n)*acosh(a+b*x^n) +--R +--R +--R n - 1 n +--R (270) x acosh(b x + a) +--R Type: Expression Integer +--E 367 + +--S 368 OF 506 +r0172:= -(-1+a+b*x^n)^(1/2)*(1+a+b*x^n)^(1/2)/b/n+(a+b*x^n)*acosh(a+b*x^n)/b/n +--R +--R +--R +------------+ +------------+ +--R | n | n n n +--R - \|b x + a - 1 \|b x + a + 1 + (b x + a)acosh(b x + a) +--R (271) ------------------------------------------------------------ +--R b n +--R Type: Expression Integer +--E 368 + +--S 369 OF 506 +a0172:= integrate(t0172,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 369 + +--S 370 OF 506 +--m0172:= a0172-r0172 +--E 370 + +--S 371 OF 506 +--d0172:= D(m0172,x) +--E 371 + +--S 372 OF 506 +t0173:= x^(-1+n)*atanh(a+b*x^n) +--R +--R +--R n - 1 n +--R (272) x atanh(b x + a) +--R Type: Expression Integer +--E 372 + +--S 373 OF 506 +r0173:= (a+b*x^n)*atanh(a+b*x^n)/b/n+1/2*log(1-(a+b*x^n)^2)/b/n +--R +--R +--R 2 n 2 n 2 n n +--R log(- b (x ) - 2a b x - a + 1) + (2b x + 2a)atanh(b x + a) +--R (273) --------------------------------------------------------------- +--R 2b n +--R Type: Expression Integer +--E 373 + +--S 374 OF 506 +a0173:= integrate(t0173,x) +--R +--R +--R (274) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R - b sinh(n log(x)) - b cosh(n log(x)) - a - 1 +--R log(---------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R / +--R 2b n +--R Type: Union(Expression Integer,...) +--E 374 + +--S 375 OF 506 +m0173:= a0173-r0173 +--R +--R +--R (275) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R - b sinh(n log(x)) - b cosh(n log(x)) - a - 1 +--R log(---------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R 2 n 2 n 2 n n +--R - log(- b (x ) - 2a b x - a + 1) + (- 2b x - 2a)atanh(b x + a) +--R / +--R 2b n +--R Type: Expression Integer +--E 375 + +--S 376 OF 506 +d0173:= D(m0173,x) +--R +--R +--R (276) +--R (sinh(n log(x)) + cosh(n log(x))) +--R * +--R - b sinh(n log(x)) - b cosh(n log(x)) - a - 1 +--R log(---------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R n - 1 n +--R - 2x x atanh(b x + a) +--R / +--R 2x +--R Type: Expression Integer +--E 376 + +--S 377 OF 506 +t0174:= x^(-1+n)*acoth(a+b*x^n) +--R +--R +--R n - 1 n +--R (277) x acoth(b x + a) +--R Type: Expression Integer +--E 377 + +--S 378 OF 506 +r0174:= (a+b*x^n)*acoth(a+b*x^n)/b/n+1/2*log(1-(a+b*x^n)^2)/b/n +--R +--R +--R 2 n 2 n 2 n n +--R log(- b (x ) - 2a b x - a + 1) + (2b x + 2a)acoth(b x + a) +--R (278) --------------------------------------------------------------- +--R 2b n +--R Type: Expression Integer +--E 378 + +--S 379 OF 506 +a0174:= integrate(t0174,x) +--R +--R +--R (279) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R b sinh(n log(x)) + b cosh(n log(x)) + a + 1 +--R log(-------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R / +--R 2b n +--R Type: Union(Expression Integer,...) +--E 379 + +--S 380 OF 506 +m0174:= a0174-r0174 +--R +--R +--R (280) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R b sinh(n log(x)) + b cosh(n log(x)) + a + 1 +--R log(-------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R 2 n 2 n 2 n n +--R - log(- b (x ) - 2a b x - a + 1) + (- 2b x - 2a)acoth(b x + a) +--R / +--R 2b n +--R Type: Expression Integer +--E 380 + +--S 381 OF 506 +d0174:= D(m0174,x) +--R +--R +--R (281) +--R (sinh(n log(x)) + cosh(n log(x))) +--R * +--R b sinh(n log(x)) + b cosh(n log(x)) + a + 1 +--R log(-------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R n - 1 n +--R - 2x x acoth(b x + a) +--R / +--R 2x +--R Type: Expression Integer +--E 381 + +--S 382 OF 506 +t0175:= x^(-1+n)*asech(a+b*x^n) +--R +--R +--R n - 1 n +--R (282) x asech(b x + a) +--R Type: Expression Integer +--E 382 + +--S 383 OF 506 +r0175:= (a+b*x^n)*asech(a+b*x^n)/b/n-_ + 2*atan(((1-a-b*x^n)/(1+a+b*x^n))^(1/2))/b/n +--R +--R +--R +--------------+ +--R | n +--R |- b x - a + 1 n n +--R - 2atan( |-------------- ) + (b x + a)asech(b x + a) +--R | n +--R \| b x + a + 1 +--R (283) ------------------------------------------------------ +--R b n +--R Type: Expression Integer +--E 383 + +--S 384 OF 506 +a0175:= integrate(t0175,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 384 + +--S 385 OF 506 +--m0175:= a0175-r0175 +--E 385 + +--S 386 OF 506 +--d0175:= D(m0175,x) +--E 386 + +--S 387 OF 506 +t0176:= x^(-1+n)*acsch(a+b*x^n) +--R +--R +--R n - 1 n +--R (284) x acsch(b x + a) +--R Type: Expression Integer +--E 387 + +--S 388 OF 506 +r0176:= (a+b*x^n)*acsch(a+b*x^n)/b/n+atanh((1+1/(a+b*x^n)^2)^(1/2))/b/n +--R +--R +--R +--------------------------+ +--R | 2 n 2 n 2 +--R |b (x ) + 2a b x + a + 1 n n +--R atanh( |-------------------------- ) + (b x + a)acsch(b x + a) +--R | 2 n 2 n 2 +--R \| b (x ) + 2a b x + a +--R (285) ---------------------------------------------------------------- +--R b n +--R Type: Expression Integer +--E 388 + +--S 389 OF 506 +a0176:= integrate(t0176,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 389 + +--S 390 OF 506 +--m0176:= a0176-r0176 +--E 390 + +--S 391 OF 506 +--d0176:= D(m0176,x) +--E 391 + +--S 392 OF 506 +t0177:= asinh(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (286) asinh(c %e ) +--R Type: Expression Integer +--E 392 + +--S 393 OF 506 +r0177:= 1/2*asinh(c*exp(1)^(a+b*x))^2/b+asinh(c*exp(1)^(a+b*x))*_ + log(1-exp(1)^(-2*asinh(c*exp(1)^(a+b*x))))/b-_ + 1/2*polylog(2,exp(1)^(-2*asinh(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 393 + +--S 394 OF 506 +a0177:= integrate(t0177,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 394 + +--S 395 OF 506 +--m0177:= a0177-r0177 +--E 395 + +--S 396 OF 506 +--d0177:= D(m0177,x) +--E 396 + +--S 397 OF 506 +t0178:= acosh(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (287) acosh(c %e ) +--R Type: Expression Integer +--E 397 + +--S 398 OF 506 +r0178:= 1/2*acosh(c*exp(1)^(a+b*x))^2/b+acosh(c*exp(1)^(a+b*x))*_ + log(1+exp(1)^(-2*acosh(c*exp(1)^(a+b*x))))/b-_ + 1/2*polylog(2,-exp(1)^(-2*acosh(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 398 + +--S 399 OF 506 +a0178:= integrate(t0178,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 399 + +--S 400 OF 506 +--m0178:= a0178-r0178 +--E 400 + +--S 401 OF 506 +--d0178:= D(m0178,x) +--E 401 + +--S 402 OF 506 +t0179:= asech(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (288) asech(c %e ) +--R Type: Expression Integer +--E 402 + +--S 403 OF 506 +r0179:= -1/2*asech(c*exp(1)^(a+b*x))^2/b-asech(c*exp(1)^(a+b*x))*_ + log(1+exp(1)^(-2*asech(c*exp(1)^(a+b*x))))/b+_ + 1/2*polylog(2,-exp(1)^(-2*asech(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 403 + +--S 404 OF 506 +a0179:= integrate(t0179,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 404 + +--S 405 OF 506 +--m0179:= a0179-r0179 +--E 405 + +--S 406 OF 506 +--d0179:= D(m0179,x) +--E 406 + +--S 407 OF 506 +t0180:= acsch(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (289) acsch(c %e ) +--R Type: Expression Integer +--E 407 + +--S 408 OF 506 +r0180:= -1/2*acsch(c*exp(1)^(a+b*x))^2/b-acsch(c*exp(1)^(a+b*x))*_ + log(1-exp(1)^(-2*acsch(c*exp(1)^(a+b*x))))/b+_ + 1/2*polylog(2,exp(1)^(-2*acsch(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 408 + +--S 409 OF 506 +a0180:= integrate(t0180,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 409 + +--S 410 OF 506 +--m0180:= a0180-r0180 +--E 410 + +--S 411 OF 506 +--d0180:= D(m0180,x) +--E 411 + +--S 412 OF 506 +t0181:= atanh(exp(x)) +--R +--R +--R x +--R (290) atanh(%e ) +--R Type: Expression Integer +--E 412 + +--S 413 OF 506 +r0181:= -1/2*polylog(2,-exp(x))+1/2*polylog(2,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 413 + +--S 414 OF 506 +a0181:= integrate(t0181,x) +--R +--R +--R x +--R ++ %Q +--R (291) | atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 414 + +--S 415 OF 506 +--m0181:= a0181-r0181 +--E 415 + +--S 416 OF 506 +--d0181:= D(m0181,x) +--E 416 + +--S 417 OF 506 +t0182:= x*atanh(exp(x)) +--R +--R +--R x +--R (292) x atanh(%e ) +--R Type: Expression Integer +--E 417 + +--S 418 OF 506 +r0182:= -1/2*x*polylog(2,-exp(x))+1/2*x*polylog(2,exp(x))+_ + 1/2*polylog(3,-exp(x))-1/2*polylog(3,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 418 + +--S 419 OF 506 +a0182:= integrate(t0182,x) +--R +--R +--R x +--R ++ %Q +--R (293) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 419 + +--S 420 OF 506 +--m0182:= a0182-r0182 +--E 420 + +--S 421 OF 506 +--d0182:= D(m0182,x) +--E 421 + +--S 422 OF 506 +t0183:= x^2*atanh(exp(x)) +--R +--R +--R 2 x +--R (294) x atanh(%e ) +--R Type: Expression Integer +--E 422 + +--S 423 OF 506 +r0183:= -1/2*x^2*polylog(2,-exp(x))+1/2*x^2*polylog(2,exp(x))+_ + x*polylog(3,-exp(x))-x*polylog(3,exp(x))-_ + polylog(4,-exp(x))+polylog(4,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 423 + +--S 424 OF 506 +a0183:= integrate(t0183,x) +--R +--R +--R x +--R ++ 2 %Q +--R (295) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 424 + +--S 425 OF 506 +--m0183:= a0183-r0183 +--E 425 + +--S 426 OF 506 +--d0183:= D(m0183,x) +--E 426 + +--S 427 OF 506 +t0184:= atanh(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (296) atanh(%e ) +--R Type: Expression Integer +--E 427 + +--S 428 OF 506 +r0184:= -1/2*(polylog(2,-exp(a+b*x))-polylog(2,exp(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 428 + +--S 429 OF 506 +a0184:= integrate(t0184,x) +--R +--R +--R x +--R ++ %Q b + a +--R (297) | atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 429 + +--S 430 OF 506 +--m0184:= a0184-r0184 +--E 430 + +--S 431 OF 506 +--d0184:= D(m0184,x) +--E 431 + +--S 432 OF 506 +t0185:= x*atanh(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (298) x atanh(%e ) +--R Type: Expression Integer +--E 432 + +--S 433 OF 506 +r0185:= 1/2*(-x*polylog(2,-exp(a+b*x))*b+x*polylog(2,exp(a+b*x))*b+_ + polylog(3,-exp(a+b*x))-polylog(3,exp(a+b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 433 + +--S 434 OF 506 +a0185:= integrate(t0185,x) +--R +--R +--R x +--R ++ %Q b + a +--R (299) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 434 + +--S 435 OF 506 +--m0185:= a0185-r0185 +--E 435 + +--S 436 OF 506 +--d0185:= D(m0185,x) +--E 436 + +--S 437 OF 506 +t0186:= x^2*atanh(exp(1)^(a+b*x)) +--R +--R +--R 2 b x + a +--R (300) x atanh(%e ) +--R Type: Expression Integer +--E 437 + +--S 438 OF 506 +r0186:= 1/2*(-x^2*polylog(2,-exp(a+b*x))*b^2+_ + x^2*polylog(2,exp(a+b*x))*b^2+_ + 2*x*polylog(3,-exp(a+b*x))*b-_ + 2*x*polylog(3,exp(a+b*x))*b-_ + 2*polylog(4,-exp(a+b*x))+_ + 2*polylog(4,exp(a+b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 438 + +--S 439 OF 506 +a0186:= integrate(t0186,x) +--R +--R +--R x +--R ++ 2 %Q b + a +--R (301) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 439 + +--S 440 OF 506 +--m0186:= a0186-r0186 +--E 440 + +--S 441 OF 506 +--d0186:= D(m0186,x) +--E 441 + +--S 442 OF 506 +t0187:= atanh(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (302) atanh(b f + a) +--R Type: Expression Integer +--E 442 + +--S 443 OF 506 +r0187:= 1/2/d/log(f)*(2*x*atanh(a+b*f^(c+d*x))*d*log(f)+_ + x*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d*log(f)-_ + x*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d*log(f)+_ + polylog(2,-b*f^(c+d*x)/(-1+a))-polylog(2,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 443 + +--S 444 OF 506 +a0187:= integrate(t0187,x) +--R +--R +--R x +--R ++ %Q d + c +--R (303) | atanh(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 444 + +--S 445 OF 506 +--m0187:= a0187-r0187 +--E 445 + +--S 446 OF 506 +--d0187:= D(m0187,x) +--E 446 + +--S 447 OF 506 +t0188:= x*atanh(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (304) x atanh(b f + a) +--R Type: Expression Integer +--E 447 + +--S 448 OF 506 +r0188:= 1/4/d^2/log(f)^2*(2*x^2*atanh(a+b*f^(c+d*x))*d^2*log(f)^2+_ + x^2*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^2*log(f)^2-_ + x^2*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^2*log(f)^2+_ + 2*x*polylog(2,-b*f^(c+d*x)/(-1+a))*d*log(f)-_ + 2*x*polylog(2,-b*f^(c+d*x)/(1+a))*d*log(f)-_ + 2*polylog(3,-b*f^(c+d*x)/(-1+a))+2*polylog(3,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 448 + +--S 449 OF 506 +a0188:= integrate(t0188,x) +--R +--R +--R x +--R ++ %Q d + c +--R (305) | %Q atanh(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 449 + +--S 450 OF 506 +--m0188:= a0188-r0188 +--E 450 + +--S 451 OF 506 +--d0188:= D(m0188,x) +--E 451 + +--S 452 OF 506 +t0189:= x^2*atanh(a+b*f^(c+d*x)) +--R +--R +--R 2 d x + c +--R (306) x atanh(b f + a) +--R Type: Expression Integer +--E 452 + +--S 453 OF 506 +r0189:= 1/6/d^3/log(f)^3*(2*x^3*atanh(a+b*f^(c+d*x))*d^3*log(f)^3+_ + x^3*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^3*log(f)^3-_ + x^3*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^3*log(f)^3+_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(-1+a))*d^2*log(f)^2-_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(1+a))*d^2*log(f)^2-_ + 6*x*polylog(3,-b*f^(c+d*x)/(-1+a))*d*log(f)+_ + 6*x*polylog(3,-b*f^(c+d*x)/(1+a))*d*log(f)+_ + 6*polylog(4,-b*f^(c+d*x)/(-1+a))-6*polylog(4,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 453 + +--S 454 OF 506 +a0189:= integrate(t0189,x) +--R +--R +--R x +--R ++ 2 %Q d + c +--R (307) | %Q atanh(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 454 + +--S 455 OF 506 +--m0189:= a0189-r0189 +--E 455 + +--S 456 OF 506 +--d0189:= D(m0189,x) +--E 456 + +--S 457 OF 506 +t0190:= acoth(exp(x)) +--R +--R +--R x +--R (308) acoth(%e ) +--R Type: Expression Integer +--E 457 + +--S 458 OF 506 +r0190:= 1/2*polylog(2,-exp(-x))-1/2*polylog(2,exp(-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 458 + +--S 459 OF 506 +a0190:= integrate(t0190,x) +--R +--R +--R x +--R ++ %Q +--R (309) | acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 459 + +--S 460 OF 506 +--m0190:= a0190-r0190 +--E 460 + +--S 461 OF 506 +--d0190:= D(m0190,x) +--E 461 + +--S 462 OF 506 +t0191:= x*acoth(exp(x)) +--R +--R +--R x +--R (310) x acoth(%e ) +--R Type: Expression Integer +--E 462 + +--S 463 OF 506 +r0191:= 1/2*x*polylog(2,-exp(-x))-1/2*x*polylog(2,exp(-x))+_ + 1/2*polylog(3,-exp(-x))-1/2*polylog(3,exp(-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 463 + +--S 464 OF 506 +a0191:= integrate(t0191,x) +--R +--R +--R x +--R ++ %Q +--R (311) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 464 + +--S 465 OF 506 +--m0191:= a0191-r0191 +--E 465 + +--S 466 OF 506 +--d0191:= D(m0191,x) +--E 466 + +--S 467 OF 506 +t0192:= x^2*acoth(exp(x)) +--R +--R +--R 2 x +--R (312) x acoth(%e ) +--R Type: Expression Integer +--E 467 + +--S 468 OF 506 +r0192:= 1/2*x^2*polylog(2,-exp(-x))-1/2*x^2*polylog(2,exp(-x))+_ + x*polylog(3,-exp(-x))-x*polylog(3,exp(-x))+_ + polylog(4,-exp(-x))-polylog(4,exp(-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 468 + +--S 469 OF 506 +a0192:= integrate(t0192,x) +--R +--R +--R x +--R ++ 2 %Q +--R (313) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 469 + +--S 470 OF 506 +--m0192:= a0192-r0192 +--E 470 + +--S 471 OF 506 +--d0192:= D(m0192,x) +--E 471 + +--S 472 OF 506 +t0193:= acoth(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (314) acoth(%e ) +--R Type: Expression Integer +--E 472 + +--S 473 OF 506 +r0193:= 1/2*(polylog(2,-exp(-a-b*x))-polylog(2,exp(-a-b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 473 + +--S 474 OF 506 +a0193:= integrate(t0193,x) +--R +--R +--R x +--R ++ %Q b + a +--R (315) | acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 474 + +--S 475 OF 506 +--m0193:= a0193-r0193 +--E 475 + +--S 476 OF 506 +--d0193:= D(m0193,x) +--E 476 + +--S 477 OF 506 +t0194:= x*acoth(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (316) x acoth(%e ) +--R Type: Expression Integer +--E 477 + +--S 478 OF 506 +r0194:= 1/2*(x*polylog(2,-exp(-a-b*x))*b-_ + x*polylog(2,exp(-a-b*x))*b+polylog(3,-exp(-a-b*x))-_ + polylog(3,exp(-a-b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 478 + +--S 479 OF 506 +a0194:= integrate(t0194,x) +--R +--R +--R x +--R ++ %Q b + a +--R (317) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 479 + +--S 480 OF 506 +--m0194:= a0194-r0194 +--E 480 + +--S 481 OF 506 +--d0194:= D(m0194,x) +--E 481 + +--S 482 OF 506 +t0195:= x^2*acoth(exp(1)^(a+b*x)) +--R +--R +--R 2 b x + a +--R (318) x acoth(%e ) +--R Type: Expression Integer +--E 482 + +--S 483 OF 506 +r0195:= 1/2*(x^2*polylog(2,-exp(-a-b*x))*b^2-_ + x^2*polylog(2,exp(-a-b*x))*b^2+_ + 2*x*polylog(3,-exp(-a-b*x))*b-_ + 2*x*polylog(3,exp(-a-b*x))*b+_ + 2*polylog(4,-exp(-a-b*x))-_ + 2*polylog(4,exp(-a-b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 483 + +--S 484 OF 506 +a0195:= integrate(t0195,x) +--R +--R +--R x +--R ++ 2 %Q b + a +--R (319) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 484 + +--S 485 OF 506 +--m0195:= a0195-r0195 +--E 485 + +--S 486 OF 506 +--d0195:= D(m0195,x) +--E 486 + +--S 487 OF 506 +t0196:= acoth(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (320) acoth(b f + a) +--R Type: Expression Integer +--E 487 + +--S 488 OF 506 +r0196:= 1/2/d/log(f)*(2*x*acoth(a+b*f^(c+d*x))*d*log(f)+_ + x*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d*log(f)-_ + x*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d*log(f)+_ + polylog(2,-b*f^(c+d*x)/(-1+a))-polylog(2,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 488 + +--S 489 OF 506 +a0196:= integrate(t0196,x) +--R +--R +--R x +--R ++ %Q d + c +--R (321) | acoth(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 489 + +--S 490 OF 506 +--m0196:= a0196-r0196 +--E 490 + +--S 491 OF 506 +--d0196:= D(m0196,x) +--E 491 + +--S 492 OF 506 +t0197:= x*acoth(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (322) x acoth(b f + a) +--R Type: Expression Integer +--E 492 + +--S 493 OF 506 +r0197:= 1/4/d^2/log(f)^2*(2*x^2*acoth(a+b*f^(c+d*x))*d^2*log(f)^2+_ + x^2*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^2*log(f)^2-_ + x^2*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^2*log(f)^2+_ + 2*x*polylog(2,-b*f^(c+d*x)/(-1+a))*d*log(f)-_ + 2*x*polylog(2,-b*f^(c+d*x)/(1+a))*d*log(f)-_ + 2*polylog(3,-b*f^(c+d*x)/(-1+a))+2*polylog(3,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 493 + +--S 494 OF 506 +a0197:= integrate(t0197,x) +--R +--R +--R x +--R ++ %Q d + c +--R (323) | %Q acoth(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 494 + +--S 495 OF 506 +--m0197:= a0197-r0197 +--E 495 + +--S 496 OF 506 +--d0197:= D(m0197,x) +--E 496 + +--S 497 OF 506 +t0198:= x^2*acoth(a+b*f^(c+d*x)) +--R +--R +--R 2 d x + c +--R (324) x acoth(b f + a) +--R Type: Expression Integer +--E 497 + +--S 498 OF 506 +r0198:= 1/6/d^3/log(f)^3*(2*x^3*acoth(a+b*f^(c+d*x))*d^3*log(f)^3+_ + x^3*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^3*log(f)^3-_ + x^3*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^3*log(f)^3+_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(-1+a))*d^2*log(f)^2-_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(1+a))*d^2*log(f)^2-_ + 6*x*polylog(3,-b*f^(c+d*x)/(-1+a))*d*log(f)+_ + 6*x*polylog(3,-b*f^(c+d*x)/(1+a))*d*log(f)+_ + 6*polylog(4,-b*f^(c+d*x)/(-1+a))-6*polylog(4,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 498 + +--S 499 OF 506 +a0198:= integrate(t0198,x) +--R +--R +--R x +--R ++ 2 %Q d + c +--R (325) | %Q acoth(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 499 + +--S 500 OF 506 +--m0198:= a0198-r0198 +--E 500 + +--S 501 OF 506 +--d0198:= D(m0198,x) +--E 501 + +--S 502 OF 506 +t0199:= atanh(cosh(x)) +--R +--R +--R (326) atanh(cosh(x)) +--R Type: Expression Integer +--E 502 + +--S 503 OF 506 +r0199:= -2*x*atanh(exp(x))+x*atanh(cosh(x))-_ + polylog(2,-exp(x))+polylog(2,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 503 + +--S 504 OF 506 +a0199:= integrate(t0199,x) +--R +--R +--R x +--R ++ +--R (327) | atanh(cosh(%Q))d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 504 + +--S 505 OF 506 +--m0199:= a0199-r0199 +--E 505 + +--S 506 OF 506 +--d0199:= D(m0199,x) +--E 506 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}