diff --git a/changelog b/changelog index 9367297..d244a0c 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100616 tpd src/axiom-website/patches.html 20100616.01.tpd.patch +20100616 tpd src/input/Makefile rule-based hyper integration +20100616 tpd src/input/richhyper800-899.input rule-based hyper integration 20100615 tpd src/axiom-website/patches.html 20100615.04.tpd.patch 20100615 tpd src/input/Makefile rule-based hyper integration 20100615 tpd src/input/richhyper700-799.input rule-based hyper integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index bd11f9c..89f85b2 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2904,6 +2904,8 @@ src/input/richhyper500-599.input rule-based hyper integration
src/input/richhyper600-699.input rule-based hyper integration
20100615.04.tpd.patch src/input/richhyper700-799.input rule-based hyper integration
+20100616.01.tpd.patch +src/input/richhyper800-899.input rule-based hyper integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 1c41af0..a3a6286 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -383,6 +383,7 @@ REGRES= ackermann.regress \ richhyper500-599.regress \ richhyper600-699.regress \ richhyper700-799.regress \ + richhyper800-899.regress \ richrational.regress \ richtrig000-099.regress \ richtrig100-199.regress \ @@ -720,6 +721,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richhyper500-599.input \ ${OUT}/richhyper600-699.input \ ${OUT}/richhyper700-799.input \ + ${OUT}/richhyper800-899.input \ ${OUT}/richrational.input \ ${OUT}/richtrig000-099.input \ ${OUT}/richtrig100-199.input \ @@ -1086,6 +1088,7 @@ DOCFILES= \ ${DOC}/richhyper500-599.input.dvi \ ${DOC}/richhyper600-699.input.dvi \ ${DOC}/richhyper700-799.input.dvi \ + ${DOC}/richhyper800-899.input.dvi \ ${DOC}/richrational.input.dvi \ ${DOC}/richtrig000-099.input.dvi \ ${DOC}/richtrig100-199.input.dvi \ diff --git a/src/input/richhyper800-899.input.pamphlet b/src/input/richhyper800-899.input.pamphlet new file mode 100644 index 0000000..88b883f --- /dev/null +++ b/src/input/richhyper800-899.input.pamphlet @@ -0,0 +1,14551 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richhyper800-899.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper800-899.output +)spool richhyper800-899.output +)set message auto off +)clear all + +--S 1 of 502 +t0800:= sinh(a+b*x)*cosh(a+b*x)/x^2 +--R +--R +--R cosh(b x + a)sinh(b x + a) +--R (1) -------------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 1 + +--S 2 of 502 +r0800:= b*cosh(2*a)*Chi(2*b*x)-1/2*sinh(2*a+2*b*x)/x+b*sinh(2*a)*Shi(2*b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 502 +a0800:= integrate(t0800,x) +--R +--R +--R x +--R ++ cosh(%I b + a)sinh(%I b + a) +--R (2) | ---------------------------- d%I +--R ++ 2 +--R %I +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 502 +--m0800:= a0800-r0800 +--E 4 + +--S 5 of 502 +--d0800:= D(m0800,x) +--E 5 + +--S 6 of 502 +t0801:= sinh(a+b*x)*cosh(a+b*x)/x^3 +--R +--R +--R cosh(b x + a)sinh(b x + a) +--R (3) -------------------------- +--R 3 +--R x +--R Type: Expression Integer +--E 6 + +--S 7 of 502 +r0801:= -1/2*b*cosh(2*a+2*b*x)/x+b^2*Chi(2*b*x)*sinh(2*a)-_ + 1/4*sinh(2*a+2*b*x)/x^2+b^2*cosh(2*a)*Shi(2*b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 502 +a0801:= integrate(t0801,x) +--R +--R +--R x +--R ++ cosh(%I b + a)sinh(%I b + a) +--R (4) | ---------------------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 502 +--m0801:= a0801-r0801 +--E 9 + +--S 10 of 502 +--d0801:= D(m0801,x) +--E 10 + +--S 11 of 502 +t0802:= sinh(a+b*x)^2*cosh(a+b*x)/x^2 +--R +--R +--R 2 +--R cosh(b x + a)sinh(b x + a) +--R (5) --------------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 11 + +--S 12 of 502 +r0802:= 1/4*(cosh(a+b*x)-cosh(3*a+3*b*x)-b*Chi(b*x)*sinh(a)*x+_ + 3*b*Chi(3*b*x)*sinh(3*a)*x-b*cosh(a)*Shi(b*x)*x+_ + 3*b*cosh(3*a)*Shi(3*b*x)*x)/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 12 + +--S 13 of 502 +a0802:= integrate(t0802,x) +--R +--R +--R x 2 +--R ++ cosh(%I b + a)sinh(%I b + a) +--R (6) | ----------------------------- d%I +--R ++ 2 +--R %I +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 502 +--m0802:= a0802-r0802 +--E 14 + +--S 15 of 502 +--d0802:= D(m0802,x) +--E 15 + +--S 16 of 502 +t0803:= sinh(a+b*x)^2*cosh(a+b*x)/x^3 +--R +--R +--R 2 +--R cosh(b x + a)sinh(b x + a) +--R (7) --------------------------- +--R 3 +--R x +--R Type: Expression Integer +--E 16 + +--S 17 of 502 +r0803:= 1/8*(cosh(a+b*x)-cosh(3*a+3*b*x)-b^2*cosh(a)*Chi(b*x)*x^2+_ + 9*b^2*cosh(3*a)*Chi(3*b*x)*x^2+b*x*sinh(a+b*x)-_ + 3*b*x*sinh(3*a+3*b*x)-b^2*sinh(a)*Shi(b*x)*x^2+_ + 9*b^2*sinh(3*a)*Shi(3*b*x)*x^2)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 502 +a0803:= integrate(t0803,x) +--R +--R +--R x 2 +--R ++ cosh(%I b + a)sinh(%I b + a) +--R (8) | ----------------------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 502 +--m0803:= a0803-r0803 +--E 19 + +--S 20 of 502 +--d0803:= D(m0803,x) +--E 20 + +--S 21 of 502 +t0804:= sinh(a+b*x)*cosh(a+b*x)^2/x^2 +--R +--R +--R 2 +--R cosh(b x + a) sinh(b x + a) +--R (9) --------------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 21 + +--S 22 of 502 +r0804:= -1/4*(-b*cosh(a)*Chi(b*x)*x-3*b*cosh(3*a)*Chi(3*b*x)*x+_ + sinh(a+b*x)+sinh(3*a+3*b*x)-b*sinh(a)*Shi(b*x)*x-_ + 3*b*sinh(3*a)*Shi(3*b*x)*x)/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 502 +a0804:= integrate(t0804,x) +--R +--R +--R x 2 +--R ++ cosh(%I b + a) sinh(%I b + a) +--R (10) | ----------------------------- d%I +--R ++ 2 +--R %I +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 502 +--m0804:= a0804-r0804 +--E 24 + +--S 25 of 502 +--d0804:= D(m0804,x) +--E 25 + +--S 26 of 502 +t0805:= sinh(a+b*x)*cosh(a+b*x)^2/x^3 +--R +--R +--R 2 +--R cosh(b x + a) sinh(b x + a) +--R (11) --------------------------- +--R 3 +--R x +--R Type: Expression Integer +--E 26 + +--S 27 of 502 +r0805:= -1/8*(b*cosh(a+b*x)*x+3*b*cosh(3*a+3*b*x)*x-_ + b^2*Chi(b*x)*sinh(a)*x^2-9*b^2*Chi(3*b*x)*sinh(3*a)*x^2+_ + sinh(a+b*x)+sinh(3*a+3*b*x)-b^2*cosh(a)*Shi(b*x)*x^2-_ + 9*b^2*cosh(3*a)*Shi(3*b*x)*x^2)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 502 +a0805:= integrate(t0805,x) +--R +--R +--R x 2 +--R ++ cosh(%I b + a) sinh(%I b + a) +--R (12) | ----------------------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 502 +--m0805:= a0805-r0805 +--E 29 + +--S 30 of 502 +--d0805:= D(m0805,x) +--E 30 + +--S 31 of 502 +t0806:= x*sinh(a+b*x)^2*cosh(a+b*x)^2 +--R +--R +--R 2 2 +--R (13) x cosh(b x + a) sinh(b x + a) +--R Type: Expression Integer +--E 31 + +--S 32 of 502 +r0806:= -1/128*(8*b^2*x^2+cosh(4*a+4*b*x)-4*x*sinh(4*a+4*b*x)*b)/b^2 +--R +--R +--R 2 2 +--R 4b x sinh(4b x + 4a) - cosh(4b x + 4a) - 8b x +--R (14) ---------------------------------------------- +--R 2 +--R 128b +--R Type: Expression Integer +--E 32 + +--S 33 of 502 +a0806:= integrate(t0806,x) +--R +--R +--R (15) +--R 4 3 +--R - sinh(b x + a) + 16b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 3 +--R - 6cosh(b x + a) sinh(b x + a) + 16b x cosh(b x + a) sinh(b x + a) +--R + +--R 4 2 2 +--R - cosh(b x + a) - 8b x +--R / +--R 2 +--R 128b +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 502 +m0806:= a0806-r0806 +--R +--R +--R (16) +--R 4 +--R - 4b x sinh(4b x + 4a) - sinh(b x + a) +--R + +--R 3 2 2 +--R 16b x cosh(b x + a)sinh(b x + a) - 6cosh(b x + a) sinh(b x + a) +--R + +--R 3 4 +--R 16b x cosh(b x + a) sinh(b x + a) + cosh(4b x + 4a) - cosh(b x + a) +--R / +--R 2 +--R 128b +--R Type: Expression Integer +--E 34 + +--S 35 of 502 +d0806:= D(m0806,x) +--R +--R +--R (17) +--R 4 2 2 +--R x sinh(b x + a) + 6x cosh(b x + a) sinh(b x + a) - x cosh(4b x + 4a) +--R + +--R 4 +--R x cosh(b x + a) +--R / +--R 8 +--R Type: Expression Integer +--E 35 + +--S 36 of 502 +t0807:= x^2*sinh(a+b*x)^2*cosh(a+b*x)^2 +--R +--R +--R 2 2 2 +--R (18) x cosh(b x + a) sinh(b x + a) +--R Type: Expression Integer +--E 36 + +--S 37 of 502 +r0807:= -1/768*(32*b^3*x^3+12*b*x*cosh(4*a+4*b*x)-3*sinh(4*a+4*b*x)-_ + 24*x^2*sinh(4*a+4*b*x)*b^2)/b^3 +--R +--R +--R 2 2 3 3 +--R (24b x + 3)sinh(4b x + 4a) - 12b x cosh(4b x + 4a) - 32b x +--R (19) ------------------------------------------------------------ +--R 3 +--R 768b +--R Type: Expression Integer +--E 37 + +--S 38 of 502 +a0807:= integrate(t0807,x) +--R +--R +--R (20) +--R 4 2 2 3 +--R - 3b x sinh(b x + a) + (24b x + 3)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R - 18b x cosh(b x + a) sinh(b x + a) +--R + +--R 2 2 3 4 3 3 +--R (24b x + 3)cosh(b x + a) sinh(b x + a) - 3b x cosh(b x + a) - 8b x +--R / +--R 3 +--R 192b +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 502 +m0807:= a0807-r0807 +--R +--R +--R (21) +--R 2 2 4 +--R (- 8b x - 1)sinh(4b x + 4a) - 4b x sinh(b x + a) +--R + +--R 2 2 3 +--R (32b x + 4)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R - 24b x cosh(b x + a) sinh(b x + a) +--R + +--R 2 2 3 +--R (32b x + 4)cosh(b x + a) sinh(b x + a) + 4b x cosh(4b x + 4a) +--R + +--R 4 +--R - 4b x cosh(b x + a) +--R / +--R 3 +--R 256b +--R Type: Expression Integer +--E 39 + +--S 40 of 502 +d0807:= D(m0807,x) +--R +--R +--R (22) +--R 2 4 2 2 2 2 +--R x sinh(b x + a) + 6x cosh(b x + a) sinh(b x + a) - x cosh(4b x + 4a) +--R + +--R 2 4 +--R x cosh(b x + a) +--R / +--R 8 +--R Type: Expression Integer +--E 40 + +--S 41 of 502 +t0808:= x^3*sinh(a+b*x)^2*cosh(a+b*x)^2 +--R +--R +--R 3 2 2 +--R (23) x cosh(b x + a) sinh(b x + a) +--R Type: Expression Integer +--E 41 + +--S 42 of 502 +r0808:= -1/1024*(32*b^4*x^4+3*cosh(4*a+4*b*x)+24*b^2*x^2*cosh(4*a+4*b*x)-_ + 12*x*sinh(4*a+4*b*x)*b-32*x^3*sinh(4*a+4*b*x)*b^3)/b^4 +--R +--R +--R (24) +--R 3 3 2 2 4 4 +--R (32b x + 12b x)sinh(4b x + 4a) + (- 24b x - 3)cosh(4b x + 4a) - 32b x +--R ------------------------------------------------------------------------ +--R 4 +--R 1024b +--R Type: Expression Integer +--E 42 + +--S 43 of 502 +a0808:= integrate(t0808,x) +--R +--R +--R (25) +--R 2 2 4 +--R (- 24b x - 3)sinh(b x + a) +--R + +--R 3 3 3 +--R (128b x + 48b x)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 +--R (- 144b x - 18)cosh(b x + a) sinh(b x + a) +--R + +--R 3 3 3 +--R (128b x + 48b x)cosh(b x + a) sinh(b x + a) +--R + +--R 2 2 4 4 4 +--R (- 24b x - 3)cosh(b x + a) - 32b x +--R / +--R 4 +--R 1024b +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 502 +m0808:= a0808-r0808 +--R +--R +--R (26) +--R 3 3 2 2 4 +--R (- 32b x - 12b x)sinh(4b x + 4a) + (- 24b x - 3)sinh(b x + a) +--R + +--R 3 3 3 +--R (128b x + 48b x)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 +--R (- 144b x - 18)cosh(b x + a) sinh(b x + a) +--R + +--R 3 3 3 +--R (128b x + 48b x)cosh(b x + a) sinh(b x + a) +--R + +--R 2 2 2 2 4 +--R (24b x + 3)cosh(4b x + 4a) + (- 24b x - 3)cosh(b x + a) +--R / +--R 4 +--R 1024b +--R Type: Expression Integer +--E 44 + +--S 45 of 502 +d0808:= D(m0808,x) +--R +--R +--R (27) +--R 3 4 3 2 2 3 +--R x sinh(b x + a) + 6x cosh(b x + a) sinh(b x + a) - x cosh(4b x + 4a) +--R + +--R 3 4 +--R x cosh(b x + a) +--R / +--R 8 +--R Type: Expression Integer +--E 45 + +--S 46 of 502 +t0809:= sinh(a+b*x)^2*cosh(a+b*x)^2/x^3 +--R +--R +--R 2 2 +--R cosh(b x + a) sinh(b x + a) +--R (28) ---------------------------- +--R 3 +--R x +--R Type: Expression Integer +--E 46 + +--S 47 of 502 +r0809:= 1/16/x^2-1/16*cosh(4*a+4*b*x)/x^2+b^2*cosh(4*a)*Chi(4*b*x)-_ + 1/4*b*sinh(4*a+4*b*x)/x+b^2*sinh(4*a)*Shi(4*b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 47 + +--S 48 of 502 +a0809:= integrate(t0809,x) +--R +--R +--R x 2 2 +--R ++ cosh(%I b + a) sinh(%I b + a) +--R (29) | ------------------------------ d%I +--R ++ 3 +--R %I +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 502 +--m0809:= a0809-r0809 +--E 49 + +--S 50 of 502 +--d0809:= D(m0809,x) +--E 50 + +--S 51 of 502 +t0810:= x*sech(a+b*x)*tanh(a+b*x) +--R +--R +--R (30) x sech(b x + a)tanh(b x + a) +--R Type: Expression Integer +--E 51 + +--S 52 of 502 +r0810:= atan(sinh(a+b*x))/b^2-x*sech(a+b*x)/b +--R +--R +--R atan(sinh(b x + a)) - b x sech(b x + a) +--R (31) --------------------------------------- +--R 2 +--R b +--R Type: Expression Integer +--E 52 + +--S 53 of 502 +a0810:= integrate(t0810,x) +--R +--R +--R (32) +--R 2 2 +--R (2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) + 2) +--R * +--R atan(sinh(b x + a) + cosh(b x + a)) +--R + +--R - 2b x sinh(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) + b +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 502 +m0810:= a0810-r0810 +--R +--R +--R (33) +--R 2 2 +--R (2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) + 2) +--R * +--R atan(sinh(b x + a) + cosh(b x + a)) +--R + +--R 2 2 +--R (- sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) - 1) +--R * +--R atan(sinh(b x + a)) +--R + +--R 2 +--R b x sech(b x + a)sinh(b x + a) +--R + +--R (2b x cosh(b x + a)sech(b x + a) - 2b x)sinh(b x + a) +--R + +--R 2 +--R (b x cosh(b x + a) + b x)sech(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) + b +--R Type: Expression Integer +--E 54 + +--S 55 of 502 +d0810:= D(m0810,x) +--R +--R +--R (34) +--R 6 +--R - b x sech(b x + a)sinh(b x + a) +--R + +--R 5 +--R - 4b x cosh(b x + a)sech(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 6b x cosh(b x + a) - 3b x)sech(b x + a)sinh(b x + a) +--R + +--R 3 +--R (- 4b x cosh(b x + a) - 8b x cosh(b x + a))sech(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- b x cosh(b x + a) - 8b x cosh(b x + a) - 3b x)sech(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 3 +--R (- 4b x cosh(b x + a) - 4b x cosh(b x + a))sech(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 4 2 +--R (- b x cosh(b x + a) - 2b x cosh(b x + a) - b x)sech(b x + a) +--R * +--R tanh(b x + a) +--R + +--R 6 +--R sech(b x + a)sinh(b x + a) +--R + +--R 5 +--R (4cosh(b x + a)sech(b x + a) + 2b x)sinh(b x + a) +--R + +--R 2 +--R ((6cosh(b x + a) + 3)sech(b x + a) + (6b x - 1)cosh(b x + a)) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 +--R (4cosh(b x + a) + 8cosh(b x + a))sech(b x + a) +--R + +--R 2 +--R (6b x - 4)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (cosh(b x + a) + 8cosh(b x + a) + 3)sech(b x + a) +--R + +--R 3 +--R (2b x - 6)cosh(b x + a) + (4b x - 2)cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 3 4 +--R (4cosh(b x + a) + 4cosh(b x + a))sech(b x + a) - 4cosh(b x + a) +--R + +--R 2 +--R (6b x - 4)cosh(b x + a) - 2b x +--R * +--R sinh(b x + a) +--R + +--R 4 2 5 +--R (cosh(b x + a) + 2cosh(b x + a) + 1)sech(b x + a) - cosh(b x + a) +--R + +--R 3 +--R (2b x - 2)cosh(b x + a) + (- 2b x - 1)cosh(b x + a) +--R / +--R 6 5 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (6b cosh(b x + a) + 3b)sinh(b x + a) +--R + +--R 3 3 +--R (4b cosh(b x + a) + 8b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (b cosh(b x + a) + 8b cosh(b x + a) + 3b)sinh(b x + a) +--R + +--R 3 4 +--R (4b cosh(b x + a) + 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 2 +--R 2b cosh(b x + a) + b +--R Type: Expression Integer +--E 55 + +--S 56 of 502 +t0811:= x^2*sech(a+b*x)*tanh(a+b*x) +--R +--R +--R 2 +--R (35) x sech(b x + a)tanh(b x + a) +--R Type: Expression Integer +--E 56 + +--S 57 of 502 +r0811:= 4*x*atan(exp(1)^(a+b*x))/b^2-2*%i*polylog(2,-%i*exp(1)^(a+b*x))/b^3+_ + 2*%i*polylog(2,%i*exp(1)^(a+b*x))/b^3-x^2*sech(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 502 +a0811:= integrate(t0811,x) +--R +--R +--R x +--R ++ 2 +--R (36) | %I sech(%I b + a)tanh(%I b + a)d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 502 +--m0811:= a0811-r0811 +--E 59 + +--S 60 of 502 +--d0811:= D(m0811,x) +--E 60 + +--S 61 of 502 +t0812:= x^3*sech(a+b*x)*tanh(a+b*x) +--R +--R +--R 3 +--R (37) x sech(b x + a)tanh(b x + a) +--R Type: Expression Integer +--E 61 + +--S 62 of 502 +r0812:= 6*x^2*atan(exp(1)^(a+b*x))/b^2-6*%i*x*_ + polylog(2,-%i*exp(1)^(a+b*x))/b^3+6*%i*x*_ + polylog(2,%i*exp(1)^(a+b*x))/b^3+6*%i*_ + polylog(3,-%i*exp(1)^(a+b*x))/b^4-6*%i*_ + polylog(3,%i*exp(1)^(a+b*x))/b^4-x^3*sech(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 502 +a0812:= integrate(t0812,x) +--R +--R +--R x +--R ++ 3 +--R (38) | %I sech(%I b + a)tanh(%I b + a)d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 502 +--m0812:= a0812-r0812 +--E 64 + +--S 65 of 502 +--d0812:= D(m0812,x) +--E 65 + +--S 66 of 502 +t0813:= x*sech(a+b*x)^2*tanh(a+b*x) +--R +--R +--R 2 +--R (39) x sech(b x + a) tanh(b x + a) +--R Type: Expression Integer +--E 66 + +--S 67 of 502 +r0813:= -1/2*x*sech(a+b*x)^2/b+1/2*tanh(a+b*x)/b^2 +--R +--R +--R 2 +--R tanh(b x + a) - b x sech(b x + a) +--R (40) ---------------------------------- +--R 2 +--R 2b +--R Type: Expression Integer +--E 67 + +--S 68 of 502 +a0813:= integrate(t0813,x) +--R +--R +--R (41) +--R - 2b x sinh(b x + a) + (- 2b x - 2)cosh(b x + a) +--R / +--R 2 3 2 2 +--R b sinh(b x + a) + 3b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 3 2 +--R (3b cosh(b x + a) + b )sinh(b x + a) + b cosh(b x + a) + 3b cosh(b x + a) +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 502 +m0813:= a0813-r0813 +--R +--R +--R (42) +--R 3 2 +--R - sinh(b x + a) - 3cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R (- 3cosh(b x + a) - 1)sinh(b x + a) - cosh(b x + a) - 3cosh(b x + a) +--R * +--R tanh(b x + a) +--R + +--R 2 3 +--R b x sech(b x + a) sinh(b x + a) +--R + +--R 2 2 +--R 3b x cosh(b x + a)sech(b x + a) sinh(b x + a) +--R + +--R 2 2 +--R ((3b x cosh(b x + a) + b x)sech(b x + a) - 4b x)sinh(b x + a) +--R + +--R 3 2 +--R (b x cosh(b x + a) + 3b x cosh(b x + a))sech(b x + a) +--R + +--R (- 4b x - 4)cosh(b x + a) +--R / +--R 2 3 2 2 +--R 2b sinh(b x + a) + 6b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 3 +--R (6b cosh(b x + a) + 2b )sinh(b x + a) + 2b cosh(b x + a) +--R + +--R 2 +--R 6b cosh(b x + a) +--R Type: Expression Integer +--E 69 + +--S 70 of 502 +d0813:= D(m0813,x) +--R +--R +--R (43) +--R 6 5 +--R sinh(b x + a) + 6cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (15cosh(b x + a) + 2)sinh(b x + a) +--R + +--R 3 3 +--R (20cosh(b x + a) + 12cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (15cosh(b x + a) + 24cosh(b x + a) + 1)sinh(b x + a) +--R + +--R 5 3 +--R (6cosh(b x + a) + 20cosh(b x + a) + 6cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 2 +--R cosh(b x + a) + 6cosh(b x + a) + 9cosh(b x + a) +--R * +--R 2 +--R tanh(b x + a) +--R + +--R 2 6 +--R - 2b x sech(b x + a) sinh(b x + a) +--R + +--R 2 5 +--R - 12b x cosh(b x + a)sech(b x + a) sinh(b x + a) +--R + +--R 2 2 4 +--R (- 30b x cosh(b x + a) - 4b x)sech(b x + a) sinh(b x + a) +--R + +--R 3 2 +--R (- 40b x cosh(b x + a) - 24b x cosh(b x + a))sech(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 30b x cosh(b x + a) - 48b x cosh(b x + a) - 2b x) +--R * +--R 2 2 +--R sech(b x + a) sinh(b x + a) +--R + +--R 5 3 +--R - 12b x cosh(b x + a) - 40b x cosh(b x + a) +--R + +--R - 12b x cosh(b x + a) +--R * +--R 2 +--R sech(b x + a) sinh(b x + a) +--R + +--R 6 4 +--R - 2b x cosh(b x + a) - 12b x cosh(b x + a) +--R + +--R 2 +--R - 18b x cosh(b x + a) +--R * +--R 2 +--R sech(b x + a) +--R * +--R tanh(b x + a) +--R + +--R 2 6 +--R (sech(b x + a) - 1)sinh(b x + a) +--R + +--R 2 5 +--R (6cosh(b x + a)sech(b x + a) - 6cosh(b x + a))sinh(b x + a) +--R + +--R 2 2 2 +--R ((15cosh(b x + a) + 2)sech(b x + a) - 15cosh(b x + a) + 8b x - 10) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 2 3 +--R (20cosh(b x + a) + 12cosh(b x + a))sech(b x + a) - 20cosh(b x + a) +--R + +--R (32b x - 28)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (15cosh(b x + a) + 24cosh(b x + a) + 1)sech(b x + a) +--R + +--R 4 2 +--R - 15cosh(b x + a) + (48b x - 24)cosh(b x + a) + 8b x - 9 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 2 +--R (6cosh(b x + a) + 20cosh(b x + a) + 6cosh(b x + a))sech(b x + a) +--R + +--R 5 3 +--R - 6cosh(b x + a) + (32b x - 4)cosh(b x + a) - 22cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 2 +--R (cosh(b x + a) + 6cosh(b x + a) + 9cosh(b x + a) )sech(b x + a) +--R + +--R 6 4 2 +--R - cosh(b x + a) + (8b x + 2)cosh(b x + a) + (- 8b x - 17)cosh(b x + a) +--R / +--R 6 5 +--R 2b sinh(b x + a) + 12b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (30b cosh(b x + a) + 4b)sinh(b x + a) +--R + +--R 3 3 +--R (40b cosh(b x + a) + 24b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (30b cosh(b x + a) + 48b cosh(b x + a) + 2b)sinh(b x + a) +--R + +--R 5 3 +--R (12b cosh(b x + a) + 40b cosh(b x + a) + 12b cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 2b cosh(b x + a) + 12b cosh(b x + a) + 18b cosh(b x + a) +--R Type: Expression Integer +--E 70 + +--S 71 of 502 +t0814:= x^2*sech(a+b*x)^2*tanh(a+b*x) +--R +--R +--R 2 2 +--R (44) x sech(b x + a) tanh(b x + a) +--R Type: Expression Integer +--E 71 + +--S 72 of 502 +r0814:= -log(cosh(a+b*x))/b^3-1/2*x^2*sech(a+b*x)^2/b+x*tanh(a+b*x)/b^2 +--R +--R +--R 2 2 2 +--R - 2log(cosh(b x + a)) + 2b x tanh(b x + a) - b x sech(b x + a) +--R (45) --------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression Integer +--E 72 + +--S 73 of 502 +a0814:= integrate(t0814,x) +--R +--R +--R (46) +--R 4 3 +--R - sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 6cosh(b x + a) - 2)sinh(b x + a) +--R + +--R 3 4 +--R (- 4cosh(b x + a) - 4cosh(b x + a))sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R - 2cosh(b x + a) - 1 +--R * +--R 2cosh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 4 3 +--R 2b x sinh(b x + a) + 8b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 +--R (12b x cosh(b x + a) - 2b x + 2b x)sinh(b x + a) +--R + +--R 3 2 2 +--R (8b x cosh(b x + a) + (- 4b x + 4b x)cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 2 +--R 2b x cosh(b x + a) + (- 2b x + 2b x)cosh(b x + a) +--R / +--R 3 4 3 3 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 3 2 3 2 +--R (6b cosh(b x + a) + 2b )sinh(b x + a) +--R + +--R 3 3 3 3 4 +--R (4b cosh(b x + a) + 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 3 2 3 +--R 2b cosh(b x + a) + b +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 502 +m0814:= a0814-r0814 +--R +--R +--R (47) +--R 4 3 +--R 2sinh(b x + a) + 8cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (12cosh(b x + a) + 4)sinh(b x + a) +--R + +--R 3 4 +--R (8cosh(b x + a) + 8cosh(b x + a))sinh(b x + a) + 2cosh(b x + a) +--R + +--R 2 +--R 4cosh(b x + a) + 2 +--R * +--R log(cosh(b x + a)) +--R + +--R 4 3 +--R - 2sinh(b x + a) - 8cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 12cosh(b x + a) - 4)sinh(b x + a) +--R + +--R 3 4 +--R (- 8cosh(b x + a) - 8cosh(b x + a))sinh(b x + a) - 2cosh(b x + a) +--R + +--R 2 +--R - 4cosh(b x + a) - 2 +--R * +--R 2cosh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 4 3 +--R - 2b x sinh(b x + a) - 8b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 12b x cosh(b x + a) - 4b x)sinh(b x + a) +--R + +--R 3 +--R (- 8b x cosh(b x + a) - 8b x cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R - 2b x cosh(b x + a) - 4b x cosh(b x + a) - 2b x +--R * +--R tanh(b x + a) +--R + +--R 2 2 2 4 +--R (b x sech(b x + a) + 4b x)sinh(b x + a) +--R + +--R 2 2 2 3 +--R (4b x cosh(b x + a)sech(b x + a) + 16b x cosh(b x + a))sinh(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R (6b x cosh(b x + a) + 2b x )sech(b x + a) + 24b x cosh(b x + a) +--R + +--R 2 2 +--R - 4b x + 4b x +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 2 3 2 2 2 +--R (4b x cosh(b x + a) + 4b x cosh(b x + a))sech(b x + a) +--R + +--R 3 2 2 +--R 16b x cosh(b x + a) + (- 8b x + 8b x)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 2 2 4 2 2 2 2 2 2 +--R (b x cosh(b x + a) + 2b x cosh(b x + a) + b x )sech(b x + a) +--R + +--R 4 2 2 2 +--R 4b x cosh(b x + a) + (- 4b x + 4b x)cosh(b x + a) +--R / +--R 3 4 3 3 +--R 2b sinh(b x + a) + 8b cosh(b x + a)sinh(b x + a) +--R + +--R 3 2 3 2 +--R (12b cosh(b x + a) + 4b )sinh(b x + a) +--R + +--R 3 3 3 3 4 +--R (8b cosh(b x + a) + 8b cosh(b x + a))sinh(b x + a) + 2b cosh(b x + a) +--R + +--R 3 2 3 +--R 4b cosh(b x + a) + 2b +--R Type: Expression Integer +--E 74 + +--S 75 of 502 +d0814:= D(m0814,x) +--R +--R +--R (48) +--R 6 5 +--R b x sinh(b x + a) + 6b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (15b x cosh(b x + a) + 3b x)sinh(b x + a) +--R + +--R 3 3 +--R (20b x cosh(b x + a) + 12b x cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (15b x cosh(b x + a) + 18b x cosh(b x + a) + 3b x)sinh(b x + a) +--R + +--R 5 3 +--R (6b x cosh(b x + a) + 12b x cosh(b x + a) + 6b x cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R b x cosh(b x + a) + 3b x cosh(b x + a) + 3b x cosh(b x + a) + b x +--R * +--R 2 +--R tanh(b x + a) +--R + +--R 2 2 2 6 +--R (- b x sech(b x + a) - 1)sinh(b x + a) +--R + +--R 2 2 2 5 +--R (- 6b x cosh(b x + a)sech(b x + a) - 6cosh(b x + a))sinh(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R (- 15b x cosh(b x + a) - 3b x )sech(b x + a) - 15cosh(b x + a) +--R + +--R - 3 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 2 2 3 2 2 2 +--R (- 20b x cosh(b x + a) - 12b x cosh(b x + a))sech(b x + a) +--R + +--R 3 +--R - 20cosh(b x + a) - 12cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 15b x cosh(b x + a) - 18b x cosh(b x + a) - 3b x ) +--R * +--R 2 +--R sech(b x + a) +--R + +--R 4 2 +--R - 15cosh(b x + a) - 18cosh(b x + a) - 3 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 2 5 2 2 3 +--R - 6b x cosh(b x + a) - 12b x cosh(b x + a) +--R + +--R 2 2 +--R - 6b x cosh(b x + a) +--R * +--R 2 +--R sech(b x + a) +--R + +--R 5 3 +--R - 6cosh(b x + a) - 12cosh(b x + a) - 6cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 2 2 6 2 2 4 2 2 2 +--R - b x cosh(b x + a) - 3b x cosh(b x + a) - 3b x cosh(b x + a) +--R + +--R 2 2 +--R - b x +--R * +--R 2 +--R sech(b x + a) +--R + +--R 6 4 2 +--R - cosh(b x + a) - 3cosh(b x + a) - 3cosh(b x + a) - 1 +--R * +--R tanh(b x + a) +--R + +--R 2 6 +--R (b x sech(b x + a) - b x + 1)sinh(b x + a) +--R + +--R 2 +--R (6b x cosh(b x + a)sech(b x + a) + (- 6b x + 6)cosh(b x + a)) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 2 2 +--R (15b x cosh(b x + a) + 3b x)sech(b x + a) +--R + +--R 2 2 2 +--R (- 15b x + 15)cosh(b x + a) + 4b x - 3b x + 1 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 2 +--R (20b x cosh(b x + a) + 12b x cosh(b x + a))sech(b x + a) +--R + +--R 3 2 2 +--R (- 20b x + 20)cosh(b x + a) + (16b x - 12b x + 4)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (15b x cosh(b x + a) + 18b x cosh(b x + a) + 3b x)sech(b x + a) +--R + +--R 4 2 2 2 +--R (- 15b x + 15)cosh(b x + a) + (24b x - 18b x + 6)cosh(b x + a) +--R + +--R 2 2 +--R - 4b x - 3b x - 1 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R (6b x cosh(b x + a) + 12b x cosh(b x + a) + 6b x cosh(b x + a)) +--R * +--R 2 +--R sech(b x + a) +--R + +--R 5 2 2 3 +--R (- 6b x + 6)cosh(b x + a) + (16b x - 12b x + 4)cosh(b x + a) +--R + +--R 2 2 +--R (- 8b x - 6b x - 2)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (b x cosh(b x + a) + 3b x cosh(b x + a) + 3b x cosh(b x + a) + b x) +--R * +--R 2 +--R sech(b x + a) +--R + +--R 6 2 2 4 +--R (- b x + 1)cosh(b x + a) + (4b x - 3b x + 1)cosh(b x + a) +--R + +--R 2 2 2 +--R (- 4b x - 3b x - 1)cosh(b x + a) - b x - 1 +--R / +--R 2 6 2 5 +--R b sinh(b x + a) + 6b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 4 +--R (15b cosh(b x + a) + 3b )sinh(b x + a) +--R + +--R 2 3 2 3 +--R (20b cosh(b x + a) + 12b cosh(b x + a))sinh(b x + a) +--R + +--R 2 4 2 2 2 2 +--R (15b cosh(b x + a) + 18b cosh(b x + a) + 3b )sinh(b x + a) +--R + +--R 2 5 2 3 2 +--R (6b cosh(b x + a) + 12b cosh(b x + a) + 6b cosh(b x + a))sinh(b x + a) +--R + +--R 2 6 2 4 2 2 2 +--R b cosh(b x + a) + 3b cosh(b x + a) + 3b cosh(b x + a) + b +--R Type: Expression Integer +--E 75 + +--S 76 of 502 +t0815:= x^3*sech(a+b*x)^2*tanh(a+b*x) +--R +--R +--R 3 2 +--R (49) x sech(b x + a) tanh(b x + a) +--R Type: Expression Integer +--E 76 + +--S 77 of 502 +r0815:= 3/2*x^2/b^2-3*x*log(1+exp(1)^(2*a+2*b*x))/b^3-_ + 3/2*polylog(2,-exp(1)^(2*a+2*b*x))/b^4-1/2*x^3*sech(a+b*x)^2/b+_ + 3/2*x^2*tanh(a+b*x)/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 502 +a0815:= integrate(t0815,x) +--R +--R +--R x +--R ++ 3 2 +--R (50) | %I sech(%I b + a) tanh(%I b + a)d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 502 +--m0815:= a0815-r0815 +--E 79 + +--S 80 of 502 +--d0815:= D(m0815,x) +--E 80 + +--S 81 of 502 +t0816:= x*csch(a+b*x)*coth(a+b*x) +--R +--R +--R (51) x coth(b x + a)csch(b x + a) +--R Type: Expression Integer +--E 81 + +--S 82 of 502 +r0816:= -acoth(cosh(a+b*x))/b^2-x*csch(a+b*x)/b +--R +--R +--R - acoth(cosh(b x + a)) - b x csch(b x + a) +--R (52) ------------------------------------------ +--R 2 +--R b +--R Type: Expression Integer +--E 82 + +--S 83 of 502 +a0816:= integrate(t0816,x) +--R +--R +--R (53) +--R 2 2 +--R (- sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) + 1) +--R * +--R log(sinh(b x + a) + cosh(b x + a) + 1) +--R + +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1) +--R * +--R log(sinh(b x + a) + cosh(b x + a) - 1) +--R + +--R - 2b x sinh(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 502 +m0816:= a0816-r0816 +--R +--R +--R (54) +--R 2 2 +--R (- sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) + 1) +--R * +--R log(sinh(b x + a) + cosh(b x + a) + 1) +--R + +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1) +--R * +--R log(sinh(b x + a) + cosh(b x + a) - 1) +--R + +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1) +--R * +--R acoth(cosh(b x + a)) +--R + +--R 2 +--R b x csch(b x + a)sinh(b x + a) +--R + +--R (2b x cosh(b x + a)csch(b x + a) - 2b x)sinh(b x + a) +--R + +--R 2 +--R (b x cosh(b x + a) - b x)csch(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Expression Integer +--E 84 + +--S 85 of 502 +d0816:= D(m0816,x) +--R +--R +--R (55) +--R 5 +--R - sinh(b x + a) +--R + +--R 2 2 +--R ((- b x cosh(b x + a) + b x)coth(b x + a) + cosh(b x + a) - 1) +--R * +--R csch(b x + a) +--R + +--R - 4cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 +--R (- 4b x cosh(b x + a) + 4b x cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R 4cosh(b x + a) - 4cosh(b x + a) +--R * +--R csch(b x + a) +--R + +--R 2 +--R (2b x - 6)cosh(b x + a) - 2b x + 2 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 6b x cosh(b x + a) + 8b x cosh(b x + a) - 2b x)coth(b x + a) +--R + +--R 4 2 +--R 6cosh(b x + a) - 8cosh(b x + a) + 2 +--R * +--R csch(b x + a) +--R + +--R 3 +--R (6b x - 4)cosh(b x + a) + (- 6b x + 4)cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R - 4b x cosh(b x + a) + 8b x cosh(b x + a) +--R + +--R - 4b x cosh(b x + a) +--R * +--R coth(b x + a) +--R + +--R 5 3 +--R 4cosh(b x + a) - 8cosh(b x + a) + 4cosh(b x + a) +--R * +--R csch(b x + a) +--R + +--R 4 2 +--R (6b x - 1)cosh(b x + a) + (- 4b x + 2)cosh(b x + a) - 2b x - 1 +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - b x cosh(b x + a) + 3b x cosh(b x + a) - 3b x cosh(b x + a) +--R + +--R b x +--R * +--R coth(b x + a) +--R + +--R 6 4 2 +--R cosh(b x + a) - 3cosh(b x + a) + 3cosh(b x + a) - 1 +--R * +--R csch(b x + a) +--R + +--R 5 +--R 2b x cosh(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 4 +--R (b cosh(b x + a) - b)sinh(b x + a) +--R + +--R 3 3 +--R (4b cosh(b x + a) - 4b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (6b cosh(b x + a) - 8b cosh(b x + a) + 2b)sinh(b x + a) +--R + +--R 5 3 +--R (4b cosh(b x + a) - 8b cosh(b x + a) + 4b cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 2 +--R b cosh(b x + a) - 3b cosh(b x + a) + 3b cosh(b x + a) - b +--R Type: Expression Integer +--E 85 + +--S 86 of 502 +t0817:= x^2*csch(a+b*x)*coth(a+b*x) +--R +--R +--R 2 +--R (56) x coth(b x + a)csch(b x + a) +--R Type: Expression Integer +--E 86 + +--S 87 of 502 +r0817:= -4*x*atanh(exp(1)^(a+b*x))/b^2-x^2*csch(a+b*x)/b-_ + 2*polylog(2,-exp(1)^(a+b*x))/b^3+2*polylog(2,exp(1)^(a+b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 502 +a0817:= integrate(t0817,x) +--R +--R +--R x +--R ++ 2 +--R (57) | %I coth(%I b + a)csch(%I b + a)d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 502 +--m0817:= a0817-r0817 +--E 89 + +--S 90 of 502 +--d0817:= D(m0817,x) +--E 90 + +--S 91 of 502 +t0818:= x^3*csch(a+b*x)*coth(a+b*x) +--R +--R +--R 3 +--R (58) x coth(b x + a)csch(b x + a) +--R Type: Expression Integer +--E 91 + +--S 92 of 502 +r0818:= -6*x^2*atanh(exp(1)^(a+b*x))/b^2-x^3*csch(a+b*x)/b-_ + 6*x*polylog(2,-exp(1)^(a+b*x))/b^3+_ + 6*x*polylog(2,exp(1)^(a+b*x))/b^3+_ + 6*polylog(3,-exp(1)^(a+b*x))/b^4-_ + 6*polylog(3,exp(1)^(a+b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 502 +a0818:= integrate(t0818,x) +--R +--R +--R x +--R ++ 3 +--R (59) | %I coth(%I b + a)csch(%I b + a)d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 502 +--m0818:= a0818-r0818 +--E 94 + +--S 95 of 502 +--d0818:= D(m0818,x) +--E 95 + +--S 96 of 502 +t0819:= x*csch(a+b*x)^2*coth(a+b*x) +--R +--R +--R 2 +--R (60) x coth(b x + a)csch(b x + a) +--R Type: Expression Integer +--E 96 + +--S 97 of 502 +r0819:= -1/2*coth(a+b*x)/b^2-1/2*x*csch(a+b*x)^2/b +--R +--R +--R 2 +--R - b x csch(b x + a) - coth(b x + a) +--R (61) ------------------------------------ +--R 2 +--R 2b +--R Type: Expression Integer +--E 97 + +--S 98 of 502 +a0819:= integrate(t0819,x) +--R +--R +--R (62) +--R (- 2b x - 2)sinh(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 3 2 2 +--R b sinh(b x + a) + 3b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 3 2 +--R (3b cosh(b x + a) - 3b )sinh(b x + a) + b cosh(b x + a) - b cosh(b x + a) +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 of 502 +m0819:= a0819-r0819 +--R +--R +--R (63) +--R 2 3 +--R (b x csch(b x + a) + coth(b x + a))sinh(b x + a) +--R + +--R 2 +--R (3b x cosh(b x + a)csch(b x + a) + 3cosh(b x + a)coth(b x + a)) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 2 +--R (3b x cosh(b x + a) - 3b x)csch(b x + a) +--R + +--R 2 +--R (3cosh(b x + a) - 3)coth(b x + a) - 4b x - 4 +--R * +--R sinh(b x + a) +--R + +--R 3 2 +--R (b x cosh(b x + a) - b x cosh(b x + a))csch(b x + a) +--R + +--R 3 +--R (cosh(b x + a) - cosh(b x + a))coth(b x + a) - 4b x cosh(b x + a) +--R / +--R 2 3 2 2 +--R 2b sinh(b x + a) + 6b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 3 +--R (6b cosh(b x + a) - 6b )sinh(b x + a) + 2b cosh(b x + a) +--R + +--R 2 +--R - 2b cosh(b x + a) +--R Type: Expression Integer +--E 99 + +--S 100 of 502 +d0819:= D(m0819,x) +--R +--R +--R (64) +--R 2 2 +--R ((- 2b x coth(b x + a) + 1)csch(b x + a) - coth(b x + a) + 1) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 2 +--R (- 12b x cosh(b x + a)coth(b x + a) + 6cosh(b x + a))csch(b x + a) +--R + +--R 2 +--R - 6cosh(b x + a)coth(b x + a) + 6cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 2 2 +--R (- 30b x cosh(b x + a) + 12b x)coth(b x + a) + 15cosh(b x + a) +--R + +--R - 6 +--R * +--R 2 +--R csch(b x + a) +--R + +--R 2 2 2 +--R (- 15cosh(b x + a) + 6)coth(b x + a) + 15cosh(b x + a) + 8b x + 2 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 +--R (- 40b x cosh(b x + a) + 40b x cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R 20cosh(b x + a) - 20cosh(b x + a) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 3 2 +--R (- 20cosh(b x + a) + 20cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R 20cosh(b x + a) + (32b x - 4)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 30b x cosh(b x + a) + 48b x cosh(b x + a) - 18b x) +--R * +--R coth(b x + a) +--R + +--R 4 2 +--R 15cosh(b x + a) - 24cosh(b x + a) + 9 +--R * +--R 2 +--R csch(b x + a) +--R + +--R 4 2 2 +--R (- 15cosh(b x + a) + 24cosh(b x + a) - 9)coth(b x + a) +--R + +--R 4 2 +--R 15cosh(b x + a) + (48b x - 24)cosh(b x + a) + 8b x + 17 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R - 12b x cosh(b x + a) + 24b x cosh(b x + a) +--R + +--R - 12b x cosh(b x + a) +--R * +--R coth(b x + a) +--R + +--R 5 3 +--R 6cosh(b x + a) - 12cosh(b x + a) + 6cosh(b x + a) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 5 3 2 +--R (- 6cosh(b x + a) + 12cosh(b x + a) - 6cosh(b x + a))coth(b x + a) +--R + +--R 5 3 +--R 6cosh(b x + a) + (32b x - 28)cosh(b x + a) + 22cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 2b x cosh(b x + a) + 4b x cosh(b x + a) - 2b x cosh(b x + a) ) +--R * +--R coth(b x + a) +--R + +--R 6 4 2 +--R cosh(b x + a) - 2cosh(b x + a) + cosh(b x + a) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 6 4 2 2 +--R (- cosh(b x + a) + 2cosh(b x + a) - cosh(b x + a) )coth(b x + a) +--R + +--R 6 4 2 +--R cosh(b x + a) + (8b x - 10)cosh(b x + a) + (- 8b x + 9)cosh(b x + a) +--R / +--R 6 5 +--R 2b sinh(b x + a) + 12b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (30b cosh(b x + a) - 12b)sinh(b x + a) +--R + +--R 3 3 +--R (40b cosh(b x + a) - 40b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (30b cosh(b x + a) - 48b cosh(b x + a) + 18b)sinh(b x + a) +--R + +--R 5 3 +--R (12b cosh(b x + a) - 24b cosh(b x + a) + 12b cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 2b cosh(b x + a) - 4b cosh(b x + a) + 2b cosh(b x + a) +--R Type: Expression Integer +--E 100 + +--S 101 of 502 +t0820:= x^2*csch(a+b*x)^2*coth(a+b*x) +--R +--R +--R 2 2 +--R (65) x coth(b x + a)csch(b x + a) +--R Type: Expression Integer +--E 101 + +--S 102 of 502 +r0820:= -x*coth(a+b*x)/b^2-1/2*x^2*csch(a+b*x)^2/b+log(sinh(a+b*x))/b^3 +--R +--R +--R 2 2 2 +--R 2log(sinh(b x + a)) - b x csch(b x + a) - 2b x coth(b x + a) +--R (66) ------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression Integer +--E 102 + +--S 103 of 502 +a0820:= integrate(t0820,x) +--R +--R +--R (67) +--R 4 3 +--R sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (6cosh(b x + a) - 2)sinh(b x + a) +--R + +--R 3 4 +--R (4cosh(b x + a) - 4cosh(b x + a))sinh(b x + a) + cosh(b x + a) +--R + +--R 2 +--R - 2cosh(b x + a) + 1 +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 4 3 +--R - 2b x sinh(b x + a) - 8b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 +--R (- 12b x cosh(b x + a) - 2b x + 2b x)sinh(b x + a) +--R + +--R 3 2 2 +--R (- 8b x cosh(b x + a) + (- 4b x + 4b x)cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 2 +--R - 2b x cosh(b x + a) + (- 2b x + 2b x)cosh(b x + a) +--R / +--R 3 4 3 3 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 3 2 3 2 +--R (6b cosh(b x + a) - 2b )sinh(b x + a) +--R + +--R 3 3 3 3 4 +--R (4b cosh(b x + a) - 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 3 2 3 +--R - 2b cosh(b x + a) + b +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 502 +m0820:= a0820-r0820 +--R +--R +--R (68) +--R 4 3 +--R - 2sinh(b x + a) - 8cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 12cosh(b x + a) + 4)sinh(b x + a) +--R + +--R 3 4 +--R (- 8cosh(b x + a) + 8cosh(b x + a))sinh(b x + a) - 2cosh(b x + a) +--R + +--R 2 +--R 4cosh(b x + a) - 2 +--R * +--R log(sinh(b x + a)) +--R + +--R 4 3 +--R 2sinh(b x + a) + 8cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (12cosh(b x + a) - 4)sinh(b x + a) +--R + +--R 3 4 +--R (8cosh(b x + a) - 8cosh(b x + a))sinh(b x + a) + 2cosh(b x + a) +--R + +--R 2 +--R - 4cosh(b x + a) + 2 +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 2 4 +--R (b x csch(b x + a) + 2b x coth(b x + a) - 4b x)sinh(b x + a) +--R + +--R 2 2 2 +--R 4b x cosh(b x + a)csch(b x + a) + 8b x cosh(b x + a)coth(b x + a) +--R + +--R - 16b x cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (6b x cosh(b x + a) - 2b x )csch(b x + a) +--R + +--R 2 2 +--R (12b x cosh(b x + a) - 4b x)coth(b x + a) - 24b x cosh(b x + a) +--R + +--R 2 2 +--R - 4b x + 4b x +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 2 3 2 2 2 +--R (4b x cosh(b x + a) - 4b x cosh(b x + a))csch(b x + a) +--R + +--R 3 +--R (8b x cosh(b x + a) - 8b x cosh(b x + a))coth(b x + a) +--R + +--R 3 2 2 +--R - 16b x cosh(b x + a) + (- 8b x + 8b x)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 2 2 4 2 2 2 2 2 2 +--R (b x cosh(b x + a) - 2b x cosh(b x + a) + b x )csch(b x + a) +--R + +--R 4 2 +--R (2b x cosh(b x + a) - 4b x cosh(b x + a) + 2b x)coth(b x + a) +--R + +--R 4 2 2 2 +--R - 4b x cosh(b x + a) + (- 4b x + 4b x)cosh(b x + a) +--R / +--R 3 4 3 3 +--R 2b sinh(b x + a) + 8b cosh(b x + a)sinh(b x + a) +--R + +--R 3 2 3 2 +--R (12b cosh(b x + a) - 4b )sinh(b x + a) +--R + +--R 3 3 3 3 4 +--R (8b cosh(b x + a) - 8b cosh(b x + a))sinh(b x + a) + 2b cosh(b x + a) +--R + +--R 3 2 3 +--R - 4b cosh(b x + a) + 2b +--R Type: Expression Integer +--E 104 + +--S 105 of 502 +d0820:= D(m0820,x) +--R +--R +--R (69) +--R 2 2 2 2 +--R (- b x coth(b x + a) + b x)csch(b x + a) - b x coth(b x + a) +--R + +--R coth(b x + a) + b x - 1 +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 2 2 +--R (- 6b x cosh(b x + a)coth(b x + a) + 6b x cosh(b x + a)) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 2 +--R - 6b x cosh(b x + a)coth(b x + a) + 6cosh(b x + a)coth(b x + a) +--R + +--R (6b x - 6)cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 2 2 2 2 2 +--R (- 15b x cosh(b x + a) + 3b x )coth(b x + a) +--R + +--R 2 +--R 15b x cosh(b x + a) - 3b x +--R * +--R 2 +--R csch(b x + a) +--R + +--R 2 2 +--R (- 15b x cosh(b x + a) + 3b x)coth(b x + a) +--R + +--R 2 2 +--R (15cosh(b x + a) - 3)coth(b x + a) + (15b x - 15)cosh(b x + a) +--R + +--R 2 2 +--R 4b x - 3b x + 1 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 2 2 3 2 2 +--R (- 20b x cosh(b x + a) + 12b x cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R 20b x cosh(b x + a) - 12b x cosh(b x + a) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 3 2 +--R (- 20b x cosh(b x + a) + 12b x cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R (20cosh(b x + a) - 12cosh(b x + a))coth(b x + a) +--R + +--R 3 2 2 +--R (20b x - 20)cosh(b x + a) + (16b x - 12b x + 4)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 15b x cosh(b x + a) + 18b x cosh(b x + a) - 3b x ) +--R * +--R coth(b x + a) +--R + +--R 4 2 +--R 15b x cosh(b x + a) - 18b x cosh(b x + a) + 3b x +--R * +--R 2 +--R csch(b x + a) +--R + +--R 4 2 2 +--R (- 15b x cosh(b x + a) + 18b x cosh(b x + a) - 3b x)coth(b x + a) +--R + +--R 4 2 +--R (15cosh(b x + a) - 18cosh(b x + a) + 3)coth(b x + a) +--R + +--R 4 2 2 2 +--R (15b x - 15)cosh(b x + a) + (24b x - 18b x + 6)cosh(b x + a) +--R + +--R 2 2 +--R 4b x + 3b x + 1 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 2 5 2 2 3 +--R - 6b x cosh(b x + a) + 12b x cosh(b x + a) +--R + +--R 2 2 +--R - 6b x cosh(b x + a) +--R * +--R coth(b x + a) +--R + +--R 5 3 +--R 6b x cosh(b x + a) - 12b x cosh(b x + a) + 6b x cosh(b x + a) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 5 3 +--R (- 6b x cosh(b x + a) + 12b x cosh(b x + a) - 6b x cosh(b x + a)) +--R * +--R 2 +--R coth(b x + a) +--R + +--R 5 3 +--R (6cosh(b x + a) - 12cosh(b x + a) + 6cosh(b x + a))coth(b x + a) +--R + +--R 5 2 2 3 +--R (6b x - 6)cosh(b x + a) + (16b x - 12b x + 4)cosh(b x + a) +--R + +--R 2 2 +--R (8b x + 6b x + 2)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 2 2 6 2 2 4 2 2 2 +--R - b x cosh(b x + a) + 3b x cosh(b x + a) - 3b x cosh(b x + a) +--R + +--R 2 2 +--R b x +--R * +--R coth(b x + a) +--R + +--R 6 4 2 +--R b x cosh(b x + a) - 3b x cosh(b x + a) + 3b x cosh(b x + a) - b x +--R * +--R 2 +--R csch(b x + a) +--R + +--R 6 4 2 +--R - b x cosh(b x + a) + 3b x cosh(b x + a) - 3b x cosh(b x + a) +--R + +--R b x +--R * +--R 2 +--R coth(b x + a) +--R + +--R 6 4 2 +--R (cosh(b x + a) - 3cosh(b x + a) + 3cosh(b x + a) - 1)coth(b x + a) +--R + +--R 6 2 2 4 +--R (b x - 1)cosh(b x + a) + (4b x - 3b x + 1)cosh(b x + a) +--R + +--R 2 2 2 +--R (4b x + 3b x + 1)cosh(b x + a) - b x - 1 +--R / +--R 2 6 2 5 +--R b sinh(b x + a) + 6b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 4 +--R (15b cosh(b x + a) - 3b )sinh(b x + a) +--R + +--R 2 3 2 3 +--R (20b cosh(b x + a) - 12b cosh(b x + a))sinh(b x + a) +--R + +--R 2 4 2 2 2 2 +--R (15b cosh(b x + a) - 18b cosh(b x + a) + 3b )sinh(b x + a) +--R + +--R 2 5 2 3 2 +--R (6b cosh(b x + a) - 12b cosh(b x + a) + 6b cosh(b x + a))sinh(b x + a) +--R + +--R 2 6 2 4 2 2 2 +--R b cosh(b x + a) - 3b cosh(b x + a) + 3b cosh(b x + a) - b +--R Type: Expression Integer +--E 105 + +--S 106 of 502 +t0821:= x^3*csch(a+b*x)^2*coth(a+b*x) +--R +--R +--R 3 2 +--R (70) x coth(b x + a)csch(b x + a) +--R Type: Expression Integer +--E 106 + +--S 107 of 502 +r0821:= -3/2*x^2/b^2-3/2*x^2*coth(a+b*x)/b^2-1/2*x^3*csch(a+b*x)^2/b+_ + 3*x*log(1-exp(1)^(2*a+2*b*x))/b^3+_ + 3/2*polylog(2,exp(1)^(2*a+2*b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 502 +a0821:= integrate(t0821,x) +--R +--R +--R x +--R ++ 3 2 +--R (71) | %I coth(%I b + a)csch(%I b + a) d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 502 +--m0821:= a0821-r0821 +--E 109 + +--S 110 of 502 +--d0821:= D(m0821,x) +--E 110 + +--S 111 of 502 +t0822:= x*csch(x)*sech(x)^2 +--R +--R +--R 2 +--R (72) x csch(x)sech(x) +--R Type: Expression Integer +--E 111 + +--S 112 of 502 +r0822:= -2*atan(tanh(1/2*x))+x*log(1-exp(1)^(-x))-_ + x*log(1+exp(1)^(-x))+polylog(2,-exp(1)^(-x))-_ + polylog(2,exp(1)^(-x))+x*sech(x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 112 + +--S 113 of 502 +a0822:= integrate(t0822,x) +--R +--R +--R x +--R ++ 2 +--R (73) | %I csch(%I)sech(%I) d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 113 + +--S 114 of 502 +--m0822:= a0822-r0822 +--E 114 + +--S 115 of 502 +--d0822:= D(m0822,x) +--E 115 + +--S 116 of 502 +t0823:= x*sinh(a+b*x)*cosh(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (74) x cosh(b x + a)sinh(b x + a)\|cosh(b x + a) +--R Type: Expression Integer +--E 116 + +--S 117 of 502 +r0823:= -2/25*(-5*x*cosh(a+b*x)^(5/2)*b-6*%i*EllipticE(1/2*%i*(a+b*x),2)+_ + 2*cosh(a+b*x)^(3/2)*sinh(a+b*x))/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Complex Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 117 + +--S 118 of 502 +a0823:= integrate(t0823,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 118 + +--S 119 of 502 +--m0823:= a0823-r0823 +--E 119 + +--S 120 of 502 +--d0823:= D(m0823,x) +--E 120 + +--S 121 of 502 +t0824:= x*sinh(a+b*x)*cosh(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (75) x sinh(b x + a)\|cosh(b x + a) +--R Type: Expression Integer +--E 121 + +--S 122 of 502 +r0824:= -2/9*(-3*x*cosh(a+b*x)^(3/2)*b-_ + 2*%i*EllipticF(1/2*%i*(a+b*x),2)+2*cosh(a+b*x)^(1/2)*sinh(a+b*x))/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Complex Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 122 + +--S 123 of 502 +a0824:= integrate(t0824,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 123 + +--S 124 of 502 +--m0824:= a0824-r0824 +--E 124 + +--S 125 of 502 +--d0824:= D(m0824,x) +--E 125 + +--S 126 of 502 +t0825:= x*sinh(a+b*x)/cosh(a+b*x)^(1/2) +--R +--R +--R x sinh(b x + a) +--R (76) ---------------- +--R +-------------+ +--R \|cosh(b x + a) +--R Type: Expression Integer +--E 126 + +--S 127 of 502 +r0825:= 2*(x*cosh(a+b*x)^(1/2)*b+2*%i*EllipticE(1/2*%i*(a+b*x),2))/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Complex Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 127 + +--S 128 of 502 +a0825:= integrate(t0825,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 128 + +--S 129 of 502 +--m0825:= a0825-r0825 +--E 129 + +--S 130 of 502 +--d0825:= D(m0825,x) +--E 130 + +--S 131 of 502 +t0826:= x*sinh(a+b*x)/cosh(a+b*x)^(3/2) +--R +--R +--R x sinh(b x + a) +--R (77) ----------------------------- +--R +-------------+ +--R cosh(b x + a)\|cosh(b x + a) +--R Type: Expression Integer +--E 131 + +--S 132 of 502 +r0826:= -2*x/b/cosh(a+b*x)^(1/2)-4*%i*EllipticF(1/2*%i*(a+b*x),2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Complex Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 132 + +--S 133 of 502 +a0826:= integrate(t0826,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 133 + +--S 134 of 502 +--m0826:= a0826-r0826 +--E 134 + +--S 135 of 502 +--d0826:= D(m0826,x) +--E 135 + +--S 136 of 502 +t0827:= x*sinh(a+b*x)/cosh(a+b*x)^(5/2) +--R +--R +--R x sinh(b x + a) +--R (78) ------------------------------ +--R 2 +-------------+ +--R cosh(b x + a) \|cosh(b x + a) +--R Type: Expression Integer +--E 136 + +--S 137 of 502 +r0827:= -2/3*x/b/cosh(a+b*x)^(3/2)+4/3*%i*EllipticE(1/2*%i*(a+b*x),2)/b^2+_ + 4/3*sinh(a+b*x)/b^2/cosh(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Complex Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 137 + +--S 138 of 502 +a0827:= integrate(t0827,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 138 + +--S 139 of 502 +--m0827:= a0827-r0827 +--E 139 + +--S 140 of 502 +--d0827:= D(m0827,x) +--E 140 + +--S 141 of 502 +t0828:= x*cosh(a+b*x)*sinh(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (79) x cosh(b x + a)sinh(b x + a)\|sinh(b x + a) +--R Type: Expression Integer +--E 141 + +--S 142 of 502 +r0828:= -12/25*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)*_ + sinh(a+b*x)^(1/2)/b^2/(%i*sinh(a+b*x))^(1/2)-4/25*_ + cosh(a+b*x)*sinh(a+b*x)^(3/2)/b^2+2/5*x*sinh(a+b*x)^(5/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 142 + +--S 143 of 502 +a0828:= integrate(t0828,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 143 + +--S 144 of 502 +--m0828:= a0828-r0828 +--E 144 + +--S 145 of 502 +--d0828:= D(m0828,x) +--E 145 + +--S 146 of 502 +t0829:= x*cosh(a+b*x)*sinh(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (80) x cosh(b x + a)\|sinh(b x + a) +--R Type: Expression Integer +--E 146 + +--S 147 of 502 +r0829:= 2/9*(-2*%i*EllipticF(-1/4*%pi+1/2*%i*a+1/2*%i*b*x,2)*_ + (%i*sinh(a+b*x))^(1/2)-2*cosh(a+b*x)*sinh(a+b*x)+_ + 3*b*x*cosh(a+b*x)^2-3*b*x)/sinh(a+b*x)^(1/2)/b^2 +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Expression Complex Integer +--R Polynomial Complex Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 147 + +--S 148 of 502 +a0829:= integrate(t0829,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 148 + +--S 149 of 502 +--m0829:= a0829-r0829 +--E 149 + +--S 150 of 502 +--d0829:= D(m0829,x) +--E 150 + +--S 151 of 502 +t0830:= x*cosh(a+b*x)/sinh(a+b*x)^(1/2) +--R +--R +--R x cosh(b x + a) +--R (81) ---------------- +--R +-------------+ +--R \|sinh(b x + a) +--R Type: Expression Integer +--E 151 + +--S 152 of 502 +r0830:= 2*x*sinh(a+b*x)^(1/2)/b+4*%i*EllipticE(-1/4*%pi+_ + 1/2*%i*(a+b*x),2)*sinh(a+b*x)^(1/2)/b^2/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 152 + +--S 153 of 502 +a0830:= integrate(t0830,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 153 + +--S 154 of 502 +--m0830:= a0830-r0830 +--E 154 + +--S 155 of 502 +--d0830:= D(m0830,x) +--E 155 + +--S 156 of 502 +t0831:= x*cosh(a+b*x)/sinh(a+b*x)^(3/2) +--R +--R +--R x cosh(b x + a) +--R (82) ----------------------------- +--R +-------------+ +--R sinh(b x + a)\|sinh(b x + a) +--R Type: Expression Integer +--E 156 + +--S 157 of 502 +r0831:= -2*(b*x+2*%i*EllipticF(-1/4*%pi+1/2*%i*a+1/2*%i*b*x,2)*_ + (%i*sinh(a+b*x))^(1/2))/sinh(a+b*x)^(1/2)/b^2 +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Expression Complex Integer +--R Polynomial Complex Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 157 + +--S 158 of 502 +a0831:= integrate(t0831,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 158 + +--S 159 of 502 +--m0831:= a0831-r0831 +--E 159 + +--S 160 of 502 +--d0831:= D(m0831,x) +--E 160 + +--S 161 of 502 +t0832:= x*cosh(a+b*x)/sinh(a+b*x)^(5/2) +--R +--R +--R x cosh(b x + a) +--R (83) ------------------------------ +--R 2 +-------------+ +--R sinh(b x + a) \|sinh(b x + a) +--R Type: Expression Integer +--E 161 + +--S 162 of 502 +r0832:= -2/3*x/b/sinh(a+b*x)^(3/2)-4/3*cosh(a+b*x)/b^2/sinh(a+b*x)^(1/2)-_ + 4/3*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)*_ + sinh(a+b*x)^(1/2)/b^2/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 502 +a0832:= integrate(t0832,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 163 + +--S 164 of 502 +--m0832:= a0832-r0832 +--E 164 + +--S 165 of 502 +--d0832:= D(m0832,x) +--E 165 + +--S 166 of 502 +t0833:= x*sinh(a+b*x)*sech(a+b*x)^(5/2) +--R +--R +--R 2 +-------------+ +--R (84) x sech(b x + a) sinh(b x + a)\|sech(b x + a) +--R Type: Expression Integer +--E 166 + +--S 167 of 502 +r0833:= 2/3*(1/cosh(a+b*x))^(1/2)*(2*%i*cosh(a+b*x)^(3/2)*_ + EllipticE(1/2*%i*(a+b*x),2)-b*x+2*cosh(a+b*x)*_ + sinh(a+b*x))/cosh(a+b*x)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Complex Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 167 + +--S 168 of 502 +a0833:= integrate(t0833,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 168 + +--S 169 of 502 +--m0833:= a0833-r0833 +--E 169 + +--S 170 of 502 +--d0833:= D(m0833,x) +--E 170 + +--S 171 of 502 +t0834:= x*sinh(a+b*x)*sech(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (85) x sech(b x + a)sinh(b x + a)\|sech(b x + a) +--R Type: Expression Integer +--E 171 + +--S 172 of 502 +r0834:= -2*(1/cosh(a+b*x))^(1/2)*(b*x+2*%i*cosh(a+b*x)^(1/2)*_ + EllipticF(1/2*%i*(a+b*x),2))/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Complex Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 172 + +--S 173 of 502 +a0834:= integrate(t0834,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 173 + +--S 174 of 502 +--m0834:= a0834-r0834 +--E 174 + +--S 175 of 502 +--d0834:= D(m0834,x) +--E 175 + +--S 176 of 502 +t0835:= x*sinh(a+b*x)*sech(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (86) x sinh(b x + a)\|sech(b x + a) +--R Type: Expression Integer +--E 176 + +--S 177 of 502 +r0835:= 2*x/b/sech(a+b*x)^(1/2)+4*%i*cosh(a+b*x)^(1/2)*_ + EllipticE(1/2*%i*(a+b*x),2)*sech(a+b*x)^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Complex Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 177 + +--S 178 of 502 +a0835:= integrate(t0835,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 178 + +--S 179 of 502 +--m0835:= a0835-r0835 +--E 179 + +--S 180 of 502 +--d0835:= D(m0835,x) +--E 180 + +--S 181 of 502 +t0836:= x*sinh(a+b*x)/sech(a+b*x)^(1/2) +--R +--R +--R x sinh(b x + a) +--R (87) ---------------- +--R +-------------+ +--R \|sech(b x + a) +--R Type: Expression Integer +--E 181 + +--S 182 of 502 +r0836:= -2/9*(-3*b*x*cosh(a+b*x)^(3/2)-2*%i*EllipticF(1/2*%i*(a+b*x),2)+_ + 2*sinh(a+b*x)*cosh(a+b*x)^(1/2))/cosh(a+b*x)^(1/2)/_ + (1/cosh(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Complex Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 182 + +--S 183 of 502 +a0836:= integrate(t0836,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 183 + +--S 184 of 502 +--m0836:= a0836-r0836 +--E 184 + +--S 185 of 502 +--d0836:= D(m0836,x) +--E 185 + +--S 186 of 502 +t0837:= x*sinh(a+b*x)/sech(a+b*x)^(3/2) +--R +--R +--R x sinh(b x + a) +--R (88) ----------------------------- +--R +-------------+ +--R sech(b x + a)\|sech(b x + a) +--R Type: Expression Integer +--E 186 + +--S 187 of 502 +r0837:= 2/25*(5*b*x*cosh(a+b*x)^(5/2)+6*%i*EllipticE(1/2*%i*(a+b*x),2)-_ + 2*sinh(a+b*x)*cosh(a+b*x)^(3/2))/cosh(a+b*x)^(1/2)/_ + (1/cosh(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Complex Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 187 + +--S 188 of 502 +a0837:= integrate(t0837,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 188 + +--S 189 of 502 +--m0837:= a0837-r0837 +--E 189 + +--S 190 of 502 +--d0837:= D(m0837,x) +--E 190 + +--S 191 of 502 +t0838:= x*cosh(a+b*x)*csch(a+b*x)^(5/2) +--R +--R +--R 2 +-------------+ +--R (89) x cosh(b x + a)csch(b x + a) \|csch(b x + a) +--R Type: Expression Integer +--E 191 + +--S 192 of 502 +r0838:= -4/3*cosh(a+b*x)*csch(a+b*x)^(1/2)/b^2-2/3*x*csch(a+b*x)^(3/2)/b-_ + 4/3*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)/b^2/_ + csch(a+b*x)^(1/2)/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 192 + +--S 193 of 502 +a0838:= integrate(t0838,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 193 + +--S 194 of 502 +--m0838:= a0838-r0838 +--E 194 + +--S 195 of 502 +--d0838:= D(m0838,x) +--E 195 + +--S 196 of 502 +t0839:= x*cosh(a+b*x)*csch(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (90) x cosh(b x + a)csch(b x + a)\|csch(b x + a) +--R Type: Expression Integer +--E 196 + +--S 197 of 502 +r0839:= -2*(1/sinh(a+b*x))^(1/2)*(b*x+2*%i*_ + EllipticF(-1/4*%pi+1/2*%i*a+1/2*%i*b*x,2)*(%i*sinh(a+b*x))^(1/2))/b^2 +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Expression Complex Integer +--R Polynomial Complex Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 197 + +--S 198 of 502 +a0839:= integrate(t0839,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 198 + +--S 199 of 502 +--m0839:= a0839-r0839 +--E 199 + +--S 200 of 502 +--d0839:= D(m0839,x) +--E 200 + +--S 201 of 502 +t0840:= x*cosh(a+b*x)*csch(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (91) x cosh(b x + a)\|csch(b x + a) +--R Type: Expression Integer +--E 201 + +--S 202 of 502 +r0840:= 2*x/b/csch(a+b*x)^(1/2)+4*%i*_ + EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)/b^2/csch(a+b*x)^(1/2)/_ + (%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 202 + +--S 203 of 502 +a0840:= integrate(t0840,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 203 + +--S 204 of 502 +--m0840:= a0840-r0840 +--E 204 + +--S 205 of 502 +--d0840:= D(m0840,x) +--E 205 + +--S 206 of 502 +t0841:= x*cosh(a+b*x)/csch(a+b*x)^(1/2) +--R +--R +--R x cosh(b x + a) +--R (92) ---------------- +--R +-------------+ +--R \|csch(b x + a) +--R Type: Expression Integer +--E 206 + +--S 207 of 502 +r0841:= 2/3*x/b/csch(a+b*x)^(3/2)-4/9*cosh(a+b*x)/b^2/csch(a+b*x)^(1/2)-_ + 4/9*%i*csch(a+b*x)^(1/2)*EllipticF(-1/4*%pi+1/2*%i*(a+b*x),2)*_ + (%i*sinh(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 207 + +--S 208 of 502 +a0841:= integrate(t0841,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 208 + +--S 209 of 502 +--m0841:= a0841-r0841 +--E 209 + +--S 210 of 502 +--d0841:= D(m0841,x) +--E 210 + +--S 211 of 502 +t0842:= x*cosh(a+b*x)/csch(a+b*x)^(3/2) +--R +--R +--R x cosh(b x + a) +--R (93) ----------------------------- +--R +-------------+ +--R csch(b x + a)\|csch(b x + a) +--R Type: Expression Integer +--E 211 + +--S 212 of 502 +r0842:= 2/5*x/b/csch(a+b*x)^(5/2)-4/25*cosh(a+b*x)/b^2/csch(a+b*x)^(3/2)-_ + 12/25*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)/b^2/_ + csch(a+b*x)^(1/2)/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 212 + +--S 213 of 502 +a0842:= integrate(t0842,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 213 + +--S 214 of 502 +--m0842:= a0842-r0842 +--E 214 + +--S 215 of 502 +--d0842:= D(m0842,x) +--E 215 + +--S 216 of 502 +t0843:= csch(x)^(1/2)*(x*cosh(x)-4*sech(x)*tanh(x)) +--R +--R +--R +-------+ +--R (94) (- 4sech(x)tanh(x) + x cosh(x))\|csch(x) +--R Type: Expression Integer +--E 216 + +--S 217 of 502 +r0843:= 2*x/csch(x)^(1/2)-4*sech(x)/csch(x)^(3/2) +--R +--R +--R - 4sech(x) + 2x csch(x) +--R (95) ----------------------- +--R +-------+ +--R csch(x)\|csch(x) +--R Type: Expression Integer +--E 217 + +--S 218 of 502 +a0843:= integrate(t0843,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 218 + +--S 219 of 502 +--m0843:= a0843-r0843 +--E 219 + +--S 220 of 502 +--d0843:= D(m0843,x) +--E 220 + +--S 221 of 502 +t0844:= 1/(a+b*sinh(x)*cosh(x)) +--R +--R +--R 1 +--R (96) -------------------- +--R b cosh(x)sinh(x) + a +--R Type: Expression Integer +--E 221 + +--S 222 of 502 +r0844:= -2*atanh((b-2*a*tanh(x))/(4*a^2+b^2)^(1/2))/(4*a^2+b^2)^(1/2) +--R +--R +--R 2a tanh(x) - b +--R 2atanh(--------------) +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R (97) ---------------------- +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R Type: Expression Integer +--E 222 + +--S 223 of 502 +a0844:= integrate(t0844,x) +--R +--R +--R (98) +--R log +--R 2 4 2 3 2 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 4 2 +--R (4b cosh(x) + 8a b cosh(x))sinh(x) + b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 +--R b + 8a +--R * +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R + +--R 3 2 2 3 2 +--R (- 2b - 8a b)sinh(x) + (- 4b - 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (- 2b - 8a b)cosh(x) - 4a b - 16a +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 4a)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 8a cosh(x))sinh(x) + b cosh(x) + 4a cosh(x) - b +--R / +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R Type: Union(Expression Integer,...) +--E 223 + +--S 224 of 502 +m0844:= a0844-r0844 +--R +--R +--R (99) +--R log +--R 2 4 2 3 2 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 4 +--R (4b cosh(x) + 8a b cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 +--R 4a b cosh(x) + b + 8a +--R * +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R + +--R 3 2 2 3 2 +--R (- 2b - 8a b)sinh(x) + (- 4b - 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (- 2b - 8a b)cosh(x) - 4a b - 16a +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 4a)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 8a cosh(x))sinh(x) + b cosh(x) + 4a cosh(x) - b +--R + +--R 2a tanh(x) - b +--R - 2atanh(--------------) +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R / +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R Type: Expression Integer +--E 224 + +--S 225 of 502 +d0844:= D(m0844,x) +--R +--R +--R (100) +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) - 6b cosh(x) sinh(x) +--R + +--R 3 4 +--R - 4b cosh(x) sinh(x) - b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 +--R (- 4b sinh(x) - 8b cosh(x)sinh(x) - 4b cosh(x) )tanh(x) + b sinh(x) +--R + +--R 3 2 2 3 +--R 4b cosh(x)sinh(x) + 6b cosh(x) sinh(x) + 4b cosh(x) sinh(x) +--R + +--R 4 +--R b cosh(x) - b +--R / +--R 4 3 2 2 2 +--R a b sinh(x) + 4a b cosh(x)sinh(x) + (6a b cosh(x) + 4a )sinh(x) +--R + +--R 3 2 4 2 2 +--R (4a b cosh(x) + 8a cosh(x))sinh(x) + a b cosh(x) + 4a cosh(x) - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 2 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) - 4a b)sinh(x) +--R + +--R 2 3 2 4 2 2 +--R (- 4b cosh(x) - 8a b cosh(x))sinh(x) - b cosh(x) - 4a b cosh(x) + b +--R * +--R tanh(x) +--R + +--R 4 3 2 2 2 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) + (- 6a b cosh(x) - 4a )sinh(x) +--R + +--R 3 2 4 2 2 +--R (- 4a b cosh(x) - 8a cosh(x))sinh(x) - a b cosh(x) - 4a cosh(x) + a b +--R Type: Expression Integer +--E 225 + +--S 226 of 502 +t0845:= x/(a+b*sinh(x)*cosh(x)) +--R +--R +--R x +--R (101) -------------------- +--R b cosh(x)sinh(x) + a +--R Type: Expression Integer +--E 226 + +--S 227 of 502 +r0845:= 1/2*(2*x*log((-2*a+(4*a^2+b^2)^(1/2)-b*exp(2*x))/_ + (-2*a+(4*a^2+b^2)^(1/2)))-2*x*log((2*a+(4*a^2+b^2)^(1/2)+_ + b*exp(2*x))/(2*a+(4*a^2+b^2)^(1/2)))+polylog(2,b*exp(2*x)/_ + (-2*a+(4*a^2+b^2)^(1/2)))-_ + polylog(2,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x)))/(4*a^2+b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 227 + +--S 228 of 502 +a0845:= integrate(t0845,x) +--R +--R +--R x +--R ++ %I +--R (102) | ---------------------- d%I +--R ++ b cosh(%I)sinh(%I) + a +--R Type: Union(Expression Integer,...) +--E 228 + +--S 229 of 502 +--m0845:= a0845-r0845 +--E 229 + +--S 230 of 502 +--d0845:= D(m0845,x) +--E 230 + +--S 231 of 502 +t0846:= x^2/(a+b*sinh(x)*cosh(x)) +--R +--R +--R 2 +--R x +--R (103) -------------------- +--R b cosh(x)sinh(x) + a +--R Type: Expression Integer +--E 231 + +--S 232 of 502 +r0846:= 1/2*(2*x^2*log((-2*a+(4*a^2+b^2)^(1/2)-b*exp(2*x))/_ + (-2*a+(4*a^2+b^2)^(1/2)))-2*x^2*log((2*a+(4*a^2+b^2)^(1/2)+_ + b*exp(2*x))/(2*a+(4*a^2+b^2)^(1/2)))+_ + 2*x*polylog(2,b*exp(2*x)/(-2*a+(4*a^2+b^2)^(1/2)))-_ + 2*x*polylog(2,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x))-_ + polylog(3,b*exp(2*x)/(-2*a+(4*a^2+b^2)^(1/2)))+_ + polylog(3,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x)))/(4*a^2+b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 232 + +--S 233 of 502 +a0846:= integrate(t0846,x) +--R +--R +--R x 2 +--R ++ %I +--R (104) | ---------------------- d%I +--R ++ b cosh(%I)sinh(%I) + a +--R Type: Union(Expression Integer,...) +--E 233 + +--S 234 of 502 +--m0846:= a0846-r0846 +--E 234 + +--S 235 of 502 +--d0846:= D(m0846,x) +--E 235 + +--S 236 of 502 +t0847:= x^3/(a+b*sinh(x)*cosh(x)) +--R +--R +--R 3 +--R x +--R (105) -------------------- +--R b cosh(x)sinh(x) + a +--R Type: Expression Integer +--E 236 + +--S 237 of 502 +r0847:= 1/4*(4*x^3*log((-2*a+(4*a^2+b^2)^(1/2)-b*exp(2*x))/_ + (-2*a+(4*a^2+b^2)^(1/2)))-4*x^3*log((2*a+(4*a^2+b^2)^(1/2)+_ + b*exp(2*x))/(2*a+(4*a^2+b^2)^(1/2)))+_ + 6*x^2*polylog(2,b*exp(2*x)/(-2*a+(4*a^2+b^2)^(1/2)))-_ + 6*x^2*polylog(2,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x))-_ + 6*x*polylog(3,b*exp(2*x)/(-2*a+(4*a^2+b^2)^(1/2)))+_ + 6*x*polylog(3,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x))+_ + 3*polylog(4,b*exp(2*x)/(-2*a+(4*a^2+b^2)^(1/2)))-_ + 3*polylog(4,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x)))/(4*a^2+b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 502 +a0847:= integrate(t0847,x) +--R +--R +--R x 3 +--R ++ %I +--R (106) | ---------------------- d%I +--R ++ b cosh(%I)sinh(%I) + a +--R Type: Union(Expression Integer,...) +--E 238 + +--S 239 of 502 +--m0847:= a0847-r0847 +--E 239 + +--S 240 of 502 +--d0847:= D(m0847,x) +--E 240 + +--S 241 of 502 +t0848:= (a-b*sinh(x))/(b+a*sinh(x))^2 +--R +--R +--R - b sinh(x) + a +--R (107) ------------------------------ +--R 2 2 2 +--R a sinh(x) + 2a b sinh(x) + b +--R Type: Expression Integer +--E 241 + +--S 242 of 502 +r0848:= -cosh(x)/(b+a*sinh(x)) +--R +--R +--R cosh(x) +--R (108) - ------------- +--R a sinh(x) + b +--R Type: Expression Integer +--E 242 + +--S 243 of 502 +a0848:= integrate(t0848,x) +--R +--R +--R (109) +--R 2b sinh(x) + 2b cosh(x) - 2a +--R ------------------------------------------------------------------------ +--R 2 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) - a +--R Type: Union(Expression Integer,...) +--E 243 + +--S 244 of 502 +m0848:= a0848-r0848 +--R +--R +--R (110) +--R 2 2 +--R (a cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (2a cosh(x) + 4a b cosh(x) + 2b - 2a )sinh(x) + a cosh(x) +--R + +--R 2 2 2 +--R 2a b cosh(x) + (2b - a )cosh(x) - 2a b +--R / +--R 3 3 3 2 2 +--R a sinh(x) + (2a cosh(x) + 3a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (a cosh(x) + 4a b cosh(x) + 2a b - a )sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - a b +--R Type: Expression Integer +--E 244 + +--S 245 of 502 +d0848:= D(m0848,x) +--R +--R +--R (111) +--R 3 6 3 2 5 +--R a sinh(x) + (4a cosh(x) + 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (5a cosh(x) + 10a b cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 2 2 3 3 2 3 +--R (8a b cosh(x) + (8a b + 4a )cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 3 4 2 3 3 2 3 2 +--R - 5a cosh(x) - 6a b cosh(x) + 4a cosh(x) + (2b + 10a b)cosh(x) +--R + +--R 2 3 +--R 4a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R - 4a cosh(x) - 11a b cosh(x) + (- 8a b + 4a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 2b + 10a b)cosh(x) + 8a b cosh(x) + 2b + a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R - a cosh(x) - 4a b cosh(x) + (- 4a b + 2a )cosh(x) +--R + +--R 3 2 3 2 3 2 3 +--R (- 2b + 4a b)cosh(x) + (4a b - a )cosh(x) + 2b cosh(x) +--R / +--R 4 6 4 3 5 +--R a sinh(x) + (4a cosh(x) + 6a b)sinh(x) +--R + +--R 4 2 3 2 2 4 4 +--R (6a cosh(x) + 20a b cosh(x) + 13a b - 2a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 3 +--R (4a cosh(x) + 24a b cosh(x) + (36a b - 4a )cosh(x) + 12a b - 8a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R a cosh(x) + 12a b cosh(x) + (34a b - 2a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (28a b - 12a b)cosh(x) + 4b - 10a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R 2a b cosh(x) + 12a b cosh(x) + (20a b - 4a b)cosh(x) +--R + +--R 4 2 2 3 3 +--R (8b - 12a b )cosh(x) - 4a b + 2a b +--R * +--R sinh(x) +--R + +--R 2 2 4 3 3 4 2 2 2 3 2 2 +--R a b cosh(x) + 4a b cosh(x) + (4b - 2a b )cosh(x) - 4a b cosh(x) + a b +--R Type: Expression Integer +--E 245 + +--S 246 of 502 +t0849:= x*(b-a*sinh(x))/(a+b*sinh(x))^2 +--R +--R +--R - a x sinh(x) + b x +--R (112) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression Integer +--E 246 + +--S 247 of 502 +r0849:= log(a+b*sinh(x))/b-x*cosh(x)/(a+b*sinh(x)) +--R +--R +--R (b sinh(x) + a)log(b sinh(x) + a) - b x cosh(x) +--R (113) ----------------------------------------------- +--R 2 +--R b sinh(x) + a b +--R Type: Expression Integer +--E 247 + +--S 248 of 502 +a0849:= integrate(t0849,x) +--R +--R +--R (114) +--R 2 2 +--R (b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) - b) +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 2b x sinh(x) + (- 4b x cosh(x) - 2a x)sinh(x) - 2b x cosh(x) +--R + +--R - 2a x cosh(x) +--R / +--R 2 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) - b +--R Type: Union(Expression Integer,...) +--E 248 + +--S 249 of 502 +m0849:= a0849-r0849 +--R +--R +--R (115) +--R 2 3 2 2 +--R - b sinh(x) + (- 2b cosh(x) - 3a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- b cosh(x) - 4a b cosh(x) + b - 2a )sinh(x) - a b cosh(x) +--R + +--R 2 +--R - 2a cosh(x) + a b +--R * +--R log(b sinh(x) + a) +--R + +--R 2 3 2 2 +--R b sinh(x) + (2b cosh(x) + 3a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b cosh(x) + 4a b cosh(x) - b + 2a )sinh(x) + a b cosh(x) +--R + +--R 2 +--R 2a cosh(x) - a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 2 +--R - 2b x sinh(x) + (- 3b x cosh(x) - 4a b x)sinh(x) +--R + +--R 2 2 3 2 2 +--R (- 4a b x cosh(x) - 2a x)sinh(x) + b x cosh(x) + (- b - 2a )x cosh(x) +--R / +--R 3 3 3 2 2 +--R b sinh(x) + (2b cosh(x) + 3a b )sinh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (b cosh(x) + 4a b cosh(x) - b + 2a b)sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - a b +--R Type: Expression Integer +--E 249 + +--S 250 of 502 +d0849:= D(m0849,x) +--R +--R +--R (116) +--R 3 3 6 3 3 2 2 5 +--R (b x - b )sinh(x) + ((4b x - 3b )cosh(x) + 3a b x - 4a b )sinh(x) +--R + +--R 3 3 2 2 2 3 2 +--R (5b x - 2b )cosh(x) + (10a b x - 9a b )cosh(x) + (2b + 4a b)x +--R + +--R 2 +--R - 5a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 +--R 2b cosh(x) + (8a b x - 2a b )cosh(x) +--R + +--R 3 2 3 2 2 3 2 3 +--R ((4b + 8a b)x - 2b - 8a b)cosh(x) + (4a b + 2a )x - 2a b - 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 2 3 +--R (- 5b x + 3b )cosh(x) + (- 6a b x + 8a b )cosh(x) +--R + +--R 3 3 2 2 2 3 2 3 +--R (4b x - 4b + 2a b)cosh(x) + ((10a b + 2a )x - 8a b - 2a )cosh(x) +--R + +--R 3 2 3 2 +--R (b + 4a b)x + b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 2 4 +--R (- 4b x + b )cosh(x) + (- 11a b x + 6a b )cosh(x) +--R + +--R 3 2 3 2 3 +--R ((4b - 8a b)x - 2b + 8a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 2 +--R ((10a b - 2a )x - 8a b + 2a )cosh(x) + (8a b x + b - 8a b)cosh(x) +--R + +--R 2 3 2 3 +--R (a b + 2a )x + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 3 6 2 2 5 +--R - b x cosh(x) + (- 4a b x + a b )cosh(x) +--R + +--R 3 2 2 4 2 3 2 3 3 +--R ((2b - 4a b)x + 3a b)cosh(x) + ((4a b - 2a )x - 2a b + 2a )cosh(x) +--R + +--R 3 2 2 2 3 2 3 2 +--R ((- b + 4a b)x - 4a b)cosh(x) + (2a x + a b - 2a )cosh(x) + a b +--R / +--R 4 6 4 3 5 +--R b sinh(x) + (4b cosh(x) + 6a b )sinh(x) +--R + +--R 4 2 3 4 2 2 4 +--R (6b cosh(x) + 20a b cosh(x) - 2b + 13a b )sinh(x) +--R + +--R 4 3 3 2 4 2 2 3 +--R 4b cosh(x) + 24a b cosh(x) + (- 4b + 36a b )cosh(x) - 8a b +--R + +--R 3 +--R 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 3 3 4 2 2 2 +--R b cosh(x) + 12a b cosh(x) + (- 2b + 34a b )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 12a b + 28a b)cosh(x) + b - 10a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R 2a b cosh(x) + 12a b cosh(x) + (- 4a b + 20a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (- 12a b + 8a )cosh(x) + 2a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 2 4 3 3 2 2 4 2 3 +--R a b cosh(x) + 4a b cosh(x) + (- 2a b + 4a )cosh(x) - 4a b cosh(x) +--R + +--R 2 2 +--R a b +--R Type: Expression Integer +--E 250 + +--S 251 of 502 +t0850:= x*(b+a*cosh(x))/(a+b*cosh(x))^2 +--R +--R +--R a x cosh(x) + b x +--R (117) ------------------------------ +--R 2 2 2 +--R b cosh(x) + 2a b cosh(x) + a +--R Type: Expression Integer +--E 251 + +--S 252 of 502 +r0850:= -log(a+b*cosh(x))/b+x*sinh(x)/(a+b*cosh(x)) +--R +--R +--R (- b cosh(x) - a)log(b cosh(x) + a) + b x sinh(x) +--R (118) ------------------------------------------------- +--R 2 +--R b cosh(x) + a b +--R Type: Expression Integer +--E 252 + +--S 253 of 502 +a0850:= integrate(t0850,x) +--R +--R +--R (119) +--R 2 2 +--R - b sinh(x) + (- 2b cosh(x) - 2a)sinh(x) - b cosh(x) - 2a cosh(x) +--R + +--R - b +--R * +--R - 2b cosh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R 2b x sinh(x) + (4b x cosh(x) + 2a x)sinh(x) + 2b x cosh(x) + 2a x cosh(x) +--R / +--R 2 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b +--R Type: Union(Expression Integer,...) +--E 253 + +--S 254 of 502 +m0850:= a0850-r0850 +--R +--R +--R (120) +--R 2 2 2 2 2 +--R (b cosh(x) + a b)sinh(x) + (2b cosh(x) + 4a b cosh(x) + 2a )sinh(x) +--R + +--R 2 3 2 2 2 +--R b cosh(x) + 3a b cosh(x) + (b + 2a )cosh(x) + a b +--R * +--R log(b cosh(x) + a) +--R + +--R 2 2 +--R (- b cosh(x) - a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 2b cosh(x) - 4a b cosh(x) - 2a )sinh(x) - b cosh(x) +--R + +--R 2 2 2 +--R - 3a b cosh(x) + (- b - 2a )cosh(x) - a b +--R * +--R - 2b cosh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 2 2 2 +--R - b x sinh(x) + (3b x cosh(x) + 4a b x cosh(x) + (- b + 2a )x)sinh(x) +--R + +--R 2 3 2 2 +--R 2b x cosh(x) + 4a b x cosh(x) + 2a x cosh(x) +--R / +--R 3 2 2 3 2 2 2 +--R (b cosh(x) + a b )sinh(x) + (2b cosh(x) + 4a b cosh(x) + 2a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R b cosh(x) + 3a b cosh(x) + (b + 2a b)cosh(x) + a b +--R Type: Expression Integer +--E 254 + +--S 255 of 502 +d0850:= D(m0850,x) +--R +--R +--R (121) +--R 3 6 3 3 2 2 5 +--R b x sinh(x) + ((4b x - b )cosh(x) + 4a b x - a b )sinh(x) +--R + +--R 3 3 2 2 2 3 2 +--R (5b x - 3b )cosh(x) + (11a b x - 6a b )cosh(x) + (2b + 4a b)x +--R + +--R 2 +--R - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 +--R - 2b cosh(x) + (6a b x - 8a b )cosh(x) +--R + +--R 3 2 3 2 2 3 2 3 +--R ((4b + 8a b)x - 2b - 8a b)cosh(x) + (4a b + 2a )x - 2a b - 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 2 3 +--R (- 5b x + 2b )cosh(x) + (- 8a b x + 2a b )cosh(x) +--R + +--R 3 3 2 2 2 3 2 3 +--R (4b x - 4b - 2a b)cosh(x) + ((10a b + 2a )x - 8a b - 2a )cosh(x) +--R + +--R 3 2 2 +--R (b + 4a b)x - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 2 4 +--R (- 4b x + 3b )cosh(x) + (- 10a b x + 9a b )cosh(x) +--R + +--R 3 2 3 2 3 +--R ((4b - 8a b)x - 2b + 8a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 2 +--R ((10a b - 2a )x - 8a b + 2a )cosh(x) + (8a b x - b - 8a b)cosh(x) +--R + +--R 3 2 3 +--R 2a x - a b - 2a +--R * +--R sinh(x) +--R + +--R 3 3 6 2 2 5 +--R (- b x + b )cosh(x) + (- 3a b x + 4a b )cosh(x) +--R + +--R 3 2 2 4 2 3 2 3 3 +--R ((2b - 4a b)x + 5a b)cosh(x) + ((4a b - 2a )x - 2a b + 2a )cosh(x) +--R + +--R 3 2 3 2 2 +--R ((- b + 4a b)x - b - 4a b)cosh(x) +--R + +--R 2 3 2 3 2 +--R ((- a b + 2a )x - 2a b - 2a )cosh(x) - a b +--R / +--R 4 2 3 2 2 4 +--R (b cosh(x) + 2a b cosh(x) + a b )sinh(x) +--R + +--R 4 3 3 2 2 2 3 3 +--R (4b cosh(x) + 12a b cosh(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 4 4 3 3 4 2 2 2 +--R 6b cosh(x) + 24a b cosh(x) + (2b + 34a b )cosh(x) +--R + +--R 3 3 2 2 4 +--R (4a b + 20a b)cosh(x) + 2a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 3 4 4 2 2 3 +--R 4b cosh(x) + 20a b cosh(x) + (4b + 36a b )cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (12a b + 28a b)cosh(x) + (12a b + 8a )cosh(x) + 4a b +--R * +--R sinh(x) +--R + +--R 4 6 3 5 4 2 2 4 +--R b cosh(x) + 6a b cosh(x) + (2b + 13a b )cosh(x) +--R + +--R 3 3 3 4 2 2 4 2 +--R (8a b + 12a b)cosh(x) + (b + 10a b + 4a )cosh(x) +--R + +--R 3 3 2 2 +--R (2a b + 4a b)cosh(x) + a b +--R Type: Expression Integer +--E 255 + +--S 256 of 502 +t0851:= sinh(x)/(a+%i*a*sinh(x))^(1/2) +--R +--R +--R sinh(x) +--R (122) ------------------- +--R +----------------+ +--R \|%i a sinh(x) + a +--R Type: Expression Complex Integer +--E 256 + +--S 257 of 502 +r0851:= 2*(cosh(x)+%i*atan(sinh(1/4*%i*%pi+1/2*x))*_ + cosh(1/4*%i*%pi+1/2*x))/(a*(1+%i*sinh(x)))^(1/2) +--R +--R +--R 2x + %i %pi 2x + %i %pi +--R 2%i cosh(-----------)atan(sinh(-----------)) + 2cosh(x) +--R 4 4 +--R (123) ------------------------------------------------------- +--R +----------------+ +--R \|%i a sinh(x) + a +--R Type: Expression Complex Integer +--E 257 + +--S 258 of 502 +a0851:= integrate(t0851,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 258 + +--S 259 of 502 +--m0851:= a0851-r0851 +--E 259 + +--S 260 of 502 +--d0851:= D(m0851,x) +--E 260 + +--S 261 of 502 +t0852:= sinh(x)/(a-%i*a*sinh(x))^(1/2) +--R +--R +--R sinh(x) +--R (124) --------------------- +--R +------------------+ +--R \|- %i a sinh(x) + a +--R Type: Expression Complex Integer +--E 261 + +--S 262 of 502 +r0852:= 2*(cosh(x)+%i*atanh(cosh(1/4*%i*%pi+1/2*x))*_ + sinh(1/4*%i*%pi+1/2*x))/(-a*(-1+%i*sinh(x)))^(1/2) +--R +--R +--R 2x + %i %pi 2x + %i %pi +--R 2%i sinh(-----------)atanh(cosh(-----------)) + 2cosh(x) +--R 4 4 +--R (125) -------------------------------------------------------- +--R +------------------+ +--R \|- %i a sinh(x) + a +--R Type: Expression Complex Integer +--E 262 + +--S 263 of 502 +a0852:= integrate(t0852,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 263 + +--S 264 of 502 +--m0852:= a0852-r0852 +--E 264 + +--S 265 of 502 +--d0852:= D(m0852,x) +--E 265 + +--S 266 of 502 +t0853:= sinh(x)/(a+b*sinh(x))^(1/2) +--R +--R +--R sinh(x) +--R (126) ---------------- +--R +-------------+ +--R \|b sinh(x) + a +--R Type: Expression Integer +--E 266 + +--S 267 of 502 +r0853:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*x,2*%i*b/(a-%i*b))*_ + (a+b*sinh(x))^(1/2)/b/((a+b*sinh(x))/(a-%i*b))^(1/2)+_ + 2*%i*a*EllipticF(-1/4*%pi+1/2*%i*x,2*%i*b/(a-%i*b))*_ + ((a+b*sinh(x))/(a-%i*b))^(1/2)/b/(a+b*sinh(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R Fraction Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 502 +a0853:= integrate(t0853,x) +--R +--R +--R x +--R ++ sinh(%I) +--R (127) | ----------------- d%I +--R ++ +--------------+ +--R \|b sinh(%I) + a +--R Type: Union(Expression Integer,...) +--E 268 + +--S 269 of 502 +--m0853:= a0853-r0853 +--E 269 + +--S 270 of 502 +--d0853:= D(m0853,x) +--E 270 + +--S 271 of 502 +t0854:= (A+B*sinh(x))/(a+%i*a*sinh(x))^(1/2) +--R +--R +--R B sinh(x) + A +--R (128) ------------------- +--R +----------------+ +--R \|%i a sinh(x) + a +--R Type: Expression Complex Integer +--E 271 + +--S 272 of 502 +r0854:= 2*B*cosh(x)/(a+%i*a*sinh(x))^(1/2)-2*%i*(%i*A-B)*_ + atan(sinh(1/4*%i*%pi+1/2*x))*cosh(1/4*%i*%pi+1/2*x)/_ + (a+%i*a*sinh(x))^(1/2) +--R +--R +--R 2x + %i %pi 2x + %i %pi +--R (2%i B + 2A)cosh(-----------)atan(sinh(-----------)) + 2B cosh(x) +--R 4 4 +--R (129) ----------------------------------------------------------------- +--R +----------------+ +--R \|%i a sinh(x) + a +--R Type: Expression Complex Integer +--E 272 + +--S 273 of 502 +a0854:= integrate(t0854,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 273 + +--S 274 of 502 +--m0854:= a0854-r0854 +--E 274 + +--S 275 of 502 +--d0854:= D(m0854,x) +--E 275 + +--S 276 of 502 +t0855:= (A+B*sinh(x))/(a-%i*a*sinh(x))^(1/2) +--R +--R +--R B sinh(x) + A +--R (130) --------------------- +--R +------------------+ +--R \|- %i a sinh(x) + a +--R Type: Expression Complex Integer +--E 276 + +--S 277 of 502 +r0855:= 2*B*cosh(x)/(a-%i*a*sinh(x))^(1/2)+2*%i*(%i*A+B)*_ + atanh(cosh(1/4*%i*%pi+1/2*x))*sinh(1/4*%i*%pi+1/2*x)/_ + (a-%i*a*sinh(x))^(1/2) +--R +--R +--R 2x + %i %pi 2x + %i %pi +--R (2%i B - 2A)sinh(-----------)atanh(cosh(-----------)) + 2B cosh(x) +--R 4 4 +--R (131) ------------------------------------------------------------------ +--R +------------------+ +--R \|- %i a sinh(x) + a +--R Type: Expression Complex Integer +--E 277 + +--S 278 of 502 +a0855:= integrate(t0855,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 278 + +--S 279 of 502 +--m0855:= a0855-r0855 +--E 279 + +--S 280 of 502 +--d0855:= D(m0855,x) +--E 280 + +--S 281 of 502 +t0856:= (A+B*sinh(x))/(a+b*sinh(x))^(1/2) +--R +--R +--R B sinh(x) + A +--R (132) ---------------- +--R +-------------+ +--R \|b sinh(x) + a +--R Type: Expression Integer +--E 281 + +--S 282 of 502 +r0856:= -2*%i*B*EllipticE(-1/4*%pi+1/2*%i*x,2*%i*b/(a-%i*b))*_ + (a+b*sinh(x))^(1/2)/b/((a+b*sinh(x))/(a-%i*b))^(1/2)-_ + 2*%i*(A*b-a*B)*EllipticF(-1/4*%pi+1/2*%i*x,2*%i*b/(a-%i*b))*_ + ((a+b*sinh(x))/(a-%i*b))^(1/2)/b/(a+b*sinh(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R Fraction Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 282 + +--S 283 of 502 +a0856:= integrate(t0856,x) +--R +--R +--R x +--R ++ B sinh(%I) + A +--R (133) | ----------------- d%I +--R ++ +--------------+ +--R \|b sinh(%I) + a +--R Type: Union(Expression Integer,...) +--E 283 + +--S 284 of 502 +--m0856:= a0856-r0856 +--E 284 + +--S 285 of 502 +--d0856:= D(m0856,x) +--E 285 + +--S 286 of 502 +t0857:= cosh(x)/(a+a*cosh(x))^(1/2) +--R +--R +--R cosh(x) +--R (134) ---------------- +--R +-------------+ +--R \|a cosh(x) + a +--R Type: Expression Integer +--E 286 + +--S 287 of 502 +r0857:= -2*(atan(sinh(1/2*x))*cosh(1/2*x)-sinh(x))/(a*(1+cosh(x)))^(1/2) +--R +--R +--R x x +--R - 2cosh(-)atan(sinh(-)) + 2sinh(x) +--R 2 2 +--R (135) ---------------------------------- +--R +-------------+ +--R \|a cosh(x) + a +--R Type: Expression Integer +--E 287 + +--S 288 of 502 +a0857:= integrate(t0857,x) +--R +--R +--R (136) +--R +-+ +-------------------+ +--R |2 | a +--R (2sinh(x) + 2cosh(x)) |- |------------------- +--R \|a \|2sinh(x) + 2cosh(x) +--R * +--R +-------------------+ +--R | a +--R 2 |------------------- +--R \|2sinh(x) + 2cosh(x) +--R atan(-----------------------) +--R +-+ +--R |2 +--R a |- +--R \|a +--R + +--R sinh(x) + cosh(x) - 1 +--R / +--R +-------------------+ +--R | a +--R (sinh(x) + cosh(x)) |------------------- +--R \|2sinh(x) + 2cosh(x) +--R Type: Union(Expression Integer,...) +--E 288 + +--S 289 of 502 +m0857:= a0857-r0857 +--R +--R +--R (137) +--R +-+ +-------------------+ +--R |2 | a +-------------+ +--R (2sinh(x) + 2cosh(x)) |- |------------------- \|a cosh(x) + a +--R \|a \|2sinh(x) + 2cosh(x) +--R * +--R +-------------------+ +--R | a +--R 2 |------------------- +--R \|2sinh(x) + 2cosh(x) +--R atan(-----------------------) +--R +-+ +--R |2 +--R a |- +--R \|a +--R + +--R +-------------+ +--R (sinh(x) + cosh(x) - 1)\|a cosh(x) + a +--R + +--R x x x 2 +--R (2cosh(-)sinh(x) + 2cosh(-)cosh(x))atan(sinh(-)) - 2sinh(x) +--R 2 2 2 +--R + +--R - 2cosh(x)sinh(x) +--R * +--R +-------------------+ +--R | a +--R |------------------- +--R \|2sinh(x) + 2cosh(x) +--R / +--R +-------------------+ +--R | a +-------------+ +--R (sinh(x) + cosh(x)) |------------------- \|a cosh(x) + a +--R \|2sinh(x) + 2cosh(x) +--R Type: Expression Integer +--E 289 + +--S 290 of 502 +d0857:= D(m0857,x) +--R +--R +--R (138) +--R x 2 2 +--R ((cosh(x) + 1)sinh(-) + cosh(x) + 1)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R ((2cosh(x) + 2cosh(x))sinh(-) + 2cosh(x) + 2cosh(x))sinh(x) +--R 2 +--R + +--R 3 2 x 2 3 2 +--R (cosh(x) + cosh(x) + cosh(x) + 1)sinh(-) + cosh(x) + cosh(x) +--R 2 +--R + +--R cosh(x) + 1 +--R * +--R +-------------+ +--R \|a cosh(x) + a +--R + +--R x x 2 x 3 +--R (- 2cosh(-)sinh(-) - 2cosh(-))sinh(x) +--R 2 2 2 +--R + +--R x 3 +--R (2cosh(x) + 2)sinh(-) +--R 2 +--R + +--R x x x 2 +--R (- 4cosh(-)cosh(x) - 2cosh(-))sinh(-) +--R 2 2 2 +--R + +--R x x x +--R (2cosh(x) + 2)sinh(-) - 4cosh(-)cosh(x) - 2cosh(-) +--R 2 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 2 x 3 +--R (4cosh(x) + 6cosh(x) + 2)sinh(-) +--R 2 +--R + +--R x 2 x x 2 +--R (- 2cosh(-)cosh(x) - 2cosh(-)cosh(x))sinh(-) +--R 2 2 2 +--R + +--R 2 x x 2 +--R (4cosh(x) + 6cosh(x) + 2)sinh(-) - 2cosh(-)cosh(x) +--R 2 2 +--R + +--R x +--R - 2cosh(-)cosh(x) +--R 2 +--R * +--R sinh(x) +--R + +--R 3 2 x 3 +--R (2cosh(x) + 4cosh(x) + 2cosh(x))sinh(-) +--R 2 +--R + +--R 3 2 x +--R (2cosh(x) + 4cosh(x) + 2cosh(x))sinh(-) +--R 2 +--R * +--R x +--R atan(sinh(-)) +--R 2 +--R + +--R x 2 4 +--R (2sinh(-) + 2)sinh(x) +--R 2 +--R + +--R x 2 3 +--R ((4cosh(x) + 2)sinh(-) + 4cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R (- 2cosh(x) - 2cosh(x))sinh(-) - 2cosh(x) +--R 2 +--R + +--R x 2 x 2 +--R (2cosh(-) - 2)cosh(x) + 2cosh(-) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 x 2 3 +--R (- 8cosh(x) - 12cosh(x) - 4cosh(x))sinh(-) - 8cosh(x) +--R 2 +--R + +--R x 2 2 x 2 x 2 +--R (4cosh(-) - 12)cosh(x) + (6cosh(-) - 4)cosh(x) + 2cosh(-) +--R 2 2 2 +--R * +--R sinh(x) +--R + +--R 4 3 2 x 2 4 +--R (- 4cosh(x) - 8cosh(x) - 4cosh(x) )sinh(-) - 4cosh(x) +--R 2 +--R + +--R x 2 3 x 2 2 x 2 +--R (2cosh(-) - 8)cosh(x) + (4cosh(-) - 4)cosh(x) + 2cosh(-) cosh(x) +--R 2 2 2 +--R * +--R +-------------------+ +--R | a +--R |------------------- +--R \|2sinh(x) + 2cosh(x) +--R / +--R x 2 2 +--R ((2cosh(x) + 2)sinh(-) + 2cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R ((4cosh(x) + 6cosh(x) + 2)sinh(-) + 4cosh(x) + 6cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 3 2 x 2 3 2 +--R (2cosh(x) + 4cosh(x) + 2cosh(x))sinh(-) + 2cosh(x) + 4cosh(x) +--R 2 +--R + +--R 2cosh(x) +--R * +--R +-------------------+ +--R | a +-------------+ +--R |------------------- \|a cosh(x) + a +--R \|2sinh(x) + 2cosh(x) +--R Type: Expression Integer +--E 290 + +--S 291 of 502 +t0858:= cosh(x)/(a-a*cosh(x))^(1/2) +--R +--R +--R cosh(x) +--R (139) ------------------ +--R +---------------+ +--R \|- a cosh(x) + a +--R Type: Expression Integer +--E 291 + +--S 292 of 502 +r0858:= -2*(atanh(cosh(1/2*x))*sinh(1/2*x)-sinh(x))/(-(cosh(x)-1)*a)^(1/2) +--R +--R +--R x x +--R - 2sinh(-)atanh(cosh(-)) + 2sinh(x) +--R 2 2 +--R (140) ----------------------------------- +--R +---------------+ +--R \|- a cosh(x) + a +--R Type: Expression Integer +--E 292 + +--S 293 of 502 +a0858:= integrate(t0858,x) +--R +--R +--R (141) +--R +---+ +---------------------+ +--R | 2 | a +--R (sinh(x) + cosh(x)) |- - |- ------------------- +--R \| a \| 2sinh(x) + 2cosh(x) +--R * +--R log +--R +---+ +---------------------+ +--R | 2 | a +--R (2sinh(x) + 2cosh(x)) |- - |- ------------------- - sinh(x) +--R \| a \| 2sinh(x) + 2cosh(x) +--R + +--R - cosh(x) - 1 +--R / +--R sinh(x) + cosh(x) - 1 +--R + +--R sinh(x) + cosh(x) + 1 +--R / +--R +---------------------+ +--R | a +--R (sinh(x) + cosh(x)) |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Union(Expression Integer,...) +--E 293 + +--S 294 of 502 +m0858:= a0858-r0858 +--R +--R +--R (142) +--R +---+ +---------------------+ +--R | 2 +---------------+ | a +--R (sinh(x) + cosh(x)) |- - \|- a cosh(x) + a |- ------------------- +--R \| a \| 2sinh(x) + 2cosh(x) +--R * +--R log +--R +---+ +---------------------+ +--R | 2 | a +--R (2sinh(x) + 2cosh(x)) |- - |- ------------------- - sinh(x) +--R \| a \| 2sinh(x) + 2cosh(x) +--R + +--R - cosh(x) - 1 +--R / +--R sinh(x) + cosh(x) - 1 +--R + +--R x x x 2 +--R (2sinh(-)sinh(x) + 2cosh(x)sinh(-))atanh(cosh(-)) - 2sinh(x) +--R 2 2 2 +--R + +--R - 2cosh(x)sinh(x) +--R * +--R +---------------------+ +--R | a +--R |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R + +--R +---------------+ +--R (sinh(x) + cosh(x) + 1)\|- a cosh(x) + a +--R / +--R +---------------------+ +--R +---------------+ | a +--R (sinh(x) + cosh(x))\|- a cosh(x) + a |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Expression Integer +--E 294 + +--S 295 of 502 +d0858:= D(m0858,x) +--R +--R +--R (143) +--R x 2 x 3 +--R (- 2cosh(-) + 2)sinh(-)sinh(x) +--R 2 2 +--R + +--R x 2 x 2 x +--R ((- 4cosh(-) + 4)cosh(x) + 2cosh(-) - 2)sinh(-) +--R 2 2 2 +--R + +--R x 3 x x 3 x +--R (2cosh(-) - 2cosh(-))cosh(x) - 2cosh(-) + 2cosh(-) +--R 2 2 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R x 2 2 x 2 x +--R ((- 2cosh(-) + 2)cosh(x) + (2cosh(-) - 2)cosh(x))sinh(-) +--R 2 2 2 +--R + +--R x 3 x 2 +--R (4cosh(-) - 4cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x x 3 x +--R (- 6cosh(-) + 6cosh(-))cosh(x) + 2cosh(-) - 2cosh(-) +--R 2 2 2 2 +--R * +--R sinh(x) +--R + +--R x 3 x 3 x 3 x 2 +--R (2cosh(-) - 2cosh(-))cosh(x) + (- 4cosh(-) + 4cosh(-))cosh(x) +--R 2 2 2 2 +--R + +--R x 3 x +--R (2cosh(-) - 2cosh(-))cosh(x) +--R 2 2 +--R * +--R x +--R atanh(cosh(-)) +--R 2 +--R + +--R x 2 4 +--R (2cosh(-) - 2)sinh(x) +--R 2 +--R + +--R x 2 x 2 3 +--R ((4cosh(-) - 4)cosh(x) - 2cosh(-) + 2)sinh(x) +--R 2 2 +--R + +--R x 2 x 2 2 +--R (- 2cosh(x) + 2)sinh(-) + (- 2cosh(-) + 2)cosh(x) +--R 2 2 +--R + +--R x 2 +--R (2cosh(-) - 2)cosh(x) +--R 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 2 x 2 x 2 3 +--R (- 4cosh(x) + 6cosh(x) - 2)sinh(-) + (- 8cosh(-) + 8)cosh(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (12cosh(-) - 12)cosh(x) + (- 4cosh(-) + 4)cosh(x) +--R 2 2 +--R * +--R sinh(x) +--R + +--R 3 2 x 2 +--R (- 2cosh(x) + 4cosh(x) - 2cosh(x))sinh(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (- 4cosh(-) + 4)cosh(x) + (8cosh(-) - 8)cosh(x) +--R 2 2 +--R + +--R x 2 2 +--R (- 4cosh(-) + 4)cosh(x) +--R 2 +--R * +--R +---------------------+ +--R | a +--R |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R + +--R x 2 x 2 2 +--R ((cosh(-) - 1)cosh(x) - cosh(-) + 1)sinh(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R ((2cosh(-) - 2)cosh(x) + (- 2cosh(-) + 2)cosh(x))sinh(x) +--R 2 2 +--R + +--R x 2 3 x 2 2 +--R (cosh(-) - 1)cosh(x) + (- cosh(-) + 1)cosh(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (cosh(-) - 1)cosh(x) - cosh(-) + 1 +--R 2 2 +--R * +--R +---------------+ +--R \|- a cosh(x) + a +--R / +--R x 2 x 2 2 +--R ((2cosh(-) - 2)cosh(x) - 2cosh(-) + 2)sinh(x) +--R 2 2 +--R + +--R x 2 2 x 2 x 2 +--R ((4cosh(-) - 4)cosh(x) + (- 6cosh(-) + 6)cosh(x) + 2cosh(-) - 2) +--R 2 2 2 +--R * +--R sinh(x) +--R + +--R x 2 3 x 2 2 +--R (2cosh(-) - 2)cosh(x) + (- 4cosh(-) + 4)cosh(x) +--R 2 2 +--R + +--R x 2 +--R (2cosh(-) - 2)cosh(x) +--R 2 +--R * +--R +---------------------+ +--R +---------------+ | a +--R \|- a cosh(x) + a |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Expression Integer +--E 295 + +--S 296 of 502 +t0859:= cosh(x)/(a+b*cosh(x))^(1/2) +--R +--R +--R cosh(x) +--R (144) ---------------- +--R +-------------+ +--R \|b cosh(x) + a +--R Type: Expression Integer +--E 296 + +--S 297 of 502 +r0859:= -2*%i*(a+b*cosh(x))^(1/2)*(EllipticE(1/2*%i*x,2*b/(a+b))*a+_ + EllipticE(1/2*%i*x,2*b/(a+b))*b-_ + a*EllipticF(1/2*%i*x,2*b/(a+b)))/(a+b)/b/((a+b*cosh(x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Complex Fraction Integer +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 297 + +--S 298 of 502 +a0859:= integrate(t0859,x) +--R +--R +--R x +--R ++ cosh(%I) +--R (145) | ----------------- d%I +--R ++ +--------------+ +--R \|b cosh(%I) + a +--R Type: Union(Expression Integer,...) +--E 298 + +--S 299 of 502 +--m0859:= a0859-r0859 +--E 299 + +--S 300 of 502 +--d0859:= D(m0859,x) +--E 300 + +--S 301 of 502 +t0860:= (A+B*cosh(x))/(a+a*cosh(x))^(1/2) +--R +--R +--R B cosh(x) + A +--R (146) ---------------- +--R +-------------+ +--R \|a cosh(x) + a +--R Type: Expression Integer +--E 301 + +--S 302 of 502 +r0860:= 2*(A-B)*atan(sinh(1/2*x))*cosh(1/2*x)/(a+a*cosh(x))^(1/2)+_ + 2*B*sinh(x)/(a+a*cosh(x))^(1/2) +--R +--R +--R x x +--R (- 2B + 2A)cosh(-)atan(sinh(-)) + 2B sinh(x) +--R 2 2 +--R (147) -------------------------------------------- +--R +-------------+ +--R \|a cosh(x) + a +--R Type: Expression Integer +--E 302 + +--S 303 of 502 +a0860:= integrate(t0860,x) +--R +--R +--R (148) +--R +-+ +-------------------+ +--R |2 | a +--R ((2B - 2A)sinh(x) + (2B - 2A)cosh(x)) |- |------------------- +--R \|a \|2sinh(x) + 2cosh(x) +--R * +--R +-------------------+ +--R | a +--R 2 |------------------- +--R \|2sinh(x) + 2cosh(x) +--R atan(-----------------------) +--R +-+ +--R |2 +--R a |- +--R \|a +--R + +--R B sinh(x) + B cosh(x) - B +--R / +--R +-------------------+ +--R | a +--R (sinh(x) + cosh(x)) |------------------- +--R \|2sinh(x) + 2cosh(x) +--R Type: Union(Expression Integer,...) +--E 303 + +--S 304 of 502 +m0860:= a0860-r0860 +--R +--R +--R (149) +--R +-+ +-------------------+ +--R |2 | a +--R ((2B - 2A)sinh(x) + (2B - 2A)cosh(x)) |- |------------------- +--R \|a \|2sinh(x) + 2cosh(x) +--R * +--R +-------------------+ +--R | a +--R 2 |------------------- +--R +-------------+ \|2sinh(x) + 2cosh(x) +--R \|a cosh(x) + a atan(-----------------------) +--R +-+ +--R |2 +--R a |- +--R \|a +--R + +--R +-------------+ +--R (B sinh(x) + B cosh(x) - B)\|a cosh(x) + a +--R + +--R x x x +--R ((2B - 2A)cosh(-)sinh(x) + (2B - 2A)cosh(-)cosh(x))atan(sinh(-)) +--R 2 2 2 +--R + +--R 2 +--R - 2B sinh(x) - 2B cosh(x)sinh(x) +--R * +--R +-------------------+ +--R | a +--R |------------------- +--R \|2sinh(x) + 2cosh(x) +--R / +--R +-------------------+ +--R | a +-------------+ +--R (sinh(x) + cosh(x)) |------------------- \|a cosh(x) + a +--R \|2sinh(x) + 2cosh(x) +--R Type: Expression Integer +--E 304 + +--S 305 of 502 +d0860:= D(m0860,x) +--R +--R +--R (150) +--R x 2 2 +--R ((B cosh(x) + B)sinh(-) + B cosh(x) + B)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R (2B cosh(x) + (2B + 2A)cosh(x) + 2A)sinh(-) + 2B cosh(x) +--R 2 +--R + +--R (2B + 2A)cosh(x) + 2A +--R * +--R sinh(x) +--R + +--R 3 2 x 2 +--R (B cosh(x) + (B + 2A)cosh(x) + (B + 2A)cosh(x) + B)sinh(-) +--R 2 +--R + +--R 3 2 +--R B cosh(x) + (B + 2A)cosh(x) + (B + 2A)cosh(x) + B +--R * +--R +-------------+ +--R \|a cosh(x) + a +--R + +--R x x 2 x 3 +--R ((- 2B + 2A)cosh(-)sinh(-) + (- 2B + 2A)cosh(-))sinh(x) +--R 2 2 2 +--R + +--R x 3 +--R ((2B - 2A)cosh(x) + 2B - 2A)sinh(-) +--R 2 +--R + +--R x x x 2 +--R ((- 4B + 4A)cosh(-)cosh(x) + (- 2B + 2A)cosh(-))sinh(-) +--R 2 2 2 +--R + +--R x +--R ((2B - 2A)cosh(x) + 2B - 2A)sinh(-) +--R 2 +--R + +--R x x +--R (- 4B + 4A)cosh(-)cosh(x) + (- 2B + 2A)cosh(-) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 2 x 3 +--R ((4B - 4A)cosh(x) + (6B - 6A)cosh(x) + 2B - 2A)sinh(-) +--R 2 +--R + +--R x 2 x +--R ((- 2B + 2A)cosh(-)cosh(x) + (- 2B + 2A)cosh(-)cosh(x)) +--R 2 2 +--R * +--R x 2 +--R sinh(-) +--R 2 +--R + +--R 2 x +--R ((4B - 4A)cosh(x) + (6B - 6A)cosh(x) + 2B - 2A)sinh(-) +--R 2 +--R + +--R x 2 x +--R (- 2B + 2A)cosh(-)cosh(x) + (- 2B + 2A)cosh(-)cosh(x) +--R 2 2 +--R * +--R sinh(x) +--R + +--R 3 2 +--R ((2B - 2A)cosh(x) + (4B - 4A)cosh(x) + (2B - 2A)cosh(x)) +--R * +--R x 3 +--R sinh(-) +--R 2 +--R + +--R 3 2 x +--R ((2B - 2A)cosh(x) + (4B - 4A)cosh(x) + (2B - 2A)cosh(x))sinh(-) +--R 2 +--R * +--R x +--R atan(sinh(-)) +--R 2 +--R + +--R x 2 4 +--R (2B sinh(-) + 2B)sinh(x) +--R 2 +--R + +--R x 2 3 +--R ((4B cosh(x) + 2B)sinh(-) + 4B cosh(x) + 2B)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R (- 2B cosh(x) - 2B cosh(x))sinh(-) - 2B cosh(x) +--R 2 +--R + +--R x 2 x 2 +--R ((2B - 2A)cosh(-) - 2B)cosh(x) + (2B - 2A)cosh(-) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 x 2 3 +--R (- 8B cosh(x) - 12B cosh(x) - 4B cosh(x))sinh(-) - 8B cosh(x) +--R 2 +--R + +--R x 2 2 +--R ((4B - 4A)cosh(-) - 12B)cosh(x) +--R 2 +--R + +--R x 2 x 2 +--R ((6B - 6A)cosh(-) - 4B)cosh(x) + (2B - 2A)cosh(-) +--R 2 2 +--R * +--R sinh(x) +--R + +--R 4 3 2 x 2 4 +--R (- 4B cosh(x) - 8B cosh(x) - 4B cosh(x) )sinh(-) - 4B cosh(x) +--R 2 +--R + +--R x 2 3 x 2 2 +--R ((2B - 2A)cosh(-) - 8B)cosh(x) + ((4B - 4A)cosh(-) - 4B)cosh(x) +--R 2 2 +--R + +--R x 2 +--R (2B - 2A)cosh(-) cosh(x) +--R 2 +--R * +--R +-------------------+ +--R | a +--R |------------------- +--R \|2sinh(x) + 2cosh(x) +--R / +--R x 2 2 +--R ((2cosh(x) + 2)sinh(-) + 2cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R ((4cosh(x) + 6cosh(x) + 2)sinh(-) + 4cosh(x) + 6cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 3 2 x 2 3 2 +--R (2cosh(x) + 4cosh(x) + 2cosh(x))sinh(-) + 2cosh(x) + 4cosh(x) +--R 2 +--R + +--R 2cosh(x) +--R * +--R +-------------------+ +--R | a +-------------+ +--R |------------------- \|a cosh(x) + a +--R \|2sinh(x) + 2cosh(x) +--R Type: Expression Integer +--E 305 + +--S 306 of 502 +t0861:= (A+B*cosh(x))/(a-a*cosh(x))^(1/2) +--R +--R +--R B cosh(x) + A +--R (151) ------------------ +--R +---------------+ +--R \|- a cosh(x) + a +--R Type: Expression Integer +--E 306 + +--S 307 of 502 +r0861:= -2*(A+B)*atanh(cosh(1/2*x))*sinh(1/2*x)/(a-a*cosh(x))^(1/2)+_ + 2*B*sinh(x)/(a-a*cosh(x))^(1/2) +--R +--R +--R x x +--R (- 2B - 2A)sinh(-)atanh(cosh(-)) + 2B sinh(x) +--R 2 2 +--R (152) --------------------------------------------- +--R +---------------+ +--R \|- a cosh(x) + a +--R Type: Expression Integer +--E 307 + +--S 308 of 502 +a0861:= integrate(t0861,x) +--R +--R +--R (153) +--R +---+ +---------------------+ +--R | 2 | a +--R ((B + A)sinh(x) + (B + A)cosh(x)) |- - |- ------------------- +--R \| a \| 2sinh(x) + 2cosh(x) +--R * +--R log +--R +---+ +---------------------+ +--R | 2 | a +--R (2sinh(x) + 2cosh(x)) |- - |- ------------------- - sinh(x) +--R \| a \| 2sinh(x) + 2cosh(x) +--R + +--R - cosh(x) - 1 +--R / +--R sinh(x) + cosh(x) - 1 +--R + +--R B sinh(x) + B cosh(x) + B +--R / +--R +---------------------+ +--R | a +--R (sinh(x) + cosh(x)) |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Union(Expression Integer,...) +--E 308 + +--S 309 of 502 +m0861:= a0861-r0861 +--R +--R +--R (154) +--R +---+ +--R | 2 +---------------+ +--R ((B + A)sinh(x) + (B + A)cosh(x)) |- - \|- a cosh(x) + a +--R \| a +--R * +--R +---------------------+ +--R | a +--R |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R * +--R log +--R +---+ +---------------------+ +--R | 2 | a +--R (2sinh(x) + 2cosh(x)) |- - |- ------------------- - sinh(x) +--R \| a \| 2sinh(x) + 2cosh(x) +--R + +--R - cosh(x) - 1 +--R / +--R sinh(x) + cosh(x) - 1 +--R + +--R x x x +--R ((2B + 2A)sinh(-)sinh(x) + (2B + 2A)cosh(x)sinh(-))atanh(cosh(-)) +--R 2 2 2 +--R + +--R 2 +--R - 2B sinh(x) - 2B cosh(x)sinh(x) +--R * +--R +---------------------+ +--R | a +--R |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R + +--R +---------------+ +--R (B sinh(x) + B cosh(x) + B)\|- a cosh(x) + a +--R / +--R +---------------------+ +--R +---------------+ | a +--R (sinh(x) + cosh(x))\|- a cosh(x) + a |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Expression Integer +--E 309 + +--S 310 of 502 +d0861:= D(m0861,x) +--R +--R +--R (155) +--R x 2 x 3 +--R ((- 2B - 2A)cosh(-) + 2B + 2A)sinh(-)sinh(x) +--R 2 2 +--R + +--R x 2 +--R ((- 4B - 4A)cosh(-) + 4B + 4A)cosh(x) +--R 2 +--R + +--R x 2 +--R (2B + 2A)cosh(-) - 2B - 2A +--R 2 +--R * +--R x +--R sinh(-) +--R 2 +--R + +--R x 3 x +--R ((2B + 2A)cosh(-) + (- 2B - 2A)cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x +--R (- 2B - 2A)cosh(-) + (2B + 2A)cosh(-) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R x 2 2 +--R ((- 2B - 2A)cosh(-) + 2B + 2A)cosh(x) +--R 2 +--R + +--R x 2 +--R ((2B + 2A)cosh(-) - 2B - 2A)cosh(x) +--R 2 +--R * +--R x +--R sinh(-) +--R 2 +--R + +--R x 3 x 2 +--R ((4B + 4A)cosh(-) + (- 4B - 4A)cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x +--R ((- 6B - 6A)cosh(-) + (6B + 6A)cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x +--R (2B + 2A)cosh(-) + (- 2B - 2A)cosh(-) +--R 2 2 +--R * +--R sinh(x) +--R + +--R x 3 x 3 +--R ((2B + 2A)cosh(-) + (- 2B - 2A)cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x 2 +--R ((- 4B - 4A)cosh(-) + (4B + 4A)cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x +--R ((2B + 2A)cosh(-) + (- 2B - 2A)cosh(-))cosh(x) +--R 2 2 +--R * +--R x +--R atanh(cosh(-)) +--R 2 +--R + +--R x 2 4 +--R (2B cosh(-) - 2B)sinh(x) +--R 2 +--R + +--R x 2 x 2 3 +--R ((4B cosh(-) - 4B)cosh(x) - 2B cosh(-) + 2B)sinh(x) +--R 2 2 +--R + +--R x 2 +--R ((- 2B - 2A)cosh(x) + 2B + 2A)sinh(-) +--R 2 +--R + +--R x 2 2 x 2 +--R (- 2B cosh(-) + 2B)cosh(x) + (2B cosh(-) - 2B)cosh(x) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 2 x 2 +--R ((- 4B - 4A)cosh(x) + (6B + 6A)cosh(x) - 2B - 2A)sinh(-) +--R 2 +--R + +--R x 2 3 x 2 2 +--R (- 8B cosh(-) + 8B)cosh(x) + (12B cosh(-) - 12B)cosh(x) +--R 2 2 +--R + +--R x 2 +--R (- 4B cosh(-) + 4B)cosh(x) +--R 2 +--R * +--R sinh(x) +--R + +--R 3 2 +--R ((- 2B - 2A)cosh(x) + (4B + 4A)cosh(x) + (- 2B - 2A)cosh(x)) +--R * +--R x 2 +--R sinh(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (- 4B cosh(-) + 4B)cosh(x) + (8B cosh(-) - 8B)cosh(x) +--R 2 2 +--R + +--R x 2 2 +--R (- 4B cosh(-) + 4B)cosh(x) +--R 2 +--R * +--R +---------------------+ +--R | a +--R |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R + +--R x 2 x 2 2 +--R ((B cosh(-) - B)cosh(x) - B cosh(-) + B)sinh(x) +--R 2 2 +--R + +--R x 2 2 +--R (2B cosh(-) - 2B)cosh(x) +--R 2 +--R + +--R x 2 x 2 +--R ((- 2B + 2A)cosh(-) + 2B - 2A)cosh(x) - 2A cosh(-) + 2A +--R 2 2 +--R * +--R sinh(x) +--R + +--R x 2 3 x 2 2 +--R (B cosh(-) - B)cosh(x) + ((- B + 2A)cosh(-) + B - 2A)cosh(x) +--R 2 2 +--R + +--R x 2 x 2 +--R ((B - 2A)cosh(-) - B + 2A)cosh(x) - B cosh(-) + B +--R 2 2 +--R * +--R +---------------+ +--R \|- a cosh(x) + a +--R / +--R x 2 x 2 2 +--R ((2cosh(-) - 2)cosh(x) - 2cosh(-) + 2)sinh(x) +--R 2 2 +--R + +--R x 2 2 x 2 x 2 +--R ((4cosh(-) - 4)cosh(x) + (- 6cosh(-) + 6)cosh(x) + 2cosh(-) - 2) +--R 2 2 2 +--R * +--R sinh(x) +--R + +--R x 2 3 x 2 2 +--R (2cosh(-) - 2)cosh(x) + (- 4cosh(-) + 4)cosh(x) +--R 2 2 +--R + +--R x 2 +--R (2cosh(-) - 2)cosh(x) +--R 2 +--R * +--R +---------------------+ +--R +---------------+ | a +--R \|- a cosh(x) + a |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Expression Integer +--E 310 + +--S 311 of 502 +t0862:= (A+B*cosh(x))/(a+b*cosh(x))^(1/2) +--R +--R +--R B cosh(x) + A +--R (156) ---------------- +--R +-------------+ +--R \|b cosh(x) + a +--R Type: Expression Integer +--E 311 + +--S 312 of 502 +r0862:= -2*%i*B*(a+b*cosh(x))^(1/2)*EllipticE(1/2*%i*x,2*b/(a+b))/b/_ + ((a+b*cosh(x))/(a+b))^(1/2)-2*%i*(A*b-a*B)*_ + ((a+b*cosh(x))/(a+b))^(1/2)*EllipticF(1/2*%i*x,2*b/(a+b))/_ + b/(a+b*cosh(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Complex Fraction Integer +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 312 + +--S 313 of 502 +a0862:= integrate(t0862,x) +--R +--R +--R x +--R ++ B cosh(%I) + A +--R (157) | ----------------- d%I +--R ++ +--------------+ +--R \|b cosh(%I) + a +--R Type: Union(Expression Integer,...) +--E 313 + +--S 314 of 502 +--m0862:= a0862-r0862 +--E 314 + +--S 315 of 502 +--d0862:= D(m0862,x) +--E 315 + +--S 316 of 502 +t0863:= (1+sinh(x)^2)/(1-sinh(x)^2) +--R +--R +--R 2 +--R - sinh(x) - 1 +--R (158) -------------- +--R 2 +--R sinh(x) - 1 +--R Type: Expression Integer +--E 316 + +--S 317 of 502 +r0863:= -x+atanh(2^(1/2)*tanh(x))*2^(1/2) +--R +--R +--R +-+ +-+ +--R (159) \|2 atanh(\|2 tanh(x)) - x +--R Type: Expression Integer +--E 317 + +--S 318 of 502 +a0863:= integrate(t0863,x) +--R +--R +--R (160) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R - 2x +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 318 + +--S 319 of 502 +m0863:= a0863-r0863 +--R +--R +--R (161) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ +-+ +--R - 2\|2 atanh(\|2 tanh(x)) +--R / +--R 2 +--R Type: Expression Integer +--E 319 + +--S 320 of 502 +d0863:= D(m0863,x) +--R +--R +--R (162) +--R +-+ 4 +-+ 3 +--R (4\|2 - 6)sinh(x) + (24\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 56\|2 + 84)cosh(x) - 8\|2 + 12)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((24\|2 - 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 - 6)cosh(x) + (- 8\|2 + 12)cosh(x) - 12\|2 + 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (4\|2 - 6)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((40\|2 - 60)cosh(x) - 16\|2 + 24)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 - 6)cosh(x) + (- 16\|2 + 24)cosh(x) + 12\|2 - 18 +--R / +--R +-+ 4 +-+ 3 +--R (12\|2 - 18)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((24\|2 - 36)cosh(x) - 40\|2 + 60)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (72\|2 - 96)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (12\|2 - 18)cosh(x) + (- 40\|2 + 60)cosh(x) + 12\|2 - 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 12\|2 + 18)cosh(x) + 20\|2 - 30)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((12\|2 - 16)cosh(x) + (- 36\|2 + 48)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + (20\|2 - 30)cosh(x) - 6\|2 + 9 +--R Type: Expression Integer +--E 320 + +--S 321 of 502 +t0864:= (1-sinh(x)^2)/(1+sinh(x)^2) +--R +--R +--R 2 +--R - sinh(x) + 1 +--R (163) -------------- +--R 2 +--R sinh(x) + 1 +--R Type: Expression Integer +--E 321 + +--S 322 of 502 +r0864:= -x+2*tanh(x) +--R +--R +--R (164) 2tanh(x) - x +--R Type: Expression Integer +--E 322 + +--S 323 of 502 +a0864:= integrate(t0864,x) +--R +--R +--R 2sinh(x) + (- x - 2)cosh(x) +--R (165) --------------------------- +--R cosh(x) +--R Type: Union(Expression Integer,...) +--E 323 + +--S 324 of 502 +m0864:= a0864-r0864 +--R +--R +--R - 2cosh(x)tanh(x) + 2sinh(x) - 2cosh(x) +--R (166) --------------------------------------- +--R cosh(x) +--R Type: Expression Integer +--E 324 + +--S 325 of 502 +d0864:= D(m0864,x) +--R +--R +--R 2 2 2 +--R 2cosh(x) tanh(x) - 2sinh(x) +--R (167) ----------------------------- +--R 2 +--R cosh(x) +--R Type: Expression Integer +--E 325 + +--S 326 of 502 +t0865:= (1+cosh(x)^2)/(1-cosh(x)^2) +--R +--R +--R 2 +--R - cosh(x) - 1 +--R (168) -------------- +--R 2 +--R cosh(x) - 1 +--R Type: Expression Integer +--E 326 + +--S 327 of 502 +r0865:= -x+2*coth(x) +--R +--R +--R (169) 2coth(x) - x +--R Type: Expression Integer +--E 327 + +--S 328 of 502 +a0865:= integrate(t0865,x) +--R +--R +--R (- x - 2)sinh(x) + 2cosh(x) +--R (170) --------------------------- +--R sinh(x) +--R Type: Union(Expression Integer,...) +--E 328 + +--S 329 of 502 +m0865:= a0865-r0865 +--R +--R +--R (- 2coth(x) - 2)sinh(x) + 2cosh(x) +--R (171) ---------------------------------- +--R sinh(x) +--R Type: Expression Integer +--E 329 + +--S 330 of 502 +d0865:= D(m0865,x) +--R +--R +--R 2 2 2 +--R 2coth(x) sinh(x) - 2cosh(x) +--R (172) ----------------------------- +--R 2 +--R sinh(x) +--R Type: Expression Integer +--E 330 + +--S 331 of 502 +t0866:= (1-cosh(x)^2)/(1+cosh(x)^2) +--R +--R +--R 2 +--R - cosh(x) + 1 +--R (173) -------------- +--R 2 +--R cosh(x) + 1 +--R Type: Expression Integer +--E 331 + +--S 332 of 502 +r0866:= -x+atanh(1/2*2^(1/2)*tanh(x))*2^(1/2) +--R +--R +--R +-+ +--R +-+ \|2 tanh(x) +--R (174) \|2 atanh(-----------) - x +--R 2 +--R Type: Expression Integer +--E 332 + +--S 333 of 502 +a0866:= integrate(t0866,x) +--R +--R +--R (175) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) - 2\|2 + 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R - 2x +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 333 + +--S 334 of 502 +m0866:= a0866-r0866 +--R +--R +--R (176) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) - 2\|2 + 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +-+ +--R +-+ \|2 tanh(x) +--R - 2\|2 atanh(-----------) +--R 2 +--R / +--R 2 +--R Type: Expression Integer +--E 334 + +--S 335 of 502 +d0866:= D(m0866,x) +--R +--R +--R (177) +--R +-+ 4 +-+ 3 +--R (- 4\|2 + 6)sinh(x) + (24\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 40\|2 + 60)cosh(x) - 16\|2 + 24)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((24\|2 - 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 4\|2 + 6)cosh(x) + (- 16\|2 + 24)cosh(x) - 12\|2 + 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 4\|2 + 6)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((56\|2 - 84)cosh(x) - 8\|2 + 12)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 4\|2 + 6)cosh(x) + (- 8\|2 + 12)cosh(x) + 12\|2 - 18 +--R / +--R +-+ 4 +-+ 3 +--R (6\|2 - 9)sinh(x) + (- 12\|2 + 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((12\|2 - 18)cosh(x) + 20\|2 - 30)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 12\|2 + 16)cosh(x) + (- 36\|2 + 48)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (6\|2 - 9)cosh(x) + (20\|2 - 30)cosh(x) + 6\|2 - 9 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 12\|2 + 18)sinh(x) + (24\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 24\|2 + 36)cosh(x) - 40\|2 + 60)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((24\|2 - 32)cosh(x) + (72\|2 - 96)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 12\|2 + 18)cosh(x) + (- 40\|2 + 60)cosh(x) - 12\|2 + 18 +--R Type: Expression Integer +--E 335 + +--S 336 of 502 +t0867:= (cosh(x)*coth(x))^(1/2) +--R +--R +--R +--------------+ +--R (178) \|cosh(x)coth(x) +--R Type: Expression Integer +--E 336 + +--S 337 of 502 +r0867:= 2*(cosh(x)*coth(x))^(1/2)*tanh(x) +--R +--R +--R +--------------+ +--R (179) 2tanh(x)\|cosh(x)coth(x) +--R Type: Expression Integer +--E 337 + +--S 338 of 502 +a0867:= integrate(t0867,x) +--R +--R +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R (180) ------------------------------------------------ +--R sinh(x) + cosh(x) +--R Type: Union(Expression Integer,...) +--E 338 + +--S 339 of 502 +m0867:= a0867-r0867 +--R +--R +--R (181) +--R +--------------+ +--R (- 2sinh(x) - 2cosh(x))tanh(x)\|cosh(x)coth(x) +--R + +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R sinh(x) + cosh(x) +--R Type: Expression Integer +--E 339 + +--S 340 of 502 +d0867:= D(m0867,x) +--R +--R +--R (182) +--R 2 2 +--------------+ +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)\|cosh(x)coth(x) +--R + +--R 2 3 2 +--R (2cosh(x)coth(x)sinh(x) - 2cosh(x) coth(x))tanh(x) +--R + +--R 3 2 2 +--R - coth(x)sinh(x) + (cosh(x)coth(x) - cosh(x))sinh(x) +--R + +--R 2 3 2 3 +--R cosh(x) coth(x)sinh(x) - cosh(x) coth(x) + cosh(x) +--R * +--R tanh(x) +--R + +--R 2 3 +--R - 2cosh(x)coth(x)sinh(x) + 2cosh(x) coth(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R +---------------------------------------------+ +--R | 2 2 +--R 2 2 |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R (sinh(x) - cosh(x) ) |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R Type: Expression Integer +--E 340 + +--S 341 of 502 +t0868:= (cosh(x)*coth(x))^(3/2) +--R +--R +--R +--------------+ +--R (183) cosh(x)coth(x)\|cosh(x)coth(x) +--R Type: Expression Integer +--E 341 + +--S 342 of 502 +r0868:= -2/3*(4-cosh(x)^2)*(cosh(x)*coth(x))^(1/2)*sech(x) +--R +--R +--R 2 +--------------+ +--R (2cosh(x) - 8)sech(x)\|cosh(x)coth(x) +--R (184) --------------------------------------- +--R 3 +--R Type: Expression Integer +--E 342 + +--S 343 of 502 +a0868:= integrate(t0868,x) +--R +--R +--R (185) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 14)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 28cosh(x))sinh(x) + cosh(x) - 14cosh(x) + 1 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) - 6)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) - 12cosh(x))sinh(x) + 6cosh(x) - 6cosh(x) +--R Type: Union(Expression Integer,...) +--E 343 + +--S 344 of 502 +m0868:= a0868-r0868 +--R +--R +--R (186) +--R 2 4 +--R (- 4cosh(x) + 16)sech(x)sinh(x) +--R + +--R 3 3 +--R (- 16cosh(x) + 64cosh(x))sech(x)sinh(x) +--R + +--R 4 2 2 +--R (- 24cosh(x) + 100cosh(x) - 16)sech(x)sinh(x) +--R + +--R 5 3 +--R (- 16cosh(x) + 72cosh(x) - 32cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 +--R (- 4cosh(x) + 20cosh(x) - 16cosh(x) )sech(x) +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 14)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 28cosh(x))sinh(x) + cosh(x) - 14cosh(x) + 1 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) - 6)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) - 12cosh(x))sinh(x) + 6cosh(x) - 6cosh(x) +--R Type: Expression Integer +--E 344 + +--S 345 of 502 +d0868:= D(m0868,x) +--R +--R +--R (187) +--R 6 5 2 4 +--R - 3sinh(x) - 18cosh(x)sinh(x) + (- 45cosh(x) - 9)sinh(x) +--R + +--R 3 3 +--R (- 60cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) - 54cosh(x) - 9)sinh(x) +--R + +--R 5 3 6 +--R (- 18cosh(x) - 36cosh(x) - 18cosh(x))sinh(x) - 3cosh(x) +--R + +--R 4 2 +--R - 9cosh(x) - 9cosh(x) - 3 +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R + +--R 3 5 +--R (4cosh(x) - 16cosh(x))coth(x)sech(x)sinh(x) +--R + +--R 4 2 4 +--R (12cosh(x) - 48cosh(x) )coth(x)sech(x)sinh(x) +--R + +--R 5 3 3 +--R (8cosh(x) - 36cosh(x) + 16cosh(x))coth(x)sech(x)sinh(x) +--R + +--R 6 4 2 2 +--R (- 8cosh(x) + 28cosh(x) + 16cosh(x) )coth(x)sech(x)sinh(x) +--R + +--R 7 5 3 +--R (- 12cosh(x) + 52cosh(x) - 16cosh(x) )coth(x)sech(x)sinh(x) +--R + +--R 8 6 4 +--R (- 4cosh(x) + 20cosh(x) - 16cosh(x) )coth(x)sech(x) +--R * +--R tanh(x) +--R + +--R 2 6 +--R (- 10cosh(x) + 8)coth(x)sech(x)sinh(x) +--R + +--R 3 2 +--R (2cosh(x) - 8cosh(x))coth(x) +--R + +--R 3 3 +--R (- 30cosh(x) + 24cosh(x))coth(x) - 2cosh(x) + 8cosh(x) +--R * +--R 5 +--R sech(x)sinh(x) +--R + +--R 4 2 2 +--R (6cosh(x) - 24cosh(x) )coth(x) +--R + +--R 4 2 4 2 +--R (- 20cosh(x) + 26cosh(x) - 8)coth(x) - 6cosh(x) + 24cosh(x) +--R * +--R 4 +--R sech(x)sinh(x) +--R + +--R 5 3 2 +--R (4cosh(x) - 18cosh(x) + 8cosh(x))coth(x) +--R + +--R 5 3 5 +--R (20cosh(x) - 6cosh(x) - 8cosh(x))coth(x) - 4cosh(x) +--R + +--R 3 +--R 18cosh(x) - 8cosh(x) +--R * +--R 3 +--R sech(x)sinh(x) +--R + +--R 6 4 2 2 +--R (- 4cosh(x) + 14cosh(x) + 8cosh(x) )coth(x) +--R + +--R 6 4 2 6 +--R (30cosh(x) - 34cosh(x) + 8cosh(x) )coth(x) + 4cosh(x) +--R + +--R 4 2 +--R - 14cosh(x) - 8cosh(x) +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 7 5 3 2 +--R (- 6cosh(x) + 26cosh(x) - 8cosh(x) )coth(x) +--R + +--R 7 5 3 7 +--R (10cosh(x) - 18cosh(x) + 8cosh(x) )coth(x) + 6cosh(x) +--R + +--R 5 3 +--R - 26cosh(x) + 8cosh(x) +--R * +--R sech(x)sinh(x) +--R + +--R 8 6 4 2 8 +--R (- 2cosh(x) + 10cosh(x) - 8cosh(x) )coth(x) + 2cosh(x) +--R + +--R 6 4 +--R - 10cosh(x) + 8cosh(x) +--R * +--R sech(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 5 4 2 3 +--R 6sinh(x) + 18cosh(x)sinh(x) + (12cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 2 +--R (- 12cosh(x) - 6cosh(x))sinh(x) + (- 18cosh(x) + 6cosh(x) )sinh(x) +--R + +--R 5 3 +--R - 6cosh(x) + 6cosh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--------------+ +--R |--------------------------------------------- \|cosh(x)coth(x) +--R \| sinh(x) - cosh(x) +--R Type: Expression Integer +--E 345 + +--S 346 of 502 +t0869:= (cosh(x)*coth(x))^(5/2) +--R +--R +--R 2 2 +--------------+ +--R (188) cosh(x) coth(x) \|cosh(x)coth(x) +--R Type: Expression Integer +--E 346 + +--S 347 of 502 +r0869:= 2/15*(cosh(x)*coth(x))^(1/2)*(32-(8-3*cosh(x)^2)*coth(x)^2)*tanh(x) +--R +--R +--R 2 2 +--------------+ +--R ((6cosh(x) - 16)coth(x) + 64)tanh(x)\|cosh(x)coth(x) +--R (189) ------------------------------------------------------- +--R 15 +--R Type: Expression Integer +--E 347 + +--S 348 of 502 +a0869:= integrate(t0869,x) +--R +--R +--R (190) +--R 8 7 2 6 +--R 3sinh(x) + 24cosh(x)sinh(x) + (84cosh(x) + 108)sinh(x) +--R + +--R 3 5 +--R (168cosh(x) + 648cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (210cosh(x) + 1620cosh(x) - 302)sinh(x) +--R + +--R 5 3 3 +--R (168cosh(x) + 2160cosh(x) - 1208cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (84cosh(x) + 1620cosh(x) - 1812cosh(x) + 108)sinh(x) +--R + +--R 7 5 3 +--R (24cosh(x) + 648cosh(x) - 1208cosh(x) + 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 3cosh(x) + 108cosh(x) - 302cosh(x) + 108cosh(x) + 3 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 7 6 2 5 +--R 60sinh(x) + 420cosh(x)sinh(x) + (1260cosh(x) - 120)sinh(x) +--R + +--R 3 4 +--R (2100cosh(x) - 600cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (2100cosh(x) - 1200cosh(x) + 60)sinh(x) +--R + +--R 5 3 2 +--R (1260cosh(x) - 1200cosh(x) + 180cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (420cosh(x) - 600cosh(x) + 180cosh(x) )sinh(x) + 60cosh(x) +--R + +--R 5 3 +--R - 120cosh(x) + 60cosh(x) +--R Type: Union(Expression Integer,...) +--E 348 + +--S 349 of 502 +m0869:= a0869-r0869 +--R +--R +--R (191) +--R 2 2 7 +--R ((- 24cosh(x) + 64)coth(x) - 256)sinh(x) +--R + +--R 3 2 6 +--R ((- 168cosh(x) + 448cosh(x))coth(x) - 1792cosh(x))sinh(x) +--R + +--R 4 2 2 2 +--R ((- 504cosh(x) + 1392cosh(x) - 128)coth(x) - 5376cosh(x) + 512) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 840cosh(x) + 2480cosh(x) - 640cosh(x))coth(x) +--R + +--R 3 +--R - 8960cosh(x) + 2560cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 840cosh(x) + 2720cosh(x) - 1304cosh(x) + 64)coth(x) +--R + +--R 4 2 +--R - 8960cosh(x) + 5120cosh(x) - 256 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 5 3 +--R (- 504cosh(x) + 1824cosh(x) - 1352cosh(x) + 192cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 5 3 +--R - 5376cosh(x) + 5120cosh(x) - 768cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 168cosh(x) + 688cosh(x) - 712cosh(x) + 192cosh(x) )coth(x) +--R + +--R 6 4 2 +--R - 1792cosh(x) + 2560cosh(x) - 768cosh(x) +--R * +--R sinh(x) +--R + +--R 9 7 5 3 2 +--R (- 24cosh(x) + 112cosh(x) - 152cosh(x) + 64cosh(x) )coth(x) +--R + +--R 7 5 3 +--R - 256cosh(x) + 512cosh(x) - 256cosh(x) +--R * +--R +--------------+ +--R tanh(x)\|cosh(x)coth(x) +--R + +--R 8 7 2 6 +--R 3sinh(x) + 24cosh(x)sinh(x) + (84cosh(x) + 108)sinh(x) +--R + +--R 3 5 +--R (168cosh(x) + 648cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (210cosh(x) + 1620cosh(x) - 302)sinh(x) +--R + +--R 5 3 3 +--R (168cosh(x) + 2160cosh(x) - 1208cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (84cosh(x) + 1620cosh(x) - 1812cosh(x) + 108)sinh(x) +--R + +--R 7 5 3 +--R (24cosh(x) + 648cosh(x) - 1208cosh(x) + 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 3cosh(x) + 108cosh(x) - 302cosh(x) + 108cosh(x) + 3 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 7 6 2 5 +--R 60sinh(x) + 420cosh(x)sinh(x) + (1260cosh(x) - 120)sinh(x) +--R + +--R 3 4 +--R (2100cosh(x) - 600cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (2100cosh(x) - 1200cosh(x) + 60)sinh(x) +--R + +--R 5 3 2 +--R (1260cosh(x) - 1200cosh(x) + 180cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (420cosh(x) - 600cosh(x) + 180cosh(x) )sinh(x) + 60cosh(x) +--R + +--R 5 3 +--R - 120cosh(x) + 60cosh(x) +--R Type: Expression Integer +--E 349 + +--S 350 of 502 +d0869:= D(m0869,x) +--R +--R +--R (192) +--R 10 9 2 8 +--R - 15sinh(x) - 150cosh(x)sinh(x) + (- 675cosh(x) - 75)sinh(x) +--R + +--R 3 7 +--R (- 1800cosh(x) - 600cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (- 3150cosh(x) - 2100cosh(x) - 150)sinh(x) +--R + +--R 5 3 5 +--R (- 3780cosh(x) - 4200cosh(x) - 900cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 3150cosh(x) - 5250cosh(x) - 2250cosh(x) - 150)sinh(x) +--R + +--R 7 5 3 3 +--R (- 1800cosh(x) - 4200cosh(x) - 3000cosh(x) - 600cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 675cosh(x) - 2100cosh(x) - 2250cosh(x) - 900cosh(x) - 75) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 150cosh(x) - 600cosh(x) - 900cosh(x) - 600cosh(x) +--R + +--R - 150cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 15cosh(x) - 75cosh(x) - 150cosh(x) - 150cosh(x) - 75cosh(x) +--R + +--R - 15 +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R + +--R 3 3 8 +--R ((24cosh(x) - 64cosh(x))coth(x) + 256cosh(x)coth(x))sinh(x) +--R + +--R 4 2 3 2 +--R ((144cosh(x) - 384cosh(x) )coth(x) + 1536cosh(x) coth(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 3 3 +--R (336cosh(x) - 944cosh(x) + 128cosh(x))coth(x) +--R + +--R 3 +--R (3584cosh(x) - 512cosh(x))coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (336cosh(x) - 1088cosh(x) + 512cosh(x) )coth(x) +--R + +--R 4 2 +--R (3584cosh(x) - 2048cosh(x) )coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 240cosh(x) + 664cosh(x) - 64cosh(x))coth(x) +--R + +--R 3 +--R (- 2560cosh(x) + 256cosh(x))coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 336cosh(x) + 896cosh(x) + 48cosh(x) - 128cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 6 2 +--R (- 3584cosh(x) + 512cosh(x) )coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (- 336cosh(x) + 1136cosh(x) - 640cosh(x) )coth(x) +--R + +--R 7 5 +--R (- 3584cosh(x) + 2560cosh(x) )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 +--R (- 144cosh(x) + 576cosh(x) - 560cosh(x) + 128cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 8 6 4 +--R (- 1536cosh(x) + 2048cosh(x) - 512cosh(x) )coth(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R (- 24cosh(x) + 112cosh(x) - 152cosh(x) + 64cosh(x) )coth(x) +--R + +--R 9 7 5 +--R (- 256cosh(x) + 512cosh(x) - 256cosh(x) )coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 3 9 +--R ((- 60cosh(x) + 32)coth(x) - 128coth(x))sinh(x) +--R + +--R 3 4 +--R (60cosh(x) - 160cosh(x))coth(x) +--R + +--R 3 3 +--R (- 360cosh(x) + 192cosh(x))coth(x) +--R + +--R 3 2 +--R (- 60cosh(x) + 288cosh(x))coth(x) - 768cosh(x)coth(x) +--R + +--R - 128cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 4 +--R (360cosh(x) - 960cosh(x) )coth(x) +--R + +--R 4 2 3 +--R (- 840cosh(x) + 568cosh(x) - 64)coth(x) +--R + +--R 4 2 2 +--R (- 360cosh(x) + 1728cosh(x) )coth(x) +--R + +--R 2 2 +--R (- 1792cosh(x) + 256)coth(x) - 768cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 3 4 +--R (840cosh(x) - 2360cosh(x) + 320cosh(x))coth(x) +--R + +--R 5 3 3 +--R (- 840cosh(x) + 928cosh(x) - 256cosh(x))coth(x) +--R + +--R 5 3 2 +--R (- 840cosh(x) + 4152cosh(x) - 576cosh(x))coth(x) +--R + +--R 3 3 +--R (- 1792cosh(x) + 1024cosh(x))coth(x) - 1792cosh(x) +--R + +--R 256cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 4 +--R (840cosh(x) - 2720cosh(x) + 1280cosh(x) )coth(x) +--R + +--R 4 2 3 +--R (600cosh(x) - 380cosh(x) + 32)coth(x) +--R + +--R 6 4 2 2 +--R (- 840cosh(x) + 4512cosh(x) - 2304cosh(x) )coth(x) +--R + +--R 2 4 2 +--R (1280cosh(x) - 128)coth(x) - 1792cosh(x) + 1024cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 4 +--R (- 600cosh(x) + 1660cosh(x) - 160cosh(x))coth(x) +--R + +--R 7 5 3 3 +--R (840cosh(x) - 448cosh(x) - 120cosh(x) + 64cosh(x))coth(x) +--R + +--R 5 3 2 +--R (600cosh(x) - 2940cosh(x) + 288cosh(x))coth(x) +--R + +--R 5 3 +--R (1792cosh(x) - 256cosh(x))coth(x) + 1280cosh(x) - 128cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 840cosh(x) + 2240cosh(x) + 120cosh(x) - 320cosh(x) ) +--R * +--R 4 +--R coth(x) +--R + +--R 8 6 4 3 +--R (840cosh(x) - 1048cosh(x) + 320cosh(x) )coth(x) +--R + +--R 8 6 4 2 +--R (840cosh(x) - 4032cosh(x) - 120cosh(x) + 576cosh(x) ) +--R * +--R 2 +--R coth(x) +--R + +--R 6 4 6 +--R (1792cosh(x) - 1280cosh(x) )coth(x) + 1792cosh(x) +--R + +--R 2 +--R - 256cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 4 +--R (- 840cosh(x) + 2840cosh(x) - 1600cosh(x) )coth(x) +--R + +--R 9 7 5 3 +--R (360cosh(x) - 672cosh(x) + 376cosh(x) - 64cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 9 7 5 2 +--R (840cosh(x) - 4632cosh(x) + 2880cosh(x) )coth(x) +--R + +--R 7 5 3 +--R (768cosh(x) - 1024cosh(x) + 256cosh(x) )coth(x) +--R + +--R 7 5 +--R 1792cosh(x) - 1280cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 +--R - 360cosh(x) + 1440cosh(x) - 1400cosh(x) +--R + +--R 4 +--R 320cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 10 8 6 4 +--R (60cosh(x) - 152cosh(x) + 124cosh(x) - 32cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 10 8 6 4 +--R (360cosh(x) - 2208cosh(x) + 2424cosh(x) - 576cosh(x) ) +--R * +--R 2 +--R coth(x) +--R + +--R 8 6 4 +--R (128cosh(x) - 256cosh(x) + 128cosh(x) )coth(x) +--R + +--R 8 6 4 +--R 768cosh(x) - 1024cosh(x) + 256cosh(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 4 +--R (- 60cosh(x) + 280cosh(x) - 380cosh(x) + 160cosh(x) )coth(x) +--R + +--R 11 9 7 5 2 +--R (60cosh(x) - 408cosh(x) + 636cosh(x) - 288cosh(x) )coth(x) +--R + +--R 9 7 5 +--R 128cosh(x) - 256cosh(x) + 128cosh(x) +--R * +--R tanh(x) +--R + +--R 3 3 8 +--R ((- 24cosh(x) + 64cosh(x))coth(x) - 256cosh(x)coth(x))sinh(x) +--R + +--R 4 2 3 2 7 +--R ((- 144cosh(x) + 384cosh(x) )coth(x) - 1536cosh(x) coth(x))sinh(x) +--R + +--R 5 3 3 +--R (- 336cosh(x) + 944cosh(x) - 128cosh(x))coth(x) +--R + +--R 3 +--R (- 3584cosh(x) + 512cosh(x))coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- 336cosh(x) + 1088cosh(x) - 512cosh(x) )coth(x) +--R + +--R 4 2 +--R (- 3584cosh(x) + 2048cosh(x) )coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 +--R (240cosh(x) - 664cosh(x) + 64cosh(x))coth(x) +--R + +--R 3 +--R (2560cosh(x) - 256cosh(x))coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (336cosh(x) - 896cosh(x) - 48cosh(x) + 128cosh(x) )coth(x) +--R + +--R 6 2 +--R (3584cosh(x) - 512cosh(x) )coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (336cosh(x) - 1136cosh(x) + 640cosh(x) )coth(x) +--R + +--R 7 5 +--R (3584cosh(x) - 2560cosh(x) )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 3 +--R (144cosh(x) - 576cosh(x) + 560cosh(x) - 128cosh(x) )coth(x) +--R + +--R 8 6 4 +--R (1536cosh(x) - 2048cosh(x) + 512cosh(x) )coth(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R (24cosh(x) - 112cosh(x) + 152cosh(x) - 64cosh(x) )coth(x) +--R + +--R 9 7 5 +--R (256cosh(x) - 512cosh(x) + 256cosh(x) )coth(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 8 7 2 6 +--R 60sinh(x) + 360cosh(x)sinh(x) + (840cosh(x) - 120)sinh(x) +--R + +--R 3 5 2 4 +--R (840cosh(x) - 480cosh(x))sinh(x) + (- 600cosh(x) + 60)sinh(x) +--R + +--R 5 3 +--R (- 840cosh(x) + 120cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 840cosh(x) + 600cosh(x) )sinh(x) +--R + +--R 7 5 3 8 +--R (- 360cosh(x) + 480cosh(x) - 120cosh(x) )sinh(x) - 60cosh(x) +--R + +--R 6 4 +--R 120cosh(x) - 60cosh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--------------+ +--R |--------------------------------------------- \|cosh(x)coth(x) +--R \| sinh(x) - cosh(x) +--R Type: Expression Integer +--E 350 + +--S 351 of 502 +t0870:= (sinh(x)*tanh(x))^(1/2) +--R +--R +--R +--------------+ +--R (193) \|sinh(x)tanh(x) +--R Type: Expression Integer +--E 351 + +--S 352 of 502 +r0870:= 2*coth(x)*(sinh(x)*tanh(x))^(1/2) +--R +--R +--R +--------------+ +--R (194) 2coth(x)\|sinh(x)tanh(x) +--R Type: Expression Integer +--E 352 + +--S 353 of 502 +a0870:= integrate(t0870,x) +--R +--R +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R (195) ------------------------------------------------ +--R sinh(x) + cosh(x) +--R Type: Union(Expression Integer,...) +--E 353 + +--S 354 of 502 +m0870:= a0870-r0870 +--R +--R +--R (196) +--R +--------------+ +--R (- 2coth(x)sinh(x) - 2cosh(x)coth(x))\|sinh(x)tanh(x) +--R + +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R sinh(x) + cosh(x) +--R Type: Expression Integer +--E 354 + +--S 355 of 502 +d0870:= D(m0870,x) +--R +--R +--R (197) +--R 2 2 +--------------+ +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)\|sinh(x)tanh(x) +--R + +--R 3 2 2 +--R (coth(x)sinh(x) - cosh(x) coth(x)sinh(x))tanh(x) +--R + +--R 2 3 2 +--R (2coth(x) - 2)sinh(x) - cosh(x)coth(x)sinh(x) +--R + +--R 2 2 2 3 +--R (- 2cosh(x) coth(x) + 2cosh(x) )sinh(x) + cosh(x) coth(x) +--R * +--R tanh(x) +--R + +--R 3 2 +--R - coth(x)sinh(x) + cosh(x) coth(x)sinh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R +---------------------------------------------+ +--R | 2 2 +--R 2 2 |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R (sinh(x) - cosh(x) ) |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R * +--R +--------------+ +--R \|sinh(x)tanh(x) +--R Type: Expression Integer +--E 355 + +--S 356 of 502 +t0871:= (sinh(x)*tanh(x))^(3/2) +--R +--R +--R +--------------+ +--R (198) sinh(x)tanh(x)\|sinh(x)tanh(x) +--R Type: Expression Integer +--E 356 + +--S 357 of 502 +r0871:= 2/3*csch(x)*(4+sinh(x)^2)*(sinh(x)*tanh(x))^(1/2) +--R +--R +--R 2 +--------------+ +--R (2csch(x)sinh(x) + 8csch(x))\|sinh(x)tanh(x) +--R (199) ---------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 357 + +--S 358 of 502 +a0871:= integrate(t0871,x) +--R +--R +--R (200) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 14)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 28cosh(x))sinh(x) + cosh(x) + 14cosh(x) + 1 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) + 6)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) + 12cosh(x))sinh(x) + 6cosh(x) + 6cosh(x) +--R Type: Union(Expression Integer,...) +--E 358 + +--S 359 of 502 +m0871:= a0871-r0871 +--R +--R +--R (201) +--R 6 5 +--R - 4csch(x)sinh(x) - 16cosh(x)csch(x)sinh(x) +--R + +--R 2 4 +--R (- 24cosh(x) - 20)csch(x)sinh(x) +--R + +--R 3 3 +--R (- 16cosh(x) - 72cosh(x))csch(x)sinh(x) +--R + +--R 4 2 2 +--R (- 4cosh(x) - 100cosh(x) - 16)csch(x)sinh(x) +--R + +--R 3 +--R (- 64cosh(x) - 32cosh(x))csch(x)sinh(x) +--R + +--R 4 2 +--R (- 16cosh(x) - 16cosh(x) )csch(x) +--R * +--R +--------------+ +--R \|sinh(x)tanh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 14)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 28cosh(x))sinh(x) + cosh(x) + 14cosh(x) + 1 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) + 6)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) + 12cosh(x))sinh(x) + 6cosh(x) + 6cosh(x) +--R Type: Expression Integer +--E 359 + +--S 360 of 502 +d0871:= D(m0871,x) +--R +--R +--R (202) +--R 6 5 2 4 +--R - 3sinh(x) - 18cosh(x)sinh(x) + (- 45cosh(x) + 9)sinh(x) +--R + +--R 3 3 +--R (- 60cosh(x) + 36cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) + 54cosh(x) - 9)sinh(x) +--R + +--R 5 3 6 +--R (- 18cosh(x) + 36cosh(x) - 18cosh(x))sinh(x) - 3cosh(x) +--R + +--R 4 2 +--R 9cosh(x) - 9cosh(x) + 3 +--R * +--R +--------------+ +--R \|sinh(x)tanh(x) +--R + +--R 8 7 +--R 2csch(x)sinh(x) + 6cosh(x)csch(x)sinh(x) +--R + +--R 2 6 +--R (4cosh(x) + 10)csch(x)sinh(x) +--R + +--R 3 5 +--R (- 4cosh(x) + 26cosh(x))csch(x)sinh(x) +--R + +--R 4 2 4 +--R (- 6cosh(x) + 14cosh(x) + 8)csch(x)sinh(x) +--R + +--R 5 3 3 +--R (- 2cosh(x) - 18cosh(x) + 8cosh(x))csch(x)sinh(x) +--R + +--R 4 2 2 +--R (- 24cosh(x) - 8cosh(x) )csch(x)sinh(x) +--R + +--R 5 3 +--R (- 8cosh(x) - 8cosh(x) )csch(x)sinh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 8 +--R 4coth(x)csch(x)sinh(x) +--R + +--R 7 +--R (12cosh(x)coth(x) - 10cosh(x))csch(x)sinh(x) +--R + +--R 2 2 6 +--R ((8cosh(x) + 20)coth(x) - 30cosh(x) )csch(x)sinh(x) +--R + +--R 3 3 +--R ((- 8cosh(x) + 52cosh(x))coth(x) - 20cosh(x) - 18cosh(x)) +--R * +--R 5 +--R csch(x)sinh(x) +--R + +--R 4 2 4 +--R (- 12cosh(x) + 28cosh(x) + 16)coth(x) + 20cosh(x) +--R + +--R 2 +--R - 34cosh(x) +--R * +--R 4 +--R csch(x)sinh(x) +--R + +--R 5 3 5 +--R (- 4cosh(x) - 36cosh(x) + 16cosh(x))coth(x) + 30cosh(x) +--R + +--R 3 +--R - 6cosh(x) - 8cosh(x) +--R * +--R 3 +--R csch(x)sinh(x) +--R + +--R 4 2 6 4 +--R (- 48cosh(x) - 16cosh(x) )coth(x) + 10cosh(x) + 26cosh(x) +--R + +--R 2 +--R - 8cosh(x) +--R * +--R 2 +--R csch(x)sinh(x) +--R + +--R 5 3 5 3 +--R ((- 16cosh(x) - 16cosh(x) )coth(x) + 24cosh(x) + 8cosh(x) ) +--R * +--R csch(x)sinh(x) +--R + +--R 6 4 +--R (8cosh(x) + 8cosh(x) )csch(x) +--R * +--R tanh(x) +--R + +--R 8 7 +--R - 2csch(x)sinh(x) - 6cosh(x)csch(x)sinh(x) +--R + +--R 2 6 +--R (- 4cosh(x) - 10)csch(x)sinh(x) +--R + +--R 3 5 +--R (4cosh(x) - 26cosh(x))csch(x)sinh(x) +--R + +--R 4 2 4 +--R (6cosh(x) - 14cosh(x) - 8)csch(x)sinh(x) +--R + +--R 5 3 3 +--R (2cosh(x) + 18cosh(x) - 8cosh(x))csch(x)sinh(x) +--R + +--R 4 2 2 +--R (24cosh(x) + 8cosh(x) )csch(x)sinh(x) +--R + +--R 5 3 +--R (8cosh(x) + 8cosh(x) )csch(x)sinh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 5 4 2 3 +--R 6sinh(x) + 18cosh(x)sinh(x) + (12cosh(x) + 6)sinh(x) +--R + +--R 3 2 4 2 +--R (- 12cosh(x) + 6cosh(x))sinh(x) + (- 18cosh(x) - 6cosh(x) )sinh(x) +--R + +--R 5 3 +--R - 6cosh(x) - 6cosh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--------------+ +--R |--------------------------------------------- \|sinh(x)tanh(x) +--R \| sinh(x) - cosh(x) +--R Type: Expression Integer +--E 360 + +--S 361 of 502 +t0872:= (sinh(x)*tanh(x))^(5/2) +--R +--R +--R 2 2 +--------------+ +--R (203) sinh(x) tanh(x) \|sinh(x)tanh(x) +--R Type: Expression Integer +--E 361 + +--S 362 of 502 +r0872:= -2/15*coth(x)*(sinh(x)*tanh(x))^(1/2)*(32-(8+3*sinh(x)^2)*tanh(x)^2) +--R +--R +--R (204) +--R 2 2 +--------------+ +--R ((6coth(x)sinh(x) + 16coth(x))tanh(x) - 64coth(x))\|sinh(x)tanh(x) +--R --------------------------------------------------------------------- +--R 15 +--R Type: Expression Integer +--E 362 + +--S 363 of 502 +a0872:= integrate(t0872,x) +--R +--R +--R (205) +--R 8 7 2 6 +--R 3sinh(x) + 24cosh(x)sinh(x) + (84cosh(x) - 108)sinh(x) +--R + +--R 3 5 +--R (168cosh(x) - 648cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (210cosh(x) - 1620cosh(x) - 302)sinh(x) +--R + +--R 5 3 3 +--R (168cosh(x) - 2160cosh(x) - 1208cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (84cosh(x) - 1620cosh(x) - 1812cosh(x) - 108)sinh(x) +--R + +--R 7 5 3 +--R (24cosh(x) - 648cosh(x) - 1208cosh(x) - 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 3cosh(x) - 108cosh(x) - 302cosh(x) - 108cosh(x) + 3 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 7 6 2 5 +--R 60sinh(x) + 420cosh(x)sinh(x) + (1260cosh(x) + 120)sinh(x) +--R + +--R 3 4 +--R (2100cosh(x) + 600cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (2100cosh(x) + 1200cosh(x) + 60)sinh(x) +--R + +--R 5 3 2 +--R (1260cosh(x) + 1200cosh(x) + 180cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (420cosh(x) + 600cosh(x) + 180cosh(x) )sinh(x) + 60cosh(x) +--R + +--R 5 3 +--R 120cosh(x) + 60cosh(x) +--R Type: Union(Expression Integer,...) +--E 363 + +--S 364 of 502 +m0872:= a0872-r0872 +--R +--R +--R (206) +--R 9 8 +--R - 24coth(x)sinh(x) - 168cosh(x)coth(x)sinh(x) +--R + +--R 2 7 +--R (- 504cosh(x) - 112)coth(x)sinh(x) +--R + +--R 3 6 +--R (- 840cosh(x) - 688cosh(x))coth(x)sinh(x) +--R + +--R 4 2 5 +--R (- 840cosh(x) - 1824cosh(x) - 152)coth(x)sinh(x) +--R + +--R 5 3 4 +--R (- 504cosh(x) - 2720cosh(x) - 712cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 3 +--R (- 168cosh(x) - 2480cosh(x) - 1352cosh(x) - 64)coth(x)sinh(x) +--R + +--R 7 5 3 +--R (- 24cosh(x) - 1392cosh(x) - 1304cosh(x) - 192cosh(x)) +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 6 4 2 +--R (- 448cosh(x) - 640cosh(x) - 192cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (- 64cosh(x) - 128cosh(x) - 64cosh(x) )coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 7 6 +--R 256coth(x)sinh(x) + 1792cosh(x)coth(x)sinh(x) +--R + +--R 2 5 +--R (5376cosh(x) + 512)coth(x)sinh(x) +--R + +--R 3 4 +--R (8960cosh(x) + 2560cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (8960cosh(x) + 5120cosh(x) + 256)coth(x)sinh(x) +--R + +--R 5 3 2 +--R (5376cosh(x) + 5120cosh(x) + 768cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (1792cosh(x) + 2560cosh(x) + 768cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (256cosh(x) + 512cosh(x) + 256cosh(x) )coth(x) +--R * +--R +--------------+ +--R \|sinh(x)tanh(x) +--R + +--R 8 7 2 6 +--R 3sinh(x) + 24cosh(x)sinh(x) + (84cosh(x) - 108)sinh(x) +--R + +--R 3 5 +--R (168cosh(x) - 648cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (210cosh(x) - 1620cosh(x) - 302)sinh(x) +--R + +--R 5 3 3 +--R (168cosh(x) - 2160cosh(x) - 1208cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (84cosh(x) - 1620cosh(x) - 1812cosh(x) - 108)sinh(x) +--R + +--R 7 5 3 +--R (24cosh(x) - 648cosh(x) - 1208cosh(x) - 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 3cosh(x) - 108cosh(x) - 302cosh(x) - 108cosh(x) + 3 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 7 6 2 5 +--R 60sinh(x) + 420cosh(x)sinh(x) + (1260cosh(x) + 120)sinh(x) +--R + +--R 3 4 +--R (2100cosh(x) + 600cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (2100cosh(x) + 1200cosh(x) + 60)sinh(x) +--R + +--R 5 3 2 +--R (1260cosh(x) + 1200cosh(x) + 180cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (420cosh(x) + 600cosh(x) + 180cosh(x) )sinh(x) + 60cosh(x) +--R + +--R 5 3 +--R 120cosh(x) + 60cosh(x) +--R Type: Expression Integer +--E 364 + +--S 365 of 502 +d0872:= D(m0872,x) +--R +--R +--R (207) +--R 10 9 2 8 +--R - 15sinh(x) - 150cosh(x)sinh(x) + (- 675cosh(x) + 75)sinh(x) +--R + +--R 3 7 +--R (- 1800cosh(x) + 600cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (- 3150cosh(x) + 2100cosh(x) - 150)sinh(x) +--R + +--R 5 3 5 +--R (- 3780cosh(x) + 4200cosh(x) - 900cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 3150cosh(x) + 5250cosh(x) - 2250cosh(x) + 150)sinh(x) +--R + +--R 7 5 3 3 +--R (- 1800cosh(x) + 4200cosh(x) - 3000cosh(x) + 600cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 675cosh(x) + 2100cosh(x) - 2250cosh(x) + 900cosh(x) - 75) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 150cosh(x) + 600cosh(x) - 900cosh(x) + 600cosh(x) +--R + +--R - 150cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 15cosh(x) + 75cosh(x) - 150cosh(x) + 150cosh(x) - 75cosh(x) +--R + +--R 15 +--R * +--R +--------------+ +--R \|sinh(x)tanh(x) +--R + +--R 11 10 +--R 60coth(x)sinh(x) + 360cosh(x)coth(x)sinh(x) +--R + +--R 2 9 +--R (840cosh(x) + 280)coth(x)sinh(x) +--R + +--R 3 8 +--R (840cosh(x) + 1440cosh(x))coth(x)sinh(x) +--R + +--R 2 7 +--R (2840cosh(x) + 380)coth(x)sinh(x) +--R + +--R 5 3 6 +--R (- 840cosh(x) + 2240cosh(x) + 1400cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 5 +--R (- 840cosh(x) - 600cosh(x) + 1600cosh(x) + 160)coth(x)sinh(x) +--R + +--R 7 5 3 +--R (- 360cosh(x) - 2720cosh(x) - 120cosh(x) + 320cosh(x)) +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 8 6 4 3 +--R (- 60cosh(x) - 2360cosh(x) - 1660cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 2 +--R (- 960cosh(x) - 1280cosh(x) - 320cosh(x) )coth(x)sinh(x) +--R + +--R 8 6 4 +--R (- 160cosh(x) - 320cosh(x) - 160cosh(x) )coth(x)sinh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 2 11 +--R (24coth(x) - 24)sinh(x) +--R + +--R 2 10 +--R (144cosh(x)coth(x) - 60cosh(x)coth(x) - 144cosh(x))sinh(x) +--R + +--R 2 2 2 +--R (336cosh(x) + 112)coth(x) - 360cosh(x) coth(x) +--R + +--R 2 +--R - 336cosh(x) - 112 +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 +--R (336cosh(x) + 576cosh(x))coth(x) +--R + +--R 3 3 +--R (- 840cosh(x) - 152cosh(x))coth(x) - 336cosh(x) - 576cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 +--R (1136cosh(x) + 152)coth(x) +--R + +--R 4 2 2 +--R (- 840cosh(x) - 672cosh(x) )coth(x) - 1136cosh(x) - 152 +--R * +--R 7 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 336cosh(x) + 896cosh(x) + 560cosh(x))coth(x) +--R + +--R 3 5 +--R (- 1048cosh(x) - 124cosh(x))coth(x) + 336cosh(x) +--R + +--R 3 +--R - 896cosh(x) - 560cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 336cosh(x) - 240cosh(x) + 640cosh(x) + 64)coth(x) +--R + +--R 6 4 2 +--R (840cosh(x) - 448cosh(x) - 376cosh(x) )coth(x) +--R + +--R 6 4 2 +--R 336cosh(x) + 240cosh(x) - 640cosh(x) - 64 +--R * +--R 5 +--R sinh(x) +--R + +--R 7 5 3 +--R (- 144cosh(x) - 1088cosh(x) - 48cosh(x) + 128cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 7 5 3 +--R (840cosh(x) + 600cosh(x) - 320cosh(x) - 32cosh(x))coth(x) +--R + +--R 7 5 3 +--R 144cosh(x) + 1088cosh(x) + 48cosh(x) - 128cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 24cosh(x) - 944cosh(x) - 664cosh(x) )coth(x) +--R + +--R 8 6 4 2 +--R (360cosh(x) + 928cosh(x) + 120cosh(x) - 64cosh(x) )coth(x) +--R + +--R 8 6 4 +--R 24cosh(x) + 944cosh(x) + 664cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (- 384cosh(x) - 512cosh(x) - 128cosh(x) )coth(x) +--R + +--R 9 7 5 7 +--R (60cosh(x) + 568cosh(x) + 380cosh(x) )coth(x) + 384cosh(x) +--R + +--R 5 3 +--R 512cosh(x) + 128cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 64cosh(x) - 128cosh(x) - 64cosh(x) )coth(x) +--R + +--R 8 6 4 8 +--R (192cosh(x) + 256cosh(x) + 64cosh(x) )coth(x) + 64cosh(x) +--R + +--R 6 4 +--R 128cosh(x) + 64cosh(x) +--R * +--R sinh(x) +--R + +--R 9 7 5 +--R (32cosh(x) + 64cosh(x) + 32cosh(x) )coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 11 10 +--R - 60coth(x)sinh(x) - 360cosh(x)coth(x)sinh(x) +--R + +--R 2 9 +--R (- 840cosh(x) - 408)coth(x)sinh(x) +--R + +--R 3 8 +--R (- 840cosh(x) - 2208cosh(x))coth(x)sinh(x) +--R + +--R 2 7 +--R (- 4632cosh(x) - 636)coth(x)sinh(x) +--R + +--R 5 3 6 +--R (840cosh(x) - 4032cosh(x) - 2424cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 5 +--R (840cosh(x) + 600cosh(x) - 2880cosh(x) - 288)coth(x)sinh(x) +--R + +--R 7 5 3 +--R (360cosh(x) + 4512cosh(x) + 120cosh(x) - 576cosh(x))coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 3 +--R (60cosh(x) + 4152cosh(x) + 2940cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 2 +--R (1728cosh(x) + 2304cosh(x) + 576cosh(x) )coth(x)sinh(x) +--R + +--R 8 6 4 +--R (288cosh(x) + 576cosh(x) + 288cosh(x) )coth(x)sinh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 9 +--R (- 256coth(x) + 256)sinh(x) +--R + +--R 2 8 +--R (- 1536cosh(x)coth(x) + 128cosh(x)coth(x) + 1536cosh(x))sinh(x) +--R + +--R 2 2 2 +--R (- 3584cosh(x) - 512)coth(x) + 768cosh(x) coth(x) +--R + +--R 2 +--R 3584cosh(x) + 512 +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 +--R (- 3584cosh(x) - 2048cosh(x))coth(x) +--R + +--R 3 3 +--R (1792cosh(x) + 256cosh(x))coth(x) + 3584cosh(x) + 2048cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 +--R (- 2560cosh(x) - 256)coth(x) +--R + +--R 4 2 2 +--R (1792cosh(x) + 1024cosh(x) )coth(x) + 2560cosh(x) + 256 +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 +--R (3584cosh(x) - 512cosh(x))coth(x) +--R + +--R 3 5 +--R (1280cosh(x) + 128cosh(x))coth(x) - 3584cosh(x) + 512cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 4 2 +--R (3584cosh(x) + 2560cosh(x) )coth(x) +--R + +--R 6 2 6 +--R (- 1792cosh(x) + 256cosh(x) )coth(x) - 3584cosh(x) +--R + +--R 4 +--R - 2560cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (1536cosh(x) + 2048cosh(x) + 512cosh(x) )coth(x) +--R + +--R 7 5 7 +--R (- 1792cosh(x) - 1280cosh(x) )coth(x) - 1536cosh(x) +--R + +--R 5 3 +--R - 2048cosh(x) - 512cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (256cosh(x) + 512cosh(x) + 256cosh(x) )coth(x) +--R + +--R 8 6 4 +--R (- 768cosh(x) - 1024cosh(x) - 256cosh(x) )coth(x) +--R + +--R 8 6 4 +--R - 256cosh(x) - 512cosh(x) - 256cosh(x) +--R * +--R sinh(x) +--R + +--R 9 7 5 +--R (- 128cosh(x) - 256cosh(x) - 128cosh(x) )coth(x) +--R * +--R tanh(x) +--R + +--R 9 8 +--R 128coth(x)sinh(x) + 768cosh(x)coth(x)sinh(x) +--R + +--R 2 7 +--R (1792cosh(x) + 256)coth(x)sinh(x) +--R + +--R 3 6 +--R (1792cosh(x) + 1024cosh(x))coth(x)sinh(x) +--R + +--R 2 5 +--R (1280cosh(x) + 128)coth(x)sinh(x) +--R + +--R 5 4 +--R (- 1792cosh(x) + 256cosh(x))coth(x)sinh(x) +--R + +--R 6 4 3 +--R (- 1792cosh(x) - 1280cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 2 +--R (- 768cosh(x) - 1024cosh(x) - 256cosh(x) )coth(x)sinh(x) +--R + +--R 8 6 4 +--R (- 128cosh(x) - 256cosh(x) - 128cosh(x) )coth(x)sinh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 8 7 2 6 +--R 60sinh(x) + 360cosh(x)sinh(x) + (840cosh(x) + 120)sinh(x) +--R + +--R 3 5 2 4 +--R (840cosh(x) + 480cosh(x))sinh(x) + (600cosh(x) + 60)sinh(x) +--R + +--R 5 3 +--R (- 840cosh(x) + 120cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 840cosh(x) - 600cosh(x) )sinh(x) +--R + +--R 7 5 3 8 +--R (- 360cosh(x) - 480cosh(x) - 120cosh(x) )sinh(x) - 60cosh(x) +--R + +--R 6 4 +--R - 120cosh(x) - 60cosh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--------------+ +--R |--------------------------------------------- \|sinh(x)tanh(x) +--R \| sinh(x) - cosh(x) +--R Type: Expression Integer +--E 365 + +--S 366 of 502 +t0873:= (a+b*sinh(x)*cosh(x))^(1/2) +--R +--R +--R +--------------------+ +--R (208) \|b cosh(x)sinh(x) + a +--R Type: Expression Integer +--E 366 + +--S 367 of 502 +r0873:= -1/2*%i*EllipticE(-1/4*%pi+%i*x,2*%i*b/(2*a-%i*b))*_ + (2*a+b*sinh(2*x))^(1/2)*2^(1/2)/((2*a+b*sinh(2*x))/(2*a-%i*b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R Fraction Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 367 + +--S 368 of 502 +a0873:= integrate(t0873,x) +--R +--R +--R x +--R ++ +----------------------+ +--R (209) | \|b cosh(%I)sinh(%I) + a d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 368 + +--S 369 of 502 +--m0873:= a0873-r0873 +--E 369 + +--S 370 of 502 +--d0873:= D(m0873,x) +--E 370 + +--S 371 of 502 +t0874:= 1/(a+b*sinh(x)*cosh(x))^(1/2) +--R +--R +--R 1 +--R (210) ----------------------- +--R +--------------------+ +--R \|b cosh(x)sinh(x) + a +--R Type: Expression Integer +--E 371 + +--S 372 of 502 +r0874:= -%i*2^(1/2)*EllipticF(-1/4*%pi+%i*x,2*%i*b/(2*a-%i*b))*_ + ((2*a+b*sinh(2*x))/(2*a-%i*b))^(1/2)/(2*a+b*sinh(2*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Complex Integer +--R Fraction Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 372 + +--S 373 of 502 +a0874:= integrate(t0874,x) +--R +--R +--R x +--R ++ 1 +--R (211) | ------------------------- d%I +--R ++ +----------------------+ +--R \|b cosh(%I)sinh(%I) + a +--R Type: Union(Expression Integer,...) +--E 373 + +--S 374 of 502 +--m0874:= a0874-r0874 +--E 374 + +--S 375 of 502 +--d0874:= D(m0874,x) +--E 375 + +--S 376 of 502 +t0875:= (a*cosh(x)+b*sinh(x))^4 +--R +--R +--R (212) +--R 4 4 3 3 2 2 2 2 +--R b sinh(x) + 4a b cosh(x)sinh(x) + 6a b cosh(x) sinh(x) +--R + +--R 3 3 4 4 +--R 4a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 376 + +--S 377 of 502 +r0875:= 3/8*(a^2-b^2)^2*x+3/8*(a^2-b^2)*(b*cosh(x)+a*sinh(x))*_ + (a*cosh(x)+b*sinh(x))+1/4*(b*cosh(x)+a*sinh(x))*(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R (213) +--R 3 4 4 2 2 3 +--R 2a b sinh(x) + (2b + 6a b )cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 2 +--R ((6a b + 6a b)cosh(x) - 3a b + 3a b)sinh(x) +--R + +--R 2 2 4 3 4 4 3 4 +--R ((6a b + 2a )cosh(x) + (- 3b + 3a )cosh(x))sinh(x) + 2a b cosh(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 3a b + 3a b)cosh(x) + (3b - 6a b + 3a )x +--R / +--R 8 +--R Type: Expression Integer +--E 377 + +--S 378 of 502 +a0875:= integrate(t0875,x) +--R +--R +--R (214) +--R 3 3 4 4 2 2 4 3 +--R (a b + a b)sinh(x) + (b + 6a b + a )cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 2 +--R ((6a b + 6a b)cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 4 2 2 4 3 4 4 +--R ((b + 6a b + a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 4 2 2 4 +--R (a b + a b)cosh(x) + (- 4a b + 4a b)cosh(x) + (3b - 6a b + 3a )x +--R / +--R 8 +--R Type: Union(Expression Integer,...) +--E 378 + +--S 379 of 502 +m0875:= a0875-r0875 +--R +--R +--R (215) +--R 3 3 4 4 4 3 +--R (- a b + a b)sinh(x) + (- b + a )cosh(x)sinh(x) +--R + +--R 3 3 2 4 4 3 4 4 +--R (- a b + a b)sinh(x) + ((b - a )cosh(x) + (- b + a )cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 +--R (a b - a b)cosh(x) + (- a b + a b)cosh(x) +--R / +--R 8 +--R Type: Expression Integer +--E 379 + +--S 380 of 502 +d0875:= D(m0875,x) +--R +--R +--R (216) +--R 4 4 4 3 3 3 +--R (- b + a )sinh(x) + (- 4a b + 4a b)cosh(x)sinh(x) +--R + +--R 4 4 2 +--R (- b + a )sinh(x) +--R + +--R 3 3 3 3 3 +--R ((4a b - 4a b)cosh(x) + (- 4a b + 4a b)cosh(x))sinh(x) +--R + +--R 4 4 4 4 4 2 +--R (b - a )cosh(x) + (- b + a )cosh(x) +--R / +--R 8 +--R Type: Expression Integer +--E 380 + +--S 381 of 502 +t0876:= 1/(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R (217) +--R 1 +--R --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 381 + +--S 382 of 502 +r0876:= 1/2*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+1/2*(b*cosh(x)+a*sinh(x))/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R (218) +--R 2 2 2 2 +--R (- b sinh(x) - 2a b cosh(x)sinh(x) - a cosh(x) ) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R (- a sinh(x) - b cosh(x))\|- b + a +--R / +--R 4 2 2 2 3 3 +--R (2b - 2a b )sinh(x) + (4a b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 4 2 +--R (2a b - 2a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 382 + +--S 383 of 502 +a0876:= integrate(t0876,x) +--R +--R +--R (219) +--R [ +--R 2 2 4 2 2 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a b + 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a b + 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (- 2b + 2a )cosh(x) + b - 2a b + a +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 3 2 +--R (- 2b - 2a)sinh(x) + (- 6b - 6a)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((- 6b - 6a)cosh(x) - 2b + 2a)sinh(x) + (- 2b - 2a)cosh(x) +--R + +--R (- 2b + 2a)cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 3 3 4 4 +--R (2b + 4a b - 4a b - 2a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (8b + 16a b - 16a b - 8a )cosh(x)sinh(x) +--R + +--R 4 3 3 4 2 4 2 2 4 2 +--R ((12b + 24a b - 24a b - 12a )cosh(x) - 4b + 8a b - 4a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (8b + 16a b - 16a b - 8a )cosh(x) +--R + +--R 4 2 2 4 +--R (- 8b + 16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 3 4 4 4 2 2 4 2 +--R (2b + 4a b - 4a b - 2a )cosh(x) + (- 4b + 8a b - 4a )cosh(x) +--R + +--R 4 3 3 4 +--R 2b - 4a b + 4a b - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 2 2 4 2 2 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a b + 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a b + 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (- 2b + 2a )cosh(x) + b - 2a b + a +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 2 +--R (- b - a)sinh(x) + (- 3b - 3a)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((- 3b - 3a)cosh(x) - b + a)sinh(x) + (- b - a)cosh(x) +--R + +--R (- b + a)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 3 4 4 +--R (b + 2a b - 2a b - a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (4b + 8a b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 4 3 3 4 2 4 2 2 4 2 +--R ((6b + 12a b - 12a b - 6a )cosh(x) - 2b + 4a b - 2a )sinh(x) +--R + +--R 4 3 3 4 3 4 2 2 4 +--R ((4b + 8a b - 8a b - 4a )cosh(x) + (- 4b + 8a b - 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 4 3 3 4 4 4 2 2 4 2 4 +--R (b + 2a b - 2a b - a )cosh(x) + (- 2b + 4a b - 2a )cosh(x) + b +--R + +--R 3 3 4 +--R - 2a b + 2a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 383 + +--S 384 of 502 +--m0876:= a0876-r0876 +--E 384 + +--S 385 of 502 +--d0876:= D(m0876,x) +--E 385 + +--S 386 of 502 +t0877:= 1/(a*cosh(x)+b*sinh(x))^4 +--R +--R +--R (220) +--R 1 +--R / +--R 4 4 3 3 2 2 2 2 +--R b sinh(x) + 4a b cosh(x)sinh(x) + 6a b cosh(x) sinh(x) +--R + +--R 3 3 4 4 +--R 4a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 386 + +--S 387 of 502 +r0877:= 1/3*(b*cosh(x)+a*sinh(x))/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^3+_ + 2/3*sinh(x)/a/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R (221) +--R 2 3 2 2 2 2 +--R - 2b sinh(x) - 4a b cosh(x)sinh(x) + (- 2a cosh(x) - a )sinh(x) +--R + +--R - a b cosh(x) +--R / +--R 5 3 3 3 2 4 4 2 2 +--R (3a b - 3a b )sinh(x) + (9a b - 9a b )cosh(x)sinh(x) +--R + +--R 3 3 5 2 4 2 6 3 +--R (9a b - 9a b)cosh(x) sinh(x) + (3a b - 3a )cosh(x) +--R Type: Expression Integer +--E 387 + +--S 388 of 502 +a0877:= integrate(t0877,x) +--R +--R +--R (222) +--R (- 16b - 8a)sinh(x) + (- 8b - 16a)cosh(x) +--R / +--R 5 4 2 3 3 2 4 5 5 +--R (3b + 15a b + 30a b + 30a b + 15a b + 3a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (15b + 75a b + 150a b + 150a b + 75a b + 15a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (30b + 150a b + 300a b + 300a b + 150a b + 30a )cosh(x) - 9b +--R + +--R 4 2 3 3 2 4 5 +--R - 27a b - 18a b + 18a b + 27a b + 9a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (30b + 150a b + 300a b + 300a b + 150a b + 30a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 27b - 81a b - 54a b + 54a b + 81a b + 27a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (15b + 75a b + 150a b + 150a b + 75a b + 15a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (- 27b - 81a b - 54a b + 54a b + 81a b + 27a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 4 5 +--R 6a b - 24a b - 12a b + 12a b + 6a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (3b + 15a b + 30a b + 30a b + 15a b + 3a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 9b - 27a b - 18a b + 18a b + 27a b + 9a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (6b + 12a b - 12a b - 24a b + 6a b + 12a )cosh(x) +--R Type: Union(Expression Integer,...) +--E 388 + +--S 389 of 502 +m0877:= a0877-r0877 +--R +--R +--R (223) +--R 6 5 2 4 3 3 4 2 8 +--R (2b + 8a b + 12a b + 8a b + 2a b )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (10b + 44a b + 76a b + 64a b + 26a b + 4a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (20b + 100a b + 202a b + 208a b + 112a b + 28a b + 2a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R - 6b - 12a b + a b + 16a b + 12a b + 4a b + a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (20b + 120a b + 290a b + 360a b + 240a b + 80a b + 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 18b - 47a b - 15a b + 62a b + 76a b + 33a b + 5a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (10b + 80a b + 240a b + 360a b + 290a b + 120a b + 20a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 18b - 67a b - 48a b + 94a b + 170a b + 93a b + 16a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R 8b - 20a b - 7a b + 6a b + 4a b + 6a b + 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (2b + 28a b + 112a b + 208a b + 202a b + 100a b + 20a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (- 6b - 38a b - 40a b + 76a b + 178a b + 122a b + 28a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (4b + 9a b - 91a b - 6a b + 46a b + 29a b + 9a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (4a b + 26a b + 64a b + 76a b + 44a b + 10a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (- 2a b + 3a b + 44a b + 94a b + 78a b + 23a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 2 4 +--R (- a b - 35a b - 118a b + 70a b + 71a b + 13a )cosh(x) + 4a b +--R + +--R 3 3 4 2 5 6 +--R - 2a b - 6a b + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (2a b + 8a b + 12a b + 8a b + 2a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (5a b + 15a b + 22a b + 26a b + 21a b + 7a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 9a b - 17a b - 26a b - 34a b + 67a b + 19a )cosh(x) +--R + +--R 5 3 3 4 2 6 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (a b + 4a b + 6a b + 4a b + a b)cosh(x) +--R + +--R 5 2 4 4 2 5 6 4 +--R (- 3a b - 6a b - 2a b - 5a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (2a b + 2a b - 6a b - 2a b + 4a b)cosh(x) +--R / +--R 9 2 8 3 7 5 5 6 4 7 3 8 +--R (3a b + 12a b + 15a b - 15a b - 12a b - 3a b )sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 15a b + 69a b + 111a b + 45a b - 75a b - 105a b - 51a b +--R + +--R 8 2 +--R - 9a b +--R * +--R 7 +--R cosh(x)sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 30a b + 165a b + 339a b + 261a b - 105a b - 345a b +--R + +--R 7 3 8 2 9 +--R - 255a b - 81a b - 9a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 9a b - 18a b + 9a b + 36a b + 9a b - 18a b - 9a b +--R * +--R 6 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 30a b + 210a b + 555a b + 633a b + 87a b - 555a b - 615a b +--R + +--R 8 2 9 10 +--R - 285a b - 57a b - 3a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 27a b - 81a b - 27a b + 135a b + 135a b - 27a b - 81a b +--R + +--R 8 2 +--R - 27a b +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 15a b + 150a b + 525a b + 825a b + 435a b - 435a b +--R + +--R 7 3 8 2 9 10 +--R - 825a b - 525a b - 150a b - 15a +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 27a b - 135a b - 162a b + 135a b + 378a b + 135a b +--R + +--R 7 3 8 2 9 +--R - 162a b - 135a b - 27a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 12a b - 6a b - 30a b + 12a b + 24a b - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 3a b + 57a b + 285a b + 615a b + 555a b - 87a b - 633a b +--R + +--R 8 2 9 10 +--R - 555a b - 210a b - 30a +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 9a b - 99a b - 234a b - 54a b + 396a b + 396a b - 54a b +--R + +--R 8 2 9 10 +--R - 234a b - 99a b - 9a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 6a b + 42a b - 42a b - 102a b + 66a b + 78a b - 30a b +--R + +--R 8 2 +--R - 18a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 9a b + 81a b + 255a b + 345a b + 105a b - 261a b - 339a b +--R + +--R 9 10 +--R - 165a b - 30a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 27a b - 135a b - 162a b + 135a b + 378a b + 135a b +--R + +--R 8 2 9 10 +--R - 162a b - 135a b - 27a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 18a b + 54a b - 90a b - 126a b + 126a b + 90a b - 54a b +--R + +--R 9 +--R - 18a b +--R * +--R 2 +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 9a b + 51a b + 105a b + 75a b - 45a b - 111a b - 69a b +--R + +--R 10 +--R - 15a +--R * +--R 7 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 27a b - 81a b - 27a b + 135a b + 135a b - 27a b - 81a b +--R + +--R 10 +--R - 27a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 18a b + 30a b - 78a b - 66a b + 102a b + 42a b - 42a b +--R + +--R 10 +--R - 6a +--R * +--R 3 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 4 6 5 5 6 4 8 2 9 10 8 +--R (3a b + 12a b + 15a b - 15a b - 12a b - 3a )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 10 6 +--R (- 9a b - 18a b + 9a b + 36a b + 9a b - 18a b - 9a )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 10 4 +--R (6a b + 6a b - 24a b - 12a b + 30a b + 6a b - 12a )cosh(x) +--R Type: Expression Integer +--E 389 + +--S 390 of 502 +--d0877:= D(m0877,x) +--E 390 + +--S 391 of 502 +t0878:= 1/(a*cosh(x)+b*sinh(x))^5 +--R +--R +--R (224) +--R 1 +--R / +--R 5 5 4 4 2 3 2 3 +--R b sinh(x) + 5a b cosh(x)sinh(x) + 10a b cosh(x) sinh(x) +--R + +--R 3 2 3 2 4 4 5 5 +--R 10a b cosh(x) sinh(x) + 5a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 391 + +--S 392 of 502 +r0878:= 3/8*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)+_ + 1/4*(b*cosh(x)+a*sinh(x))/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^4+_ + 3/8*(b*cosh(x)+a*sinh(x))/(a^2-b^2)^2/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R (225) +--R 4 4 3 3 2 2 2 2 +--R 3b sinh(x) + 12a b cosh(x)sinh(x) + 18a b cosh(x) sinh(x) +--R + +--R 3 3 4 4 +--R 12a b cosh(x) sinh(x) + 3a cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 2 +--R 3a b sinh(x) + (3b + 6a b)cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 3 +--R ((6a b + 3a )cosh(x) - 2a b + 2a )sinh(x) + 3a b cosh(x) +--R + +--R 3 2 +--R (- 2b + 2a b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 8 2 6 4 4 4 +--R (8b - 16a b + 8a b )sinh(x) +--R + +--R 7 3 5 5 3 3 +--R (32a b - 64a b + 32a b )cosh(x)sinh(x) +--R + +--R 2 6 4 4 6 2 2 2 +--R (48a b - 96a b + 48a b )cosh(x) sinh(x) +--R + +--R 3 5 5 3 7 3 4 4 6 2 8 4 +--R (32a b - 64a b + 32a b)cosh(x) sinh(x) + (8a b - 16a b + 8a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 392 + +--S 393 of 502 +a0878:= integrate(t0878,x) +--R +--R +--R (226) +--R [ +--R 4 3 2 2 3 4 8 +--R (3b + 12a b + 18a b + 12a b + 3a )sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (24b + 96a b + 144a b + 96a b + 24a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (84b + 336a b + 504a b + 336a b + 84a )cosh(x) - 12b +--R + +--R 3 3 4 +--R - 24a b + 24a b + 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (168b + 672a b + 1008a b + 672a b + 168a )cosh(x) +--R + +--R 4 3 3 4 +--R (- 72b - 144a b + 144a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (210b + 840a b + 1260a b + 840a b + 210a )cosh(x) +--R + +--R 4 3 3 4 2 4 2 2 +--R (- 180b - 360a b + 360a b + 180a )cosh(x) + 18b - 36a b +--R + +--R 4 +--R 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (168b + 672a b + 1008a b + 672a b + 168a )cosh(x) +--R + +--R 4 3 3 4 3 +--R (- 240b - 480a b + 480a b + 240a )cosh(x) +--R + +--R 4 2 2 4 +--R (72b - 144a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (84b + 336a b + 504a b + 336a b + 84a )cosh(x) +--R + +--R 4 3 3 4 4 +--R (- 180b - 360a b + 360a b + 180a )cosh(x) +--R + +--R 4 2 2 4 2 4 3 3 4 +--R (108b - 216a b + 108a )cosh(x) - 12b + 24a b - 24a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (24b + 96a b + 144a b + 96a b + 24a )cosh(x) +--R + +--R 4 3 3 4 5 +--R (- 72b - 144a b + 144a b + 72a )cosh(x) +--R + +--R 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) +--R + +--R 4 3 3 4 +--R (- 24b + 48a b - 48a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 8 +--R (3b + 12a b + 18a b + 12a b + 3a )cosh(x) +--R + +--R 4 3 3 4 6 +--R (- 12b - 24a b + 24a b + 12a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (18b - 36a b + 18a )cosh(x) +--R + +--R 4 3 3 4 2 4 3 2 2 +--R (- 12b + 24a b - 24a b + 12a )cosh(x) + 3b - 12a b + 18a b +--R + +--R 3 4 +--R - 12a b + 3a +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 3 2 2 3 7 +--R (6b + 18a b + 18a b + 6a )sinh(x) +--R + +--R 3 2 2 3 6 +--R (42b + 126a b + 126a b + 42a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (126b + 378a b + 378a b + 126a )cosh(x) - 22b - 22a b +--R + +--R 2 3 +--R 22a b + 22a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (210b + 630a b + 630a b + 210a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 110b - 110a b + 110a b + 110a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (210b + 630a b + 630a b + 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 220b - 220a b + 220a b + 220a )cosh(x) - 22b + 22a b +--R + +--R 2 3 +--R 22a b - 22a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (126b + 378a b + 378a b + 126a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 220b - 220a b + 220a b + 220a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 66b + 66a b + 66a b - 66a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (42b + 126a b + 126a b + 42a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 110b - 110a b + 110a b + 110a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 66b + 66a b + 66a b - 66a )cosh(x) + 6b - 18a b + 18a b +--R + +--R 3 +--R - 6a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (6b + 18a b + 18a b + 6a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 22b - 22a b + 22a b + 22a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 22b + 22a b + 22a b - 22a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 18a b + 18a b - 6a )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 +--R 8b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b + 32a b +--R + +--R 8 +--R 8a +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 64b + 256a b + 256a b - 256a b - 640a b - 256a b + 256a b +--R + +--R 7 8 +--R 256a b + 64a +--R * +--R 7 +--R cosh(x)sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 224b + 896a b + 896a b - 896a b - 2240a b - 896a b +--R + +--R 6 2 7 8 +--R 896a b + 896a b + 224a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 32b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 8 +--R 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 448b + 1792a b + 1792a b - 1792a b - 4480a b - 1792a b +--R + +--R 6 2 7 8 +--R 1792a b + 1792a b + 448a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 192b - 384a b + 384a b + 1152a b - 1152a b - 384a b +--R + +--R 7 8 +--R 384a b + 192a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 560b + 2240a b + 2240a b - 2240a b - 5600a b - 2240a b +--R + +--R 6 2 7 8 +--R 2240a b + 2240a b + 560a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 480b - 960a b + 960a b + 2880a b - 2880a b - 960a b +--R + +--R 7 8 +--R 960a b + 480a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R 48b - 192a b + 288a b - 192a b + 48a +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 448b + 1792a b + 1792a b - 1792a b - 4480a b - 1792a b +--R + +--R 6 2 7 8 +--R 1792a b + 1792a b + 448a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 +--R - 640b - 1280a b + 1280a b + 3840a b - 3840a b +--R + +--R 6 2 7 8 +--R - 1280a b + 1280a b + 640a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R (192b - 768a b + 1152a b - 768a b + 192a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 224b + 896a b + 896a b - 896a b - 2240a b - 896a b +--R + +--R 6 2 7 8 +--R 896a b + 896a b + 224a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 480b - 960a b + 960a b + 2880a b - 2880a b - 960a b +--R + +--R 7 8 +--R 960a b + 480a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 8 +--R (288b - 1152a b + 1728a b - 1152a b + 288a )cosh(x) - 32b +--R + +--R 7 2 6 3 5 5 3 6 2 7 8 +--R 64a b + 64a b - 192a b + 192a b - 64a b - 64a b + 32a +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 64b + 256a b + 256a b - 256a b - 640a b - 256a b +--R + +--R 6 2 7 8 +--R 256a b + 256a b + 64a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 192b - 384a b + 384a b + 1152a b - 1152a b - 384a b +--R + +--R 7 8 +--R 384a b + 192a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (192b - 768a b + 1152a b - 768a b + 192a )cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 64b + 128a b + 128a b - 384a b + 384a b - 128a b +--R + +--R 7 8 +--R - 128a b + 64a +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 +--R 8b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b + 32a b +--R + +--R 8 +--R 8a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 32b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 8 +--R 32a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (48b - 192a b + 288a b - 192a b + 48a )cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 32b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 8 +--R 32a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 8 +--R 8b - 32a b + 32a b + 32a b - 80a b + 32a b + 32a b - 32a b + 8a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 4 3 2 2 3 4 8 +--R (- 3b - 12a b - 18a b - 12a b - 3a )sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 24b - 96a b - 144a b - 96a b - 24a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (- 84b - 336a b - 504a b - 336a b - 84a )cosh(x) + 12b +--R + +--R 3 3 4 +--R 24a b - 24a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 168b - 672a b - 1008a b - 672a b - 168a )cosh(x) +--R + +--R 4 3 3 4 +--R (72b + 144a b - 144a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 210b - 840a b - 1260a b - 840a b - 210a )cosh(x) +--R + +--R 4 3 3 4 2 4 2 2 4 +--R (180b + 360a b - 360a b - 180a )cosh(x) - 18b + 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 168b - 672a b - 1008a b - 672a b - 168a )cosh(x) +--R + +--R 4 3 3 4 3 +--R (240b + 480a b - 480a b - 240a )cosh(x) +--R + +--R 4 2 2 4 +--R (- 72b + 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 84b - 336a b - 504a b - 336a b - 84a )cosh(x) +--R + +--R 4 3 3 4 4 +--R (180b + 360a b - 360a b - 180a )cosh(x) +--R + +--R 4 2 2 4 2 4 3 3 +--R (- 108b + 216a b - 108a )cosh(x) + 12b - 24a b + 24a b +--R + +--R 4 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 24b - 96a b - 144a b - 96a b - 24a )cosh(x) +--R + +--R 4 3 3 4 5 +--R (72b + 144a b - 144a b - 72a )cosh(x) +--R + +--R 4 2 2 4 3 +--R (- 72b + 144a b - 72a )cosh(x) +--R + +--R 4 3 3 4 +--R (24b - 48a b + 48a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 3b - 12a b - 18a b - 12a b - 3a )cosh(x) +--R + +--R 4 3 3 4 6 +--R (12b + 24a b - 24a b - 12a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (- 18b + 36a b - 18a )cosh(x) +--R + +--R 4 3 3 4 2 4 3 2 2 +--R (12b - 24a b + 24a b - 12a )cosh(x) - 3b + 12a b - 18a b +--R + +--R 3 4 +--R 12a b - 3a +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 2 2 3 7 +--R (3b + 9a b + 9a b + 3a )sinh(x) +--R + +--R 3 2 2 3 6 +--R (21b + 63a b + 63a b + 21a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (63b + 189a b + 189a b + 63a )cosh(x) - 11b - 11a b +--R + +--R 2 3 +--R 11a b + 11a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (105b + 315a b + 315a b + 105a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 55b - 55a b + 55a b + 55a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (105b + 315a b + 315a b + 105a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 110b - 110a b + 110a b + 110a )cosh(x) - 11b + 11a b +--R + +--R 2 3 +--R 11a b - 11a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (63b + 189a b + 189a b + 63a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 110b - 110a b + 110a b + 110a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 33b + 33a b + 33a b - 33a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (21b + 63a b + 63a b + 21a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 55b - 55a b + 55a b + 55a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 33b + 33a b + 33a b - 33a )cosh(x) + 3b - 9a b + 9a b +--R + +--R 3 +--R - 3a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (3b + 9a b + 9a b + 3a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 11b - 11a b + 11a b + 11a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 11b + 11a b + 11a b - 11a )cosh(x) +--R + +--R 3 2 2 3 +--R (3b - 9a b + 9a b - 3a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4b + 16a b + 16a b - 16a b - 40a b - 16a b + 16a b + 16a b +--R + +--R 8 +--R 4a +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 32b + 128a b + 128a b - 128a b - 320a b - 128a b + 128a b +--R + +--R 7 8 +--R 128a b + 32a +--R * +--R 7 +--R cosh(x)sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 112b + 448a b + 448a b - 448a b - 1120a b - 448a b +--R + +--R 6 2 7 8 +--R 448a b + 448a b + 112a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R - 16b - 32a b + 32a b + 96a b - 96a b - 32a b + 32a b + 16a +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 224b + 896a b + 896a b - 896a b - 2240a b - 896a b +--R + +--R 6 2 7 8 +--R 896a b + 896a b + 224a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 96b - 192a b + 192a b + 576a b - 576a b - 192a b +--R + +--R 7 8 +--R 192a b + 96a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 280b + 1120a b + 1120a b - 1120a b - 2800a b - 1120a b +--R + +--R 6 2 7 8 +--R 1120a b + 1120a b + 280a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 240b - 480a b + 480a b + 1440a b - 1440a b - 480a b +--R + +--R 7 8 +--R 480a b + 240a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R 24b - 96a b + 144a b - 96a b + 24a +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 224b + 896a b + 896a b - 896a b - 2240a b - 896a b +--R + +--R 6 2 7 8 +--R 896a b + 896a b + 224a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 320b - 640a b + 640a b + 1920a b - 1920a b - 640a b +--R + +--R 7 8 +--R 640a b + 320a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R (96b - 384a b + 576a b - 384a b + 96a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 112b + 448a b + 448a b - 448a b - 1120a b - 448a b +--R + +--R 6 2 7 8 +--R 448a b + 448a b + 112a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 240b - 480a b + 480a b + 1440a b - 1440a b - 480a b +--R + +--R 7 8 +--R 480a b + 240a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 8 +--R (144b - 576a b + 864a b - 576a b + 144a )cosh(x) - 16b +--R + +--R 7 2 6 3 5 5 3 6 2 7 8 +--R 32a b + 32a b - 96a b + 96a b - 32a b - 32a b + 16a +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 32b + 128a b + 128a b - 128a b - 320a b - 128a b +--R + +--R 6 2 7 8 +--R 128a b + 128a b + 32a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 96b - 192a b + 192a b + 576a b - 576a b - 192a b +--R + +--R 7 8 +--R 192a b + 96a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (96b - 384a b + 576a b - 384a b + 96a )cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 32b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 8 +--R 32a +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4b + 16a b + 16a b - 16a b - 40a b - 16a b + 16a b + 16a b +--R + +--R 8 +--R 4a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 16b - 32a b + 32a b + 96a b - 96a b - 32a b + 32a b +--R + +--R 8 +--R 16a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (24b - 96a b + 144a b - 96a b + 24a )cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 16b + 32a b + 32a b - 96a b + 96a b - 32a b - 32a b +--R + +--R 8 +--R 16a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 8 +--R 4b - 16a b + 16a b + 16a b - 40a b + 16a b + 16a b - 16a b + 4a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 393 + +--S 394 of 502 +m0878a:= a0878.1-r0878 +--R +--R +--R (227) +--R 8 7 2 6 3 5 4 4 12 +--R (3b + 12a b + 18a b + 12a b + 3a b )sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (24b + 108a b + 192a b + 168a b + 72a b + 12a b )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 84b + 432a b + 906a b + 984a b + 576a b + 168a b +--R + +--R 6 2 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R - 12b - 24a b + 24a b + 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 168b + 1008a b + 2496a b + 3276a b + 2424a b + 984a b +--R + +--R 6 2 7 +--R 192a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 72b - 192a b - 96a b + 144a b + 168a b + 48a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 210b + 1512a b + 4452a b + 6984a b + 6309a b + 3276a b +--R + +--R 6 2 7 8 +--R 906a b + 108a b + 3a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 180b - 648a b - 648a b + 216a b + 756a b + 432a b +--R + +--R 6 2 +--R 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 +--R 18b - 36a b + 18a b +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 168b + 1512a b + 5376a b + 10080a b + 10944a b +--R + +--R 5 3 6 2 7 8 +--R 6984a b + 2496a b + 432a b + 24a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 240b - 1200a b - 1872a b - 432a b + 1584a b + 1584a b +--R + +--R 6 2 7 +--R 528a b + 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (72b + 72a b - 144a b - 144a b + 72a b + 72a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 84b + 1008a b + 4452a b + 10080a b + 13104a b +--R + +--R 5 3 6 2 7 8 +--R 10080a b + 4452a b + 1008a b + 84a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 180b - 1320a b - 3000a b - 2088a b + 1512a b +--R + +--R 5 3 6 2 7 8 +--R 3096a b + 1656a b + 312a b + 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 108b + 288a b - 108a b - 576a b - 108a b + 288a b +--R + +--R 6 2 +--R 108a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R - 12b + 24a b - 24a b + 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 24b + 432a b + 2496a b + 6984a b + 10944a b + 10080a b +--R + +--R 6 2 7 8 +--R 5376a b + 1512a b + 168a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 72b - 864a b - 2880a b - 3456a b + 3456a b + 2880a b +--R + +--R 7 8 +--R 864a b + 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 72b + 432a b + 288a b - 792a b - 792a b + 288a b +--R + +--R 6 2 7 +--R 432a b + 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 3 5 4 4 5 3 +--R (- 24b + 96a b - 48a b - 72a b + 48a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 3b + 108a b + 906a b + 3276a b + 6309a b + 6984a b +--R + +--R 6 2 7 8 +--R 4452a b + 1512a b + 210a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 12b - 312a b - 1656a b - 3096a b - 1512a b + 2088a b +--R + +--R 6 2 7 8 +--R 3000a b + 1320a b + 180a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 18b + 288a b + 612a b - 288a b - 1260a b - 288a b +--R + +--R 6 2 7 8 +--R 612a b + 288a b + 18a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 12b - 72a b + 120a b + 120a b - 180a b - 48a b +--R + +--R 6 2 +--R 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 3b - 12a b + 18a b - 12a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 12a b + 192a b + 984a b + 2424a b + 3276a b + 2496a b +--R + +--R 7 8 +--R 1008a b + 168a +--R * +--R 9 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 48a b - 528a b - 1584a b - 1584a b + 432a b + 1872a b +--R + +--R 7 8 +--R 1200a b + 240a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 72a b + 432a b + 288a b - 792a b - 792a b + 288a b +--R + +--R 7 8 +--R 432a b + 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 2 6 3 5 5 3 6 2 7 3 +--R (- 48a b - 48a b + 240a b - 240a b + 48a b + 48a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (12a b - 48a b + 72a b - 48a b + 12a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 18a b + 168a b + 576a b + 984a b + 906a b + 432a b +--R + +--R 8 +--R 84a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 72a b - 432a b - 756a b - 216a b + 648a b + 648a b +--R + +--R 8 +--R 180a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 108a b + 288a b - 108a b - 576a b - 108a b + 288a b +--R + +--R 8 +--R 108a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 72a b + 48a b + 180a b - 120a b - 120a b + 72a b +--R + +--R 8 +--R 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (18a b - 72a b + 108a b - 72a b + 18a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 11 +--R (12a b + 72a b + 168a b + 192a b + 108a b + 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 9 +--R (- 48a b - 168a b - 144a b + 96a b + 192a b + 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 7 +--R (72a b + 72a b - 144a b - 144a b + 72a b + 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 5 +--R (- 48a b + 72a b + 48a b - 96a b + 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 3 +--R (12a b - 48a b + 72a b - 48a b + 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (3a b + 12a b + 18a b + 12a b + 3a )cosh(x) +--R + +--R 4 4 5 3 7 8 10 +--R (- 12a b - 24a b + 24a b + 12a )cosh(x) +--R + +--R 4 4 6 2 8 8 +--R (18a b - 36a b + 18a )cosh(x) +--R + +--R 4 4 5 3 7 8 6 +--R (- 12a b + 24a b - 24a b + 12a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (3a b - 12a b + 18a b - 12a b + 3a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R 8 7 2 6 3 5 4 4 12 +--R (- 3b - 12a b - 18a b - 12a b - 3a b )sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 24b - 108a b - 192a b - 168a b - 72a b - 12a b )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 84b - 432a b - 906a b - 984a b - 576a b - 168a b +--R + +--R 6 2 +--R - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 12b + 24a b - 24a b - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 168b - 1008a b - 2496a b - 3276a b - 2424a b - 984a b +--R + +--R 6 2 7 +--R - 192a b - 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (72b + 192a b + 96a b - 144a b - 168a b - 48a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 210b - 1512a b - 4452a b - 6984a b - 6309a b +--R + +--R 5 3 6 2 7 8 +--R - 3276a b - 906a b - 108a b - 3a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 180b + 648a b + 648a b - 216a b - 756a b - 432a b +--R + +--R 6 2 +--R - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 +--R - 18b + 36a b - 18a b +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 168b - 1512a b - 5376a b - 10080a b - 10944a b +--R + +--R 5 3 6 2 7 8 +--R - 6984a b - 2496a b - 432a b - 24a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 240b + 1200a b + 1872a b + 432a b - 1584a b - 1584a b +--R + +--R 6 2 7 +--R - 528a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 72b - 72a b + 144a b + 144a b - 72a b - 72a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 84b - 1008a b - 4452a b - 10080a b - 13104a b +--R + +--R 5 3 6 2 7 8 +--R - 10080a b - 4452a b - 1008a b - 84a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 180b + 1320a b + 3000a b + 2088a b - 1512a b - 3096a b +--R + +--R 6 2 7 8 +--R - 1656a b - 312a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 108b - 288a b + 108a b + 576a b + 108a b - 288a b +--R + +--R 6 2 +--R - 108a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 12b - 24a b + 24a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 24b - 432a b - 2496a b - 6984a b - 10944a b +--R + +--R 5 3 6 2 7 8 +--R - 10080a b - 5376a b - 1512a b - 168a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R 72b + 864a b + 2880a b + 3456a b - 3456a b - 2880a b +--R + +--R 7 8 +--R - 864a b - 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 72b - 432a b - 288a b + 792a b + 792a b - 288a b +--R + +--R 6 2 7 +--R - 432a b - 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 3 5 4 4 5 3 +--R (24b - 96a b + 48a b + 72a b - 48a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 3b - 108a b - 906a b - 3276a b - 6309a b - 6984a b +--R + +--R 6 2 7 8 +--R - 4452a b - 1512a b - 210a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 12b + 312a b + 1656a b + 3096a b + 1512a b - 2088a b +--R + +--R 6 2 7 8 +--R - 3000a b - 1320a b - 180a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 18b - 288a b - 612a b + 288a b + 1260a b + 288a b +--R + +--R 6 2 7 8 +--R - 612a b - 288a b - 18a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R (12b + 72a b - 120a b - 120a b + 180a b + 48a b - 72a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 3b + 12a b - 18a b + 12a b - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 12a b - 192a b - 984a b - 2424a b - 3276a b - 2496a b +--R + +--R 7 8 +--R - 1008a b - 168a +--R * +--R 9 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 48a b + 528a b + 1584a b + 1584a b - 432a b - 1872a b +--R + +--R 7 8 +--R - 1200a b - 240a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 72a b - 432a b - 288a b + 792a b + 792a b - 288a b +--R + +--R 7 8 +--R - 432a b - 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 2 6 3 5 5 3 6 2 7 3 +--R (48a b + 48a b - 240a b + 240a b - 48a b - 48a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (- 12a b + 48a b - 72a b + 48a b - 12a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 18a b - 168a b - 576a b - 984a b - 906a b - 432a b +--R + +--R 8 +--R - 84a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 72a b + 432a b + 756a b + 216a b - 648a b - 648a b +--R + +--R 8 +--R - 180a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 108a b - 288a b + 108a b + 576a b + 108a b - 288a b +--R + +--R 8 +--R - 108a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (72a b - 48a b - 180a b + 120a b + 120a b - 72a b - 12a ) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (- 18a b + 72a b - 108a b + 72a b - 18a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 11 +--R (- 12a b - 72a b - 168a b - 192a b - 108a b - 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 9 +--R (48a b + 168a b + 144a b - 96a b - 192a b - 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 7 +--R (- 72a b - 72a b + 144a b + 144a b - 72a b - 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 5 +--R (48a b - 72a b - 48a b + 96a b - 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 3 +--R (- 12a b + 48a b - 72a b + 48a b - 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (- 3a b - 12a b - 18a b - 12a b - 3a )cosh(x) +--R + +--R 4 4 5 3 7 8 10 +--R (12a b + 24a b - 24a b - 12a )cosh(x) +--R + +--R 4 4 6 2 8 8 +--R (- 18a b + 36a b - 18a )cosh(x) +--R + +--R 4 4 5 3 7 8 6 +--R (12a b - 24a b + 24a b - 12a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (- 3a b + 12a b - 18a b + 12a b - 3a )cosh(x) +--R * +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R \|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 7 6 2 5 3 4 4 3 5 2 11 +--R (6b + 15a b + 6a b - 12a b - 12a b - 3a b )sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (39b + 114a b + 78a b - 66a b - 111a b - 48a b - 6a b)cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 102b + 360a b + 366a b - 93a b - 408a b - 264a b +--R + +--R 6 7 +--R - 60a b - 3a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R - 22b - 8a b + 54a b + 32a b - 24a b - 22a b - 8a b - 2a +--R * +--R 9 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 126b + 582a b + 855a b + 162a b - 738a b - 720a b +--R + +--R 6 7 +--R - 243a b - 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 96b - 78a b + 264a b + 302a b - 78a b - 208a b +--R + +--R 6 7 +--R - 90a b - 16a +--R * +--R cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 42b + 420a b + 1026a b + 702a b - 558a b - 1044a b +--R + +--R 6 7 +--R - 510a b - 78a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 132b - 192a b + 504a b + 964a b + 36a b - 704a b +--R + +--R 6 7 +--R - 408a b - 68a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R - 22b - 4a b + 6a b + 22a b + 32a b - 10a b - 16a b - 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 84b - 126a b + 378a b + 882a b + 252a b - 630a b +--R + +--R 6 7 +--R - 546a b - 126a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 16b - 20a b + 548a b + 1368a b + 368a b - 1164a b +--R + +--R 6 7 +--R - 932a b - 184a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 92b - 158a b + 66a b + 246a b + 166a b - 40a b +--R + +--R 6 7 +--R - 140a b - 48a +--R * +--R cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 126b - 546a b - 630a b + 252a b + 882a b + 378a b +--R + +--R 6 7 +--R - 126a b - 84a +--R * +--R 6 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 242b + 618a b + 662a b + 734a b + 218a b - 1054a b +--R + +--R 6 7 +--R - 1122a b - 298a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 186b - 558a b + 6a b + 912a b + 612a b - 216a b +--R + +--R 6 7 +--R - 432a b - 138a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R 6b + 6a b - 6a b - 42a b + 24a b + 24a b - 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 78b - 510a b - 1044a b - 558a b + 702a b + 1026a b +--R + +--R 6 7 +--R 420a b + 42a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 298b + 1122a b + 1054a b - 218a b - 734a b - 662a b +--R + +--R 6 7 +--R - 618a b - 242a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 250b - 858a b - 328a b + 1550a b + 1340a b - 460a b +--R + +--R 6 7 +--R - 762a b - 232a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 30b + 54a b - 114a b - 102a b + 48a b + 168a b - 36a b +--R + +--R 7 +--R - 48a +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 24b - 243a b - 720a b - 738a b + 162a b + 855a b +--R + +--R 6 7 +--R 582a b + 126a +--R * +--R 8 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 184b + 932a b + 1164a b - 368a b - 1368a b - 548a b +--R + +--R 6 7 +--R 20a b - 16a +--R * +--R 6 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 232b - 762a b - 460a b + 1340a b + 1550a b - 328a b +--R + +--R 6 7 +--R - 858a b - 250a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 72b + 84a b - 204a b - 288a b + 252a b + 240a b - 72a b +--R + +--R 7 +--R - 84a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R - 11a b + 28a b - 10a b - 20a b + 5a b + 16a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 3b - 60a b - 264a b - 408a b - 93a b + 366a b +--R + +--R 6 7 +--R 360a b + 102a +--R * +--R 9 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 68b + 408a b + 704a b - 36a b - 964a b - 504a b +--R + +--R 6 7 +--R 192a b + 132a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 138b - 432a b - 216a b + 612a b + 912a b + 6a b +--R + +--R 6 7 +--R - 558a b - 186a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 84b + 72a b - 240a b - 252a b + 288a b + 204a b - 84a b +--R + +--R 7 +--R - 72a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 11b + 12a b + 16a b + 20a b - 95a b + 56a b + 18a b +--R + +--R 7 +--R - 16a +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 6a b - 48a b - 111a b - 66a b + 78a b + 114a b + 39a ) +--R * +--R 10 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 16b + 90a b + 208a b + 78a b - 302a b - 264a b + 78a b +--R + +--R 7 +--R 96a +--R * +--R 8 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 48b - 140a b - 40a b + 166a b + 246a b + 66a b +--R + +--R 6 7 +--R - 158a b - 92a +--R * +--R 6 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 48b + 36a b - 168a b - 48a b + 102a b + 114a b - 54a b +--R + +--R 7 +--R - 30a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 16b + 18a b + 56a b - 95a b + 20a b + 16a b + 12a b +--R + +--R 7 +--R - 11a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 5 2 6 7 +--R 2a b - 8a b + 10a b - 10a b + 8a b - 2a +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 11 +--R (- 3a b - 12a b - 12a b + 6a b + 15a b + 6a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (2b + 8a b + 22a b + 24a b - 32a b - 54a b + 8a b + 22a ) +--R * +--R 9 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (- 8b - 16a b - 10a b + 32a b + 22a b + 6a b - 4a b - 22a ) +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (12b - 24a b - 24a b + 42a b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (- 8b + 16a b + 5a b - 20a b - 10a b + 28a b - 11a b)cosh(x) +--R + +--R 7 6 2 5 4 3 5 2 6 +--R (2b - 8a b + 10a b - 10a b + 8a b - 2a b)cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R 8b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b +--R + +--R 7 5 8 4 +--R 32a b + 8a b +--R * +--R 12 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R 64b + 288a b + 384a b - 128a b - 768a b - 576a b + 128a b +--R + +--R 7 5 8 4 9 3 +--R 384a b + 192a b + 32a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 224b + 1152a b + 1968a b + 320a b - 3072a b - 3648a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R - 608a b + 1728a b + 1440a b + 448a b + 48a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 5 7 6 6 7 5 +--R - 32b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 8 4 +--R 32a b +--R * +--R 10 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 448b + 2688a b + 5760a b + 3360a b - 6400a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 12160a b - 5760a b + 3520a b + 5440a b + 2560a b +--R + +--R 10 2 11 +--R 512a b + 32a b +--R * +--R 3 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R - 192b - 512a b + 128a b + 1408a b + 768a b - 1152a b +--R + +--R 6 6 7 5 8 4 9 3 +--R - 1152a b + 128a b + 448a b + 128a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 560b + 4032a b + 10752a b + 10560a b - 6360a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 24480a b - 19360a b + 1440a b + 12000a b + 8160a b +--R + +--R 10 2 11 12 +--R 2400a b + 288a b + 8a +--R * +--R 4 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 480b - 1728a b - 768a b + 4032a b + 4992a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 10 2 +--R - 1728a b - 5568a b - 1728a b + 1632a b + 1152a b + 192a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R 48b - 192a b + 288a b - 192a b + 48a b +--R * +--R 8 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 448b + 4032a b + 13440a b + 18816a b + 960a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 31104a b - 37376a b - 9216a b + 15936a b + 16320a b +--R + +--R 10 2 11 12 +--R 6528a b + 1152a b + 64a +--R * +--R 5 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 640b - 3200a b - 3712a b + 5248a b + 13568a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 3328a b - 12032a b - 9472a b + 1408a b + 3968a b +--R + +--R 10 2 11 +--R 1408a b + 128a b +--R * +--R 3 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 192b + 192a b - 768a b - 768a b + 1152a b + 1152a b +--R + +--R 6 6 7 5 8 4 9 3 +--R - 768a b - 768a b + 192a b + 192a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 224b + 2688a b + 11424a b + 21504a b + 11424a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 24192a b - 46144a b - 24192a b + 11424a b + 21504a b +--R + +--R 10 2 11 12 +--R 11424a b + 2688a b + 224a +--R * +--R 6 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 480b - 3520a b - 7040a b + 1472a b + 19552a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 15872a b - 11648a b - 21248a b - 4768a b + 6592a b +--R + +--R 10 2 11 12 +--R 4352a b + 832a b + 32a +--R * +--R 4 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 288b + 768a b - 864a b - 3072a b + 576a b + 4608a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 576a b - 3072a b - 864a b + 768a b + 288a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 5 7 6 6 7 5 +--R - 32b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 8 4 +--R 32a b +--R * +--R 6 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 64b + 1152a b + 6528a b + 16320a b + 15936a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 9216a b - 37376a b - 31104a b + 960a b + 18816a b +--R + +--R 10 2 11 12 +--R 13440a b + 4032a b + 448a +--R * +--R 7 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 192b - 2304a b - 7296a b - 4608a b + 15168a b +--R + +--R 5 7 7 5 8 4 9 3 10 2 +--R 25344a b - 25344a b - 15168a b + 4608a b + 7296a b +--R + +--R 11 12 +--R 2304a b + 192a +--R * +--R 5 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 192b + 1152a b + 384a b - 4416a b - 3456a b + 6144a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 11 +--R 6144a b - 3456a b - 4416a b + 384a b + 1152a b + 192a b +--R * +--R 3 +--R cosh(x) +--R + +--R 12 2 10 3 9 4 8 5 7 6 6 +--R - 64b + 384a b - 128a b - 768a b + 384a b + 640a b +--R + +--R 7 5 8 4 9 3 +--R - 384a b - 192a b + 128a b +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 8b + 288a b + 2400a b + 8160a b + 12000a b + 1440a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R - 19360a b - 24480a b - 6360a b + 10560a b + 10752a b +--R + +--R 11 12 +--R 4032a b + 560a +--R * +--R 8 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 32b - 832a b - 4352a b - 6592a b + 4768a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 21248a b + 11648a b - 15872a b - 19552a b - 1472a b +--R + +--R 10 2 11 12 +--R 7040a b + 3520a b + 480a +--R * +--R 6 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 48b + 768a b + 1536a b - 2304a b - 6576a b + 1536a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 11 +--R 9984a b + 1536a b - 6576a b - 2304a b + 1536a b + 768a b +--R + +--R 12 +--R 48a +--R * +--R 4 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R - 32b - 192a b + 384a b + 704a b - 1152a b - 960a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 1472a b + 576a b - 864a b - 128a b + 192a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R 8b - 32a b + 32a b + 32a b - 80a b + 32a b + 32a b +--R + +--R 7 5 8 4 +--R - 32a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 32a b + 512a b + 2560a b + 5440a b + 3520a b - 5760a b +--R + +--R 7 5 8 4 9 3 10 2 11 12 +--R - 12160a b - 6400a b + 3360a b + 5760a b + 2688a b + 448a +--R * +--R 9 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 +--R - 128a b - 1408a b - 3968a b - 1408a b + 9472a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 12032a b - 3328a b - 13568a b - 5248a b + 3712a b +--R + +--R 11 12 +--R 3200a b + 640a +--R * +--R 7 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 192a b + 1152a b + 384a b - 4416a b - 3456a b + 6144a b +--R + +--R 7 5 8 4 9 3 10 2 11 12 +--R 6144a b - 3456a b - 4416a b + 384a b + 1152a b + 192a +--R * +--R 5 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 7 5 +--R - 128a b - 128a b + 896a b + 256a b - 2048a b + 2048a b +--R + +--R 8 4 9 3 10 2 11 +--R - 256a b - 896a b + 128a b + 128a b +--R * +--R 3 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 32a b - 128a b + 128a b + 128a b - 320a b + 128a b +--R + +--R 7 5 8 4 9 3 +--R 128a b - 128a b + 32a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 48a b + 448a b + 1440a b + 1728a b - 608a b - 3648a b +--R + +--R 8 4 9 3 10 2 11 12 +--R - 3072a b + 320a b + 1968a b + 1152a b + 224a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 +--R - 192a b - 1152a b - 1632a b + 1728a b + 5568a b +--R + +--R 7 5 8 4 9 3 10 2 11 12 +--R 1728a b - 4992a b - 4032a b + 768a b + 1728a b + 480a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 288a b + 768a b - 864a b - 3072a b + 576a b + 4608a b +--R + +--R 8 4 9 3 10 2 11 12 +--R 576a b - 3072a b - 864a b + 768a b + 288a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R - 192a b + 128a b + 864a b - 576a b - 1472a b + 960a b +--R + +--R 8 4 9 3 10 2 11 12 +--R 1152a b - 704a b - 384a b + 192a b + 32a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 48a b - 192a b + 192a b + 192a b - 480a b + 192a b +--R + +--R 8 4 9 3 10 2 +--R 192a b - 192a b + 48a b +--R * +--R 2 +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 32a b + 192a b + 384a b + 128a b - 576a b - 768a b +--R + +--R 9 3 10 2 11 12 +--R - 128a b + 384a b + 288a b + 64a +--R * +--R 11 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R - 128a b - 448a b - 128a b + 1152a b + 1152a b - 768a b +--R + +--R 9 3 10 2 11 12 +--R - 1408a b - 128a b + 512a b + 192a +--R * +--R 9 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 192a b + 192a b - 768a b - 768a b + 1152a b + 1152a b +--R + +--R 9 3 10 2 11 12 +--R - 768a b - 768a b + 192a b + 192a +--R * +--R 7 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R - 128a b + 192a b + 384a b - 640a b - 384a b + 768a b +--R + +--R 9 3 10 2 12 +--R 128a b - 384a b + 64a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 32a b - 128a b + 128a b + 128a b - 320a b + 128a b +--R + +--R 9 3 10 2 11 +--R 128a b - 128a b + 32a b +--R * +--R 3 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R 8a b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b +--R + +--R 11 12 +--R 32a b + 8a +--R * +--R 12 +--R cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 9 3 10 2 11 +--R - 32a b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 12 +--R 32a +--R * +--R 10 +--R cosh(x) +--R + +--R 4 8 6 6 8 4 10 2 12 8 +--R (48a b - 192a b + 288a b - 192a b + 48a )cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 9 3 10 2 11 +--R - 32a b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 12 +--R 32a +--R * +--R 6 +--R cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R 8a b - 32a b + 32a b + 32a b - 80a b + 32a b + 32a b +--R + +--R 11 12 +--R - 32a b + 8a +--R * +--R 4 +--R cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 394 + +--S 395 of 502 +--d0878a:= D(m0878a,x) +--E 395 + +--S 396 of 502 +m0878b:= a0878.2-r0878 +--R +--R +--R (228) +--R 8 7 2 6 3 5 4 4 12 +--R (- 6b - 24a b - 36a b - 24a b - 6a b )sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 48b - 216a b - 384a b - 336a b - 144a b - 24a b )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 168b - 864a b - 1812a b - 1968a b - 1152a b - 336a b +--R + +--R 6 2 +--R - 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 24b + 48a b - 48a b - 24a b +--R * +--R 10 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 336b - 2016a b - 4992a b - 6552a b - 4848a b +--R + +--R 5 3 6 2 7 +--R - 1968a b - 384a b - 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (144b + 384a b + 192a b - 288a b - 336a b - 96a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 420b - 3024a b - 8904a b - 13968a b - 12618a b +--R + +--R 5 3 6 2 7 8 +--R - 6552a b - 1812a b - 216a b - 6a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 360b + 1296a b + 1296a b - 432a b - 1512a b - 864a b +--R + +--R 6 2 +--R - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 +--R - 36b + 72a b - 36a b +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 336b - 3024a b - 10752a b - 20160a b - 21888a b +--R + +--R 5 3 6 2 7 8 +--R - 13968a b - 4992a b - 864a b - 48a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 480b + 2400a b + 3744a b + 864a b - 3168a b - 3168a b +--R + +--R 6 2 7 +--R - 1056a b - 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 144b - 144a b + 288a b + 288a b - 144a b - 144a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 168b - 2016a b - 8904a b - 20160a b - 26208a b +--R + +--R 5 3 6 2 7 8 +--R - 20160a b - 8904a b - 2016a b - 168a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 360b + 2640a b + 6000a b + 4176a b - 3024a b - 6192a b +--R + +--R 6 2 7 8 +--R - 3312a b - 624a b - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 216b - 576a b + 216a b + 1152a b + 216a b - 576a b +--R + +--R 6 2 +--R - 216a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 24b - 48a b + 48a b - 24a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 48b - 864a b - 4992a b - 13968a b - 21888a b +--R + +--R 5 3 6 2 7 8 +--R - 20160a b - 10752a b - 3024a b - 336a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R 144b + 1728a b + 5760a b + 6912a b - 6912a b - 5760a b +--R + +--R 7 8 +--R - 1728a b - 144a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 144b - 864a b - 576a b + 1584a b + 1584a b - 576a b +--R + +--R 6 2 7 +--R - 864a b - 144a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 3 5 4 4 5 3 +--R (48b - 192a b + 96a b + 144a b - 96a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 6b - 216a b - 1812a b - 6552a b - 12618a b - 13968a b +--R + +--R 6 2 7 8 +--R - 8904a b - 3024a b - 420a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 24b + 624a b + 3312a b + 6192a b + 3024a b - 4176a b +--R + +--R 6 2 7 8 +--R - 6000a b - 2640a b - 360a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 36b - 576a b - 1224a b + 576a b + 2520a b + 576a b +--R + +--R 6 2 7 8 +--R - 1224a b - 576a b - 36a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 24b + 144a b - 240a b - 240a b + 360a b + 96a b +--R + +--R 6 2 +--R - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 6b + 24a b - 36a b + 24a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 24a b - 384a b - 1968a b - 4848a b - 6552a b +--R + +--R 6 2 7 8 +--R - 4992a b - 2016a b - 336a +--R * +--R 9 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 96a b + 1056a b + 3168a b + 3168a b - 864a b - 3744a b +--R + +--R 7 8 +--R - 2400a b - 480a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 144a b - 864a b - 576a b + 1584a b + 1584a b - 576a b +--R + +--R 7 8 +--R - 864a b - 144a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 2 6 3 5 5 3 6 2 7 3 +--R (96a b + 96a b - 480a b + 480a b - 96a b - 96a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (- 24a b + 96a b - 144a b + 96a b - 24a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 36a b - 336a b - 1152a b - 1968a b - 1812a b - 864a b +--R + +--R 8 +--R - 168a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 144a b + 864a b + 1512a b + 432a b - 1296a b - 1296a b +--R + +--R 8 +--R - 360a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 216a b - 576a b + 216a b + 1152a b + 216a b - 576a b +--R + +--R 8 +--R - 216a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 144a b - 96a b - 360a b + 240a b + 240a b - 144a b +--R + +--R 8 +--R - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (- 36a b + 144a b - 216a b + 144a b - 36a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 11 +--R (- 24a b - 144a b - 336a b - 384a b - 216a b - 48a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 9 +--R (96a b + 336a b + 288a b - 192a b - 384a b - 144a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (- 144a b - 144a b + 288a b + 288a b - 144a b - 144a ) +--R * +--R 7 +--R cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 5 +--R (96a b - 144a b - 96a b + 192a b - 48a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 3 +--R (- 24a b + 96a b - 144a b + 96a b - 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (- 6a b - 24a b - 36a b - 24a b - 6a )cosh(x) +--R + +--R 4 4 5 3 7 8 10 +--R (24a b + 48a b - 48a b - 24a )cosh(x) +--R + +--R 4 4 6 2 8 8 +--R (- 36a b + 72a b - 36a )cosh(x) +--R + +--R 4 4 5 3 7 8 6 +--R (24a b - 48a b + 48a b - 24a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (- 6a b + 24a b - 36a b + 24a b - 6a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 8 7 2 6 3 5 4 4 12 +--R (- 3b - 12a b - 18a b - 12a b - 3a b )sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 24b - 108a b - 192a b - 168a b - 72a b - 12a b )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 84b - 432a b - 906a b - 984a b - 576a b - 168a b +--R + +--R 6 2 +--R - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 12b + 24a b - 24a b - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 168b - 1008a b - 2496a b - 3276a b - 2424a b - 984a b +--R + +--R 6 2 7 +--R - 192a b - 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (72b + 192a b + 96a b - 144a b - 168a b - 48a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 210b - 1512a b - 4452a b - 6984a b - 6309a b +--R + +--R 5 3 6 2 7 8 +--R - 3276a b - 906a b - 108a b - 3a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 180b + 648a b + 648a b - 216a b - 756a b - 432a b +--R + +--R 6 2 +--R - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 +--R - 18b + 36a b - 18a b +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 168b - 1512a b - 5376a b - 10080a b - 10944a b +--R + +--R 5 3 6 2 7 8 +--R - 6984a b - 2496a b - 432a b - 24a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 240b + 1200a b + 1872a b + 432a b - 1584a b - 1584a b +--R + +--R 6 2 7 +--R - 528a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 72b - 72a b + 144a b + 144a b - 72a b - 72a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 84b - 1008a b - 4452a b - 10080a b - 13104a b +--R + +--R 5 3 6 2 7 8 +--R - 10080a b - 4452a b - 1008a b - 84a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 180b + 1320a b + 3000a b + 2088a b - 1512a b - 3096a b +--R + +--R 6 2 7 8 +--R - 1656a b - 312a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 108b - 288a b + 108a b + 576a b + 108a b - 288a b +--R + +--R 6 2 +--R - 108a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 12b - 24a b + 24a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 24b - 432a b - 2496a b - 6984a b - 10944a b +--R + +--R 5 3 6 2 7 8 +--R - 10080a b - 5376a b - 1512a b - 168a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R 72b + 864a b + 2880a b + 3456a b - 3456a b - 2880a b +--R + +--R 7 8 +--R - 864a b - 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 72b - 432a b - 288a b + 792a b + 792a b - 288a b +--R + +--R 6 2 7 +--R - 432a b - 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 3 5 4 4 5 3 +--R (24b - 96a b + 48a b + 72a b - 48a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 3b - 108a b - 906a b - 3276a b - 6309a b - 6984a b +--R + +--R 6 2 7 8 +--R - 4452a b - 1512a b - 210a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 12b + 312a b + 1656a b + 3096a b + 1512a b - 2088a b +--R + +--R 6 2 7 8 +--R - 3000a b - 1320a b - 180a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 18b - 288a b - 612a b + 288a b + 1260a b + 288a b +--R + +--R 6 2 7 8 +--R - 612a b - 288a b - 18a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R (12b + 72a b - 120a b - 120a b + 180a b + 48a b - 72a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 3b + 12a b - 18a b + 12a b - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 12a b - 192a b - 984a b - 2424a b - 3276a b - 2496a b +--R + +--R 7 8 +--R - 1008a b - 168a +--R * +--R 9 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 48a b + 528a b + 1584a b + 1584a b - 432a b - 1872a b +--R + +--R 7 8 +--R - 1200a b - 240a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 72a b - 432a b - 288a b + 792a b + 792a b - 288a b +--R + +--R 7 8 +--R - 432a b - 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 2 6 3 5 5 3 6 2 7 3 +--R (48a b + 48a b - 240a b + 240a b - 48a b - 48a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (- 12a b + 48a b - 72a b + 48a b - 12a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 18a b - 168a b - 576a b - 984a b - 906a b - 432a b +--R + +--R 8 +--R - 84a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 72a b + 432a b + 756a b + 216a b - 648a b - 648a b +--R + +--R 8 +--R - 180a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 108a b - 288a b + 108a b + 576a b + 108a b - 288a b +--R + +--R 8 +--R - 108a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (72a b - 48a b - 180a b + 120a b + 120a b - 72a b - 12a ) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (- 18a b + 72a b - 108a b + 72a b - 18a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 11 +--R (- 12a b - 72a b - 168a b - 192a b - 108a b - 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 9 +--R (48a b + 168a b + 144a b - 96a b - 192a b - 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 7 +--R (- 72a b - 72a b + 144a b + 144a b - 72a b - 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 5 +--R (48a b - 72a b - 48a b + 96a b - 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 3 +--R (- 12a b + 48a b - 72a b + 48a b - 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (- 3a b - 12a b - 18a b - 12a b - 3a )cosh(x) +--R + +--R 4 4 5 3 7 8 10 +--R (12a b + 24a b - 24a b - 12a )cosh(x) +--R + +--R 4 4 6 2 8 8 +--R (- 18a b + 36a b - 18a )cosh(x) +--R + +--R 4 4 5 3 7 8 6 +--R (12a b - 24a b + 24a b - 12a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (- 3a b + 12a b - 18a b + 12a b - 3a )cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 7 6 2 5 3 4 4 3 5 2 11 +--R (6b + 15a b + 6a b - 12a b - 12a b - 3a b )sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (39b + 114a b + 78a b - 66a b - 111a b - 48a b - 6a b)cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 102b + 360a b + 366a b - 93a b - 408a b - 264a b +--R + +--R 6 7 +--R - 60a b - 3a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R - 22b - 8a b + 54a b + 32a b - 24a b - 22a b - 8a b - 2a +--R * +--R 9 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 126b + 582a b + 855a b + 162a b - 738a b - 720a b +--R + +--R 6 7 +--R - 243a b - 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 96b - 78a b + 264a b + 302a b - 78a b - 208a b +--R + +--R 6 7 +--R - 90a b - 16a +--R * +--R cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 42b + 420a b + 1026a b + 702a b - 558a b - 1044a b +--R + +--R 6 7 +--R - 510a b - 78a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 132b - 192a b + 504a b + 964a b + 36a b - 704a b +--R + +--R 6 7 +--R - 408a b - 68a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R - 22b - 4a b + 6a b + 22a b + 32a b - 10a b - 16a b - 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 84b - 126a b + 378a b + 882a b + 252a b - 630a b +--R + +--R 6 7 +--R - 546a b - 126a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 16b - 20a b + 548a b + 1368a b + 368a b - 1164a b +--R + +--R 6 7 +--R - 932a b - 184a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 92b - 158a b + 66a b + 246a b + 166a b - 40a b +--R + +--R 6 7 +--R - 140a b - 48a +--R * +--R cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 126b - 546a b - 630a b + 252a b + 882a b + 378a b +--R + +--R 6 7 +--R - 126a b - 84a +--R * +--R 6 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 242b + 618a b + 662a b + 734a b + 218a b - 1054a b +--R + +--R 6 7 +--R - 1122a b - 298a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 186b - 558a b + 6a b + 912a b + 612a b - 216a b +--R + +--R 6 7 +--R - 432a b - 138a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R 6b + 6a b - 6a b - 42a b + 24a b + 24a b - 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 78b - 510a b - 1044a b - 558a b + 702a b + 1026a b +--R + +--R 6 7 +--R 420a b + 42a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 298b + 1122a b + 1054a b - 218a b - 734a b - 662a b +--R + +--R 6 7 +--R - 618a b - 242a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 250b - 858a b - 328a b + 1550a b + 1340a b - 460a b +--R + +--R 6 7 +--R - 762a b - 232a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 30b + 54a b - 114a b - 102a b + 48a b + 168a b - 36a b +--R + +--R 7 +--R - 48a +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 24b - 243a b - 720a b - 738a b + 162a b + 855a b +--R + +--R 6 7 +--R 582a b + 126a +--R * +--R 8 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 184b + 932a b + 1164a b - 368a b - 1368a b - 548a b +--R + +--R 6 7 +--R 20a b - 16a +--R * +--R 6 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 232b - 762a b - 460a b + 1340a b + 1550a b - 328a b +--R + +--R 6 7 +--R - 858a b - 250a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 72b + 84a b - 204a b - 288a b + 252a b + 240a b - 72a b +--R + +--R 7 +--R - 84a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R - 11a b + 28a b - 10a b - 20a b + 5a b + 16a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 3b - 60a b - 264a b - 408a b - 93a b + 366a b +--R + +--R 6 7 +--R 360a b + 102a +--R * +--R 9 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 68b + 408a b + 704a b - 36a b - 964a b - 504a b +--R + +--R 6 7 +--R 192a b + 132a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 138b - 432a b - 216a b + 612a b + 912a b + 6a b +--R + +--R 6 7 +--R - 558a b - 186a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 84b + 72a b - 240a b - 252a b + 288a b + 204a b - 84a b +--R + +--R 7 +--R - 72a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 11b + 12a b + 16a b + 20a b - 95a b + 56a b + 18a b +--R + +--R 7 +--R - 16a +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 6a b - 48a b - 111a b - 66a b + 78a b + 114a b + 39a ) +--R * +--R 10 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 16b + 90a b + 208a b + 78a b - 302a b - 264a b + 78a b +--R + +--R 7 +--R 96a +--R * +--R 8 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 48b - 140a b - 40a b + 166a b + 246a b + 66a b +--R + +--R 6 7 +--R - 158a b - 92a +--R * +--R 6 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 48b + 36a b - 168a b - 48a b + 102a b + 114a b - 54a b +--R + +--R 7 +--R - 30a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 16b + 18a b + 56a b - 95a b + 20a b + 16a b + 12a b +--R + +--R 7 +--R - 11a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 5 2 6 7 +--R 2a b - 8a b + 10a b - 10a b + 8a b - 2a +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 11 +--R (- 3a b - 12a b - 12a b + 6a b + 15a b + 6a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (2b + 8a b + 22a b + 24a b - 32a b - 54a b + 8a b + 22a ) +--R * +--R 9 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (- 8b - 16a b - 10a b + 32a b + 22a b + 6a b - 4a b - 22a ) +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (12b - 24a b - 24a b + 42a b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (- 8b + 16a b + 5a b - 20a b - 10a b + 28a b - 11a b)cosh(x) +--R + +--R 7 6 2 5 4 3 5 2 6 +--R (2b - 8a b + 10a b - 10a b + 8a b - 2a b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R 8b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b +--R + +--R 7 5 8 4 +--R 32a b + 8a b +--R * +--R 12 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R 64b + 288a b + 384a b - 128a b - 768a b - 576a b + 128a b +--R + +--R 7 5 8 4 9 3 +--R 384a b + 192a b + 32a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 224b + 1152a b + 1968a b + 320a b - 3072a b - 3648a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R - 608a b + 1728a b + 1440a b + 448a b + 48a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 5 7 6 6 7 5 +--R - 32b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 8 4 +--R 32a b +--R * +--R 10 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 448b + 2688a b + 5760a b + 3360a b - 6400a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 12160a b - 5760a b + 3520a b + 5440a b + 2560a b +--R + +--R 10 2 11 +--R 512a b + 32a b +--R * +--R 3 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R - 192b - 512a b + 128a b + 1408a b + 768a b - 1152a b +--R + +--R 6 6 7 5 8 4 9 3 +--R - 1152a b + 128a b + 448a b + 128a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 560b + 4032a b + 10752a b + 10560a b - 6360a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 24480a b - 19360a b + 1440a b + 12000a b + 8160a b +--R + +--R 10 2 11 12 +--R 2400a b + 288a b + 8a +--R * +--R 4 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 480b - 1728a b - 768a b + 4032a b + 4992a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 10 2 +--R - 1728a b - 5568a b - 1728a b + 1632a b + 1152a b + 192a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R 48b - 192a b + 288a b - 192a b + 48a b +--R * +--R 8 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 448b + 4032a b + 13440a b + 18816a b + 960a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 31104a b - 37376a b - 9216a b + 15936a b + 16320a b +--R + +--R 10 2 11 12 +--R 6528a b + 1152a b + 64a +--R * +--R 5 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 640b - 3200a b - 3712a b + 5248a b + 13568a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 3328a b - 12032a b - 9472a b + 1408a b + 3968a b +--R + +--R 10 2 11 +--R 1408a b + 128a b +--R * +--R 3 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 192b + 192a b - 768a b - 768a b + 1152a b + 1152a b +--R + +--R 6 6 7 5 8 4 9 3 +--R - 768a b - 768a b + 192a b + 192a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 224b + 2688a b + 11424a b + 21504a b + 11424a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 24192a b - 46144a b - 24192a b + 11424a b + 21504a b +--R + +--R 10 2 11 12 +--R 11424a b + 2688a b + 224a +--R * +--R 6 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 480b - 3520a b - 7040a b + 1472a b + 19552a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 15872a b - 11648a b - 21248a b - 4768a b + 6592a b +--R + +--R 10 2 11 12 +--R 4352a b + 832a b + 32a +--R * +--R 4 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 288b + 768a b - 864a b - 3072a b + 576a b + 4608a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 576a b - 3072a b - 864a b + 768a b + 288a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 5 7 6 6 7 5 +--R - 32b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 8 4 +--R 32a b +--R * +--R 6 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 64b + 1152a b + 6528a b + 16320a b + 15936a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 9216a b - 37376a b - 31104a b + 960a b + 18816a b +--R + +--R 10 2 11 12 +--R 13440a b + 4032a b + 448a +--R * +--R 7 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 192b - 2304a b - 7296a b - 4608a b + 15168a b +--R + +--R 5 7 7 5 8 4 9 3 10 2 +--R 25344a b - 25344a b - 15168a b + 4608a b + 7296a b +--R + +--R 11 12 +--R 2304a b + 192a +--R * +--R 5 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 192b + 1152a b + 384a b - 4416a b - 3456a b + 6144a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 11 +--R 6144a b - 3456a b - 4416a b + 384a b + 1152a b + 192a b +--R * +--R 3 +--R cosh(x) +--R + +--R 12 2 10 3 9 4 8 5 7 6 6 +--R - 64b + 384a b - 128a b - 768a b + 384a b + 640a b +--R + +--R 7 5 8 4 9 3 +--R - 384a b - 192a b + 128a b +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 8b + 288a b + 2400a b + 8160a b + 12000a b + 1440a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R - 19360a b - 24480a b - 6360a b + 10560a b + 10752a b +--R + +--R 11 12 +--R 4032a b + 560a +--R * +--R 8 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 32b - 832a b - 4352a b - 6592a b + 4768a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 21248a b + 11648a b - 15872a b - 19552a b - 1472a b +--R + +--R 10 2 11 12 +--R 7040a b + 3520a b + 480a +--R * +--R 6 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 48b + 768a b + 1536a b - 2304a b - 6576a b + 1536a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 11 +--R 9984a b + 1536a b - 6576a b - 2304a b + 1536a b + 768a b +--R + +--R 12 +--R 48a +--R * +--R 4 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R - 32b - 192a b + 384a b + 704a b - 1152a b - 960a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 1472a b + 576a b - 864a b - 128a b + 192a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R 8b - 32a b + 32a b + 32a b - 80a b + 32a b + 32a b +--R + +--R 7 5 8 4 +--R - 32a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 32a b + 512a b + 2560a b + 5440a b + 3520a b - 5760a b +--R + +--R 7 5 8 4 9 3 10 2 11 12 +--R - 12160a b - 6400a b + 3360a b + 5760a b + 2688a b + 448a +--R * +--R 9 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 +--R - 128a b - 1408a b - 3968a b - 1408a b + 9472a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 12032a b - 3328a b - 13568a b - 5248a b + 3712a b +--R + +--R 11 12 +--R 3200a b + 640a +--R * +--R 7 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 192a b + 1152a b + 384a b - 4416a b - 3456a b + 6144a b +--R + +--R 7 5 8 4 9 3 10 2 11 12 +--R 6144a b - 3456a b - 4416a b + 384a b + 1152a b + 192a +--R * +--R 5 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 7 5 +--R - 128a b - 128a b + 896a b + 256a b - 2048a b + 2048a b +--R + +--R 8 4 9 3 10 2 11 +--R - 256a b - 896a b + 128a b + 128a b +--R * +--R 3 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 32a b - 128a b + 128a b + 128a b - 320a b + 128a b +--R + +--R 7 5 8 4 9 3 +--R 128a b - 128a b + 32a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 48a b + 448a b + 1440a b + 1728a b - 608a b - 3648a b +--R + +--R 8 4 9 3 10 2 11 12 +--R - 3072a b + 320a b + 1968a b + 1152a b + 224a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 +--R - 192a b - 1152a b - 1632a b + 1728a b + 5568a b +--R + +--R 7 5 8 4 9 3 10 2 11 12 +--R 1728a b - 4992a b - 4032a b + 768a b + 1728a b + 480a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 288a b + 768a b - 864a b - 3072a b + 576a b + 4608a b +--R + +--R 8 4 9 3 10 2 11 12 +--R 576a b - 3072a b - 864a b + 768a b + 288a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R - 192a b + 128a b + 864a b - 576a b - 1472a b + 960a b +--R + +--R 8 4 9 3 10 2 11 12 +--R 1152a b - 704a b - 384a b + 192a b + 32a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 48a b - 192a b + 192a b + 192a b - 480a b + 192a b +--R + +--R 8 4 9 3 10 2 +--R 192a b - 192a b + 48a b +--R * +--R 2 +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 32a b + 192a b + 384a b + 128a b - 576a b - 768a b +--R + +--R 9 3 10 2 11 12 +--R - 128a b + 384a b + 288a b + 64a +--R * +--R 11 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R - 128a b - 448a b - 128a b + 1152a b + 1152a b - 768a b +--R + +--R 9 3 10 2 11 12 +--R - 1408a b - 128a b + 512a b + 192a +--R * +--R 9 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 192a b + 192a b - 768a b - 768a b + 1152a b + 1152a b +--R + +--R 9 3 10 2 11 12 +--R - 768a b - 768a b + 192a b + 192a +--R * +--R 7 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R - 128a b + 192a b + 384a b - 640a b - 384a b + 768a b +--R + +--R 9 3 10 2 12 +--R 128a b - 384a b + 64a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 32a b - 128a b + 128a b + 128a b - 320a b + 128a b +--R + +--R 9 3 10 2 11 +--R 128a b - 128a b + 32a b +--R * +--R 3 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R 8a b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b +--R + +--R 11 12 +--R 32a b + 8a +--R * +--R 12 +--R cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 9 3 10 2 11 +--R - 32a b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 12 +--R 32a +--R * +--R 10 +--R cosh(x) +--R + +--R 4 8 6 6 8 4 10 2 12 8 +--R (48a b - 192a b + 288a b - 192a b + 48a )cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 9 3 10 2 11 +--R - 32a b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 12 +--R 32a +--R * +--R 6 +--R cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R 8a b - 32a b + 32a b + 32a b - 80a b + 32a b + 32a b +--R + +--R 11 12 +--R - 32a b + 8a +--R * +--R 4 +--R cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 396 + +--S 397 of 502 +--d0878b:= D(m0878b,x) +--E 397 + +--S 398 of 502 +t0879:= (a*cosh(x)+b*sinh(x))^(1/2) +--R +--R +--R +---------------------+ +--R (229) \|b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 398 + +--S 399 of 502 +r0879:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (a*cosh(x)+b*sinh(x))^(1/2)/(-(a*cosh(x)+b*sinh(x))/_ + (a^2-b^2)^(1/2))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial Complex Integer +--R Variable a +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 399 + +--S 400 of 502 +a0879:= integrate(t0879,x) +--R +--R +--R x +--R ++ +-----------------------+ +--R (230) | \|b sinh(%I) + a cosh(%I) d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 400 + +--S 401 of 502 +--m0879:= a0879-r0879 +--E 401 + +--S 402 of 502 +--d0879:= D(m0879,x) +--E 402 + +--S 403 of 502 +t0880:= (a*cosh(x)+b*sinh(x))^(3/2) +--R +--R +--R +---------------------+ +--R (231) (b sinh(x) + a cosh(x))\|b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 403 + +--S 404 of 502 +r0880:= 2/3*(b*cosh(x)+a*sinh(x))*(a*cosh(x)+b*sinh(x))^(1/2)-_ + 2/3*%i*(a^2-b^2)*EllipticF(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (-(a*cosh(x)+b*sinh(x))/(a^2-b^2)^(1/2))^(1/2)/(a*cosh(x)+_ + b*sinh(x))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial Complex Integer +--R Variable a +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 404 + +--S 405 of 502 +a0880:= integrate(t0880,x) +--R +--R +--R x +--R ++ +-----------------------+ +--R (232) | (b sinh(%I) + a cosh(%I))\|b sinh(%I) + a cosh(%I) d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 405 + +--S 406 of 502 +--m0880:= a0880-r0880 +--E 406 + +--S 407 of 502 +--d0880:= D(m0880,x) +--E 407 + +--S 408 of 502 +t0881:= (a*cosh(x)+b*sinh(x))^(5/2) +--R +--R +--R (233) +--R 2 2 2 2 +---------------------+ +--R (b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) )\|b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 408 + +--S 409 of 502 +r0881:= 2/5*(b*cosh(x)+a*sinh(x))*(a*cosh(x)+b*sinh(x))^(3/2)-_ + 6/5*%i*(a^2-b^2)*EllipticE(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (a*cosh(x)+b*sinh(x))^(1/2)/(-(a*cosh(x)+b*sinh(x))/_ + (a^2-b^2)^(1/2))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial Complex Integer +--R Variable a +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 409 + +--S 410 of 502 +a0881:= integrate(t0881,x) +--R +--R +--R (234) +--R INTSIGN +--R , +--R x +--R , +--R 2 2 2 2 +--R (b sinh(%I) + 2a b cosh(%I)sinh(%I) + a cosh(%I) ) +--R * +--R +-----------------------+ +--R \|b sinh(%I) + a cosh(%I) d%I +--R Type: Union(Expression Integer,...) +--E 410 + +--S 411 of 502 +--m0881:= a0881-r0881 +--E 411 + +--S 412 of 502 +--d0881:= D(m0881,x) +--E 412 + +--S 413 of 502 +t0882:= 1/(a*cosh(x)+b*sinh(x))^(1/2) +--R +--R +--R 1 +--R (235) ------------------------ +--R +---------------------+ +--R \|b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 413 + +--S 414 of 502 +r0882:= -2*%i*EllipticF(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (-(a*cosh(x)+b*sinh(x))/(a^2-b^2)^(1/2))^(1/2)/_ + (a*cosh(x)+b*sinh(x))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial Complex Integer +--R Variable a +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 414 + +--S 415 of 502 +a0882:= integrate(t0882,x) +--R +--R +--R x +--R ++ 1 +--R (236) | -------------------------- d%I +--R ++ +-----------------------+ +--R \|b sinh(%I) + a cosh(%I) +--R Type: Union(Expression Integer,...) +--E 415 + +--S 416 of 502 +--m0882:= a0882-r0882 +--E 416 + +--S 417 of 502 +--d0882:= D(m0882,x) +--E 417 + +--S 418 of 502 +t0883:= 1/(a*cosh(x)+b*sinh(x))^(3/2) +--R +--R +--R 1 +--R (237) ----------------------------------------------- +--R +---------------------+ +--R (b sinh(x) + a cosh(x))\|b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 418 + +--S 419 of 502 +r0883:= 2*(b*cosh(x)+a*sinh(x))/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^(1/2)+_ + 2*%i*EllipticE(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (a*cosh(x)+b*sinh(x))^(1/2)/(a^2-b^2)/_ + (-(a*cosh(x)+b*sinh(x))/(a^2-b^2)^(1/2))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial Complex Integer +--R Variable a +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 419 + +--S 420 of 502 +a0883:= integrate(t0883,x) +--R +--R +--R x +--R ++ 1 +--R (238) | --------------------------------------------------- d%I +--R ++ +-----------------------+ +--R (b sinh(%I) + a cosh(%I))\|b sinh(%I) + a cosh(%I) +--R Type: Union(Expression Integer,...) +--E 420 + +--S 421 of 502 +--m0883:= a0883-r0883 +--E 421 + +--S 422 of 502 +--d0883:= D(m0883,x) +--E 422 + +--S 423 of 502 +t0884:= 1/(a*cosh(x)+b*sinh(x))^(5/2) +--R +--R +--R (239) +--R 1 +--R ----------------------------------------------------------------------- +--R 2 2 2 2 +---------------------+ +--R (b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) )\|b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 423 + +--S 424 of 502 +r0884:= 2/3*(b*cosh(x)+a*sinh(x))/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^(3/2)-_ + 2/3*%i*EllipticF(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (-(a*cosh(x)+b*sinh(x))/(a^2-b^2)^(1/2))^(1/2)/_ + (a^2-b^2)/(a*cosh(x)+b*sinh(x))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial Complex Integer +--R Variable a +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 424 + +--S 425 of 502 +a0884:= integrate(t0884,x) +--R +--R +--R (240) +--R INTSIGN +--R , +--R x +--R , +--R 1 +--R / +--R 2 2 2 2 +--R (b sinh(%I) + 2a b cosh(%I)sinh(%I) + a cosh(%I) ) +--R * +--R +-----------------------+ +--R \|b sinh(%I) + a cosh(%I) +--R * +--R d%I +--R Type: Union(Expression Integer,...) +--E 425 + +--S 426 of 502 +--m0884:= a0884-r0884 +--E 426 + +--S 427 of 502 +--d0884:= D(m0884,x) +--E 427 + +--S 428 of 502 +t0885:= (sech(x)+%i*tanh(x))^3 +--R +--R +--R 3 2 2 3 +--R (241) - %i tanh(x) - 3sech(x)tanh(x) + 3%i sech(x) tanh(x) + sech(x) +--R Type: Expression Complex Integer +--E 428 + +--S 429 of 502 +r0885:= -%i*log(1-%i*sinh(x))-2*%i/(1-%i*sinh(x)) +--R +--R +--R (- %i sinh(x) + 1)log(- %i sinh(x) + 1) + 2 +--R (242) ------------------------------------------- +--R sinh(x) + %i +--R Type: Expression Complex Integer +--E 429 + +--S 430 of 502 +a0885:= integrate(t0885,x) +--R +--R +--R (243) +--R 2 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) + 4)sinh(x) - 2%i cosh(x) + 4cosh(x) +--R + +--R 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 2 2 +--R %i x sinh(x) + (2%i x cosh(x) - 2x + 4)sinh(x) + %i x cosh(x) +--R + +--R (- 2x + 4)cosh(x) - %i x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2%i)sinh(x) + cosh(x) + 2%i cosh(x) - 1 +--R Type: Union(Expression Complex Integer,...) +--E 430 + +--S 431 of 502 +m0885:= a0885-r0885 +--R +--R +--R (244) +--R 3 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) + 6)sinh(x) +--R + +--R 2 2 +--R (- 2%i cosh(x) + 8cosh(x) + 6%i)sinh(x) + 2cosh(x) + 4%i cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 3 2 +--R %i sinh(x) + (2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (%i cosh(x) - 4cosh(x) - 3%i)sinh(x) - cosh(x) - 2%i cosh(x) + 1 +--R * +--R log(- %i sinh(x) + 1) +--R + +--R 3 2 +--R %i x sinh(x) + (2%i x cosh(x) - 3x + 2)sinh(x) +--R + +--R 2 2 +--R (%i x cosh(x) - 4x cosh(x) - 3%i x)sinh(x) + (- x - 2)cosh(x) +--R + +--R - 2%i x cosh(x) + x + 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) + 3%i)sinh(x) + (cosh(x) + 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R %i cosh(x) - 2cosh(x) - %i +--R Type: Expression Complex Integer +--E 431 + +--S 432 of 502 +d0885:= D(m0885,x) +--R +--R +--R (245) +--R 5 4 3 +--R - %i sinh(x) + (- 2%i cosh(x) - 1)sinh(x) + (- 2cosh(x) - 2%i)sinh(x) +--R + +--R 3 2 +--R (2%i cosh(x) - 6%i cosh(x) - 2)sinh(x) +--R + +--R 4 3 4 +--R (%i cosh(x) + 2cosh(x) - 2cosh(x) - %i)sinh(x) + cosh(x) +--R + +--R 3 +--R 4%i cosh(x) - 4%i cosh(x) - 1 +--R / +--R 5 4 +--R sinh(x) + (3cosh(x) + 5%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) + 12%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) + 9%i cosh(x) - 18cosh(x) - 10%i)sinh(x) +--R + +--R 3 2 3 +--R (2%i cosh(x) - 9cosh(x) - 12%i cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 2 +--R - 3%i cosh(x) + 3cosh(x) + %i +--R Type: Expression Complex Integer +--E 432 + +--S 433 of 502 +t0886:= (sech(x)+%i*tanh(x))^5 +--R +--R +--R (246) +--R 5 4 2 3 3 2 +--R %i tanh(x) + 5sech(x)tanh(x) - 10%i sech(x) tanh(x) - 10sech(x) tanh(x) +--R + +--R 4 5 +--R 5%i sech(x) tanh(x) + sech(x) +--R Type: Expression Complex Integer +--E 433 + +--S 434 of 502 +r0886:= %i*log(1-%i*sinh(x))-2*%i/(1-%i*sinh(x))^2+4*%i/(1-%i*sinh(x)) +--R +--R +--R 2 +--R (%i sinh(x) - 2sinh(x) - %i)log(- %i sinh(x) + 1) - 4sinh(x) - 2%i +--R (247) ------------------------------------------------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression Complex Integer +--E 434 + +--S 435 of 502 +a0886:= integrate(t0886,x) +--R +--R +--R (248) +--R 4 3 +--R 2%i sinh(x) + (8%i cosh(x) - 8)sinh(x) +--R + +--R 2 2 +--R (12%i cosh(x) - 24cosh(x) - 12%i)sinh(x) +--R + +--R 3 2 4 +--R (8%i cosh(x) - 24cosh(x) - 24%i cosh(x) + 8)sinh(x) + 2%i cosh(x) +--R + +--R 3 2 +--R - 8cosh(x) - 12%i cosh(x) + 8cosh(x) + 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 4 3 +--R - %i x sinh(x) + (- 4%i x cosh(x) + 4x - 8)sinh(x) +--R + +--R 2 2 +--R (- 6%i x cosh(x) + (12x - 24)cosh(x) + 6%i x - 8%i)sinh(x) +--R + +--R 3 2 +--R - 4%i x cosh(x) + (12x - 24)cosh(x) + (12%i x - 16%i)cosh(x) - 4x +--R + +--R 8 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R - %i x cosh(x) + (4x - 8)cosh(x) + (6%i x - 8%i)cosh(x) +--R + +--R (- 4x + 8)cosh(x) - %i x +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) + 4%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) + 12%i cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) + 12%i cosh(x) - 12cosh(x) - 4%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R 4%i cosh(x) - 6cosh(x) - 4%i cosh(x) + 1 +--R Type: Union(Expression Complex Integer,...) +--E 435 + +--S 436 of 502 +m0886:= a0886-r0886 +--R +--R +--R (249) +--R 6 5 +--R 2%i sinh(x) + (8%i cosh(x) - 12)sinh(x) +--R + +--R 2 4 +--R (12%i cosh(x) - 40cosh(x) - 30%i)sinh(x) +--R + +--R 3 2 3 +--R (8%i cosh(x) - 48cosh(x) - 80%i cosh(x) + 40)sinh(x) +--R + +--R 4 3 2 +--R (2%i cosh(x) - 24cosh(x) - 72%i cosh(x) + 80cosh(x) + 30%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 4cosh(x) - 24%i cosh(x) + 48cosh(x) + 40%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R - 2%i cosh(x) + 8cosh(x) + 12%i cosh(x) - 8cosh(x) - 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 6 5 +--R - %i sinh(x) + (- 4%i cosh(x) + 6)sinh(x) +--R + +--R 2 4 +--R (- 6%i cosh(x) + 20cosh(x) + 15%i)sinh(x) +--R + +--R 3 2 3 +--R (- 4%i cosh(x) + 24cosh(x) + 40%i cosh(x) - 20)sinh(x) +--R + +--R 4 3 2 +--R (- %i cosh(x) + 12cosh(x) + 36%i cosh(x) - 40cosh(x) - 15%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2cosh(x) + 12%i cosh(x) - 24cosh(x) - 20%i cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 +--R %i cosh(x) - 4cosh(x) - 6%i cosh(x) + 4cosh(x) + %i +--R * +--R log(- %i sinh(x) + 1) +--R + +--R 6 5 +--R - %i x sinh(x) + (- 4%i x cosh(x) + 6x - 4)sinh(x) +--R + +--R 2 4 +--R (- 6%i x cosh(x) + (20x - 8)cosh(x) + 15%i x - 6%i)sinh(x) +--R + +--R 3 2 3 +--R (- 4%i x cosh(x) + 24x cosh(x) + (40%i x - 8%i)cosh(x) - 20x)sinh(x) +--R + +--R 4 3 2 +--R - %i x cosh(x) + (12x + 8)cosh(x) + (36%i x + 4%i)cosh(x) +--R + +--R (- 40x - 8)cosh(x) - 15%i x - 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2x + 4)cosh(x) + (12%i x + 8%i)cosh(x) + (- 24x - 8)cosh(x) +--R + +--R (- 20%i x - 8%i)cosh(x) + 6x + 4 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (%i x + 2%i)cosh(x) - 4x cosh(x) + (- 6%i x - 4%i)cosh(x) + 4x cosh(x) +--R + +--R %i x + 2%i +--R / +--R 6 5 +--R sinh(x) + (4cosh(x) + 6%i)sinh(x) +--R + +--R 2 4 +--R (6cosh(x) + 20%i cosh(x) - 15)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) + 24%i cosh(x) - 40cosh(x) - 20%i)sinh(x) +--R + +--R 4 3 2 2 +--R (cosh(x) + 12%i cosh(x) - 36cosh(x) - 40%i cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 +--R (2%i cosh(x) - 12cosh(x) - 24%i cosh(x) + 20cosh(x) + 6%i)sinh(x) +--R + +--R 4 3 2 +--R - cosh(x) - 4%i cosh(x) + 6cosh(x) + 4%i cosh(x) - 1 +--R Type: Expression Complex Integer +--E 436 + +--S 437 of 502 +d0886:= D(m0886,x) +--R +--R +--R (250) +--R 8 7 +--R %i sinh(x) + (4%i cosh(x) + 2)sinh(x) +--R + +--R 2 6 +--R (5%i cosh(x) + 8cosh(x) + 2%i)sinh(x) +--R + +--R 2 5 +--R (10cosh(x) + 16%i cosh(x) + 6)sinh(x) +--R + +--R 4 2 4 +--R (- 5%i cosh(x) + 25%i cosh(x) + 20cosh(x))sinh(x) +--R + +--R 5 4 2 3 +--R (- 4%i cosh(x) - 10cosh(x) + 20cosh(x) + 20%i cosh(x) + 6)sinh(x) +--R + +--R 6 5 4 2 +--R - %i cosh(x) - 8cosh(x) - 20%i cosh(x) + 35%i cosh(x) + 16cosh(x) +--R + +--R - 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 2 +--R - 2cosh(x) - 8%i cosh(x) - 10cosh(x) + 10cosh(x) + 8%i cosh(x) +--R + +--R 2 +--R * +--R sinh(x) +--R + +--R 6 5 4 2 +--R %i cosh(x) - 4cosh(x) - 15%i cosh(x) + 15%i cosh(x) + 4cosh(x) - %i +--R / +--R 8 7 +--R sinh(x) + (5cosh(x) + 8%i)sinh(x) +--R + +--R 2 6 +--R (10cosh(x) + 35%i cosh(x) - 28)sinh(x) +--R + +--R 3 2 5 +--R (10cosh(x) + 60%i cosh(x) - 105cosh(x) - 56%i)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) + 50%i cosh(x) - 150cosh(x) - 175%i cosh(x) + 70)sinh(x) +--R + +--R 5 4 3 2 +--R cosh(x) + 20%i cosh(x) - 100cosh(x) - 200%i cosh(x) + 175cosh(x) +--R + +--R 56%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 3%i cosh(x) - 30cosh(x) - 100%i cosh(x) + 150cosh(x) +--R + +--R 105%i cosh(x) - 28 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3cosh(x) - 20%i cosh(x) + 50cosh(x) + 60%i cosh(x) - 35cosh(x) +--R + +--R - 8%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R - %i cosh(x) + 5cosh(x) + 10%i cosh(x) - 10cosh(x) - 5%i cosh(x) + 1 +--R Type: Expression Complex Integer +--E 437 + +--S 438 of 502 +t0887:= 1/(sech(x)+%i*tanh(x)) +--R +--R +--R %i +--R (251) - -------------------- +--R tanh(x) - %i sech(x) +--R Type: Expression Complex Integer +--E 438 + +--S 439 of 502 +r0887:= -%i*log(1+%i*sinh(x)) +--R +--R +--R (252) - %i log(%i sinh(x) + 1) +--R Type: Expression Complex Integer +--E 439 + +--S 440 of 502 +a0887:= integrate(t0887,x) +--R +--R +--R (253) - 2%i log(sinh(x) + cosh(x) - %i) + %i x +--R Type: Union(Expression Complex Integer,...) +--E 440 + +--S 441 of 502 +m0887:= a0887-r0887 +--R +--R +--R (254) - 2%i log(sinh(x) + cosh(x) - %i) + %i log(%i sinh(x) + 1) + %i x +--R Type: Expression Complex Integer +--E 441 + +--S 442 of 502 +d0887:= D(m0887,x) +--R +--R +--R 2 2 +--R - %i sinh(x) + %i cosh(x) - %i +--R (255) -------------------------------------------------- +--R 2 +--R sinh(x) + (cosh(x) - 2%i)sinh(x) - %i cosh(x) - 1 +--R Type: Expression Complex Integer +--E 442 + +--S 443 of 502 +t0888:= 1/(sech(x)+%i*tanh(x))^2 +--R +--R +--R 1 +--R (256) - ---------------------------------------- +--R 2 2 +--R tanh(x) - 2%i sech(x)tanh(x) - sech(x) +--R Type: Expression Complex Integer +--E 443 + +--S 444 of 502 +r0888:= -x+2*%i*sech(x)+2*tanh(x) +--R +--R +--R (257) 2tanh(x) + 2%i sech(x) - x +--R Type: Expression Complex Integer +--E 444 + +--S 445 of 502 +a0888:= integrate(t0888,x) +--R +--R +--R - x sinh(x) - x cosh(x) + %i x + 4%i +--R (258) ------------------------------------ +--R sinh(x) + cosh(x) - %i +--R Type: Union(Expression Complex Integer,...) +--E 445 + +--S 446 of 502 +m0888:= a0888-r0888 +--R +--R +--R (259) +--R (- 2sinh(x) - 2cosh(x) + 2%i)tanh(x) - 2%i sech(x)sinh(x) +--R + +--R (- 2%i cosh(x) - 2)sech(x) + 4%i +--R / +--R sinh(x) + cosh(x) - %i +--R Type: Expression Complex Integer +--E 446 + +--S 447 of 502 +d0888:= D(m0888,x) +--R +--R +--R (260) +--R 2 2 +--R (2sinh(x) + (4cosh(x) - 4%i)sinh(x) + 2cosh(x) - 4%i cosh(x) - 2) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 +--R 2%i sech(x)sinh(x) + (4%i cosh(x) + 4)sech(x)sinh(x) +--R + +--R 2 +--R (2%i cosh(x) + 4cosh(x) - 2%i)sech(x) +--R * +--R tanh(x) +--R + +--R 2 2 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2%i)sinh(x) + cosh(x) - 2%i cosh(x) - 1 +--R Type: Expression Complex Integer +--E 447 + +--S 448 of 502 +t0889:= 1/(sech(x)+%i*tanh(x))^3 +--R +--R +--R %i +--R (261) --------------------------------------------------------------- +--R 3 2 2 3 +--R tanh(x) - 3%i sech(x)tanh(x) - 3sech(x) tanh(x) + %i sech(x) +--R Type: Expression Complex Integer +--E 448 + +--S 449 of 502 +r0889:= %i*log(1+%i*sinh(x))+2*%i/(1+%i*sinh(x)) +--R +--R +--R (%i sinh(x) + 1)log(%i sinh(x) + 1) + 2 +--R (262) --------------------------------------- +--R sinh(x) - %i +--R Type: Expression Complex Integer +--E 449 + +--S 450 of 502 +a0889:= integrate(t0889,x) +--R +--R +--R (263) +--R 2 2 +--R 2%i sinh(x) + (4%i cosh(x) + 4)sinh(x) + 2%i cosh(x) + 4cosh(x) +--R + +--R - 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 2 2 +--R - %i x sinh(x) + (- 2%i x cosh(x) - 2x + 4)sinh(x) - %i x cosh(x) +--R + +--R (- 2x + 4)cosh(x) + %i x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2%i)sinh(x) + cosh(x) - 2%i cosh(x) - 1 +--R Type: Union(Expression Complex Integer,...) +--E 450 + +--S 451 of 502 +m0889:= a0889-r0889 +--R +--R +--R (264) +--R 3 2 +--R 2%i sinh(x) + (4%i cosh(x) + 6)sinh(x) +--R + +--R 2 2 +--R (2%i cosh(x) + 8cosh(x) - 6%i)sinh(x) + 2cosh(x) - 4%i cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 3 2 +--R - %i sinh(x) + (- 2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (- %i cosh(x) - 4cosh(x) + 3%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R * +--R log(%i sinh(x) + 1) +--R + +--R 3 2 +--R - %i x sinh(x) + (- 2%i x cosh(x) - 3x + 2)sinh(x) +--R + +--R 2 2 +--R (- %i x cosh(x) - 4x cosh(x) + 3%i x)sinh(x) + (- x - 2)cosh(x) +--R + +--R 2%i x cosh(x) + x + 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) - 3%i)sinh(x) + (cosh(x) - 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R - %i cosh(x) - 2cosh(x) + %i +--R Type: Expression Complex Integer +--E 451 + +--S 452 of 502 +d0889:= D(m0889,x) +--R +--R +--R (265) +--R 5 4 3 +--R %i sinh(x) + (2%i cosh(x) - 1)sinh(x) + (- 2cosh(x) + 2%i)sinh(x) +--R + +--R 3 2 +--R (- 2%i cosh(x) + 6%i cosh(x) - 2)sinh(x) +--R + +--R 4 3 4 +--R (- %i cosh(x) + 2cosh(x) - 2cosh(x) + %i)sinh(x) + cosh(x) +--R + +--R 3 +--R - 4%i cosh(x) + 4%i cosh(x) - 1 +--R / +--R 5 4 +--R sinh(x) + (3cosh(x) - 5%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 12%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) - 9%i cosh(x) - 18cosh(x) + 10%i)sinh(x) +--R + +--R 3 2 3 +--R (- 2%i cosh(x) - 9cosh(x) + 12%i cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 2 +--R 3%i cosh(x) + 3cosh(x) - %i +--R Type: Expression Complex Integer +--E 452 + +--S 453 of 502 +t0890:= 1/(sech(x)+%i*tanh(x))^4 +--R +--R +--R (266) +--R 1 +--R / +--R 4 3 2 2 3 +--R tanh(x) - 4%i sech(x)tanh(x) - 6sech(x) tanh(x) + 4%i sech(x) tanh(x) +--R + +--R 4 +--R sech(x) +--R Type: Expression Complex Integer +--E 453 + +--S 454 of 502 +r0890:= x-4*%i*sech(x)+8/3*%i*sech(x)^3-8/3*tanh(x)^3 +--R +--R +--R 8 3 8 3 +--R (267) - - tanh(x) + - %i sech(x) - 4%i sech(x) + x +--R 3 3 +--R Type: Expression Complex Fraction Integer +--E 454 + +--S 455 of 502 +a0890:= integrate(t0890,x) +--R +--R +--R (268) +--R 2 2 +--R 3x sinh(x) + (6x cosh(x) - 12%i x - 40%i)sinh(x) + 3x cosh(x) +--R + +--R (- 6%i x - 8%i)cosh(x) - 9x - 24 +--R / +--R 2 2 +--R 3sinh(x) + (6cosh(x) - 12%i)sinh(x) + 3cosh(x) - 6%i cosh(x) - 9 +--R Type: Union(Expression Complex Integer,...) +--E 455 + +--S 456 of 502 +m0890:= a0890-r0890 +--R +--R +--R (269) +--R 8 2 16 32 8 2 16 +--R - sinh(x) + (-- cosh(x) - -- %i)sinh(x) + - cosh(x) - -- %i cosh(x) +--R 3 3 3 3 3 +--R + +--R - 8 +--R * +--R 3 +--R tanh(x) +--R + +--R 8 3 2 +--R (- - %i sech(x) + 4%i sech(x))sinh(x) +--R 3 +--R + +--R 16 32 3 40 +--R ((- -- %i cosh(x) - --)sech(x) + (8%i cosh(x) + 16)sech(x) - -- %i) +--R 3 3 3 +--R * +--R sinh(x) +--R + +--R 8 2 16 3 +--R (- - %i cosh(x) - -- cosh(x) + 8%i)sech(x) +--R 3 3 +--R + +--R 2 8 +--R (4%i cosh(x) + 8cosh(x) - 12%i)sech(x) - - %i cosh(x) - 8 +--R 3 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 4%i)sinh(x) + cosh(x) - 2%i cosh(x) - 3 +--R Type: Expression Complex Fraction Integer +--E 456 + +--S 457 of 502 +d0890:= D(m0890,x) +--R +--R +--R (270) +--R 4 3 +--R - 8sinh(x) + (- 32cosh(x) + 64%i)sinh(x) +--R + +--R 2 2 +--R (- 48cosh(x) + 160%i cosh(x) + 176)sinh(x) +--R + +--R 3 2 +--R (- 32cosh(x) + 128%i cosh(x) + 224cosh(x) - 192%i)sinh(x) +--R + +--R 4 3 2 +--R - 8cosh(x) + 32%i cosh(x) + 80cosh(x) - 96%i cosh(x) - 72 +--R * +--R 4 +--R tanh(x) +--R + +--R 4 3 +--R 8sinh(x) + (32cosh(x) - 64%i)sinh(x) +--R + +--R 2 2 +--R (48cosh(x) - 160%i cosh(x) - 176)sinh(x) +--R + +--R 3 2 4 +--R (32cosh(x) - 128%i cosh(x) - 224cosh(x) + 192%i)sinh(x) + 8cosh(x) +--R + +--R 3 2 +--R - 32%i cosh(x) - 80cosh(x) + 96%i cosh(x) + 72 +--R * +--R 2 +--R tanh(x) +--R + +--R 3 4 +--R (8%i sech(x) - 4%i sech(x))sinh(x) +--R + +--R 3 3 +--R ((32%i cosh(x) + 64)sech(x) + (- 16%i cosh(x) - 32)sech(x))sinh(x) +--R + +--R 2 3 +--R (48%i cosh(x) + 160cosh(x) - 176%i)sech(x) +--R + +--R 2 +--R (- 24%i cosh(x) - 80cosh(x) + 88%i)sech(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3 +--R (32%i cosh(x) + 128cosh(x) - 224%i cosh(x) - 192)sech(x) +--R + +--R 3 2 +--R (- 16%i cosh(x) - 64cosh(x) + 112%i cosh(x) + 96)sech(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (8%i cosh(x) + 32cosh(x) - 80%i cosh(x) - 96cosh(x) + 72%i) +--R * +--R 3 +--R sech(x) +--R + +--R 4 3 2 +--R (- 4%i cosh(x) - 16cosh(x) + 40%i cosh(x) + 48cosh(x) - 36%i)sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 +--R 24%i sinh(x) + (40%i cosh(x) + 32)sinh(x) +--R + +--R 2 3 +--R (8%i cosh(x) + 32cosh(x) - 8%i)sinh(x) - 8%i cosh(x) + 8%i cosh(x) +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) - 8%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) - 20%i cosh(x) - 22)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 16%i cosh(x) - 28cosh(x) + 24%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R - 4%i cosh(x) - 10cosh(x) + 12%i cosh(x) + 9 +--R Type: Expression Complex Fraction Integer +--E 457 + +--S 458 of 502 +t0891:= 1/(sech(x)+%i*tanh(x))^5 +--R +--R +--R (271) +--R - +--R %i +--R / +--R 5 4 2 3 +--R tanh(x) - 5%i sech(x)tanh(x) - 10sech(x) tanh(x) +--R + +--R 3 2 4 5 +--R 10%i sech(x) tanh(x) + 5sech(x) tanh(x) - %i sech(x) +--R Type: Expression Complex Integer +--E 458 + +--S 459 of 502 +r0891:= -%i*log(1+%i*sinh(x))+2*%i/(1+%i*sinh(x))^2-4*%i/(1+%i*sinh(x)) +--R +--R +--R 2 +--R (- %i sinh(x) - 2sinh(x) + %i)log(%i sinh(x) + 1) - 4sinh(x) + 2%i +--R (272) ------------------------------------------------------------------- +--R 2 +--R sinh(x) - 2%i sinh(x) - 1 +--R Type: Expression Complex Integer +--E 459 + +--S 460 of 502 +a0891:= integrate(t0891,x) +--R +--R +--R (273) +--R 4 3 +--R - 2%i sinh(x) + (- 8%i cosh(x) - 8)sinh(x) +--R + +--R 2 2 +--R (- 12%i cosh(x) - 24cosh(x) + 12%i)sinh(x) +--R + +--R 3 2 +--R (- 8%i cosh(x) - 24cosh(x) + 24%i cosh(x) + 8)sinh(x) +--R + +--R 4 3 2 +--R - 2%i cosh(x) - 8cosh(x) + 12%i cosh(x) + 8cosh(x) - 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 4 3 +--R %i x sinh(x) + (4%i x cosh(x) + 4x - 8)sinh(x) +--R + +--R 2 2 +--R (6%i x cosh(x) + (12x - 24)cosh(x) - 6%i x + 8%i)sinh(x) +--R + +--R 3 2 +--R 4%i x cosh(x) + (12x - 24)cosh(x) + (- 12%i x + 16%i)cosh(x) - 4x +--R + +--R 8 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R %i x cosh(x) + (4x - 8)cosh(x) + (- 6%i x + 8%i)cosh(x) +--R + +--R (- 4x + 8)cosh(x) + %i x +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) - 12%i cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 12%i cosh(x) - 12cosh(x) + 4%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R - 4%i cosh(x) - 6cosh(x) + 4%i cosh(x) + 1 +--R Type: Union(Expression Complex Integer,...) +--E 460 + +--S 461 of 502 +m0891:= a0891-r0891 +--R +--R +--R (274) +--R 6 5 +--R - 2%i sinh(x) + (- 8%i cosh(x) - 12)sinh(x) +--R + +--R 2 4 +--R (- 12%i cosh(x) - 40cosh(x) + 30%i)sinh(x) +--R + +--R 3 2 3 +--R (- 8%i cosh(x) - 48cosh(x) + 80%i cosh(x) + 40)sinh(x) +--R + +--R 4 3 2 +--R (- 2%i cosh(x) - 24cosh(x) + 72%i cosh(x) + 80cosh(x) - 30%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 4cosh(x) + 24%i cosh(x) + 48cosh(x) - 40%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R 2%i cosh(x) + 8cosh(x) - 12%i cosh(x) - 8cosh(x) + 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 6 5 +--R %i sinh(x) + (4%i cosh(x) + 6)sinh(x) +--R + +--R 2 4 +--R (6%i cosh(x) + 20cosh(x) - 15%i)sinh(x) +--R + +--R 3 2 3 +--R (4%i cosh(x) + 24cosh(x) - 40%i cosh(x) - 20)sinh(x) +--R + +--R 4 3 2 2 +--R (%i cosh(x) + 12cosh(x) - 36%i cosh(x) - 40cosh(x) + 15%i)sinh(x) +--R + +--R 4 3 2 +--R (2cosh(x) - 12%i cosh(x) - 24cosh(x) + 20%i cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 +--R - %i cosh(x) - 4cosh(x) + 6%i cosh(x) + 4cosh(x) - %i +--R * +--R log(%i sinh(x) + 1) +--R + +--R 6 5 +--R %i x sinh(x) + (4%i x cosh(x) + 6x - 4)sinh(x) +--R + +--R 2 4 +--R (6%i x cosh(x) + (20x - 8)cosh(x) - 15%i x + 6%i)sinh(x) +--R + +--R 3 2 3 +--R (4%i x cosh(x) + 24x cosh(x) + (- 40%i x + 8%i)cosh(x) - 20x)sinh(x) +--R + +--R 4 3 2 +--R %i x cosh(x) + (12x + 8)cosh(x) + (- 36%i x - 4%i)cosh(x) +--R + +--R (- 40x - 8)cosh(x) + 15%i x + 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2x + 4)cosh(x) + (- 12%i x - 8%i)cosh(x) + (- 24x - 8)cosh(x) +--R + +--R (20%i x + 8%i)cosh(x) + 6x + 4 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (- %i x - 2%i)cosh(x) - 4x cosh(x) + (6%i x + 4%i)cosh(x) + 4x cosh(x) +--R + +--R - %i x - 2%i +--R / +--R 6 5 +--R sinh(x) + (4cosh(x) - 6%i)sinh(x) +--R + +--R 2 4 +--R (6cosh(x) - 20%i cosh(x) - 15)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) - 24%i cosh(x) - 40cosh(x) + 20%i)sinh(x) +--R + +--R 4 3 2 2 +--R (cosh(x) - 12%i cosh(x) - 36cosh(x) + 40%i cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 +--R (- 2%i cosh(x) - 12cosh(x) + 24%i cosh(x) + 20cosh(x) - 6%i)sinh(x) +--R + +--R 4 3 2 +--R - cosh(x) + 4%i cosh(x) + 6cosh(x) - 4%i cosh(x) - 1 +--R Type: Expression Complex Integer +--E 461 + +--S 462 of 502 +d0891:= D(m0891,x) +--R +--R +--R (275) +--R 8 7 +--R - %i sinh(x) + (- 4%i cosh(x) + 2)sinh(x) +--R + +--R 2 6 +--R (- 5%i cosh(x) + 8cosh(x) - 2%i)sinh(x) +--R + +--R 2 5 +--R (10cosh(x) - 16%i cosh(x) + 6)sinh(x) +--R + +--R 4 2 4 +--R (5%i cosh(x) - 25%i cosh(x) + 20cosh(x))sinh(x) +--R + +--R 5 4 2 3 +--R (4%i cosh(x) - 10cosh(x) + 20cosh(x) - 20%i cosh(x) + 6)sinh(x) +--R + +--R 6 5 4 2 +--R %i cosh(x) - 8cosh(x) + 20%i cosh(x) - 35%i cosh(x) + 16cosh(x) +--R + +--R 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 2 +--R - 2cosh(x) + 8%i cosh(x) - 10cosh(x) + 10cosh(x) - 8%i cosh(x) +--R + +--R 2 +--R * +--R sinh(x) +--R + +--R 6 5 4 2 +--R - %i cosh(x) - 4cosh(x) + 15%i cosh(x) - 15%i cosh(x) + 4cosh(x) + %i +--R / +--R 8 7 +--R sinh(x) + (5cosh(x) - 8%i)sinh(x) +--R + +--R 2 6 +--R (10cosh(x) - 35%i cosh(x) - 28)sinh(x) +--R + +--R 3 2 5 +--R (10cosh(x) - 60%i cosh(x) - 105cosh(x) + 56%i)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) - 50%i cosh(x) - 150cosh(x) + 175%i cosh(x) + 70)sinh(x) +--R + +--R 5 4 3 2 +--R cosh(x) - 20%i cosh(x) - 100cosh(x) + 200%i cosh(x) + 175cosh(x) +--R + +--R - 56%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3%i cosh(x) - 30cosh(x) + 100%i cosh(x) + 150cosh(x) +--R + +--R - 105%i cosh(x) - 28 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3cosh(x) + 20%i cosh(x) + 50cosh(x) - 60%i cosh(x) - 35cosh(x) +--R + +--R 8%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R %i cosh(x) + 5cosh(x) - 10%i cosh(x) - 10cosh(x) + 5%i cosh(x) + 1 +--R Type: Expression Complex Integer +--E 462 + +--S 463 of 502 +t0892:= (sech(x)-%i*tanh(x))^3 +--R +--R +--R 3 2 2 3 +--R (276) %i tanh(x) - 3sech(x)tanh(x) - 3%i sech(x) tanh(x) + sech(x) +--R Type: Expression Complex Integer +--E 463 + +--S 464 of 502 +r0892:= %i*log(-%i+sinh(x))-2/(%i-sinh(x)) +--R +--R +--R (%i sinh(x) + 1)log(sinh(x) - %i) + 2 +--R (277) ------------------------------------- +--R sinh(x) - %i +--R Type: Expression Complex Integer +--E 464 + +--S 465 of 502 +a0892:= integrate(t0892,x) +--R +--R +--R (278) +--R 2 2 +--R 2%i sinh(x) + (4%i cosh(x) + 4)sinh(x) + 2%i cosh(x) + 4cosh(x) +--R + +--R - 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 2 2 +--R - %i x sinh(x) + (- 2%i x cosh(x) - 2x + 4)sinh(x) - %i x cosh(x) +--R + +--R (- 2x + 4)cosh(x) + %i x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2%i)sinh(x) + cosh(x) - 2%i cosh(x) - 1 +--R Type: Union(Expression Complex Integer,...) +--E 465 + +--S 466 of 502 +m0892:= a0892-r0892 +--R +--R +--R (279) +--R 3 2 +--R 2%i sinh(x) + (4%i cosh(x) + 6)sinh(x) +--R + +--R 2 2 +--R (2%i cosh(x) + 8cosh(x) - 6%i)sinh(x) + 2cosh(x) - 4%i cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 3 2 +--R - %i sinh(x) + (- 2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (- %i cosh(x) - 4cosh(x) + 3%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R * +--R log(sinh(x) - %i) +--R + +--R 3 2 +--R - %i x sinh(x) + (- 2%i x cosh(x) - 3x + 2)sinh(x) +--R + +--R 2 2 +--R (- %i x cosh(x) - 4x cosh(x) + 3%i x)sinh(x) + (- x - 2)cosh(x) +--R + +--R 2%i x cosh(x) + x + 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) - 3%i)sinh(x) + (cosh(x) - 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R - %i cosh(x) - 2cosh(x) + %i +--R Type: Expression Complex Integer +--E 466 + +--S 467 of 502 +d0892:= D(m0892,x) +--R +--R +--R (280) +--R 5 4 3 +--R %i sinh(x) + (2%i cosh(x) - 1)sinh(x) + (- 2cosh(x) + 2%i)sinh(x) +--R + +--R 3 2 +--R (- 2%i cosh(x) + 6%i cosh(x) - 2)sinh(x) +--R + +--R 4 3 4 +--R (- %i cosh(x) + 2cosh(x) - 2cosh(x) + %i)sinh(x) + cosh(x) +--R + +--R 3 +--R - 4%i cosh(x) + 4%i cosh(x) - 1 +--R / +--R 5 4 +--R sinh(x) + (3cosh(x) - 5%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 12%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) - 9%i cosh(x) - 18cosh(x) + 10%i)sinh(x) +--R + +--R 3 2 3 +--R (- 2%i cosh(x) - 9cosh(x) + 12%i cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 2 +--R 3%i cosh(x) + 3cosh(x) - %i +--R Type: Expression Complex Integer +--E 467 + +--S 468 of 502 +t0893:= (sech(x)-%i*tanh(x))^5 +--R +--R +--R (281) +--R 5 4 2 3 +--R - %i tanh(x) + 5sech(x)tanh(x) + 10%i sech(x) tanh(x) +--R + +--R 3 2 4 5 +--R - 10sech(x) tanh(x) - 5%i sech(x) tanh(x) + sech(x) +--R Type: Expression Complex Integer +--E 468 + +--S 469 of 502 +r0893:= -%i*log(1+%i*sinh(x))+2*%i/(1+%i*sinh(x))^2-4*%i/(1+%i*sinh(x)) +--R +--R +--R 2 +--R (- %i sinh(x) - 2sinh(x) + %i)log(%i sinh(x) + 1) - 4sinh(x) + 2%i +--R (282) ------------------------------------------------------------------- +--R 2 +--R sinh(x) - 2%i sinh(x) - 1 +--R Type: Expression Complex Integer +--E 469 + +--S 470 of 502 +a0893:= integrate(t0893,x) +--R +--R +--R (283) +--R 4 3 +--R - 2%i sinh(x) + (- 8%i cosh(x) - 8)sinh(x) +--R + +--R 2 2 +--R (- 12%i cosh(x) - 24cosh(x) + 12%i)sinh(x) +--R + +--R 3 2 +--R (- 8%i cosh(x) - 24cosh(x) + 24%i cosh(x) + 8)sinh(x) +--R + +--R 4 3 2 +--R - 2%i cosh(x) - 8cosh(x) + 12%i cosh(x) + 8cosh(x) - 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 4 3 +--R %i x sinh(x) + (4%i x cosh(x) + 4x - 8)sinh(x) +--R + +--R 2 2 +--R (6%i x cosh(x) + (12x - 24)cosh(x) - 6%i x + 8%i)sinh(x) +--R + +--R 3 2 +--R 4%i x cosh(x) + (12x - 24)cosh(x) + (- 12%i x + 16%i)cosh(x) - 4x +--R + +--R 8 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R %i x cosh(x) + (4x - 8)cosh(x) + (- 6%i x + 8%i)cosh(x) +--R + +--R (- 4x + 8)cosh(x) + %i x +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) - 12%i cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 12%i cosh(x) - 12cosh(x) + 4%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R - 4%i cosh(x) - 6cosh(x) + 4%i cosh(x) + 1 +--R Type: Union(Expression Complex Integer,...) +--E 470 + +--S 471 of 502 +m0893:= a0893-r0893 +--R +--R +--R (284) +--R 6 5 +--R - 2%i sinh(x) + (- 8%i cosh(x) - 12)sinh(x) +--R + +--R 2 4 +--R (- 12%i cosh(x) - 40cosh(x) + 30%i)sinh(x) +--R + +--R 3 2 3 +--R (- 8%i cosh(x) - 48cosh(x) + 80%i cosh(x) + 40)sinh(x) +--R + +--R 4 3 2 +--R (- 2%i cosh(x) - 24cosh(x) + 72%i cosh(x) + 80cosh(x) - 30%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 4cosh(x) + 24%i cosh(x) + 48cosh(x) - 40%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R 2%i cosh(x) + 8cosh(x) - 12%i cosh(x) - 8cosh(x) + 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 6 5 +--R %i sinh(x) + (4%i cosh(x) + 6)sinh(x) +--R + +--R 2 4 +--R (6%i cosh(x) + 20cosh(x) - 15%i)sinh(x) +--R + +--R 3 2 3 +--R (4%i cosh(x) + 24cosh(x) - 40%i cosh(x) - 20)sinh(x) +--R + +--R 4 3 2 2 +--R (%i cosh(x) + 12cosh(x) - 36%i cosh(x) - 40cosh(x) + 15%i)sinh(x) +--R + +--R 4 3 2 +--R (2cosh(x) - 12%i cosh(x) - 24cosh(x) + 20%i cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 +--R - %i cosh(x) - 4cosh(x) + 6%i cosh(x) + 4cosh(x) - %i +--R * +--R log(%i sinh(x) + 1) +--R + +--R 6 5 +--R %i x sinh(x) + (4%i x cosh(x) + 6x - 4)sinh(x) +--R + +--R 2 4 +--R (6%i x cosh(x) + (20x - 8)cosh(x) - 15%i x + 6%i)sinh(x) +--R + +--R 3 2 3 +--R (4%i x cosh(x) + 24x cosh(x) + (- 40%i x + 8%i)cosh(x) - 20x)sinh(x) +--R + +--R 4 3 2 +--R %i x cosh(x) + (12x + 8)cosh(x) + (- 36%i x - 4%i)cosh(x) +--R + +--R (- 40x - 8)cosh(x) + 15%i x + 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2x + 4)cosh(x) + (- 12%i x - 8%i)cosh(x) + (- 24x - 8)cosh(x) +--R + +--R (20%i x + 8%i)cosh(x) + 6x + 4 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (- %i x - 2%i)cosh(x) - 4x cosh(x) + (6%i x + 4%i)cosh(x) + 4x cosh(x) +--R + +--R - %i x - 2%i +--R / +--R 6 5 +--R sinh(x) + (4cosh(x) - 6%i)sinh(x) +--R + +--R 2 4 +--R (6cosh(x) - 20%i cosh(x) - 15)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) - 24%i cosh(x) - 40cosh(x) + 20%i)sinh(x) +--R + +--R 4 3 2 2 +--R (cosh(x) - 12%i cosh(x) - 36cosh(x) + 40%i cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 +--R (- 2%i cosh(x) - 12cosh(x) + 24%i cosh(x) + 20cosh(x) - 6%i)sinh(x) +--R + +--R 4 3 2 +--R - cosh(x) + 4%i cosh(x) + 6cosh(x) - 4%i cosh(x) - 1 +--R Type: Expression Complex Integer +--E 471 + +--S 472 of 502 +d0893:= D(m0893,x) +--R +--R +--R (285) +--R 8 7 +--R - %i sinh(x) + (- 4%i cosh(x) + 2)sinh(x) +--R + +--R 2 6 +--R (- 5%i cosh(x) + 8cosh(x) - 2%i)sinh(x) +--R + +--R 2 5 +--R (10cosh(x) - 16%i cosh(x) + 6)sinh(x) +--R + +--R 4 2 4 +--R (5%i cosh(x) - 25%i cosh(x) + 20cosh(x))sinh(x) +--R + +--R 5 4 2 3 +--R (4%i cosh(x) - 10cosh(x) + 20cosh(x) - 20%i cosh(x) + 6)sinh(x) +--R + +--R 6 5 4 2 +--R %i cosh(x) - 8cosh(x) + 20%i cosh(x) - 35%i cosh(x) + 16cosh(x) +--R + +--R 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 2 +--R - 2cosh(x) + 8%i cosh(x) - 10cosh(x) + 10cosh(x) - 8%i cosh(x) +--R + +--R 2 +--R * +--R sinh(x) +--R + +--R 6 5 4 2 +--R - %i cosh(x) - 4cosh(x) + 15%i cosh(x) - 15%i cosh(x) + 4cosh(x) + %i +--R / +--R 8 7 +--R sinh(x) + (5cosh(x) - 8%i)sinh(x) +--R + +--R 2 6 +--R (10cosh(x) - 35%i cosh(x) - 28)sinh(x) +--R + +--R 3 2 5 +--R (10cosh(x) - 60%i cosh(x) - 105cosh(x) + 56%i)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) - 50%i cosh(x) - 150cosh(x) + 175%i cosh(x) + 70)sinh(x) +--R + +--R 5 4 3 2 +--R cosh(x) - 20%i cosh(x) - 100cosh(x) + 200%i cosh(x) + 175cosh(x) +--R + +--R - 56%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3%i cosh(x) - 30cosh(x) + 100%i cosh(x) + 150cosh(x) +--R + +--R - 105%i cosh(x) - 28 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3cosh(x) + 20%i cosh(x) + 50cosh(x) - 60%i cosh(x) - 35cosh(x) +--R + +--R 8%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R %i cosh(x) + 5cosh(x) - 10%i cosh(x) - 10cosh(x) + 5%i cosh(x) + 1 +--R Type: Expression Complex Integer +--E 472 + +--S 473 of 502 +t0894:= 1/(sech(x)-%i*tanh(x)) +--R +--R +--R %i +--R (286) -------------------- +--R tanh(x) + %i sech(x) +--R Type: Expression Complex Integer +--E 473 + +--S 474 of 502 +r0894:= %i*log(1-%i*sinh(x)) +--R +--R +--R (287) %i log(- %i sinh(x) + 1) +--R Type: Expression Complex Integer +--E 474 + +--S 475 of 502 +a0894:= integrate(t0894,x) +--R +--R +--R (288) 2%i log(sinh(x) + cosh(x) + %i) - %i x +--R Type: Union(Expression Complex Integer,...) +--E 475 + +--S 476 of 502 +m0894:= a0894-r0894 +--R +--R +--R (289) 2%i log(sinh(x) + cosh(x) + %i) - %i log(- %i sinh(x) + 1) - %i x +--R Type: Expression Complex Integer +--E 476 + +--S 477 of 502 +d0894:= D(m0894,x) +--R +--R +--R 2 2 +--R %i sinh(x) - %i cosh(x) + %i +--R (290) -------------------------------------------------- +--R 2 +--R sinh(x) + (cosh(x) + 2%i)sinh(x) + %i cosh(x) - 1 +--R Type: Expression Complex Integer +--E 477 + +--S 478 of 502 +t0895:= 1/(sech(x)-%i*tanh(x))^2 +--R +--R +--R 1 +--R (291) - ---------------------------------------- +--R 2 2 +--R tanh(x) + 2%i sech(x)tanh(x) - sech(x) +--R Type: Expression Complex Integer +--E 478 + +--S 479 of 502 +r0895:= -x-2*%i*sech(x)+2*tanh(x) +--R +--R +--R (292) 2tanh(x) - 2%i sech(x) - x +--R Type: Expression Complex Integer +--E 479 + +--S 480 of 502 +a0895:= integrate(t0895,x) +--R +--R +--R - x sinh(x) - x cosh(x) - %i x - 4%i +--R (293) ------------------------------------ +--R sinh(x) + cosh(x) + %i +--R Type: Union(Expression Complex Integer,...) +--E 480 + +--S 481 of 502 +m0895:= a0895-r0895 +--R +--R +--R (294) +--R (- 2sinh(x) - 2cosh(x) - 2%i)tanh(x) + 2%i sech(x)sinh(x) +--R + +--R (2%i cosh(x) - 2)sech(x) - 4%i +--R / +--R sinh(x) + cosh(x) + %i +--R Type: Expression Complex Integer +--E 481 + +--S 482 of 502 +d0895:= D(m0895,x) +--R +--R +--R (295) +--R 2 2 +--R (2sinh(x) + (4cosh(x) + 4%i)sinh(x) + 2cosh(x) + 4%i cosh(x) - 2) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 +--R - 2%i sech(x)sinh(x) + (- 4%i cosh(x) + 4)sech(x)sinh(x) +--R + +--R 2 +--R (- 2%i cosh(x) + 4cosh(x) + 2%i)sech(x) +--R * +--R tanh(x) +--R + +--R 2 2 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2%i)sinh(x) + cosh(x) + 2%i cosh(x) - 1 +--R Type: Expression Complex Integer +--E 482 + +--S 483 of 502 +t0896:= 1/(sech(x)-%i*tanh(x))^3 +--R +--R +--R %i +--R (296) - --------------------------------------------------------------- +--R 3 2 2 3 +--R tanh(x) + 3%i sech(x)tanh(x) - 3sech(x) tanh(x) - %i sech(x) +--R Type: Expression Complex Integer +--E 483 + +--S 484 of 502 +r0896:= -%i*log(1-%i*sinh(x))-2*%i/(1-%i*sinh(x)) +--R +--R +--R (- %i sinh(x) + 1)log(- %i sinh(x) + 1) + 2 +--R (297) ------------------------------------------- +--R sinh(x) + %i +--R Type: Expression Complex Integer +--E 484 + +--S 485 of 502 +a0896:= integrate(t0896,x) +--R +--R +--R (298) +--R 2 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) + 4)sinh(x) - 2%i cosh(x) + 4cosh(x) +--R + +--R 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 2 2 +--R %i x sinh(x) + (2%i x cosh(x) - 2x + 4)sinh(x) + %i x cosh(x) +--R + +--R (- 2x + 4)cosh(x) - %i x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2%i)sinh(x) + cosh(x) + 2%i cosh(x) - 1 +--R Type: Union(Expression Complex Integer,...) +--E 485 + +--S 486 of 502 +m0896:= a0896-r0896 +--R +--R +--R (299) +--R 3 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) + 6)sinh(x) +--R + +--R 2 2 +--R (- 2%i cosh(x) + 8cosh(x) + 6%i)sinh(x) + 2cosh(x) + 4%i cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 3 2 +--R %i sinh(x) + (2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (%i cosh(x) - 4cosh(x) - 3%i)sinh(x) - cosh(x) - 2%i cosh(x) + 1 +--R * +--R log(- %i sinh(x) + 1) +--R + +--R 3 2 +--R %i x sinh(x) + (2%i x cosh(x) - 3x + 2)sinh(x) +--R + +--R 2 2 +--R (%i x cosh(x) - 4x cosh(x) - 3%i x)sinh(x) + (- x - 2)cosh(x) +--R + +--R - 2%i x cosh(x) + x + 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) + 3%i)sinh(x) + (cosh(x) + 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R %i cosh(x) - 2cosh(x) - %i +--R Type: Expression Complex Integer +--E 486 + +--S 487 of 502 +d0896:= D(m0896,x) +--R +--R +--R (300) +--R 5 4 3 +--R - %i sinh(x) + (- 2%i cosh(x) - 1)sinh(x) + (- 2cosh(x) - 2%i)sinh(x) +--R + +--R 3 2 +--R (2%i cosh(x) - 6%i cosh(x) - 2)sinh(x) +--R + +--R 4 3 4 +--R (%i cosh(x) + 2cosh(x) - 2cosh(x) - %i)sinh(x) + cosh(x) +--R + +--R 3 +--R 4%i cosh(x) - 4%i cosh(x) - 1 +--R / +--R 5 4 +--R sinh(x) + (3cosh(x) + 5%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) + 12%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) + 9%i cosh(x) - 18cosh(x) - 10%i)sinh(x) +--R + +--R 3 2 3 +--R (2%i cosh(x) - 9cosh(x) - 12%i cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 2 +--R - 3%i cosh(x) + 3cosh(x) + %i +--R Type: Expression Complex Integer +--E 487 + +--S 488 of 502 +t0897:= 1/(sech(x)-%i*tanh(x))^4 +--R +--R +--R (301) +--R 1 +--R / +--R 4 3 2 2 3 +--R tanh(x) + 4%i sech(x)tanh(x) - 6sech(x) tanh(x) - 4%i sech(x) tanh(x) +--R + +--R 4 +--R sech(x) +--R Type: Expression Complex Integer +--E 488 + +--S 489 of 502 +r0897:= x+4*%i*sech(x)-8/3*%i*sech(x)^3-8/3*tanh(x)^3 +--R +--R +--R 8 3 8 3 +--R (302) - - tanh(x) - - %i sech(x) + 4%i sech(x) + x +--R 3 3 +--R Type: Expression Complex Fraction Integer +--E 489 + +--S 490 of 502 +a0897:= integrate(t0897,x) +--R +--R +--R (303) +--R 2 2 +--R 3x sinh(x) + (6x cosh(x) + 12%i x + 40%i)sinh(x) + 3x cosh(x) +--R + +--R (6%i x + 8%i)cosh(x) - 9x - 24 +--R / +--R 2 2 +--R 3sinh(x) + (6cosh(x) + 12%i)sinh(x) + 3cosh(x) + 6%i cosh(x) - 9 +--R Type: Union(Expression Complex Integer,...) +--E 490 + +--S 491 of 502 +m0897:= a0897-r0897 +--R +--R +--R (304) +--R 8 2 16 32 8 2 16 +--R - sinh(x) + (-- cosh(x) + -- %i)sinh(x) + - cosh(x) + -- %i cosh(x) +--R 3 3 3 3 3 +--R + +--R - 8 +--R * +--R 3 +--R tanh(x) +--R + +--R 8 3 2 +--R (- %i sech(x) - 4%i sech(x))sinh(x) +--R 3 +--R + +--R 16 32 3 40 +--R ((-- %i cosh(x) - --)sech(x) + (- 8%i cosh(x) + 16)sech(x) + -- %i) +--R 3 3 3 +--R * +--R sinh(x) +--R + +--R 8 2 16 3 +--R (- %i cosh(x) - -- cosh(x) - 8%i)sech(x) +--R 3 3 +--R + +--R 2 8 +--R (- 4%i cosh(x) + 8cosh(x) + 12%i)sech(x) + - %i cosh(x) - 8 +--R 3 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 4%i)sinh(x) + cosh(x) + 2%i cosh(x) - 3 +--R Type: Expression Complex Fraction Integer +--E 491 + +--S 492 of 502 +d0897:= D(m0897,x) +--R +--R +--R (305) +--R 4 3 +--R - 8sinh(x) + (- 32cosh(x) - 64%i)sinh(x) +--R + +--R 2 2 +--R (- 48cosh(x) - 160%i cosh(x) + 176)sinh(x) +--R + +--R 3 2 +--R (- 32cosh(x) - 128%i cosh(x) + 224cosh(x) + 192%i)sinh(x) +--R + +--R 4 3 2 +--R - 8cosh(x) - 32%i cosh(x) + 80cosh(x) + 96%i cosh(x) - 72 +--R * +--R 4 +--R tanh(x) +--R + +--R 4 3 +--R 8sinh(x) + (32cosh(x) + 64%i)sinh(x) +--R + +--R 2 2 +--R (48cosh(x) + 160%i cosh(x) - 176)sinh(x) +--R + +--R 3 2 4 +--R (32cosh(x) + 128%i cosh(x) - 224cosh(x) - 192%i)sinh(x) + 8cosh(x) +--R + +--R 3 2 +--R 32%i cosh(x) - 80cosh(x) - 96%i cosh(x) + 72 +--R * +--R 2 +--R tanh(x) +--R + +--R 3 4 +--R (- 8%i sech(x) + 4%i sech(x))sinh(x) +--R + +--R 3 3 +--R ((- 32%i cosh(x) + 64)sech(x) + (16%i cosh(x) - 32)sech(x))sinh(x) +--R + +--R 2 3 +--R (- 48%i cosh(x) + 160cosh(x) + 176%i)sech(x) +--R + +--R 2 +--R (24%i cosh(x) - 80cosh(x) - 88%i)sech(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3 +--R (- 32%i cosh(x) + 128cosh(x) + 224%i cosh(x) - 192)sech(x) +--R + +--R 3 2 +--R (16%i cosh(x) - 64cosh(x) - 112%i cosh(x) + 96)sech(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (- 8%i cosh(x) + 32cosh(x) + 80%i cosh(x) - 96cosh(x) - 72%i) +--R * +--R 3 +--R sech(x) +--R + +--R 4 3 2 +--R (4%i cosh(x) - 16cosh(x) - 40%i cosh(x) + 48cosh(x) + 36%i)sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 +--R - 24%i sinh(x) + (- 40%i cosh(x) + 32)sinh(x) +--R + +--R 2 3 +--R (- 8%i cosh(x) + 32cosh(x) + 8%i)sinh(x) + 8%i cosh(x) - 8%i cosh(x) +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) + 8%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) + 20%i cosh(x) - 22)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) + 16%i cosh(x) - 28cosh(x) - 24%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R 4%i cosh(x) - 10cosh(x) - 12%i cosh(x) + 9 +--R Type: Expression Complex Fraction Integer +--E 492 + +--S 493 of 502 +t0898:= 1/(sech(x)-%i*tanh(x))^5 +--R +--R +--R (306) +--R %i +--R / +--R 5 4 2 3 +--R tanh(x) + 5%i sech(x)tanh(x) - 10sech(x) tanh(x) +--R + +--R 3 2 4 5 +--R - 10%i sech(x) tanh(x) + 5sech(x) tanh(x) + %i sech(x) +--R Type: Expression Complex Integer +--E 493 + +--S 494 of 502 +r0898:= %i*log(1-%i*sinh(x))-2*%i/(1-%i*sinh(x))^2+4*%i/(1-%i*sinh(x)) +--R +--R +--R 2 +--R (%i sinh(x) - 2sinh(x) - %i)log(- %i sinh(x) + 1) - 4sinh(x) - 2%i +--R (307) ------------------------------------------------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression Complex Integer +--E 494 + +--S 495 of 502 +a0898:= integrate(t0898,x) +--R +--R +--R (308) +--R 4 3 +--R 2%i sinh(x) + (8%i cosh(x) - 8)sinh(x) +--R + +--R 2 2 +--R (12%i cosh(x) - 24cosh(x) - 12%i)sinh(x) +--R + +--R 3 2 4 +--R (8%i cosh(x) - 24cosh(x) - 24%i cosh(x) + 8)sinh(x) + 2%i cosh(x) +--R + +--R 3 2 +--R - 8cosh(x) - 12%i cosh(x) + 8cosh(x) + 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 4 3 +--R - %i x sinh(x) + (- 4%i x cosh(x) + 4x - 8)sinh(x) +--R + +--R 2 2 +--R (- 6%i x cosh(x) + (12x - 24)cosh(x) + 6%i x - 8%i)sinh(x) +--R + +--R 3 2 +--R - 4%i x cosh(x) + (12x - 24)cosh(x) + (12%i x - 16%i)cosh(x) - 4x +--R + +--R 8 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R - %i x cosh(x) + (4x - 8)cosh(x) + (6%i x - 8%i)cosh(x) +--R + +--R (- 4x + 8)cosh(x) - %i x +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) + 4%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) + 12%i cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) + 12%i cosh(x) - 12cosh(x) - 4%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R 4%i cosh(x) - 6cosh(x) - 4%i cosh(x) + 1 +--R Type: Union(Expression Complex Integer,...) +--E 495 + +--S 496 of 502 +m0898:= a0898-r0898 +--R +--R +--R (309) +--R 6 5 +--R 2%i sinh(x) + (8%i cosh(x) - 12)sinh(x) +--R + +--R 2 4 +--R (12%i cosh(x) - 40cosh(x) - 30%i)sinh(x) +--R + +--R 3 2 3 +--R (8%i cosh(x) - 48cosh(x) - 80%i cosh(x) + 40)sinh(x) +--R + +--R 4 3 2 +--R (2%i cosh(x) - 24cosh(x) - 72%i cosh(x) + 80cosh(x) + 30%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 4cosh(x) - 24%i cosh(x) + 48cosh(x) + 40%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R - 2%i cosh(x) + 8cosh(x) + 12%i cosh(x) - 8cosh(x) - 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 6 5 +--R - %i sinh(x) + (- 4%i cosh(x) + 6)sinh(x) +--R + +--R 2 4 +--R (- 6%i cosh(x) + 20cosh(x) + 15%i)sinh(x) +--R + +--R 3 2 3 +--R (- 4%i cosh(x) + 24cosh(x) + 40%i cosh(x) - 20)sinh(x) +--R + +--R 4 3 2 +--R (- %i cosh(x) + 12cosh(x) + 36%i cosh(x) - 40cosh(x) - 15%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2cosh(x) + 12%i cosh(x) - 24cosh(x) - 20%i cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 +--R %i cosh(x) - 4cosh(x) - 6%i cosh(x) + 4cosh(x) + %i +--R * +--R log(- %i sinh(x) + 1) +--R + +--R 6 5 +--R - %i x sinh(x) + (- 4%i x cosh(x) + 6x - 4)sinh(x) +--R + +--R 2 4 +--R (- 6%i x cosh(x) + (20x - 8)cosh(x) + 15%i x - 6%i)sinh(x) +--R + +--R 3 2 3 +--R (- 4%i x cosh(x) + 24x cosh(x) + (40%i x - 8%i)cosh(x) - 20x)sinh(x) +--R + +--R 4 3 2 +--R - %i x cosh(x) + (12x + 8)cosh(x) + (36%i x + 4%i)cosh(x) +--R + +--R (- 40x - 8)cosh(x) - 15%i x - 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2x + 4)cosh(x) + (12%i x + 8%i)cosh(x) + (- 24x - 8)cosh(x) +--R + +--R (- 20%i x - 8%i)cosh(x) + 6x + 4 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (%i x + 2%i)cosh(x) - 4x cosh(x) + (- 6%i x - 4%i)cosh(x) + 4x cosh(x) +--R + +--R %i x + 2%i +--R / +--R 6 5 +--R sinh(x) + (4cosh(x) + 6%i)sinh(x) +--R + +--R 2 4 +--R (6cosh(x) + 20%i cosh(x) - 15)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) + 24%i cosh(x) - 40cosh(x) - 20%i)sinh(x) +--R + +--R 4 3 2 2 +--R (cosh(x) + 12%i cosh(x) - 36cosh(x) - 40%i cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 +--R (2%i cosh(x) - 12cosh(x) - 24%i cosh(x) + 20cosh(x) + 6%i)sinh(x) +--R + +--R 4 3 2 +--R - cosh(x) - 4%i cosh(x) + 6cosh(x) + 4%i cosh(x) - 1 +--R Type: Expression Complex Integer +--E 496 + +--S 497 of 502 +d0898:= D(m0898,x) +--R +--R +--R (310) +--R 8 7 +--R %i sinh(x) + (4%i cosh(x) + 2)sinh(x) +--R + +--R 2 6 +--R (5%i cosh(x) + 8cosh(x) + 2%i)sinh(x) +--R + +--R 2 5 +--R (10cosh(x) + 16%i cosh(x) + 6)sinh(x) +--R + +--R 4 2 4 +--R (- 5%i cosh(x) + 25%i cosh(x) + 20cosh(x))sinh(x) +--R + +--R 5 4 2 3 +--R (- 4%i cosh(x) - 10cosh(x) + 20cosh(x) + 20%i cosh(x) + 6)sinh(x) +--R + +--R 6 5 4 2 +--R - %i cosh(x) - 8cosh(x) - 20%i cosh(x) + 35%i cosh(x) + 16cosh(x) +--R + +--R - 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 2 +--R - 2cosh(x) - 8%i cosh(x) - 10cosh(x) + 10cosh(x) + 8%i cosh(x) +--R + +--R 2 +--R * +--R sinh(x) +--R + +--R 6 5 4 2 +--R %i cosh(x) - 4cosh(x) - 15%i cosh(x) + 15%i cosh(x) + 4cosh(x) - %i +--R / +--R 8 7 +--R sinh(x) + (5cosh(x) + 8%i)sinh(x) +--R + +--R 2 6 +--R (10cosh(x) + 35%i cosh(x) - 28)sinh(x) +--R + +--R 3 2 5 +--R (10cosh(x) + 60%i cosh(x) - 105cosh(x) - 56%i)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) + 50%i cosh(x) - 150cosh(x) - 175%i cosh(x) + 70)sinh(x) +--R + +--R 5 4 3 2 +--R cosh(x) + 20%i cosh(x) - 100cosh(x) - 200%i cosh(x) + 175cosh(x) +--R + +--R 56%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 3%i cosh(x) - 30cosh(x) - 100%i cosh(x) + 150cosh(x) +--R + +--R 105%i cosh(x) - 28 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3cosh(x) - 20%i cosh(x) + 50cosh(x) + 60%i cosh(x) - 35cosh(x) +--R + +--R - 8%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R - %i cosh(x) + 5cosh(x) + 10%i cosh(x) - 10cosh(x) - 5%i cosh(x) + 1 +--R Type: Expression Complex Integer +--E 497 + +--S 498 of 502 +t0899:= (coth(x)+csch(x))^3 +--R +--R +--R 3 2 2 3 +--R (311) csch(x) + 3coth(x)csch(x) + 3coth(x) csch(x) + coth(x) +--R Type: Expression Integer +--E 498 + +--S 499 of 502 +r0899:= 2/(1-cosh(x))+log(1-cosh(x)) +--R +--R +--R (cosh(x) - 1)log(- cosh(x) + 1) - 2 +--R (312) ----------------------------------- +--R cosh(x) - 1 +--R Type: Expression Integer +--E 499 + +--S 500 of 502 +a0899:= integrate(t0899,x) +--R +--R +--R (313) +--R 2 2 +--R (2sinh(x) + (4cosh(x) - 4)sinh(x) + 2cosh(x) - 4cosh(x) + 2) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R - x sinh(x) + (- 2x cosh(x) + 2x - 4)sinh(x) - x cosh(x) +--R + +--R (2x - 4)cosh(x) - x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2)sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Union(Expression Integer,...) +--E 500 + +--S 501 of 502 +m0899:= a0899-r0899 +--R +--R +--R (314) +--R 2 2 +--R (2cosh(x) - 2)sinh(x) + (4cosh(x) - 8cosh(x) + 4)sinh(x) +--R + +--R 3 2 +--R 2cosh(x) - 6cosh(x) + 6cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R (- cosh(x) + 1)sinh(x) + (- 2cosh(x) + 4cosh(x) - 2)sinh(x) +--R + +--R 3 2 +--R - cosh(x) + 3cosh(x) - 3cosh(x) + 1 +--R * +--R log(- cosh(x) + 1) +--R + +--R 2 2 +--R (- x cosh(x) + x + 2)sinh(x) + (- 2x cosh(x) + 4x cosh(x) - 2x)sinh(x) +--R + +--R 3 2 +--R - x cosh(x) + (3x - 2)cosh(x) - 3x cosh(x) + x + 2 +--R / +--R 2 2 3 +--R (cosh(x) - 1)sinh(x) + (2cosh(x) - 4cosh(x) + 2)sinh(x) + cosh(x) +--R + +--R 2 +--R - 3cosh(x) + 3cosh(x) - 1 +--R Type: Expression Integer +--E 501 + +--S 502 of 502 +d0899:= D(m0899,x) +--R +--R +--R (315) +--R 4 2 3 +--R (- cosh(x) - 1)sinh(x) + (- 2cosh(x) - 2cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 5 +--R (2cosh(x) + 2cosh(x) - 6cosh(x) - 2cosh(x) + 4)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R cosh(x) - 2cosh(x) - 2cosh(x) + cosh(x) + 1 +--R / +--R 2 3 +--R (cosh(x) - 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 2 +--R (3cosh(x) - 9cosh(x) + 9cosh(x) - 3)sinh(x) +--R + +--R 4 3 2 5 +--R (3cosh(x) - 12cosh(x) + 18cosh(x) - 12cosh(x) + 3)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R - 5cosh(x) + 10cosh(x) - 10cosh(x) + 5cosh(x) - 1 +--R Type: Expression Integer +--E 502 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}