1,1,47,22,0.0752031,"\int \frac{2}{-1+3 \cosh (4+6 x)} \, dx","Integrate[2/(-1 + 3*Cosh[4 + 6*x]),x]","\frac{\tan ^{-1}\left(\frac{\left(3+2 e^4+3 e^8\right) \tanh (3 x)+3 \left(e^8-1\right)}{4 \sqrt{2} e^4}\right)}{3 \sqrt{2}}","\frac{\tan ^{-1}\left(\sqrt{2} \tanh (3 x+2)\right)}{3 \sqrt{2}}",1,"ArcTan[(3*(-1 + E^8) + (3 + 2*E^4 + 3*E^8)*Tanh[3*x])/(4*Sqrt[2]*E^4)]/(3*Sqrt[2])","B",1
2,1,47,22,0.0701417,"\int \frac{1}{\cosh ^2(2+3 x)+2 \sinh ^2(2+3 x)} \, dx","Integrate[(Cosh[2 + 3*x]^2 + 2*Sinh[2 + 3*x]^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\left(3+2 e^4+3 e^8\right) \tanh (3 x)+3 \left(e^8-1\right)}{4 \sqrt{2} e^4}\right)}{3 \sqrt{2}}","\frac{\tan ^{-1}\left(\sqrt{2} \tanh (3 x+2)\right)}{3 \sqrt{2}}",1,"ArcTan[(3*(-1 + E^8) + (3 + 2*E^4 + 3*E^8)*Tanh[3*x])/(4*Sqrt[2]*E^4)]/(3*Sqrt[2])","B",1
3,1,47,22,0.0830772,"\int \frac{\text{sech}^2(2+3 x)}{1+2 \tanh ^2(2+3 x)} \, dx","Integrate[Sech[2 + 3*x]^2/(1 + 2*Tanh[2 + 3*x]^2),x]","\frac{\tan ^{-1}\left(\frac{\left(3+2 e^4+3 e^8\right) \tanh (3 x)+3 \left(e^8-1\right)}{4 \sqrt{2} e^4}\right)}{3 \sqrt{2}}","\frac{\tan ^{-1}\left(\sqrt{2} \tanh (3 x+2)\right)}{3 \sqrt{2}}",1,"ArcTan[(3*(-1 + E^8) + (3 + 2*E^4 + 3*E^8)*Tanh[3*x])/(4*Sqrt[2]*E^4)]/(3*Sqrt[2])","B",1
4,1,47,22,0.0756441,"\int \frac{\text{csch}^2(2+3 x)}{2+\coth ^2(2+3 x)} \, dx","Integrate[Csch[2 + 3*x]^2/(2 + Coth[2 + 3*x]^2),x]","\frac{\tan ^{-1}\left(\frac{\left(3+2 e^4+3 e^8\right) \tanh (3 x)+3 \left(e^8-1\right)}{4 \sqrt{2} e^4}\right)}{3 \sqrt{2}}","\frac{\tan ^{-1}\left(\sqrt{2} \tanh (3 x+2)\right)}{3 \sqrt{2}}",1,"ArcTan[(3*(-1 + E^8) + (3 + 2*E^4 + 3*E^8)*Tanh[3*x])/(4*Sqrt[2]*E^4)]/(3*Sqrt[2])","B",1
5,1,42,22,0.1052133,"\int \frac{\text{csch}^2(2+3 x)}{2-\coth ^2(2+3 x)} \, dx","Integrate[Csch[2 + 3*x]^2/(2 - Coth[2 + 3*x]^2),x]","-\frac{\tanh ^{-1}\left(\frac{\left(1+6 e^4+e^8\right) \tanh (3 x)+e^8-1}{4 \sqrt{2} e^4}\right)}{3 \sqrt{2}}","-\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (3 x+2)\right)}{3 \sqrt{2}}",1,"-1/3*ArcTanh[(-1 + E^8 + (1 + 6*E^4 + E^8)*Tanh[3*x])/(4*Sqrt[2]*E^4)]/Sqrt[2]","A",1
6,1,47,22,0.1059621,"\int \frac{\text{csch}^2(2+3 x)}{1+2 \coth ^2(2+3 x)} \, dx","Integrate[Csch[2 + 3*x]^2/(1 + 2*Coth[2 + 3*x]^2),x]","\frac{\tan ^{-1}\left(\frac{\left(3-2 e^4+3 e^8\right) \tanh (3 x)+3 \left(e^8-1\right)}{4 \sqrt{2} e^4}\right)}{3 \sqrt{2}}","\frac{\tan ^{-1}\left(\frac{\tanh (3 x+2)}{\sqrt{2}}\right)}{3 \sqrt{2}}",1,"ArcTan[(3*(-1 + E^8) + (3 - 2*E^4 + 3*E^8)*Tanh[3*x])/(4*Sqrt[2]*E^4)]/(3*Sqrt[2])","B",1
7,1,42,22,0.1108564,"\int \frac{\text{csch}^2(2+3 x)}{1-2 \coth ^2(2+3 x)} \, dx","Integrate[Csch[2 + 3*x]^2/(1 - 2*Coth[2 + 3*x]^2),x]","\frac{\tanh ^{-1}\left(\frac{\left(1-6 e^4+e^8\right) \tanh (3 x)+e^8-1}{4 \sqrt{2} e^4}\right)}{3 \sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{\tanh (3 x+2)}{\sqrt{2}}\right)}{3 \sqrt{2}}",1,"ArcTanh[(-1 + E^8 + (1 - 6*E^4 + E^8)*Tanh[3*x])/(4*Sqrt[2]*E^4)]/(3*Sqrt[2])","A",1
8,1,37,15,0.0139153,"\int \cosh (a+b x) \sinh (a+b x) \, dx","Integrate[Cosh[a + b*x]*Sinh[a + b*x],x]","\frac{1}{2} \left(\frac{\sinh (2 a) \sinh (2 b x)}{2 b}+\frac{\cosh (2 a) \cosh (2 b x)}{2 b}\right)","\frac{\sinh ^2(a+b x)}{2 b}",1,"((Cosh[2*a]*Cosh[2*b*x])/(2*b) + (Sinh[2*a]*Sinh[2*b*x])/(2*b))/2","B",1
9,1,19,19,0.0094599,"\int \cosh (a+b x) \sinh ^n(a+b x) \, dx","Integrate[Cosh[a + b*x]*Sinh[a + b*x]^n,x]","\frac{\sinh ^{n+1}(a+b x)}{b (n+1)}","\frac{\sinh ^{n+1}(a+b x)}{b (n+1)}",1,"Sinh[a + b*x]^(1 + n)/(b*(1 + n))","A",1
10,1,39,39,0.0633736,"\int \cosh ^3(a+b x) \sinh ^n(a+b x) \, dx","Integrate[Cosh[a + b*x]^3*Sinh[a + b*x]^n,x]","\frac{\sinh ^{n+1}(a+b x)}{b (n+1)}+\frac{\sinh ^{n+3}(a+b x)}{b (n+3)}","\frac{\sinh ^{n+1}(a+b x)}{b (n+1)}+\frac{\sinh ^{n+3}(a+b x)}{b (n+3)}",1,"Sinh[a + b*x]^(1 + n)/(b*(1 + n)) + Sinh[a + b*x]^(3 + n)/(b*(3 + n))","A",1
11,1,49,59,0.200467,"\int \cosh ^5(a+b x) \sinh ^n(a+b x) \, dx","Integrate[Cosh[a + b*x]^5*Sinh[a + b*x]^n,x]","\frac{\sinh ^{n+1}(a+b x) \left(\frac{\sinh ^4(a+b x)}{n+5}+\frac{2 \sinh ^2(a+b x)}{n+3}+\frac{1}{n+1}\right)}{b}","\frac{\sinh ^{n+1}(a+b x)}{b (n+1)}+\frac{2 \sinh ^{n+3}(a+b x)}{b (n+3)}+\frac{\sinh ^{n+5}(a+b x)}{b (n+5)}",1,"(Sinh[a + b*x]^(1 + n)*((1 + n)^(-1) + (2*Sinh[a + b*x]^2)/(3 + n) + Sinh[a + b*x]^4/(5 + n)))/b","A",1
12,1,19,19,0.0102438,"\int \cosh ^m(a+b x) \sinh (a+b x) \, dx","Integrate[Cosh[a + b*x]^m*Sinh[a + b*x],x]","\frac{\cosh ^{m+1}(a+b x)}{b (m+1)}","\frac{\cosh ^{m+1}(a+b x)}{b (m+1)}",1,"Cosh[a + b*x]^(1 + m)/(b*(1 + m))","A",1
13,1,44,40,0.1348566,"\int \cosh ^m(a+b x) \sinh ^3(a+b x) \, dx","Integrate[Cosh[a + b*x]^m*Sinh[a + b*x]^3,x]","\frac{\cosh ^{m+1}(a+b x) ((m+1) \cosh (2 (a+b x))-m-5)}{2 b (m+1) (m+3)}","\frac{\cosh ^{m+3}(a+b x)}{b (m+3)}-\frac{\cosh ^{m+1}(a+b x)}{b (m+1)}",1,"(Cosh[a + b*x]^(1 + m)*(-5 - m + (1 + m)*Cosh[2*(a + b*x)]))/(2*b*(1 + m)*(3 + m))","A",1
14,1,77,59,0.2283281,"\int \cosh ^m(a+b x) \sinh ^5(a+b x) \, dx","Integrate[Cosh[a + b*x]^m*Sinh[a + b*x]^5,x]","\frac{\cosh ^{m+1}(a+b x) \left(-4 \left(m^2+8 m+7\right) \cosh (2 (a+b x))+\left(m^2+4 m+3\right) \cosh (4 (a+b x))+3 m^2+28 m+89\right)}{8 b (m+1) (m+3) (m+5)}","\frac{\cosh ^{m+1}(a+b x)}{b (m+1)}-\frac{2 \cosh ^{m+3}(a+b x)}{b (m+3)}+\frac{\cosh ^{m+5}(a+b x)}{b (m+5)}",1,"(Cosh[a + b*x]^(1 + m)*(89 + 28*m + 3*m^2 - 4*(7 + 8*m + m^2)*Cosh[2*(a + b*x)] + (3 + 4*m + m^2)*Cosh[4*(a + b*x)]))/(8*b*(1 + m)*(3 + m)*(5 + m))","A",1
15,1,23,46,0.0318126,"\int \cosh ^2(a+b x) \sinh ^2(a+b x) \, dx","Integrate[Cosh[a + b*x]^2*Sinh[a + b*x]^2,x]","\frac{\sinh (4 (a+b x))-4 (a+b x)}{32 b}","\frac{\sinh (a+b x) \cosh ^3(a+b x)}{4 b}-\frac{\sinh (a+b x) \cosh (a+b x)}{8 b}-\frac{x}{8}",1,"(-4*(a + b*x) + Sinh[4*(a + b*x)])/(32*b)","A",1
16,1,40,69,0.0804923,"\int \cosh ^2(a+b x) \sinh ^4(a+b x) \, dx","Integrate[Cosh[a + b*x]^2*Sinh[a + b*x]^4,x]","\frac{-3 \sinh (2 (a+b x))-3 \sinh (4 (a+b x))+\sinh (6 (a+b x))+12 b x}{192 b}","\frac{\sinh ^3(a+b x) \cosh ^3(a+b x)}{6 b}-\frac{\sinh (a+b x) \cosh ^3(a+b x)}{8 b}+\frac{\sinh (a+b x) \cosh (a+b x)}{16 b}+\frac{x}{16}",1,"(12*b*x - 3*Sinh[2*(a + b*x)] - 3*Sinh[4*(a + b*x)] + Sinh[6*(a + b*x)])/(192*b)","A",1
17,1,52,92,0.1287174,"\int \cosh ^2(a+b x) \sinh ^6(a+b x) \, dx","Integrate[Cosh[a + b*x]^2*Sinh[a + b*x]^6,x]","\frac{48 \sinh (2 (a+b x))+24 \sinh (4 (a+b x))-16 \sinh (6 (a+b x))+3 \sinh (8 (a+b x))-120 b x}{3072 b}","\frac{\sinh ^5(a+b x) \cosh ^3(a+b x)}{8 b}-\frac{5 \sinh ^3(a+b x) \cosh ^3(a+b x)}{48 b}+\frac{5 \sinh (a+b x) \cosh ^3(a+b x)}{64 b}-\frac{5 \sinh (a+b x) \cosh (a+b x)}{128 b}-\frac{5 x}{128}",1,"(-120*b*x + 48*Sinh[2*(a + b*x)] + 24*Sinh[4*(a + b*x)] - 16*Sinh[6*(a + b*x)] + 3*Sinh[8*(a + b*x)])/(3072*b)","A",1
18,1,40,67,0.061234,"\int \cosh ^4(a+b x) \sinh ^2(a+b x) \, dx","Integrate[Cosh[a + b*x]^4*Sinh[a + b*x]^2,x]","\frac{-3 \sinh (2 (a+b x))+3 \sinh (4 (a+b x))+\sinh (6 (a+b x))-12 b x}{192 b}","\frac{\sinh (a+b x) \cosh ^5(a+b x)}{6 b}-\frac{\sinh (a+b x) \cosh ^3(a+b x)}{24 b}-\frac{\sinh (a+b x) \cosh (a+b x)}{16 b}-\frac{x}{16}",1,"(-12*b*x - 3*Sinh[2*(a + b*x)] + 3*Sinh[4*(a + b*x)] + Sinh[6*(a + b*x)])/(192*b)","A",1
19,1,33,90,0.0454869,"\int \cosh ^4(a+b x) \sinh ^4(a+b x) \, dx","Integrate[Cosh[a + b*x]^4*Sinh[a + b*x]^4,x]","\frac{24 (a+b x)-8 \sinh (4 (a+b x))+\sinh (8 (a+b x))}{1024 b}","\frac{\sinh ^3(a+b x) \cosh ^5(a+b x)}{8 b}-\frac{\sinh (a+b x) \cosh ^5(a+b x)}{16 b}+\frac{\sinh (a+b x) \cosh ^3(a+b x)}{64 b}+\frac{3 \sinh (a+b x) \cosh (a+b x)}{128 b}+\frac{3 x}{128}",1,"(24*(a + b*x) - 8*Sinh[4*(a + b*x)] + Sinh[8*(a + b*x)])/(1024*b)","A",1
20,1,62,113,0.1839219,"\int \cosh ^4(a+b x) \sinh ^6(a+b x) \, dx","Integrate[Cosh[a + b*x]^4*Sinh[a + b*x]^6,x]","\frac{20 \sinh (2 (a+b x))+40 \sinh (4 (a+b x))-10 \sinh (6 (a+b x))-5 \sinh (8 (a+b x))+2 \sinh (10 (a+b x))-120 b x}{10240 b}","\frac{\sinh ^5(a+b x) \cosh ^5(a+b x)}{10 b}-\frac{\sinh ^3(a+b x) \cosh ^5(a+b x)}{16 b}+\frac{\sinh (a+b x) \cosh ^5(a+b x)}{32 b}-\frac{\sinh (a+b x) \cosh ^3(a+b x)}{128 b}-\frac{3 \sinh (a+b x) \cosh (a+b x)}{256 b}-\frac{3 x}{256}",1,"(-120*b*x + 20*Sinh[2*(a + b*x)] + 40*Sinh[4*(a + b*x)] - 10*Sinh[6*(a + b*x)] - 5*Sinh[8*(a + b*x)] + 2*Sinh[10*(a + b*x)])/(10240*b)","A",1
21,1,52,88,0.0979556,"\int \cosh ^6(a+b x) \sinh ^2(a+b x) \, dx","Integrate[Cosh[a + b*x]^6*Sinh[a + b*x]^2,x]","\frac{-48 \sinh (2 (a+b x))+24 \sinh (4 (a+b x))+16 \sinh (6 (a+b x))+3 \sinh (8 (a+b x))-120 b x}{3072 b}","\frac{\sinh (a+b x) \cosh ^7(a+b x)}{8 b}-\frac{\sinh (a+b x) \cosh ^5(a+b x)}{48 b}-\frac{5 \sinh (a+b x) \cosh ^3(a+b x)}{192 b}-\frac{5 \sinh (a+b x) \cosh (a+b x)}{128 b}-\frac{5 x}{128}",1,"(-120*b*x - 48*Sinh[2*(a + b*x)] + 24*Sinh[4*(a + b*x)] + 16*Sinh[6*(a + b*x)] + 3*Sinh[8*(a + b*x)])/(3072*b)","A",1
22,1,62,111,0.1318747,"\int \cosh ^6(a+b x) \sinh ^4(a+b x) \, dx","Integrate[Cosh[a + b*x]^6*Sinh[a + b*x]^4,x]","\frac{20 \sinh (2 (a+b x))-40 \sinh (4 (a+b x))-10 \sinh (6 (a+b x))+5 \sinh (8 (a+b x))+2 \sinh (10 (a+b x))+120 b x}{10240 b}","\frac{\sinh ^3(a+b x) \cosh ^7(a+b x)}{10 b}-\frac{3 \sinh (a+b x) \cosh ^7(a+b x)}{80 b}+\frac{\sinh (a+b x) \cosh ^5(a+b x)}{160 b}+\frac{\sinh (a+b x) \cosh ^3(a+b x)}{128 b}+\frac{3 \sinh (a+b x) \cosh (a+b x)}{256 b}+\frac{3 x}{256}",1,"(120*b*x + 20*Sinh[2*(a + b*x)] - 40*Sinh[4*(a + b*x)] - 10*Sinh[6*(a + b*x)] + 5*Sinh[8*(a + b*x)] + 2*Sinh[10*(a + b*x)])/(10240*b)","A",1
23,1,43,134,0.0903353,"\int \cosh ^6(a+b x) \sinh ^6(a+b x) \, dx","Integrate[Cosh[a + b*x]^6*Sinh[a + b*x]^6,x]","\frac{45 \sinh (4 (a+b x))-9 \sinh (8 (a+b x))+\sinh (12 (a+b x))-120 a-120 b x}{24576 b}","\frac{\sinh ^5(a+b x) \cosh ^7(a+b x)}{12 b}-\frac{\sinh ^3(a+b x) \cosh ^7(a+b x)}{24 b}+\frac{\sinh (a+b x) \cosh ^7(a+b x)}{64 b}-\frac{\sinh (a+b x) \cosh ^5(a+b x)}{384 b}-\frac{5 \sinh (a+b x) \cosh ^3(a+b x)}{1536 b}-\frac{5 \sinh (a+b x) \cosh (a+b x)}{1024 b}-\frac{5 x}{1024}",1,"(-120*a - 120*b*x + 45*Sinh[4*(a + b*x)] - 9*Sinh[8*(a + b*x)] + Sinh[12*(a + b*x)])/(24576*b)","A",1
24,1,31,11,0.0224946,"\int \text{csch}(a+b x) \text{sech}(a+b x) \, dx","Integrate[Csch[a + b*x]*Sech[a + b*x],x]","2 \left(\frac{\log (\sinh (a+b x))}{2 b}-\frac{\log (\cosh (a+b x))}{2 b}\right)","\frac{\log (\tanh (a+b x))}{b}",1,"2*(-1/2*Log[Cosh[a + b*x]]/b + Log[Sinh[a + b*x]]/(2*b))","B",1
25,1,26,23,0.0339209,"\int \text{csch}(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[Csch[a + b*x]*Sech[a + b*x]^2,x]","\frac{\text{sech}(a+b x)}{b}+\frac{\log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{b}","\frac{\text{sech}(a+b x)}{b}-\frac{\tanh ^{-1}(\cosh (a+b x))}{b}",1,"Log[Tanh[(a + b*x)/2]]/b + Sech[a + b*x]/b","A",1
26,1,36,27,0.0376002,"\int \text{csch}(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[Csch[a + b*x]*Sech[a + b*x]^3,x]","-\frac{-\text{sech}^2(a+b x)-2 \log (\sinh (a+b x))+2 \log (\cosh (a+b x))}{2 b}","\frac{\log (\tanh (a+b x))}{b}-\frac{\tanh ^2(a+b x)}{2 b}",1,"-1/2*(2*Log[Cosh[a + b*x]] - 2*Log[Sinh[a + b*x]] - Sech[a + b*x]^2)/b","A",1
27,1,41,38,0.0279846,"\int \text{csch}(a+b x) \text{sech}^4(a+b x) \, dx","Integrate[Csch[a + b*x]*Sech[a + b*x]^4,x]","\frac{\text{sech}^3(a+b x)}{3 b}+\frac{\text{sech}(a+b x)}{b}+\frac{\log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{b}","\frac{\text{sech}^3(a+b x)}{3 b}+\frac{\text{sech}(a+b x)}{b}-\frac{\tanh ^{-1}(\cosh (a+b x))}{b}",1,"Log[Tanh[(a + b*x)/2]]/b + Sech[a + b*x]/b + Sech[a + b*x]^3/(3*b)","A",1
28,1,46,40,0.0998196,"\int \text{csch}(a+b x) \text{sech}^5(a+b x) \, dx","Integrate[Csch[a + b*x]*Sech[a + b*x]^5,x]","-\frac{-\text{sech}^4(a+b x)-2 \text{sech}^2(a+b x)-4 \log (\sinh (a+b x))+4 \log (\cosh (a+b x))}{4 b}","\frac{\tanh ^4(a+b x)}{4 b}-\frac{\tanh ^2(a+b x)}{b}+\frac{\log (\tanh (a+b x))}{b}",1,"-1/4*(4*Log[Cosh[a + b*x]] - 4*Log[Sinh[a + b*x]] - 2*Sech[a + b*x]^2 - Sech[a + b*x]^4)/b","A",1
29,1,29,24,0.0197344,"\int \text{csch}^2(a+b x) \text{sech}(a+b x) \, dx","Integrate[Csch[a + b*x]^2*Sech[a + b*x],x]","-\frac{\text{csch}(a+b x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\sinh ^2(a+b x)\right)}{b}","-\frac{\text{csch}(a+b x)}{b}-\frac{\tan ^{-1}(\sinh (a+b x))}{b}",1,"-((Csch[a + b*x]*Hypergeometric2F1[-1/2, 1, 1/2, -Sinh[a + b*x]^2])/b)","C",1
30,1,13,23,0.0159164,"\int \text{csch}^2(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[Csch[a + b*x]^2*Sech[a + b*x]^2,x]","-\frac{2 \coth (2 (a+b x))}{b}","-\frac{\tanh (a+b x)}{b}-\frac{\coth (a+b x)}{b}",1,"(-2*Coth[2*(a + b*x)])/b","A",1
31,1,29,49,0.0153296,"\int \text{csch}^2(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[Csch[a + b*x]^2*Sech[a + b*x]^3,x]","-\frac{\text{csch}(a+b x) \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\sinh ^2(a+b x)\right)}{b}","-\frac{3 \text{csch}(a+b x)}{2 b}-\frac{3 \tan ^{-1}(\sinh (a+b x))}{2 b}+\frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{2 b}",1,"-((Csch[a + b*x]*Hypergeometric2F1[-1/2, 2, 1/2, -Sinh[a + b*x]^2])/b)","C",1
32,1,46,38,0.0403191,"\int \text{csch}^2(a+b x) \text{sech}^4(a+b x) \, dx","Integrate[Csch[a + b*x]^2*Sech[a + b*x]^4,x]","-\frac{5 \tanh (a+b x)}{3 b}-\frac{\coth (a+b x)}{b}-\frac{\tanh (a+b x) \text{sech}^2(a+b x)}{3 b}","\frac{\tanh ^3(a+b x)}{3 b}-\frac{2 \tanh (a+b x)}{b}-\frac{\coth (a+b x)}{b}",1,"-(Coth[a + b*x]/b) - (5*Tanh[a + b*x])/(3*b) - (Sech[a + b*x]^2*Tanh[a + b*x])/(3*b)","A",1
33,1,29,70,0.0154432,"\int \text{csch}^2(a+b x) \text{sech}^5(a+b x) \, dx","Integrate[Csch[a + b*x]^2*Sech[a + b*x]^5,x]","-\frac{\text{csch}(a+b x) \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};-\sinh ^2(a+b x)\right)}{b}","-\frac{15 \text{csch}(a+b x)}{8 b}-\frac{15 \tan ^{-1}(\sinh (a+b x))}{8 b}+\frac{\text{csch}(a+b x) \text{sech}^4(a+b x)}{4 b}+\frac{5 \text{csch}(a+b x) \text{sech}^2(a+b x)}{8 b}",1,"-((Csch[a + b*x]*Hypergeometric2F1[-1/2, 3, 1/2, -Sinh[a + b*x]^2])/b)","C",1
34,1,34,28,0.0479037,"\int \text{csch}^3(a+b x) \text{sech}(a+b x) \, dx","Integrate[Csch[a + b*x]^3*Sech[a + b*x],x]","-\frac{\text{csch}^2(a+b x)+2 \log (\sinh (a+b x))-2 \log (\cosh (a+b x))}{2 b}","-\frac{\coth ^2(a+b x)}{2 b}-\frac{\log (\tanh (a+b x))}{b}",1,"-1/2*(Csch[a + b*x]^2 - 2*Log[Cosh[a + b*x]] + 2*Log[Sinh[a + b*x]])/b","A",1
35,1,68,49,0.0340961,"\int \text{csch}^3(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[Csch[a + b*x]^3*Sech[a + b*x]^2,x]","-\frac{\text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{\text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{\text{sech}(a+b x)}{b}-\frac{3 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b}","-\frac{3 \text{sech}(a+b x)}{2 b}+\frac{3 \tanh ^{-1}(\cosh (a+b x))}{2 b}-\frac{\text{csch}^2(a+b x) \text{sech}(a+b x)}{2 b}",1,"-1/8*Csch[(a + b*x)/2]^2/b - (3*Log[Tanh[(a + b*x)/2]])/(2*b) - Sech[(a + b*x)/2]^2/(8*b) - Sech[a + b*x]/b","A",1
36,1,47,43,0.0160215,"\int \text{csch}^3(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[Csch[a + b*x]^3*Sech[a + b*x]^3,x]","8 \left(-\frac{\text{csch}^2(a+b x)}{16 b}-\frac{\text{sech}^2(a+b x)}{16 b}-\frac{\log (\tanh (a+b x))}{4 b}\right)","\frac{\tanh ^2(a+b x)}{2 b}-\frac{\coth ^2(a+b x)}{2 b}-\frac{2 \log (\tanh (a+b x))}{b}",1,"8*(-1/16*Csch[a + b*x]^2/b - Log[Tanh[a + b*x]]/(4*b) - Sech[a + b*x]^2/(16*b))","A",1
37,1,83,66,0.0339567,"\int \text{csch}^3(a+b x) \text{sech}^4(a+b x) \, dx","Integrate[Csch[a + b*x]^3*Sech[a + b*x]^4,x]","-\frac{\text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{\text{sech}^3(a+b x)}{3 b}-\frac{\text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{2 \text{sech}(a+b x)}{b}-\frac{5 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b}","-\frac{5 \text{sech}^3(a+b x)}{6 b}-\frac{5 \text{sech}(a+b x)}{2 b}+\frac{5 \tanh ^{-1}(\cosh (a+b x))}{2 b}-\frac{\text{csch}^2(a+b x) \text{sech}^3(a+b x)}{2 b}",1,"-1/8*Csch[(a + b*x)/2]^2/b - (5*Log[Tanh[(a + b*x)/2]])/(2*b) - Sech[(a + b*x)/2]^2/(8*b) - (2*Sech[a + b*x])/b - Sech[a + b*x]^3/(3*b)","A",1
38,1,54,58,0.4547612,"\int \text{csch}^3(a+b x) \text{sech}^5(a+b x) \, dx","Integrate[Csch[a + b*x]^3*Sech[a + b*x]^5,x]","-\frac{2 \text{csch}^2(a+b x)+\text{sech}^4(a+b x)+4 \text{sech}^2(a+b x)+12 \log (\sinh (a+b x))-12 \log (\cosh (a+b x))}{4 b}","-\frac{\tanh ^4(a+b x)}{4 b}+\frac{3 \tanh ^2(a+b x)}{2 b}-\frac{\coth ^2(a+b x)}{2 b}-\frac{3 \log (\tanh (a+b x))}{b}",1,"-1/4*(2*Csch[a + b*x]^2 - 12*Log[Cosh[a + b*x]] + 12*Log[Sinh[a + b*x]] + 4*Sech[a + b*x]^2 + Sech[a + b*x]^4)/b","A",1
39,1,33,37,0.0171261,"\int \text{csch}^4(a+b x) \text{sech}(a+b x) \, dx","Integrate[Csch[a + b*x]^4*Sech[a + b*x],x]","-\frac{\text{csch}^3(a+b x) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\sinh ^2(a+b x)\right)}{3 b}","-\frac{\text{csch}^3(a+b x)}{3 b}+\frac{\text{csch}(a+b x)}{b}+\frac{\tan ^{-1}(\sinh (a+b x))}{b}",1,"-1/3*(Csch[a + b*x]^3*Hypergeometric2F1[-3/2, 1, -1/2, -Sinh[a + b*x]^2])/b","C",1
40,1,45,37,0.041711,"\int \text{csch}^4(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[Csch[a + b*x]^4*Sech[a + b*x]^2,x]","\frac{\tanh (a+b x)}{b}+\frac{5 \coth (a+b x)}{3 b}-\frac{\coth (a+b x) \text{csch}^2(a+b x)}{3 b}","\frac{\tanh (a+b x)}{b}-\frac{\coth ^3(a+b x)}{3 b}+\frac{2 \coth (a+b x)}{b}",1,"(5*Coth[a + b*x])/(3*b) - (Coth[a + b*x]*Csch[a + b*x]^2)/(3*b) + Tanh[a + b*x]/b","A",1
41,1,33,66,0.0160848,"\int \text{csch}^4(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[Csch[a + b*x]^4*Sech[a + b*x]^3,x]","-\frac{\text{csch}^3(a+b x) \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};-\sinh ^2(a+b x)\right)}{3 b}","-\frac{5 \text{csch}^3(a+b x)}{6 b}+\frac{5 \text{csch}(a+b x)}{2 b}+\frac{5 \tan ^{-1}(\sinh (a+b x))}{2 b}+\frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{2 b}",1,"-1/3*(Csch[a + b*x]^3*Hypergeometric2F1[-3/2, 2, -1/2, -Sinh[a + b*x]^2])/b","C",1
42,1,43,53,0.0200483,"\int \text{csch}^4(a+b x) \text{sech}^4(a+b x) \, dx","Integrate[Csch[a + b*x]^4*Sech[a + b*x]^4,x]","16 \left(\frac{\coth (2 (a+b x))}{3 b}-\frac{\coth (2 (a+b x)) \text{csch}^2(2 (a+b x))}{6 b}\right)","-\frac{\tanh ^3(a+b x)}{3 b}+\frac{3 \tanh (a+b x)}{b}-\frac{\coth ^3(a+b x)}{3 b}+\frac{3 \coth (a+b x)}{b}",1,"16*(Coth[2*(a + b*x)]/(3*b) - (Coth[2*(a + b*x)]*Csch[2*(a + b*x)]^2)/(6*b))","A",1
43,1,33,89,0.0192463,"\int \text{csch}^4(a+b x) \text{sech}^5(a+b x) \, dx","Integrate[Csch[a + b*x]^4*Sech[a + b*x]^5,x]","-\frac{\text{csch}^3(a+b x) \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};-\sinh ^2(a+b x)\right)}{3 b}","-\frac{35 \text{csch}^3(a+b x)}{24 b}+\frac{35 \text{csch}(a+b x)}{8 b}+\frac{35 \tan ^{-1}(\sinh (a+b x))}{8 b}+\frac{\text{csch}^3(a+b x) \text{sech}^4(a+b x)}{4 b}+\frac{7 \text{csch}^3(a+b x) \text{sech}^2(a+b x)}{8 b}",1,"-1/3*(Csch[a + b*x]^3*Hypergeometric2F1[-3/2, 3, -1/2, -Sinh[a + b*x]^2])/b","C",1
44,1,46,39,0.1279108,"\int \text{csch}^5(a+b x) \text{sech}(a+b x) \, dx","Integrate[Csch[a + b*x]^5*Sech[a + b*x],x]","\frac{-\text{csch}^4(a+b x)+2 \text{csch}^2(a+b x)+4 \log (\sinh (a+b x))-4 \log (\cosh (a+b x))}{4 b}","-\frac{\coth ^4(a+b x)}{4 b}+\frac{\coth ^2(a+b x)}{b}+\frac{\log (\tanh (a+b x))}{b}",1,"(2*Csch[a + b*x]^2 - Csch[a + b*x]^4 - 4*Log[Cosh[a + b*x]] + 4*Log[Sinh[a + b*x]])/(4*b)","A",1
45,1,105,70,0.0365363,"\int \text{csch}^5(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[Csch[a + b*x]^5*Sech[a + b*x]^2,x]","-\frac{\text{csch}^4\left(\frac{1}{2} (a+b x)\right)}{64 b}+\frac{7 \text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{32 b}+\frac{\text{sech}^4\left(\frac{1}{2} (a+b x)\right)}{64 b}+\frac{7 \text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{32 b}+\frac{\text{sech}(a+b x)}{b}+\frac{15 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{8 b}","\frac{15 \text{sech}(a+b x)}{8 b}-\frac{15 \tanh ^{-1}(\cosh (a+b x))}{8 b}-\frac{\text{csch}^4(a+b x) \text{sech}(a+b x)}{4 b}+\frac{5 \text{csch}^2(a+b x) \text{sech}(a+b x)}{8 b}",1,"(7*Csch[(a + b*x)/2]^2)/(32*b) - Csch[(a + b*x)/2]^4/(64*b) + (15*Log[Tanh[(a + b*x)/2]])/(8*b) + (7*Sech[(a + b*x)/2]^2)/(32*b) + Sech[(a + b*x)/2]^4/(64*b) + Sech[a + b*x]/b","A",1
46,1,56,58,0.1996463,"\int \text{csch}^5(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[Csch[a + b*x]^5*Sech[a + b*x]^3,x]","\frac{-\text{csch}^4(a+b x)+4 \text{csch}^2(a+b x)+2 \text{sech}^2(a+b x)+12 \log (\sinh (a+b x))-12 \log (\cosh (a+b x))}{4 b}","-\frac{\tanh ^2(a+b x)}{2 b}-\frac{\coth ^4(a+b x)}{4 b}+\frac{3 \coth ^2(a+b x)}{2 b}+\frac{3 \log (\tanh (a+b x))}{b}",1,"(4*Csch[a + b*x]^2 - Csch[a + b*x]^4 - 12*Log[Cosh[a + b*x]] + 12*Log[Sinh[a + b*x]] + 2*Sech[a + b*x]^2)/(4*b)","A",1
47,1,121,89,0.0401556,"\int \text{csch}^5(a+b x) \text{sech}^4(a+b x) \, dx","Integrate[Csch[a + b*x]^5*Sech[a + b*x]^4,x]","-\frac{\text{csch}^4\left(\frac{1}{2} (a+b x)\right)}{64 b}+\frac{11 \text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{32 b}+\frac{\text{sech}^4\left(\frac{1}{2} (a+b x)\right)}{64 b}+\frac{\text{sech}^3(a+b x)}{3 b}+\frac{11 \text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{32 b}+\frac{3 \text{sech}(a+b x)}{b}+\frac{35 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{8 b}","\frac{35 \text{sech}^3(a+b x)}{24 b}+\frac{35 \text{sech}(a+b x)}{8 b}-\frac{35 \tanh ^{-1}(\cosh (a+b x))}{8 b}-\frac{\text{csch}^4(a+b x) \text{sech}^3(a+b x)}{4 b}+\frac{7 \text{csch}^2(a+b x) \text{sech}^3(a+b x)}{8 b}",1,"(11*Csch[(a + b*x)/2]^2)/(32*b) - Csch[(a + b*x)/2]^4/(64*b) + (35*Log[Tanh[(a + b*x)/2]])/(8*b) + (11*Sech[(a + b*x)/2]^2)/(32*b) + Sech[(a + b*x)/2]^4/(64*b) + (3*Sech[a + b*x])/b + Sech[a + b*x]^3/(3*b)","A",1
48,1,77,69,0.0271661,"\int \text{csch}^5(a+b x) \text{sech}^5(a+b x) \, dx","Integrate[Csch[a + b*x]^5*Sech[a + b*x]^5,x]","32 \left(-\frac{\text{csch}^4(a+b x)}{128 b}+\frac{3 \text{csch}^2(a+b x)}{64 b}+\frac{\text{sech}^4(a+b x)}{128 b}+\frac{3 \text{sech}^2(a+b x)}{64 b}+\frac{3 \log (\tanh (a+b x))}{16 b}\right)","\frac{\tanh ^4(a+b x)}{4 b}-\frac{2 \tanh ^2(a+b x)}{b}-\frac{\coth ^4(a+b x)}{4 b}+\frac{2 \coth ^2(a+b x)}{b}+\frac{6 \log (\tanh (a+b x))}{b}",1,"32*((3*Csch[a + b*x]^2)/(64*b) - Csch[a + b*x]^4/(128*b) + (3*Log[Tanh[a + b*x]])/(16*b) + (3*Sech[a + b*x]^2)/(64*b) + Sech[a + b*x]^4/(128*b))","A",1
49,1,59,106,0.0613707,"\int \frac{\sinh ^{\frac{7}{2}}(a+b x)}{\cosh ^{\frac{7}{2}}(a+b x)} \, dx","Integrate[Sinh[a + b*x]^(7/2)/Cosh[a + b*x]^(7/2),x]","\frac{2 \sinh ^{\frac{9}{2}}(a+b x) \sqrt[4]{\cosh ^2(a+b x)} \, _2F_1\left(\frac{9}{4},\frac{9}{4};\frac{13}{4};-\sinh ^2(a+b x)\right)}{9 b \sqrt{\cosh (a+b x)}}","-\frac{2 \sinh ^{\frac{5}{2}}(a+b x)}{5 b \cosh ^{\frac{5}{2}}(a+b x)}-\frac{2 \sqrt{\sinh (a+b x)}}{b \sqrt{\cosh (a+b x)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\cosh (a+b x)}}{\sqrt{\sinh (a+b x)}}\right)}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\cosh (a+b x)}}{\sqrt{\sinh (a+b x)}}\right)}{b}",1,"(2*(Cosh[a + b*x]^2)^(1/4)*Hypergeometric2F1[9/4, 9/4, 13/4, -Sinh[a + b*x]^2]*Sinh[a + b*x]^(9/2))/(9*b*Sqrt[Cosh[a + b*x]])","C",1
50,1,59,81,0.0492285,"\int \frac{\sinh ^{\frac{5}{2}}(a+b x)}{\cosh ^{\frac{5}{2}}(a+b x)} \, dx","Integrate[Sinh[a + b*x]^(5/2)/Cosh[a + b*x]^(5/2),x]","\frac{2 \sinh ^{\frac{7}{2}}(a+b x) \cosh ^2(a+b x)^{3/4} \, _2F_1\left(\frac{7}{4},\frac{7}{4};\frac{11}{4};-\sinh ^2(a+b x)\right)}{7 b \cosh ^{\frac{3}{2}}(a+b x)}","-\frac{2 \sinh ^{\frac{3}{2}}(a+b x)}{3 b \cosh ^{\frac{3}{2}}(a+b x)}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sinh (a+b x)}}{\sqrt{\cosh (a+b x)}}\right)}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\sinh (a+b x)}}{\sqrt{\cosh (a+b x)}}\right)}{b}",1,"(2*(Cosh[a + b*x]^2)^(3/4)*Hypergeometric2F1[7/4, 7/4, 11/4, -Sinh[a + b*x]^2]*Sinh[a + b*x]^(7/2))/(7*b*Cosh[a + b*x]^(3/2))","C",1
51,1,59,79,0.0529779,"\int \frac{\sinh ^{\frac{3}{2}}(a+b x)}{\cosh ^{\frac{3}{2}}(a+b x)} \, dx","Integrate[Sinh[a + b*x]^(3/2)/Cosh[a + b*x]^(3/2),x]","\frac{2 \sinh ^{\frac{5}{2}}(a+b x) \sqrt[4]{\cosh ^2(a+b x)} \, _2F_1\left(\frac{5}{4},\frac{5}{4};\frac{9}{4};-\sinh ^2(a+b x)\right)}{5 b \sqrt{\cosh (a+b x)}}","-\frac{2 \sqrt{\sinh (a+b x)}}{b \sqrt{\cosh (a+b x)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\cosh (a+b x)}}{\sqrt{\sinh (a+b x)}}\right)}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\cosh (a+b x)}}{\sqrt{\sinh (a+b x)}}\right)}{b}",1,"(2*(Cosh[a + b*x]^2)^(1/4)*Hypergeometric2F1[5/4, 5/4, 9/4, -Sinh[a + b*x]^2]*Sinh[a + b*x]^(5/2))/(5*b*Sqrt[Cosh[a + b*x]])","C",1
52,1,59,54,0.0352813,"\int \frac{\sqrt{\sinh (a+b x)}}{\sqrt{\cosh (a+b x)}} \, dx","Integrate[Sqrt[Sinh[a + b*x]]/Sqrt[Cosh[a + b*x]],x]","\frac{2 \sinh ^{\frac{3}{2}}(a+b x) \cosh ^2(a+b x)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-\sinh ^2(a+b x)\right)}{3 b \cosh ^{\frac{3}{2}}(a+b x)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\sinh (a+b x)}}{\sqrt{\cosh (a+b x)}}\right)}{b}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sinh (a+b x)}}{\sqrt{\cosh (a+b x)}}\right)}{b}",1,"(2*(Cosh[a + b*x]^2)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -Sinh[a + b*x]^2]*Sinh[a + b*x]^(3/2))/(3*b*Cosh[a + b*x]^(3/2))","C",1
53,1,57,54,0.024825,"\int \frac{\sqrt{\cosh (a+b x)}}{\sqrt{\sinh (a+b x)}} \, dx","Integrate[Sqrt[Cosh[a + b*x]]/Sqrt[Sinh[a + b*x]],x]","\frac{2 \sqrt{\sinh (a+b x)} \sqrt[4]{\cosh ^2(a+b x)} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};-\sinh ^2(a+b x)\right)}{b \sqrt{\cosh (a+b x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\cosh (a+b x)}}{\sqrt{\sinh (a+b x)}}\right)}{b}-\frac{\tan ^{-1}\left(\frac{\sqrt{\cosh (a+b x)}}{\sqrt{\sinh (a+b x)}}\right)}{b}",1,"(2*(Cosh[a + b*x]^2)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, -Sinh[a + b*x]^2]*Sqrt[Sinh[a + b*x]])/(b*Sqrt[Cosh[a + b*x]])","C",1
54,1,57,79,0.0321725,"\int \frac{\cosh ^{\frac{3}{2}}(a+b x)}{\sinh ^{\frac{3}{2}}(a+b x)} \, dx","Integrate[Cosh[a + b*x]^(3/2)/Sinh[a + b*x]^(3/2),x]","-\frac{2 \cosh ^2(a+b x)^{3/4} \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};-\sinh ^2(a+b x)\right)}{b \sqrt{\sinh (a+b x)} \cosh ^{\frac{3}{2}}(a+b x)}","-\frac{2 \sqrt{\cosh (a+b x)}}{b \sqrt{\sinh (a+b x)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sinh (a+b x)}}{\sqrt{\cosh (a+b x)}}\right)}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\sinh (a+b x)}}{\sqrt{\cosh (a+b x)}}\right)}{b}",1,"(-2*(Cosh[a + b*x]^2)^(3/4)*Hypergeometric2F1[-1/4, -1/4, 3/4, -Sinh[a + b*x]^2])/(b*Cosh[a + b*x]^(3/2)*Sqrt[Sinh[a + b*x]])","C",1
55,1,59,81,0.0311431,"\int \frac{\cosh ^{\frac{5}{2}}(a+b x)}{\sinh ^{\frac{5}{2}}(a+b x)} \, dx","Integrate[Cosh[a + b*x]^(5/2)/Sinh[a + b*x]^(5/2),x]","-\frac{2 \sqrt[4]{\cosh ^2(a+b x)} \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};-\sinh ^2(a+b x)\right)}{3 b \sinh ^{\frac{3}{2}}(a+b x) \sqrt{\cosh (a+b x)}}","-\frac{2 \cosh ^{\frac{3}{2}}(a+b x)}{3 b \sinh ^{\frac{3}{2}}(a+b x)}-\frac{\tan ^{-1}\left(\frac{\sqrt{\cosh (a+b x)}}{\sqrt{\sinh (a+b x)}}\right)}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\cosh (a+b x)}}{\sqrt{\sinh (a+b x)}}\right)}{b}",1,"(-2*(Cosh[a + b*x]^2)^(1/4)*Hypergeometric2F1[-3/4, -3/4, 1/4, -Sinh[a + b*x]^2])/(3*b*Sqrt[Cosh[a + b*x]]*Sinh[a + b*x]^(3/2))","C",1
56,1,59,106,0.0401744,"\int \frac{\cosh ^{\frac{7}{2}}(a+b x)}{\sinh ^{\frac{7}{2}}(a+b x)} \, dx","Integrate[Cosh[a + b*x]^(7/2)/Sinh[a + b*x]^(7/2),x]","-\frac{2 \cosh ^2(a+b x)^{3/4} \, _2F_1\left(-\frac{5}{4},-\frac{5}{4};-\frac{1}{4};-\sinh ^2(a+b x)\right)}{5 b \sinh ^{\frac{5}{2}}(a+b x) \cosh ^{\frac{3}{2}}(a+b x)}","-\frac{2 \cosh ^{\frac{5}{2}}(a+b x)}{5 b \sinh ^{\frac{5}{2}}(a+b x)}-\frac{2 \sqrt{\cosh (a+b x)}}{b \sqrt{\sinh (a+b x)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sinh (a+b x)}}{\sqrt{\cosh (a+b x)}}\right)}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\sinh (a+b x)}}{\sqrt{\cosh (a+b x)}}\right)}{b}",1,"(-2*(Cosh[a + b*x]^2)^(3/4)*Hypergeometric2F1[-5/4, -5/4, -1/4, -Sinh[a + b*x]^2])/(5*b*Cosh[a + b*x]^(3/2)*Sinh[a + b*x]^(5/2))","C",1
57,1,59,155,0.0566048,"\int \frac{\sinh ^{\frac{7}{3}}(a+b x)}{\cosh ^{\frac{7}{3}}(a+b x)} \, dx","Integrate[Sinh[a + b*x]^(7/3)/Cosh[a + b*x]^(7/3),x]","\frac{3 \sinh ^{\frac{10}{3}}(a+b x) \cosh ^2(a+b x)^{2/3} \, _2F_1\left(\frac{5}{3},\frac{5}{3};\frac{8}{3};-\sinh ^2(a+b x)\right)}{10 b \cosh ^{\frac{4}{3}}(a+b x)}","-\frac{3 \sinh ^{\frac{4}{3}}(a+b x)}{4 b \cosh ^{\frac{4}{3}}(a+b x)}-\frac{\log \left(1-\frac{\sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}\right)}{2 b}+\frac{\log \left(\frac{\sinh ^{\frac{4}{3}}(a+b x)}{\cosh ^{\frac{4}{3}}(a+b x)}+\frac{\sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}+1}{\sqrt{3}}\right)}{2 b}",1,"(3*(Cosh[a + b*x]^2)^(2/3)*Hypergeometric2F1[5/3, 5/3, 8/3, -Sinh[a + b*x]^2]*Sinh[a + b*x]^(10/3))/(10*b*Cosh[a + b*x]^(4/3))","C",1
58,1,59,155,0.0594234,"\int \frac{\sinh ^{\frac{5}{3}}(a+b x)}{\cosh ^{\frac{5}{3}}(a+b x)} \, dx","Integrate[Sinh[a + b*x]^(5/3)/Cosh[a + b*x]^(5/3),x]","\frac{3 \sinh ^{\frac{8}{3}}(a+b x) \sqrt[3]{\cosh ^2(a+b x)} \, _2F_1\left(\frac{4}{3},\frac{4}{3};\frac{7}{3};-\sinh ^2(a+b x)\right)}{8 b \cosh ^{\frac{2}{3}}(a+b x)}","-\frac{3 \sinh ^{\frac{2}{3}}(a+b x)}{2 b \cosh ^{\frac{2}{3}}(a+b x)}-\frac{\log \left(1-\frac{\cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}\right)}{2 b}+\frac{\log \left(\frac{\cosh ^{\frac{4}{3}}(a+b x)}{\sinh ^{\frac{4}{3}}(a+b x)}+\frac{\cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}+1}{\sqrt{3}}\right)}{2 b}",1,"(3*(Cosh[a + b*x]^2)^(1/3)*Hypergeometric2F1[4/3, 4/3, 7/3, -Sinh[a + b*x]^2]*Sinh[a + b*x]^(8/3))/(8*b*Cosh[a + b*x]^(2/3))","C",1
59,1,59,243,0.0522033,"\int \frac{\sinh ^{\frac{4}{3}}(a+b x)}{\cosh ^{\frac{4}{3}}(a+b x)} \, dx","Integrate[Sinh[a + b*x]^(4/3)/Cosh[a + b*x]^(4/3),x]","\frac{3 \sinh ^{\frac{7}{3}}(a+b x) \sqrt[6]{\cosh ^2(a+b x)} \, _2F_1\left(\frac{7}{6},\frac{7}{6};\frac{13}{6};-\sinh ^2(a+b x)\right)}{7 b \sqrt[3]{\cosh (a+b x)}}","-\frac{3 \sqrt[3]{\sinh (a+b x)}}{b \sqrt[3]{\cosh (a+b x)}}-\frac{\log \left(\frac{\cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt[3]{\cosh (a+b x)}}{\sqrt[3]{\sinh (a+b x)}}+1\right)}{4 b}+\frac{\log \left(\frac{\cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt[3]{\cosh (a+b x)}}{\sqrt[3]{\sinh (a+b x)}}+1\right)}{4 b}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\cosh (a+b x)}}{\sqrt[3]{\sinh (a+b x)}}}{\sqrt{3}}\right)}{2 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\cosh (a+b x)}}{\sqrt[3]{\sinh (a+b x)}}+1}{\sqrt{3}}\right)}{2 b}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{\cosh (a+b x)}}{\sqrt[3]{\sinh (a+b x)}}\right)}{b}",1,"(3*(Cosh[a + b*x]^2)^(1/6)*Hypergeometric2F1[7/6, 7/6, 13/6, -Sinh[a + b*x]^2]*Sinh[a + b*x]^(7/3))/(7*b*Cosh[a + b*x]^(1/3))","C",1
60,1,59,218,0.0421442,"\int \frac{\sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)} \, dx","Integrate[Sinh[a + b*x]^(2/3)/Cosh[a + b*x]^(2/3),x]","\frac{3 \sinh ^{\frac{5}{3}}(a+b x) \cosh ^2(a+b x)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{5}{6};\frac{11}{6};-\sinh ^2(a+b x)\right)}{5 b \cosh ^{\frac{5}{3}}(a+b x)}","-\frac{\log \left(\frac{\sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt[3]{\sinh (a+b x)}}{\sqrt[3]{\cosh (a+b x)}}+1\right)}{4 b}+\frac{\log \left(\frac{\sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt[3]{\sinh (a+b x)}}{\sqrt[3]{\cosh (a+b x)}}+1\right)}{4 b}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\sinh (a+b x)}}{\sqrt[3]{\cosh (a+b x)}}}{\sqrt{3}}\right)}{2 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\sinh (a+b x)}}{\sqrt[3]{\cosh (a+b x)}}+1}{\sqrt{3}}\right)}{2 b}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{\sinh (a+b x)}}{\sqrt[3]{\cosh (a+b x)}}\right)}{b}",1,"(3*(Cosh[a + b*x]^2)^(5/6)*Hypergeometric2F1[5/6, 5/6, 11/6, -Sinh[a + b*x]^2]*Sinh[a + b*x]^(5/3))/(5*b*Cosh[a + b*x]^(5/3))","C",1
61,1,59,128,0.0365245,"\int \frac{\sqrt[3]{\sinh (a+b x)}}{\sqrt[3]{\cosh (a+b x)}} \, dx","Integrate[Sinh[a + b*x]^(1/3)/Cosh[a + b*x]^(1/3),x]","\frac{3 \sinh ^{\frac{4}{3}}(a+b x) \cosh ^2(a+b x)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};-\sinh ^2(a+b x)\right)}{4 b \cosh ^{\frac{4}{3}}(a+b x)}","-\frac{\log \left(1-\frac{\sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}\right)}{2 b}+\frac{\log \left(\frac{\sinh ^{\frac{4}{3}}(a+b x)}{\cosh ^{\frac{4}{3}}(a+b x)}+\frac{\sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}+1}{\sqrt{3}}\right)}{2 b}",1,"(3*(Cosh[a + b*x]^2)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, -Sinh[a + b*x]^2]*Sinh[a + b*x]^(4/3))/(4*b*Cosh[a + b*x]^(4/3))","C",1
62,1,59,128,0.0259218,"\int \frac{\sqrt[3]{\cosh (a+b x)}}{\sqrt[3]{\sinh (a+b x)}} \, dx","Integrate[Cosh[a + b*x]^(1/3)/Sinh[a + b*x]^(1/3),x]","\frac{3 \sinh ^{\frac{2}{3}}(a+b x) \sqrt[3]{\cosh ^2(a+b x)} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\sinh ^2(a+b x)\right)}{2 b \cosh ^{\frac{2}{3}}(a+b x)}","-\frac{\log \left(1-\frac{\cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}\right)}{2 b}+\frac{\log \left(\frac{\cosh ^{\frac{4}{3}}(a+b x)}{\sinh ^{\frac{4}{3}}(a+b x)}+\frac{\cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}+1}{\sqrt{3}}\right)}{2 b}",1,"(3*(Cosh[a + b*x]^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -Sinh[a + b*x]^2]*Sinh[a + b*x]^(2/3))/(2*b*Cosh[a + b*x]^(2/3))","C",1
63,1,57,218,0.0292447,"\int \frac{\cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)} \, dx","Integrate[Cosh[a + b*x]^(2/3)/Sinh[a + b*x]^(2/3),x]","\frac{3 \sqrt[3]{\sinh (a+b x)} \sqrt[6]{\cosh ^2(a+b x)} \, _2F_1\left(\frac{1}{6},\frac{1}{6};\frac{7}{6};-\sinh ^2(a+b x)\right)}{b \sqrt[3]{\cosh (a+b x)}}","-\frac{\log \left(\frac{\cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt[3]{\cosh (a+b x)}}{\sqrt[3]{\sinh (a+b x)}}+1\right)}{4 b}+\frac{\log \left(\frac{\cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt[3]{\cosh (a+b x)}}{\sqrt[3]{\sinh (a+b x)}}+1\right)}{4 b}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\cosh (a+b x)}}{\sqrt[3]{\sinh (a+b x)}}}{\sqrt{3}}\right)}{2 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\cosh (a+b x)}}{\sqrt[3]{\sinh (a+b x)}}+1}{\sqrt{3}}\right)}{2 b}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{\cosh (a+b x)}}{\sqrt[3]{\sinh (a+b x)}}\right)}{b}",1,"(3*(Cosh[a + b*x]^2)^(1/6)*Hypergeometric2F1[1/6, 1/6, 7/6, -Sinh[a + b*x]^2]*Sinh[a + b*x]^(1/3))/(b*Cosh[a + b*x]^(1/3))","C",1
64,1,57,243,0.0299822,"\int \frac{\cosh ^{\frac{4}{3}}(a+b x)}{\sinh ^{\frac{4}{3}}(a+b x)} \, dx","Integrate[Cosh[a + b*x]^(4/3)/Sinh[a + b*x]^(4/3),x]","-\frac{3 \cosh ^2(a+b x)^{5/6} \, _2F_1\left(-\frac{1}{6},-\frac{1}{6};\frac{5}{6};-\sinh ^2(a+b x)\right)}{b \sqrt[3]{\sinh (a+b x)} \cosh ^{\frac{5}{3}}(a+b x)}","-\frac{3 \sqrt[3]{\cosh (a+b x)}}{b \sqrt[3]{\sinh (a+b x)}}-\frac{\log \left(\frac{\sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt[3]{\sinh (a+b x)}}{\sqrt[3]{\cosh (a+b x)}}+1\right)}{4 b}+\frac{\log \left(\frac{\sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt[3]{\sinh (a+b x)}}{\sqrt[3]{\cosh (a+b x)}}+1\right)}{4 b}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\sinh (a+b x)}}{\sqrt[3]{\cosh (a+b x)}}}{\sqrt{3}}\right)}{2 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\sinh (a+b x)}}{\sqrt[3]{\cosh (a+b x)}}+1}{\sqrt{3}}\right)}{2 b}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{\sinh (a+b x)}}{\sqrt[3]{\cosh (a+b x)}}\right)}{b}",1,"(-3*(Cosh[a + b*x]^2)^(5/6)*Hypergeometric2F1[-1/6, -1/6, 5/6, -Sinh[a + b*x]^2])/(b*Cosh[a + b*x]^(5/3)*Sinh[a + b*x]^(1/3))","C",1
65,1,59,155,0.0371621,"\int \frac{\cosh ^{\frac{5}{3}}(a+b x)}{\sinh ^{\frac{5}{3}}(a+b x)} \, dx","Integrate[Cosh[a + b*x]^(5/3)/Sinh[a + b*x]^(5/3),x]","-\frac{3 \cosh ^2(a+b x)^{2/3} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\sinh ^2(a+b x)\right)}{2 b \sinh ^{\frac{2}{3}}(a+b x) \cosh ^{\frac{4}{3}}(a+b x)}","-\frac{3 \cosh ^{\frac{2}{3}}(a+b x)}{2 b \sinh ^{\frac{2}{3}}(a+b x)}-\frac{\log \left(1-\frac{\sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}\right)}{2 b}+\frac{\log \left(\frac{\sinh ^{\frac{4}{3}}(a+b x)}{\cosh ^{\frac{4}{3}}(a+b x)}+\frac{\sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sinh ^{\frac{2}{3}}(a+b x)}{\cosh ^{\frac{2}{3}}(a+b x)}+1}{\sqrt{3}}\right)}{2 b}",1,"(-3*(Cosh[a + b*x]^2)^(2/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -Sinh[a + b*x]^2])/(2*b*Cosh[a + b*x]^(4/3)*Sinh[a + b*x]^(2/3))","C",1
66,1,59,155,0.0318397,"\int \frac{\cosh ^{\frac{7}{3}}(a+b x)}{\sinh ^{\frac{7}{3}}(a+b x)} \, dx","Integrate[Cosh[a + b*x]^(7/3)/Sinh[a + b*x]^(7/3),x]","-\frac{3 \sqrt[3]{\cosh ^2(a+b x)} \, _2F_1\left(-\frac{2}{3},-\frac{2}{3};\frac{1}{3};-\sinh ^2(a+b x)\right)}{4 b \sinh ^{\frac{4}{3}}(a+b x) \cosh ^{\frac{2}{3}}(a+b x)}","-\frac{3 \cosh ^{\frac{4}{3}}(a+b x)}{4 b \sinh ^{\frac{4}{3}}(a+b x)}-\frac{\log \left(1-\frac{\cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}\right)}{2 b}+\frac{\log \left(\frac{\cosh ^{\frac{4}{3}}(a+b x)}{\sinh ^{\frac{4}{3}}(a+b x)}+\frac{\cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \cosh ^{\frac{2}{3}}(a+b x)}{\sinh ^{\frac{2}{3}}(a+b x)}+1}{\sqrt{3}}\right)}{2 b}",1,"(-3*(Cosh[a + b*x]^2)^(1/3)*Hypergeometric2F1[-2/3, -2/3, 1/3, -Sinh[a + b*x]^2])/(4*b*Cosh[a + b*x]^(2/3)*Sinh[a + b*x]^(4/3))","C",1
67,1,16,16,0.0110874,"\int \frac{\cosh ^{\frac{2}{3}}(x)}{\sinh ^{\frac{8}{3}}(x)} \, dx","Integrate[Cosh[x]^(2/3)/Sinh[x]^(8/3),x]","-\frac{3 \cosh ^{\frac{5}{3}}(x)}{5 \sinh ^{\frac{5}{3}}(x)}","-\frac{3 \cosh ^{\frac{5}{3}}(x)}{5 \sinh ^{\frac{5}{3}}(x)}",1,"(-3*Cosh[x]^(5/3))/(5*Sinh[x]^(5/3))","A",1
68,1,16,16,0.0171443,"\int \frac{\sinh ^{\frac{2}{3}}(x)}{\cosh ^{\frac{8}{3}}(x)} \, dx","Integrate[Sinh[x]^(2/3)/Cosh[x]^(8/3),x]","\frac{3 \sinh ^{\frac{5}{3}}(x)}{5 \cosh ^{\frac{5}{3}}(x)}","\frac{3 \sinh ^{\frac{5}{3}}(x)}{5 \cosh ^{\frac{5}{3}}(x)}",1,"(3*Sinh[x]^(5/3))/(5*Cosh[x]^(5/3))","A",1
69,1,10,10,0.0081555,"\int \cosh (x) \text{csch}^{\frac{7}{3}}(x) \, dx","Integrate[Cosh[x]*Csch[x]^(7/3),x]","-\frac{3}{4} \text{csch}^{\frac{4}{3}}(x)","-\frac{3}{4} \text{csch}^{\frac{4}{3}}(x)",1,"(-3*Csch[x]^(4/3))/4","A",1
70,1,23,23,0.0130275,"\int \sinh (a+b x) \tanh (a+b x) \, dx","Integrate[Sinh[a + b*x]*Tanh[a + b*x],x]","\frac{\sinh (a+b x)}{b}-\frac{\tan ^{-1}(\sinh (a+b x))}{b}","\frac{\sinh (a+b x)}{b}-\frac{\tan ^{-1}(\sinh (a+b x))}{b}",1,"-(ArcTan[Sinh[a + b*x]]/b) + Sinh[a + b*x]/b","A",1
71,1,21,21,0.0315749,"\int \sinh (a+b x) \tanh ^2(a+b x) \, dx","Integrate[Sinh[a + b*x]*Tanh[a + b*x]^2,x]","\frac{\cosh (a+b x)}{b}+\frac{\text{sech}(a+b x)}{b}","\frac{\cosh (a+b x)}{b}+\frac{\text{sech}(a+b x)}{b}",1,"Cosh[a + b*x]/b + Sech[a + b*x]/b","A",1
72,1,48,49,0.0549425,"\int \sinh (a+b x) \tanh ^3(a+b x) \, dx","Integrate[Sinh[a + b*x]*Tanh[a + b*x]^3,x]","\frac{\sinh (a+b x) \tanh ^2(a+b x)}{b}-\frac{3 \left(\tan ^{-1}(\sinh (a+b x))-\tanh (a+b x) \text{sech}(a+b x)\right)}{2 b}","\frac{3 \sinh (a+b x)}{2 b}-\frac{3 \tan ^{-1}(\sinh (a+b x))}{2 b}-\frac{\sinh (a+b x) \tanh ^2(a+b x)}{2 b}",1,"(Sinh[a + b*x]*Tanh[a + b*x]^2)/b - (3*(ArcTan[Sinh[a + b*x]] - Sech[a + b*x]*Tanh[a + b*x]))/(2*b)","A",1
73,1,37,37,0.0366075,"\int \sinh (a+b x) \tanh ^4(a+b x) \, dx","Integrate[Sinh[a + b*x]*Tanh[a + b*x]^4,x]","\frac{\cosh (a+b x)}{b}-\frac{\text{sech}^3(a+b x)}{3 b}+\frac{2 \text{sech}(a+b x)}{b}","\frac{\cosh (a+b x)}{b}-\frac{\text{sech}^3(a+b x)}{3 b}+\frac{2 \text{sech}(a+b x)}{b}",1,"Cosh[a + b*x]/b + (2*Sech[a + b*x])/b - Sech[a + b*x]^3/(3*b)","A",1
74,1,25,28,0.0191454,"\int \sinh ^2(a+b x) \tanh (a+b x) \, dx","Integrate[Sinh[a + b*x]^2*Tanh[a + b*x],x]","-\frac{\log (\cosh (a+b x))-\frac{1}{2} \cosh ^2(a+b x)}{b}","\frac{\cosh ^2(a+b x)}{2 b}-\frac{\log (\cosh (a+b x))}{b}",1,"-((-1/2*Cosh[a + b*x]^2 + Log[Cosh[a + b*x]])/b)","A",1
75,1,31,40,0.1132783,"\int \sinh ^2(a+b x) \tanh ^2(a+b x) \, dx","Integrate[Sinh[a + b*x]^2*Tanh[a + b*x]^2,x]","\frac{-6 (a+b x)+\sinh (2 (a+b x))+4 \tanh (a+b x)}{4 b}","\frac{3 \tanh (a+b x)}{2 b}+\frac{\sinh ^2(a+b x) \tanh (a+b x)}{2 b}-\frac{3 x}{2}",1,"(-6*(a + b*x) + Sinh[2*(a + b*x)] + 4*Tanh[a + b*x])/(4*b)","A",1
76,1,35,43,0.0549097,"\int \sinh ^2(a+b x) \tanh ^3(a+b x) \, dx","Integrate[Sinh[a + b*x]^2*Tanh[a + b*x]^3,x]","-\frac{-\sinh ^2(a+b x)+\text{sech}^2(a+b x)+4 \log (\cosh (a+b x))}{2 b}","\frac{\cosh ^2(a+b x)}{2 b}-\frac{\text{sech}^2(a+b x)}{2 b}-\frac{2 \log (\cosh (a+b x))}{b}",1,"-1/2*(4*Log[Cosh[a + b*x]] + Sech[a + b*x]^2 - Sinh[a + b*x]^2)/b","A",1
77,1,38,38,0.0148806,"\int \sinh ^3(a+b x) \tanh (a+b x) \, dx","Integrate[Sinh[a + b*x]^3*Tanh[a + b*x],x]","\frac{\sinh ^3(a+b x)}{3 b}-\frac{\sinh (a+b x)}{b}+\frac{\tan ^{-1}(\sinh (a+b x))}{b}","\frac{\sinh ^3(a+b x)}{3 b}-\frac{\sinh (a+b x)}{b}+\frac{\tan ^{-1}(\sinh (a+b x))}{b}",1,"ArcTan[Sinh[a + b*x]]/b - Sinh[a + b*x]/b + Sinh[a + b*x]^3/(3*b)","A",1
78,1,40,38,0.0332277,"\int \sinh ^3(a+b x) \tanh ^2(a+b x) \, dx","Integrate[Sinh[a + b*x]^3*Tanh[a + b*x]^2,x]","-\frac{7 \cosh (a+b x)}{4 b}+\frac{\cosh (3 (a+b x))}{12 b}-\frac{\text{sech}(a+b x)}{b}","\frac{\cosh ^3(a+b x)}{3 b}-\frac{2 \cosh (a+b x)}{b}-\frac{\text{sech}(a+b x)}{b}",1,"(-7*Cosh[a + b*x])/(4*b) + Cosh[3*(a + b*x)]/(12*b) - Sech[a + b*x]/b","A",1
79,1,65,66,0.1056913,"\int \sinh ^3(a+b x) \tanh ^3(a+b x) \, dx","Integrate[Sinh[a + b*x]^3*Tanh[a + b*x]^3,x]","\frac{2 \sinh ^3(a+b x) \tanh ^2(a+b x)+15 \tan ^{-1}(\sinh (a+b x))-10 \sinh (a+b x) \tanh ^2(a+b x)-15 \tanh (a+b x) \text{sech}(a+b x)}{6 b}","\frac{5 \sinh ^3(a+b x)}{6 b}-\frac{5 \sinh (a+b x)}{2 b}-\frac{\sinh ^3(a+b x) \tanh ^2(a+b x)}{2 b}+\frac{5 \tan ^{-1}(\sinh (a+b x))}{2 b}",1,"(15*ArcTan[Sinh[a + b*x]] - 15*Sech[a + b*x]*Tanh[a + b*x] - 10*Sinh[a + b*x]*Tanh[a + b*x]^2 + 2*Sinh[a + b*x]^3*Tanh[a + b*x]^2)/(6*b)","A",1
80,1,34,40,0.030756,"\int \sinh ^4(a+b x) \tanh (a+b x) \, dx","Integrate[Sinh[a + b*x]^4*Tanh[a + b*x],x]","\frac{\frac{1}{4} \cosh ^4(a+b x)-\cosh ^2(a+b x)+\log (\cosh (a+b x))}{b}","\frac{\cosh ^4(a+b x)}{4 b}-\frac{\cosh ^2(a+b x)}{b}+\frac{\log (\cosh (a+b x))}{b}",1,"(-Cosh[a + b*x]^2 + Cosh[a + b*x]^4/4 + Log[Cosh[a + b*x]])/b","A",1
81,1,11,11,0.0072814,"\int \text{sech}(a+b x) \tanh (a+b x) \, dx","Integrate[Sech[a + b*x]*Tanh[a + b*x],x]","-\frac{\text{sech}(a+b x)}{b}","-\frac{\text{sech}(a+b x)}{b}",1,"-(Sech[a + b*x]/b)","A",1
82,1,15,15,0.0114495,"\int \text{sech}^2(a+b x) \tanh (a+b x) \, dx","Integrate[Sech[a + b*x]^2*Tanh[a + b*x],x]","-\frac{\text{sech}^2(a+b x)}{2 b}","-\frac{\text{sech}^2(a+b x)}{2 b}",1,"-1/2*Sech[a + b*x]^2/b","A",1
83,1,16,16,0.0397554,"\int \text{sech}^{1+n}(a+b x) \sinh (a+b x) \, dx","Integrate[Sech[a + b*x]^(1 + n)*Sinh[a + b*x],x]","-\frac{\text{sech}^n(a+b x)}{b n}","-\frac{\text{sech}^n(a+b x)}{b n}",1,"-(Sech[a + b*x]^n/(b*n))","A",1
84,1,15,15,0.0071759,"\int \text{sech}^2(a+b x) \tanh ^2(a+b x) \, dx","Integrate[Sech[a + b*x]^2*Tanh[a + b*x]^2,x]","\frac{\tanh ^3(a+b x)}{3 b}","\frac{\tanh ^3(a+b x)}{3 b}",1,"Tanh[a + b*x]^3/(3*b)","A",1
85,1,15,15,0.00519,"\int \text{sech}^2(a+b x) \tanh ^3(a+b x) \, dx","Integrate[Sech[a + b*x]^2*Tanh[a + b*x]^3,x]","\frac{\tanh ^4(a+b x)}{4 b}","\frac{\tanh ^4(a+b x)}{4 b}",1,"Tanh[a + b*x]^4/(4*b)","A",1
86,1,19,19,0.0202341,"\int \text{sech}^2(a+b x) \tanh ^n(a+b x) \, dx","Integrate[Sech[a + b*x]^2*Tanh[a + b*x]^n,x]","\frac{\tanh ^{n+1}(a+b x)}{b (n+1)}","\frac{\tanh ^{n+1}(a+b x)}{b (n+1)}",1,"Tanh[a + b*x]^(1 + n)/(b*(1 + n))","A",1
87,1,27,27,0.0319496,"\int \text{sech}(a+b x) \tanh ^3(a+b x) \, dx","Integrate[Sech[a + b*x]*Tanh[a + b*x]^3,x]","\frac{\text{sech}^3(a+b x)}{3 b}-\frac{\text{sech}(a+b x)}{b}","\frac{\text{sech}^3(a+b x)}{3 b}-\frac{\text{sech}(a+b x)}{b}",1,"-(Sech[a + b*x]/b) + Sech[a + b*x]^3/(3*b)","A",1
88,1,31,31,0.061922,"\int \text{sech}^3(a+b x) \tanh ^3(a+b x) \, dx","Integrate[Sech[a + b*x]^3*Tanh[a + b*x]^3,x]","\frac{\text{sech}^5(a+b x)}{5 b}-\frac{\text{sech}^3(a+b x)}{3 b}","\frac{\text{sech}^5(a+b x)}{5 b}-\frac{\text{sech}^3(a+b x)}{3 b}",1,"-1/3*Sech[a + b*x]^3/b + Sech[a + b*x]^5/(5*b)","A",1
89,1,32,36,0.1325302,"\int \text{sech}^{3+n}(a+b x) \sinh ^3(a+b x) \, dx","Integrate[Sech[a + b*x]^(3 + n)*Sinh[a + b*x]^3,x]","\frac{\text{sech}^n(a+b x) \left(\frac{\text{sech}^2(a+b x)}{n+2}-\frac{1}{n}\right)}{b}","\frac{\text{sech}^{n+2}(a+b x)}{b (n+2)}-\frac{\text{sech}^n(a+b x)}{b n}",1,"(Sech[a + b*x]^n*(-n^(-1) + Sech[a + b*x]^2/(2 + n)))/b","A",1
90,1,56,31,0.0421334,"\int \text{sech}^4(a+b x) \tanh ^2(a+b x) \, dx","Integrate[Sech[a + b*x]^4*Tanh[a + b*x]^2,x]","\frac{2 \tanh (a+b x)}{15 b}-\frac{\tanh (a+b x) \text{sech}^4(a+b x)}{5 b}+\frac{\tanh (a+b x) \text{sech}^2(a+b x)}{15 b}","\frac{\tanh ^3(a+b x)}{3 b}-\frac{\tanh ^5(a+b x)}{5 b}",1,"(2*Tanh[a + b*x])/(15*b) + (Sech[a + b*x]^2*Tanh[a + b*x])/(15*b) - (Sech[a + b*x]^4*Tanh[a + b*x])/(5*b)","A",1
91,1,29,35,0.1118071,"\int \text{sech}^4(a+b x) \sqrt{\tanh (a+b x)} \, dx","Integrate[Sech[a + b*x]^4*Sqrt[Tanh[a + b*x]],x]","\frac{2 \tanh ^{\frac{3}{2}}(a+b x) \left(3 \text{sech}^2(a+b x)+4\right)}{21 b}","\frac{2 \tanh ^{\frac{3}{2}}(a+b x)}{3 b}-\frac{2 \tanh ^{\frac{7}{2}}(a+b x)}{7 b}",1,"(2*(4 + 3*Sech[a + b*x]^2)*Tanh[a + b*x]^(3/2))/(21*b)","A",1
92,1,73,40,0.9252462,"\int \text{sech}^4(a+b x) \tanh ^n(a+b x) \, dx","Integrate[Sech[a + b*x]^4*Tanh[a + b*x]^n,x]","\frac{\tanh ^{n-1}(a+b x) \left(\tanh ^2(a+b x) \text{sech}^2(a+b x) (\cosh (2 (a+b x))+n+2)-2 \tanh ^2(a+b x)^{\frac{1-n}{2}}\right)}{b (n+1) (n+3)}","\frac{\tanh ^{n+1}(a+b x)}{b (n+1)}-\frac{\tanh ^{n+3}(a+b x)}{b (n+3)}",1,"(Tanh[a + b*x]^(-1 + n)*((2 + n + Cosh[2*(a + b*x)])*Sech[a + b*x]^2*Tanh[a + b*x]^2 - 2*(Tanh[a + b*x]^2)^((1 - n)/2)))/(b*(1 + n)*(3 + n))","A",1
93,1,34,34,0.0160412,"\int \text{sech}(a+b x) \tanh ^2(a+b x) \, dx","Integrate[Sech[a + b*x]*Tanh[a + b*x]^2,x]","\frac{\tan ^{-1}(\sinh (a+b x))}{2 b}-\frac{\tanh (a+b x) \text{sech}(a+b x)}{2 b}","\frac{\tan ^{-1}(\sinh (a+b x))}{2 b}-\frac{\tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"ArcTan[Sinh[a + b*x]]/(2*b) - (Sech[a + b*x]*Tanh[a + b*x])/(2*b)","A",1
94,1,59,55,0.1728504,"\int \text{sech}(a+b x) \tanh ^4(a+b x) \, dx","Integrate[Sech[a + b*x]*Tanh[a + b*x]^4,x]","\frac{3 \tan ^{-1}(\sinh (a+b x))-6 \tanh (a+b x) \text{sech}^3(a+b x)+\left(3 \tanh (a+b x)-8 \tanh ^3(a+b x)\right) \text{sech}(a+b x)}{8 b}","\frac{3 \tan ^{-1}(\sinh (a+b x))}{8 b}-\frac{\tanh ^3(a+b x) \text{sech}(a+b x)}{4 b}-\frac{3 \tanh (a+b x) \text{sech}(a+b x)}{8 b}",1,"(3*ArcTan[Sinh[a + b*x]] - 6*Sech[a + b*x]^3*Tanh[a + b*x] + Sech[a + b*x]*(3*Tanh[a + b*x] - 8*Tanh[a + b*x]^3))/(8*b)","A",1
95,1,55,55,0.0227319,"\int \text{sech}^3(a+b x) \tanh ^2(a+b x) \, dx","Integrate[Sech[a + b*x]^3*Tanh[a + b*x]^2,x]","\frac{\tan ^{-1}(\sinh (a+b x))}{8 b}-\frac{\tanh (a+b x) \text{sech}^3(a+b x)}{4 b}+\frac{\tanh (a+b x) \text{sech}(a+b x)}{8 b}","\frac{\tan ^{-1}(\sinh (a+b x))}{8 b}-\frac{\tanh (a+b x) \text{sech}^3(a+b x)}{4 b}+\frac{\tanh (a+b x) \text{sech}(a+b x)}{8 b}",1,"ArcTan[Sinh[a + b*x]]/(8*b) + (Sech[a + b*x]*Tanh[a + b*x])/(8*b) - (Sech[a + b*x]^3*Tanh[a + b*x])/(4*b)","A",1
96,1,21,21,0.0130502,"\int \text{sech}(x) \tanh ^5(x) \, dx","Integrate[Sech[x]*Tanh[x]^5,x]","-\frac{1}{5} \text{sech}^5(x)+\frac{2 \text{sech}^3(x)}{3}-\text{sech}(x)","-\frac{1}{5} \text{sech}^5(x)+\frac{2 \text{sech}^3(x)}{3}-\text{sech}(x)",1,"-Sech[x] + (2*Sech[x]^3)/3 - Sech[x]^5/5","A",1
97,1,25,25,0.0155546,"\int \text{sech}^7(x) \tanh ^5(x) \, dx","Integrate[Sech[x]^7*Tanh[x]^5,x]","-\frac{1}{11} \text{sech}^{11}(x)+\frac{2 \text{sech}^9(x)}{9}-\frac{\text{sech}^7(x)}{7}","-\frac{1}{11} \text{sech}^{11}(x)+\frac{2 \text{sech}^9(x)}{9}-\frac{\text{sech}^7(x)}{7}",1,"-1/7*Sech[x]^7 + (2*Sech[x]^9)/9 - Sech[x]^11/11","A",1
98,1,48,38,0.0095701,"\int \text{sech}^3(x) \tanh ^4(x) \, dx","Integrate[Sech[x]^3*Tanh[x]^4,x]","\frac{1}{16} \tan ^{-1}(\sinh (x))-\frac{1}{6} \tanh (x) \text{sech}^5(x)-\frac{1}{3} \tanh ^3(x) \text{sech}^3(x)+\frac{1}{24} \tanh (x) \text{sech}^3(x)+\frac{1}{16} \tanh (x) \text{sech}(x)","\frac{1}{16} \tan ^{-1}(\sinh (x))-\frac{1}{6} \tanh ^3(x) \text{sech}^3(x)-\frac{1}{8} \tanh (x) \text{sech}^3(x)+\frac{1}{16} \tanh (x) \text{sech}(x)",1,"ArcTan[Sinh[x]]/16 + (Sech[x]*Tanh[x])/16 + (Sech[x]^3*Tanh[x])/24 - (Sech[x]^5*Tanh[x])/6 - (Sech[x]^3*Tanh[x]^3)/3","A",1
99,1,36,36,0.0091098,"\int \text{sech}^5(x) \tanh ^2(x) \, dx","Integrate[Sech[x]^5*Tanh[x]^2,x]","\frac{1}{16} \tan ^{-1}(\sinh (x))-\frac{1}{6} \tanh (x) \text{sech}^5(x)+\frac{1}{24} \tanh (x) \text{sech}^3(x)+\frac{1}{16} \tanh (x) \text{sech}(x)","\frac{1}{16} \tan ^{-1}(\sinh (x))-\frac{1}{6} \tanh (x) \text{sech}^5(x)+\frac{1}{24} \tanh (x) \text{sech}^3(x)+\frac{1}{16} \tanh (x) \text{sech}(x)",1,"ArcTan[Sinh[x]]/16 + (Sech[x]*Tanh[x])/16 + (Sech[x]^3*Tanh[x])/24 - (Sech[x]^5*Tanh[x])/6","A",1
100,1,67,33,0.0254771,"\int \text{sech}^8(x) \tanh ^6(x) \, dx","Integrate[Sech[x]^8*Tanh[x]^6,x]","\frac{16 \tanh (x)}{3003}-\frac{1}{13} \tanh (x) \text{sech}^{12}(x)+\frac{27}{143} \tanh (x) \text{sech}^{10}(x)-\frac{53}{429} \tanh (x) \text{sech}^8(x)+\frac{5 \tanh (x) \text{sech}^6(x)}{3003}+\frac{2 \tanh (x) \text{sech}^4(x)}{1001}+\frac{8 \tanh (x) \text{sech}^2(x)}{3003}","-\frac{1}{13} \tanh ^{13}(x)+\frac{3 \tanh ^{11}(x)}{11}-\frac{\tanh ^9(x)}{3}+\frac{\tanh ^7(x)}{7}",1,"(16*Tanh[x])/3003 + (8*Sech[x]^2*Tanh[x])/3003 + (2*Sech[x]^4*Tanh[x])/1001 + (5*Sech[x]^6*Tanh[x])/3003 - (53*Sech[x]^8*Tanh[x])/429 + (27*Sech[x]^10*Tanh[x])/143 - (Sech[x]^12*Tanh[x])/13","B",1
101,1,26,23,0.0284015,"\int \cosh (a+b x) \coth (a+b x) \, dx","Integrate[Cosh[a + b*x]*Coth[a + b*x],x]","\frac{\cosh (a+b x)}{b}+\frac{\log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{b}","\frac{\cosh (a+b x)}{b}-\frac{\tanh ^{-1}(\cosh (a+b x))}{b}",1,"Cosh[a + b*x]/b + Log[Tanh[(a + b*x)/2]]/b","A",1
102,1,22,22,0.0144828,"\int \cosh (a+b x) \coth ^2(a+b x) \, dx","Integrate[Cosh[a + b*x]*Coth[a + b*x]^2,x]","\frac{\sinh (a+b x)}{b}-\frac{\text{csch}(a+b x)}{b}","\frac{\sinh (a+b x)}{b}-\frac{\text{csch}(a+b x)}{b}",1,"-(Csch[a + b*x]/b) + Sinh[a + b*x]/b","A",1
103,1,67,49,0.0331087,"\int \cosh (a+b x) \coth ^3(a+b x) \, dx","Integrate[Cosh[a + b*x]*Coth[a + b*x]^3,x]","\frac{\cosh (a+b x)}{b}-\frac{\text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{\text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}+\frac{3 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b}","\frac{3 \cosh (a+b x)}{2 b}-\frac{3 \tanh ^{-1}(\cosh (a+b x))}{2 b}-\frac{\cosh (a+b x) \coth ^2(a+b x)}{2 b}",1,"Cosh[a + b*x]/b - Csch[(a + b*x)/2]^2/(8*b) + (3*Log[Tanh[(a + b*x)/2]])/(2*b) - Sech[(a + b*x)/2]^2/(8*b)","A",1
104,1,37,37,0.0216677,"\int \cosh (a+b x) \coth ^4(a+b x) \, dx","Integrate[Cosh[a + b*x]*Coth[a + b*x]^4,x]","\frac{\sinh (a+b x)}{b}-\frac{\text{csch}^3(a+b x)}{3 b}-\frac{2 \text{csch}(a+b x)}{b}","\frac{\sinh (a+b x)}{b}-\frac{\text{csch}^3(a+b x)}{3 b}-\frac{2 \text{csch}(a+b x)}{b}",1,"(-2*Csch[a + b*x])/b - Csch[a + b*x]^3/(3*b) + Sinh[a + b*x]/b","A",1
105,1,25,27,0.0228021,"\int \cosh ^2(a+b x) \coth (a+b x) \, dx","Integrate[Cosh[a + b*x]^2*Coth[a + b*x],x]","\frac{\sinh ^2(a+b x)+2 \log (\sinh (a+b x))}{2 b}","\frac{\sinh ^2(a+b x)}{2 b}+\frac{\log (\sinh (a+b x))}{b}",1,"(2*Log[Sinh[a + b*x]] + Sinh[a + b*x]^2)/(2*b)","A",1
106,1,31,40,0.111303,"\int \cosh ^2(a+b x) \coth ^2(a+b x) \, dx","Integrate[Cosh[a + b*x]^2*Coth[a + b*x]^2,x]","\frac{6 (a+b x)+\sinh (2 (a+b x))-4 \coth (a+b x)}{4 b}","-\frac{3 \coth (a+b x)}{2 b}+\frac{\cosh ^2(a+b x) \coth (a+b x)}{2 b}+\frac{3 x}{2}",1,"(6*(a + b*x) - 4*Coth[a + b*x] + Sinh[2*(a + b*x)])/(4*b)","A",1
107,1,35,43,0.0514172,"\int \cosh ^2(a+b x) \coth ^3(a+b x) \, dx","Integrate[Cosh[a + b*x]^2*Coth[a + b*x]^3,x]","-\frac{-\sinh ^2(a+b x)+\text{csch}^2(a+b x)-4 \log (\sinh (a+b x))}{2 b}","\frac{\sinh ^2(a+b x)}{2 b}-\frac{\text{csch}^2(a+b x)}{2 b}+\frac{2 \log (\sinh (a+b x))}{b}",1,"-1/2*(Csch[a + b*x]^2 - 4*Log[Sinh[a + b*x]] - Sinh[a + b*x]^2)/b","A",1
108,1,44,38,0.0312999,"\int \cosh ^3(a+b x) \coth (a+b x) \, dx","Integrate[Cosh[a + b*x]^3*Coth[a + b*x],x]","\frac{5 \cosh (a+b x)}{4 b}+\frac{\cosh (3 (a+b x))}{12 b}+\frac{\log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{b}","\frac{\cosh ^3(a+b x)}{3 b}+\frac{\cosh (a+b x)}{b}-\frac{\tanh ^{-1}(\cosh (a+b x))}{b}",1,"(5*Cosh[a + b*x])/(4*b) + Cosh[3*(a + b*x)]/(12*b) + Log[Tanh[(a + b*x)/2]]/b","A",1
109,1,38,38,0.0192491,"\int \cosh ^3(a+b x) \coth ^2(a+b x) \, dx","Integrate[Cosh[a + b*x]^3*Coth[a + b*x]^2,x]","\frac{\sinh ^3(a+b x)}{3 b}+\frac{2 \sinh (a+b x)}{b}-\frac{\text{csch}(a+b x)}{b}","\frac{\sinh ^3(a+b x)}{3 b}+\frac{2 \sinh (a+b x)}{b}-\frac{\text{csch}(a+b x)}{b}",1,"-(Csch[a + b*x]/b) + (2*Sinh[a + b*x])/b + Sinh[a + b*x]^3/(3*b)","A",1
110,1,85,66,0.0425706,"\int \cosh ^3(a+b x) \coth ^3(a+b x) \, dx","Integrate[Cosh[a + b*x]^3*Coth[a + b*x]^3,x]","\frac{9 \cosh (a+b x)}{4 b}+\frac{\cosh (3 (a+b x))}{12 b}-\frac{\text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{\text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}+\frac{5 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b}","\frac{5 \cosh ^3(a+b x)}{6 b}+\frac{5 \cosh (a+b x)}{2 b}-\frac{\cosh ^3(a+b x) \coth ^2(a+b x)}{2 b}-\frac{5 \tanh ^{-1}(\cosh (a+b x))}{2 b}",1,"(9*Cosh[a + b*x])/(4*b) + Cosh[3*(a + b*x)]/(12*b) - Csch[(a + b*x)/2]^2/(8*b) + (5*Log[Tanh[(a + b*x)/2]])/(2*b) - Sech[(a + b*x)/2]^2/(8*b)","A",1
111,1,35,39,0.0339533,"\int \cosh ^4(a+b x) \coth (a+b x) \, dx","Integrate[Cosh[a + b*x]^4*Coth[a + b*x],x]","\frac{\sinh ^4(a+b x)+4 \sinh ^2(a+b x)+4 \log (\sinh (a+b x))}{4 b}","\frac{\sinh ^4(a+b x)}{4 b}+\frac{\sinh ^2(a+b x)}{b}+\frac{\log (\sinh (a+b x))}{b}",1,"(4*Log[Sinh[a + b*x]] + 4*Sinh[a + b*x]^2 + Sinh[a + b*x]^4)/(4*b)","A",1
112,1,11,11,0.010429,"\int \coth (a+b x) \text{csch}(a+b x) \, dx","Integrate[Coth[a + b*x]*Csch[a + b*x],x]","-\frac{\text{csch}(a+b x)}{b}","-\frac{\text{csch}(a+b x)}{b}",1,"-(Csch[a + b*x]/b)","A",1
113,1,15,15,0.0140866,"\int \coth (a+b x) \text{csch}^2(a+b x) \, dx","Integrate[Coth[a + b*x]*Csch[a + b*x]^2,x]","-\frac{\text{csch}^2(a+b x)}{2 b}","-\frac{\text{csch}^2(a+b x)}{2 b}",1,"-1/2*Csch[a + b*x]^2/b","A",1
114,1,16,16,0.02195,"\int \cosh (a+b x) \text{csch}^{1+n}(a+b x) \, dx","Integrate[Cosh[a + b*x]*Csch[a + b*x]^(1 + n),x]","-\frac{\text{csch}^n(a+b x)}{b n}","-\frac{\text{csch}^n(a+b x)}{b n}",1,"-(Csch[a + b*x]^n/(b*n))","A",1
115,1,15,15,0.0045661,"\int \coth ^2(a+b x) \text{csch}^2(a+b x) \, dx","Integrate[Coth[a + b*x]^2*Csch[a + b*x]^2,x]","-\frac{\coth ^3(a+b x)}{3 b}","-\frac{\coth ^3(a+b x)}{3 b}",1,"-1/3*Coth[a + b*x]^3/b","A",1
116,1,15,15,0.0052003,"\int \coth ^3(a+b x) \text{csch}^2(a+b x) \, dx","Integrate[Coth[a + b*x]^3*Csch[a + b*x]^2,x]","-\frac{\coth ^4(a+b x)}{4 b}","-\frac{\coth ^4(a+b x)}{4 b}",1,"-1/4*Coth[a + b*x]^4/b","A",1
117,1,20,20,0.024163,"\int \coth ^n(a+b x) \text{csch}^2(a+b x) \, dx","Integrate[Coth[a + b*x]^n*Csch[a + b*x]^2,x]","-\frac{\coth ^{n+1}(a+b x)}{b (n+1)}","-\frac{\coth ^{n+1}(a+b x)}{b (n+1)}",1,"-(Coth[a + b*x]^(1 + n)/(b*(1 + n)))","A",1
118,1,27,27,0.0142925,"\int \coth ^3(a+b x) \text{csch}(a+b x) \, dx","Integrate[Coth[a + b*x]^3*Csch[a + b*x],x]","-\frac{\text{csch}^3(a+b x)}{3 b}-\frac{\text{csch}(a+b x)}{b}","-\frac{\text{csch}^3(a+b x)}{3 b}-\frac{\text{csch}(a+b x)}{b}",1,"-(Csch[a + b*x]/b) - Csch[a + b*x]^3/(3*b)","A",1
119,1,31,31,0.0254304,"\int \coth ^3(a+b x) \text{csch}^3(a+b x) \, dx","Integrate[Coth[a + b*x]^3*Csch[a + b*x]^3,x]","-\frac{\text{csch}^5(a+b x)}{5 b}-\frac{\text{csch}^3(a+b x)}{3 b}","-\frac{\text{csch}^5(a+b x)}{5 b}-\frac{\text{csch}^3(a+b x)}{3 b}",1,"-1/3*Csch[a + b*x]^3/b - Csch[a + b*x]^5/(5*b)","A",1
120,1,34,37,0.0737596,"\int \cosh ^3(a+b x) \text{csch}^{3+n}(a+b x) \, dx","Integrate[Cosh[a + b*x]^3*Csch[a + b*x]^(3 + n),x]","-\frac{\text{csch}^n(a+b x) \left(n \text{csch}^2(a+b x)+n+2\right)}{b n (n+2)}","-\frac{\text{csch}^{n+2}(a+b x)}{b (n+2)}-\frac{\text{csch}^n(a+b x)}{b n}",1,"-((Csch[a + b*x]^n*(2 + n + n*Csch[a + b*x]^2))/(b*n*(2 + n)))","A",1
121,1,57,34,0.0330177,"\int \coth ^2(a+b x) \text{csch}(a+b x) \, dx","Integrate[Coth[a + b*x]^2*Csch[a + b*x],x]","-\frac{\text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{\text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}+\frac{\log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b}","-\frac{\tanh ^{-1}(\cosh (a+b x))}{2 b}-\frac{\coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-1/8*Csch[(a + b*x)/2]^2/b + Log[Tanh[(a + b*x)/2]]/(2*b) - Sech[(a + b*x)/2]^2/(8*b)","A",1
122,1,95,55,0.0431318,"\int \coth ^2(a+b x) \text{csch}^3(a+b x) \, dx","Integrate[Coth[a + b*x]^2*Csch[a + b*x]^3,x]","-\frac{\text{csch}^4\left(\frac{1}{2} (a+b x)\right)}{64 b}-\frac{\text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{32 b}+\frac{\text{sech}^4\left(\frac{1}{2} (a+b x)\right)}{64 b}-\frac{\text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{32 b}-\frac{\log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{8 b}","\frac{\tanh ^{-1}(\cosh (a+b x))}{8 b}-\frac{\coth (a+b x) \text{csch}^3(a+b x)}{4 b}-\frac{\coth (a+b x) \text{csch}(a+b x)}{8 b}",1,"-1/32*Csch[(a + b*x)/2]^2/b - Csch[(a + b*x)/2]^4/(64*b) - Log[Tanh[(a + b*x)/2]]/(8*b) - Sech[(a + b*x)/2]^2/(32*b) + Sech[(a + b*x)/2]^4/(64*b)","A",1
123,1,95,55,0.0401959,"\int \coth ^4(a+b x) \text{csch}(a+b x) \, dx","Integrate[Coth[a + b*x]^4*Csch[a + b*x],x]","-\frac{\text{csch}^4\left(\frac{1}{2} (a+b x)\right)}{64 b}-\frac{5 \text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{32 b}+\frac{\text{sech}^4\left(\frac{1}{2} (a+b x)\right)}{64 b}-\frac{5 \text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{32 b}+\frac{3 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{8 b}","-\frac{3 \tanh ^{-1}(\cosh (a+b x))}{8 b}-\frac{\coth ^3(a+b x) \text{csch}(a+b x)}{4 b}-\frac{3 \coth (a+b x) \text{csch}(a+b x)}{8 b}",1,"(-5*Csch[(a + b*x)/2]^2)/(32*b) - Csch[(a + b*x)/2]^4/(64*b) + (3*Log[Tanh[(a + b*x)/2]])/(8*b) - (5*Sech[(a + b*x)/2]^2)/(32*b) + Sech[(a + b*x)/2]^4/(64*b)","A",1
124,1,27,17,0.0236195,"\int \coth ^2(x) \text{csch}^4(x) \, dx","Integrate[Coth[x]^2*Csch[x]^4,x]","\frac{2 \coth (x)}{15}-\frac{1}{5} \coth (x) \text{csch}^4(x)-\frac{1}{15} \coth (x) \text{csch}^2(x)","\frac{\coth ^3(x)}{3}-\frac{\coth ^5(x)}{5}",1,"(2*Coth[x])/15 - (Coth[x]*Csch[x]^2)/15 - (Coth[x]*Csch[x]^4)/5","A",1
125,1,17,17,0.009879,"\int \coth ^3(x) \text{csch}^4(x) \, dx","Integrate[Coth[x]^3*Csch[x]^4,x]","-\frac{1}{6} \text{csch}^6(x)-\frac{\text{csch}^4(x)}{4}","-\frac{1}{6} \text{csch}^6(x)-\frac{\text{csch}^4(x)}{4}",1,"-1/4*Csch[x]^4 - Csch[x]^6/6","A",1
126,1,30,26,0.091369,"\int \coth ^n(x) \text{csch}^4(x) \, dx","Integrate[Coth[x]^n*Csch[x]^4,x]","\frac{\text{csch}^2(x) (-n+\cosh (2 x)-2) \coth ^{n+1}(x)}{(n+1) (n+3)}","\frac{\coth ^{n+1}(x)}{n+1}-\frac{\coth ^{n+3}(x)}{n+3}",1,"((-2 - n + Cosh[2*x])*Coth[x]^(1 + n)*Csch[x]^2)/((1 + n)*(3 + n))","A",1
127,1,84,38,0.0200625,"\int \coth ^4(x) \text{csch}^3(x) \, dx","Integrate[Coth[x]^4*Csch[x]^3,x]","-\frac{1}{384} \text{csch}^6\left(\frac{x}{2}\right)-\frac{1}{64} \text{csch}^4\left(\frac{x}{2}\right)-\frac{1}{64} \text{csch}^2\left(\frac{x}{2}\right)-\frac{1}{384} \text{sech}^6\left(\frac{x}{2}\right)+\frac{1}{64} \text{sech}^4\left(\frac{x}{2}\right)-\frac{1}{64} \text{sech}^2\left(\frac{x}{2}\right)-\frac{1}{16} \log \left(\tanh \left(\frac{x}{2}\right)\right)","\frac{1}{16} \tanh ^{-1}(\cosh (x))-\frac{1}{6} \coth ^3(x) \text{csch}^3(x)-\frac{1}{8} \coth (x) \text{csch}^3(x)-\frac{1}{16} \coth (x) \text{csch}(x)",1,"-1/64*Csch[x/2]^2 - Csch[x/2]^4/64 - Csch[x/2]^6/384 - Log[Tanh[x/2]]/16 - Sech[x/2]^2/64 + Sech[x/2]^4/64 - Sech[x/2]^6/384","B",1
128,1,47,25,0.0280497,"\int \coth ^4(x) \text{csch}^6(x) \, dx","Integrate[Coth[x]^4*Csch[x]^6,x]","-\frac{8 \coth (x)}{315}-\frac{1}{9} \coth (x) \text{csch}^8(x)-\frac{10}{63} \coth (x) \text{csch}^6(x)-\frac{1}{105} \coth (x) \text{csch}^4(x)+\frac{4}{315} \coth (x) \text{csch}^2(x)","-\frac{1}{9} \coth ^9(x)+\frac{2 \coth ^7(x)}{7}-\frac{\coth ^5(x)}{5}",1,"(-8*Coth[x])/315 + (4*Coth[x]*Csch[x]^2)/315 - (Coth[x]*Csch[x]^4)/105 - (10*Coth[x]*Csch[x]^6)/63 - (Coth[x]*Csch[x]^8)/9","A",1
129,1,29,29,0.0182397,"\int \coth ^5(6 x) \text{csch}(6 x) \, dx","Integrate[Coth[6*x]^5*Csch[6*x],x]","-\frac{1}{30} \text{csch}^5(6 x)-\frac{1}{9} \text{csch}^3(6 x)-\frac{1}{6} \text{csch}(6 x)","-\frac{1}{30} \text{csch}^5(6 x)-\frac{1}{9} \text{csch}^3(6 x)-\frac{1}{6} \text{csch}(6 x)",1,"-1/6*Csch[6*x] - Csch[6*x]^3/9 - Csch[6*x]^5/30","A",1
130,1,33,33,0.0125146,"\int \coth ^7(x) \text{csch}^3(x) \, dx","Integrate[Coth[x]^7*Csch[x]^3,x]","-\frac{1}{9} \text{csch}^9(x)-\frac{3 \text{csch}^7(x)}{7}-\frac{3 \text{csch}^5(x)}{5}-\frac{\text{csch}^3(x)}{3}","-\frac{1}{9} \text{csch}^9(x)-\frac{3 \text{csch}^7(x)}{7}-\frac{3 \text{csch}^5(x)}{5}-\frac{\text{csch}^3(x)}{3}",1,"-1/3*Csch[x]^3 - (3*Csch[x]^5)/5 - (3*Csch[x]^7)/7 - Csch[x]^9/9","A",1
131,1,26,27,0.0342532,"\int \sinh (a+b x) \sinh (c+b x) \, dx","Integrate[Sinh[a + b*x]*Sinh[c + b*x],x]","\frac{\sinh (a+2 b x+c)-2 b x \cosh (a-c)}{4 b}","\frac{\sinh (a+2 b x+c)}{4 b}-\frac{1}{2} x \cosh (a-c)",1,"(-2*b*x*Cosh[a - c] + Sinh[a + c + 2*b*x])/(4*b)","A",1
132,1,27,27,0.0436754,"\int \sinh (c-b x) \sinh (a+b x) \, dx","Integrate[Sinh[c - b*x]*Sinh[a + b*x],x]","\frac{1}{2} x \cosh (a+c)-\frac{\sinh (a+2 b x-c)}{4 b}","\frac{1}{2} x \cosh (a+c)-\frac{\sinh (a+2 b x-c)}{4 b}",1,"(x*Cosh[a + c])/2 - Sinh[a - c + 2*b*x]/(4*b)","A",1
133,1,26,27,0.0236921,"\int \cosh (a+b x) \cosh (c+b x) \, dx","Integrate[Cosh[a + b*x]*Cosh[c + b*x],x]","\frac{\sinh (a+2 b x+c)+2 b x \cosh (a-c)}{4 b}","\frac{\sinh (a+2 b x+c)}{4 b}+\frac{1}{2} x \cosh (a-c)",1,"(2*b*x*Cosh[a - c] + Sinh[a + c + 2*b*x])/(4*b)","A",1
134,1,26,27,0.0244503,"\int \cosh (c-b x) \cosh (a+b x) \, dx","Integrate[Cosh[c - b*x]*Cosh[a + b*x],x]","\frac{\sinh (a+2 b x-c)+2 b x \cosh (a+c)}{4 b}","\frac{\sinh (a+2 b x-c)}{4 b}+\frac{1}{2} x \cosh (a+c)",1,"(2*b*x*Cosh[a + c] + Sinh[a - c + 2*b*x])/(4*b)","A",1
135,1,29,37,0.5171749,"\int \tanh (a+b x) \tanh (c+b x) \, dx","Integrate[Tanh[a + b*x]*Tanh[c + b*x],x]","\frac{\coth (a-c) (\log (\cosh (b x+c))-\log (\cosh (a+b x)))}{b}+x","-\frac{\coth (a-c) \log (\cosh (a+b x))}{b}+\frac{\coth (a-c) \log (\cosh (b x+c))}{b}+x",1,"x + (Coth[a - c]*(-Log[Cosh[a + b*x]] + Log[Cosh[c + b*x]]))/b","A",1
136,1,30,36,0.5185812,"\int \tanh (c-b x) \tanh (a+b x) \, dx","Integrate[Tanh[c - b*x]*Tanh[a + b*x],x]","\frac{\coth (a+c) (\log (\cosh (a+b x))-\log (\cosh (c-b x)))}{b}-x","-\frac{\coth (a+c) \log (\cosh (c-b x))}{b}+\frac{\coth (a+c) \log (\cosh (a+b x))}{b}-x",1,"-x + (Coth[a + c]*(-Log[Cosh[c - b*x]] + Log[Cosh[a + b*x]]))/b","A",1
137,1,29,37,0.5049947,"\int \coth (a+b x) \coth (c+b x) \, dx","Integrate[Coth[a + b*x]*Coth[c + b*x],x]","\frac{\coth (a-c) (\log (\sinh (b x+c))-\log (\sinh (a+b x)))}{b}+x","-\frac{\coth (a-c) \log (\sinh (a+b x))}{b}+\frac{\coth (a-c) \log (\sinh (b x+c))}{b}+x",1,"x + (Coth[a - c]*(-Log[Sinh[a + b*x]] + Log[Sinh[c + b*x]]))/b","A",1
138,1,32,36,0.4899166,"\int \coth (c-b x) \coth (a+b x) \, dx","Integrate[Coth[c - b*x]*Coth[a + b*x],x]","\frac{\coth (a+c) (\log (-\sinh (a+b x))-\log (\sinh (c-b x)))}{b}-x","-\frac{\coth (a+c) \log (\sinh (c-b x))}{b}+\frac{\coth (a+c) \log (\sinh (a+b x))}{b}-x",1,"-x + (Coth[a + c]*(-Log[Sinh[c - b*x]] + Log[-Sinh[a + b*x]]))/b","A",1
139,1,27,36,0.2125993,"\int \text{sech}(a+b x) \text{sech}(c+b x) \, dx","Integrate[Sech[a + b*x]*Sech[c + b*x],x]","\frac{\text{csch}(a-c) (\log (\cosh (a+b x))-\log (\cosh (b x+c)))}{b}","\frac{\text{csch}(a-c) \log (\cosh (a+b x))}{b}-\frac{\text{csch}(a-c) \log (\cosh (b x+c))}{b}",1,"(Csch[a - c]*(Log[Cosh[a + b*x]] - Log[Cosh[c + b*x]]))/b","A",1
140,1,27,33,0.2017409,"\int \text{sech}(c-b x) \text{sech}(a+b x) \, dx","Integrate[Sech[c - b*x]*Sech[a + b*x],x]","-\frac{\text{csch}(a+c) (\log (\cosh (c-b x))-\log (\cosh (a+b x)))}{b}","\frac{\text{csch}(a+c) \log (\cosh (a+b x))}{b}-\frac{\text{csch}(a+c) \log (\cosh (c-b x))}{b}",1,"-((Csch[a + c]*(Log[Cosh[c - b*x]] - Log[Cosh[a + b*x]]))/b)","A",1
141,1,28,36,0.2293051,"\int \text{csch}(a+b x) \text{csch}(c+b x) \, dx","Integrate[Csch[a + b*x]*Csch[c + b*x],x]","-\frac{\text{csch}(a-c) (\log (\sinh (a+b x))-\log (\sinh (b x+c)))}{b}","\frac{\text{csch}(a-c) \log (\sinh (b x+c))}{b}-\frac{\text{csch}(a-c) \log (\sinh (a+b x))}{b}",1,"-((Csch[a - c]*(Log[Sinh[a + b*x]] - Log[Sinh[c + b*x]]))/b)","A",1
142,1,29,33,0.2037472,"\int \text{csch}(c-b x) \text{csch}(a+b x) \, dx","Integrate[Csch[c - b*x]*Csch[a + b*x],x]","-\frac{\text{csch}(a+c) (\log (\sinh (c-b x))-\log (-\sinh (a+b x)))}{b}","\frac{\text{csch}(a+c) \log (\sinh (a+b x))}{b}-\frac{\text{csch}(a+c) \log (\sinh (c-b x))}{b}",1,"-((Csch[a + c]*(Log[Sinh[c - b*x]] - Log[-Sinh[a + b*x]]))/b)","A",1
143,1,86,29,0.0626818,"\int \sinh (a+b x) \tanh (c+b x) \, dx","Integrate[Sinh[a + b*x]*Tanh[c + b*x],x]","-\frac{2 \cosh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \cosh \left(\frac{b x}{2}\right)+\cosh (c) \sinh \left(\frac{b x}{2}\right)\right)}{\cosh (c) \cosh \left(\frac{b x}{2}\right)-\sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}+\frac{\sinh (a) \cosh (b x)}{b}+\frac{\cosh (a) \sinh (b x)}{b}","\frac{\sinh (a+b x)}{b}-\frac{\cosh (a-c) \tan ^{-1}(\sinh (b x+c))}{b}",1,"(-2*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[(b*x)/2]*Sinh[c] + Cosh[c]*Sinh[(b*x)/2]))/(Cosh[c]*Cosh[(b*x)/2] - Cosh[(b*x)/2]*Sinh[c])]*Cosh[a - c])/b + (Cosh[b*x]*Sinh[a])/b + (Cosh[a]*Sinh[b*x])/b","B",1
144,1,102,45,0.1063868,"\int \sinh (a+b x) \tanh ^2(c+b x) \, dx","Integrate[Sinh[a + b*x]*Tanh[c + b*x]^2,x]","\frac{\cosh (a-c) \text{sech}(b x+c)}{b}-\frac{2 \sinh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \cosh \left(\frac{b x}{2}\right)+\cosh (c) \sinh \left(\frac{b x}{2}\right)\right)}{\cosh (c) \cosh \left(\frac{b x}{2}\right)-\sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}+\frac{\sinh (a) \sinh (b x)}{b}+\frac{\cosh (a) \cosh (b x)}{b}","-\frac{\sinh (a-c) \tan ^{-1}(\sinh (b x+c))}{b}+\frac{\cosh (a-c) \text{sech}(b x+c)}{b}+\frac{\cosh (a+b x)}{b}",1,"(Cosh[a]*Cosh[b*x])/b + (Cosh[a - c]*Sech[c + b*x])/b - (2*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[(b*x)/2]*Sinh[c] + Cosh[c]*Sinh[(b*x)/2]))/(Cosh[c]*Cosh[(b*x)/2] - Cosh[(b*x)/2]*Sinh[c])]*Sinh[a - c])/b + (Sinh[a]*Sinh[b*x])/b","B",1
145,1,70,72,0.3486966,"\int \sinh (a+b x) \tanh ^3(c+b x) \, dx","Integrate[Sinh[a + b*x]*Tanh[c + b*x]^3,x]","\frac{\text{sech}^2(b x+c) (2 \sinh (a-b x-2 c)+\sinh (a+3 b x+2 c)+5 \sinh (a+b x))-12 \cosh (a-c) \tan ^{-1}\left(\cosh (c) \tanh \left(\frac{b x}{2}\right)+\sinh (c)\right)}{4 b}","\frac{\sinh (a-c) \text{sech}(b x+c)}{b}-\frac{3 \cosh (a-c) \tan ^{-1}(\sinh (b x+c))}{2 b}+\frac{\cosh (a-c) \tanh (b x+c) \text{sech}(b x+c)}{2 b}+\frac{\sinh (a+b x)}{b}",1,"(-12*ArcTan[Sinh[c] + Cosh[c]*Tanh[(b*x)/2]]*Cosh[a - c] + Sech[c + b*x]^2*(2*Sinh[a - 2*c - b*x] + 5*Sinh[a + b*x] + Sinh[a + 2*c + 3*b*x]))/(4*b)","A",1
146,1,93,29,0.0591892,"\int \coth (c+b x) \sinh (a+b x) \, dx","Integrate[Coth[c + b*x]*Sinh[a + b*x],x]","-\frac{2 i \sinh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \sinh \left(\frac{b x}{2}\right)+\cosh (c) \cosh \left(\frac{b x}{2}\right)\right)}{i \cosh (c) \cosh \left(\frac{b x}{2}\right)-i \sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}+\frac{\sinh (a) \cosh (b x)}{b}+\frac{\cosh (a) \sinh (b x)}{b}","\frac{\sinh (a+b x)}{b}-\frac{\sinh (a-c) \tanh ^{-1}(\cosh (b x+c))}{b}",1,"(Cosh[b*x]*Sinh[a])/b - ((2*I)*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[c]*Cosh[(b*x)/2] + Sinh[c]*Sinh[(b*x)/2]))/(I*Cosh[c]*Cosh[(b*x)/2] - I*Cosh[(b*x)/2]*Sinh[c])]*Sinh[a - c])/b + (Cosh[a]*Sinh[b*x])/b","C",1
147,1,110,46,0.103371,"\int \coth ^2(c+b x) \sinh (a+b x) \, dx","Integrate[Coth[c + b*x]^2*Sinh[a + b*x],x]","-\frac{\sinh (a-c) \text{csch}(b x+c)}{b}-\frac{2 i \cosh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \sinh \left(\frac{b x}{2}\right)+\cosh (c) \cosh \left(\frac{b x}{2}\right)\right)}{i \cosh (c) \cosh \left(\frac{b x}{2}\right)-i \sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}+\frac{\sinh (a) \sinh (b x)}{b}+\frac{\cosh (a) \cosh (b x)}{b}","-\frac{\cosh (a-c) \tanh ^{-1}(\cosh (b x+c))}{b}-\frac{\sinh (a-c) \text{csch}(b x+c)}{b}+\frac{\cosh (a+b x)}{b}",1,"((-2*I)*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[c]*Cosh[(b*x)/2] + Sinh[c]*Sinh[(b*x)/2]))/(I*Cosh[c]*Cosh[(b*x)/2] - I*Cosh[(b*x)/2]*Sinh[c])]*Cosh[a - c])/b + (Cosh[a]*Cosh[b*x])/b - (Csch[c + b*x]*Sinh[a - c])/b + (Sinh[a]*Sinh[b*x])/b","C",1
148,1,70,73,0.3572476,"\int \coth ^3(c+b x) \sinh (a+b x) \, dx","Integrate[Coth[c + b*x]^3*Sinh[a + b*x],x]","\frac{\text{csch}^2(b x+c) (2 \sinh (a-b x-2 c)+\sinh (a+3 b x+2 c)-5 \sinh (a+b x))-12 \sinh (a-c) \tanh ^{-1}\left(\sinh (c) \tanh \left(\frac{b x}{2}\right)+\cosh (c)\right)}{4 b}","-\frac{\cosh (a-c) \text{csch}(b x+c)}{b}-\frac{3 \sinh (a-c) \tanh ^{-1}(\cosh (b x+c))}{2 b}-\frac{\sinh (a-c) \coth (b x+c) \text{csch}(b x+c)}{2 b}+\frac{\sinh (a+b x)}{b}",1,"(-12*ArcTanh[Cosh[c] + Sinh[c]*Tanh[(b*x)/2]]*Sinh[a - c] + Csch[c + b*x]^2*(2*Sinh[a - 2*c - b*x] - 5*Sinh[a + b*x] + Sinh[a + 2*c + 3*b*x]))/(4*b)","A",1
149,1,26,26,0.1259541,"\int \text{sech}(c+b x) \sinh (a+b x) \, dx","Integrate[Sech[c + b*x]*Sinh[a + b*x],x]","\frac{\cosh (a-c) \log (\cosh (b x+c))}{b}+x \sinh (a-c)","\frac{\cosh (a-c) \log (\cosh (b x+c))}{b}+x \sinh (a-c)",1,"(Cosh[a - c]*Log[Cosh[c + b*x]])/b + x*Sinh[a - c]","A",1
150,1,83,35,0.0903385,"\int \text{sech}^2(c+b x) \sinh (a+b x) \, dx","Integrate[Sech[c + b*x]^2*Sinh[a + b*x],x]","\frac{2 \sinh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \cosh \left(\frac{b x}{2}\right)+\cosh (c) \sinh \left(\frac{b x}{2}\right)\right)}{\cosh (c) \cosh \left(\frac{b x}{2}\right)-\sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}-\frac{\cosh (a-c) \text{sech}(b x+c)}{b}","\frac{\sinh (a-c) \tan ^{-1}(\sinh (b x+c))}{b}-\frac{\cosh (a-c) \text{sech}(b x+c)}{b}",1,"-((Cosh[a - c]*Sech[c + b*x])/b) + (2*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[(b*x)/2]*Sinh[c] + Cosh[c]*Sinh[(b*x)/2]))/(Cosh[c]*Cosh[(b*x)/2] - Cosh[(b*x)/2]*Sinh[c])]*Sinh[a - c])/b","B",1
151,1,35,38,0.171552,"\int \text{sech}^3(c+b x) \sinh (a+b x) \, dx","Integrate[Sech[c + b*x]^3*Sinh[a + b*x],x]","-\frac{\text{sech}(c) \text{sech}^2(b x+c) (\cosh (a)-\sinh (a-c) \sinh (2 b x+c))}{2 b}","\frac{\sinh (a-c) \tanh (b x+c)}{b}-\frac{\cosh (a-c) \text{sech}^2(b x+c)}{2 b}",1,"-1/2*(Sech[c]*Sech[c + b*x]^2*(Cosh[a] - Sinh[a - c]*Sinh[c + 2*b*x]))/b","A",1
152,1,26,26,0.1192474,"\int \text{csch}(c+b x) \sinh (a+b x) \, dx","Integrate[Csch[c + b*x]*Sinh[a + b*x],x]","\frac{\sinh (a-c) \log (\sinh (b x+c))}{b}+x \cosh (a-c)","\frac{\sinh (a-c) \log (\sinh (b x+c))}{b}+x \cosh (a-c)",1,"x*Cosh[a - c] + (Log[Sinh[c + b*x]]*Sinh[a - c])/b","A",1
153,1,90,36,0.0832363,"\int \text{csch}^2(c+b x) \sinh (a+b x) \, dx","Integrate[Csch[c + b*x]^2*Sinh[a + b*x],x]","-\frac{\sinh (a-c) \text{csch}(b x+c)}{b}-\frac{2 i \cosh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \sinh \left(\frac{b x}{2}\right)+\cosh (c) \cosh \left(\frac{b x}{2}\right)\right)}{i \cosh (c) \cosh \left(\frac{b x}{2}\right)-i \sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}","-\frac{\cosh (a-c) \tanh ^{-1}(\cosh (b x+c))}{b}-\frac{\sinh (a-c) \text{csch}(b x+c)}{b}",1,"((-2*I)*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[c]*Cosh[(b*x)/2] + Sinh[c]*Sinh[(b*x)/2]))/(I*Cosh[c]*Cosh[(b*x)/2] - I*Cosh[(b*x)/2]*Sinh[c])]*Cosh[a - c])/b - (Csch[c + b*x]*Sinh[a - c])/b","C",1
154,1,35,39,0.1846097,"\int \text{csch}^3(c+b x) \sinh (a+b x) \, dx","Integrate[Csch[c + b*x]^3*Sinh[a + b*x],x]","-\frac{\text{csch}(c) \text{csch}^2(b x+c) (\cosh (a)-\cosh (a-c) \cosh (2 b x+c))}{2 b}","-\frac{\cosh (a-c) \coth (b x+c)}{b}-\frac{\sinh (a-c) \text{csch}^2(b x+c)}{2 b}",1,"-1/2*((Cosh[a] - Cosh[a - c]*Cosh[c + 2*b*x])*Csch[c]*Csch[c + b*x]^2)/b","A",1
155,1,86,29,0.0566685,"\int \cosh (a+b x) \tanh (c+b x) \, dx","Integrate[Cosh[a + b*x]*Tanh[c + b*x],x]","-\frac{2 \sinh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \cosh \left(\frac{b x}{2}\right)+\cosh (c) \sinh \left(\frac{b x}{2}\right)\right)}{\cosh (c) \cosh \left(\frac{b x}{2}\right)-\sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}+\frac{\sinh (a) \sinh (b x)}{b}+\frac{\cosh (a) \cosh (b x)}{b}","\frac{\cosh (a+b x)}{b}-\frac{\sinh (a-c) \tan ^{-1}(\sinh (b x+c))}{b}",1,"(Cosh[a]*Cosh[b*x])/b - (2*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[(b*x)/2]*Sinh[c] + Cosh[c]*Sinh[(b*x)/2]))/(Cosh[c]*Cosh[(b*x)/2] - Cosh[(b*x)/2]*Sinh[c])]*Sinh[a - c])/b + (Sinh[a]*Sinh[b*x])/b","B",1
156,1,102,45,0.0985381,"\int \cosh (a+b x) \tanh ^2(c+b x) \, dx","Integrate[Cosh[a + b*x]*Tanh[c + b*x]^2,x]","\frac{\sinh (a-c) \text{sech}(b x+c)}{b}-\frac{2 \cosh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \cosh \left(\frac{b x}{2}\right)+\cosh (c) \sinh \left(\frac{b x}{2}\right)\right)}{\cosh (c) \cosh \left(\frac{b x}{2}\right)-\sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}+\frac{\sinh (a) \cosh (b x)}{b}+\frac{\cosh (a) \sinh (b x)}{b}","\frac{\sinh (a-c) \text{sech}(b x+c)}{b}-\frac{\cosh (a-c) \tan ^{-1}(\sinh (b x+c))}{b}+\frac{\sinh (a+b x)}{b}",1,"(-2*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[(b*x)/2]*Sinh[c] + Cosh[c]*Sinh[(b*x)/2]))/(Cosh[c]*Cosh[(b*x)/2] - Cosh[(b*x)/2]*Sinh[c])]*Cosh[a - c])/b + (Cosh[b*x]*Sinh[a])/b + (Sech[c + b*x]*Sinh[a - c])/b + (Cosh[a]*Sinh[b*x])/b","B",1
157,1,115,72,0.3197865,"\int \cosh (a+b x) \tanh ^3(c+b x) \, dx","Integrate[Cosh[a + b*x]*Tanh[c + b*x]^3,x]","\frac{\text{sech}(c) \text{sech}^2(b x+c) (-\cosh (a-b x-c))+\text{sech}(c) \text{sech}^2(b x+c) \cosh (a+b x-c)+\text{sech}(c) \cosh (a-2 c) \text{sech}(b x+c)+\cosh (a) (3 \text{sech}(c) \text{sech}(b x+c)+4 \cosh (b x))-12 \sinh (a-c) \tan ^{-1}\left(\cosh (c) \tanh \left(\frac{b x}{2}\right)+\sinh (c)\right)+4 \sinh (a) \sinh (b x)}{4 b}","-\frac{3 \sinh (a-c) \tan ^{-1}(\sinh (b x+c))}{2 b}+\frac{\cosh (a-c) \text{sech}(b x+c)}{b}+\frac{\sinh (a-c) \tanh (b x+c) \text{sech}(b x+c)}{2 b}+\frac{\cosh (a+b x)}{b}",1,"(Cosh[a - 2*c]*Sech[c]*Sech[c + b*x] - Cosh[a - c - b*x]*Sech[c]*Sech[c + b*x]^2 + Cosh[a - c + b*x]*Sech[c]*Sech[c + b*x]^2 + Cosh[a]*(4*Cosh[b*x] + 3*Sech[c]*Sech[c + b*x]) - 12*ArcTan[Sinh[c] + Cosh[c]*Tanh[(b*x)/2]]*Sinh[a - c] + 4*Sinh[a]*Sinh[b*x])/(4*b)","A",1
158,1,93,29,0.0573268,"\int \cosh (a+b x) \coth (c+b x) \, dx","Integrate[Cosh[a + b*x]*Coth[c + b*x],x]","-\frac{2 i \cosh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \sinh \left(\frac{b x}{2}\right)+\cosh (c) \cosh \left(\frac{b x}{2}\right)\right)}{i \cosh (c) \cosh \left(\frac{b x}{2}\right)-i \sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}+\frac{\sinh (a) \sinh (b x)}{b}+\frac{\cosh (a) \cosh (b x)}{b}","\frac{\cosh (a+b x)}{b}-\frac{\cosh (a-c) \tanh ^{-1}(\cosh (b x+c))}{b}",1,"((-2*I)*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[c]*Cosh[(b*x)/2] + Sinh[c]*Sinh[(b*x)/2]))/(I*Cosh[c]*Cosh[(b*x)/2] - I*Cosh[(b*x)/2]*Sinh[c])]*Cosh[a - c])/b + (Cosh[a]*Cosh[b*x])/b + (Sinh[a]*Sinh[b*x])/b","C",1
159,1,110,46,0.0982235,"\int \cosh (a+b x) \coth ^2(c+b x) \, dx","Integrate[Cosh[a + b*x]*Coth[c + b*x]^2,x]","-\frac{\cosh (a-c) \text{csch}(b x+c)}{b}-\frac{2 i \sinh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \sinh \left(\frac{b x}{2}\right)+\cosh (c) \cosh \left(\frac{b x}{2}\right)\right)}{i \cosh (c) \cosh \left(\frac{b x}{2}\right)-i \sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}+\frac{\sinh (a) \cosh (b x)}{b}+\frac{\cosh (a) \sinh (b x)}{b}","-\frac{\cosh (a-c) \text{csch}(b x+c)}{b}-\frac{\sinh (a-c) \tanh ^{-1}(\cosh (b x+c))}{b}+\frac{\sinh (a+b x)}{b}",1,"-((Cosh[a - c]*Csch[c + b*x])/b) + (Cosh[b*x]*Sinh[a])/b - ((2*I)*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[c]*Cosh[(b*x)/2] + Sinh[c]*Sinh[(b*x)/2]))/(I*Cosh[c]*Cosh[(b*x)/2] - I*Cosh[(b*x)/2]*Sinh[c])]*Sinh[a - c])/b + (Cosh[a]*Sinh[b*x])/b","C",1
160,1,70,73,0.3421916,"\int \cosh (a+b x) \coth ^3(c+b x) \, dx","Integrate[Cosh[a + b*x]*Coth[c + b*x]^3,x]","\frac{\text{csch}^2(b x+c) (2 \cosh (a-b x-2 c)+\cosh (a+3 b x+2 c)-5 \cosh (a+b x))-12 \cosh (a-c) \tanh ^{-1}\left(\sinh (c) \tanh \left(\frac{b x}{2}\right)+\cosh (c)\right)}{4 b}","-\frac{3 \cosh (a-c) \tanh ^{-1}(\cosh (b x+c))}{2 b}-\frac{\sinh (a-c) \text{csch}(b x+c)}{b}-\frac{\cosh (a-c) \coth (b x+c) \text{csch}(b x+c)}{2 b}+\frac{\cosh (a+b x)}{b}",1,"(-12*ArcTanh[Cosh[c] + Sinh[c]*Tanh[(b*x)/2]]*Cosh[a - c] + (2*Cosh[a - 2*c - b*x] - 5*Cosh[a + b*x] + Cosh[a + 2*c + 3*b*x])*Csch[c + b*x]^2)/(4*b)","A",1
161,1,26,26,0.1135417,"\int \cosh (a+b x) \text{sech}(c+b x) \, dx","Integrate[Cosh[a + b*x]*Sech[c + b*x],x]","\frac{\sinh (a-c) \log (\cosh (b x+c))}{b}+x \cosh (a-c)","\frac{\sinh (a-c) \log (\cosh (b x+c))}{b}+x \cosh (a-c)",1,"x*Cosh[a - c] + (Log[Cosh[c + b*x]]*Sinh[a - c])/b","A",1
162,1,83,35,0.0870064,"\int \cosh (a+b x) \text{sech}^2(c+b x) \, dx","Integrate[Cosh[a + b*x]*Sech[c + b*x]^2,x]","\frac{2 \cosh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \cosh \left(\frac{b x}{2}\right)+\cosh (c) \sinh \left(\frac{b x}{2}\right)\right)}{\cosh (c) \cosh \left(\frac{b x}{2}\right)-\sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}-\frac{\sinh (a-c) \text{sech}(b x+c)}{b}","\frac{\cosh (a-c) \tan ^{-1}(\sinh (b x+c))}{b}-\frac{\sinh (a-c) \text{sech}(b x+c)}{b}",1,"(2*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[(b*x)/2]*Sinh[c] + Cosh[c]*Sinh[(b*x)/2]))/(Cosh[c]*Cosh[(b*x)/2] - Cosh[(b*x)/2]*Sinh[c])]*Cosh[a - c])/b - (Sech[c + b*x]*Sinh[a - c])/b","B",1
163,1,35,38,0.1773027,"\int \cosh (a+b x) \text{sech}^3(c+b x) \, dx","Integrate[Cosh[a + b*x]*Sech[c + b*x]^3,x]","-\frac{\text{sech}(c) \text{sech}^2(b x+c) (\sinh (a)-\cosh (a-c) \sinh (2 b x+c))}{2 b}","\frac{\cosh (a-c) \tanh (b x+c)}{b}-\frac{\sinh (a-c) \text{sech}^2(b x+c)}{2 b}",1,"-1/2*(Sech[c]*Sech[c + b*x]^2*(Sinh[a] - Cosh[a - c]*Sinh[c + 2*b*x]))/b","A",1
164,1,26,26,0.1120964,"\int \cosh (a+b x) \text{csch}(c+b x) \, dx","Integrate[Cosh[a + b*x]*Csch[c + b*x],x]","\frac{\cosh (a-c) \log (\sinh (b x+c))}{b}+x \sinh (a-c)","\frac{\cosh (a-c) \log (\sinh (b x+c))}{b}+x \sinh (a-c)",1,"(Cosh[a - c]*Log[Sinh[c + b*x]])/b + x*Sinh[a - c]","A",1
165,1,90,36,0.0690376,"\int \cosh (a+b x) \text{csch}^2(c+b x) \, dx","Integrate[Cosh[a + b*x]*Csch[c + b*x]^2,x]","-\frac{\cosh (a-c) \text{csch}(b x+c)}{b}-\frac{2 i \sinh (a-c) \tan ^{-1}\left(\frac{(\cosh (c)-\sinh (c)) \left(\sinh (c) \sinh \left(\frac{b x}{2}\right)+\cosh (c) \cosh \left(\frac{b x}{2}\right)\right)}{i \cosh (c) \cosh \left(\frac{b x}{2}\right)-i \sinh (c) \cosh \left(\frac{b x}{2}\right)}\right)}{b}","-\frac{\cosh (a-c) \text{csch}(b x+c)}{b}-\frac{\sinh (a-c) \tanh ^{-1}(\cosh (b x+c))}{b}",1,"-((Cosh[a - c]*Csch[c + b*x])/b) - ((2*I)*ArcTan[((Cosh[c] - Sinh[c])*(Cosh[c]*Cosh[(b*x)/2] + Sinh[c]*Sinh[(b*x)/2]))/(I*Cosh[c]*Cosh[(b*x)/2] - I*Cosh[(b*x)/2]*Sinh[c])]*Sinh[a - c])/b","C",1
166,1,35,39,0.1789445,"\int \cosh (a+b x) \text{csch}^3(c+b x) \, dx","Integrate[Cosh[a + b*x]*Csch[c + b*x]^3,x]","-\frac{\text{csch}(c) \text{csch}^2(b x+c) (\sinh (a)-\sinh (a-c) \cosh (2 b x+c))}{2 b}","-\frac{\cosh (a-c) \text{csch}^2(b x+c)}{2 b}-\frac{\sinh (a-c) \coth (b x+c)}{b}",1,"-1/2*(Csch[c]*Csch[c + b*x]^2*(Sinh[a] - Cosh[c + 2*b*x]*Sinh[a - c]))/b","A",1
167,1,43,43,0.2254462,"\int \sinh (a+b x) \sinh (c+d x) \, dx","Integrate[Sinh[a + b*x]*Sinh[c + d*x],x]","\frac{\sinh (a+x (b+d)+c)}{2 (b+d)}-\frac{\sinh (a+x (b-d)-c)}{2 (b-d)}","\frac{\sinh (a+x (b+d)+c)}{2 (b+d)}-\frac{\sinh (a+x (b-d)-c)}{2 (b-d)}",1,"-1/2*Sinh[a - c + (b - d)*x]/(b - d) + Sinh[a + c + (b + d)*x]/(2*(b + d))","A",1
168,1,69,62,0.7958461,"\int \sinh (a+b x) \sinh ^2(c+d x) \, dx","Integrate[Sinh[a + b*x]*Sinh[c + d*x]^2,x]","\frac{1}{4} \left(\frac{\cosh (a+b x-2 c-2 d x)}{b-2 d}+\frac{\cosh (a+b x+2 c+2 d x)}{b+2 d}-\frac{2 \sinh (a) \sinh (b x)}{b}-\frac{2 \cosh (a) \cosh (b x)}{b}\right)","\frac{\cosh (a+x (b-2 d)-2 c)}{4 (b-2 d)}+\frac{\cosh (a+x (b+2 d)+2 c)}{4 (b+2 d)}-\frac{\cosh (a+b x)}{2 b}",1,"((-2*Cosh[a]*Cosh[b*x])/b + Cosh[a - 2*c + b*x - 2*d*x]/(b - 2*d) + Cosh[a + 2*c + b*x + 2*d*x]/(b + 2*d) - (2*Sinh[a]*Sinh[b*x])/b)/4","A",1
169,1,86,91,0.4846971,"\int \sinh (a+b x) \sinh ^3(c+d x) \, dx","Integrate[Sinh[a + b*x]*Sinh[c + d*x]^3,x]","\frac{1}{8} \left(-\frac{\sinh (a+b x-3 c-3 d x)}{b-3 d}+\frac{3 \sinh (a+b x-c-d x)}{b-d}+\frac{\sinh (a+b x+3 c+3 d x)}{b+3 d}-\frac{3 \sinh (a+x (b+d)+c)}{b+d}\right)","-\frac{\sinh (a+x (b-3 d)-3 c)}{8 (b-3 d)}+\frac{3 \sinh (a+x (b-d)-c)}{8 (b-d)}-\frac{3 \sinh (a+x (b+d)+c)}{8 (b+d)}+\frac{\sinh (a+x (b+3 d)+3 c)}{8 (b+3 d)}",1,"(-(Sinh[a - 3*c + b*x - 3*d*x]/(b - 3*d)) + (3*Sinh[a - c + b*x - d*x])/(b - d) + Sinh[a + 3*c + b*x + 3*d*x]/(b + 3*d) - (3*Sinh[a + c + (b + d)*x])/(b + d))/8","A",1
170,1,106,88,0.7384264,"\int \sinh ^2(a+b x) \sinh ^2(c+d x) \, dx","Integrate[Sinh[a + b*x]^2*Sinh[c + d*x]^2,x]","\frac{\left(2 d^3-2 b^2 d\right) \sinh (2 (a+b x))+b d (b+d) \sinh (2 (a+x (b-d)-c))+b (b-d) (d (\sinh (2 (a+x (b+d)+c))+4 x (b+d))-2 (b+d) \sinh (2 (c+d x)))}{16 b d (b-d) (b+d)}","\frac{\sinh (2 (a-c)+2 x (b-d))}{16 (b-d)}+\frac{\sinh (2 (a+c)+2 x (b+d))}{16 (b+d)}-\frac{\sinh (2 a+2 b x)}{8 b}-\frac{\sinh (2 c+2 d x)}{8 d}+\frac{x}{4}",1,"((-2*b^2*d + 2*d^3)*Sinh[2*(a + b*x)] + b*d*(b + d)*Sinh[2*(a - c + (b - d)*x)] + b*(b - d)*(-2*(b + d)*Sinh[2*(c + d*x)] + d*(4*(b + d)*x + Sinh[2*(a + c + (b + d)*x)])))/(16*b*(b - d)*d*(b + d))","A",1
171,1,158,144,1.6030629,"\int \sinh ^2(a+b x) \sinh ^3(c+d x) \, dx","Integrate[Sinh[a + b*x]^2*Sinh[c + d*x]^3,x]","\frac{1}{48} \left(-\frac{3 \cosh (2 a+2 b x-3 c-3 d x)}{2 b-3 d}+\frac{9 \cosh (2 a+2 b x-c-d x)}{2 b-d}-\frac{9 \cosh (2 a+2 b x+c+d x)}{2 b+d}+\frac{3 \cosh (2 a+2 b x+3 c+3 d x)}{2 b+3 d}+\frac{18 \sinh (c) \sinh (d x)}{d}-\frac{2 \sinh (3 c) \sinh (3 d x)}{d}+\frac{18 \cosh (c) \cosh (d x)}{d}-\frac{2 \cosh (3 c) \cosh (3 d x)}{d}\right)","-\frac{\cosh (2 a+x (2 b-3 d)-3 c)}{16 (2 b-3 d)}+\frac{3 \cosh (2 a+x (2 b-d)-c)}{16 (2 b-d)}-\frac{3 \cosh (2 a+x (2 b+d)+c)}{16 (2 b+d)}+\frac{\cosh (2 a+x (2 b+3 d)+3 c)}{16 (2 b+3 d)}+\frac{3 \cosh (c+d x)}{8 d}-\frac{\cosh (3 c+3 d x)}{24 d}",1,"((18*Cosh[c]*Cosh[d*x])/d - (2*Cosh[3*c]*Cosh[3*d*x])/d - (3*Cosh[2*a - 3*c + 2*b*x - 3*d*x])/(2*b - 3*d) + (9*Cosh[2*a - c + 2*b*x - d*x])/(2*b - d) - (9*Cosh[2*a + c + 2*b*x + d*x])/(2*b + d) + (3*Cosh[2*a + 3*c + 2*b*x + 3*d*x])/(2*b + 3*d) + (18*Sinh[c]*Sinh[d*x])/d - (2*Sinh[3*c]*Sinh[3*d*x])/d)/48","A",1
172,1,177,195,1.5898118,"\int \sinh ^3(a+b x) \sinh ^3(c+d x) \, dx","Integrate[Sinh[a + b*x]^3*Sinh[c + d*x]^3,x]","\frac{1}{96} \left(\frac{9 \sinh (a+b x-3 c-3 d x)}{b-3 d}-\frac{27 \sinh (a+b x-c-d x)}{b-d}-\frac{\sinh (3 (a+b x-c-d x))}{b-d}+\frac{9 \sinh (3 a+3 b x-c-d x)}{3 b-d}-\frac{9 \sinh (3 a+3 b x+c+d x)}{3 b+d}-\frac{9 \sinh (a+b x+3 c+3 d x)}{b+3 d}+\frac{27 \sinh (a+x (b+d)+c)}{b+d}+\frac{\sinh (3 (a+x (b+d)+c))}{b+d}\right)","\frac{3 \sinh (a+x (b-3 d)-3 c)}{32 (b-3 d)}-\frac{9 \sinh (a+x (b-d)-c)}{32 (b-d)}-\frac{\sinh (3 (a-c)+3 x (b-d))}{96 (b-d)}+\frac{3 \sinh (3 a+x (3 b-d)-c)}{32 (3 b-d)}+\frac{9 \sinh (a+x (b+d)+c)}{32 (b+d)}+\frac{\sinh (3 (a+c)+3 x (b+d))}{96 (b+d)}-\frac{3 \sinh (3 a+x (3 b+d)+c)}{32 (3 b+d)}-\frac{3 \sinh (a+x (b+3 d)+3 c)}{32 (b+3 d)}",1,"((9*Sinh[a - 3*c + b*x - 3*d*x])/(b - 3*d) - (27*Sinh[a - c + b*x - d*x])/(b - d) - Sinh[3*(a - c + b*x - d*x)]/(b - d) + (9*Sinh[3*a - c + 3*b*x - d*x])/(3*b - d) - (9*Sinh[3*a + c + 3*b*x + d*x])/(3*b + d) - (9*Sinh[a + 3*c + b*x + 3*d*x])/(b + 3*d) + (27*Sinh[a + c + (b + d)*x])/(b + d) + Sinh[3*(a + c + (b + d)*x)]/(b + d))/96","A",1
173,1,43,43,0.1839655,"\int \cosh (a+b x) \cosh (c+d x) \, dx","Integrate[Cosh[a + b*x]*Cosh[c + d*x],x]","\frac{\sinh (a+x (b-d)-c)}{2 (b-d)}+\frac{\sinh (a+x (b+d)+c)}{2 (b+d)}","\frac{\sinh (a+x (b-d)-c)}{2 (b-d)}+\frac{\sinh (a+x (b+d)+c)}{2 (b+d)}",1,"Sinh[a - c + (b - d)*x]/(2*(b - d)) + Sinh[a + c + (b + d)*x]/(2*(b + d))","A",1
174,1,69,62,0.7201653,"\int \cosh (a+b x) \cosh ^2(c+d x) \, dx","Integrate[Cosh[a + b*x]*Cosh[c + d*x]^2,x]","\frac{1}{4} \left(\frac{\sinh (a+b x-2 c-2 d x)}{b-2 d}+\frac{\sinh (a+b x+2 c+2 d x)}{b+2 d}+\frac{2 \sinh (a) \cosh (b x)}{b}+\frac{2 \cosh (a) \sinh (b x)}{b}\right)","\frac{\sinh (a+x (b-2 d)-2 c)}{4 (b-2 d)}+\frac{\sinh (a+x (b+2 d)+2 c)}{4 (b+2 d)}+\frac{\sinh (a+b x)}{2 b}",1,"((2*Cosh[b*x]*Sinh[a])/b + (2*Cosh[a]*Sinh[b*x])/b + Sinh[a - 2*c + b*x - 2*d*x]/(b - 2*d) + Sinh[a + 2*c + b*x + 2*d*x]/(b + 2*d))/4","A",1
175,1,85,91,0.4566945,"\int \cosh (a+b x) \cosh ^3(c+d x) \, dx","Integrate[Cosh[a + b*x]*Cosh[c + d*x]^3,x]","\frac{1}{8} \left(\frac{\sinh (a+b x-3 c-3 d x)}{b-3 d}+\frac{3 \sinh (a+b x-c-d x)}{b-d}+\frac{\sinh (a+b x+3 c+3 d x)}{b+3 d}+\frac{3 \sinh (a+x (b+d)+c)}{b+d}\right)","\frac{\sinh (a+x (b-3 d)-3 c)}{8 (b-3 d)}+\frac{3 \sinh (a+x (b-d)-c)}{8 (b-d)}+\frac{3 \sinh (a+x (b+d)+c)}{8 (b+d)}+\frac{\sinh (a+x (b+3 d)+3 c)}{8 (b+3 d)}",1,"(Sinh[a - 3*c + b*x - 3*d*x]/(b - 3*d) + (3*Sinh[a - c + b*x - d*x])/(b - d) + Sinh[a + 3*c + b*x + 3*d*x]/(b + 3*d) + (3*Sinh[a + c + (b + d)*x])/(b + d))/8","A",1
176,1,105,88,0.7048164,"\int \cosh ^2(a+b x) \cosh ^2(c+d x) \, dx","Integrate[Cosh[a + b*x]^2*Cosh[c + d*x]^2,x]","\frac{2 d \left(b^2-d^2\right) \sinh (2 (a+b x))+b d (b+d) \sinh (2 (a+x (b-d)-c))+b (b-d) (d (\sinh (2 (a+x (b+d)+c))+4 x (b+d))+2 (b+d) \sinh (2 (c+d x)))}{16 b d (b-d) (b+d)}","\frac{\sinh (2 (a-c)+2 x (b-d))}{16 (b-d)}+\frac{\sinh (2 (a+c)+2 x (b+d))}{16 (b+d)}+\frac{\sinh (2 a+2 b x)}{8 b}+\frac{\sinh (2 c+2 d x)}{8 d}+\frac{x}{4}",1,"(2*d*(b^2 - d^2)*Sinh[2*(a + b*x)] + b*d*(b + d)*Sinh[2*(a - c + (b - d)*x)] + b*(b - d)*(2*(b + d)*Sinh[2*(c + d*x)] + d*(4*(b + d)*x + Sinh[2*(a + c + (b + d)*x)])))/(16*b*(b - d)*d*(b + d))","A",1
177,1,158,144,1.6004262,"\int \cosh ^2(a+b x) \cosh ^3(c+d x) \, dx","Integrate[Cosh[a + b*x]^2*Cosh[c + d*x]^3,x]","\frac{1}{48} \left(\frac{3 \sinh (2 a+2 b x-3 c-3 d x)}{2 b-3 d}+\frac{9 \sinh (2 a+2 b x-c-d x)}{2 b-d}+\frac{9 \sinh (2 a+2 b x+c+d x)}{2 b+d}+\frac{3 \sinh (2 a+2 b x+3 c+3 d x)}{2 b+3 d}+\frac{18 \sinh (c) \cosh (d x)}{d}+\frac{2 \sinh (3 c) \cosh (3 d x)}{d}+\frac{18 \cosh (c) \sinh (d x)}{d}+\frac{2 \cosh (3 c) \sinh (3 d x)}{d}\right)","\frac{\sinh (2 a+x (2 b-3 d)-3 c)}{16 (2 b-3 d)}+\frac{3 \sinh (2 a+x (2 b-d)-c)}{16 (2 b-d)}+\frac{3 \sinh (2 a+x (2 b+d)+c)}{16 (2 b+d)}+\frac{\sinh (2 a+x (2 b+3 d)+3 c)}{16 (2 b+3 d)}+\frac{3 \sinh (c+d x)}{8 d}+\frac{\sinh (3 c+3 d x)}{24 d}",1,"((18*Cosh[d*x]*Sinh[c])/d + (2*Cosh[3*d*x]*Sinh[3*c])/d + (18*Cosh[c]*Sinh[d*x])/d + (2*Cosh[3*c]*Sinh[3*d*x])/d + (3*Sinh[2*a - 3*c + 2*b*x - 3*d*x])/(2*b - 3*d) + (9*Sinh[2*a - c + 2*b*x - d*x])/(2*b - d) + (9*Sinh[2*a + c + 2*b*x + d*x])/(2*b + d) + (3*Sinh[2*a + 3*c + 2*b*x + 3*d*x])/(2*b + 3*d))/48","A",1
178,1,176,195,1.5015959,"\int \cosh ^3(a+b x) \cosh ^3(c+d x) \, dx","Integrate[Cosh[a + b*x]^3*Cosh[c + d*x]^3,x]","\frac{1}{96} \left(\frac{9 \sinh (a+b x-3 c-3 d x)}{b-3 d}+\frac{27 \sinh (a+b x-c-d x)}{b-d}+\frac{\sinh (3 (a+b x-c-d x))}{b-d}+\frac{9 \sinh (3 a+3 b x-c-d x)}{3 b-d}+\frac{9 \sinh (3 a+3 b x+c+d x)}{3 b+d}+\frac{9 \sinh (a+b x+3 c+3 d x)}{b+3 d}+\frac{27 \sinh (a+x (b+d)+c)}{b+d}+\frac{\sinh (3 (a+x (b+d)+c))}{b+d}\right)","\frac{3 \sinh (a+x (b-3 d)-3 c)}{32 (b-3 d)}+\frac{9 \sinh (a+x (b-d)-c)}{32 (b-d)}+\frac{\sinh (3 (a-c)+3 x (b-d))}{96 (b-d)}+\frac{3 \sinh (3 a+x (3 b-d)-c)}{32 (3 b-d)}+\frac{9 \sinh (a+x (b+d)+c)}{32 (b+d)}+\frac{\sinh (3 (a+c)+3 x (b+d))}{96 (b+d)}+\frac{3 \sinh (3 a+x (3 b+d)+c)}{32 (3 b+d)}+\frac{3 \sinh (a+x (b+3 d)+3 c)}{32 (b+3 d)}",1,"((9*Sinh[a - 3*c + b*x - 3*d*x])/(b - 3*d) + (27*Sinh[a - c + b*x - d*x])/(b - d) + Sinh[3*(a - c + b*x - d*x)]/(b - d) + (9*Sinh[3*a - c + 3*b*x - d*x])/(3*b - d) + (9*Sinh[3*a + c + 3*b*x + d*x])/(3*b + d) + (9*Sinh[a + 3*c + b*x + 3*d*x])/(b + 3*d) + (27*Sinh[a + c + (b + d)*x])/(b + d) + Sinh[3*(a + c + (b + d)*x)]/(b + d))/96","A",1
179,1,43,43,0.2051685,"\int \cosh (c+d x) \sinh (a+b x) \, dx","Integrate[Cosh[c + d*x]*Sinh[a + b*x],x]","\frac{\cosh (a+x (b-d)-c)}{2 (b-d)}+\frac{\cosh (a+x (b+d)+c)}{2 (b+d)}","\frac{\cosh (a+x (b-d)-c)}{2 (b-d)}+\frac{\cosh (a+x (b+d)+c)}{2 (b+d)}",1,"Cosh[a - c + (b - d)*x]/(2*(b - d)) + Cosh[a + c + (b + d)*x]/(2*(b + d))","A",1
180,1,69,62,0.7099758,"\int \cosh ^2(c+d x) \sinh (a+b x) \, dx","Integrate[Cosh[c + d*x]^2*Sinh[a + b*x],x]","\frac{1}{4} \left(\frac{\cosh (a+b x-2 c-2 d x)}{b-2 d}+\frac{\cosh (a+b x+2 c+2 d x)}{b+2 d}+\frac{2 \sinh (a) \sinh (b x)}{b}+\frac{2 \cosh (a) \cosh (b x)}{b}\right)","\frac{\cosh (a+x (b-2 d)-2 c)}{4 (b-2 d)}+\frac{\cosh (a+x (b+2 d)+2 c)}{4 (b+2 d)}+\frac{\cosh (a+b x)}{2 b}",1,"((2*Cosh[a]*Cosh[b*x])/b + Cosh[a - 2*c + b*x - 2*d*x]/(b - 2*d) + Cosh[a + 2*c + b*x + 2*d*x]/(b + 2*d) + (2*Sinh[a]*Sinh[b*x])/b)/4","A",1
181,1,85,91,0.4617552,"\int \cosh ^3(c+d x) \sinh (a+b x) \, dx","Integrate[Cosh[c + d*x]^3*Sinh[a + b*x],x]","\frac{1}{8} \left(\frac{\cosh (a+b x-3 c-3 d x)}{b-3 d}+\frac{3 \cosh (a+b x-c-d x)}{b-d}+\frac{\cosh (a+b x+3 c+3 d x)}{b+3 d}+\frac{3 \cosh (a+x (b+d)+c)}{b+d}\right)","\frac{\cosh (a+x (b-3 d)-3 c)}{8 (b-3 d)}+\frac{3 \cosh (a+x (b-d)-c)}{8 (b-d)}+\frac{3 \cosh (a+x (b+d)+c)}{8 (b+d)}+\frac{\cosh (a+x (b+3 d)+3 c)}{8 (b+3 d)}",1,"(Cosh[a - 3*c + b*x - 3*d*x]/(b - 3*d) + (3*Cosh[a - c + b*x - d*x])/(b - d) + Cosh[a + 3*c + b*x + 3*d*x]/(b + 3*d) + (3*Cosh[a + c + (b + d)*x])/(b + d))/8","A",1
182,1,74,68,0.7341657,"\int \cosh (c+d x) \sinh ^2(a+b x) \, dx","Integrate[Cosh[c + d*x]*Sinh[a + b*x]^2,x]","\frac{1}{4} \left(\frac{\sinh (2 a+2 b x-c-d x)}{2 b-d}+\frac{\sinh (2 a+2 b x+c+d x)}{2 b+d}-\frac{2 \sinh (c) \cosh (d x)}{d}-\frac{2 \cosh (c) \sinh (d x)}{d}\right)","\frac{\sinh (2 a+x (2 b-d)-c)}{4 (2 b-d)}+\frac{\sinh (2 a+x (2 b+d)+c)}{4 (2 b+d)}-\frac{\sinh (c+d x)}{2 d}",1,"((-2*Cosh[d*x]*Sinh[c])/d - (2*Cosh[c]*Sinh[d*x])/d + Sinh[2*a - c + 2*b*x - d*x]/(2*b - d) + Sinh[2*a + c + 2*b*x + d*x]/(2*b + d))/4","A",1
183,1,107,88,0.7223454,"\int \cosh ^2(c+d x) \sinh ^2(a+b x) \, dx","Integrate[Cosh[c + d*x]^2*Sinh[a + b*x]^2,x]","\frac{2 d \left(b^2-d^2\right) \sinh (2 (a+b x))+b d (b+d) \sinh (2 (a+x (b-d)-c))-b (b-d) (-d \sinh (2 (a+x (b+d)+c))+2 (b+d) \sinh (2 (c+d x))+4 d x (b+d))}{16 b d (b-d) (b+d)}","\frac{\sinh (2 (a-c)+2 x (b-d))}{16 (b-d)}+\frac{\sinh (2 (a+c)+2 x (b+d))}{16 (b+d)}+\frac{\sinh (2 a+2 b x)}{8 b}-\frac{\sinh (2 c+2 d x)}{8 d}-\frac{x}{4}",1,"(2*d*(b^2 - d^2)*Sinh[2*(a + b*x)] + b*d*(b + d)*Sinh[2*(a - c + (b - d)*x)] - b*(b - d)*(4*d*(b + d)*x + 2*(b + d)*Sinh[2*(c + d*x)] - d*Sinh[2*(a + c + (b + d)*x)]))/(16*b*(b - d)*d*(b + d))","A",1
184,1,158,144,1.5262654,"\int \cosh ^3(c+d x) \sinh ^2(a+b x) \, dx","Integrate[Cosh[c + d*x]^3*Sinh[a + b*x]^2,x]","\frac{1}{48} \left(\frac{3 \sinh (2 a+2 b x-3 c-3 d x)}{2 b-3 d}+\frac{9 \sinh (2 a+2 b x-c-d x)}{2 b-d}+\frac{9 \sinh (2 a+2 b x+c+d x)}{2 b+d}+\frac{3 \sinh (2 a+2 b x+3 c+3 d x)}{2 b+3 d}-\frac{18 \sinh (c) \cosh (d x)}{d}-\frac{2 \sinh (3 c) \cosh (3 d x)}{d}-\frac{18 \cosh (c) \sinh (d x)}{d}-\frac{2 \cosh (3 c) \sinh (3 d x)}{d}\right)","\frac{\sinh (2 a+x (2 b-3 d)-3 c)}{16 (2 b-3 d)}+\frac{3 \sinh (2 a+x (2 b-d)-c)}{16 (2 b-d)}+\frac{3 \sinh (2 a+x (2 b+d)+c)}{16 (2 b+d)}+\frac{\sinh (2 a+x (2 b+3 d)+3 c)}{16 (2 b+3 d)}-\frac{3 \sinh (c+d x)}{8 d}-\frac{\sinh (3 c+3 d x)}{24 d}",1,"((-18*Cosh[d*x]*Sinh[c])/d - (2*Cosh[3*d*x]*Sinh[3*c])/d - (18*Cosh[c]*Sinh[d*x])/d - (2*Cosh[3*c]*Sinh[3*d*x])/d + (3*Sinh[2*a - 3*c + 2*b*x - 3*d*x])/(2*b - 3*d) + (9*Sinh[2*a - c + 2*b*x - d*x])/(2*b - d) + (9*Sinh[2*a + c + 2*b*x + d*x])/(2*b + d) + (3*Sinh[2*a + 3*c + 2*b*x + 3*d*x])/(2*b + 3*d))/48","A",1
185,1,90,97,0.5150779,"\int \cosh (c+d x) \sinh ^3(a+b x) \, dx","Integrate[Cosh[c + d*x]*Sinh[a + b*x]^3,x]","\frac{1}{8} \left(-\frac{3 \cosh (a+b x-c-d x)}{b-d}+\frac{\cosh (3 a+3 b x-c-d x)}{3 b-d}+\frac{\cosh (3 a+3 b x+c+d x)}{3 b+d}-\frac{3 \cosh (a+x (b+d)+c)}{b+d}\right)","-\frac{3 \cosh (a+x (b-d)-c)}{8 (b-d)}+\frac{\cosh (3 a+x (3 b-d)-c)}{8 (3 b-d)}-\frac{3 \cosh (a+x (b+d)+c)}{8 (b+d)}+\frac{\cosh (3 a+x (3 b+d)+c)}{8 (3 b+d)}",1,"((-3*Cosh[a - c + b*x - d*x])/(b - d) + Cosh[3*a - c + 3*b*x - d*x]/(3*b - d) + Cosh[3*a + c + 3*b*x + d*x]/(3*b + d) - (3*Cosh[a + c + (b + d)*x])/(b + d))/8","A",1
186,1,153,138,1.635837,"\int \cosh ^2(c+d x) \sinh ^3(a+b x) \, dx","Integrate[Cosh[c + d*x]^2*Sinh[a + b*x]^3,x]","\frac{1}{48} \left(-\frac{9 \cosh (a+b x-2 c-2 d x)}{b-2 d}+\frac{3 \cosh (3 a+3 b x-2 c-2 d x)}{3 b-2 d}-\frac{9 \cosh (a+b x+2 c+2 d x)}{b+2 d}+\frac{3 \cosh (3 a+3 b x+2 c+2 d x)}{3 b+2 d}-\frac{18 \sinh (a) \sinh (b x)}{b}+\frac{2 \sinh (3 a) \sinh (3 b x)}{b}-\frac{18 \cosh (a) \cosh (b x)}{b}+\frac{2 \cosh (3 a) \cosh (3 b x)}{b}\right)","-\frac{3 \cosh (a+x (b-2 d)-2 c)}{16 (b-2 d)}+\frac{\cosh (3 a+x (3 b-2 d)-2 c)}{16 (3 b-2 d)}-\frac{3 \cosh (a+x (b+2 d)+2 c)}{16 (b+2 d)}+\frac{\cosh (3 a+x (3 b+2 d)+2 c)}{16 (3 b+2 d)}-\frac{3 \cosh (a+b x)}{8 b}+\frac{\cosh (3 a+3 b x)}{24 b}",1,"((-18*Cosh[a]*Cosh[b*x])/b + (2*Cosh[3*a]*Cosh[3*b*x])/b - (9*Cosh[a - 2*c + b*x - 2*d*x])/(b - 2*d) + (3*Cosh[3*a - 2*c + 3*b*x - 2*d*x])/(3*b - 2*d) - (9*Cosh[a + 2*c + b*x + 2*d*x])/(b + 2*d) + (3*Cosh[3*a + 2*c + 3*b*x + 2*d*x])/(3*b + 2*d) - (18*Sinh[a]*Sinh[b*x])/b + (2*Sinh[3*a]*Sinh[3*b*x])/b)/48","A",1
187,1,176,195,1.687988,"\int \cosh ^3(c+d x) \sinh ^3(a+b x) \, dx","Integrate[Cosh[c + d*x]^3*Sinh[a + b*x]^3,x]","\frac{1}{96} \left(-\frac{9 \cosh (a+b x-3 c-3 d x)}{b-3 d}-\frac{27 \cosh (a+b x-c-d x)}{b-d}+\frac{\cosh (3 (a+b x-c-d x))}{b-d}+\frac{9 \cosh (3 a+3 b x-c-d x)}{3 b-d}+\frac{9 \cosh (3 a+3 b x+c+d x)}{3 b+d}-\frac{9 \cosh (a+b x+3 c+3 d x)}{b+3 d}-\frac{27 \cosh (a+x (b+d)+c)}{b+d}+\frac{\cosh (3 (a+x (b+d)+c))}{b+d}\right)","-\frac{3 \cosh (a+x (b-3 d)-3 c)}{32 (b-3 d)}-\frac{9 \cosh (a+x (b-d)-c)}{32 (b-d)}+\frac{\cosh (3 (a-c)+3 x (b-d))}{96 (b-d)}+\frac{3 \cosh (3 a+x (3 b-d)-c)}{32 (3 b-d)}-\frac{9 \cosh (a+x (b+d)+c)}{32 (b+d)}+\frac{\cosh (3 (a+c)+3 x (b+d))}{96 (b+d)}+\frac{3 \cosh (3 a+x (3 b+d)+c)}{32 (3 b+d)}-\frac{3 \cosh (a+x (b+3 d)+3 c)}{32 (b+3 d)}",1,"((-9*Cosh[a - 3*c + b*x - 3*d*x])/(b - 3*d) - (27*Cosh[a - c + b*x - d*x])/(b - d) + Cosh[3*(a - c + b*x - d*x)]/(b - d) + (9*Cosh[3*a - c + 3*b*x - d*x])/(3*b - d) + (9*Cosh[3*a + c + 3*b*x + d*x])/(3*b + d) - (9*Cosh[a + 3*c + b*x + 3*d*x])/(b + 3*d) - (27*Cosh[a + c + (b + d)*x])/(b + d) + Cosh[3*(a + c + (b + d)*x)]/(b + d))/96","A",1
188,1,278,121,14.6989213,"\int \sinh (a+b x) \tanh (c+d x) \, dx","Integrate[Sinh[a + b*x]*Tanh[c + d*x],x]","\frac{e^{-a-b x-c} \left((b-2 d) \left(2 b \text{sech}(c) e^{2 (a+x (b+d)+c)} \, _2F_1\left(1,\frac{b}{2 d}+1;\frac{b}{2 d}+2;-e^{2 (c+d x)}\right)-(b+2 d) \left(\left(e^{2 a}+2 e^{2 c}+1\right) \text{sech}(c) \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};-e^{2 (c+d x)}\right)+2 \text{sech}(c) e^{2 (a+b x+c)} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;-e^{2 (c+d x)}\right)-4 \tanh (c) e^{a+b x+c} \cosh (a+b x)-e^{2 a} \text{sech}(c)-\text{sech}(c)\right)\right)-\left(e^{2 a}-1\right) b (b+2 d) \text{sech}(c) e^{2 (c+d x)} \, _2F_1\left(1,1-\frac{b}{2 d};2-\frac{b}{2 d};-e^{2 (c+d x)}\right)\right)}{4 \left(b^3-4 b d^2\right)}","-\frac{e^{-a-b x} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};-e^{2 (c+d x)}\right)}{b}-\frac{e^{a+b x} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;-e^{2 (c+d x)}\right)}{b}+\frac{e^{-a-b x}}{2 b}+\frac{e^{a+b x}}{2 b}",1,"(E^(-a - c - b*x)*(-(b*(b + 2*d)*E^(2*(c + d*x))*(-1 + E^(2*a))*Hypergeometric2F1[1, 1 - b/(2*d), 2 - b/(2*d), -E^(2*(c + d*x))]*Sech[c]) + (b - 2*d)*(2*b*E^(2*(a + c + (b + d)*x))*Hypergeometric2F1[1, 1 + b/(2*d), 2 + b/(2*d), -E^(2*(c + d*x))]*Sech[c] - (b + 2*d)*(-Sech[c] - E^(2*a)*Sech[c] + (1 + E^(2*a) + 2*E^(2*c))*Hypergeometric2F1[1, -1/2*b/d, 1 - b/(2*d), -E^(2*(c + d*x))]*Sech[c] + 2*E^(2*(a + c + b*x))*Hypergeometric2F1[1, b/(2*d), 1 + b/(2*d), -E^(2*(c + d*x))]*Sech[c] - 4*E^(a + c + b*x)*Cosh[a + b*x]*Tanh[c]))))/(4*(b^3 - 4*b*d^2))","B",1
189,1,240,117,6.9187832,"\int \coth (c+d x) \sinh (a+b x) \, dx","Integrate[Coth[c + d*x]*Sinh[a + b*x],x]","\frac{e^{-a-b x+2 c} \left(b e^{2 d x} \, _2F_1\left(1,1-\frac{b}{2 d};2-\frac{b}{2 d};e^{2 (c+d x)}\right)-(b-2 d) \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};e^{2 (c+d x)}\right)\right)}{b \left(e^{2 c}-1\right) (b-2 d)}-\frac{e^{a+2 c} \left(\frac{e^{b x} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;e^{2 (c+d x)}\right)}{b}-\frac{e^{x (b+2 d)} \, _2F_1\left(1,\frac{b}{2 d}+1;\frac{b}{2 d}+2;e^{2 (c+d x)}\right)}{b+2 d}\right)}{e^{2 c}-1}+\frac{\cosh (a) \coth (c) \cosh (b x)}{b}+\frac{\sinh (a) \coth (c) \sinh (b x)}{b}","-\frac{e^{-a-b x} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};e^{2 (c+d x)}\right)}{b}-\frac{e^{a+b x} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;e^{2 (c+d x)}\right)}{b}+\frac{e^{-a-b x}}{2 b}+\frac{e^{a+b x}}{2 b}",1,"(Cosh[a]*Cosh[b*x]*Coth[c])/b + (E^(-a + 2*c - b*x)*(b*E^(2*d*x)*Hypergeometric2F1[1, 1 - b/(2*d), 2 - b/(2*d), E^(2*(c + d*x))] - (b - 2*d)*Hypergeometric2F1[1, -1/2*b/d, 1 - b/(2*d), E^(2*(c + d*x))]))/(b*(b - 2*d)*(-1 + E^(2*c))) - (E^(a + 2*c)*(-((E^((b + 2*d)*x)*Hypergeometric2F1[1, 1 + b/(2*d), 2 + b/(2*d), E^(2*(c + d*x))])/(b + 2*d)) + (E^(b*x)*Hypergeometric2F1[1, b/(2*d), 1 + b/(2*d), E^(2*(c + d*x))])/b))/(-1 + E^(2*c)) + (Coth[c]*Sinh[a]*Sinh[b*x])/b","B",1
190,1,99,116,9.5646352,"\int \cosh (a+b x) \coth (c+d x) \, dx","Integrate[Cosh[a + b*x]*Coth[c + d*x],x]","\frac{e^{-a-b x} \left(-2 e^{2 (a+b x)} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;e^{2 (c+d x)}\right)+e^{2 (a+b x)}+2 \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};e^{2 (c+d x)}\right)-1\right)}{2 b}","\frac{e^{-a-b x} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};e^{2 (c+d x)}\right)}{b}-\frac{e^{a+b x} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;e^{2 (c+d x)}\right)}{b}-\frac{e^{-a-b x}}{2 b}+\frac{e^{a+b x}}{2 b}",1,"(E^(-a - b*x)*(-1 + E^(2*(a + b*x)) + 2*Hypergeometric2F1[1, -1/2*b/d, 1 - b/(2*d), E^(2*(c + d*x))] - 2*E^(2*(a + b*x))*Hypergeometric2F1[1, b/(2*d), 1 + b/(2*d), E^(2*(c + d*x))]))/(2*b)","A",1
191,1,103,120,11.7071992,"\int \cosh (a+b x) \tanh (c+d x) \, dx","Integrate[Cosh[a + b*x]*Tanh[c + d*x],x]","\frac{e^{-a-b x} \left(-2 e^{2 (a+b x)} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;-e^{2 (c+d x)}\right)+e^{2 (a+b x)}+2 \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};-e^{2 (c+d x)}\right)-1\right)}{2 b}","\frac{e^{-a-b x} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};-e^{2 (c+d x)}\right)}{b}-\frac{e^{a+b x} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;-e^{2 (c+d x)}\right)}{b}-\frac{e^{-a-b x}}{2 b}+\frac{e^{a+b x}}{2 b}",1,"(E^(-a - b*x)*(-1 + E^(2*(a + b*x)) + 2*Hypergeometric2F1[1, -1/2*b/d, 1 - b/(2*d), -E^(2*(c + d*x))] - 2*E^(2*(a + b*x))*Hypergeometric2F1[1, b/(2*d), 1 + b/(2*d), -E^(2*(c + d*x))]))/(2*b)","A",1
192,1,15,8,0.0057881,"\int \sinh (x) \sinh (2 x) \, dx","Integrate[Sinh[x]*Sinh[2*x],x]","\frac{1}{6} \sinh (3 x)-\frac{\sinh (x)}{2}","\frac{2 \sinh ^3(x)}{3}",1,"-1/2*Sinh[x] + Sinh[3*x]/6","A",1
193,1,17,17,0.0074894,"\int \sinh (x) \sinh (3 x) \, dx","Integrate[Sinh[x]*Sinh[3*x],x]","\frac{1}{8} \sinh (4 x)-\frac{1}{4} \sinh (2 x)","\frac{1}{8} \sinh (4 x)-\frac{1}{4} \sinh (2 x)",1,"-1/4*Sinh[2*x] + Sinh[4*x]/8","A",1
194,1,17,17,0.0068897,"\int \sinh (x) \sinh (4 x) \, dx","Integrate[Sinh[x]*Sinh[4*x],x]","\frac{1}{10} \sinh (5 x)-\frac{1}{6} \sinh (3 x)","\frac{1}{10} \sinh (5 x)-\frac{1}{6} \sinh (3 x)",1,"-1/6*Sinh[3*x] + Sinh[5*x]/10","A",1
195,1,25,35,0.0426269,"\int \sinh (x) \sinh (m x) \, dx","Integrate[Sinh[x]*Sinh[m*x],x]","\frac{m \sinh (x) \cosh (m x)-\cosh (x) \sinh (m x)}{m^2-1}","\frac{\sinh ((m+1) x)}{2 (m+1)}-\frac{\sinh ((1-m) x)}{2 (1-m)}",1,"(m*Cosh[m*x]*Sinh[x] - Cosh[x]*Sinh[m*x])/(-1 + m^2)","A",1
196,1,15,15,0.0056937,"\int \cosh (2 x) \sinh (x) \, dx","Integrate[Cosh[2*x]*Sinh[x],x]","\frac{1}{6} \cosh (3 x)-\frac{\cosh (x)}{2}","\frac{1}{6} \cosh (3 x)-\frac{\cosh (x)}{2}",1,"-1/2*Cosh[x] + Cosh[3*x]/6","A",1
197,1,17,17,0.0062371,"\int \cosh (3 x) \sinh (x) \, dx","Integrate[Cosh[3*x]*Sinh[x],x]","\frac{1}{8} \cosh (4 x)-\frac{\cosh ^2(x)}{2}","\frac{1}{8} \cosh (4 x)-\frac{1}{4} \cosh (2 x)",1,"-1/2*Cosh[x]^2 + Cosh[4*x]/8","A",1
198,1,17,17,0.0066179,"\int \cosh (4 x) \sinh (x) \, dx","Integrate[Cosh[4*x]*Sinh[x],x]","\frac{1}{10} \cosh (5 x)-\frac{1}{6} \cosh (3 x)","\frac{1}{10} \cosh (5 x)-\frac{1}{6} \cosh (3 x)",1,"-1/6*Cosh[3*x] + Cosh[5*x]/10","A",1
199,1,25,35,0.042202,"\int \cosh (m x) \sinh (x) \, dx","Integrate[Cosh[m*x]*Sinh[x],x]","\frac{m \sinh (x) \sinh (m x)-\cosh (x) \cosh (m x)}{m^2-1}","\frac{\cosh ((1-m) x)}{2 (1-m)}+\frac{\cosh ((m+1) x)}{2 (m+1)}",1,"(-(Cosh[x]*Cosh[m*x]) + m*Sinh[x]*Sinh[m*x])/(-1 + m^2)","A",1
200,1,19,19,0.0153012,"\int \sinh (x) \tanh (2 x) \, dx","Integrate[Sinh[x]*Tanh[2*x],x]","\sinh (x)-\frac{\tan ^{-1}\left(\sqrt{2} \sinh (x)\right)}{\sqrt{2}}","\sinh (x)-\frac{\tan ^{-1}\left(\sqrt{2} \sinh (x)\right)}{\sqrt{2}}",1,"-(ArcTan[Sqrt[2]*Sinh[x]]/Sqrt[2]) + Sinh[x]","A",1
201,1,19,19,0.0304443,"\int \sinh (x) \tanh (3 x) \, dx","Integrate[Sinh[x]*Tanh[3*x],x]","\sinh (x)-\frac{1}{3} \tan ^{-1}(\sinh (x))-\frac{1}{3} \tan ^{-1}(2 \sinh (x))","\sinh (x)-\frac{1}{3} \tan ^{-1}(\sinh (x))-\frac{1}{3} \tan ^{-1}(2 \sinh (x))",1,"-1/3*ArcTan[Sinh[x]] - ArcTan[2*Sinh[x]]/3 + Sinh[x]","A",1
202,1,69,69,0.1484839,"\int \sinh (x) \tanh (4 x) \, dx","Integrate[Sinh[x]*Tanh[4*x],x]","\sinh (x)-\frac{1}{4} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2-\sqrt{2}}}\right)-\frac{1}{4} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2+\sqrt{2}}}\right)","\sinh (x)-\frac{1}{4} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2-\sqrt{2}}}\right)-\frac{1}{4} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2+\sqrt{2}}}\right)",1,"-1/4*(Sqrt[2 - Sqrt[2]]*ArcTan[(2*Sinh[x])/Sqrt[2 - Sqrt[2]]]) - (Sqrt[2 + Sqrt[2]]*ArcTan[(2*Sinh[x])/Sqrt[2 + Sqrt[2]]])/4 + Sinh[x]","A",1
203,1,81,87,0.1994137,"\int \sinh (x) \tanh (5 x) \, dx","Integrate[Sinh[x]*Tanh[5*x],x]","\frac{1}{10} \left(10 \sinh (x)-2 \tan ^{-1}(\sinh (x))-\sqrt{2 \left(3+\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{3+\sqrt{5}}} \sinh (x)\right)-\sqrt{6-2 \sqrt{5}} \tan ^{-1}\left(\sqrt{2 \left(3+\sqrt{5}\right)} \sinh (x)\right)\right)","\sinh (x)-\frac{1}{5} \tan ^{-1}(\sinh (x))-\frac{1}{5} \sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{3+\sqrt{5}}} \sinh (x)\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(3-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{2 \left(3+\sqrt{5}\right)} \sinh (x)\right)",1,"(-2*ArcTan[Sinh[x]] - Sqrt[2*(3 + Sqrt[5])]*ArcTan[2*Sqrt[2/(3 + Sqrt[5])]*Sinh[x]] - Sqrt[6 - 2*Sqrt[5]]*ArcTan[Sqrt[2*(3 + Sqrt[5])]*Sinh[x]] + 10*Sinh[x])/10","A",1
204,1,87,87,0.1322732,"\int \sinh (x) \tanh (6 x) \, dx","Integrate[Sinh[x]*Tanh[6*x],x]","\sinh (x)-\frac{\tan ^{-1}\left(\sqrt{2} \sinh (x)\right)}{3 \sqrt{2}}-\frac{1}{6} \sqrt{2-\sqrt{3}} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2-\sqrt{3}}}\right)-\frac{1}{6} \sqrt{2+\sqrt{3}} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2+\sqrt{3}}}\right)","\sinh (x)-\frac{\tan ^{-1}\left(\sqrt{2} \sinh (x)\right)}{3 \sqrt{2}}-\frac{1}{6} \sqrt{2-\sqrt{3}} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2-\sqrt{3}}}\right)-\frac{1}{6} \sqrt{2+\sqrt{3}} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2+\sqrt{3}}}\right)",1,"-1/3*ArcTan[Sqrt[2]*Sinh[x]]/Sqrt[2] - (Sqrt[2 - Sqrt[3]]*ArcTan[(2*Sinh[x])/Sqrt[2 - Sqrt[3]]])/6 - (Sqrt[2 + Sqrt[3]]*ArcTan[(2*Sinh[x])/Sqrt[2 + Sqrt[3]]])/6 + Sinh[x]","A",1
205,1,164,81,0.1810525,"\int \sinh (x) \tanh (n x) \, dx","Integrate[Sinh[x]*Tanh[n*x],x]","\frac{1}{2} e^{-2 x} \left(-\frac{e^{2 n x+x} \, _2F_1\left(1,1-\frac{1}{2 n};2-\frac{1}{2 n};-e^{2 n x}\right)}{2 n-1}+\frac{e^{(2 n+3) x} \, _2F_1\left(1,1+\frac{1}{2 n};2+\frac{1}{2 n};-e^{2 n x}\right)}{2 n+1}-e^x \left(\, _2F_1\left(1,-\frac{1}{2 n};1-\frac{1}{2 n};-e^{2 n x}\right)+e^{2 x} \, _2F_1\left(1,\frac{1}{2 n};1+\frac{1}{2 n};-e^{2 n x}\right)\right)\right)","-e^{-x} \, _2F_1\left(1,-\frac{1}{2 n};1-\frac{1}{2 n};-e^{2 n x}\right)-e^x \, _2F_1\left(1,\frac{1}{2 n};\frac{1}{2} \left(2+\frac{1}{n}\right);-e^{2 n x}\right)+\frac{e^{-x}}{2}+\frac{e^x}{2}",1,"(-((E^(x + 2*n*x)*Hypergeometric2F1[1, 1 - 1/(2*n), 2 - 1/(2*n), -E^(2*n*x)])/(-1 + 2*n)) + (E^((3 + 2*n)*x)*Hypergeometric2F1[1, 1 + 1/(2*n), 2 + 1/(2*n), -E^(2*n*x)])/(1 + 2*n) - E^x*(Hypergeometric2F1[1, -1/2*1/n, 1 - 1/(2*n), -E^(2*n*x)] + E^(2*x)*Hypergeometric2F1[1, 1/(2*n), 1 + 1/(2*n), -E^(2*n*x)]))/(2*E^(2*x))","B",1
206,1,10,10,0.0089891,"\int \coth (2 x) \sinh (x) \, dx","Integrate[Coth[2*x]*Sinh[x],x]","\sinh (x)-\frac{1}{2} \tan ^{-1}(\sinh (x))","\sinh (x)-\frac{1}{2} \tan ^{-1}(\sinh (x))",1,"-1/2*ArcTan[Sinh[x]] + Sinh[x]","A",1
207,1,20,20,0.0172057,"\int \coth (3 x) \sinh (x) \, dx","Integrate[Coth[3*x]*Sinh[x],x]","\sinh (x)-\frac{\tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{3}}\right)}{\sqrt{3}}","\sinh (x)-\frac{\tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(2*Sinh[x])/Sqrt[3]]/Sqrt[3]) + Sinh[x]","A",1
208,1,28,28,0.0315798,"\int \coth (4 x) \sinh (x) \, dx","Integrate[Coth[4*x]*Sinh[x],x]","\sinh (x)-\frac{1}{4} \tan ^{-1}(\sinh (x))-\frac{\tan ^{-1}\left(\sqrt{2} \sinh (x)\right)}{2 \sqrt{2}}","\sinh (x)-\frac{1}{4} \tan ^{-1}(\sinh (x))-\frac{\tan ^{-1}\left(\sqrt{2} \sinh (x)\right)}{2 \sqrt{2}}",1,"-1/4*ArcTan[Sinh[x]] - ArcTan[Sqrt[2]*Sinh[x]]/(2*Sqrt[2]) + Sinh[x]","A",1
209,1,76,82,0.2407331,"\int \coth (5 x) \sinh (x) \, dx","Integrate[Coth[5*x]*Sinh[x],x]","\frac{1}{10} \left(10 \sinh (x)-\sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\sqrt{2+\frac{2}{\sqrt{5}}} \sinh (x)\right)-\sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} \sinh (x)\right)\right)","\sinh (x)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} \sinh (x)\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} \sinh (x)\right)",1,"(-(Sqrt[10 - 2*Sqrt[5]]*ArcTan[Sqrt[2 + 2/Sqrt[5]]*Sinh[x]]) - Sqrt[2*(5 + Sqrt[5])]*ArcTan[2*Sqrt[2/(5 + Sqrt[5])]*Sinh[x]] + 10*Sinh[x])/10","A",1
210,1,38,38,0.0614839,"\int \coth (6 x) \sinh (x) \, dx","Integrate[Coth[6*x]*Sinh[x],x]","\sinh (x)-\frac{1}{6} \tan ^{-1}(\sinh (x))-\frac{1}{6} \tan ^{-1}(2 \sinh (x))-\frac{\tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{3}}\right)}{2 \sqrt{3}}","\sinh (x)-\frac{1}{6} \tan ^{-1}(\sinh (x))-\frac{1}{6} \tan ^{-1}(2 \sinh (x))-\frac{\tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-1/6*ArcTan[Sinh[x]] - ArcTan[2*Sinh[x]]/6 - ArcTan[(2*Sinh[x])/Sqrt[3]]/(2*Sqrt[3]) + Sinh[x]","A",1
211,1,155,16,0.2966901,"\int \text{sech}(2 x) \sinh (x) \, dx","Integrate[Sech[2*x]*Sinh[x],x]","\frac{-4 \tanh ^{-1}\left(\sqrt{2}-i \tanh \left(\frac{x}{2}\right)\right)+\log \left(\sqrt{2}-2 \cosh (x)\right)-\log \left(2 \cosh (x)+\sqrt{2}\right)-2 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(1+\sqrt{2}\right) \cosh \left(\frac{x}{2}\right)-\left(\sqrt{2}-1\right) \sinh \left(\frac{x}{2}\right)}\right)+2 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(\sqrt{2}-1\right) \cosh \left(\frac{x}{2}\right)-\left(1+\sqrt{2}\right) \sinh \left(\frac{x}{2}\right)}\right)}{4 \sqrt{2}}","-\frac{\tanh ^{-1}\left(\sqrt{2} \cosh (x)\right)}{\sqrt{2}}",1,"((-2*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((1 + Sqrt[2])*Cosh[x/2] - (-1 + Sqrt[2])*Sinh[x/2])] + (2*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((-1 + Sqrt[2])*Cosh[x/2] - (1 + Sqrt[2])*Sinh[x/2])] - 4*ArcTanh[Sqrt[2] - I*Tanh[x/2]] + Log[Sqrt[2] - 2*Cosh[x]] - Log[Sqrt[2] + 2*Cosh[x]])/(4*Sqrt[2])","C",1
212,1,17,21,0.0090391,"\int \text{sech}(3 x) \sinh (x) \, dx","Integrate[Sech[3*x]*Sinh[x],x]","-\frac{1}{3} \tanh ^{-1}\left(\frac{1}{3} \left(8 \sinh ^2(x)+5\right)\right)","\frac{1}{6} \log \left(3-4 \cosh ^2(x)\right)-\frac{1}{3} \log (\cosh (x))",1,"-1/3*ArcTanh[(5 + 8*Sinh[x]^2)/3]","A",1
213,1,110,71,0.025377,"\int \text{sech}(4 x) \sinh (x) \, dx","Integrate[Sech[4*x]*Sinh[x],x]","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8+1\&,\frac{\text{$\#$1}^2 x+2 \text{$\#$1}^2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-x}{\text{$\#$1}^5}\&\right]","\frac{\tanh ^{-1}\left(\frac{2 \cosh (x)}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tanh ^{-1}\left(\frac{2 \cosh (x)}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2 \left(2+\sqrt{2}\right)}}",1,"RootSum[1 + #1^8 & , (-x - 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1] + x*#1^2 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^2)/#1^5 & ]/16","C",1
214,1,57,62,0.0845803,"\int \text{sech}(5 x) \sinh (x) \, dx","Integrate[Sech[5*x]*Sinh[x],x]","\frac{1}{20} \left(\left(\sqrt{5}-1\right) \log \left(8 \sinh ^2(x)-\sqrt{5}+3\right)-\left(1+\sqrt{5}\right) \log \left(8 \sinh ^2(x)+\sqrt{5}+3\right)+4 \log (\cosh (x))\right)","-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(-8 \cosh ^2(x)-\sqrt{5}+5\right)-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(-8 \cosh ^2(x)+\sqrt{5}+5\right)+\frac{1}{5} \log (\cosh (x))",1,"(4*Log[Cosh[x]] + (-1 + Sqrt[5])*Log[3 - Sqrt[5] + 8*Sinh[x]^2] - (1 + Sqrt[5])*Log[3 + Sqrt[5] + 8*Sinh[x]^2])/20","A",1
215,1,385,85,0.2821692,"\int \text{sech}(6 x) \sinh (x) \, dx","Integrate[Sech[6*x]*Sinh[x],x]","\frac{\sqrt{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\text{$\#$1}^6 x+2 \text{$\#$1}^6 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-\text{$\#$1}^4 x-2 \text{$\#$1}^4 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+\text{$\#$1}^2 x+2 \text{$\#$1}^2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-x}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]+8 \tanh ^{-1}\left(\sqrt{2}-i \tanh \left(\frac{x}{2}\right)\right)-2 \log \left(\sqrt{2}-2 \cosh (x)\right)+2 \log \left(2 \cosh (x)+\sqrt{2}\right)+4 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(1+\sqrt{2}\right) \cosh \left(\frac{x}{2}\right)-\left(\sqrt{2}-1\right) \sinh \left(\frac{x}{2}\right)}\right)-4 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(\sqrt{2}-1\right) \cosh \left(\frac{x}{2}\right)-\left(1+\sqrt{2}\right) \sinh \left(\frac{x}{2}\right)}\right)}{24 \sqrt{2}}","\frac{\tanh ^{-1}\left(\sqrt{2} \cosh (x)\right)}{3 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{2 \cosh (x)}{\sqrt{2-\sqrt{3}}}\right)}{6 \sqrt{2-\sqrt{3}}}-\frac{\tanh ^{-1}\left(\frac{2 \cosh (x)}{\sqrt{2+\sqrt{3}}}\right)}{6 \sqrt{2+\sqrt{3}}}",1,"((4*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((1 + Sqrt[2])*Cosh[x/2] - (-1 + Sqrt[2])*Sinh[x/2])] - (4*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((-1 + Sqrt[2])*Cosh[x/2] - (1 + Sqrt[2])*Sinh[x/2])] + 8*ArcTanh[Sqrt[2] - I*Tanh[x/2]] - 2*Log[Sqrt[2] - 2*Cosh[x]] + 2*Log[Sqrt[2] + 2*Cosh[x]] + Sqrt[2]*RootSum[1 - #1^4 + #1^8 & , (-x - 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1] + x*#1^2 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^2 - x*#1^4 - 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^4 + x*#1^6 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^6)/(-#1^3 + 2*#1^7) & ])/(24*Sqrt[2])","C",1
216,1,7,7,0.0031237,"\int \text{csch}(2 x) \sinh (x) \, dx","Integrate[Csch[2*x]*Sinh[x],x]","\tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)","\frac{1}{2} \tan ^{-1}(\sinh (x))",1,"ArcTan[Tanh[x/2]]","A",1
217,1,44,15,0.0263547,"\int \text{csch}(3 x) \sinh (x) \, dx","Integrate[Csch[3*x]*Sinh[x],x]","-\frac{1}{4} e^{2 x} \left(e^{2 x} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};e^{6 x}\right)-2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};e^{6 x}\right)\right)","\frac{\tan ^{-1}\left(\frac{\tanh (x)}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-1/4*(E^(2*x)*(-2*Hypergeometric2F1[1/3, 1, 4/3, E^(6*x)] + E^(2*x)*Hypergeometric2F1[2/3, 1, 5/3, E^(6*x)]))","C",1
218,1,26,26,0.0233043,"\int \text{csch}(4 x) \sinh (x) \, dx","Integrate[Csch[4*x]*Sinh[x],x]","\frac{\tan ^{-1}\left(\sqrt{2} \sinh (x)\right)}{2 \sqrt{2}}-\frac{1}{4} \tan ^{-1}(\sinh (x))","\frac{\tan ^{-1}\left(\sqrt{2} \sinh (x)\right)}{2 \sqrt{2}}-\frac{1}{4} \tan ^{-1}(\sinh (x))",1,"-1/4*ArcTan[Sinh[x]] + ArcTan[Sqrt[2]*Sinh[x]]/(2*Sqrt[2])","A",1
219,1,84,75,0.1109042,"\int \text{csch}(5 x) \sinh (x) \, dx","Integrate[Csch[5*x]*Sinh[x],x]","\frac{\sqrt{5+\sqrt{5}} \tan ^{-1}\left(\frac{\left(\sqrt{5}-3\right) \tanh (x)}{\sqrt{10-2 \sqrt{5}}}\right)+\sqrt{5-\sqrt{5}} \tan ^{-1}\left(\frac{\left(3+\sqrt{5}\right) \tanh (x)}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)}{5 \sqrt{2}}","\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\tanh (x)}{\sqrt{5-2 \sqrt{5}}}\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\tanh (x)}{\sqrt{5+2 \sqrt{5}}}\right)",1,"(Sqrt[5 + Sqrt[5]]*ArcTan[((-3 + Sqrt[5])*Tanh[x])/Sqrt[10 - 2*Sqrt[5]]] + Sqrt[5 - Sqrt[5]]*ArcTan[((3 + Sqrt[5])*Tanh[x])/Sqrt[2*(5 + Sqrt[5])]])/(5*Sqrt[2])","A",0
220,1,30,36,0.0356822,"\int \text{csch}(6 x) \sinh (x) \, dx","Integrate[Csch[6*x]*Sinh[x],x]","\frac{1}{6} \left(\tan ^{-1}(\sinh (x))+\tan ^{-1}(2 \sinh (x))-\sqrt{3} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{3}}\right)\right)","\frac{1}{6} \tan ^{-1}(\sinh (x))+\frac{1}{6} \tan ^{-1}(2 \sinh (x))-\frac{\tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(ArcTan[Sinh[x]] + ArcTan[2*Sinh[x]] - Sqrt[3]*ArcTan[(2*Sinh[x])/Sqrt[3]])/6","A",1
221,1,15,8,0.0059735,"\int \cosh (x) \sinh (2 x) \, dx","Integrate[Cosh[x]*Sinh[2*x],x]","\frac{\cosh (x)}{2}+\frac{1}{6} \cosh (3 x)","\frac{2 \cosh ^3(x)}{3}",1,"Cosh[x]/2 + Cosh[3*x]/6","A",1
222,1,17,17,0.0064269,"\int \cosh (x) \sinh (3 x) \, dx","Integrate[Cosh[x]*Sinh[3*x],x]","\frac{\cosh ^2(x)}{2}+\frac{1}{8} \cosh (4 x)","\frac{1}{4} \cosh (2 x)+\frac{1}{8} \cosh (4 x)",1,"Cosh[x]^2/2 + Cosh[4*x]/8","A",1
223,1,17,17,0.0063632,"\int \cosh (x) \sinh (4 x) \, dx","Integrate[Cosh[x]*Sinh[4*x],x]","\frac{1}{6} \cosh (3 x)+\frac{1}{10} \cosh (5 x)","\frac{1}{6} \cosh (3 x)+\frac{1}{10} \cosh (5 x)",1,"Cosh[3*x]/6 + Cosh[5*x]/10","A",1
224,1,25,35,0.0385478,"\int \cosh (x) \sinh (m x) \, dx","Integrate[Cosh[x]*Sinh[m*x],x]","\frac{m \cosh (x) \cosh (m x)-\sinh (x) \sinh (m x)}{m^2-1}","\frac{\cosh ((m+1) x)}{2 (m+1)}-\frac{\cosh ((1-m) x)}{2 (1-m)}",1,"(m*Cosh[x]*Cosh[m*x] - Sinh[x]*Sinh[m*x])/(-1 + m^2)","A",1
225,1,15,15,0.0056383,"\int \cosh (x) \cosh (2 x) \, dx","Integrate[Cosh[x]*Cosh[2*x],x]","\frac{\sinh (x)}{2}+\frac{1}{6} \sinh (3 x)","\frac{\sinh (x)}{2}+\frac{1}{6} \sinh (3 x)",1,"Sinh[x]/2 + Sinh[3*x]/6","A",1
226,1,17,17,0.0064284,"\int \cosh (x) \cosh (3 x) \, dx","Integrate[Cosh[x]*Cosh[3*x],x]","\frac{1}{4} \sinh (2 x)+\frac{1}{8} \sinh (4 x)","\frac{1}{4} \sinh (2 x)+\frac{1}{8} \sinh (4 x)",1,"Sinh[2*x]/4 + Sinh[4*x]/8","A",1
227,1,17,17,0.0048458,"\int \cosh (x) \cosh (4 x) \, dx","Integrate[Cosh[x]*Cosh[4*x],x]","\frac{1}{6} \sinh (3 x)+\frac{1}{10} \sinh (5 x)","\frac{1}{6} \sinh (3 x)+\frac{1}{10} \sinh (5 x)",1,"Sinh[3*x]/6 + Sinh[5*x]/10","A",1
228,1,25,35,0.037742,"\int \cosh (x) \cosh (m x) \, dx","Integrate[Cosh[x]*Cosh[m*x],x]","\frac{m \cosh (x) \sinh (m x)-\sinh (x) \cosh (m x)}{m^2-1}","\frac{\sinh ((1-m) x)}{2 (1-m)}+\frac{\sinh ((m+1) x)}{2 (m+1)}",1,"(-(Cosh[m*x]*Sinh[x]) + m*Cosh[x]*Sinh[m*x])/(-1 + m^2)","A",1
229,1,164,19,0.1809762,"\int \cosh (x) \tanh (2 x) \, dx","Integrate[Cosh[x]*Tanh[2*x],x]","\frac{4 \sqrt{2} \cosh (x)-4 \tanh ^{-1}\left(\sqrt{2}-i \tanh \left(\frac{x}{2}\right)\right)+\log \left(\sqrt{2}-2 \cosh (x)\right)-\log \left(2 \cosh (x)+\sqrt{2}\right)-2 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(1+\sqrt{2}\right) \cosh \left(\frac{x}{2}\right)-\left(\sqrt{2}-1\right) \sinh \left(\frac{x}{2}\right)}\right)+2 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(\sqrt{2}-1\right) \cosh \left(\frac{x}{2}\right)-\left(1+\sqrt{2}\right) \sinh \left(\frac{x}{2}\right)}\right)}{4 \sqrt{2}}","\cosh (x)-\frac{\tanh ^{-1}\left(\sqrt{2} \cosh (x)\right)}{\sqrt{2}}",1,"((-2*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((1 + Sqrt[2])*Cosh[x/2] - (-1 + Sqrt[2])*Sinh[x/2])] + (2*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((-1 + Sqrt[2])*Cosh[x/2] - (1 + Sqrt[2])*Sinh[x/2])] - 4*ArcTanh[Sqrt[2] - I*Tanh[x/2]] + 4*Sqrt[2]*Cosh[x] + Log[Sqrt[2] - 2*Cosh[x]] - Log[Sqrt[2] + 2*Cosh[x]])/(4*Sqrt[2])","C",1
230,1,55,20,0.0605834,"\int \cosh (x) \tanh (3 x) \, dx","Integrate[Cosh[x]*Tanh[3*x],x]","\cosh (x)-\frac{\tanh ^{-1}\left(\frac{2-i \tanh \left(\frac{x}{2}\right)}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{2+i \tanh \left(\frac{x}{2}\right)}{\sqrt{3}}\right)}{\sqrt{3}}","\cosh (x)-\frac{\tanh ^{-1}\left(\frac{2 \cosh (x)}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTanh[(2 - I*Tanh[x/2])/Sqrt[3]]/Sqrt[3]) - ArcTanh[(2 + I*Tanh[x/2])/Sqrt[3]]/Sqrt[3] + Cosh[x]","C",1
231,1,113,69,0.02481,"\int \cosh (x) \tanh (4 x) \, dx","Integrate[Cosh[x]*Tanh[4*x],x]","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8+1\&,\frac{\text{$\#$1}^6 x+2 \text{$\#$1}^6 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-x}{\text{$\#$1}^7}\&\right]+\cosh (x)","\cosh (x)-\frac{1}{4} \sqrt{2-\sqrt{2}} \tanh ^{-1}\left(\frac{2 \cosh (x)}{\sqrt{2-\sqrt{2}}}\right)-\frac{1}{4} \sqrt{2+\sqrt{2}} \tanh ^{-1}\left(\frac{2 \cosh (x)}{\sqrt{2+\sqrt{2}}}\right)",1,"Cosh[x] + RootSum[1 + #1^8 & , (-x - 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1] + x*#1^6 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^6)/#1^7 & ]/16","C",1
232,1,249,82,0.0294137,"\int \cosh (x) \tanh (5 x) \, dx","Integrate[Cosh[x]*Tanh[5*x],x]","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^6+\text{$\#$1}^4-\text{$\#$1}^2+1\&,\frac{\text{$\#$1}^6 x+2 \text{$\#$1}^6 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-\text{$\#$1}^4 x-2 \text{$\#$1}^4 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+\text{$\#$1}^2 x+2 \text{$\#$1}^2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-x}{4 \text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3-\text{$\#$1}}\&\right]+\cosh (x)","\cosh (x)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tanh ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} \cosh (x)\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} \cosh (x)\right)",1,"Cosh[x] + RootSum[1 - #1^2 + #1^4 - #1^6 + #1^8 & , (-x - 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1] + x*#1^2 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^2 - x*#1^4 - 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^4 + x*#1^6 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^6)/(-#1 + 2*#1^3 - 3*#1^5 + 4*#1^7) & ]/4","C",1
233,1,395,87,0.3055909,"\int \cosh (x) \tanh (6 x) \, dx","Integrate[Cosh[x]*Tanh[6*x],x]","\frac{\sqrt{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{2 \text{$\#$1}^6 x+4 \text{$\#$1}^6 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+\text{$\#$1}^4 x+2 \text{$\#$1}^4 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-\text{$\#$1}^2 x-2 \text{$\#$1}^2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-4 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-2 x}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]+24 \sqrt{2} \cosh (x)-8 \tanh ^{-1}\left(\sqrt{2}-i \tanh \left(\frac{x}{2}\right)\right)+2 \log \left(\sqrt{2}-2 \cosh (x)\right)-2 \log \left(2 \cosh (x)+\sqrt{2}\right)-4 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(1+\sqrt{2}\right) \cosh \left(\frac{x}{2}\right)-\left(\sqrt{2}-1\right) \sinh \left(\frac{x}{2}\right)}\right)+4 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(\sqrt{2}-1\right) \cosh \left(\frac{x}{2}\right)-\left(1+\sqrt{2}\right) \sinh \left(\frac{x}{2}\right)}\right)}{24 \sqrt{2}}","\cosh (x)-\frac{\tanh ^{-1}\left(\sqrt{2} \cosh (x)\right)}{3 \sqrt{2}}-\frac{1}{6} \sqrt{2-\sqrt{3}} \tanh ^{-1}\left(\frac{2 \cosh (x)}{\sqrt{2-\sqrt{3}}}\right)-\frac{1}{6} \sqrt{2+\sqrt{3}} \tanh ^{-1}\left(\frac{2 \cosh (x)}{\sqrt{2+\sqrt{3}}}\right)",1,"((-4*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((1 + Sqrt[2])*Cosh[x/2] - (-1 + Sqrt[2])*Sinh[x/2])] + (4*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((-1 + Sqrt[2])*Cosh[x/2] - (1 + Sqrt[2])*Sinh[x/2])] - 8*ArcTanh[Sqrt[2] - I*Tanh[x/2]] + 24*Sqrt[2]*Cosh[x] + 2*Log[Sqrt[2] - 2*Cosh[x]] - 2*Log[Sqrt[2] + 2*Cosh[x]] + Sqrt[2]*RootSum[1 - #1^4 + #1^8 & , (-2*x - 4*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1] - x*#1^2 - 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^2 + x*#1^4 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^4 + 2*x*#1^6 + 4*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^6)/(-#1^3 + 2*#1^7) & ])/(24*Sqrt[2])","C",1
234,1,14,10,0.0149306,"\int \cosh (x) \coth (2 x) \, dx","Integrate[Cosh[x]*Coth[2*x],x]","\cosh (x)+\frac{1}{2} \log \left(\tanh \left(\frac{x}{2}\right)\right)","\cosh (x)-\frac{1}{2} \tanh ^{-1}(\cosh (x))",1,"Cosh[x] + Log[Tanh[x/2]]/2","A",1
235,1,47,45,0.0188563,"\int \cosh (x) \coth (3 x) \, dx","Integrate[Cosh[x]*Coth[3*x],x]","\cosh (x)+\frac{1}{3} \log \left(\sinh \left(\frac{x}{2}\right)\right)-\frac{1}{3} \log \left(\cosh \left(\frac{x}{2}\right)\right)+\frac{1}{6} \log (1-2 \cosh (x))-\frac{1}{6} \log (2 \cosh (x)+1)","\cosh (x)+\frac{1}{6} \log (1-2 \cosh (x))+\frac{1}{6} \log (1-\cosh (x))-\frac{1}{6} \log (\cosh (x)+1)-\frac{1}{6} \log (2 \cosh (x)+1)",1,"Cosh[x] - Log[Cosh[x/2]]/3 + Log[1 - 2*Cosh[x]]/6 - Log[1 + 2*Cosh[x]]/6 + Log[Sinh[x/2]]/3","A",1
236,1,192,28,0.2397256,"\int \cosh (x) \coth (4 x) \, dx","Integrate[Cosh[x]*Coth[4*x],x]","\frac{8 \sqrt{2} \cosh (x)-4 \tanh ^{-1}\left(\sqrt{2}-i \tanh \left(\frac{x}{2}\right)\right)+2 \sqrt{2} \log \left(\sinh \left(\frac{x}{2}\right)\right)-2 \sqrt{2} \log \left(\cosh \left(\frac{x}{2}\right)\right)+\log \left(\sqrt{2}-2 \cosh (x)\right)-\log \left(2 \cosh (x)+\sqrt{2}\right)-2 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(1+\sqrt{2}\right) \cosh \left(\frac{x}{2}\right)-\left(\sqrt{2}-1\right) \sinh \left(\frac{x}{2}\right)}\right)+2 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(\sqrt{2}-1\right) \cosh \left(\frac{x}{2}\right)-\left(1+\sqrt{2}\right) \sinh \left(\frac{x}{2}\right)}\right)}{8 \sqrt{2}}","\cosh (x)-\frac{1}{4} \tanh ^{-1}(\cosh (x))-\frac{\tanh ^{-1}\left(\sqrt{2} \cosh (x)\right)}{2 \sqrt{2}}",1,"((-2*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((1 + Sqrt[2])*Cosh[x/2] - (-1 + Sqrt[2])*Sinh[x/2])] + (2*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((-1 + Sqrt[2])*Cosh[x/2] - (1 + Sqrt[2])*Sinh[x/2])] - 4*ArcTanh[Sqrt[2] - I*Tanh[x/2]] + 8*Sqrt[2]*Cosh[x] - 2*Sqrt[2]*Log[Cosh[x/2]] + Log[Sqrt[2] - 2*Cosh[x]] - Log[Sqrt[2] + 2*Cosh[x]] + 2*Sqrt[2]*Log[Sinh[x/2]])/(8*Sqrt[2])","C",1
237,1,133,110,0.1211556,"\int \cosh (x) \coth (5 x) \, dx","Integrate[Cosh[x]*Coth[5*x],x]","\frac{1}{100} \left(100 \cosh (x)+20 \log \left(\sinh \left(\frac{x}{2}\right)\right)-20 \log \left(\cosh \left(\frac{x}{2}\right)\right)+\sqrt{5} \left(\sqrt{5}-5\right) \log \left(-4 \cosh (x)-\sqrt{5}+1\right)+\sqrt{5} \left(5+\sqrt{5}\right) \log \left(-4 \cosh (x)+\sqrt{5}+1\right)-\sqrt{5} \left(\sqrt{5}-5\right) \log \left(4 \cosh (x)-\sqrt{5}+1\right)-\sqrt{5} \left(5+\sqrt{5}\right) \log \left(4 \cosh (x)+\sqrt{5}+1\right)\right)","\cosh (x)+\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(-4 \cosh (x)-\sqrt{5}+1\right)+\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(-4 \cosh (x)+\sqrt{5}+1\right)-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(4 \cosh (x)-\sqrt{5}+1\right)-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(4 \cosh (x)+\sqrt{5}+1\right)-\frac{1}{5} \tanh ^{-1}(\cosh (x))",1,"(100*Cosh[x] - 20*Log[Cosh[x/2]] + Sqrt[5]*(-5 + Sqrt[5])*Log[1 - Sqrt[5] - 4*Cosh[x]] + Sqrt[5]*(5 + Sqrt[5])*Log[1 + Sqrt[5] - 4*Cosh[x]] - Sqrt[5]*(-5 + Sqrt[5])*Log[1 - Sqrt[5] + 4*Cosh[x]] - Sqrt[5]*(5 + Sqrt[5])*Log[1 + Sqrt[5] + 4*Cosh[x]] + 20*Log[Sinh[x/2]])/100","A",1
238,1,95,38,0.0762665,"\int \cosh (x) \coth (6 x) \, dx","Integrate[Cosh[x]*Coth[6*x],x]","\frac{1}{12} \left(12 \cosh (x)-2 \sqrt{3} \tanh ^{-1}\left(\frac{2-i \tanh \left(\frac{x}{2}\right)}{\sqrt{3}}\right)-2 \sqrt{3} \tanh ^{-1}\left(\frac{2+i \tanh \left(\frac{x}{2}\right)}{\sqrt{3}}\right)+2 \log \left(\sinh \left(\frac{x}{2}\right)\right)-2 \log \left(\cosh \left(\frac{x}{2}\right)\right)+\log (1-2 \cosh (x))-\log (2 \cosh (x)+1)\right)","\cosh (x)-\frac{1}{6} \tanh ^{-1}(\cosh (x))-\frac{1}{6} \tanh ^{-1}(2 \cosh (x))-\frac{\tanh ^{-1}\left(\frac{2 \cosh (x)}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(-2*Sqrt[3]*ArcTanh[(2 - I*Tanh[x/2])/Sqrt[3]] - 2*Sqrt[3]*ArcTanh[(2 + I*Tanh[x/2])/Sqrt[3]] + 12*Cosh[x] - 2*Log[Cosh[x/2]] + Log[1 - 2*Cosh[x]] - Log[1 + 2*Cosh[x]] + 2*Log[Sinh[x/2]])/12","C",1
239,1,156,76,0.1788374,"\int \cosh (x) \coth (n x) \, dx","Integrate[Cosh[x]*Coth[n*x],x]","\frac{1}{2} e^{-2 x} \left(-\frac{e^{2 n x+x} \, _2F_1\left(1,1-\frac{1}{2 n};2-\frac{1}{2 n};e^{2 n x}\right)}{2 n-1}-\frac{e^{(2 n+3) x} \, _2F_1\left(1,1+\frac{1}{2 n};2+\frac{1}{2 n};e^{2 n x}\right)}{2 n+1}+e^x \, _2F_1\left(1,-\frac{1}{2 n};1-\frac{1}{2 n};e^{2 n x}\right)-e^{3 x} \, _2F_1\left(1,\frac{1}{2 n};1+\frac{1}{2 n};e^{2 n x}\right)\right)","e^{-x} \, _2F_1\left(1,-\frac{1}{2 n};1-\frac{1}{2 n};e^{2 n x}\right)-e^x \, _2F_1\left(1,\frac{1}{2 n};\frac{1}{2} \left(2+\frac{1}{n}\right);e^{2 n x}\right)-\frac{e^{-x}}{2}+\frac{e^x}{2}",1,"(-((E^(x + 2*n*x)*Hypergeometric2F1[1, 1 - 1/(2*n), 2 - 1/(2*n), E^(2*n*x)])/(-1 + 2*n)) - (E^((3 + 2*n)*x)*Hypergeometric2F1[1, 1 + 1/(2*n), 2 + 1/(2*n), E^(2*n*x)])/(1 + 2*n) + E^x*Hypergeometric2F1[1, -1/2*1/n, 1 - 1/(2*n), E^(2*n*x)] - E^(3*x)*Hypergeometric2F1[1, 1/(2*n), 1 + 1/(2*n), E^(2*n*x)])/(2*E^(2*x))","B",1
240,1,15,15,0.0073102,"\int \cosh (x) \text{sech}(2 x) \, dx","Integrate[Cosh[x]*Sech[2*x],x]","\frac{\tan ^{-1}\left(\sqrt{2} \sinh (x)\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\sqrt{2} \sinh (x)\right)}{\sqrt{2}}",1,"ArcTan[Sqrt[2]*Sinh[x]]/Sqrt[2]","A",1
241,1,48,15,0.0233225,"\int \cosh (x) \text{sech}(3 x) \, dx","Integrate[Cosh[x]*Sech[3*x],x]","\frac{1}{4} e^{2 x} \left(2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-e^{6 x}\right)+e^{2 x} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-e^{6 x}\right)\right)","\frac{\tan ^{-1}\left(\sqrt{3} \tanh (x)\right)}{\sqrt{3}}",1,"(E^(2*x)*(2*Hypergeometric2F1[1/3, 1, 4/3, -E^(6*x)] + E^(2*x)*Hypergeometric2F1[2/3, 1, 5/3, -E^(6*x)]))/4","C",1
242,1,67,71,0.1060005,"\int \cosh (x) \text{sech}(4 x) \, dx","Integrate[Cosh[x]*Sech[4*x],x]","\frac{1}{4} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2-\sqrt{2}}}\right)-\frac{\tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2 \left(2+\sqrt{2}\right)}}","\frac{\tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2 \left(2+\sqrt{2}\right)}}",1,"(Sqrt[2 + Sqrt[2]]*ArcTan[(2*Sinh[x])/Sqrt[2 - Sqrt[2]]])/4 - ArcTan[(2*Sinh[x])/Sqrt[2 + Sqrt[2]]]/(2*Sqrt[2*(2 + Sqrt[2])])","A",1
243,1,84,75,0.1067282,"\int \cosh (x) \text{sech}(5 x) \, dx","Integrate[Cosh[x]*Sech[5*x],x]","\frac{\sqrt{5+\sqrt{5}} \tan ^{-1}\left(\frac{\left(5+\sqrt{5}\right) \tanh (x)}{\sqrt{10-2 \sqrt{5}}}\right)+\sqrt{5-\sqrt{5}} \tan ^{-1}\left(\frac{\left(\sqrt{5}-5\right) \tanh (x)}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)}{5 \sqrt{2}}","\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{5+2 \sqrt{5}} \tanh (x)\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{5-2 \sqrt{5}} \tanh (x)\right)",1,"(Sqrt[5 + Sqrt[5]]*ArcTan[((5 + Sqrt[5])*Tanh[x])/Sqrt[10 - 2*Sqrt[5]]] + Sqrt[5 - Sqrt[5]]*ArcTan[((-5 + Sqrt[5])*Tanh[x])/Sqrt[2*(5 + Sqrt[5])]])/(5*Sqrt[2])","A",1
244,1,81,85,0.0905562,"\int \cosh (x) \text{sech}(6 x) \, dx","Integrate[Cosh[x]*Sech[6*x],x]","\frac{1}{6} \left(-\sqrt{2} \tan ^{-1}\left(\sqrt{2} \sinh (x)\right)+\sqrt{2+\sqrt{3}} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2-\sqrt{3}}}\right)+\sqrt{2-\sqrt{3}} \tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2+\sqrt{3}}}\right)\right)","-\frac{\tan ^{-1}\left(\sqrt{2} \sinh (x)\right)}{3 \sqrt{2}}+\frac{\tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2-\sqrt{3}}}\right)}{6 \sqrt{2-\sqrt{3}}}+\frac{\tan ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{2+\sqrt{3}}}\right)}{6 \sqrt{2+\sqrt{3}}}",1,"(-(Sqrt[2]*ArcTan[Sqrt[2]*Sinh[x]]) + Sqrt[2 + Sqrt[3]]*ArcTan[(2*Sinh[x])/Sqrt[2 - Sqrt[3]]] + Sqrt[2 - Sqrt[3]]*ArcTan[(2*Sinh[x])/Sqrt[2 + Sqrt[3]]])/6","A",1
245,1,11,7,0.0025178,"\int \cosh (x) \text{csch}(2 x) \, dx","Integrate[Cosh[x]*Csch[2*x],x]","\frac{1}{2} \log \left(\tanh \left(\frac{x}{2}\right)\right)","-\frac{1}{2} \tanh ^{-1}(\cosh (x))",1,"Log[Tanh[x/2]]/2","A",1
246,1,21,21,0.0097802,"\int \cosh (x) \text{csch}(3 x) \, dx","Integrate[Cosh[x]*Csch[3*x],x]","\frac{1}{3} \log (\sinh (x))-\frac{1}{6} \log \left(4 \sinh ^2(x)+3\right)","\frac{1}{3} \log (\sinh (x))-\frac{1}{6} \log \left(4 \sinh ^2(x)+3\right)",1,"Log[Sinh[x]]/3 - Log[3 + 4*Sinh[x]^2]/6","A",1
247,1,183,26,0.3142239,"\int \cosh (x) \text{csch}(4 x) \, dx","Integrate[Cosh[x]*Csch[4*x],x]","\frac{4 \tanh ^{-1}\left(\sqrt{2}-i \tanh \left(\frac{x}{2}\right)\right)+2 \sqrt{2} \log \left(\sinh \left(\frac{x}{2}\right)\right)-2 \sqrt{2} \log \left(\cosh \left(\frac{x}{2}\right)\right)-\log \left(\sqrt{2}-2 \cosh (x)\right)+\log \left(2 \cosh (x)+\sqrt{2}\right)+2 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(1+\sqrt{2}\right) \cosh \left(\frac{x}{2}\right)-\left(\sqrt{2}-1\right) \sinh \left(\frac{x}{2}\right)}\right)-2 i \tan ^{-1}\left(\frac{\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)}{\left(\sqrt{2}-1\right) \cosh \left(\frac{x}{2}\right)-\left(1+\sqrt{2}\right) \sinh \left(\frac{x}{2}\right)}\right)}{8 \sqrt{2}}","\frac{\tanh ^{-1}\left(\sqrt{2} \cosh (x)\right)}{2 \sqrt{2}}-\frac{1}{4} \tanh ^{-1}(\cosh (x))",1,"((2*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((1 + Sqrt[2])*Cosh[x/2] - (-1 + Sqrt[2])*Sinh[x/2])] - (2*I)*ArcTan[(Cosh[x/2] + Sinh[x/2])/((-1 + Sqrt[2])*Cosh[x/2] - (1 + Sqrt[2])*Sinh[x/2])] + 4*ArcTanh[Sqrt[2] - I*Tanh[x/2]] - 2*Sqrt[2]*Log[Cosh[x/2]] - Log[Sqrt[2] - 2*Cosh[x]] + Log[Sqrt[2] + 2*Cosh[x]] + 2*Sqrt[2]*Log[Sinh[x/2]])/(8*Sqrt[2])","C",1
248,1,57,62,0.06171,"\int \cosh (x) \text{csch}(5 x) \, dx","Integrate[Cosh[x]*Csch[5*x],x]","\frac{1}{20} \left(4 \log (\sinh (x))-\left(\left(1+\sqrt{5}\right) \log \left(4 \cosh (2 x)-\sqrt{5}+1\right)\right)+\left(\sqrt{5}-1\right) \log \left(4 \cosh (2 x)+\sqrt{5}+1\right)\right)","-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(8 \sinh ^2(x)-\sqrt{5}+5\right)-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(8 \sinh ^2(x)+\sqrt{5}+5\right)+\frac{1}{5} \log (\sinh (x))",1,"(-((1 + Sqrt[5])*Log[1 - Sqrt[5] + 4*Cosh[2*x]]) + (-1 + Sqrt[5])*Log[1 + Sqrt[5] + 4*Cosh[2*x]] + 4*Log[Sinh[x]])/20","A",1
249,1,91,36,0.0702922,"\int \cosh (x) \text{csch}(6 x) \, dx","Integrate[Cosh[x]*Csch[6*x],x]","\frac{1}{12} \left(2 \sqrt{3} \tanh ^{-1}\left(\frac{2-i \tanh \left(\frac{x}{2}\right)}{\sqrt{3}}\right)+2 \sqrt{3} \tanh ^{-1}\left(\frac{2+i \tanh \left(\frac{x}{2}\right)}{\sqrt{3}}\right)+2 \log \left(\sinh \left(\frac{x}{2}\right)\right)-2 \log \left(\cosh \left(\frac{x}{2}\right)\right)+\log (1-2 \cosh (x))-\log (2 \cosh (x)+1)\right)","-\frac{1}{6} \tanh ^{-1}(\cosh (x))-\frac{1}{6} \tanh ^{-1}(2 \cosh (x))+\frac{\tanh ^{-1}\left(\frac{2 \cosh (x)}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(2*Sqrt[3]*ArcTanh[(2 - I*Tanh[x/2])/Sqrt[3]] + 2*Sqrt[3]*ArcTanh[(2 + I*Tanh[x/2])/Sqrt[3]] - 2*Log[Cosh[x/2]] + Log[1 - 2*Cosh[x]] - Log[1 + 2*Cosh[x]] + 2*Log[Sinh[x/2]])/12","C",1
250,1,66,70,0.0500267,"\int x^m \cosh (a+b x) \sinh (a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]*Sinh[a + b*x],x]","\frac{e^{-2 a} 2^{-m-3} x^m \left(-b^2 x^2\right)^{-m} \left(e^{4 a} (b x)^m \Gamma (m+1,-2 b x)+(-b x)^m \Gamma (m+1,2 b x)\right)}{b}","\frac{e^{2 a} 2^{-m-3} x^m (-b x)^{-m} \Gamma (m+1,-2 b x)}{b}+\frac{e^{-2 a} 2^{-m-3} x^m (b x)^{-m} \Gamma (m+1,2 b x)}{b}",1,"(2^(-3 - m)*x^m*(E^(4*a)*(b*x)^m*Gamma[1 + m, -2*b*x] + (-(b*x))^m*Gamma[1 + m, 2*b*x]))/(b*E^(2*a)*(-(b^2*x^2))^m)","A",1
251,1,50,94,0.1128688,"\int x^3 \cosh (a+b x) \sinh (a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]*Sinh[a + b*x],x]","\frac{\left(4 b^3 x^3+6 b x\right) \cosh (2 (a+b x))-3 \left(2 b^2 x^2+1\right) \sinh (2 (a+b x))}{16 b^4}","-\frac{3 \sinh (a+b x) \cosh (a+b x)}{8 b^4}+\frac{3 x \sinh ^2(a+b x)}{4 b^3}-\frac{3 x^2 \sinh (a+b x) \cosh (a+b x)}{4 b^2}+\frac{x^3 \sinh ^2(a+b x)}{2 b}+\frac{3 x}{8 b^3}+\frac{x^3}{4 b}",1,"((6*b*x + 4*b^3*x^3)*Cosh[2*(a + b*x)] - 3*(1 + 2*b^2*x^2)*Sinh[2*(a + b*x)])/(16*b^4)","A",1
252,1,39,64,0.074701,"\int x^2 \cosh (a+b x) \sinh (a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]*Sinh[a + b*x],x]","\frac{\left(2 b^2 x^2+1\right) \cosh (2 (a+b x))-2 b x \sinh (2 (a+b x))}{8 b^3}","\frac{\sinh ^2(a+b x)}{4 b^3}-\frac{x \sinh (a+b x) \cosh (a+b x)}{2 b^2}+\frac{x^2 \sinh ^2(a+b x)}{2 b}+\frac{x^2}{4 b}",1,"((1 + 2*b^2*x^2)*Cosh[2*(a + b*x)] - 2*b*x*Sinh[2*(a + b*x)])/(8*b^3)","A",1
253,1,28,44,0.0605329,"\int x \cosh (a+b x) \sinh (a+b x) \, dx","Integrate[x*Cosh[a + b*x]*Sinh[a + b*x],x]","-\frac{\sinh (2 (a+b x))-2 b x \cosh (2 (a+b x))}{8 b^2}","-\frac{\sinh (a+b x) \cosh (a+b x)}{4 b^2}+\frac{x \sinh ^2(a+b x)}{2 b}+\frac{x}{4 b}",1,"-1/8*(-2*b*x*Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)])/b^2","A",1
254,1,37,15,0.0113269,"\int \cosh (a+b x) \sinh (a+b x) \, dx","Integrate[Cosh[a + b*x]*Sinh[a + b*x],x]","\frac{1}{2} \left(\frac{\sinh (2 a) \sinh (2 b x)}{2 b}+\frac{\cosh (2 a) \cosh (2 b x)}{2 b}\right)","\frac{\sinh ^2(a+b x)}{2 b}",1,"((Cosh[2*a]*Cosh[2*b*x])/(2*b) + (Sinh[2*a]*Sinh[2*b*x])/(2*b))/2","B",1
255,1,25,27,0.0267984,"\int \frac{\cosh (a+b x) \sinh (a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x])/x,x]","\frac{1}{2} (\sinh (2 a) \text{Chi}(2 b x)+\cosh (2 a) \text{Shi}(2 b x))","\frac{1}{2} \sinh (2 a) \text{Chi}(2 b x)+\frac{1}{2} \cosh (2 a) \text{Shi}(2 b x)",1,"(CoshIntegral[2*b*x]*Sinh[2*a] + Cosh[2*a]*SinhIntegral[2*b*x])/2","A",1
256,1,42,39,0.0746549,"\int \frac{\cosh (a+b x) \sinh (a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x])/x^2,x]","\frac{1}{2} \left(2 b \cosh (2 a) \text{Chi}(2 b x)+2 b \sinh (2 a) \text{Shi}(2 b x)-\frac{\sinh (2 (a+b x))}{x}\right)","b \cosh (2 a) \text{Chi}(2 b x)+b \sinh (2 a) \text{Shi}(2 b x)-\frac{\sinh (2 a+2 b x)}{2 x}",1,"(2*b*Cosh[2*a]*CoshIntegral[2*b*x] - Sinh[2*(a + b*x)]/x + 2*b*Sinh[2*a]*SinhIntegral[2*b*x])/2","A",1
257,1,61,60,0.183268,"\int \frac{\cosh (a+b x) \sinh (a+b x)}{x^3} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x])/x^3,x]","\frac{1}{2} \left(2 b^2 \sinh (2 a) \text{Chi}(2 b x)+2 b^2 \cosh (2 a) \text{Shi}(2 b x)-\frac{\sinh (2 (a+b x))+2 b x \cosh (2 (a+b x))}{2 x^2}\right)","b^2 \sinh (2 a) \text{Chi}(2 b x)+b^2 \cosh (2 a) \text{Shi}(2 b x)-\frac{\sinh (2 a+2 b x)}{4 x^2}-\frac{b \cosh (2 a+2 b x)}{2 x}",1,"(2*b^2*CoshIntegral[2*b*x]*Sinh[2*a] - (2*b*x*Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)])/(2*x^2) + 2*b^2*Cosh[2*a]*SinhIntegral[2*b*x])/2","A",1
258,1,77,85,0.1669273,"\int \frac{\cosh (a+b x) \sinh (a+b x)}{x^4} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x])/x^4,x]","-\frac{-4 b^3 x^3 \cosh (2 a) \text{Chi}(2 b x)-4 b^3 x^3 \sinh (2 a) \text{Shi}(2 b x)+2 b^2 x^2 \sinh (2 (a+b x))+\sinh (2 (a+b x))+b x \cosh (2 (a+b x))}{6 x^3}","\frac{2}{3} b^3 \cosh (2 a) \text{Chi}(2 b x)+\frac{2}{3} b^3 \sinh (2 a) \text{Shi}(2 b x)-\frac{b^2 \sinh (2 a+2 b x)}{3 x}-\frac{\sinh (2 a+2 b x)}{6 x^3}-\frac{b \cosh (2 a+2 b x)}{6 x^2}",1,"-1/6*(b*x*Cosh[2*(a + b*x)] - 4*b^3*x^3*Cosh[2*a]*CoshIntegral[2*b*x] + Sinh[2*(a + b*x)] + 2*b^2*x^2*Sinh[2*(a + b*x)] - 4*b^3*x^3*Sinh[2*a]*SinhIntegral[2*b*x])/x^3","A",1
259,1,114,134,0.1836355,"\int x^m \cosh ^2(a+b x) \sinh (a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]^2*Sinh[a + b*x],x]","\frac{e^{-3 a} x^m \left(3^{-m} \left(-b^2 x^2\right)^{-m} \left(e^{6 a} (b x)^m \Gamma (m+1,-3 b x)+(-b x)^m \Gamma (m+1,3 b x)\right)+3 e^{2 a} \left(e^{2 a} (-b x)^{-m} \Gamma (m+1,-b x)+(b x)^{-m} \Gamma (m+1,b x)\right)\right)}{24 b}","\frac{e^{3 a} 3^{-m-1} x^m (-b x)^{-m} \Gamma (m+1,-3 b x)}{8 b}+\frac{e^a x^m (-b x)^{-m} \Gamma (m+1,-b x)}{8 b}+\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+1,b x)}{8 b}+\frac{e^{-3 a} 3^{-m-1} x^m (b x)^{-m} \Gamma (m+1,3 b x)}{8 b}",1,"(x^m*(3*E^(2*a)*((E^(2*a)*Gamma[1 + m, -(b*x)])/(-(b*x))^m + Gamma[1 + m, b*x]/(b*x)^m) + (E^(6*a)*(b*x)^m*Gamma[1 + m, -3*b*x] + (-(b*x))^m*Gamma[1 + m, 3*b*x])/(3^m*(-(b^2*x^2))^m)))/(24*b*E^(3*a))","A",1
260,1,86,117,0.4128224,"\int x^3 \cosh ^2(a+b x) \sinh (a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]^2*Sinh[a + b*x],x]","\frac{\left(9 b^3 x^3+6 b x\right) \cosh (3 (a+b x))+27 b x \left(b^2 x^2+6\right) \cosh (a+b x)-2 \sinh (a+b x) \left(\left(9 b^2 x^2+2\right) \cosh (2 (a+b x))+45 b^2 x^2+82\right)}{108 b^4}","-\frac{2 \sinh ^3(a+b x)}{27 b^4}-\frac{14 \sinh (a+b x)}{9 b^4}+\frac{2 x \cosh ^3(a+b x)}{9 b^3}+\frac{4 x \cosh (a+b x)}{3 b^3}-\frac{2 x^2 \sinh (a+b x)}{3 b^2}-\frac{x^2 \sinh (a+b x) \cosh ^2(a+b x)}{3 b^2}+\frac{x^3 \cosh ^3(a+b x)}{3 b}",1,"(27*b*x*(6 + b^2*x^2)*Cosh[a + b*x] + (6*b*x + 9*b^3*x^3)*Cosh[3*(a + b*x)] - 2*(82 + 45*b^2*x^2 + (2 + 9*b^2*x^2)*Cosh[2*(a + b*x)])*Sinh[a + b*x])/(108*b^4)","A",1
261,1,65,83,0.2111164,"\int x^2 \cosh ^2(a+b x) \sinh (a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]^2*Sinh[a + b*x],x]","\frac{27 \left(b^2 x^2+2\right) \cosh (a+b x)+\left(9 b^2 x^2+2\right) \cosh (3 (a+b x))-6 b x (9 \sinh (a+b x)+\sinh (3 (a+b x)))}{108 b^3}","\frac{2 \cosh ^3(a+b x)}{27 b^3}+\frac{4 \cosh (a+b x)}{9 b^3}-\frac{4 x \sinh (a+b x)}{9 b^2}-\frac{2 x \sinh (a+b x) \cosh ^2(a+b x)}{9 b^2}+\frac{x^2 \cosh ^3(a+b x)}{3 b}",1,"(27*(2 + b^2*x^2)*Cosh[a + b*x] + (2 + 9*b^2*x^2)*Cosh[3*(a + b*x)] - 6*b*x*(9*Sinh[a + b*x] + Sinh[3*(a + b*x)]))/(108*b^3)","A",1
262,1,46,45,0.1454539,"\int x \cosh ^2(a+b x) \sinh (a+b x) \, dx","Integrate[x*Cosh[a + b*x]^2*Sinh[a + b*x],x]","-\frac{9 \sinh (a+b x)+\sinh (3 (a+b x))-9 b x \cosh (a+b x)-3 b x \cosh (3 (a+b x))}{36 b^2}","-\frac{\sinh ^3(a+b x)}{9 b^2}-\frac{\sinh (a+b x)}{3 b^2}+\frac{x \cosh ^3(a+b x)}{3 b}",1,"-1/36*(-9*b*x*Cosh[a + b*x] - 3*b*x*Cosh[3*(a + b*x)] + 9*Sinh[a + b*x] + Sinh[3*(a + b*x)])/b^2","A",1
263,1,15,15,0.0037214,"\int \cosh ^2(a+b x) \sinh (a+b x) \, dx","Integrate[Cosh[a + b*x]^2*Sinh[a + b*x],x]","\frac{\cosh ^3(a+b x)}{3 b}","\frac{\cosh ^3(a+b x)}{3 b}",1,"Cosh[a + b*x]^3/(3*b)","A",1
264,1,39,47,0.0737265,"\int \frac{\cosh ^2(a+b x) \sinh (a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x])/x,x]","\frac{1}{4} (\sinh (a) \text{Chi}(b x)+\sinh (3 a) \text{Chi}(3 b x)+\cosh (a) \text{Shi}(b x)+\cosh (3 a) \text{Shi}(3 b x))","\frac{1}{4} \sinh (a) \text{Chi}(b x)+\frac{1}{4} \sinh (3 a) \text{Chi}(3 b x)+\frac{1}{4} \cosh (a) \text{Shi}(b x)+\frac{1}{4} \cosh (3 a) \text{Shi}(3 b x)",1,"(CoshIntegral[b*x]*Sinh[a] + CoshIntegral[3*b*x]*Sinh[3*a] + Cosh[a]*SinhIntegral[b*x] + Cosh[3*a]*SinhIntegral[3*b*x])/4","A",1
265,1,70,80,0.1569358,"\int \frac{\cosh ^2(a+b x) \sinh (a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x])/x^2,x]","\frac{b x \cosh (a) \text{Chi}(b x)+3 b x \cosh (3 a) \text{Chi}(3 b x)+b x \sinh (a) \text{Shi}(b x)+3 b x \sinh (3 a) \text{Shi}(3 b x)-\sinh (a+b x)-\sinh (3 (a+b x))}{4 x}","\frac{1}{4} b \cosh (a) \text{Chi}(b x)+\frac{3}{4} b \cosh (3 a) \text{Chi}(3 b x)+\frac{1}{4} b \sinh (a) \text{Shi}(b x)+\frac{3}{4} b \sinh (3 a) \text{Shi}(3 b x)-\frac{\sinh (a+b x)}{4 x}-\frac{\sinh (3 a+3 b x)}{4 x}",1,"(b*x*Cosh[a]*CoshIntegral[b*x] + 3*b*x*Cosh[3*a]*CoshIntegral[3*b*x] - Sinh[a + b*x] - Sinh[3*(a + b*x)] + b*x*Sinh[a]*SinhIntegral[b*x] + 3*b*x*Sinh[3*a]*SinhIntegral[3*b*x])/(4*x)","A",1
266,1,105,119,0.2939154,"\int \frac{\cosh ^2(a+b x) \sinh (a+b x)}{x^3} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x])/x^3,x]","-\frac{-b^2 x^2 \sinh (a) \text{Chi}(b x)-9 b^2 x^2 \sinh (3 a) \text{Chi}(3 b x)-b^2 x^2 \cosh (a) \text{Shi}(b x)-9 b^2 x^2 \cosh (3 a) \text{Shi}(3 b x)+\sinh (a+b x)+\sinh (3 (a+b x))+b x \cosh (a+b x)+3 b x \cosh (3 (a+b x))}{8 x^2}","\frac{1}{8} b^2 \sinh (a) \text{Chi}(b x)+\frac{9}{8} b^2 \sinh (3 a) \text{Chi}(3 b x)+\frac{1}{8} b^2 \cosh (a) \text{Shi}(b x)+\frac{9}{8} b^2 \cosh (3 a) \text{Shi}(3 b x)-\frac{\sinh (a+b x)}{8 x^2}-\frac{\sinh (3 a+3 b x)}{8 x^2}-\frac{b \cosh (a+b x)}{8 x}-\frac{3 b \cosh (3 a+3 b x)}{8 x}",1,"-1/8*(b*x*Cosh[a + b*x] + 3*b*x*Cosh[3*(a + b*x)] - b^2*x^2*CoshIntegral[b*x]*Sinh[a] - 9*b^2*x^2*CoshIntegral[3*b*x]*Sinh[3*a] + Sinh[a + b*x] + Sinh[3*(a + b*x)] - b^2*x^2*Cosh[a]*SinhIntegral[b*x] - 9*b^2*x^2*Cosh[3*a]*SinhIntegral[3*b*x])/x^2","A",1
267,1,138,154,0.3616484,"\int \frac{\cosh ^2(a+b x) \sinh (a+b x)}{x^4} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x])/x^4,x]","-\frac{-b^3 x^3 \cosh (a) \text{Chi}(b x)-27 b^3 x^3 \cosh (3 a) \text{Chi}(3 b x)-b^3 x^3 \sinh (a) \text{Shi}(b x)-27 b^3 x^3 \sinh (3 a) \text{Shi}(3 b x)+b^2 x^2 \sinh (a+b x)+9 b^2 x^2 \sinh (3 (a+b x))+2 \sinh (a+b x)+2 \sinh (3 (a+b x))+b x \cosh (a+b x)+3 b x \cosh (3 (a+b x))}{24 x^3}","\frac{1}{24} b^3 \cosh (a) \text{Chi}(b x)+\frac{9}{8} b^3 \cosh (3 a) \text{Chi}(3 b x)+\frac{1}{24} b^3 \sinh (a) \text{Shi}(b x)+\frac{9}{8} b^3 \sinh (3 a) \text{Shi}(3 b x)-\frac{b^2 \sinh (a+b x)}{24 x}-\frac{3 b^2 \sinh (3 a+3 b x)}{8 x}-\frac{\sinh (a+b x)}{12 x^3}-\frac{\sinh (3 a+3 b x)}{12 x^3}-\frac{b \cosh (a+b x)}{24 x^2}-\frac{b \cosh (3 a+3 b x)}{8 x^2}",1,"-1/24*(b*x*Cosh[a + b*x] + 3*b*x*Cosh[3*(a + b*x)] - b^3*x^3*Cosh[a]*CoshIntegral[b*x] - 27*b^3*x^3*Cosh[3*a]*CoshIntegral[3*b*x] + 2*Sinh[a + b*x] + b^2*x^2*Sinh[a + b*x] + 2*Sinh[3*(a + b*x)] + 9*b^2*x^2*Sinh[3*(a + b*x)] - b^3*x^3*Sinh[a]*SinhIntegral[b*x] - 27*b^3*x^3*Sinh[3*a]*SinhIntegral[3*b*x])/x^3","A",1
268,1,110,139,0.1311426,"\int x^m \cosh ^3(a+b x) \sinh (a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]^3*Sinh[a + b*x],x]","\frac{e^{-4 a} 4^{-m-3} x^m \left(-b^2 x^2\right)^{-m} \left((-b x)^m \left(e^{2 a} 2^{m+2} \Gamma (m+1,2 b x)+\Gamma (m+1,4 b x)\right)+e^{8 a} (b x)^m \Gamma (m+1,-4 b x)+e^{6 a} 2^{m+2} (b x)^m \Gamma (m+1,-2 b x)\right)}{b}","\frac{e^{4 a} 2^{-2 (m+3)} x^m (-b x)^{-m} \Gamma (m+1,-4 b x)}{b}+\frac{e^{2 a} 2^{-m-4} x^m (-b x)^{-m} \Gamma (m+1,-2 b x)}{b}+\frac{e^{-2 a} 2^{-m-4} x^m (b x)^{-m} \Gamma (m+1,2 b x)}{b}+\frac{e^{-4 a} 2^{-2 (m+3)} x^m (b x)^{-m} \Gamma (m+1,4 b x)}{b}",1,"(4^(-3 - m)*x^m*(E^(8*a)*(b*x)^m*Gamma[1 + m, -4*b*x] + 2^(2 + m)*E^(6*a)*(b*x)^m*Gamma[1 + m, -2*b*x] + (-(b*x))^m*(2^(2 + m)*E^(2*a)*Gamma[1 + m, 2*b*x] + Gamma[1 + m, 4*b*x])))/(b*E^(4*a)*(-(b^2*x^2))^m)","A",1
269,1,91,155,0.6369464,"\int x^3 \cosh ^3(a+b x) \sinh (a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]^3*Sinh[a + b*x],x]","\frac{32 b x \left(2 b^2 x^2+3\right) \cosh (2 (a+b x))+2 b x \left(8 b^2 x^2+3\right) \cosh (4 (a+b x))-3 \sinh (2 (a+b x)) \left(\left(8 b^2 x^2+1\right) \cosh (2 (a+b x))+32 b^2 x^2+16\right)}{512 b^4}","-\frac{3 \sinh (a+b x) \cosh ^3(a+b x)}{128 b^4}-\frac{45 \sinh (a+b x) \cosh (a+b x)}{256 b^4}+\frac{3 x \cosh ^4(a+b x)}{32 b^3}+\frac{9 x \cosh ^2(a+b x)}{32 b^3}-\frac{3 x^2 \sinh (a+b x) \cosh ^3(a+b x)}{16 b^2}-\frac{9 x^2 \sinh (a+b x) \cosh (a+b x)}{32 b^2}+\frac{x^3 \cosh ^4(a+b x)}{4 b}-\frac{45 x}{256 b^3}-\frac{3 x^3}{32 b}",1,"(32*b*x*(3 + 2*b^2*x^2)*Cosh[2*(a + b*x)] + 2*b*x*(3 + 8*b^2*x^2)*Cosh[4*(a + b*x)] - 3*(16 + 32*b^2*x^2 + (1 + 8*b^2*x^2)*Cosh[2*(a + b*x)])*Sinh[2*(a + b*x)])/(512*b^4)","A",1
270,1,70,101,0.2409189,"\int x^2 \cosh ^3(a+b x) \sinh (a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]^3*Sinh[a + b*x],x]","\frac{16 \left(2 b^2 x^2+1\right) \cosh (2 (a+b x))+\left(8 b^2 x^2+1\right) \cosh (4 (a+b x))-4 b x (8 \sinh (2 (a+b x))+\sinh (4 (a+b x)))}{256 b^3}","\frac{\cosh ^4(a+b x)}{32 b^3}+\frac{3 \cosh ^2(a+b x)}{32 b^3}-\frac{x \sinh (a+b x) \cosh ^3(a+b x)}{8 b^2}-\frac{3 x \sinh (a+b x) \cosh (a+b x)}{16 b^2}+\frac{x^2 \cosh ^4(a+b x)}{4 b}-\frac{3 x^2}{32 b}",1,"(16*(1 + 2*b^2*x^2)*Cosh[2*(a + b*x)] + (1 + 8*b^2*x^2)*Cosh[4*(a + b*x)] - 4*b*x*(8*Sinh[2*(a + b*x)] + Sinh[4*(a + b*x)]))/(256*b^3)","A",1
271,1,50,65,0.1600916,"\int x \cosh ^3(a+b x) \sinh (a+b x) \, dx","Integrate[x*Cosh[a + b*x]^3*Sinh[a + b*x],x]","-\frac{8 \sinh (2 (a+b x))+\sinh (4 (a+b x))-16 b x \cosh (2 (a+b x))-4 b x \cosh (4 (a+b x))}{128 b^2}","-\frac{\sinh (a+b x) \cosh ^3(a+b x)}{16 b^2}-\frac{3 \sinh (a+b x) \cosh (a+b x)}{32 b^2}+\frac{x \cosh ^4(a+b x)}{4 b}-\frac{3 x}{32 b}",1,"-1/128*(-16*b*x*Cosh[2*(a + b*x)] - 4*b*x*Cosh[4*(a + b*x)] + 8*Sinh[2*(a + b*x)] + Sinh[4*(a + b*x)])/b^2","A",1
272,1,15,15,0.0027069,"\int \cosh ^3(a+b x) \sinh (a+b x) \, dx","Integrate[Cosh[a + b*x]^3*Sinh[a + b*x],x]","\frac{\cosh ^4(a+b x)}{4 b}","\frac{\cosh ^4(a+b x)}{4 b}",1,"Cosh[a + b*x]^4/(4*b)","A",1
273,1,47,53,0.0839408,"\int \frac{\cosh ^3(a+b x) \sinh (a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x])/x,x]","\frac{1}{8} (2 \sinh (2 a) \text{Chi}(2 b x)+\sinh (4 a) \text{Chi}(4 b x)+2 \cosh (2 a) \text{Shi}(2 b x)+\cosh (4 a) \text{Shi}(4 b x))","\frac{1}{4} \sinh (2 a) \text{Chi}(2 b x)+\frac{1}{8} \sinh (4 a) \text{Chi}(4 b x)+\frac{1}{4} \cosh (2 a) \text{Shi}(2 b x)+\frac{1}{8} \cosh (4 a) \text{Shi}(4 b x)",1,"(2*CoshIntegral[2*b*x]*Sinh[2*a] + CoshIntegral[4*b*x]*Sinh[4*a] + 2*Cosh[2*a]*SinhIntegral[2*b*x] + Cosh[4*a]*SinhIntegral[4*b*x])/8","A",1
274,1,80,89,0.207886,"\int \frac{\cosh ^3(a+b x) \sinh (a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x])/x^2,x]","\frac{4 b x \cosh (2 a) \text{Chi}(2 b x)+4 b x \cosh (4 a) \text{Chi}(4 b x)+4 b x \sinh (2 a) \text{Shi}(2 b x)+4 b x \sinh (4 a) \text{Shi}(4 b x)-2 \sinh (2 (a+b x))-\sinh (4 (a+b x))}{8 x}","\frac{1}{2} b \cosh (2 a) \text{Chi}(2 b x)+\frac{1}{2} b \cosh (4 a) \text{Chi}(4 b x)+\frac{1}{2} b \sinh (2 a) \text{Shi}(2 b x)+\frac{1}{2} b \sinh (4 a) \text{Shi}(4 b x)-\frac{\sinh (2 a+2 b x)}{4 x}-\frac{\sinh (4 a+4 b x)}{8 x}",1,"(4*b*x*Cosh[2*a]*CoshIntegral[2*b*x] + 4*b*x*Cosh[4*a]*CoshIntegral[4*b*x] - 2*Sinh[2*(a + b*x)] - Sinh[4*(a + b*x)] + 4*b*x*Sinh[2*a]*SinhIntegral[2*b*x] + 4*b*x*Sinh[4*a]*SinhIntegral[4*b*x])/(8*x)","A",1
275,1,112,125,0.6130838,"\int \frac{\cosh ^3(a+b x) \sinh (a+b x)}{x^3} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x])/x^3,x]","b^2 \sinh (4 a) \text{Chi}(4 b x)+b^2 \sinh (a) \cosh (a) \text{Chi}(2 b x)+\frac{1}{2} b^2 \cosh (2 a) \text{Shi}(2 b x)+b^2 \cosh (4 a) \text{Shi}(4 b x)-\frac{\sinh (2 (a+b x))+2 b x \cosh (2 (a+b x))}{8 x^2}-\frac{\sinh (4 (a+b x))+4 b x \cosh (4 (a+b x))}{16 x^2}","\frac{1}{2} b^2 \sinh (2 a) \text{Chi}(2 b x)+b^2 \sinh (4 a) \text{Chi}(4 b x)+\frac{1}{2} b^2 \cosh (2 a) \text{Shi}(2 b x)+b^2 \cosh (4 a) \text{Shi}(4 b x)-\frac{\sinh (2 a+2 b x)}{8 x^2}-\frac{\sinh (4 a+4 b x)}{16 x^2}-\frac{b \cosh (2 a+2 b x)}{4 x}-\frac{b \cosh (4 a+4 b x)}{4 x}",1,"b^2*Cosh[a]*CoshIntegral[2*b*x]*Sinh[a] + b^2*CoshIntegral[4*b*x]*Sinh[4*a] - (2*b*x*Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)])/(8*x^2) - (4*b*x*Cosh[4*(a + b*x)] + Sinh[4*(a + b*x)])/(16*x^2) + (b^2*Cosh[2*a]*SinhIntegral[2*b*x])/2 + b^2*Cosh[4*a]*SinhIntegral[4*b*x]","A",1
276,1,150,169,0.5249942,"\int \frac{\cosh ^3(a+b x) \sinh (a+b x)}{x^4} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x])/x^4,x]","-\frac{-8 b^3 x^3 \cosh (2 a) \text{Chi}(2 b x)-32 b^3 x^3 \cosh (4 a) \text{Chi}(4 b x)-8 b^3 x^3 \sinh (2 a) \text{Shi}(2 b x)-32 b^3 x^3 \sinh (4 a) \text{Shi}(4 b x)+4 b^2 x^2 \sinh (2 (a+b x))+8 b^2 x^2 \sinh (4 (a+b x))+2 \sinh (2 (a+b x))+\sinh (4 (a+b x))+2 b x \cosh (2 (a+b x))+2 b x \cosh (4 (a+b x))}{24 x^3}","\frac{1}{3} b^3 \cosh (2 a) \text{Chi}(2 b x)+\frac{4}{3} b^3 \cosh (4 a) \text{Chi}(4 b x)+\frac{1}{3} b^3 \sinh (2 a) \text{Shi}(2 b x)+\frac{4}{3} b^3 \sinh (4 a) \text{Shi}(4 b x)-\frac{b^2 \sinh (2 a+2 b x)}{6 x}-\frac{b^2 \sinh (4 a+4 b x)}{3 x}-\frac{\sinh (2 a+2 b x)}{12 x^3}-\frac{\sinh (4 a+4 b x)}{24 x^3}-\frac{b \cosh (2 a+2 b x)}{12 x^2}-\frac{b \cosh (4 a+4 b x)}{12 x^2}",1,"-1/24*(2*b*x*Cosh[2*(a + b*x)] + 2*b*x*Cosh[4*(a + b*x)] - 8*b^3*x^3*Cosh[2*a]*CoshIntegral[2*b*x] - 32*b^3*x^3*Cosh[4*a]*CoshIntegral[4*b*x] + 2*Sinh[2*(a + b*x)] + 4*b^2*x^2*Sinh[2*(a + b*x)] + Sinh[4*(a + b*x)] + 8*b^2*x^2*Sinh[4*(a + b*x)] - 8*b^3*x^3*Sinh[2*a]*SinhIntegral[2*b*x] - 32*b^3*x^3*Sinh[4*a]*SinhIntegral[4*b*x])/x^3","A",1
277,1,8,8,0.00576,"\int \frac{\cosh (x) \sinh (x)}{x} \, dx","Integrate[(Cosh[x]*Sinh[x])/x,x]","\frac{\text{Shi}(2 x)}{2}","\frac{\text{Shi}(2 x)}{2}",1,"SinhIntegral[2*x]/2","A",1
278,1,16,16,0.0065568,"\int \frac{\cosh (x) \sinh (x)}{x^2} \, dx","Integrate[(Cosh[x]*Sinh[x])/x^2,x]","\text{Chi}(2 x)-\frac{\sinh (2 x)}{2 x}","\text{Chi}(2 x)-\frac{\sinh (2 x)}{2 x}",1,"CoshIntegral[2*x] - Sinh[2*x]/(2*x)","A",1
279,1,27,27,0.0076471,"\int \frac{\cosh (x) \sinh (x)}{x^3} \, dx","Integrate[(Cosh[x]*Sinh[x])/x^3,x]","\text{Shi}(2 x)-\frac{\sinh (2 x)}{4 x^2}-\frac{\cosh (2 x)}{2 x}","\text{Shi}(2 x)-\frac{\sinh (2 x)}{4 x^2}-\frac{\cosh (2 x)}{2 x}",1,"-1/2*Cosh[2*x]/x - Sinh[2*x]/(4*x^2) + SinhIntegral[2*x]","A",1
280,1,114,134,0.229697,"\int x^m \cosh (a+b x) \sinh ^2(a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]*Sinh[a + b*x]^2,x]","\frac{e^{-3 a} x^m \left(3^{-m} \left(-b^2 x^2\right)^{-m} \left(e^{6 a} (b x)^m \Gamma (m+1,-3 b x)-(-b x)^m \Gamma (m+1,3 b x)\right)-3 e^{4 a} (-b x)^{-m} \Gamma (m+1,-b x)+3 e^{2 a} (b x)^{-m} \Gamma (m+1,b x)\right)}{24 b}","\frac{e^{3 a} 3^{-m-1} x^m (-b x)^{-m} \Gamma (m+1,-3 b x)}{8 b}-\frac{e^a x^m (-b x)^{-m} \Gamma (m+1,-b x)}{8 b}+\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+1,b x)}{8 b}-\frac{e^{-3 a} 3^{-m-1} x^m (b x)^{-m} \Gamma (m+1,3 b x)}{8 b}",1,"(x^m*((-3*E^(4*a)*Gamma[1 + m, -(b*x)])/(-(b*x))^m + (3*E^(2*a)*Gamma[1 + m, b*x])/(b*x)^m + (E^(6*a)*(b*x)^m*Gamma[1 + m, -3*b*x] - (-(b*x))^m*Gamma[1 + m, 3*b*x])/(3^m*(-(b^2*x^2))^m)))/(24*b*E^(3*a))","A",1
281,1,84,117,0.399966,"\int x^3 \cosh (a+b x) \sinh ^2(a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]*Sinh[a + b*x]^2,x]","\frac{81 \left(b^2 x^2+2\right) \cosh (a+b x)-\left(9 b^2 x^2+2\right) \cosh (3 (a+b x))+6 b x \sinh (a+b x) \left(\left(3 b^2 x^2+2\right) \cosh (2 (a+b x))-3 b^2 x^2-26\right)}{108 b^4}","-\frac{2 \cosh ^3(a+b x)}{27 b^4}+\frac{14 \cosh (a+b x)}{9 b^4}+\frac{2 x \sinh ^3(a+b x)}{9 b^3}-\frac{4 x \sinh (a+b x)}{3 b^3}+\frac{2 x^2 \cosh (a+b x)}{3 b^2}-\frac{x^2 \sinh ^2(a+b x) \cosh (a+b x)}{3 b^2}+\frac{x^3 \sinh ^3(a+b x)}{3 b}",1,"(81*(2 + b^2*x^2)*Cosh[a + b*x] - (2 + 9*b^2*x^2)*Cosh[3*(a + b*x)] + 6*b*x*(-26 - 3*b^2*x^2 + (2 + 3*b^2*x^2)*Cosh[2*(a + b*x)])*Sinh[a + b*x])/(108*b^4)","A",1
282,1,66,83,0.4382223,"\int x^2 \cosh (a+b x) \sinh ^2(a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]*Sinh[a + b*x]^2,x]","\frac{\sinh (a+b x) \left(\left(9 b^2 x^2+2\right) \cosh (2 (a+b x))-9 b^2 x^2-26\right)+27 b x \cosh (a+b x)-3 b x \cosh (3 (a+b x))}{54 b^3}","\frac{2 \sinh ^3(a+b x)}{27 b^3}-\frac{4 \sinh (a+b x)}{9 b^3}+\frac{4 x \cosh (a+b x)}{9 b^2}-\frac{2 x \sinh ^2(a+b x) \cosh (a+b x)}{9 b^2}+\frac{x^2 \sinh ^3(a+b x)}{3 b}",1,"(27*b*x*Cosh[a + b*x] - 3*b*x*Cosh[3*(a + b*x)] + (-26 - 9*b^2*x^2 + (2 + 9*b^2*x^2)*Cosh[2*(a + b*x)])*Sinh[a + b*x])/(54*b^3)","A",1
283,1,38,45,0.1415105,"\int x \cosh (a+b x) \sinh ^2(a+b x) \, dx","Integrate[x*Cosh[a + b*x]*Sinh[a + b*x]^2,x]","\frac{12 b x \sinh ^3(a+b x)+9 \cosh (a+b x)-\cosh (3 (a+b x))}{36 b^2}","-\frac{\cosh ^3(a+b x)}{9 b^2}+\frac{\cosh (a+b x)}{3 b^2}+\frac{x \sinh ^3(a+b x)}{3 b}",1,"(9*Cosh[a + b*x] - Cosh[3*(a + b*x)] + 12*b*x*Sinh[a + b*x]^3)/(36*b^2)","A",1
284,1,15,15,0.0036388,"\int \cosh (a+b x) \sinh ^2(a+b x) \, dx","Integrate[Cosh[a + b*x]*Sinh[a + b*x]^2,x]","\frac{\sinh ^3(a+b x)}{3 b}","\frac{\sinh ^3(a+b x)}{3 b}",1,"Sinh[a + b*x]^3/(3*b)","A",1
285,1,41,47,0.0733419,"\int \frac{\cosh (a+b x) \sinh ^2(a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x]^2)/x,x]","\frac{1}{4} (-\cosh (a) \text{Chi}(b x)+\cosh (3 a) \text{Chi}(3 b x)-\sinh (a) \text{Shi}(b x)+\sinh (3 a) \text{Shi}(3 b x))","-\frac{1}{4} \cosh (a) \text{Chi}(b x)+\frac{1}{4} \cosh (3 a) \text{Chi}(3 b x)-\frac{1}{4} \sinh (a) \text{Shi}(b x)+\frac{1}{4} \sinh (3 a) \text{Shi}(3 b x)",1,"(-(Cosh[a]*CoshIntegral[b*x]) + Cosh[3*a]*CoshIntegral[3*b*x] - Sinh[a]*SinhIntegral[b*x] + Sinh[3*a]*SinhIntegral[3*b*x])/4","A",1
286,1,68,80,0.217251,"\int \frac{\cosh (a+b x) \sinh ^2(a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x]^2)/x^2,x]","-\frac{b x \sinh (a) \text{Chi}(b x)-3 b x \sinh (3 a) \text{Chi}(3 b x)+b x \cosh (a) \text{Shi}(b x)-3 b x \cosh (3 a) \text{Shi}(3 b x)-\cosh (a+b x)+\cosh (3 (a+b x))}{4 x}","-\frac{1}{4} b \sinh (a) \text{Chi}(b x)+\frac{3}{4} b \sinh (3 a) \text{Chi}(3 b x)-\frac{1}{4} b \cosh (a) \text{Shi}(b x)+\frac{3}{4} b \cosh (3 a) \text{Shi}(3 b x)+\frac{\cosh (a+b x)}{4 x}-\frac{\cosh (3 a+3 b x)}{4 x}",1,"-1/4*(-Cosh[a + b*x] + Cosh[3*(a + b*x)] + b*x*CoshIntegral[b*x]*Sinh[a] - 3*b*x*CoshIntegral[3*b*x]*Sinh[3*a] + b*x*Cosh[a]*SinhIntegral[b*x] - 3*b*x*Cosh[3*a]*SinhIntegral[3*b*x])/x","A",1
287,1,107,119,0.2582354,"\int \frac{\cosh (a+b x) \sinh ^2(a+b x)}{x^3} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x]^2)/x^3,x]","\frac{-b^2 x^2 \cosh (a) \text{Chi}(b x)+9 b^2 x^2 \cosh (3 a) \text{Chi}(3 b x)-b^2 x^2 \sinh (a) \text{Shi}(b x)+9 b^2 x^2 \sinh (3 a) \text{Shi}(3 b x)+b x \sinh (a+b x)-3 b x \sinh (3 (a+b x))+\cosh (a+b x)-\cosh (3 (a+b x))}{8 x^2}","-\frac{1}{8} b^2 \cosh (a) \text{Chi}(b x)+\frac{9}{8} b^2 \cosh (3 a) \text{Chi}(3 b x)-\frac{1}{8} b^2 \sinh (a) \text{Shi}(b x)+\frac{9}{8} b^2 \sinh (3 a) \text{Shi}(3 b x)+\frac{\cosh (a+b x)}{8 x^2}-\frac{\cosh (3 a+3 b x)}{8 x^2}+\frac{b \sinh (a+b x)}{8 x}-\frac{3 b \sinh (3 a+3 b x)}{8 x}",1,"(Cosh[a + b*x] - Cosh[3*(a + b*x)] - b^2*x^2*Cosh[a]*CoshIntegral[b*x] + 9*b^2*x^2*Cosh[3*a]*CoshIntegral[3*b*x] + b*x*Sinh[a + b*x] - 3*b*x*Sinh[3*(a + b*x)] - b^2*x^2*Sinh[a]*SinhIntegral[b*x] + 9*b^2*x^2*Sinh[3*a]*SinhIntegral[3*b*x])/(8*x^2)","A",1
288,1,138,154,0.3181694,"\int \frac{\cosh (a+b x) \sinh ^2(a+b x)}{x^4} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x]^2)/x^4,x]","\frac{-b^3 x^3 \sinh (a) \text{Chi}(b x)+27 b^3 x^3 \sinh (3 a) \text{Chi}(3 b x)-b^3 x^3 \cosh (a) \text{Shi}(b x)+27 b^3 x^3 \cosh (3 a) \text{Shi}(3 b x)+b^2 x^2 \cosh (a+b x)-9 b^2 x^2 \cosh (3 (a+b x))+b x \sinh (a+b x)-3 b x \sinh (3 (a+b x))+2 \cosh (a+b x)-2 \cosh (3 (a+b x))}{24 x^3}","-\frac{1}{24} b^3 \sinh (a) \text{Chi}(b x)+\frac{9}{8} b^3 \sinh (3 a) \text{Chi}(3 b x)-\frac{1}{24} b^3 \cosh (a) \text{Shi}(b x)+\frac{9}{8} b^3 \cosh (3 a) \text{Shi}(3 b x)+\frac{b^2 \cosh (a+b x)}{24 x}-\frac{3 b^2 \cosh (3 a+3 b x)}{8 x}+\frac{\cosh (a+b x)}{12 x^3}-\frac{\cosh (3 a+3 b x)}{12 x^3}+\frac{b \sinh (a+b x)}{24 x^2}-\frac{b \sinh (3 a+3 b x)}{8 x^2}",1,"(2*Cosh[a + b*x] + b^2*x^2*Cosh[a + b*x] - 2*Cosh[3*(a + b*x)] - 9*b^2*x^2*Cosh[3*(a + b*x)] - b^3*x^3*CoshIntegral[b*x]*Sinh[a] + 27*b^3*x^3*CoshIntegral[3*b*x]*Sinh[3*a] + b*x*Sinh[a + b*x] - 3*b*x*Sinh[3*(a + b*x)] - b^3*x^3*Cosh[a]*SinhIntegral[b*x] + 27*b^3*x^3*Cosh[3*a]*SinhIntegral[3*b*x])/(24*x^3)","A",1
289,1,76,85,0.2220065,"\int x^m \cosh ^2(a+b x) \sinh ^2(a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]^2*Sinh[a + b*x]^2,x]","\frac{1}{64} x^m \left(\frac{e^{4 a} 4^{-m} (-b x)^{-m} \Gamma (m+1,-4 b x)}{b}-\frac{e^{-4 a} 4^{-m} (b x)^{-m} \Gamma (m+1,4 b x)}{b}-\frac{8 x}{m+1}\right)","\frac{e^{4 a} 2^{-2 (m+3)} x^m (-b x)^{-m} \Gamma (m+1,-4 b x)}{b}-\frac{e^{-4 a} 2^{-2 (m+3)} x^m (b x)^{-m} \Gamma (m+1,4 b x)}{b}-\frac{x^{m+1}}{8 (m+1)}",1,"(x^m*((-8*x)/(1 + m) + (E^(4*a)*Gamma[1 + m, -4*b*x])/(4^m*b*(-(b*x))^m) - Gamma[1 + m, 4*b*x]/(4^m*b*E^(4*a)*(b*x)^m)))/64","A",1
290,1,58,79,0.2095971,"\int x^3 \cosh ^2(a+b x) \sinh ^2(a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]^2*Sinh[a + b*x]^2,x]","\frac{4 b x \left(8 b^2 x^2+3\right) \sinh (4 (a+b x))-3 \left(8 b^2 x^2+1\right) \cosh (4 (a+b x))-32 b^4 x^4}{1024 b^4}","-\frac{3 \cosh (4 a+4 b x)}{1024 b^4}+\frac{3 x \sinh (4 a+4 b x)}{256 b^3}-\frac{3 x^2 \cosh (4 a+4 b x)}{128 b^2}+\frac{x^3 \sinh (4 a+4 b x)}{32 b}-\frac{x^4}{32}",1,"(-32*b^4*x^4 - 3*(1 + 8*b^2*x^2)*Cosh[4*(a + b*x)] + 4*b*x*(3 + 8*b^2*x^2)*Sinh[4*(a + b*x)])/(1024*b^4)","A",1
291,1,48,60,0.171115,"\int x^2 \cosh ^2(a+b x) \sinh ^2(a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]^2*Sinh[a + b*x]^2,x]","\frac{3 \left(8 b^2 x^2+1\right) \sinh (4 (a+b x))-12 b x \cosh (4 (a+b x))-32 b^3 x^3}{768 b^3}","\frac{\sinh (4 a+4 b x)}{256 b^3}-\frac{x \cosh (4 a+4 b x)}{64 b^2}+\frac{x^2 \sinh (4 a+4 b x)}{32 b}-\frac{x^3}{24}",1,"(-32*b^3*x^3 - 12*b*x*Cosh[4*(a + b*x)] + 3*(1 + 8*b^2*x^2)*Sinh[4*(a + b*x)])/(768*b^3)","A",1
292,1,41,41,0.1397816,"\int x \cosh ^2(a+b x) \sinh ^2(a+b x) \, dx","Integrate[x*Cosh[a + b*x]^2*Sinh[a + b*x]^2,x]","-\frac{-8 a^2-4 b x \sinh (4 (a+b x))+\cosh (4 (a+b x))+8 b^2 x^2}{128 b^2}","-\frac{\cosh (4 a+4 b x)}{128 b^2}+\frac{x \sinh (4 a+4 b x)}{32 b}-\frac{x^2}{16}",1,"-1/128*(-8*a^2 + 8*b^2*x^2 + Cosh[4*(a + b*x)] - 4*b*x*Sinh[4*(a + b*x)])/b^2","A",1
293,1,23,46,0.0224168,"\int \cosh ^2(a+b x) \sinh ^2(a+b x) \, dx","Integrate[Cosh[a + b*x]^2*Sinh[a + b*x]^2,x]","\frac{\sinh (4 (a+b x))-4 (a+b x)}{32 b}","\frac{\sinh (a+b x) \cosh ^3(a+b x)}{4 b}-\frac{\sinh (a+b x) \cosh (a+b x)}{8 b}-\frac{x}{8}",1,"(-4*(a + b*x) + Sinh[4*(a + b*x)])/(32*b)","A",1
294,1,32,33,0.1008259,"\int \frac{\cosh ^2(a+b x) \sinh ^2(a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x]^2)/x,x]","\frac{1}{8} (\cosh (4 a) \text{Chi}(4 b x)+\sinh (4 a) \text{Shi}(4 b x)-\log (2 b x))","\frac{1}{8} \cosh (4 a) \text{Chi}(4 b x)+\frac{1}{8} \sinh (4 a) \text{Shi}(4 b x)-\frac{\log (x)}{8}",1,"(Cosh[4*a]*CoshIntegral[4*b*x] - Log[2*b*x] + Sinh[4*a]*SinhIntegral[4*b*x])/8","A",1
295,1,45,52,0.0947719,"\int \frac{\cosh ^2(a+b x) \sinh ^2(a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x]^2)/x^2,x]","\frac{4 b x \sinh (4 a) \text{Chi}(4 b x)+4 b x \cosh (4 a) \text{Shi}(4 b x)-\cosh (4 (a+b x))+1}{8 x}","\frac{1}{2} b \sinh (4 a) \text{Chi}(4 b x)+\frac{1}{2} b \cosh (4 a) \text{Shi}(4 b x)-\frac{\cosh (4 a+4 b x)}{8 x}+\frac{1}{8 x}",1,"(1 - Cosh[4*(a + b*x)] + 4*b*x*CoshIntegral[4*b*x]*Sinh[4*a] + 4*b*x*Cosh[4*a]*SinhIntegral[4*b*x])/(8*x)","A",1
296,1,65,67,0.1101926,"\int \frac{\cosh ^2(a+b x) \sinh ^2(a+b x)}{x^3} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x]^2)/x^3,x]","\frac{16 b^2 x^2 \cosh (4 a) \text{Chi}(4 b x)+16 b^2 x^2 \sinh (4 a) \text{Shi}(4 b x)-4 b x \sinh (4 (a+b x))-\cosh (4 (a+b x))+1}{16 x^2}","b^2 \cosh (4 a) \text{Chi}(4 b x)+b^2 \sinh (4 a) \text{Shi}(4 b x)-\frac{\cosh (4 a+4 b x)}{16 x^2}-\frac{b \sinh (4 a+4 b x)}{4 x}+\frac{1}{16 x^2}",1,"(1 - Cosh[4*(a + b*x)] + 16*b^2*x^2*Cosh[4*a]*CoshIntegral[4*b*x] - 4*b*x*Sinh[4*(a + b*x)] + 16*b^2*x^2*Sinh[4*a]*SinhIntegral[4*b*x])/(16*x^2)","A",1
297,1,79,92,0.1959106,"\int \frac{\cosh ^2(a+b x) \sinh ^2(a+b x)}{x^4} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x]^2)/x^4,x]","-\frac{-32 b^3 x^3 \sinh (4 a) \text{Chi}(4 b x)-32 b^3 x^3 \cosh (4 a) \text{Shi}(4 b x)+8 b^2 x^2 \cosh (4 (a+b x))+2 b x \sinh (4 (a+b x))+\cosh (4 (a+b x))-1}{24 x^3}","\frac{4}{3} b^3 \sinh (4 a) \text{Chi}(4 b x)+\frac{4}{3} b^3 \cosh (4 a) \text{Shi}(4 b x)-\frac{b^2 \cosh (4 a+4 b x)}{3 x}-\frac{\cosh (4 a+4 b x)}{24 x^3}-\frac{b \sinh (4 a+4 b x)}{12 x^2}+\frac{1}{24 x^3}",1,"-1/24*(-1 + Cosh[4*(a + b*x)] + 8*b^2*x^2*Cosh[4*(a + b*x)] - 32*b^3*x^3*CoshIntegral[4*b*x]*Sinh[4*a] + 2*b*x*Sinh[4*(a + b*x)] - 32*b^3*x^3*Cosh[4*a]*SinhIntegral[4*b*x])/x^3","A",1
298,1,175,209,0.3095909,"\int x^m \cosh ^3(a+b x) \sinh ^2(a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]^3*Sinh[a + b*x]^2,x]","\frac{e^{-5 a} x^m \left(5 e^{2 a} 3^{-m} \left(-b^2 x^2\right)^{-m} \left(e^{6 a} (b x)^m \Gamma (m+1,-3 b x)-(-b x)^m \Gamma (m+1,3 b x)\right)+3\ 5^{-m} \left(-b^2 x^2\right)^{-m} \left(e^{10 a} (b x)^m \Gamma (m+1,-5 b x)-(-b x)^m \Gamma (m+1,5 b x)\right)-30 e^{6 a} (-b x)^{-m} \Gamma (m+1,-b x)+30 e^{4 a} (b x)^{-m} \Gamma (m+1,b x)\right)}{480 b}","\frac{e^{5 a} 5^{-m-1} x^m (-b x)^{-m} \Gamma (m+1,-5 b x)}{32 b}+\frac{e^{3 a} 3^{-m-1} x^m (-b x)^{-m} \Gamma (m+1,-3 b x)}{32 b}-\frac{e^a x^m (-b x)^{-m} \Gamma (m+1,-b x)}{16 b}+\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+1,b x)}{16 b}-\frac{e^{-3 a} 3^{-m-1} x^m (b x)^{-m} \Gamma (m+1,3 b x)}{32 b}-\frac{e^{-5 a} 5^{-m-1} x^m (b x)^{-m} \Gamma (m+1,5 b x)}{32 b}",1,"(x^m*((-30*E^(6*a)*Gamma[1 + m, -(b*x)])/(-(b*x))^m + (30*E^(4*a)*Gamma[1 + m, b*x])/(b*x)^m + (5*E^(2*a)*(E^(6*a)*(b*x)^m*Gamma[1 + m, -3*b*x] - (-(b*x))^m*Gamma[1 + m, 3*b*x]))/(3^m*(-(b^2*x^2))^m) + (3*(E^(10*a)*(b*x)^m*Gamma[1 + m, -5*b*x] - (-(b*x))^m*Gamma[1 + m, 5*b*x]))/(5^m*(-(b^2*x^2))^m)))/(480*b*E^(5*a))","A",1
299,1,125,202,1.1050341,"\int x^3 \cosh ^3(a+b x) \sinh ^2(a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]^3*Sinh[a + b*x]^2,x]","\frac{101250 \left(b^2 x^2+2\right) \cosh (a+b x)-625 \left(9 b^2 x^2+2\right) \cosh (3 (a+b x))-81 \left(25 b^2 x^2+2\right) \cosh (5 (a+b x))+30 b x \sinh (a+b x) \left(8 \left(75 b^2 x^2+38\right) \cosh (2 (a+b x))+9 \left(25 b^2 x^2+6\right) \cosh (4 (a+b x))-825 b^2 x^2-6598\right)}{270000 b^4}","\frac{3 \cosh (a+b x)}{4 b^4}-\frac{\cosh (3 a+3 b x)}{216 b^4}-\frac{3 \cosh (5 a+5 b x)}{5000 b^4}-\frac{3 x \sinh (a+b x)}{4 b^3}+\frac{x \sinh (3 a+3 b x)}{72 b^3}+\frac{3 x \sinh (5 a+5 b x)}{1000 b^3}+\frac{3 x^2 \cosh (a+b x)}{8 b^2}-\frac{x^2 \cosh (3 a+3 b x)}{48 b^2}-\frac{3 x^2 \cosh (5 a+5 b x)}{400 b^2}-\frac{x^3 \sinh (a+b x)}{8 b}+\frac{x^3 \sinh (3 a+3 b x)}{48 b}+\frac{x^3 \sinh (5 a+5 b x)}{80 b}",1,"(101250*(2 + b^2*x^2)*Cosh[a + b*x] - 625*(2 + 9*b^2*x^2)*Cosh[3*(a + b*x)] - 81*(2 + 25*b^2*x^2)*Cosh[5*(a + b*x)] + 30*b*x*(-6598 - 825*b^2*x^2 + 8*(38 + 75*b^2*x^2)*Cosh[2*(a + b*x)] + 9*(6 + 25*b^2*x^2)*Cosh[4*(a + b*x)])*Sinh[a + b*x])/(270000*b^4)","A",1
300,1,105,148,0.3171814,"\int x^2 \cosh ^3(a+b x) \sinh ^2(a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]^3*Sinh[a + b*x]^2,x]","\frac{-6750 \left(\left(b^2 x^2+2\right) \sinh (a+b x)-2 b x \cosh (a+b x)\right)+125 \left(\left(9 b^2 x^2+2\right) \sinh (3 (a+b x))-6 b x \cosh (3 (a+b x))\right)+27 \left(\left(25 b^2 x^2+2\right) \sinh (5 (a+b x))-10 b x \cosh (5 (a+b x))\right)}{54000 b^3}","-\frac{\sinh (a+b x)}{4 b^3}+\frac{\sinh (3 a+3 b x)}{216 b^3}+\frac{\sinh (5 a+5 b x)}{1000 b^3}+\frac{x \cosh (a+b x)}{4 b^2}-\frac{x \cosh (3 a+3 b x)}{72 b^2}-\frac{x \cosh (5 a+5 b x)}{200 b^2}-\frac{x^2 \sinh (a+b x)}{8 b}+\frac{x^2 \sinh (3 a+3 b x)}{48 b}+\frac{x^2 \sinh (5 a+5 b x)}{80 b}",1,"(-6750*(-2*b*x*Cosh[a + b*x] + (2 + b^2*x^2)*Sinh[a + b*x]) + 125*(-6*b*x*Cosh[3*(a + b*x)] + (2 + 9*b^2*x^2)*Sinh[3*(a + b*x)]) + 27*(-10*b*x*Cosh[5*(a + b*x)] + (2 + 25*b^2*x^2)*Sinh[5*(a + b*x)]))/(54000*b^3)","A",1
301,1,70,94,0.199536,"\int x \cosh ^3(a+b x) \sinh ^2(a+b x) \, dx","Integrate[x*Cosh[a + b*x]^3*Sinh[a + b*x]^2,x]","\frac{-450 b x \sinh (a+b x)+75 b x \sinh (3 (a+b x))+45 b x \sinh (5 (a+b x))+450 \cosh (a+b x)-25 \cosh (3 (a+b x))-9 \cosh (5 (a+b x))}{3600 b^2}","\frac{\cosh (a+b x)}{8 b^2}-\frac{\cosh (3 a+3 b x)}{144 b^2}-\frac{\cosh (5 a+5 b x)}{400 b^2}-\frac{x \sinh (a+b x)}{8 b}+\frac{x \sinh (3 a+3 b x)}{48 b}+\frac{x \sinh (5 a+5 b x)}{80 b}",1,"(450*Cosh[a + b*x] - 25*Cosh[3*(a + b*x)] - 9*Cosh[5*(a + b*x)] - 450*b*x*Sinh[a + b*x] + 75*b*x*Sinh[3*(a + b*x)] + 45*b*x*Sinh[5*(a + b*x)])/(3600*b^2)","A",1
302,1,27,31,0.0617934,"\int \cosh ^3(a+b x) \sinh ^2(a+b x) \, dx","Integrate[Cosh[a + b*x]^3*Sinh[a + b*x]^2,x]","\frac{\sinh ^3(a+b x) (3 \cosh (2 (a+b x))+7)}{30 b}","\frac{\sinh ^5(a+b x)}{5 b}+\frac{\sinh ^3(a+b x)}{3 b}",1,"((7 + 3*Cosh[2*(a + b*x)])*Sinh[a + b*x]^3)/(30*b)","A",1
303,1,61,73,0.1104677,"\int \frac{\cosh ^3(a+b x) \sinh ^2(a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x]^2)/x,x]","\frac{1}{16} (-2 \cosh (a) \text{Chi}(b x)+\cosh (3 a) \text{Chi}(3 b x)+\cosh (5 a) \text{Chi}(5 b x)-2 \sinh (a) \text{Shi}(b x)+\sinh (3 a) \text{Shi}(3 b x)+\sinh (5 a) \text{Shi}(5 b x))","-\frac{1}{8} \cosh (a) \text{Chi}(b x)+\frac{1}{16} \cosh (3 a) \text{Chi}(3 b x)+\frac{1}{16} \cosh (5 a) \text{Chi}(5 b x)-\frac{1}{8} \sinh (a) \text{Shi}(b x)+\frac{1}{16} \sinh (3 a) \text{Shi}(3 b x)+\frac{1}{16} \sinh (5 a) \text{Shi}(5 b x)",1,"(-2*Cosh[a]*CoshIntegral[b*x] + Cosh[3*a]*CoshIntegral[3*b*x] + Cosh[5*a]*CoshIntegral[5*b*x] - 2*Sinh[a]*SinhIntegral[b*x] + Sinh[3*a]*SinhIntegral[3*b*x] + Sinh[5*a]*SinhIntegral[5*b*x])/16","A",1
304,1,104,124,0.3647582,"\int \frac{\cosh ^3(a+b x) \sinh ^2(a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x]^2)/x^2,x]","-\frac{2 b x \sinh (a) \text{Chi}(b x)-3 b x \sinh (3 a) \text{Chi}(3 b x)-5 b x \sinh (5 a) \text{Chi}(5 b x)+2 b x \cosh (a) \text{Shi}(b x)-3 b x \cosh (3 a) \text{Shi}(3 b x)-5 b x \cosh (5 a) \text{Shi}(5 b x)-2 \cosh (a+b x)+\cosh (3 (a+b x))+\cosh (5 (a+b x))}{16 x}","-\frac{1}{8} b \sinh (a) \text{Chi}(b x)+\frac{3}{16} b \sinh (3 a) \text{Chi}(3 b x)+\frac{5}{16} b \sinh (5 a) \text{Chi}(5 b x)-\frac{1}{8} b \cosh (a) \text{Shi}(b x)+\frac{3}{16} b \cosh (3 a) \text{Shi}(3 b x)+\frac{5}{16} b \cosh (5 a) \text{Shi}(5 b x)+\frac{\cosh (a+b x)}{8 x}-\frac{\cosh (3 a+3 b x)}{16 x}-\frac{\cosh (5 a+5 b x)}{16 x}",1,"-1/16*(-2*Cosh[a + b*x] + Cosh[3*(a + b*x)] + Cosh[5*(a + b*x)] + 2*b*x*CoshIntegral[b*x]*Sinh[a] - 3*b*x*CoshIntegral[3*b*x]*Sinh[3*a] - 5*b*x*CoshIntegral[5*b*x]*Sinh[5*a] + 2*b*x*Cosh[a]*SinhIntegral[b*x] - 3*b*x*Cosh[3*a]*SinhIntegral[3*b*x] - 5*b*x*Cosh[5*a]*SinhIntegral[5*b*x])/x","A",1
305,1,162,184,0.5553981,"\int \frac{\cosh ^3(a+b x) \sinh ^2(a+b x)}{x^3} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x]^2)/x^3,x]","-\frac{2 b^2 x^2 \cosh (a) \text{Chi}(b x)-9 b^2 x^2 \cosh (3 a) \text{Chi}(3 b x)-25 b^2 x^2 \cosh (5 a) \text{Chi}(5 b x)+2 b^2 x^2 \sinh (a) \text{Shi}(b x)-9 b^2 x^2 \sinh (3 a) \text{Shi}(3 b x)-25 b^2 x^2 \sinh (5 a) \text{Shi}(5 b x)-2 b x \sinh (a+b x)+3 b x \sinh (3 (a+b x))+5 b x \sinh (5 (a+b x))-2 \cosh (a+b x)+\cosh (3 (a+b x))+\cosh (5 (a+b x))}{32 x^2}","-\frac{1}{16} b^2 \cosh (a) \text{Chi}(b x)+\frac{9}{32} b^2 \cosh (3 a) \text{Chi}(3 b x)+\frac{25}{32} b^2 \cosh (5 a) \text{Chi}(5 b x)-\frac{1}{16} b^2 \sinh (a) \text{Shi}(b x)+\frac{9}{32} b^2 \sinh (3 a) \text{Shi}(3 b x)+\frac{25}{32} b^2 \sinh (5 a) \text{Shi}(5 b x)+\frac{\cosh (a+b x)}{16 x^2}-\frac{\cosh (3 a+3 b x)}{32 x^2}-\frac{\cosh (5 a+5 b x)}{32 x^2}+\frac{b \sinh (a+b x)}{16 x}-\frac{3 b \sinh (3 a+3 b x)}{32 x}-\frac{5 b \sinh (5 a+5 b x)}{32 x}",1,"-1/32*(-2*Cosh[a + b*x] + Cosh[3*(a + b*x)] + Cosh[5*(a + b*x)] + 2*b^2*x^2*Cosh[a]*CoshIntegral[b*x] - 9*b^2*x^2*Cosh[3*a]*CoshIntegral[3*b*x] - 25*b^2*x^2*Cosh[5*a]*CoshIntegral[5*b*x] - 2*b*x*Sinh[a + b*x] + 3*b*x*Sinh[3*(a + b*x)] + 5*b*x*Sinh[5*(a + b*x)] + 2*b^2*x^2*Sinh[a]*SinhIntegral[b*x] - 9*b^2*x^2*Sinh[3*a]*SinhIntegral[3*b*x] - 25*b^2*x^2*Sinh[5*a]*SinhIntegral[5*b*x])/x^2","A",1
306,1,212,238,0.5613016,"\int \frac{\cosh ^3(a+b x) \sinh ^2(a+b x)}{x^4} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x]^2)/x^4,x]","\frac{-2 b^3 x^3 \sinh (a) \text{Chi}(b x)+27 b^3 x^3 \sinh (3 a) \text{Chi}(3 b x)+125 b^3 x^3 \sinh (5 a) \text{Chi}(5 b x)-2 b^3 x^3 \cosh (a) \text{Shi}(b x)+27 b^3 x^3 \cosh (3 a) \text{Shi}(3 b x)+125 b^3 x^3 \cosh (5 a) \text{Shi}(5 b x)+2 b^2 x^2 \cosh (a+b x)-9 b^2 x^2 \cosh (3 (a+b x))-25 b^2 x^2 \cosh (5 (a+b x))+2 b x \sinh (a+b x)-3 b x \sinh (3 (a+b x))-5 b x \sinh (5 (a+b x))+4 \cosh (a+b x)-2 \cosh (3 (a+b x))-2 \cosh (5 (a+b x))}{96 x^3}","-\frac{1}{48} b^3 \sinh (a) \text{Chi}(b x)+\frac{9}{32} b^3 \sinh (3 a) \text{Chi}(3 b x)+\frac{125}{96} b^3 \sinh (5 a) \text{Chi}(5 b x)-\frac{1}{48} b^3 \cosh (a) \text{Shi}(b x)+\frac{9}{32} b^3 \cosh (3 a) \text{Shi}(3 b x)+\frac{125}{96} b^3 \cosh (5 a) \text{Shi}(5 b x)+\frac{b^2 \cosh (a+b x)}{48 x}-\frac{3 b^2 \cosh (3 a+3 b x)}{32 x}-\frac{25 b^2 \cosh (5 a+5 b x)}{96 x}+\frac{\cosh (a+b x)}{24 x^3}-\frac{\cosh (3 a+3 b x)}{48 x^3}-\frac{\cosh (5 a+5 b x)}{48 x^3}+\frac{b \sinh (a+b x)}{48 x^2}-\frac{b \sinh (3 a+3 b x)}{32 x^2}-\frac{5 b \sinh (5 a+5 b x)}{96 x^2}",1,"(4*Cosh[a + b*x] + 2*b^2*x^2*Cosh[a + b*x] - 2*Cosh[3*(a + b*x)] - 9*b^2*x^2*Cosh[3*(a + b*x)] - 2*Cosh[5*(a + b*x)] - 25*b^2*x^2*Cosh[5*(a + b*x)] - 2*b^3*x^3*CoshIntegral[b*x]*Sinh[a] + 27*b^3*x^3*CoshIntegral[3*b*x]*Sinh[3*a] + 125*b^3*x^3*CoshIntegral[5*b*x]*Sinh[5*a] + 2*b*x*Sinh[a + b*x] - 3*b*x*Sinh[3*(a + b*x)] - 5*b*x*Sinh[5*(a + b*x)] - 2*b^3*x^3*Cosh[a]*SinhIntegral[b*x] + 27*b^3*x^3*Cosh[3*a]*SinhIntegral[3*b*x] + 125*b^3*x^3*Cosh[5*a]*SinhIntegral[5*b*x])/(96*x^3)","A",1
307,1,112,141,0.1406503,"\int x^m \cosh (a+b x) \sinh ^3(a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]*Sinh[a + b*x]^3,x]","\frac{e^{-4 a} 4^{-m-3} x^m \left(-b^2 x^2\right)^{-m} \left((-b x)^m \left(\Gamma (m+1,4 b x)-e^{2 a} 2^{m+2} \Gamma (m+1,2 b x)\right)+e^{8 a} (b x)^m \Gamma (m+1,-4 b x)-e^{6 a} 2^{m+2} (b x)^m \Gamma (m+1,-2 b x)\right)}{b}","\frac{e^{4 a} 2^{-2 (m+3)} x^m (-b x)^{-m} \Gamma (m+1,-4 b x)}{b}-\frac{e^{2 a} 2^{-m-4} x^m (-b x)^{-m} \Gamma (m+1,-2 b x)}{b}-\frac{e^{-2 a} 2^{-m-4} x^m (b x)^{-m} \Gamma (m+1,2 b x)}{b}+\frac{e^{-4 a} 2^{-2 (m+3)} x^m (b x)^{-m} \Gamma (m+1,4 b x)}{b}",1,"(4^(-3 - m)*x^m*(E^(8*a)*(b*x)^m*Gamma[1 + m, -4*b*x] - 2^(2 + m)*E^(6*a)*(b*x)^m*Gamma[1 + m, -2*b*x] + (-(b*x))^m*(-(2^(2 + m)*E^(2*a)*Gamma[1 + m, 2*b*x]) + Gamma[1 + m, 4*b*x])))/(b*E^(4*a)*(-(b^2*x^2))^m)","A",1
308,1,95,155,0.6569062,"\int x^3 \cosh (a+b x) \sinh ^3(a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]*Sinh[a + b*x]^3,x]","\frac{48 \left(2 b^2 x^2+1\right) \sinh (2 (a+b x))+2 b x \left(8 b^2 x^2+3\right) \cosh (4 (a+b x))-\left(3 \left(8 b^2 x^2+1\right) \sinh (2 (a+b x))+32 b x \left(2 b^2 x^2+3\right)\right) \cosh (2 (a+b x))}{512 b^4}","-\frac{3 \sinh ^3(a+b x) \cosh (a+b x)}{128 b^4}+\frac{45 \sinh (a+b x) \cosh (a+b x)}{256 b^4}+\frac{3 x \sinh ^4(a+b x)}{32 b^3}-\frac{9 x \sinh ^2(a+b x)}{32 b^3}-\frac{3 x^2 \sinh ^3(a+b x) \cosh (a+b x)}{16 b^2}+\frac{9 x^2 \sinh (a+b x) \cosh (a+b x)}{32 b^2}+\frac{x^3 \sinh ^4(a+b x)}{4 b}-\frac{45 x}{256 b^3}-\frac{3 x^3}{32 b}",1,"(2*b*x*(3 + 8*b^2*x^2)*Cosh[4*(a + b*x)] + 48*(1 + 2*b^2*x^2)*Sinh[2*(a + b*x)] - Cosh[2*(a + b*x)]*(32*b*x*(3 + 2*b^2*x^2) + 3*(1 + 8*b^2*x^2)*Sinh[2*(a + b*x)]))/(512*b^4)","A",1
309,1,72,101,0.2333625,"\int x^2 \cosh (a+b x) \sinh ^3(a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]*Sinh[a + b*x]^3,x]","\frac{-16 \left(2 b^2 x^2+1\right) \cosh (2 (a+b x))+\left(8 b^2 x^2+1\right) \cosh (4 (a+b x))+4 b x (8 \sinh (2 (a+b x))-\sinh (4 (a+b x)))}{256 b^3}","\frac{\sinh ^4(a+b x)}{32 b^3}-\frac{3 \sinh ^2(a+b x)}{32 b^3}-\frac{x \sinh ^3(a+b x) \cosh (a+b x)}{8 b^2}+\frac{3 x \sinh (a+b x) \cosh (a+b x)}{16 b^2}+\frac{x^2 \sinh ^4(a+b x)}{4 b}-\frac{3 x^2}{32 b}",1,"(-16*(1 + 2*b^2*x^2)*Cosh[2*(a + b*x)] + (1 + 8*b^2*x^2)*Cosh[4*(a + b*x)] + 4*b*x*(8*Sinh[2*(a + b*x)] - Sinh[4*(a + b*x)]))/(256*b^3)","A",1
310,1,50,65,0.1631889,"\int x \cosh (a+b x) \sinh ^3(a+b x) \, dx","Integrate[x*Cosh[a + b*x]*Sinh[a + b*x]^3,x]","-\frac{-8 \sinh (2 (a+b x))+\sinh (4 (a+b x))+16 b x \cosh (2 (a+b x))-4 b x \cosh (4 (a+b x))}{128 b^2}","-\frac{\sinh ^3(a+b x) \cosh (a+b x)}{16 b^2}+\frac{3 \sinh (a+b x) \cosh (a+b x)}{32 b^2}+\frac{x \sinh ^4(a+b x)}{4 b}-\frac{3 x}{32 b}",1,"-1/128*(16*b*x*Cosh[2*(a + b*x)] - 4*b*x*Cosh[4*(a + b*x)] - 8*Sinh[2*(a + b*x)] + Sinh[4*(a + b*x)])/b^2","A",1
311,1,15,15,0.0027764,"\int \cosh (a+b x) \sinh ^3(a+b x) \, dx","Integrate[Cosh[a + b*x]*Sinh[a + b*x]^3,x]","\frac{\sinh ^4(a+b x)}{4 b}","\frac{\sinh ^4(a+b x)}{4 b}",1,"Sinh[a + b*x]^4/(4*b)","A",1
312,1,47,53,0.0826087,"\int \frac{\cosh (a+b x) \sinh ^3(a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x]^3)/x,x]","\frac{1}{8} (-2 \sinh (2 a) \text{Chi}(2 b x)+\sinh (4 a) \text{Chi}(4 b x)-2 \cosh (2 a) \text{Shi}(2 b x)+\cosh (4 a) \text{Shi}(4 b x))","-\frac{1}{4} \sinh (2 a) \text{Chi}(2 b x)+\frac{1}{8} \sinh (4 a) \text{Chi}(4 b x)-\frac{1}{4} \cosh (2 a) \text{Shi}(2 b x)+\frac{1}{8} \cosh (4 a) \text{Shi}(4 b x)",1,"(-2*CoshIntegral[2*b*x]*Sinh[2*a] + CoshIntegral[4*b*x]*Sinh[4*a] - 2*Cosh[2*a]*SinhIntegral[2*b*x] + Cosh[4*a]*SinhIntegral[4*b*x])/8","A",1
313,1,78,89,0.2512941,"\int \frac{\cosh (a+b x) \sinh ^3(a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x]^3)/x^2,x]","-\frac{4 b x \cosh (2 a) \text{Chi}(2 b x)-4 b x \cosh (4 a) \text{Chi}(4 b x)+4 b x \sinh (2 a) \text{Shi}(2 b x)-4 b x \sinh (4 a) \text{Shi}(4 b x)-2 \sinh (2 (a+b x))+\sinh (4 (a+b x))}{8 x}","-\frac{1}{2} b \cosh (2 a) \text{Chi}(2 b x)+\frac{1}{2} b \cosh (4 a) \text{Chi}(4 b x)-\frac{1}{2} b \sinh (2 a) \text{Shi}(2 b x)+\frac{1}{2} b \sinh (4 a) \text{Shi}(4 b x)+\frac{\sinh (2 a+2 b x)}{4 x}-\frac{\sinh (4 a+4 b x)}{8 x}",1,"-1/8*(4*b*x*Cosh[2*a]*CoshIntegral[2*b*x] - 4*b*x*Cosh[4*a]*CoshIntegral[4*b*x] - 2*Sinh[2*(a + b*x)] + Sinh[4*(a + b*x)] + 4*b*x*Sinh[2*a]*SinhIntegral[2*b*x] - 4*b*x*Sinh[4*a]*SinhIntegral[4*b*x])/x","A",1
314,1,113,125,0.5615362,"\int \frac{\cosh (a+b x) \sinh ^3(a+b x)}{x^3} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x]^3)/x^3,x]","b^2 \sinh (4 a) \text{Chi}(4 b x)+b^2 \sinh (a) (-\cosh (a)) \text{Chi}(2 b x)-\frac{1}{2} b^2 \cosh (2 a) \text{Shi}(2 b x)+b^2 \cosh (4 a) \text{Shi}(4 b x)+\frac{\sinh (2 (a+b x))+2 b x \cosh (2 (a+b x))}{8 x^2}-\frac{\sinh (4 (a+b x))+4 b x \cosh (4 (a+b x))}{16 x^2}","-\frac{1}{2} b^2 \sinh (2 a) \text{Chi}(2 b x)+b^2 \sinh (4 a) \text{Chi}(4 b x)-\frac{1}{2} b^2 \cosh (2 a) \text{Shi}(2 b x)+b^2 \cosh (4 a) \text{Shi}(4 b x)+\frac{\sinh (2 a+2 b x)}{8 x^2}-\frac{\sinh (4 a+4 b x)}{16 x^2}+\frac{b \cosh (2 a+2 b x)}{4 x}-\frac{b \cosh (4 a+4 b x)}{4 x}",1,"-(b^2*Cosh[a]*CoshIntegral[2*b*x]*Sinh[a]) + b^2*CoshIntegral[4*b*x]*Sinh[4*a] + (2*b*x*Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)])/(8*x^2) - (4*b*x*Cosh[4*(a + b*x)] + Sinh[4*(a + b*x)])/(16*x^2) - (b^2*Cosh[2*a]*SinhIntegral[2*b*x])/2 + b^2*Cosh[4*a]*SinhIntegral[4*b*x]","A",1
315,1,150,169,0.5608606,"\int \frac{\cosh (a+b x) \sinh ^3(a+b x)}{x^4} \, dx","Integrate[(Cosh[a + b*x]*Sinh[a + b*x]^3)/x^4,x]","-\frac{8 b^3 x^3 \cosh (2 a) \text{Chi}(2 b x)-32 b^3 x^3 \cosh (4 a) \text{Chi}(4 b x)+8 b^3 x^3 \sinh (2 a) \text{Shi}(2 b x)-32 b^3 x^3 \sinh (4 a) \text{Shi}(4 b x)-4 b^2 x^2 \sinh (2 (a+b x))+8 b^2 x^2 \sinh (4 (a+b x))-2 \sinh (2 (a+b x))+\sinh (4 (a+b x))-2 b x \cosh (2 (a+b x))+2 b x \cosh (4 (a+b x))}{24 x^3}","-\frac{1}{3} b^3 \cosh (2 a) \text{Chi}(2 b x)+\frac{4}{3} b^3 \cosh (4 a) \text{Chi}(4 b x)-\frac{1}{3} b^3 \sinh (2 a) \text{Shi}(2 b x)+\frac{4}{3} b^3 \sinh (4 a) \text{Shi}(4 b x)+\frac{b^2 \sinh (2 a+2 b x)}{6 x}-\frac{b^2 \sinh (4 a+4 b x)}{3 x}+\frac{\sinh (2 a+2 b x)}{12 x^3}-\frac{\sinh (4 a+4 b x)}{24 x^3}+\frac{b \cosh (2 a+2 b x)}{12 x^2}-\frac{b \cosh (4 a+4 b x)}{12 x^2}",1,"-1/24*(-2*b*x*Cosh[2*(a + b*x)] + 2*b*x*Cosh[4*(a + b*x)] + 8*b^3*x^3*Cosh[2*a]*CoshIntegral[2*b*x] - 32*b^3*x^3*Cosh[4*a]*CoshIntegral[4*b*x] - 2*Sinh[2*(a + b*x)] - 4*b^2*x^2*Sinh[2*(a + b*x)] + Sinh[4*(a + b*x)] + 8*b^2*x^2*Sinh[4*(a + b*x)] + 8*b^3*x^3*Sinh[2*a]*SinhIntegral[2*b*x] - 32*b^3*x^3*Sinh[4*a]*SinhIntegral[4*b*x])/x^3","A",1
316,1,174,209,0.272783,"\int x^m \cosh ^2(a+b x) \sinh ^3(a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]^2*Sinh[a + b*x]^3,x]","\frac{e^{-5 a} x^m \left(-5 e^{2 a} 3^{-m} \left(-b^2 x^2\right)^{-m} \left(e^{6 a} (b x)^m \Gamma (m+1,-3 b x)+(-b x)^m \Gamma (m+1,3 b x)\right)+3\ 5^{-m} \left(-b^2 x^2\right)^{-m} \left(e^{10 a} (b x)^m \Gamma (m+1,-5 b x)+(-b x)^m \Gamma (m+1,5 b x)\right)-30 e^{4 a} \left(e^{2 a} (-b x)^{-m} \Gamma (m+1,-b x)+(b x)^{-m} \Gamma (m+1,b x)\right)\right)}{480 b}","\frac{e^{5 a} 5^{-m-1} x^m (-b x)^{-m} \Gamma (m+1,-5 b x)}{32 b}-\frac{e^{3 a} 3^{-m-1} x^m (-b x)^{-m} \Gamma (m+1,-3 b x)}{32 b}-\frac{e^a x^m (-b x)^{-m} \Gamma (m+1,-b x)}{16 b}-\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+1,b x)}{16 b}-\frac{e^{-3 a} 3^{-m-1} x^m (b x)^{-m} \Gamma (m+1,3 b x)}{32 b}+\frac{e^{-5 a} 5^{-m-1} x^m (b x)^{-m} \Gamma (m+1,5 b x)}{32 b}",1,"(x^m*(-30*E^(4*a)*((E^(2*a)*Gamma[1 + m, -(b*x)])/(-(b*x))^m + Gamma[1 + m, b*x]/(b*x)^m) - (5*E^(2*a)*(E^(6*a)*(b*x)^m*Gamma[1 + m, -3*b*x] + (-(b*x))^m*Gamma[1 + m, 3*b*x]))/(3^m*(-(b^2*x^2))^m) + (3*(E^(10*a)*(b*x)^m*Gamma[1 + m, -5*b*x] + (-(b*x))^m*Gamma[1 + m, 5*b*x]))/(5^m*(-(b^2*x^2))^m)))/(480*b*E^(5*a))","A",1
317,1,136,202,0.5124462,"\int x^3 \cosh ^2(a+b x) \sinh ^3(a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]^2*Sinh[a + b*x]^3,x]","\frac{-33750 \left(b x \left(b^2 x^2+6\right) \cosh (a+b x)-3 \left(b^2 x^2+2\right) \sinh (a+b x)\right)+27 \left(5 b x \left(25 b^2 x^2+6\right) \cosh (5 (a+b x))-3 \left(25 b^2 x^2+2\right) \sinh (5 (a+b x))\right)-625 \left(\left(9 b^3 x^3+6 b x\right) \cosh (3 (a+b x))-\left(9 b^2 x^2+2\right) \sinh (3 (a+b x))\right)}{270000 b^4}","\frac{3 \sinh (a+b x)}{4 b^4}+\frac{\sinh (3 a+3 b x)}{216 b^4}-\frac{3 \sinh (5 a+5 b x)}{5000 b^4}-\frac{3 x \cosh (a+b x)}{4 b^3}-\frac{x \cosh (3 a+3 b x)}{72 b^3}+\frac{3 x \cosh (5 a+5 b x)}{1000 b^3}+\frac{3 x^2 \sinh (a+b x)}{8 b^2}+\frac{x^2 \sinh (3 a+3 b x)}{48 b^2}-\frac{3 x^2 \sinh (5 a+5 b x)}{400 b^2}-\frac{x^3 \cosh (a+b x)}{8 b}-\frac{x^3 \cosh (3 a+3 b x)}{48 b}+\frac{x^3 \cosh (5 a+5 b x)}{80 b}",1,"(-33750*(b*x*(6 + b^2*x^2)*Cosh[a + b*x] - 3*(2 + b^2*x^2)*Sinh[a + b*x]) - 625*((6*b*x + 9*b^3*x^3)*Cosh[3*(a + b*x)] - (2 + 9*b^2*x^2)*Sinh[3*(a + b*x)]) + 27*(5*b*x*(6 + 25*b^2*x^2)*Cosh[5*(a + b*x)] - 3*(2 + 25*b^2*x^2)*Sinh[5*(a + b*x)]))/(270000*b^4)","A",1
318,1,98,148,0.4560227,"\int x^2 \cosh ^2(a+b x) \sinh ^3(a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]^2*Sinh[a + b*x]^3,x]","\frac{-6750 \left(b^2 x^2+2\right) \cosh (a+b x)-125 \left(9 b^2 x^2+2\right) \cosh (3 (a+b x))+27 \left(25 b^2 x^2+2\right) \cosh (5 (a+b x))+30 b x (450 \sinh (a+b x)+25 \sinh (3 (a+b x))-9 \sinh (5 (a+b x)))}{54000 b^3}","-\frac{\cosh (a+b x)}{4 b^3}-\frac{\cosh (3 a+3 b x)}{216 b^3}+\frac{\cosh (5 a+5 b x)}{1000 b^3}+\frac{x \sinh (a+b x)}{4 b^2}+\frac{x \sinh (3 a+3 b x)}{72 b^2}-\frac{x \sinh (5 a+5 b x)}{200 b^2}-\frac{x^2 \cosh (a+b x)}{8 b}-\frac{x^2 \cosh (3 a+3 b x)}{48 b}+\frac{x^2 \cosh (5 a+5 b x)}{80 b}",1,"(-6750*(2 + b^2*x^2)*Cosh[a + b*x] - 125*(2 + 9*b^2*x^2)*Cosh[3*(a + b*x)] + 27*(2 + 25*b^2*x^2)*Cosh[5*(a + b*x)] + 30*b*x*(450*Sinh[a + b*x] + 25*Sinh[3*(a + b*x)] - 9*Sinh[5*(a + b*x)]))/(54000*b^3)","A",1
319,1,70,94,0.1934628,"\int x \cosh ^2(a+b x) \sinh ^3(a+b x) \, dx","Integrate[x*Cosh[a + b*x]^2*Sinh[a + b*x]^3,x]","\frac{450 \sinh (a+b x)+25 \sinh (3 (a+b x))-9 \sinh (5 (a+b x))-450 b x \cosh (a+b x)-75 b x \cosh (3 (a+b x))+45 b x \cosh (5 (a+b x))}{3600 b^2}","\frac{\sinh (a+b x)}{8 b^2}+\frac{\sinh (3 a+3 b x)}{144 b^2}-\frac{\sinh (5 a+5 b x)}{400 b^2}-\frac{x \cosh (a+b x)}{8 b}-\frac{x \cosh (3 a+3 b x)}{48 b}+\frac{x \cosh (5 a+5 b x)}{80 b}",1,"(-450*b*x*Cosh[a + b*x] - 75*b*x*Cosh[3*(a + b*x)] + 45*b*x*Cosh[5*(a + b*x)] + 450*Sinh[a + b*x] + 25*Sinh[3*(a + b*x)] - 9*Sinh[5*(a + b*x)])/(3600*b^2)","A",1
320,1,27,31,0.0714789,"\int \cosh ^2(a+b x) \sinh ^3(a+b x) \, dx","Integrate[Cosh[a + b*x]^2*Sinh[a + b*x]^3,x]","\frac{\cosh ^3(a+b x) (3 \cosh (2 (a+b x))-7)}{30 b}","\frac{\cosh ^5(a+b x)}{5 b}-\frac{\cosh ^3(a+b x)}{3 b}",1,"(Cosh[a + b*x]^3*(-7 + 3*Cosh[2*(a + b*x)]))/(30*b)","A",1
321,1,63,73,0.1152387,"\int \frac{\cosh ^2(a+b x) \sinh ^3(a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x]^3)/x,x]","\frac{1}{16} (-2 \sinh (a) \text{Chi}(b x)-\sinh (3 a) \text{Chi}(3 b x)+\sinh (5 a) \text{Chi}(5 b x)-2 \cosh (a) \text{Shi}(b x)-\cosh (3 a) \text{Shi}(3 b x)+\cosh (5 a) \text{Shi}(5 b x))","-\frac{1}{8} \sinh (a) \text{Chi}(b x)-\frac{1}{16} \sinh (3 a) \text{Chi}(3 b x)+\frac{1}{16} \sinh (5 a) \text{Chi}(5 b x)-\frac{1}{8} \cosh (a) \text{Shi}(b x)-\frac{1}{16} \cosh (3 a) \text{Shi}(3 b x)+\frac{1}{16} \cosh (5 a) \text{Shi}(5 b x)",1,"(-2*CoshIntegral[b*x]*Sinh[a] - CoshIntegral[3*b*x]*Sinh[3*a] + CoshIntegral[5*b*x]*Sinh[5*a] - 2*Cosh[a]*SinhIntegral[b*x] - Cosh[3*a]*SinhIntegral[3*b*x] + Cosh[5*a]*SinhIntegral[5*b*x])/16","A",1
322,1,106,124,0.271086,"\int \frac{\cosh ^2(a+b x) \sinh ^3(a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x]^3)/x^2,x]","\frac{-2 b x \cosh (a) \text{Chi}(b x)-3 b x \cosh (3 a) \text{Chi}(3 b x)+5 b x \cosh (5 a) \text{Chi}(5 b x)-2 b x \sinh (a) \text{Shi}(b x)-3 b x \sinh (3 a) \text{Shi}(3 b x)+5 b x \sinh (5 a) \text{Shi}(5 b x)+2 \sinh (a+b x)+\sinh (3 (a+b x))-\sinh (5 (a+b x))}{16 x}","-\frac{1}{8} b \cosh (a) \text{Chi}(b x)-\frac{3}{16} b \cosh (3 a) \text{Chi}(3 b x)+\frac{5}{16} b \cosh (5 a) \text{Chi}(5 b x)-\frac{1}{8} b \sinh (a) \text{Shi}(b x)-\frac{3}{16} b \sinh (3 a) \text{Shi}(3 b x)+\frac{5}{16} b \sinh (5 a) \text{Shi}(5 b x)+\frac{\sinh (a+b x)}{8 x}+\frac{\sinh (3 a+3 b x)}{16 x}-\frac{\sinh (5 a+5 b x)}{16 x}",1,"(-2*b*x*Cosh[a]*CoshIntegral[b*x] - 3*b*x*Cosh[3*a]*CoshIntegral[3*b*x] + 5*b*x*Cosh[5*a]*CoshIntegral[5*b*x] + 2*Sinh[a + b*x] + Sinh[3*(a + b*x)] - Sinh[5*(a + b*x)] - 2*b*x*Sinh[a]*SinhIntegral[b*x] - 3*b*x*Sinh[3*a]*SinhIntegral[3*b*x] + 5*b*x*Sinh[5*a]*SinhIntegral[5*b*x])/(16*x)","A",1
323,1,164,184,0.4241467,"\int \frac{\cosh ^2(a+b x) \sinh ^3(a+b x)}{x^3} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x]^3)/x^3,x]","\frac{-2 b^2 x^2 \sinh (a) \text{Chi}(b x)-9 b^2 x^2 \sinh (3 a) \text{Chi}(3 b x)+25 b^2 x^2 \sinh (5 a) \text{Chi}(5 b x)-2 b^2 x^2 \cosh (a) \text{Shi}(b x)-9 b^2 x^2 \cosh (3 a) \text{Shi}(3 b x)+25 b^2 x^2 \cosh (5 a) \text{Shi}(5 b x)+2 \sinh (a+b x)+\sinh (3 (a+b x))-\sinh (5 (a+b x))+2 b x \cosh (a+b x)+3 b x \cosh (3 (a+b x))-5 b x \cosh (5 (a+b x))}{32 x^2}","-\frac{1}{16} b^2 \sinh (a) \text{Chi}(b x)-\frac{9}{32} b^2 \sinh (3 a) \text{Chi}(3 b x)+\frac{25}{32} b^2 \sinh (5 a) \text{Chi}(5 b x)-\frac{1}{16} b^2 \cosh (a) \text{Shi}(b x)-\frac{9}{32} b^2 \cosh (3 a) \text{Shi}(3 b x)+\frac{25}{32} b^2 \cosh (5 a) \text{Shi}(5 b x)+\frac{\sinh (a+b x)}{16 x^2}+\frac{\sinh (3 a+3 b x)}{32 x^2}-\frac{\sinh (5 a+5 b x)}{32 x^2}+\frac{b \cosh (a+b x)}{16 x}+\frac{3 b \cosh (3 a+3 b x)}{32 x}-\frac{5 b \cosh (5 a+5 b x)}{32 x}",1,"(2*b*x*Cosh[a + b*x] + 3*b*x*Cosh[3*(a + b*x)] - 5*b*x*Cosh[5*(a + b*x)] - 2*b^2*x^2*CoshIntegral[b*x]*Sinh[a] - 9*b^2*x^2*CoshIntegral[3*b*x]*Sinh[3*a] + 25*b^2*x^2*CoshIntegral[5*b*x]*Sinh[5*a] + 2*Sinh[a + b*x] + Sinh[3*(a + b*x)] - Sinh[5*(a + b*x)] - 2*b^2*x^2*Cosh[a]*SinhIntegral[b*x] - 9*b^2*x^2*Cosh[3*a]*SinhIntegral[3*b*x] + 25*b^2*x^2*Cosh[5*a]*SinhIntegral[5*b*x])/(32*x^2)","A",1
324,1,212,238,0.5140223,"\int \frac{\cosh ^2(a+b x) \sinh ^3(a+b x)}{x^4} \, dx","Integrate[(Cosh[a + b*x]^2*Sinh[a + b*x]^3)/x^4,x]","\frac{-2 b^3 x^3 \cosh (a) \text{Chi}(b x)-27 b^3 x^3 \cosh (3 a) \text{Chi}(3 b x)+125 b^3 x^3 \cosh (5 a) \text{Chi}(5 b x)-2 b^3 x^3 \sinh (a) \text{Shi}(b x)-27 b^3 x^3 \sinh (3 a) \text{Shi}(3 b x)+125 b^3 x^3 \sinh (5 a) \text{Shi}(5 b x)+2 b^2 x^2 \sinh (a+b x)+9 b^2 x^2 \sinh (3 (a+b x))-25 b^2 x^2 \sinh (5 (a+b x))+4 \sinh (a+b x)+2 \sinh (3 (a+b x))-2 \sinh (5 (a+b x))+2 b x \cosh (a+b x)+3 b x \cosh (3 (a+b x))-5 b x \cosh (5 (a+b x))}{96 x^3}","-\frac{1}{48} b^3 \cosh (a) \text{Chi}(b x)-\frac{9}{32} b^3 \cosh (3 a) \text{Chi}(3 b x)+\frac{125}{96} b^3 \cosh (5 a) \text{Chi}(5 b x)-\frac{1}{48} b^3 \sinh (a) \text{Shi}(b x)-\frac{9}{32} b^3 \sinh (3 a) \text{Shi}(3 b x)+\frac{125}{96} b^3 \sinh (5 a) \text{Shi}(5 b x)+\frac{b^2 \sinh (a+b x)}{48 x}+\frac{3 b^2 \sinh (3 a+3 b x)}{32 x}-\frac{25 b^2 \sinh (5 a+5 b x)}{96 x}+\frac{\sinh (a+b x)}{24 x^3}+\frac{\sinh (3 a+3 b x)}{48 x^3}-\frac{\sinh (5 a+5 b x)}{48 x^3}+\frac{b \cosh (a+b x)}{48 x^2}+\frac{b \cosh (3 a+3 b x)}{32 x^2}-\frac{5 b \cosh (5 a+5 b x)}{96 x^2}",1,"(2*b*x*Cosh[a + b*x] + 3*b*x*Cosh[3*(a + b*x)] - 5*b*x*Cosh[5*(a + b*x)] - 2*b^3*x^3*Cosh[a]*CoshIntegral[b*x] - 27*b^3*x^3*Cosh[3*a]*CoshIntegral[3*b*x] + 125*b^3*x^3*Cosh[5*a]*CoshIntegral[5*b*x] + 4*Sinh[a + b*x] + 2*b^2*x^2*Sinh[a + b*x] + 2*Sinh[3*(a + b*x)] + 9*b^2*x^2*Sinh[3*(a + b*x)] - 2*Sinh[5*(a + b*x)] - 25*b^2*x^2*Sinh[5*(a + b*x)] - 2*b^3*x^3*Sinh[a]*SinhIntegral[b*x] - 27*b^3*x^3*Sinh[3*a]*SinhIntegral[3*b*x] + 125*b^3*x^3*Sinh[5*a]*SinhIntegral[5*b*x])/(96*x^3)","A",1
325,1,119,155,0.1589781,"\int x^m \cosh ^3(a+b x) \sinh ^3(a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]^3*Sinh[a + b*x]^3,x]","\frac{e^{-6 a} 2^{-m-7} 3^{-m-1} x^m \left(-b^2 x^2\right)^{-m} \left((-b x)^m \left(\Gamma (m+1,6 b x)-e^{4 a} 3^{m+2} \Gamma (m+1,2 b x)\right)+e^{12 a} (b x)^m \Gamma (m+1,-6 b x)-e^{8 a} 3^{m+2} (b x)^m \Gamma (m+1,-2 b x)\right)}{b}","\frac{e^{6 a} 2^{-m-7} 3^{-m-1} x^m (-b x)^{-m} \Gamma (m+1,-6 b x)}{b}-\frac{3 e^{2 a} 2^{-m-7} x^m (-b x)^{-m} \Gamma (m+1,-2 b x)}{b}-\frac{3 e^{-2 a} 2^{-m-7} x^m (b x)^{-m} \Gamma (m+1,2 b x)}{b}+\frac{e^{-6 a} 2^{-m-7} 3^{-m-1} x^m (b x)^{-m} \Gamma (m+1,6 b x)}{b}",1,"(2^(-7 - m)*3^(-1 - m)*x^m*(E^(12*a)*(b*x)^m*Gamma[1 + m, -6*b*x] - 3^(2 + m)*E^(8*a)*(b*x)^m*Gamma[1 + m, -2*b*x] + (-(b*x))^m*(-(3^(2 + m)*E^(4*a)*Gamma[1 + m, 2*b*x]) + Gamma[1 + m, 6*b*x])))/(b*E^(6*a)*(-(b^2*x^2))^m)","A",1
326,1,90,143,0.9031084,"\int x^3 \cosh ^3(a+b x) \sinh ^3(a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]^3*Sinh[a + b*x]^3,x]","-\frac{-3 \left(6 b^3 x^3+b x\right) \cosh (6 (a+b x))+81 b x \left(2 b^2 x^2+3\right) \cosh (2 (a+b x))+\sinh (2 (a+b x)) \left(\left(18 b^2 x^2+1\right) \cosh (4 (a+b x))-234 b^2 x^2-121\right)}{3456 b^4}","\frac{9 \sinh (2 a+2 b x)}{256 b^4}-\frac{\sinh (6 a+6 b x)}{6912 b^4}-\frac{9 x \cosh (2 a+2 b x)}{128 b^3}+\frac{x \cosh (6 a+6 b x)}{1152 b^3}+\frac{9 x^2 \sinh (2 a+2 b x)}{128 b^2}-\frac{x^2 \sinh (6 a+6 b x)}{384 b^2}-\frac{3 x^3 \cosh (2 a+2 b x)}{64 b}+\frac{x^3 \cosh (6 a+6 b x)}{192 b}",1,"-1/3456*(81*b*x*(3 + 2*b^2*x^2)*Cosh[2*(a + b*x)] - 3*(b*x + 6*b^3*x^3)*Cosh[6*(a + b*x)] + (-121 - 234*b^2*x^2 + (1 + 18*b^2*x^2)*Cosh[4*(a + b*x)])*Sinh[2*(a + b*x)])/b^4","A",1
327,1,72,105,0.2340076,"\int x^2 \cosh ^3(a+b x) \sinh ^3(a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]^3*Sinh[a + b*x]^3,x]","\frac{-81 \left(2 b^2 x^2+1\right) \cosh (2 (a+b x))+\left(18 b^2 x^2+1\right) \cosh (6 (a+b x))+6 b x (27 \sinh (2 (a+b x))-\sinh (6 (a+b x)))}{3456 b^3}","-\frac{3 \cosh (2 a+2 b x)}{128 b^3}+\frac{\cosh (6 a+6 b x)}{3456 b^3}+\frac{3 x \sinh (2 a+2 b x)}{64 b^2}-\frac{x \sinh (6 a+6 b x)}{576 b^2}-\frac{3 x^2 \cosh (2 a+2 b x)}{64 b}+\frac{x^2 \cosh (6 a+6 b x)}{192 b}",1,"(-81*(1 + 2*b^2*x^2)*Cosh[2*(a + b*x)] + (1 + 18*b^2*x^2)*Cosh[6*(a + b*x)] + 6*b*x*(27*Sinh[2*(a + b*x)] - Sinh[6*(a + b*x)]))/(3456*b^3)","A",1
328,1,50,67,0.1497907,"\int x \cosh ^3(a+b x) \sinh ^3(a+b x) \, dx","Integrate[x*Cosh[a + b*x]^3*Sinh[a + b*x]^3,x]","-\frac{-27 \sinh (2 (a+b x))+\sinh (6 (a+b x))+54 b x \cosh (2 (a+b x))-6 b x \cosh (6 (a+b x))}{1152 b^2}","\frac{3 \sinh (2 a+2 b x)}{128 b^2}-\frac{\sinh (6 a+6 b x)}{1152 b^2}-\frac{3 x \cosh (2 a+2 b x)}{64 b}+\frac{x \cosh (6 a+6 b x)}{192 b}",1,"-1/1152*(54*b*x*Cosh[2*(a + b*x)] - 6*b*x*Cosh[6*(a + b*x)] - 27*Sinh[2*(a + b*x)] + Sinh[6*(a + b*x)])/b^2","A",1
329,1,35,31,0.0120297,"\int \cosh ^3(a+b x) \sinh ^3(a+b x) \, dx","Integrate[Cosh[a + b*x]^3*Sinh[a + b*x]^3,x]","\frac{1}{8} \left(\frac{\cosh (6 (a+b x))}{24 b}-\frac{3 \cosh (2 (a+b x))}{8 b}\right)","\frac{\sinh ^6(a+b x)}{6 b}+\frac{\sinh ^4(a+b x)}{4 b}",1,"((-3*Cosh[2*(a + b*x)])/(8*b) + Cosh[6*(a + b*x)]/(24*b))/8","A",1
330,1,47,53,0.1824311,"\int \frac{\cosh ^3(a+b x) \sinh ^3(a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x]^3)/x,x]","\frac{1}{32} (\sinh (6 a) \text{Chi}(6 b x)-6 \sinh (a) \cosh (a) \text{Chi}(2 b x)-3 \cosh (2 a) \text{Shi}(2 b x)+\cosh (6 a) \text{Shi}(6 b x))","-\frac{3}{32} \sinh (2 a) \text{Chi}(2 b x)+\frac{1}{32} \sinh (6 a) \text{Chi}(6 b x)-\frac{3}{32} \cosh (2 a) \text{Shi}(2 b x)+\frac{1}{32} \cosh (6 a) \text{Shi}(6 b x)",1,"(-6*Cosh[a]*CoshIntegral[2*b*x]*Sinh[a] + CoshIntegral[6*b*x]*Sinh[6*a] - 3*Cosh[2*a]*SinhIntegral[2*b*x] + Cosh[6*a]*SinhIntegral[6*b*x])/32","A",1
331,1,78,89,0.2448816,"\int \frac{\cosh ^3(a+b x) \sinh ^3(a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x]^3)/x^2,x]","-\frac{6 b x \cosh (2 a) \text{Chi}(2 b x)-6 b x \cosh (6 a) \text{Chi}(6 b x)+6 b x \sinh (2 a) \text{Shi}(2 b x)-6 b x \sinh (6 a) \text{Shi}(6 b x)-3 \sinh (2 (a+b x))+\sinh (6 (a+b x))}{32 x}","-\frac{3}{16} b \cosh (2 a) \text{Chi}(2 b x)+\frac{3}{16} b \cosh (6 a) \text{Chi}(6 b x)-\frac{3}{16} b \sinh (2 a) \text{Shi}(2 b x)+\frac{3}{16} b \sinh (6 a) \text{Shi}(6 b x)+\frac{3 \sinh (2 a+2 b x)}{32 x}-\frac{\sinh (6 a+6 b x)}{32 x}",1,"-1/32*(6*b*x*Cosh[2*a]*CoshIntegral[2*b*x] - 6*b*x*Cosh[6*a]*CoshIntegral[6*b*x] - 3*Sinh[2*(a + b*x)] + Sinh[6*(a + b*x)] + 6*b*x*Sinh[2*a]*SinhIntegral[2*b*x] - 6*b*x*Sinh[6*a]*SinhIntegral[6*b*x])/x","A",1
332,1,118,131,0.2497467,"\int \frac{\cosh ^3(a+b x) \sinh ^3(a+b x)}{x^3} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x]^3)/x^3,x]","-\frac{12 b^2 x^2 \sinh (2 a) \text{Chi}(2 b x)-36 b^2 x^2 \sinh (6 a) \text{Chi}(6 b x)+12 b^2 x^2 \cosh (2 a) \text{Shi}(2 b x)-36 b^2 x^2 \cosh (6 a) \text{Shi}(6 b x)-3 \sinh (2 (a+b x))+\sinh (6 (a+b x))-6 b x \cosh (2 (a+b x))+6 b x \cosh (6 (a+b x))}{64 x^2}","-\frac{3}{16} b^2 \sinh (2 a) \text{Chi}(2 b x)+\frac{9}{16} b^2 \sinh (6 a) \text{Chi}(6 b x)-\frac{3}{16} b^2 \cosh (2 a) \text{Shi}(2 b x)+\frac{9}{16} b^2 \cosh (6 a) \text{Shi}(6 b x)+\frac{3 \sinh (2 a+2 b x)}{64 x^2}-\frac{\sinh (6 a+6 b x)}{64 x^2}+\frac{3 b \cosh (2 a+2 b x)}{32 x}-\frac{3 b \cosh (6 a+6 b x)}{32 x}",1,"-1/64*(-6*b*x*Cosh[2*(a + b*x)] + 6*b*x*Cosh[6*(a + b*x)] + 12*b^2*x^2*CoshIntegral[2*b*x]*Sinh[2*a] - 36*b^2*x^2*CoshIntegral[6*b*x]*Sinh[6*a] - 3*Sinh[2*(a + b*x)] + Sinh[6*(a + b*x)] + 12*b^2*x^2*Cosh[2*a]*SinhIntegral[2*b*x] - 36*b^2*x^2*Cosh[6*a]*SinhIntegral[6*b*x])/x^2","A",1
333,1,150,169,0.3378871,"\int \frac{\cosh ^3(a+b x) \sinh ^3(a+b x)}{x^4} \, dx","Integrate[(Cosh[a + b*x]^3*Sinh[a + b*x]^3)/x^4,x]","-\frac{12 b^3 x^3 \cosh (2 a) \text{Chi}(2 b x)-108 b^3 x^3 \cosh (6 a) \text{Chi}(6 b x)+12 b^3 x^3 \sinh (2 a) \text{Shi}(2 b x)-108 b^3 x^3 \sinh (6 a) \text{Shi}(6 b x)-6 b^2 x^2 \sinh (2 (a+b x))+18 b^2 x^2 \sinh (6 (a+b x))-3 \sinh (2 (a+b x))+\sinh (6 (a+b x))-3 b x \cosh (2 (a+b x))+3 b x \cosh (6 (a+b x))}{96 x^3}","-\frac{1}{8} b^3 \cosh (2 a) \text{Chi}(2 b x)+\frac{9}{8} b^3 \cosh (6 a) \text{Chi}(6 b x)-\frac{1}{8} b^3 \sinh (2 a) \text{Shi}(2 b x)+\frac{9}{8} b^3 \sinh (6 a) \text{Shi}(6 b x)+\frac{b^2 \sinh (2 a+2 b x)}{16 x}-\frac{3 b^2 \sinh (6 a+6 b x)}{16 x}+\frac{\sinh (2 a+2 b x)}{32 x^3}-\frac{\sinh (6 a+6 b x)}{96 x^3}+\frac{b \cosh (2 a+2 b x)}{32 x^2}-\frac{b \cosh (6 a+6 b x)}{32 x^2}",1,"-1/96*(-3*b*x*Cosh[2*(a + b*x)] + 3*b*x*Cosh[6*(a + b*x)] + 12*b^3*x^3*Cosh[2*a]*CoshIntegral[2*b*x] - 108*b^3*x^3*Cosh[6*a]*CoshIntegral[6*b*x] - 3*Sinh[2*(a + b*x)] - 6*b^2*x^2*Sinh[2*(a + b*x)] + Sinh[6*(a + b*x)] + 18*b^2*x^2*Sinh[6*(a + b*x)] + 12*b^3*x^3*Sinh[2*a]*SinhIntegral[2*b*x] - 108*b^3*x^3*Sinh[6*a]*SinhIntegral[6*b*x])/x^3","A",1
334,0,0,13,0.4785701,"\int x^m \tanh (a+b x) \, dx","Integrate[x^m*Tanh[a + b*x],x]","\int x^m \tanh (a+b x) \, dx","\text{Int}\left(x^m \tanh (a+b x),x\right)",0,"Integrate[x^m*Tanh[a + b*x], x]","A",-1
335,1,88,91,2.3114732,"\int x^3 \tanh (a+b x) \, dx","Integrate[x^3*Tanh[a + b*x],x]","\frac{4 b^3 x^3 \log \left(e^{-2 (a+b x)}+1\right)-6 b^2 x^2 \text{Li}_2\left(-e^{-2 (a+b x)}\right)-6 b x \text{Li}_3\left(-e^{-2 (a+b x)}\right)-3 \text{Li}_4\left(-e^{-2 (a+b x)}\right)+b^4 x^4}{4 b^4}","\frac{3 \text{Li}_4\left(-e^{2 (a+b x)}\right)}{4 b^4}-\frac{3 x \text{Li}_3\left(-e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 x^2 \text{Li}_2\left(-e^{2 (a+b x)}\right)}{2 b^2}+\frac{x^3 \log \left(e^{2 (a+b x)}+1\right)}{b}-\frac{x^4}{4}",1,"(b^4*x^4 + 4*b^3*x^3*Log[1 + E^(-2*(a + b*x))] - 6*b^2*x^2*PolyLog[2, -E^(-2*(a + b*x))] - 6*b*x*PolyLog[3, -E^(-2*(a + b*x))] - 3*PolyLog[4, -E^(-2*(a + b*x))])/(4*b^4)","A",1
336,1,66,65,2.1530849,"\int x^2 \tanh (a+b x) \, dx","Integrate[x^2*Tanh[a + b*x],x]","\frac{2 b^2 x^2 \left(3 \log \left(e^{-2 (a+b x)}+1\right)+b x\right)-6 b x \text{Li}_2\left(-e^{-2 (a+b x)}\right)-3 \text{Li}_3\left(-e^{-2 (a+b x)}\right)}{6 b^3}","-\frac{\text{Li}_3\left(-e^{2 (a+b x)}\right)}{2 b^3}+\frac{x \text{Li}_2\left(-e^{2 (a+b x)}\right)}{b^2}+\frac{x^2 \log \left(e^{2 (a+b x)}+1\right)}{b}-\frac{x^3}{3}",1,"(2*b^2*x^2*(b*x + 3*Log[1 + E^(-2*(a + b*x))]) - 6*b*x*PolyLog[2, -E^(-2*(a + b*x))] - 3*PolyLog[3, -E^(-2*(a + b*x))])/(6*b^3)","A",1
337,1,149,45,3.2395269,"\int x \tanh (a+b x) \, dx","Integrate[x*Tanh[a + b*x],x]","\frac{1}{2} \left(x^2 \tanh (a)+\frac{-b^2 x^2 \tanh (a) \sqrt{-\text{csch}^2(a)} e^{-\tanh ^{-1}(\coth (a))}-\text{Li}_2\left(e^{-2 \left(b x+\tanh ^{-1}(\coth (a))\right)}\right)+2 b x \log \left(1-e^{-2 \left(\tanh ^{-1}(\coth (a))+b x\right)}\right)+2 \tanh ^{-1}(\coth (a)) \left(\log \left(1-e^{-2 \left(\tanh ^{-1}(\coth (a))+b x\right)}\right)-\log \left(i \sinh \left(\tanh ^{-1}(\coth (a))+b x\right)\right)+b x\right)+i \pi  b x-i \pi  \log \left(e^{2 b x}+1\right)+i \pi  \log (\cosh (b x))}{b^2}\right)","\frac{\text{Li}_2\left(-e^{2 (a+b x)}\right)}{2 b^2}+\frac{x \log \left(e^{2 (a+b x)}+1\right)}{b}-\frac{x^2}{2}",1,"(x^2*Tanh[a] + (I*b*Pi*x - I*Pi*Log[1 + E^(2*b*x)] + 2*b*x*Log[1 - E^(-2*(b*x + ArcTanh[Coth[a]]))] + I*Pi*Log[Cosh[b*x]] + 2*ArcTanh[Coth[a]]*(b*x + Log[1 - E^(-2*(b*x + ArcTanh[Coth[a]]))] - Log[I*Sinh[b*x + ArcTanh[Coth[a]]]]) - PolyLog[2, E^(-2*(b*x + ArcTanh[Coth[a]]))] - (b^2*x^2*Sqrt[-Csch[a]^2]*Tanh[a])/E^ArcTanh[Coth[a]])/b^2)/2","C",0
338,1,11,11,0.008588,"\int \tanh (a+b x) \, dx","Integrate[Tanh[a + b*x],x]","\frac{\log (\cosh (a+b x))}{b}","\frac{\log (\cosh (a+b x))}{b}",1,"Log[Cosh[a + b*x]]/b","A",1
339,0,0,13,12.307015,"\int \frac{\tanh (a+b x)}{x} \, dx","Integrate[Tanh[a + b*x]/x,x]","\int \frac{\tanh (a+b x)}{x} \, dx","\text{Int}\left(\frac{\tanh (a+b x)}{x},x\right)",0,"Integrate[Tanh[a + b*x]/x, x]","A",-1
340,0,0,13,19.0654787,"\int \frac{\tanh (a+b x)}{x^2} \, dx","Integrate[Tanh[a + b*x]/x^2,x]","\int \frac{\tanh (a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\tanh (a+b x)}{x^2},x\right)",0,"Integrate[Tanh[a + b*x]/x^2, x]","A",-1
341,0,0,19,22.2850297,"\int x^m \text{sech}(a+b x) \tanh (a+b x) \, dx","Integrate[x^m*Sech[a + b*x]*Tanh[a + b*x],x]","\int x^m \text{sech}(a+b x) \tanh (a+b x) \, dx","\text{Int}\left(x^m \tanh (a+b x) \text{sech}(a+b x),x\right)",0,"Integrate[x^m*Sech[a + b*x]*Tanh[a + b*x], x]","A",-1
342,1,130,113,2.2764912,"\int x^3 \text{sech}(a+b x) \tanh (a+b x) \, dx","Integrate[x^3*Sech[a + b*x]*Tanh[a + b*x],x]","-\frac{x^3 \text{sech}(a+b x)}{b}+\frac{3 i \left(b^2 x^2 \log \left(1-i e^{a+b x}\right)-b^2 x^2 \log \left(1+i e^{a+b x}\right)-2 b x \text{Li}_2\left(-i e^{a+b x}\right)+2 b x \text{Li}_2\left(i e^{a+b x}\right)+2 \text{Li}_3\left(-i e^{a+b x}\right)-2 \text{Li}_3\left(i e^{a+b x}\right)\right)}{b^4}","\frac{6 i \text{Li}_3\left(-i e^{a+b x}\right)}{b^4}-\frac{6 i \text{Li}_3\left(i e^{a+b x}\right)}{b^4}-\frac{6 i x \text{Li}_2\left(-i e^{a+b x}\right)}{b^3}+\frac{6 i x \text{Li}_2\left(i e^{a+b x}\right)}{b^3}+\frac{6 x^2 \tan ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{x^3 \text{sech}(a+b x)}{b}",1,"((3*I)*(b^2*x^2*Log[1 - I*E^(a + b*x)] - b^2*x^2*Log[1 + I*E^(a + b*x)] - 2*b*x*PolyLog[2, (-I)*E^(a + b*x)] + 2*b*x*PolyLog[2, I*E^(a + b*x)] + 2*PolyLog[3, (-I)*E^(a + b*x)] - 2*PolyLog[3, I*E^(a + b*x)]))/b^4 - (x^3*Sech[a + b*x])/b","A",1
343,1,125,69,0.4511509,"\int x^2 \text{sech}(a+b x) \tanh (a+b x) \, dx","Integrate[x^2*Sech[a + b*x]*Tanh[a + b*x],x]","-\frac{b^2 x^2 \text{sech}(a+b x)+2 i \left(\text{Li}_2\left(-i e^{a+b x}\right)-\text{Li}_2\left(i e^{a+b x}\right)\right)+(-2 i a-2 i b x+\pi ) \left(\log \left(1-i e^{a+b x}\right)-\log \left(1+i e^{a+b x}\right)\right)-(\pi -2 i a) \log \left(\cot \left(\frac{1}{4} (2 i a+2 i b x+\pi )\right)\right)}{b^3}","-\frac{2 i \text{Li}_2\left(-i e^{a+b x}\right)}{b^3}+\frac{2 i \text{Li}_2\left(i e^{a+b x}\right)}{b^3}+\frac{4 x \tan ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{x^2 \text{sech}(a+b x)}{b}",1,"-((((-2*I)*a + Pi - (2*I)*b*x)*(Log[1 - I*E^(a + b*x)] - Log[1 + I*E^(a + b*x)]) - ((-2*I)*a + Pi)*Log[Cot[((2*I)*a + Pi + (2*I)*b*x)/4]] + (2*I)*(PolyLog[2, (-I)*E^(a + b*x)] - PolyLog[2, I*E^(a + b*x)]) + b^2*x^2*Sech[a + b*x])/b^3)","A",1
344,1,32,24,0.0475359,"\int x \text{sech}(a+b x) \tanh (a+b x) \, dx","Integrate[x*Sech[a + b*x]*Tanh[a + b*x],x]","\frac{2 \tan ^{-1}\left(\tanh \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b^2}-\frac{x \text{sech}(a+b x)}{b}","\frac{\tan ^{-1}(\sinh (a+b x))}{b^2}-\frac{x \text{sech}(a+b x)}{b}",1,"(2*ArcTan[Tanh[a/2 + (b*x)/2]])/b^2 - (x*Sech[a + b*x])/b","A",1
345,1,11,11,0.0073619,"\int \text{sech}(a+b x) \tanh (a+b x) \, dx","Integrate[Sech[a + b*x]*Tanh[a + b*x],x]","-\frac{\text{sech}(a+b x)}{b}","-\frac{\text{sech}(a+b x)}{b}",1,"-(Sech[a + b*x]/b)","A",1
346,0,0,19,7.0194266,"\int \frac{\text{sech}(a+b x) \tanh (a+b x)}{x} \, dx","Integrate[(Sech[a + b*x]*Tanh[a + b*x])/x,x]","\int \frac{\text{sech}(a+b x) \tanh (a+b x)}{x} \, dx","\text{Int}\left(\frac{\tanh (a+b x) \text{sech}(a+b x)}{x},x\right)",0,"Integrate[(Sech[a + b*x]*Tanh[a + b*x])/x, x]","A",-1
347,0,0,19,8.198043,"\int \frac{\text{sech}(a+b x) \tanh (a+b x)}{x^2} \, dx","Integrate[(Sech[a + b*x]*Tanh[a + b*x])/x^2,x]","\int \frac{\text{sech}(a+b x) \tanh (a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\tanh (a+b x) \text{sech}(a+b x)}{x^2},x\right)",0,"Integrate[(Sech[a + b*x]*Tanh[a + b*x])/x^2, x]","A",-1
348,0,0,21,36.8846711,"\int x^m \text{sech}^2(a+b x) \tanh (a+b x) \, dx","Integrate[x^m*Sech[a + b*x]^2*Tanh[a + b*x],x]","\int x^m \text{sech}^2(a+b x) \tanh (a+b x) \, dx","\text{Int}\left(x^m \tanh (a+b x) \text{sech}^2(a+b x),x\right)",0,"Integrate[x^m*Sech[a + b*x]^2*Tanh[a + b*x], x]","A",-1
349,1,227,83,6.1392903,"\int x^3 \text{sech}^2(a+b x) \tanh (a+b x) \, dx","Integrate[x^3*Sech[a + b*x]^2*Tanh[a + b*x],x]","\frac{3 x^2 \text{sech}(a) \sinh (b x) \text{sech}(a+b x)}{2 b^2}-\frac{3 \text{csch}(a) \text{sech}(a) \left(b^2 x^2 e^{-\tanh ^{-1}(\coth (a))}-\frac{i \coth (a) \left(i \text{Li}_2\left(e^{2 i \left(i b x+i \tanh ^{-1}(\coth (a))\right)}\right)-b x \left(-\pi +2 i \tanh ^{-1}(\coth (a))\right)-2 \left(i \tanh ^{-1}(\coth (a))+i b x\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}(\coth (a))+i b x\right)}\right)+2 i \tanh ^{-1}(\coth (a)) \log \left(i \sinh \left(\tanh ^{-1}(\coth (a))+b x\right)\right)-\pi  \log \left(e^{2 b x}+1\right)+\pi  \log (\cosh (b x))\right)}{\sqrt{1-\coth ^2(a)}}\right)}{2 b^4 \sqrt{\text{csch}^2(a) \left(\sinh ^2(a)-\cosh ^2(a)\right)}}-\frac{x^3 \text{sech}^2(a+b x)}{2 b}","-\frac{3 \text{Li}_2\left(-e^{2 (a+b x)}\right)}{2 b^4}-\frac{3 x \log \left(e^{2 (a+b x)}+1\right)}{b^3}+\frac{3 x^2 \tanh (a+b x)}{2 b^2}-\frac{x^3 \text{sech}^2(a+b x)}{2 b}+\frac{3 x^2}{2 b^2}",1,"-1/2*(x^3*Sech[a + b*x]^2)/b - (3*Csch[a]*((b^2*x^2)/E^ArcTanh[Coth[a]] - (I*Coth[a]*(-(b*x*(-Pi + (2*I)*ArcTanh[Coth[a]])) - Pi*Log[1 + E^(2*b*x)] - 2*(I*b*x + I*ArcTanh[Coth[a]])*Log[1 - E^((2*I)*(I*b*x + I*ArcTanh[Coth[a]]))] + Pi*Log[Cosh[b*x]] + (2*I)*ArcTanh[Coth[a]]*Log[I*Sinh[b*x + ArcTanh[Coth[a]]]] + I*PolyLog[2, E^((2*I)*(I*b*x + I*ArcTanh[Coth[a]]))]))/Sqrt[1 - Coth[a]^2])*Sech[a])/(2*b^4*Sqrt[Csch[a]^2*(-Cosh[a]^2 + Sinh[a]^2)]) + (3*x^2*Sech[a]*Sech[a + b*x]*Sinh[b*x])/(2*b^2)","C",0
350,1,55,42,0.125181,"\int x^2 \text{sech}^2(a+b x) \tanh (a+b x) \, dx","Integrate[x^2*Sech[a + b*x]^2*Tanh[a + b*x],x]","-\frac{\log (\cosh (a+b x))}{b^3}+\frac{x \tanh (a)}{b^2}+\frac{x \text{sech}(a) \sinh (b x) \text{sech}(a+b x)}{b^2}-\frac{x^2 \text{sech}^2(a+b x)}{2 b}","-\frac{\log (\cosh (a+b x))}{b^3}+\frac{x \tanh (a+b x)}{b^2}-\frac{x^2 \text{sech}^2(a+b x)}{2 b}",1,"-(Log[Cosh[a + b*x]]/b^3) - (x^2*Sech[a + b*x]^2)/(2*b) + (x*Sech[a]*Sech[a + b*x]*Sinh[b*x])/b^2 + (x*Tanh[a])/b^2","A",1
351,1,30,30,0.0762731,"\int x \text{sech}^2(a+b x) \tanh (a+b x) \, dx","Integrate[x*Sech[a + b*x]^2*Tanh[a + b*x],x]","\frac{\tanh (a+b x)}{2 b^2}-\frac{x \text{sech}^2(a+b x)}{2 b}","\frac{\tanh (a+b x)}{2 b^2}-\frac{x \text{sech}^2(a+b x)}{2 b}",1,"-1/2*(x*Sech[a + b*x]^2)/b + Tanh[a + b*x]/(2*b^2)","A",1
352,1,15,15,0.0094957,"\int \text{sech}^2(a+b x) \tanh (a+b x) \, dx","Integrate[Sech[a + b*x]^2*Tanh[a + b*x],x]","-\frac{\text{sech}^2(a+b x)}{2 b}","-\frac{\text{sech}^2(a+b x)}{2 b}",1,"-1/2*Sech[a + b*x]^2/b","A",1
353,0,0,21,24.6851646,"\int \frac{\text{sech}^2(a+b x) \tanh (a+b x)}{x} \, dx","Integrate[(Sech[a + b*x]^2*Tanh[a + b*x])/x,x]","\int \frac{\text{sech}^2(a+b x) \tanh (a+b x)}{x} \, dx","\text{Int}\left(\frac{\tanh (a+b x) \text{sech}^2(a+b x)}{x},x\right)",0,"Integrate[(Sech[a + b*x]^2*Tanh[a + b*x])/x, x]","A",-1
354,0,0,21,21.287576,"\int \frac{\text{sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx","Integrate[(Sech[a + b*x]^2*Tanh[a + b*x])/x^2,x]","\int \frac{\text{sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\tanh (a+b x) \text{sech}^2(a+b x)}{x^2},x\right)",0,"Integrate[(Sech[a + b*x]^2*Tanh[a + b*x])/x^2, x]","A",-1
355,0,0,74,14.0808249,"\int x^m \sinh (a+b x) \tanh (a+b x) \, dx","Integrate[x^m*Sinh[a + b*x]*Tanh[a + b*x],x]","\int x^m \sinh (a+b x) \tanh (a+b x) \, dx","-\text{Int}\left(x^m \text{sech}(a+b x),x\right)+\frac{e^a x^m (-b x)^{-m} \Gamma (m+1,-b x)}{2 b}-\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+1,b x)}{2 b}",0,"Integrate[x^m*Sinh[a + b*x]*Tanh[a + b*x], x]","A",-1
356,1,211,195,1.4758343,"\int x^3 \sinh (a+b x) \tanh (a+b x) \, dx","Integrate[x^3*Sinh[a + b*x]*Tanh[a + b*x],x]","-\frac{i \left(b^3 x^3 \log \left(1-i e^{a+b x}\right)-b^3 x^3 \log \left(1+i e^{a+b x}\right)+i b^3 x^3 \sinh (a+b x)-3 b^2 x^2 \text{Li}_2\left(-i e^{a+b x}\right)+3 b^2 x^2 \text{Li}_2\left(i e^{a+b x}\right)-3 i b^2 x^2 \cosh (a+b x)+6 b x \text{Li}_3\left(-i e^{a+b x}\right)-6 b x \text{Li}_3\left(i e^{a+b x}\right)-6 \text{Li}_4\left(-i e^{a+b x}\right)+6 \text{Li}_4\left(i e^{a+b x}\right)+6 i b x \sinh (a+b x)-6 i \cosh (a+b x)\right)}{b^4}","\frac{6 i \text{Li}_4\left(-i e^{a+b x}\right)}{b^4}-\frac{6 i \text{Li}_4\left(i e^{a+b x}\right)}{b^4}-\frac{6 \cosh (a+b x)}{b^4}-\frac{6 i x \text{Li}_3\left(-i e^{a+b x}\right)}{b^3}+\frac{6 i x \text{Li}_3\left(i e^{a+b x}\right)}{b^3}+\frac{6 x \sinh (a+b x)}{b^3}+\frac{3 i x^2 \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}-\frac{3 i x^2 \text{Li}_2\left(i e^{a+b x}\right)}{b^2}-\frac{3 x^2 \cosh (a+b x)}{b^2}-\frac{2 x^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{x^3 \sinh (a+b x)}{b}",1,"((-I)*((-6*I)*Cosh[a + b*x] - (3*I)*b^2*x^2*Cosh[a + b*x] + b^3*x^3*Log[1 - I*E^(a + b*x)] - b^3*x^3*Log[1 + I*E^(a + b*x)] - 3*b^2*x^2*PolyLog[2, (-I)*E^(a + b*x)] + 3*b^2*x^2*PolyLog[2, I*E^(a + b*x)] + 6*b*x*PolyLog[3, (-I)*E^(a + b*x)] - 6*b*x*PolyLog[3, I*E^(a + b*x)] - 6*PolyLog[4, (-I)*E^(a + b*x)] + 6*PolyLog[4, I*E^(a + b*x)] + (6*I)*b*x*Sinh[a + b*x] + I*b^3*x^3*Sinh[a + b*x]))/b^4","A",1
357,1,153,135,1.4681198,"\int x^2 \sinh (a+b x) \tanh (a+b x) \, dx","Integrate[x^2*Sinh[a + b*x]*Tanh[a + b*x],x]","-\frac{i \left(b^2 x^2 \log \left(1-i e^{a+b x}\right)-b^2 x^2 \log \left(1+i e^{a+b x}\right)+i b^2 x^2 \sinh (a+b x)-2 b x \text{Li}_2\left(-i e^{a+b x}\right)+2 b x \text{Li}_2\left(i e^{a+b x}\right)+2 \text{Li}_3\left(-i e^{a+b x}\right)-2 \text{Li}_3\left(i e^{a+b x}\right)+2 i \sinh (a+b x)-2 i b x \cosh (a+b x)\right)}{b^3}","-\frac{2 i \text{Li}_3\left(-i e^{a+b x}\right)}{b^3}+\frac{2 i \text{Li}_3\left(i e^{a+b x}\right)}{b^3}+\frac{2 \sinh (a+b x)}{b^3}+\frac{2 i x \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}-\frac{2 i x \text{Li}_2\left(i e^{a+b x}\right)}{b^2}-\frac{2 x \cosh (a+b x)}{b^2}-\frac{2 x^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{x^2 \sinh (a+b x)}{b}",1,"((-I)*((-2*I)*b*x*Cosh[a + b*x] + b^2*x^2*Log[1 - I*E^(a + b*x)] - b^2*x^2*Log[1 + I*E^(a + b*x)] - 2*b*x*PolyLog[2, (-I)*E^(a + b*x)] + 2*b*x*PolyLog[2, I*E^(a + b*x)] + 2*PolyLog[3, (-I)*E^(a + b*x)] - 2*PolyLog[3, I*E^(a + b*x)] + (2*I)*Sinh[a + b*x] + I*b^2*x^2*Sinh[a + b*x]))/b^3","A",1
358,1,213,77,0.1183037,"\int x \sinh (a+b x) \tanh (a+b x) \, dx","Integrate[x*Sinh[a + b*x]*Tanh[a + b*x],x]","-\frac{-i \left(\text{Li}_2\left(-e^{i \left(-i a-i b x+\frac{\pi }{2}\right)}\right)-\text{Li}_2\left(e^{i \left(-i a-i b x+\frac{\pi }{2}\right)}\right)\right)-\left(\left(-i a-i b x+\frac{\pi }{2}\right) \left(\log \left(1-e^{i \left(-i a-i b x+\frac{\pi }{2}\right)}\right)-\log \left(1+e^{i \left(-i a-i b x+\frac{\pi }{2}\right)}\right)\right)\right)+\left(\frac{\pi }{2}-i a\right) \log \left(\tan \left(\frac{1}{2} \left(-i a-i b x+\frac{\pi }{2}\right)\right)\right)}{b^2}+\frac{\cosh (b x) (b x \sinh (a)-\cosh (a))}{b^2}+\frac{\sinh (b x) (b x \cosh (a)-\sinh (a))}{b^2}","\frac{i \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}-\frac{i \text{Li}_2\left(i e^{a+b x}\right)}{b^2}-\frac{\cosh (a+b x)}{b^2}-\frac{2 x \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{x \sinh (a+b x)}{b}",1,"-((-(((-I)*a + Pi/2 - I*b*x)*(Log[1 - E^(I*((-I)*a + Pi/2 - I*b*x))] - Log[1 + E^(I*((-I)*a + Pi/2 - I*b*x))])) + ((-I)*a + Pi/2)*Log[Tan[((-I)*a + Pi/2 - I*b*x)/2]] - I*(PolyLog[2, -E^(I*((-I)*a + Pi/2 - I*b*x))] - PolyLog[2, E^(I*((-I)*a + Pi/2 - I*b*x))]))/b^2) + (Cosh[b*x]*(-Cosh[a] + b*x*Sinh[a]))/b^2 + ((b*x*Cosh[a] - Sinh[a])*Sinh[b*x])/b^2","B",1
359,1,23,23,0.011981,"\int \sinh (a+b x) \tanh (a+b x) \, dx","Integrate[Sinh[a + b*x]*Tanh[a + b*x],x]","\frac{\sinh (a+b x)}{b}-\frac{\tan ^{-1}(\sinh (a+b x))}{b}","\frac{\sinh (a+b x)}{b}-\frac{\tan ^{-1}(\sinh (a+b x))}{b}",1,"-(ArcTan[Sinh[a + b*x]]/b) + Sinh[a + b*x]/b","A",1
360,0,0,30,9.1480527,"\int \frac{\sinh (a+b x) \tanh (a+b x)}{x} \, dx","Integrate[(Sinh[a + b*x]*Tanh[a + b*x])/x,x]","\int \frac{\sinh (a+b x) \tanh (a+b x)}{x} \, dx","-\text{Int}\left(\frac{\text{sech}(a+b x)}{x},x\right)+\cosh (a) \text{Chi}(b x)+\sinh (a) \text{Shi}(b x)",0,"Integrate[(Sinh[a + b*x]*Tanh[a + b*x])/x, x]","A",-1
361,0,0,43,8.9005276,"\int \frac{\sinh (a+b x) \tanh (a+b x)}{x^2} \, dx","Integrate[(Sinh[a + b*x]*Tanh[a + b*x])/x^2,x]","\int \frac{\sinh (a+b x) \tanh (a+b x)}{x^2} \, dx","-\text{Int}\left(\frac{\text{sech}(a+b x)}{x^2},x\right)+b \sinh (a) \text{Chi}(b x)+b \cosh (a) \text{Shi}(b x)-\frac{\cosh (a+b x)}{x}",0,"Integrate[(Sinh[a + b*x]*Tanh[a + b*x])/x^2, x]","A",-1
362,0,0,15,0.6170326,"\int x^m \tanh ^2(a+b x) \, dx","Integrate[x^m*Tanh[a + b*x]^2,x]","\int x^m \tanh ^2(a+b x) \, dx","\text{Int}\left(x^m \tanh ^2(a+b x),x\right)",0,"Integrate[x^m*Tanh[a + b*x]^2, x]","A",-1
363,1,104,89,4.6473551,"\int x^3 \tanh ^2(a+b x) \, dx","Integrate[x^3*Tanh[a + b*x]^2,x]","\frac{2 b^2 x^2 \left(\frac{2 b x}{e^{2 a}+1}+3 \log \left(e^{-2 (a+b x)}+1\right)\right)-6 b x \text{Li}_2\left(-e^{-2 (a+b x)}\right)-3 \text{Li}_3\left(-e^{-2 (a+b x)}\right)}{2 b^4}-\frac{x^3 \text{sech}(a) \sinh (b x) \text{sech}(a+b x)}{b}+\frac{x^4}{4}","-\frac{3 \text{Li}_3\left(-e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 x \text{Li}_2\left(-e^{2 (a+b x)}\right)}{b^3}+\frac{3 x^2 \log \left(e^{2 (a+b x)}+1\right)}{b^2}-\frac{x^3 \tanh (a+b x)}{b}-\frac{x^3}{b}+\frac{x^4}{4}",1,"x^4/4 + (2*b^2*x^2*((2*b*x)/(1 + E^(2*a)) + 3*Log[1 + E^(-2*(a + b*x))]) - 6*b*x*PolyLog[2, -E^(-2*(a + b*x))] - 3*PolyLog[3, -E^(-2*(a + b*x))])/(2*b^4) - (x^3*Sech[a]*Sech[a + b*x]*Sinh[b*x])/b","A",1
364,1,168,65,3.3365871,"\int x^2 \tanh ^2(a+b x) \, dx","Integrate[x^2*Tanh[a + b*x]^2,x]","\frac{-3 b^2 x^2 \text{sech}(a) \sinh (b x) \text{sech}(a+b x)-3 b^2 x^2 \tanh (a) \sqrt{-\text{csch}^2(a)} e^{-\tanh ^{-1}(\coth (a))}-3 \text{Li}_2\left(e^{-2 \left(b x+\tanh ^{-1}(\coth (a))\right)}\right)+6 b x \log \left(1-e^{-2 \left(\tanh ^{-1}(\coth (a))+b x\right)}\right)+6 \tanh ^{-1}(\coth (a)) \left(\log \left(1-e^{-2 \left(\tanh ^{-1}(\coth (a))+b x\right)}\right)-\log \left(i \sinh \left(\tanh ^{-1}(\coth (a))+b x\right)\right)+b x\right)+b^3 x^3+3 i \pi  b x-3 i \pi  \log \left(e^{2 b x}+1\right)+3 i \pi  \log (\cosh (b x))}{3 b^3}","\frac{\text{Li}_2\left(-e^{2 (a+b x)}\right)}{b^3}+\frac{2 x \log \left(e^{2 (a+b x)}+1\right)}{b^2}-\frac{x^2 \tanh (a+b x)}{b}-\frac{x^2}{b}+\frac{x^3}{3}",1,"((3*I)*b*Pi*x + b^3*x^3 - (3*I)*Pi*Log[1 + E^(2*b*x)] + 6*b*x*Log[1 - E^(-2*(b*x + ArcTanh[Coth[a]]))] + (3*I)*Pi*Log[Cosh[b*x]] + 6*ArcTanh[Coth[a]]*(b*x + Log[1 - E^(-2*(b*x + ArcTanh[Coth[a]]))] - Log[I*Sinh[b*x + ArcTanh[Coth[a]]]]) - 3*PolyLog[2, E^(-2*(b*x + ArcTanh[Coth[a]]))] - 3*b^2*x^2*Sech[a]*Sech[a + b*x]*Sinh[b*x] - (3*b^2*x^2*Sqrt[-Csch[a]^2]*Tanh[a])/E^ArcTanh[Coth[a]])/(3*b^3)","C",0
365,1,46,31,0.1456599,"\int x \tanh ^2(a+b x) \, dx","Integrate[x*Tanh[a + b*x]^2,x]","\frac{-2 b x \tanh (a)+2 \log (\cosh (a+b x))-2 b x \text{sech}(a) \sinh (b x) \text{sech}(a+b x)+b^2 x^2}{2 b^2}","\frac{\log (\cosh (a+b x))}{b^2}-\frac{x \tanh (a+b x)}{b}+\frac{x^2}{2}",1,"(b^2*x^2 + 2*Log[Cosh[a + b*x]] - 2*b*x*Sech[a]*Sech[a + b*x]*Sinh[b*x] - 2*b*x*Tanh[a])/(2*b^2)","A",1
366,1,23,13,0.0072578,"\int \tanh ^2(a+b x) \, dx","Integrate[Tanh[a + b*x]^2,x]","\frac{\tanh ^{-1}(\tanh (a+b x))}{b}-\frac{\tanh (a+b x)}{b}","x-\frac{\tanh (a+b x)}{b}",1,"ArcTanh[Tanh[a + b*x]]/b - Tanh[a + b*x]/b","A",1
367,0,0,15,18.8816566,"\int \frac{\tanh ^2(a+b x)}{x} \, dx","Integrate[Tanh[a + b*x]^2/x,x]","\int \frac{\tanh ^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\tanh ^2(a+b x)}{x},x\right)",0,"Integrate[Tanh[a + b*x]^2/x, x]","A",-1
368,0,0,15,11.8906873,"\int \frac{\tanh ^2(a+b x)}{x^2} \, dx","Integrate[Tanh[a + b*x]^2/x^2,x]","\int \frac{\tanh ^2(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\tanh ^2(a+b x)}{x^2},x\right)",0,"Integrate[Tanh[a + b*x]^2/x^2, x]","A",-1
369,0,0,31,58.5074247,"\int x^m \text{sech}(a+b x) \tanh ^2(a+b x) \, dx","Integrate[x^m*Sech[a + b*x]*Tanh[a + b*x]^2,x]","\int x^m \text{sech}(a+b x) \tanh ^2(a+b x) \, dx","\text{Int}\left(x^m \text{sech}(a+b x),x\right)-\text{Int}\left(x^m \text{sech}^3(a+b x),x\right)",0,"Integrate[x^m*Sech[a + b*x]*Tanh[a + b*x]^2, x]","A",-1
370,1,245,240,3.4186494,"\int x^3 \text{sech}(a+b x) \tanh ^2(a+b x) \, dx","Integrate[x^3*Sech[a + b*x]*Tanh[a + b*x]^2,x]","-\frac{b^3 x^3 \text{sech}(a) \sinh (b x) \text{sech}^2(a+b x)+b^2 x^2 (b x \tanh (a)+3) \text{sech}(a+b x)-i \left(b^3 x^3 \log \left(1-i e^{a+b x}\right)-b^3 x^3 \log \left(1+i e^{a+b x}\right)-3 \left(b^2 x^2+2\right) \text{Li}_2\left(-i e^{a+b x}\right)+3 \left(b^2 x^2+2\right) \text{Li}_2\left(i e^{a+b x}\right)+6 b x \text{Li}_3\left(-i e^{a+b x}\right)-6 b x \text{Li}_3\left(i e^{a+b x}\right)-6 \text{Li}_4\left(-i e^{a+b x}\right)+6 \text{Li}_4\left(i e^{a+b x}\right)+6 b x \log \left(1-i e^{a+b x}\right)-6 b x \log \left(1+i e^{a+b x}\right)\right)}{2 b^4}","-\frac{3 i \text{Li}_2\left(-i e^{a+b x}\right)}{b^4}+\frac{3 i \text{Li}_2\left(i e^{a+b x}\right)}{b^4}-\frac{3 i \text{Li}_4\left(-i e^{a+b x}\right)}{b^4}+\frac{3 i \text{Li}_4\left(i e^{a+b x}\right)}{b^4}+\frac{3 i x \text{Li}_3\left(-i e^{a+b x}\right)}{b^3}-\frac{3 i x \text{Li}_3\left(i e^{a+b x}\right)}{b^3}+\frac{6 x \tan ^{-1}\left(e^{a+b x}\right)}{b^3}-\frac{3 i x^2 \text{Li}_2\left(-i e^{a+b x}\right)}{2 b^2}+\frac{3 i x^2 \text{Li}_2\left(i e^{a+b x}\right)}{2 b^2}-\frac{3 x^2 \text{sech}(a+b x)}{2 b^2}+\frac{x^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}-\frac{x^3 \tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"-1/2*((-I)*(6*b*x*Log[1 - I*E^(a + b*x)] + b^3*x^3*Log[1 - I*E^(a + b*x)] - 6*b*x*Log[1 + I*E^(a + b*x)] - b^3*x^3*Log[1 + I*E^(a + b*x)] - 3*(2 + b^2*x^2)*PolyLog[2, (-I)*E^(a + b*x)] + 3*(2 + b^2*x^2)*PolyLog[2, I*E^(a + b*x)] + 6*b*x*PolyLog[3, (-I)*E^(a + b*x)] - 6*b*x*PolyLog[3, I*E^(a + b*x)] - 6*PolyLog[4, (-I)*E^(a + b*x)] + 6*PolyLog[4, I*E^(a + b*x)]) + b^3*x^3*Sech[a]*Sech[a + b*x]^2*Sinh[b*x] + b^2*x^2*Sech[a + b*x]*(3 + b*x*Tanh[a]))/b^4","A",1
371,1,180,143,1.651814,"\int x^2 \text{sech}(a+b x) \tanh ^2(a+b x) \, dx","Integrate[x^2*Sech[a + b*x]*Tanh[a + b*x]^2,x]","-\frac{x \text{sech}(a) \text{sech}(a+b x) (b x \sinh (a)+2 \cosh (a))}{2 b^2}+\frac{i \left(b^2 x^2 \log \left(1-i e^{a+b x}\right)-b^2 x^2 \log \left(1+i e^{a+b x}\right)-2 b x \text{Li}_2\left(-i e^{a+b x}\right)+2 b x \text{Li}_2\left(i e^{a+b x}\right)+2 \text{Li}_3\left(-i e^{a+b x}\right)-2 \text{Li}_3\left(i e^{a+b x}\right)-4 i \tan ^{-1}\left(e^{a+b x}\right)\right)}{2 b^3}-\frac{x^2 \text{sech}(a) \sinh (b x) \text{sech}^2(a+b x)}{2 b}","\frac{i \text{Li}_3\left(-i e^{a+b x}\right)}{b^3}-\frac{i \text{Li}_3\left(i e^{a+b x}\right)}{b^3}+\frac{\tan ^{-1}(\sinh (a+b x))}{b^3}-\frac{i x \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}+\frac{i x \text{Li}_2\left(i e^{a+b x}\right)}{b^2}-\frac{x \text{sech}(a+b x)}{b^2}+\frac{x^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}-\frac{x^2 \tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"((I/2)*((-4*I)*ArcTan[E^(a + b*x)] + b^2*x^2*Log[1 - I*E^(a + b*x)] - b^2*x^2*Log[1 + I*E^(a + b*x)] - 2*b*x*PolyLog[2, (-I)*E^(a + b*x)] + 2*b*x*PolyLog[2, I*E^(a + b*x)] + 2*PolyLog[3, (-I)*E^(a + b*x)] - 2*PolyLog[3, I*E^(a + b*x)]))/b^3 - (x*Sech[a]*Sech[a + b*x]*(2*Cosh[a] + b*x*Sinh[a]))/(2*b^2) - (x^2*Sech[a]*Sech[a + b*x]^2*Sinh[b*x])/(2*b)","A",1
372,1,93,91,0.7789248,"\int x \text{sech}(a+b x) \tanh ^2(a+b x) \, dx","Integrate[x*Sech[a + b*x]*Tanh[a + b*x]^2,x]","-\frac{i \text{Li}_2(-i (\cosh (a+b x)+\sinh (a+b x)))-i \text{Li}_2(i (\cosh (a+b x)+\sinh (a+b x)))+\text{sech}(a+b x)+b x \tanh (a+b x) \text{sech}(a+b x)-2 b x \tan ^{-1}(\sinh (a+b x)+\cosh (a+b x))}{2 b^2}","-\frac{i \text{Li}_2\left(-i e^{a+b x}\right)}{2 b^2}+\frac{i \text{Li}_2\left(i e^{a+b x}\right)}{2 b^2}-\frac{\text{sech}(a+b x)}{2 b^2}+\frac{x \tan ^{-1}\left(e^{a+b x}\right)}{b}-\frac{x \tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"-1/2*(-2*b*x*ArcTan[Cosh[a + b*x] + Sinh[a + b*x]] + I*PolyLog[2, (-I)*(Cosh[a + b*x] + Sinh[a + b*x])] - I*PolyLog[2, I*(Cosh[a + b*x] + Sinh[a + b*x])] + Sech[a + b*x] + b*x*Sech[a + b*x]*Tanh[a + b*x])/b^2","A",0
373,1,34,34,0.0169129,"\int \text{sech}(a+b x) \tanh ^2(a+b x) \, dx","Integrate[Sech[a + b*x]*Tanh[a + b*x]^2,x]","\frac{\tan ^{-1}(\sinh (a+b x))}{2 b}-\frac{\tanh (a+b x) \text{sech}(a+b x)}{2 b}","\frac{\tan ^{-1}(\sinh (a+b x))}{2 b}-\frac{\tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"ArcTan[Sinh[a + b*x]]/(2*b) - (Sech[a + b*x]*Tanh[a + b*x])/(2*b)","A",1
374,0,0,31,16.7123904,"\int \frac{\text{sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx","Integrate[(Sech[a + b*x]*Tanh[a + b*x]^2)/x,x]","\int \frac{\text{sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{sech}(a+b x)}{x},x\right)-\text{Int}\left(\frac{\text{sech}^3(a+b x)}{x},x\right)",0,"Integrate[(Sech[a + b*x]*Tanh[a + b*x]^2)/x, x]","A",-1
375,0,0,31,13.4040158,"\int \frac{\text{sech}(a+b x) \tanh ^2(a+b x)}{x^2} \, dx","Integrate[(Sech[a + b*x]*Tanh[a + b*x]^2)/x^2,x]","\int \frac{\text{sech}(a+b x) \tanh ^2(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{sech}(a+b x)}{x^2},x\right)-\text{Int}\left(\frac{\text{sech}^3(a+b x)}{x^2},x\right)",0,"Integrate[(Sech[a + b*x]*Tanh[a + b*x]^2)/x^2, x]","A",-1
376,0,0,85,22.5971609,"\int x^m \sinh ^2(a+b x) \tanh (a+b x) \, dx","Integrate[x^m*Sinh[a + b*x]^2*Tanh[a + b*x],x]","\int x^m \sinh ^2(a+b x) \tanh (a+b x) \, dx","-\text{Int}\left(x^m \tanh (a+b x),x\right)+\frac{e^{2 a} 2^{-m-3} x^m (-b x)^{-m} \Gamma (m+1,-2 b x)}{b}+\frac{e^{-2 a} 2^{-m-3} x^m (b x)^{-m} \Gamma (m+1,2 b x)}{b}",0,"Integrate[x^m*Sinh[a + b*x]^2*Tanh[a + b*x], x]","A",-1
377,1,191,185,2.9914888,"\int x^3 \sinh ^2(a+b x) \tanh (a+b x) \, dx","Integrate[x^3*Sinh[a + b*x]^2*Tanh[a + b*x],x]","\frac{1}{16} \left(\frac{12 \left(2 b^2 x^2 \text{Li}_2\left(-e^{-2 (a+b x)}\right)+2 b x \text{Li}_3\left(-e^{-2 (a+b x)}\right)+\text{Li}_4\left(-e^{-2 (a+b x)}\right)\right)}{b^4}+\frac{\cosh (2 b x) \left(2 b x \cosh (2 a) \left(2 b^2 x^2+3\right)-3 \sinh (2 a) \left(2 b^2 x^2+1\right)\right)}{b^4}+\frac{\sinh (2 b x) \left(2 b x \sinh (2 a) \left(2 b^2 x^2+3\right)-3 \cosh (2 a) \left(2 b^2 x^2+1\right)\right)}{b^4}-\frac{16 x^3 \log \left(e^{-2 (a+b x)}+1\right)}{b}-\frac{8 x^4}{e^{2 a}+1}-4 x^4 \tanh (a)\right)","-\frac{3 \text{Li}_4\left(-e^{2 (a+b x)}\right)}{4 b^4}-\frac{3 \sinh (a+b x) \cosh (a+b x)}{8 b^4}+\frac{3 x \text{Li}_3\left(-e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 x \sinh ^2(a+b x)}{4 b^3}-\frac{3 x^2 \text{Li}_2\left(-e^{2 (a+b x)}\right)}{2 b^2}-\frac{3 x^2 \sinh (a+b x) \cosh (a+b x)}{4 b^2}-\frac{x^3 \log \left(e^{2 (a+b x)}+1\right)}{b}+\frac{x^3 \sinh ^2(a+b x)}{2 b}+\frac{3 x}{8 b^3}+\frac{x^3}{4 b}+\frac{x^4}{4}",1,"((-8*x^4)/(1 + E^(2*a)) - (16*x^3*Log[1 + E^(-2*(a + b*x))])/b + (12*(2*b^2*x^2*PolyLog[2, -E^(-2*(a + b*x))] + 2*b*x*PolyLog[3, -E^(-2*(a + b*x))] + PolyLog[4, -E^(-2*(a + b*x))]))/b^4 + (Cosh[2*b*x]*(2*b*x*(3 + 2*b^2*x^2)*Cosh[2*a] - 3*(1 + 2*b^2*x^2)*Sinh[2*a]))/b^4 + ((-3*(1 + 2*b^2*x^2)*Cosh[2*a] + 2*b*x*(3 + 2*b^2*x^2)*Sinh[2*a])*Sinh[2*b*x])/b^4 - 4*x^4*Tanh[a])/16","A",1
378,1,154,130,2.733572,"\int x^2 \sinh ^2(a+b x) \tanh (a+b x) \, dx","Integrate[x^2*Sinh[a + b*x]^2*Tanh[a + b*x],x]","\frac{1}{24} \left(\frac{4 \left(2 b^2 x^2 \left(-\frac{2 b x}{e^{2 a}+1}-3 \log \left(e^{-2 (a+b x)}+1\right)\right)+6 b x \text{Li}_2\left(-e^{-2 (a+b x)}\right)+3 \text{Li}_3\left(-e^{-2 (a+b x)}\right)\right)}{b^3}+\frac{3 \cosh (2 b x) \left(\cosh (2 a) \left(2 b^2 x^2+1\right)-2 b x \sinh (2 a)\right)}{b^3}+\frac{3 \sinh (2 b x) \left(\sinh (2 a) \left(2 b^2 x^2+1\right)-2 b x \cosh (2 a)\right)}{b^3}-8 x^3 \tanh (a)\right)","\frac{\text{Li}_3\left(-e^{2 (a+b x)}\right)}{2 b^3}+\frac{\sinh ^2(a+b x)}{4 b^3}-\frac{x \text{Li}_2\left(-e^{2 (a+b x)}\right)}{b^2}-\frac{x \sinh (a+b x) \cosh (a+b x)}{2 b^2}-\frac{x^2 \log \left(e^{2 (a+b x)}+1\right)}{b}+\frac{x^2 \sinh ^2(a+b x)}{2 b}+\frac{x^2}{4 b}+\frac{x^3}{3}",1,"((4*(2*b^2*x^2*((-2*b*x)/(1 + E^(2*a)) - 3*Log[1 + E^(-2*(a + b*x))]) + 6*b*x*PolyLog[2, -E^(-2*(a + b*x))] + 3*PolyLog[3, -E^(-2*(a + b*x))]))/b^3 + (3*Cosh[2*b*x]*((1 + 2*b^2*x^2)*Cosh[2*a] - 2*b*x*Sinh[2*a]))/b^3 + (3*(-2*b*x*Cosh[2*a] + (1 + 2*b^2*x^2)*Sinh[2*a])*Sinh[2*b*x])/b^3 - 8*x^3*Tanh[a])/24","A",1
379,1,102,89,0.2337749,"\int x \sinh ^2(a+b x) \tanh (a+b x) \, dx","Integrate[x*Sinh[a + b*x]^2*Tanh[a + b*x],x]","-\frac{4 a^2-4 \text{Li}_2\left(-e^{-2 (a+b x)}\right)+8 a b x+8 a \log \left(e^{-2 (a+b x)}+1\right)+8 b x \log \left(e^{-2 (a+b x)}+1\right)+\sinh (2 (a+b x))-2 b x \cosh (2 (a+b x))-8 a \log (\cosh (a+b x))+4 b^2 x^2}{8 b^2}","-\frac{\text{Li}_2\left(-e^{2 (a+b x)}\right)}{2 b^2}-\frac{\sinh (a+b x) \cosh (a+b x)}{4 b^2}-\frac{x \log \left(e^{2 (a+b x)}+1\right)}{b}+\frac{x \sinh ^2(a+b x)}{2 b}+\frac{x}{4 b}+\frac{x^2}{2}",1,"-1/8*(4*a^2 + 8*a*b*x + 4*b^2*x^2 - 2*b*x*Cosh[2*(a + b*x)] + 8*a*Log[1 + E^(-2*(a + b*x))] + 8*b*x*Log[1 + E^(-2*(a + b*x))] - 8*a*Log[Cosh[a + b*x]] - 4*PolyLog[2, -E^(-2*(a + b*x))] + Sinh[2*(a + b*x)])/b^2","A",1
380,1,25,28,0.0189968,"\int \sinh ^2(a+b x) \tanh (a+b x) \, dx","Integrate[Sinh[a + b*x]^2*Tanh[a + b*x],x]","-\frac{\log (\cosh (a+b x))-\frac{1}{2} \cosh ^2(a+b x)}{b}","\frac{\cosh ^2(a+b x)}{2 b}-\frac{\log (\cosh (a+b x))}{b}",1,"-((-1/2*Cosh[a + b*x]^2 + Log[Cosh[a + b*x]])/b)","A",1
381,0,0,42,19.5944948,"\int \frac{\sinh ^2(a+b x) \tanh (a+b x)}{x} \, dx","Integrate[(Sinh[a + b*x]^2*Tanh[a + b*x])/x,x]","\int \frac{\sinh ^2(a+b x) \tanh (a+b x)}{x} \, dx","-\text{Int}\left(\frac{\tanh (a+b x)}{x},x\right)+\frac{1}{2} \sinh (2 a) \text{Chi}(2 b x)+\frac{1}{2} \cosh (2 a) \text{Shi}(2 b x)",0,"Integrate[(Sinh[a + b*x]^2*Tanh[a + b*x])/x, x]","A",-1
382,0,0,54,20.2041991,"\int \frac{\sinh ^2(a+b x) \tanh (a+b x)}{x^2} \, dx","Integrate[(Sinh[a + b*x]^2*Tanh[a + b*x])/x^2,x]","\int \frac{\sinh ^2(a+b x) \tanh (a+b x)}{x^2} \, dx","-\text{Int}\left(\frac{\tanh (a+b x)}{x^2},x\right)+b \cosh (2 a) \text{Chi}(2 b x)+b \sinh (2 a) \text{Shi}(2 b x)-\frac{\sinh (2 a+2 b x)}{2 x}",0,"Integrate[(Sinh[a + b*x]^2*Tanh[a + b*x])/x^2, x]","A",-1
383,0,0,80,38.1247667,"\int x^m \sinh (a+b x) \tanh ^2(a+b x) \, dx","Integrate[x^m*Sinh[a + b*x]*Tanh[a + b*x]^2,x]","\int x^m \sinh (a+b x) \tanh ^2(a+b x) \, dx","-\text{Int}\left(x^m \tanh (a+b x) \text{sech}(a+b x),x\right)+\frac{e^a x^m (-b x)^{-m} \Gamma (m+1,-b x)}{2 b}+\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+1,b x)}{2 b}",0,"Integrate[x^m*Sinh[a + b*x]*Tanh[a + b*x]^2, x]","A",-1
384,1,196,162,3.3537254,"\int x^3 \sinh (a+b x) \tanh ^2(a+b x) \, dx","Integrate[x^3*Sinh[a + b*x]*Tanh[a + b*x]^2,x]","\frac{b^3 x^3 \text{sech}(a+b x)-3 i \left(b^2 x^2 \log \left(1-i e^{a+b x}\right)-b^2 x^2 \log \left(1+i e^{a+b x}\right)-2 b x \text{Li}_2\left(-i e^{a+b x}\right)+2 b x \text{Li}_2\left(i e^{a+b x}\right)+2 \text{Li}_3\left(-i e^{a+b x}\right)-2 \text{Li}_3\left(i e^{a+b x}\right)\right)+\cosh (b x) \left(b x \cosh (a) \left(b^2 x^2+6\right)-3 \sinh (a) \left(b^2 x^2+2\right)\right)+\sinh (b x) \left(b x \sinh (a) \left(b^2 x^2+6\right)-3 \cosh (a) \left(b^2 x^2+2\right)\right)}{b^4}","-\frac{6 i \text{Li}_3\left(-i e^{a+b x}\right)}{b^4}+\frac{6 i \text{Li}_3\left(i e^{a+b x}\right)}{b^4}-\frac{6 \sinh (a+b x)}{b^4}+\frac{6 i x \text{Li}_2\left(-i e^{a+b x}\right)}{b^3}-\frac{6 i x \text{Li}_2\left(i e^{a+b x}\right)}{b^3}+\frac{6 x \cosh (a+b x)}{b^3}-\frac{6 x^2 \tan ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{3 x^2 \sinh (a+b x)}{b^2}+\frac{x^3 \cosh (a+b x)}{b}+\frac{x^3 \text{sech}(a+b x)}{b}",1,"((-3*I)*(b^2*x^2*Log[1 - I*E^(a + b*x)] - b^2*x^2*Log[1 + I*E^(a + b*x)] - 2*b*x*PolyLog[2, (-I)*E^(a + b*x)] + 2*b*x*PolyLog[2, I*E^(a + b*x)] + 2*PolyLog[3, (-I)*E^(a + b*x)] - 2*PolyLog[3, I*E^(a + b*x)]) + b^3*x^3*Sech[a + b*x] + Cosh[b*x]*(b*x*(6 + b^2*x^2)*Cosh[a] - 3*(2 + b^2*x^2)*Sinh[a]) + (-3*(2 + b^2*x^2)*Cosh[a] + b*x*(6 + b^2*x^2)*Sinh[a])*Sinh[b*x])/b^4","A",1
385,1,172,104,0.5070634,"\int x^2 \sinh (a+b x) \tanh ^2(a+b x) \, dx","Integrate[x^2*Sinh[a + b*x]*Tanh[a + b*x]^2,x]","\frac{b^2 x^2 \text{sech}(a+b x)+\cosh (b x) \left(\cosh (a) \left(b^2 x^2+2\right)-2 b x \sinh (a)\right)+\sinh (b x) \left(\sinh (a) \left(b^2 x^2+2\right)-2 b x \cosh (a)\right)+2 i \left(\text{Li}_2\left(-i e^{a+b x}\right)-\text{Li}_2\left(i e^{a+b x}\right)\right)+(-2 i a-2 i b x+\pi ) \left(\log \left(1-i e^{a+b x}\right)-\log \left(1+i e^{a+b x}\right)\right)-(\pi -2 i a) \log \left(\cot \left(\frac{1}{4} (2 i a+2 i b x+\pi )\right)\right)}{b^3}","\frac{2 i \text{Li}_2\left(-i e^{a+b x}\right)}{b^3}-\frac{2 i \text{Li}_2\left(i e^{a+b x}\right)}{b^3}+\frac{2 \cosh (a+b x)}{b^3}-\frac{4 x \tan ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{2 x \sinh (a+b x)}{b^2}+\frac{x^2 \cosh (a+b x)}{b}+\frac{x^2 \text{sech}(a+b x)}{b}",1,"(((-2*I)*a + Pi - (2*I)*b*x)*(Log[1 - I*E^(a + b*x)] - Log[1 + I*E^(a + b*x)]) - ((-2*I)*a + Pi)*Log[Cot[((2*I)*a + Pi + (2*I)*b*x)/4]] + (2*I)*(PolyLog[2, (-I)*E^(a + b*x)] - PolyLog[2, I*E^(a + b*x)]) + b^2*x^2*Sech[a + b*x] + Cosh[b*x]*((2 + b^2*x^2)*Cosh[a] - 2*b*x*Sinh[a]) + (-2*b*x*Cosh[a] + (2 + b^2*x^2)*Sinh[a])*Sinh[b*x])/b^3","A",1
386,1,50,46,0.1186851,"\int x \sinh (a+b x) \tanh ^2(a+b x) \, dx","Integrate[x*Sinh[a + b*x]*Tanh[a + b*x]^2,x]","-\frac{\sinh (a+b x)}{b^2}-\frac{2 \tan ^{-1}\left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{b^2}+\frac{x \cosh (a+b x)}{b}+\frac{x \text{sech}(a+b x)}{b}","-\frac{\sinh (a+b x)}{b^2}-\frac{\tan ^{-1}(\sinh (a+b x))}{b^2}+\frac{x \cosh (a+b x)}{b}+\frac{x \text{sech}(a+b x)}{b}",1,"(-2*ArcTan[Tanh[(a + b*x)/2]])/b^2 + (x*Cosh[a + b*x])/b + (x*Sech[a + b*x])/b - Sinh[a + b*x]/b^2","A",1
387,1,21,21,0.0294551,"\int \sinh (a+b x) \tanh ^2(a+b x) \, dx","Integrate[Sinh[a + b*x]*Tanh[a + b*x]^2,x]","\frac{\cosh (a+b x)}{b}+\frac{\text{sech}(a+b x)}{b}","\frac{\cosh (a+b x)}{b}+\frac{\text{sech}(a+b x)}{b}",1,"Cosh[a + b*x]/b + Sech[a + b*x]/b","A",1
388,0,0,36,12.0947893,"\int \frac{\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx","Integrate[(Sinh[a + b*x]*Tanh[a + b*x]^2)/x,x]","\int \frac{\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx","-\text{Int}\left(\frac{\tanh (a+b x) \text{sech}(a+b x)}{x},x\right)+\sinh (a) \text{Chi}(b x)+\cosh (a) \text{Shi}(b x)",0,"Integrate[(Sinh[a + b*x]*Tanh[a + b*x]^2)/x, x]","A",-1
389,0,0,49,10.232132,"\int \frac{\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx","Integrate[(Sinh[a + b*x]*Tanh[a + b*x]^2)/x^2,x]","\int \frac{\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx","-\text{Int}\left(\frac{\tanh (a+b x) \text{sech}(a+b x)}{x^2},x\right)+b \cosh (a) \text{Chi}(b x)+b \sinh (a) \text{Shi}(b x)-\frac{\sinh (a+b x)}{x}",0,"Integrate[(Sinh[a + b*x]*Tanh[a + b*x]^2)/x^2, x]","A",-1
390,0,0,15,1.5280202,"\int x^m \tanh ^3(a+b x) \, dx","Integrate[x^m*Tanh[a + b*x]^3,x]","\int x^m \tanh ^3(a+b x) \, dx","\text{Int}\left(x^m \tanh ^3(a+b x),x\right)",0,"Integrate[x^m*Tanh[a + b*x]^3, x]","A",-1
391,1,230,183,2.8958353,"\int x^3 \tanh ^3(a+b x) \, dx","Integrate[x^3*Tanh[a + b*x]^3,x]","\frac{1}{4} \left(-\frac{6 x^2 \text{sech}(a) \sinh (b x) \text{sech}(a+b x)}{b^2}+\frac{e^{2 a} \left(2 e^{-2 a} b^4 x^4+4 \left(e^{-2 a}+1\right) b^3 x^3 \log \left(e^{-2 (a+b x)}+1\right)-3 e^{-2 a} \left(e^{2 a}+1\right) \left(2 b^2 x^2 \text{Li}_2\left(-e^{-2 (a+b x)}\right)+2 b x \text{Li}_3\left(-e^{-2 (a+b x)}\right)+\text{Li}_4\left(-e^{-2 (a+b x)}\right)\right)+12 e^{-2 a} b^2 x^2-6 \left(e^{-2 a}+1\right) \text{Li}_2\left(-e^{-2 (a+b x)}\right)+12 \left(e^{-2 a}+1\right) b x \log \left(e^{-2 (a+b x)}+1\right)\right)}{\left(e^{2 a}+1\right) b^4}+\frac{2 x^3 \text{sech}^2(a+b x)}{b}+x^4 \tanh (a)\right)","\frac{3 \text{Li}_2\left(-e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 \text{Li}_4\left(-e^{2 (a+b x)}\right)}{4 b^4}-\frac{3 x \text{Li}_3\left(-e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 x \log \left(e^{2 (a+b x)}+1\right)}{b^3}+\frac{3 x^2 \text{Li}_2\left(-e^{2 (a+b x)}\right)}{2 b^2}-\frac{3 x^2 \tanh (a+b x)}{2 b^2}+\frac{x^3 \log \left(e^{2 (a+b x)}+1\right)}{b}-\frac{x^3 \tanh ^2(a+b x)}{2 b}-\frac{3 x^2}{2 b^2}+\frac{x^3}{2 b}-\frac{x^4}{4}",1,"((E^(2*a)*((12*b^2*x^2)/E^(2*a) + (2*b^4*x^4)/E^(2*a) + 12*b*(1 + E^(-2*a))*x*Log[1 + E^(-2*(a + b*x))] + 4*b^3*(1 + E^(-2*a))*x^3*Log[1 + E^(-2*(a + b*x))] - 6*(1 + E^(-2*a))*PolyLog[2, -E^(-2*(a + b*x))] - (3*(1 + E^(2*a))*(2*b^2*x^2*PolyLog[2, -E^(-2*(a + b*x))] + 2*b*x*PolyLog[3, -E^(-2*(a + b*x))] + PolyLog[4, -E^(-2*(a + b*x))]))/E^(2*a)))/(b^4*(1 + E^(2*a))) + (2*x^3*Sech[a + b*x]^2)/b - (6*x^2*Sech[a]*Sech[a + b*x]*Sinh[b*x])/b^2 + x^4*Tanh[a])/4","A",1
392,1,185,116,2.3775087,"\int x^2 \tanh ^3(a+b x) \, dx","Integrate[x^2*Tanh[a + b*x]^3,x]","\frac{1}{6} \left(\frac{e^{2 a} \left(4 e^{-2 a} b^2 x^3-3 \left(e^{-2 a}+1\right) \left(2 x \text{Li}_2\left(-e^{-2 (a+b x)}\right)+\frac{\text{Li}_3\left(-e^{-2 (a+b x)}\right)}{b}\right)+6 \left(e^{-2 a}+1\right) b x^2 \log \left(e^{-2 (a+b x)}+1\right)-\frac{6 \left(e^{-2 a}+1\right) \left(2 b x-\log \left(e^{2 (a+b x)}+1\right)\right)}{b}+12 e^{-2 a} x\right)}{\left(e^{2 a}+1\right) b^2}-\frac{6 x \text{sech}(a) \sinh (b x) \text{sech}(a+b x)}{b^2}+\frac{3 x^2 \text{sech}^2(a+b x)}{b}+2 x^3 \tanh (a)\right)","-\frac{\text{Li}_3\left(-e^{2 (a+b x)}\right)}{2 b^3}+\frac{\log (\cosh (a+b x))}{b^3}+\frac{x \text{Li}_2\left(-e^{2 (a+b x)}\right)}{b^2}-\frac{x \tanh (a+b x)}{b^2}+\frac{x^2 \log \left(e^{2 (a+b x)}+1\right)}{b}-\frac{x^2 \tanh ^2(a+b x)}{2 b}+\frac{x^2}{2 b}-\frac{x^3}{3}",1,"((E^(2*a)*((12*x)/E^(2*a) + (4*b^2*x^3)/E^(2*a) + 6*b*(1 + E^(-2*a))*x^2*Log[1 + E^(-2*(a + b*x))] - (6*(1 + E^(-2*a))*(2*b*x - Log[1 + E^(2*(a + b*x))]))/b - 3*(1 + E^(-2*a))*(2*x*PolyLog[2, -E^(-2*(a + b*x))] + PolyLog[3, -E^(-2*(a + b*x))]/b)))/(b^2*(1 + E^(2*a))) + (3*x^2*Sech[a + b*x]^2)/b - (6*x*Sech[a]*Sech[a + b*x]*Sinh[b*x])/b^2 + 2*x^3*Tanh[a])/6","A",1
393,1,231,82,6.1266809,"\int x \tanh ^3(a+b x) \, dx","Integrate[x*Tanh[a + b*x]^3,x]","\frac{\text{csch}(a) \text{sech}(a) \left(b^2 x^2 e^{-\tanh ^{-1}(\coth (a))}-\frac{i \coth (a) \left(i \text{Li}_2\left(e^{2 i \left(i b x+i \tanh ^{-1}(\coth (a))\right)}\right)-b x \left(-\pi +2 i \tanh ^{-1}(\coth (a))\right)-2 \left(i \tanh ^{-1}(\coth (a))+i b x\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}(\coth (a))+i b x\right)}\right)+2 i \tanh ^{-1}(\coth (a)) \log \left(i \sinh \left(\tanh ^{-1}(\coth (a))+b x\right)\right)-\pi  \log \left(e^{2 b x}+1\right)+\pi  \log (\cosh (b x))\right)}{\sqrt{1-\coth ^2(a)}}\right)}{2 b^2 \sqrt{\text{csch}^2(a) \left(\sinh ^2(a)-\cosh ^2(a)\right)}}-\frac{\text{sech}(a) \sinh (b x) \text{sech}(a+b x)}{2 b^2}+\frac{x \text{sech}^2(a+b x)}{2 b}+\frac{1}{2} x^2 \tanh (a)","\frac{\text{Li}_2\left(-e^{2 (a+b x)}\right)}{2 b^2}-\frac{\tanh (a+b x)}{2 b^2}+\frac{x \log \left(e^{2 (a+b x)}+1\right)}{b}-\frac{x \tanh ^2(a+b x)}{2 b}+\frac{x}{2 b}-\frac{x^2}{2}",1,"(x*Sech[a + b*x]^2)/(2*b) + (Csch[a]*((b^2*x^2)/E^ArcTanh[Coth[a]] - (I*Coth[a]*(-(b*x*(-Pi + (2*I)*ArcTanh[Coth[a]])) - Pi*Log[1 + E^(2*b*x)] - 2*(I*b*x + I*ArcTanh[Coth[a]])*Log[1 - E^((2*I)*(I*b*x + I*ArcTanh[Coth[a]]))] + Pi*Log[Cosh[b*x]] + (2*I)*ArcTanh[Coth[a]]*Log[I*Sinh[b*x + ArcTanh[Coth[a]]]] + I*PolyLog[2, E^((2*I)*(I*b*x + I*ArcTanh[Coth[a]]))]))/Sqrt[1 - Coth[a]^2])*Sech[a])/(2*b^2*Sqrt[Csch[a]^2*(-Cosh[a]^2 + Sinh[a]^2)]) - (Sech[a]*Sech[a + b*x]*Sinh[b*x])/(2*b^2) + (x^2*Tanh[a])/2","C",0
394,1,27,27,0.0131494,"\int \tanh ^3(a+b x) \, dx","Integrate[Tanh[a + b*x]^3,x]","\frac{\log (\cosh (a+b x))}{b}-\frac{\tanh ^2(a+b x)}{2 b}","\frac{\log (\cosh (a+b x))}{b}-\frac{\tanh ^2(a+b x)}{2 b}",1,"Log[Cosh[a + b*x]]/b - Tanh[a + b*x]^2/(2*b)","A",1
395,0,0,15,14.1141972,"\int \frac{\tanh ^3(a+b x)}{x} \, dx","Integrate[Tanh[a + b*x]^3/x,x]","\int \frac{\tanh ^3(a+b x)}{x} \, dx","\text{Int}\left(\frac{\tanh ^3(a+b x)}{x},x\right)",0,"Integrate[Tanh[a + b*x]^3/x, x]","A",-1
396,0,0,15,8.4031986,"\int \frac{\tanh ^3(a+b x)}{x^2} \, dx","Integrate[Tanh[a + b*x]^3/x^2,x]","\int \frac{\tanh ^3(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\tanh ^3(a+b x)}{x^2},x\right)",0,"Integrate[Tanh[a + b*x]^3/x^2, x]","A",-1
397,0,0,13,7.5790555,"\int x^m \coth (a+b x) \, dx","Integrate[x^m*Coth[a + b*x],x]","\int x^m \coth (a+b x) \, dx","\text{Int}\left(x^m \coth (a+b x),x\right)",0,"Integrate[x^m*Coth[a + b*x], x]","A",-1
398,1,91,87,0.0110902,"\int x^3 \coth (a+b x) \, dx","Integrate[x^3*Coth[a + b*x],x]","\frac{3 \text{Li}_4\left(e^{2 a+2 b x}\right)}{4 b^4}-\frac{3 x \text{Li}_3\left(e^{2 a+2 b x}\right)}{2 b^3}+\frac{3 x^2 \text{Li}_2\left(e^{2 a+2 b x}\right)}{2 b^2}+\frac{x^3 \log \left(1-e^{2 a+2 b x}\right)}{b}-\frac{x^4}{4}","\frac{3 \text{Li}_4\left(e^{2 (a+b x)}\right)}{4 b^4}-\frac{3 x \text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 x^2 \text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^2}+\frac{x^3 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^4}{4}",1,"-1/4*x^4 + (x^3*Log[1 - E^(2*a + 2*b*x)])/b + (3*x^2*PolyLog[2, E^(2*a + 2*b*x)])/(2*b^2) - (3*x*PolyLog[3, E^(2*a + 2*b*x)])/(2*b^3) + (3*PolyLog[4, E^(2*a + 2*b*x)])/(4*b^4)","A",1
399,1,66,63,0.0104326,"\int x^2 \coth (a+b x) \, dx","Integrate[x^2*Coth[a + b*x],x]","-\frac{\text{Li}_3\left(e^{2 a+2 b x}\right)}{2 b^3}+\frac{x \text{Li}_2\left(e^{2 a+2 b x}\right)}{b^2}+\frac{x^2 \log \left(1-e^{2 a+2 b x}\right)}{b}-\frac{x^3}{3}","-\frac{\text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^3}+\frac{x \text{Li}_2\left(e^{2 (a+b x)}\right)}{b^2}+\frac{x^2 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^3}{3}",1,"-1/3*x^3 + (x^2*Log[1 - E^(2*a + 2*b*x)])/b + (x*PolyLog[2, E^(2*a + 2*b*x)])/b^2 - PolyLog[3, E^(2*a + 2*b*x)]/(2*b^3)","A",1
400,1,47,45,0.0066912,"\int x \coth (a+b x) \, dx","Integrate[x*Coth[a + b*x],x]","\frac{\text{Li}_2\left(e^{2 a+2 b x}\right)}{2 b^2}+\frac{x \log \left(1-e^{2 a+2 b x}\right)}{b}-\frac{x^2}{2}","\frac{\text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^2}+\frac{x \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^2}{2}",1,"-1/2*x^2 + (x*Log[1 - E^(2*a + 2*b*x)])/b + PolyLog[2, E^(2*a + 2*b*x)]/(2*b^2)","A",1
401,1,19,11,0.0146922,"\int \coth (a+b x) \, dx","Integrate[Coth[a + b*x],x]","\frac{\log (\tanh (a+b x))+\log (\cosh (a+b x))}{b}","\frac{\log (\sinh (a+b x))}{b}",1,"(Log[Cosh[a + b*x]] + Log[Tanh[a + b*x]])/b","A",1
402,0,0,13,0.4552214,"\int \frac{\coth (a+b x)}{x} \, dx","Integrate[Coth[a + b*x]/x,x]","\int \frac{\coth (a+b x)}{x} \, dx","\text{Int}\left(\frac{\coth (a+b x)}{x},x\right)",0,"Integrate[Coth[a + b*x]/x, x]","A",-1
403,0,0,13,0.8694435,"\int \frac{\coth (a+b x)}{x^2} \, dx","Integrate[Coth[a + b*x]/x^2,x]","\int \frac{\coth (a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\coth (a+b x)}{x^2},x\right)",0,"Integrate[Coth[a + b*x]/x^2, x]","A",-1
404,0,0,72,19.5886348,"\int x^m \cosh (a+b x) \coth (a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]*Coth[a + b*x],x]","\int x^m \cosh (a+b x) \coth (a+b x) \, dx","\text{Int}\left(x^m \text{csch}(a+b x),x\right)+\frac{e^a x^m (-b x)^{-m} \Gamma (m+1,-b x)}{2 b}+\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+1,b x)}{2 b}",0,"Integrate[x^m*Cosh[a + b*x]*Coth[a + b*x], x]","A",-1
405,1,202,165,4.1779314,"\int x^3 \cosh (a+b x) \coth (a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]*Coth[a + b*x],x]","\frac{b^3 x^3 \cosh (a+b x)-2 b^3 x^3 \tanh ^{-1}(\sinh (a+b x)+\cosh (a+b x))-3 b^2 x^2 \text{Li}_2(-\cosh (a+b x)-\sinh (a+b x))+3 b^2 x^2 \text{Li}_2(\cosh (a+b x)+\sinh (a+b x))-3 b^2 x^2 \sinh (a+b x)+6 b x \text{Li}_3(-\cosh (a+b x)-\sinh (a+b x))-6 b x \text{Li}_3(\cosh (a+b x)+\sinh (a+b x))-6 \text{Li}_4(-\cosh (a+b x)-\sinh (a+b x))+6 \text{Li}_4(\cosh (a+b x)+\sinh (a+b x))-6 \sinh (a+b x)+6 b x \cosh (a+b x)}{b^4}","-\frac{6 \text{Li}_4\left(-e^{a+b x}\right)}{b^4}+\frac{6 \text{Li}_4\left(e^{a+b x}\right)}{b^4}-\frac{6 \sinh (a+b x)}{b^4}+\frac{6 x \text{Li}_3\left(-e^{a+b x}\right)}{b^3}-\frac{6 x \text{Li}_3\left(e^{a+b x}\right)}{b^3}+\frac{6 x \cosh (a+b x)}{b^3}-\frac{3 x^2 \text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{3 x^2 \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{3 x^2 \sinh (a+b x)}{b^2}+\frac{x^3 \cosh (a+b x)}{b}-\frac{2 x^3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(-2*b^3*x^3*ArcTanh[Cosh[a + b*x] + Sinh[a + b*x]] + 6*b*x*Cosh[a + b*x] + b^3*x^3*Cosh[a + b*x] - 3*b^2*x^2*PolyLog[2, -Cosh[a + b*x] - Sinh[a + b*x]] + 3*b^2*x^2*PolyLog[2, Cosh[a + b*x] + Sinh[a + b*x]] + 6*b*x*PolyLog[3, -Cosh[a + b*x] - Sinh[a + b*x]] - 6*b*x*PolyLog[3, Cosh[a + b*x] + Sinh[a + b*x]] - 6*PolyLog[4, -Cosh[a + b*x] - Sinh[a + b*x]] + 6*PolyLog[4, Cosh[a + b*x] + Sinh[a + b*x]] - 6*Sinh[a + b*x] - 3*b^2*x^2*Sinh[a + b*x])/b^4","A",0
406,1,138,115,4.0750783,"\int x^2 \cosh (a+b x) \coth (a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]*Coth[a + b*x],x]","\frac{b^2 x^2 \cosh (a+b x)-2 b^2 x^2 \tanh ^{-1}(\sinh (a+b x)+\cosh (a+b x))-2 b x \text{Li}_2(-\cosh (a+b x)-\sinh (a+b x))+2 b x \text{Li}_2(\cosh (a+b x)+\sinh (a+b x))+2 \text{Li}_3(-\cosh (a+b x)-\sinh (a+b x))-2 \text{Li}_3(\cosh (a+b x)+\sinh (a+b x))-2 b x \sinh (a+b x)+2 \cosh (a+b x)}{b^3}","\frac{2 \text{Li}_3\left(-e^{a+b x}\right)}{b^3}-\frac{2 \text{Li}_3\left(e^{a+b x}\right)}{b^3}+\frac{2 \cosh (a+b x)}{b^3}-\frac{2 x \text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{2 x \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{2 x \sinh (a+b x)}{b^2}+\frac{x^2 \cosh (a+b x)}{b}-\frac{2 x^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(-2*b^2*x^2*ArcTanh[Cosh[a + b*x] + Sinh[a + b*x]] + 2*Cosh[a + b*x] + b^2*x^2*Cosh[a + b*x] - 2*b*x*PolyLog[2, -Cosh[a + b*x] - Sinh[a + b*x]] + 2*b*x*PolyLog[2, Cosh[a + b*x] + Sinh[a + b*x]] + 2*PolyLog[3, -Cosh[a + b*x] - Sinh[a + b*x]] - 2*PolyLog[3, Cosh[a + b*x] + Sinh[a + b*x]] - 2*b*x*Sinh[a + b*x])/b^3","A",0
407,1,131,66,0.1375497,"\int x \cosh (a+b x) \coth (a+b x) \, dx","Integrate[x*Cosh[a + b*x]*Coth[a + b*x],x]","-\frac{-\text{Li}_2\left(-e^{-a-b x}\right)+\text{Li}_2\left(e^{-a-b x}\right)-a \log \left(1-e^{-a-b x}\right)-b x \log \left(1-e^{-a-b x}\right)+a \log \left(e^{-a-b x}+1\right)+b x \log \left(e^{-a-b x}+1\right)+\sinh (a+b x)-b x \cosh (a+b x)+a \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{b^2}","-\frac{\text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{\text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{\sinh (a+b x)}{b^2}+\frac{x \cosh (a+b x)}{b}-\frac{2 x \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"-((-(b*x*Cosh[a + b*x]) - a*Log[1 - E^(-a - b*x)] - b*x*Log[1 - E^(-a - b*x)] + a*Log[1 + E^(-a - b*x)] + b*x*Log[1 + E^(-a - b*x)] + a*Log[Tanh[(a + b*x)/2]] - PolyLog[2, -E^(-a - b*x)] + PolyLog[2, E^(-a - b*x)] + Sinh[a + b*x])/b^2)","A",1
408,1,26,23,0.0221456,"\int \cosh (a+b x) \coth (a+b x) \, dx","Integrate[Cosh[a + b*x]*Coth[a + b*x],x]","\frac{\cosh (a+b x)}{b}+\frac{\log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{b}","\frac{\cosh (a+b x)}{b}-\frac{\tanh ^{-1}(\cosh (a+b x))}{b}",1,"Cosh[a + b*x]/b + Log[Tanh[(a + b*x)/2]]/b","A",1
409,0,0,28,26.6178086,"\int \frac{\cosh (a+b x) \coth (a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]*Coth[a + b*x])/x,x]","\int \frac{\cosh (a+b x) \coth (a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{csch}(a+b x)}{x},x\right)+\sinh (a) \text{Chi}(b x)+\cosh (a) \text{Shi}(b x)",0,"Integrate[(Cosh[a + b*x]*Coth[a + b*x])/x, x]","A",-1
410,0,0,41,38.1647853,"\int \frac{\cosh (a+b x) \coth (a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]*Coth[a + b*x])/x^2,x]","\int \frac{\cosh (a+b x) \coth (a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{csch}(a+b x)}{x^2},x\right)+b \cosh (a) \text{Chi}(b x)+b \sinh (a) \text{Shi}(b x)-\frac{\sinh (a+b x)}{x}",0,"Integrate[(Cosh[a + b*x]*Coth[a + b*x])/x^2, x]","A",-1
411,0,0,83,23.5446313,"\int x^m \cosh ^2(a+b x) \coth (a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]^2*Coth[a + b*x],x]","\int x^m \cosh ^2(a+b x) \coth (a+b x) \, dx","\text{Int}\left(x^m \coth (a+b x),x\right)+\frac{e^{2 a} 2^{-m-3} x^m (-b x)^{-m} \Gamma (m+1,-2 b x)}{b}+\frac{e^{-2 a} 2^{-m-3} x^m (b x)^{-m} \Gamma (m+1,2 b x)}{b}",0,"Integrate[x^m*Cosh[a + b*x]^2*Coth[a + b*x], x]","A",-1
412,1,236,180,2.614988,"\int x^3 \cosh ^2(a+b x) \coth (a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]^2*Coth[a + b*x],x]","\frac{\sinh (a) (\sinh (a)+\cosh (a)) \left(16 b^3 x^3 \log \left(1-e^{-a-b x}\right)+16 b^3 x^3 \log \left(e^{-a-b x}+1\right)+4 b^3 x^3 \cosh (2 (a+b x))-48 b^2 x^2 \text{Li}_2\left(-e^{-a-b x}\right)-48 b^2 x^2 \text{Li}_2\left(e^{-a-b x}\right)-6 b^2 x^2 \sinh (2 (a+b x))-96 b x \text{Li}_3\left(-e^{-a-b x}\right)-96 b x \text{Li}_3\left(e^{-a-b x}\right)-96 \text{Li}_4\left(-e^{-a-b x}\right)-96 \text{Li}_4\left(e^{-a-b x}\right)-3 \sinh (2 (a+b x))+6 b x \cosh (2 (a+b x))+4 b^4 x^4\right)}{8 \left(e^{2 a}-1\right) b^4}","\frac{3 \text{Li}_4\left(e^{2 (a+b x)}\right)}{4 b^4}-\frac{3 \sinh (a+b x) \cosh (a+b x)}{8 b^4}-\frac{3 x \text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 x \sinh ^2(a+b x)}{4 b^3}+\frac{3 x^2 \text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^2}-\frac{3 x^2 \sinh (a+b x) \cosh (a+b x)}{4 b^2}+\frac{x^3 \log \left(1-e^{2 (a+b x)}\right)}{b}+\frac{x^3 \sinh ^2(a+b x)}{2 b}+\frac{3 x}{8 b^3}+\frac{x^3}{4 b}-\frac{x^4}{4}",1,"(Sinh[a]*(Cosh[a] + Sinh[a])*(4*b^4*x^4 + 6*b*x*Cosh[2*(a + b*x)] + 4*b^3*x^3*Cosh[2*(a + b*x)] + 16*b^3*x^3*Log[1 - E^(-a - b*x)] + 16*b^3*x^3*Log[1 + E^(-a - b*x)] - 48*b^2*x^2*PolyLog[2, -E^(-a - b*x)] - 48*b^2*x^2*PolyLog[2, E^(-a - b*x)] - 96*b*x*PolyLog[3, -E^(-a - b*x)] - 96*b*x*PolyLog[3, E^(-a - b*x)] - 96*PolyLog[4, -E^(-a - b*x)] - 96*PolyLog[4, E^(-a - b*x)] - 3*Sinh[2*(a + b*x)] - 6*b^2*x^2*Sinh[2*(a + b*x)]))/(8*b^4*(-1 + E^(2*a)))","A",1
413,1,178,126,2.5905609,"\int x^2 \cosh ^2(a+b x) \coth (a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]^2*Coth[a + b*x],x]","\frac{\sinh (a) (\sinh (a)+\cosh (a)) \left(24 b^2 x^2 \log \left(1-e^{-a-b x}\right)+24 b^2 x^2 \log \left(e^{-a-b x}+1\right)+6 b^2 x^2 \cosh (2 (a+b x))-48 b x \text{Li}_2\left(-e^{-a-b x}\right)-48 b x \text{Li}_2\left(e^{-a-b x}\right)-48 \text{Li}_3\left(-e^{-a-b x}\right)-48 \text{Li}_3\left(e^{-a-b x}\right)-6 b x \sinh (2 (a+b x))+3 \cosh (2 (a+b x))+8 b^3 x^3\right)}{12 \left(e^{2 a}-1\right) b^3}","-\frac{\text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^3}+\frac{\sinh ^2(a+b x)}{4 b^3}+\frac{x \text{Li}_2\left(e^{2 (a+b x)}\right)}{b^2}-\frac{x \sinh (a+b x) \cosh (a+b x)}{2 b^2}+\frac{x^2 \log \left(1-e^{2 (a+b x)}\right)}{b}+\frac{x^2 \sinh ^2(a+b x)}{2 b}+\frac{x^2}{4 b}-\frac{x^3}{3}",1,"(Sinh[a]*(Cosh[a] + Sinh[a])*(8*b^3*x^3 + 3*Cosh[2*(a + b*x)] + 6*b^2*x^2*Cosh[2*(a + b*x)] + 24*b^2*x^2*Log[1 - E^(-a - b*x)] + 24*b^2*x^2*Log[1 + E^(-a - b*x)] - 48*b*x*PolyLog[2, -E^(-a - b*x)] - 48*b*x*PolyLog[2, E^(-a - b*x)] - 48*PolyLog[3, -E^(-a - b*x)] - 48*PolyLog[3, E^(-a - b*x)] - 6*b*x*Sinh[2*(a + b*x)]))/(12*b^3*(-1 + E^(2*a)))","A",1
414,1,82,88,0.2491748,"\int x \cosh ^2(a+b x) \coth (a+b x) \, dx","Integrate[x*Cosh[a + b*x]^2*Coth[a + b*x],x]","-\frac{4 \left(\text{Li}_2\left(e^{-2 (a+b x)}\right)-(a+b x)^2\right)-8 (a+b x) \log \left(1-e^{-2 (a+b x)}\right)+\sinh (2 (a+b x))-2 b x \cosh (2 (a+b x))+8 a \log (\sinh (a+b x))}{8 b^2}","\frac{\text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^2}-\frac{\sinh (a+b x) \cosh (a+b x)}{4 b^2}+\frac{x \log \left(1-e^{2 (a+b x)}\right)}{b}+\frac{x \sinh ^2(a+b x)}{2 b}+\frac{x}{4 b}-\frac{x^2}{2}",1,"-1/8*(-2*b*x*Cosh[2*(a + b*x)] - 8*(a + b*x)*Log[1 - E^(-2*(a + b*x))] + 8*a*Log[Sinh[a + b*x]] + 4*(-(a + b*x)^2 + PolyLog[2, E^(-2*(a + b*x))]) + Sinh[2*(a + b*x)])/b^2","A",1
415,1,25,27,0.0218268,"\int \cosh ^2(a+b x) \coth (a+b x) \, dx","Integrate[Cosh[a + b*x]^2*Coth[a + b*x],x]","\frac{\sinh ^2(a+b x)+2 \log (\sinh (a+b x))}{2 b}","\frac{\sinh ^2(a+b x)}{2 b}+\frac{\log (\sinh (a+b x))}{b}",1,"(2*Log[Sinh[a + b*x]] + Sinh[a + b*x]^2)/(2*b)","A",1
416,0,0,40,11.4137798,"\int \frac{\cosh ^2(a+b x) \coth (a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]^2*Coth[a + b*x])/x,x]","\int \frac{\cosh ^2(a+b x) \coth (a+b x)}{x} \, dx","\text{Int}\left(\frac{\coth (a+b x)}{x},x\right)+\frac{1}{2} \sinh (2 a) \text{Chi}(2 b x)+\frac{1}{2} \cosh (2 a) \text{Shi}(2 b x)",0,"Integrate[(Cosh[a + b*x]^2*Coth[a + b*x])/x, x]","A",-1
417,0,0,52,16.8504278,"\int \frac{\cosh ^2(a+b x) \coth (a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]^2*Coth[a + b*x])/x^2,x]","\int \frac{\cosh ^2(a+b x) \coth (a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\coth (a+b x)}{x^2},x\right)+b \cosh (2 a) \text{Chi}(2 b x)+b \sinh (2 a) \text{Shi}(2 b x)-\frac{\sinh (2 a+2 b x)}{2 x}",0,"Integrate[(Cosh[a + b*x]^2*Coth[a + b*x])/x^2, x]","A",-1
418,1,33,33,0.0289531,"\int x \cosh ^2(x) \coth ^2(x) \, dx","Integrate[x*Cosh[x]^2*Coth[x]^2,x]","\frac{3 x^2}{4}+\frac{1}{4} x \sinh (2 x)-\frac{1}{8} \cosh (2 x)-x \coth (x)+\log (\sinh (x))","\frac{3 x^2}{4}-\frac{\cosh ^2(x)}{4}-x \coth (x)+\log (\sinh (x))+\frac{1}{2} x \sinh (x) \cosh (x)",1,"(3*x^2)/4 - Cosh[2*x]/8 - x*Coth[x] + Log[Sinh[x]] + (x*Sinh[2*x])/4","A",1
419,1,64,73,0.0982642,"\int x^2 \cosh ^2(x) \coth ^2(x) \, dx","Integrate[x^2*Cosh[x]^2*Coth[x]^2,x]","\frac{1}{8} \left(-8 \text{Li}_2\left(e^{-2 x}\right)+4 x^3+8 x^2+2 x^2 \sinh (2 x)-8 x^2 \coth (x)+16 x \log \left(1-e^{-2 x}\right)+\sinh (2 x)-2 x \cosh (2 x)\right)","\text{Li}_2\left(e^{2 x}\right)+\frac{x^3}{2}-x^2-x^2 \coth (x)+\frac{1}{2} x^2 \sinh (x) \cosh (x)+\frac{x}{4}+2 x \log \left(1-e^{2 x}\right)-\frac{1}{2} x \cosh ^2(x)+\frac{1}{4} \sinh (x) \cosh (x)",1,"(8*x^2 + 4*x^3 - 2*x*Cosh[2*x] - 8*x^2*Coth[x] + 16*x*Log[1 - E^(-2*x)] - 8*PolyLog[2, E^(-2*x)] + Sinh[2*x] + 2*x^2*Sinh[2*x])/8","A",1
420,1,94,102,0.1519572,"\int x^3 \cosh ^2(x) \coth ^2(x) \, dx","Integrate[x^3*Cosh[x]^2*Coth[x]^2,x]","\frac{1}{16} \left(48 x \text{Li}_2\left(e^{2 x}\right)-24 \text{Li}_3\left(e^{2 x}\right)+6 x^4-16 x^3+4 x^3 \sinh (2 x)-16 x^3 \coth (x)+48 x^2 \log \left(1-e^{2 x}\right)-6 x^2 \cosh (2 x)+6 x \sinh (2 x)-3 \cosh (2 x)+2 i \pi ^3\right)","3 x \text{Li}_2\left(e^{2 x}\right)-\frac{3 \text{Li}_3\left(e^{2 x}\right)}{2}+\frac{3 x^4}{8}-x^3-x^3 \coth (x)+\frac{1}{2} x^3 \sinh (x) \cosh (x)+\frac{3 x^2}{8}+3 x^2 \log \left(1-e^{2 x}\right)-\frac{3}{4} x^2 \cosh ^2(x)-\frac{3 \cosh ^2(x)}{8}+\frac{3}{4} x \sinh (x) \cosh (x)",1,"((2*I)*Pi^3 - 16*x^3 + 6*x^4 - 3*Cosh[2*x] - 6*x^2*Cosh[2*x] - 16*x^3*Coth[x] + 48*x^2*Log[1 - E^(2*x)] + 48*x*PolyLog[2, E^(2*x)] - 24*PolyLog[3, E^(2*x)] + 6*x*Sinh[2*x] + 4*x^3*Sinh[2*x])/16","C",1
421,1,56,63,0.0798868,"\int x \cosh ^2(x) \coth ^3(x) \, dx","Integrate[x*Cosh[x]^2*Coth[x]^3,x]","\frac{1}{8} \left(-8 \text{Li}_2\left(e^{-2 x}\right)+8 x^2+16 x \log \left(1-e^{-2 x}\right)-\sinh (2 x)+2 x \cosh (2 x)-4 \coth (x)-4 x \text{csch}^2(x)\right)","\text{Li}_2\left(e^{2 x}\right)-x^2+\frac{3 x}{4}+2 x \log \left(1-e^{2 x}\right)+\frac{1}{2} x \sinh ^2(x)-\frac{1}{2} x \coth ^2(x)-\frac{\coth (x)}{2}-\frac{1}{4} \sinh (x) \cosh (x)",1,"(8*x^2 + 2*x*Cosh[2*x] - 4*Coth[x] - 4*x*Csch[x]^2 + 16*x*Log[1 - E^(-2*x)] - 8*PolyLog[2, E^(-2*x)] - Sinh[2*x])/8","A",1
422,1,98,96,0.284107,"\int x^2 \cosh ^2(x) \coth ^3(x) \, dx","Integrate[x^2*Cosh[x]^2*Coth[x]^3,x]","2 x \text{Li}_2\left(e^{2 x}\right)-\text{Li}_3\left(e^{2 x}\right)-\frac{2 x^3}{3}+2 x^2 \log \left(1-e^{2 x}\right)+\frac{1}{4} x^2 \cosh (2 x)-\frac{1}{2} x^2 \text{csch}^2(x)-\frac{1}{4} x \sinh (2 x)+\frac{1}{8} \cosh (2 x)-x \coth (x)+\log (\sinh (x))+\frac{i \pi ^3}{12}","2 x \text{Li}_2\left(e^{2 x}\right)-\text{Li}_3\left(e^{2 x}\right)-\frac{2 x^3}{3}+\frac{3 x^2}{4}+2 x^2 \log \left(1-e^{2 x}\right)+\frac{1}{2} x^2 \sinh ^2(x)-\frac{1}{2} x^2 \coth ^2(x)+\frac{\sinh ^2(x)}{4}-x \coth (x)+\log (\sinh (x))-\frac{1}{2} x \sinh (x) \cosh (x)",1,"(I/12)*Pi^3 - (2*x^3)/3 + Cosh[2*x]/8 + (x^2*Cosh[2*x])/4 - x*Coth[x] - (x^2*Csch[x]^2)/2 + 2*x^2*Log[1 - E^(2*x)] + Log[Sinh[x]] + 2*x*PolyLog[2, E^(2*x)] - PolyLog[3, E^(2*x)] - (x*Sinh[2*x])/4","C",1
423,1,133,158,0.3354973,"\int x^3 \cosh ^2(x) \coth ^3(x) \, dx","Integrate[x^3*Cosh[x]^2*Coth[x]^3,x]","\frac{1}{32} \left(96 x^2 \text{Li}_2\left(e^{2 x}\right)-96 x \text{Li}_3\left(e^{2 x}\right)-48 \text{Li}_2\left(e^{-2 x}\right)+48 \text{Li}_4\left(e^{2 x}\right)-16 x^4+64 x^3 \log \left(1-e^{2 x}\right)+8 x^3 \cosh (2 x)-16 x^3 \text{csch}^2(x)+48 x^2-12 x^2 \sinh (2 x)-48 x^2 \coth (x)+96 x \log \left(1-e^{-2 x}\right)-6 \sinh (2 x)+12 x \cosh (2 x)+\pi ^4\right)","3 x^2 \text{Li}_2\left(e^{2 x}\right)-3 x \text{Li}_3\left(e^{2 x}\right)+\frac{3 \text{Li}_2\left(e^{2 x}\right)}{2}+\frac{3 \text{Li}_4\left(e^{2 x}\right)}{2}-\frac{x^4}{2}+\frac{3 x^3}{4}+2 x^3 \log \left(1-e^{2 x}\right)+\frac{1}{2} x^3 \sinh ^2(x)-\frac{1}{2} x^3 \coth ^2(x)-\frac{3 x^2}{2}-\frac{3}{2} x^2 \coth (x)-\frac{3}{4} x^2 \sinh (x) \cosh (x)+\frac{3 x}{8}+3 x \log \left(1-e^{2 x}\right)+\frac{3}{4} x \sinh ^2(x)-\frac{3}{8} \sinh (x) \cosh (x)",1,"(Pi^4 + 48*x^2 - 16*x^4 + 12*x*Cosh[2*x] + 8*x^3*Cosh[2*x] - 48*x^2*Coth[x] - 16*x^3*Csch[x]^2 + 96*x*Log[1 - E^(-2*x)] + 64*x^3*Log[1 - E^(2*x)] - 48*PolyLog[2, E^(-2*x)] + 96*x^2*PolyLog[2, E^(2*x)] - 96*x*PolyLog[3, E^(2*x)] + 48*PolyLog[4, E^(2*x)] - 6*Sinh[2*x] - 12*x^2*Sinh[2*x])/32","A",1
424,0,0,19,31.011782,"\int x^m \coth (a+b x) \text{csch}(a+b x) \, dx","Integrate[x^m*Coth[a + b*x]*Csch[a + b*x],x]","\int x^m \coth (a+b x) \text{csch}(a+b x) \, dx","\text{Int}\left(x^m \coth (a+b x) \text{csch}(a+b x),x\right)",0,"Integrate[x^m*Coth[a + b*x]*Csch[a + b*x], x]","A",-1
425,1,167,93,7.2085903,"\int x^3 \coth (a+b x) \text{csch}(a+b x) \, dx","Integrate[x^3*Coth[a + b*x]*Csch[a + b*x],x]","-\frac{\text{csch}\left(\frac{1}{2} (a+b x)\right) \text{sech}\left(\frac{1}{2} (a+b x)\right) \left(6 b^2 x^2 \sinh (a+b x) \tanh ^{-1}(\sinh (a+b x)+\cosh (a+b x))+6 b x \sinh (a+b x) \text{Li}_2(-\cosh (a+b x)-\sinh (a+b x))-6 b x \sinh (a+b x) \text{Li}_2(\cosh (a+b x)+\sinh (a+b x))-6 \sinh (a+b x) \text{Li}_3(-\cosh (a+b x)-\sinh (a+b x))+6 \sinh (a+b x) \text{Li}_3(\cosh (a+b x)+\sinh (a+b x))+b^3 x^3\right)}{2 b^4}","\frac{6 \text{Li}_3\left(-e^{a+b x}\right)}{b^4}-\frac{6 \text{Li}_3\left(e^{a+b x}\right)}{b^4}-\frac{6 x \text{Li}_2\left(-e^{a+b x}\right)}{b^3}+\frac{6 x \text{Li}_2\left(e^{a+b x}\right)}{b^3}-\frac{6 x^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{x^3 \text{csch}(a+b x)}{b}",1,"-1/2*(Csch[(a + b*x)/2]*Sech[(a + b*x)/2]*(b^3*x^3 + 6*b^2*x^2*ArcTanh[Cosh[a + b*x] + Sinh[a + b*x]]*Sinh[a + b*x] + 6*b*x*PolyLog[2, -Cosh[a + b*x] - Sinh[a + b*x]]*Sinh[a + b*x] - 6*b*x*PolyLog[2, Cosh[a + b*x] + Sinh[a + b*x]]*Sinh[a + b*x] - 6*PolyLog[3, -Cosh[a + b*x] - Sinh[a + b*x]]*Sinh[a + b*x] + 6*PolyLog[3, Cosh[a + b*x] + Sinh[a + b*x]]*Sinh[a + b*x]))/b^4","A",0
426,1,133,59,0.7873598,"\int x^2 \coth (a+b x) \text{csch}(a+b x) \, dx","Integrate[x^2*Coth[a + b*x]*Csch[a + b*x],x]","-\frac{b^2 x^2 \text{csch}(a+b x)-2 \text{Li}_2\left(-e^{-a-b x}\right)+2 \text{Li}_2\left(e^{-a-b x}\right)-2 b x \log \left(1-e^{-a-b x}\right)+2 b x \log \left(e^{-a-b x}+1\right)-2 a \log \left(1-e^{-a-b x}\right)+2 a \log \left(e^{-a-b x}+1\right)+2 a \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{b^3}","-\frac{2 \text{Li}_2\left(-e^{a+b x}\right)}{b^3}+\frac{2 \text{Li}_2\left(e^{a+b x}\right)}{b^3}-\frac{4 x \tanh ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{x^2 \text{csch}(a+b x)}{b}",1,"-((b^2*x^2*Csch[a + b*x] - 2*a*Log[1 - E^(-a - b*x)] - 2*b*x*Log[1 - E^(-a - b*x)] + 2*a*Log[1 + E^(-a - b*x)] + 2*b*x*Log[1 + E^(-a - b*x)] + 2*a*Log[Tanh[(a + b*x)/2]] - 2*PolyLog[2, -E^(-a - b*x)] + 2*PolyLog[2, E^(-a - b*x)])/b^3)","B",1
427,1,114,25,0.0499984,"\int x \coth (a+b x) \text{csch}(a+b x) \, dx","Integrate[x*Coth[a + b*x]*Csch[a + b*x],x]","\frac{\log \left(\sinh \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b^2}-\frac{\log \left(\cosh \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b^2}-\frac{x \text{csch}(a)}{b}+\frac{x \text{csch}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{csch}\left(\frac{a}{2}+\frac{b x}{2}\right)}{2 b}+\frac{x \text{sech}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{sech}\left(\frac{a}{2}+\frac{b x}{2}\right)}{2 b}","-\frac{\tanh ^{-1}(\cosh (a+b x))}{b^2}-\frac{x \text{csch}(a+b x)}{b}",1,"-((x*Csch[a])/b) - Log[Cosh[a/2 + (b*x)/2]]/b^2 + Log[Sinh[a/2 + (b*x)/2]]/b^2 + (x*Csch[a/2]*Csch[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(2*b) + (x*Sech[a/2]*Sech[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(2*b)","B",1
428,1,11,11,0.0097336,"\int \coth (a+b x) \text{csch}(a+b x) \, dx","Integrate[Coth[a + b*x]*Csch[a + b*x],x]","-\frac{\text{csch}(a+b x)}{b}","-\frac{\text{csch}(a+b x)}{b}",1,"-(Csch[a + b*x]/b)","A",1
429,0,0,19,32.0479955,"\int \frac{\coth (a+b x) \text{csch}(a+b x)}{x} \, dx","Integrate[(Coth[a + b*x]*Csch[a + b*x])/x,x]","\int \frac{\coth (a+b x) \text{csch}(a+b x)}{x} \, dx","\text{Int}\left(\frac{\coth (a+b x) \text{csch}(a+b x)}{x},x\right)",0,"Integrate[(Coth[a + b*x]*Csch[a + b*x])/x, x]","A",-1
430,0,0,19,38.1850075,"\int \frac{\coth (a+b x) \text{csch}(a+b x)}{x^2} \, dx","Integrate[(Coth[a + b*x]*Csch[a + b*x])/x^2,x]","\int \frac{\coth (a+b x) \text{csch}(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\coth (a+b x) \text{csch}(a+b x)}{x^2},x\right)",0,"Integrate[(Coth[a + b*x]*Csch[a + b*x])/x^2, x]","A",-1
431,0,0,15,9.9591223,"\int x^m \coth ^2(a+b x) \, dx","Integrate[x^m*Coth[a + b*x]^2,x]","\int x^m \coth ^2(a+b x) \, dx","\text{Int}\left(x^m \coth ^2(a+b x),x\right)",0,"Integrate[x^m*Coth[a + b*x]^2, x]","A",-1
432,1,204,87,0.6005132,"\int x^3 \coth ^2(a+b x) \, dx","Integrate[x^3*Coth[a + b*x]^2,x]","-\frac{e^{2 a} \left(2 e^{-2 a} b^3 x^3-3 \left(1-e^{-2 a}\right) b^2 x^2 \log \left(1-e^{-a-b x}\right)-3 \left(1-e^{-2 a}\right) b^2 x^2 \log \left(e^{-a-b x}+1\right)+6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(-e^{-a-b x}\right)+\text{Li}_3\left(-e^{-a-b x}\right)\right)+6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(e^{-a-b x}\right)+\text{Li}_3\left(e^{-a-b x}\right)\right)\right)}{\left(e^{2 a}-1\right) b^4}+\frac{x^3 \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b}+\frac{x^4}{4}","-\frac{3 \text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 x \text{Li}_2\left(e^{2 (a+b x)}\right)}{b^3}+\frac{3 x^2 \log \left(1-e^{2 (a+b x)}\right)}{b^2}-\frac{x^3 \coth (a+b x)}{b}-\frac{x^3}{b}+\frac{x^4}{4}",1,"x^4/4 - (E^(2*a)*((2*b^3*x^3)/E^(2*a) - 3*b^2*(1 - E^(-2*a))*x^2*Log[1 - E^(-a - b*x)] - 3*b^2*(1 - E^(-2*a))*x^2*Log[1 + E^(-a - b*x)] + 6*(1 - E^(-2*a))*(b*x*PolyLog[2, -E^(-a - b*x)] + PolyLog[3, -E^(-a - b*x)]) + 6*(1 - E^(-2*a))*(b*x*PolyLog[2, E^(-a - b*x)] + PolyLog[3, E^(-a - b*x)])))/(b^4*(-1 + E^(2*a))) + (x^3*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b","B",1
433,1,163,65,5.0590855,"\int x^2 \coth ^2(a+b x) \, dx","Integrate[x^2*Coth[a + b*x]^2,x]","\frac{-b^2 x^2 e^{-\tanh ^{-1}(\tanh (a))} \coth (a) \sqrt{\text{sech}^2(a)}-\text{Li}_2\left(e^{-2 \left(b x+\tanh ^{-1}(\tanh (a))\right)}\right)+2 b x \log \left(1-e^{-2 \left(\tanh ^{-1}(\tanh (a))+b x\right)}\right)+2 \tanh ^{-1}(\tanh (a)) \left(\log \left(1-e^{-2 \left(\tanh ^{-1}(\tanh (a))+b x\right)}\right)-\log \left(i \sinh \left(\tanh ^{-1}(\tanh (a))+b x\right)\right)+b x\right)+i \pi  b x-i \pi  \log \left(e^{2 b x}+1\right)+i \pi  \log (\cosh (b x))}{b^3}+\frac{x^2 \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b}+\frac{x^3}{3}","\frac{\text{Li}_2\left(e^{2 (a+b x)}\right)}{b^3}+\frac{2 x \log \left(1-e^{2 (a+b x)}\right)}{b^2}-\frac{x^2 \coth (a+b x)}{b}-\frac{x^2}{b}+\frac{x^3}{3}",1,"x^3/3 + (I*b*Pi*x - I*Pi*Log[1 + E^(2*b*x)] + 2*b*x*Log[1 - E^(-2*(b*x + ArcTanh[Tanh[a]]))] + I*Pi*Log[Cosh[b*x]] + 2*ArcTanh[Tanh[a]]*(b*x + Log[1 - E^(-2*(b*x + ArcTanh[Tanh[a]]))] - Log[I*Sinh[b*x + ArcTanh[Tanh[a]]]]) - PolyLog[2, E^(-2*(b*x + ArcTanh[Tanh[a]]))] - (b^2*x^2*Coth[a]*Sqrt[Sech[a]^2])/E^ArcTanh[Tanh[a]])/b^3 + (x^2*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b","C",0
434,1,46,31,0.1554106,"\int x \coth ^2(a+b x) \, dx","Integrate[x*Coth[a + b*x]^2,x]","\frac{-2 b x \coth (a)+2 \log (\sinh (a+b x))+2 b x \text{csch}(a) \sinh (b x) \text{csch}(a+b x)+b^2 x^2}{2 b^2}","\frac{\log (\sinh (a+b x))}{b^2}-\frac{x \coth (a+b x)}{b}+\frac{x^2}{2}",1,"(b^2*x^2 - 2*b*x*Coth[a] + 2*Log[Sinh[a + b*x]] + 2*b*x*Csch[a]*Csch[a + b*x]*Sinh[b*x])/(2*b^2)","A",1
435,1,27,13,0.0139677,"\int \coth ^2(a+b x) \, dx","Integrate[Coth[a + b*x]^2,x]","-\frac{\coth (a+b x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\tanh ^2(a+b x)\right)}{b}","x-\frac{\coth (a+b x)}{b}",1,"-((Coth[a + b*x]*Hypergeometric2F1[-1/2, 1, 1/2, Tanh[a + b*x]^2])/b)","C",1
436,0,0,15,0.3964822,"\int \frac{\coth ^2(a+b x)}{x} \, dx","Integrate[Coth[a + b*x]^2/x,x]","\int \frac{\coth ^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\coth ^2(a+b x)}{x},x\right)",0,"Integrate[Coth[a + b*x]^2/x, x]","A",-1
437,0,0,15,0.9176276,"\int \frac{\coth ^2(a+b x)}{x^2} \, dx","Integrate[Coth[a + b*x]^2/x^2,x]","\int \frac{\coth ^2(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\coth ^2(a+b x)}{x^2},x\right)",0,"Integrate[Coth[a + b*x]^2/x^2, x]","A",-1
438,0,0,78,38.878154,"\int x^m \cosh (a+b x) \coth ^2(a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]*Coth[a + b*x]^2,x]","\int x^m \cosh (a+b x) \coth ^2(a+b x) \, dx","\text{Int}\left(x^m \coth (a+b x) \text{csch}(a+b x),x\right)+\frac{e^a x^m (-b x)^{-m} \Gamma (m+1,-b x)}{2 b}-\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+1,b x)}{2 b}",0,"Integrate[x^m*Cosh[a + b*x]*Coth[a + b*x]^2, x]","A",-1
439,1,225,143,0.3424768,"\int x^3 \cosh (a+b x) \coth ^2(a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]*Coth[a + b*x]^2,x]","\frac{\text{csch}\left(\frac{1}{2} (a+b x)\right) \text{sech}\left(\frac{1}{2} (a+b x)\right) \left(b^3 x^3 \cosh (2 (a+b x))-3 b^2 x^2 \sinh (2 (a+b x))-12 b^2 x^2 \sinh (a+b x) \tanh ^{-1}(\sinh (a+b x)+\cosh (a+b x))-12 b x \sinh (a+b x) \text{Li}_2(-\cosh (a+b x)-\sinh (a+b x))+12 b x \sinh (a+b x) \text{Li}_2(\cosh (a+b x)+\sinh (a+b x))+12 \sinh (a+b x) \text{Li}_3(-\cosh (a+b x)-\sinh (a+b x))-12 \sinh (a+b x) \text{Li}_3(\cosh (a+b x)+\sinh (a+b x))-6 \sinh (2 (a+b x))+6 b x \cosh (2 (a+b x))-3 b^3 x^3-6 b x\right)}{4 b^4}","\frac{6 \text{Li}_3\left(-e^{a+b x}\right)}{b^4}-\frac{6 \text{Li}_3\left(e^{a+b x}\right)}{b^4}-\frac{6 \cosh (a+b x)}{b^4}-\frac{6 x \text{Li}_2\left(-e^{a+b x}\right)}{b^3}+\frac{6 x \text{Li}_2\left(e^{a+b x}\right)}{b^3}+\frac{6 x \sinh (a+b x)}{b^3}-\frac{3 x^2 \cosh (a+b x)}{b^2}-\frac{6 x^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b^2}+\frac{x^3 \sinh (a+b x)}{b}-\frac{x^3 \text{csch}(a+b x)}{b}",1,"(Csch[(a + b*x)/2]*Sech[(a + b*x)/2]*(-6*b*x - 3*b^3*x^3 + 6*b*x*Cosh[2*(a + b*x)] + b^3*x^3*Cosh[2*(a + b*x)] - 12*b^2*x^2*ArcTanh[Cosh[a + b*x] + Sinh[a + b*x]]*Sinh[a + b*x] - 12*b*x*PolyLog[2, -Cosh[a + b*x] - Sinh[a + b*x]]*Sinh[a + b*x] + 12*b*x*PolyLog[2, Cosh[a + b*x] + Sinh[a + b*x]]*Sinh[a + b*x] + 12*PolyLog[3, -Cosh[a + b*x] - Sinh[a + b*x]]*Sinh[a + b*x] - 12*PolyLog[3, Cosh[a + b*x] + Sinh[a + b*x]]*Sinh[a + b*x] - 6*Sinh[2*(a + b*x)] - 3*b^2*x^2*Sinh[2*(a + b*x)]))/(4*b^4)","A",0
440,1,230,95,0.4543011,"\int x^2 \cosh (a+b x) \coth ^2(a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]*Coth[a + b*x]^2,x]","\frac{\text{csch}\left(\frac{1}{2} (a+b x)\right) \text{sech}\left(\frac{1}{2} (a+b x)\right) \left(b^2 x^2 \cosh (2 (a+b x))+4 \text{Li}_2\left(-e^{-a-b x}\right) \sinh (a+b x)-4 \text{Li}_2\left(e^{-a-b x}\right) \sinh (a+b x)-2 b x \sinh (2 (a+b x))+2 \cosh (2 (a+b x))+4 b x \log \left(1-e^{-a-b x}\right) \sinh (a+b x)-4 b x \log \left(e^{-a-b x}+1\right) \sinh (a+b x)+4 a \log \left(1-e^{-a-b x}\right) \sinh (a+b x)-4 a \log \left(e^{-a-b x}+1\right) \sinh (a+b x)-4 a \sinh (a+b x) \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)-3 b^2 x^2-2\right)}{4 b^3}","-\frac{2 \text{Li}_2\left(-e^{a+b x}\right)}{b^3}+\frac{2 \text{Li}_2\left(e^{a+b x}\right)}{b^3}+\frac{2 \sinh (a+b x)}{b^3}-\frac{2 x \cosh (a+b x)}{b^2}-\frac{4 x \tanh ^{-1}\left(e^{a+b x}\right)}{b^2}+\frac{x^2 \sinh (a+b x)}{b}-\frac{x^2 \text{csch}(a+b x)}{b}",1,"(Csch[(a + b*x)/2]*Sech[(a + b*x)/2]*(-2 - 3*b^2*x^2 + 2*Cosh[2*(a + b*x)] + b^2*x^2*Cosh[2*(a + b*x)] + 4*a*Log[1 - E^(-a - b*x)]*Sinh[a + b*x] + 4*b*x*Log[1 - E^(-a - b*x)]*Sinh[a + b*x] - 4*a*Log[1 + E^(-a - b*x)]*Sinh[a + b*x] - 4*b*x*Log[1 + E^(-a - b*x)]*Sinh[a + b*x] - 4*a*Log[Tanh[(a + b*x)/2]]*Sinh[a + b*x] + 4*PolyLog[2, -E^(-a - b*x)]*Sinh[a + b*x] - 4*PolyLog[2, E^(-a - b*x)]*Sinh[a + b*x] - 2*b*x*Sinh[2*(a + b*x)]))/(4*b^3)","B",1
441,1,66,47,0.2341317,"\int x \cosh (a+b x) \coth ^2(a+b x) \, dx","Integrate[x*Cosh[a + b*x]*Coth[a + b*x]^2,x]","\frac{2 b x \sinh (a+b x)-2 \cosh (a+b x)+b x \tanh \left(\frac{1}{2} (a+b x)\right)-b x \coth \left(\frac{1}{2} (a+b x)\right)+2 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b^2}","-\frac{\cosh (a+b x)}{b^2}-\frac{\tanh ^{-1}(\cosh (a+b x))}{b^2}+\frac{x \sinh (a+b x)}{b}-\frac{x \text{csch}(a+b x)}{b}",1,"(-2*Cosh[a + b*x] - b*x*Coth[(a + b*x)/2] + 2*Log[Tanh[(a + b*x)/2]] + 2*b*x*Sinh[a + b*x] + b*x*Tanh[(a + b*x)/2])/(2*b^2)","A",1
442,1,22,22,0.0134279,"\int \cosh (a+b x) \coth ^2(a+b x) \, dx","Integrate[Cosh[a + b*x]*Coth[a + b*x]^2,x]","\frac{\sinh (a+b x)}{b}-\frac{\text{csch}(a+b x)}{b}","\frac{\sinh (a+b x)}{b}-\frac{\text{csch}(a+b x)}{b}",1,"-(Csch[a + b*x]/b) + Sinh[a + b*x]/b","A",1
443,0,0,34,24.2459262,"\int \frac{\cosh (a+b x) \coth ^2(a+b x)}{x} \, dx","Integrate[(Cosh[a + b*x]*Coth[a + b*x]^2)/x,x]","\int \frac{\cosh (a+b x) \coth ^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\coth (a+b x) \text{csch}(a+b x)}{x},x\right)+\cosh (a) \text{Chi}(b x)+\sinh (a) \text{Shi}(b x)",0,"Integrate[(Cosh[a + b*x]*Coth[a + b*x]^2)/x, x]","A",-1
444,0,0,47,21.2545933,"\int \frac{\cosh (a+b x) \coth ^2(a+b x)}{x^2} \, dx","Integrate[(Cosh[a + b*x]*Coth[a + b*x]^2)/x^2,x]","\int \frac{\cosh (a+b x) \coth ^2(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\coth (a+b x) \text{csch}(a+b x)}{x^2},x\right)+b \sinh (a) \text{Chi}(b x)+b \cosh (a) \text{Shi}(b x)-\frac{\cosh (a+b x)}{x}",0,"Integrate[(Cosh[a + b*x]*Coth[a + b*x]^2)/x^2, x]","A",-1
445,0,0,21,36.7834326,"\int x^m \coth (a+b x) \text{csch}^2(a+b x) \, dx","Integrate[x^m*Coth[a + b*x]*Csch[a + b*x]^2,x]","\int x^m \coth (a+b x) \text{csch}^2(a+b x) \, dx","\text{Int}\left(x^m \coth (a+b x) \text{csch}^2(a+b x),x\right)",0,"Integrate[x^m*Coth[a + b*x]*Csch[a + b*x]^2, x]","A",-1
446,1,227,83,6.13637,"\int x^3 \coth (a+b x) \text{csch}^2(a+b x) \, dx","Integrate[x^3*Coth[a + b*x]*Csch[a + b*x]^2,x]","\frac{3 x^2 \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{2 b^2}-\frac{3 \text{csch}(a) \text{sech}(a) \left(b^2 x^2 e^{-\tanh ^{-1}(\tanh (a))}-\frac{i \tanh (a) \left(i \text{Li}_2\left(e^{2 i \left(i b x+i \tanh ^{-1}(\tanh (a))\right)}\right)-b x \left(-\pi +2 i \tanh ^{-1}(\tanh (a))\right)-2 \left(i \tanh ^{-1}(\tanh (a))+i b x\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}(\tanh (a))+i b x\right)}\right)+2 i \tanh ^{-1}(\tanh (a)) \log \left(i \sinh \left(\tanh ^{-1}(\tanh (a))+b x\right)\right)-\pi  \log \left(e^{2 b x}+1\right)+\pi  \log (\cosh (b x))\right)}{\sqrt{1-\tanh ^2(a)}}\right)}{2 b^4 \sqrt{\text{sech}^2(a) \left(\cosh ^2(a)-\sinh ^2(a)\right)}}-\frac{x^3 \text{csch}^2(a+b x)}{2 b}","\frac{3 \text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 x \log \left(1-e^{2 (a+b x)}\right)}{b^3}-\frac{3 x^2 \coth (a+b x)}{2 b^2}-\frac{x^3 \text{csch}^2(a+b x)}{2 b}-\frac{3 x^2}{2 b^2}",1,"-1/2*(x^3*Csch[a + b*x]^2)/b + (3*x^2*Csch[a]*Csch[a + b*x]*Sinh[b*x])/(2*b^2) - (3*Csch[a]*Sech[a]*((b^2*x^2)/E^ArcTanh[Tanh[a]] - (I*(-(b*x*(-Pi + (2*I)*ArcTanh[Tanh[a]])) - Pi*Log[1 + E^(2*b*x)] - 2*(I*b*x + I*ArcTanh[Tanh[a]])*Log[1 - E^((2*I)*(I*b*x + I*ArcTanh[Tanh[a]]))] + Pi*Log[Cosh[b*x]] + (2*I)*ArcTanh[Tanh[a]]*Log[I*Sinh[b*x + ArcTanh[Tanh[a]]]] + I*PolyLog[2, E^((2*I)*(I*b*x + I*ArcTanh[Tanh[a]]))])*Tanh[a])/Sqrt[1 - Tanh[a]^2]))/(2*b^4*Sqrt[Sech[a]^2*(Cosh[a]^2 - Sinh[a]^2)])","C",0
447,1,55,42,0.1222876,"\int x^2 \coth (a+b x) \text{csch}^2(a+b x) \, dx","Integrate[x^2*Coth[a + b*x]*Csch[a + b*x]^2,x]","\frac{\log (\sinh (a+b x))}{b^3}-\frac{x \coth (a)}{b^2}+\frac{x \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b^2}-\frac{x^2 \text{csch}^2(a+b x)}{2 b}","\frac{\log (\sinh (a+b x))}{b^3}-\frac{x \coth (a+b x)}{b^2}-\frac{x^2 \text{csch}^2(a+b x)}{2 b}",1,"-((x*Coth[a])/b^2) - (x^2*Csch[a + b*x]^2)/(2*b) + Log[Sinh[a + b*x]]/b^3 + (x*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b^2","A",1
448,1,30,30,0.0739841,"\int x \coth (a+b x) \text{csch}^2(a+b x) \, dx","Integrate[x*Coth[a + b*x]*Csch[a + b*x]^2,x]","-\frac{\coth (a+b x)}{2 b^2}-\frac{x \text{csch}^2(a+b x)}{2 b}","-\frac{\coth (a+b x)}{2 b^2}-\frac{x \text{csch}^2(a+b x)}{2 b}",1,"-1/2*Coth[a + b*x]/b^2 - (x*Csch[a + b*x]^2)/(2*b)","A",1
449,1,15,15,0.0119405,"\int \coth (a+b x) \text{csch}^2(a+b x) \, dx","Integrate[Coth[a + b*x]*Csch[a + b*x]^2,x]","-\frac{\text{csch}^2(a+b x)}{2 b}","-\frac{\text{csch}^2(a+b x)}{2 b}",1,"-1/2*Csch[a + b*x]^2/b","A",1
450,0,0,21,15.5830524,"\int \frac{\coth (a+b x) \text{csch}^2(a+b x)}{x} \, dx","Integrate[(Coth[a + b*x]*Csch[a + b*x]^2)/x,x]","\int \frac{\coth (a+b x) \text{csch}^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\coth (a+b x) \text{csch}^2(a+b x)}{x},x\right)",0,"Integrate[(Coth[a + b*x]*Csch[a + b*x]^2)/x, x]","A",-1
451,0,0,21,20.3734035,"\int \frac{\coth (a+b x) \text{csch}^2(a+b x)}{x^2} \, dx","Integrate[(Coth[a + b*x]*Csch[a + b*x]^2)/x^2,x]","\int \frac{\coth (a+b x) \text{csch}^2(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\coth (a+b x) \text{csch}^2(a+b x)}{x^2},x\right)",0,"Integrate[(Coth[a + b*x]*Csch[a + b*x]^2)/x^2, x]","A",-1
452,-1,0,29,180.00017,"\int x^m \coth ^2(a+b x) \text{csch}(a+b x) \, dx","Integrate[x^m*Coth[a + b*x]^2*Csch[a + b*x],x]","\text{\$Aborted}","\text{Int}\left(x^m \text{csch}^3(a+b x),x\right)+\text{Int}\left(x^m \text{csch}(a+b x),x\right)",0,"$Aborted","F",-1
453,1,280,201,6.9204571,"\int x^3 \coth ^2(a+b x) \text{csch}(a+b x) \, dx","Integrate[x^3*Coth[a + b*x]^2*Csch[a + b*x],x]","-\frac{-4 b^3 x^3 \log \left(1-e^{a+b x}\right)+4 b^3 x^3 \log \left(e^{a+b x}+1\right)+b^3 x^3 \text{csch}^2\left(\frac{1}{2} (a+b x)\right)+b^3 x^3 \text{sech}^2\left(\frac{1}{2} (a+b x)\right)+12 \left(b^2 x^2+2\right) \text{Li}_2\left(-e^{a+b x}\right)-12 \left(b^2 x^2+2\right) \text{Li}_2\left(e^{a+b x}\right)+12 b^2 x^2 \text{csch}(a)-6 b^2 x^2 \text{csch}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{csch}\left(\frac{1}{2} (a+b x)\right)-6 b^2 x^2 \text{sech}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{sech}\left(\frac{1}{2} (a+b x)\right)-24 b x \text{Li}_3\left(-e^{a+b x}\right)+24 b x \text{Li}_3\left(e^{a+b x}\right)+24 \text{Li}_4\left(-e^{a+b x}\right)-24 \text{Li}_4\left(e^{a+b x}\right)-24 b x \log \left(1-e^{a+b x}\right)+24 b x \log \left(e^{a+b x}+1\right)}{8 b^4}","-\frac{3 \text{Li}_2\left(-e^{a+b x}\right)}{b^4}+\frac{3 \text{Li}_2\left(e^{a+b x}\right)}{b^4}-\frac{3 \text{Li}_4\left(-e^{a+b x}\right)}{b^4}+\frac{3 \text{Li}_4\left(e^{a+b x}\right)}{b^4}+\frac{3 x \text{Li}_3\left(-e^{a+b x}\right)}{b^3}-\frac{3 x \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{6 x \tanh ^{-1}\left(e^{a+b x}\right)}{b^3}-\frac{3 x^2 \text{Li}_2\left(-e^{a+b x}\right)}{2 b^2}+\frac{3 x^2 \text{Li}_2\left(e^{a+b x}\right)}{2 b^2}-\frac{3 x^2 \text{csch}(a+b x)}{2 b^2}-\frac{x^3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{x^3 \coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-1/8*(12*b^2*x^2*Csch[a] + b^3*x^3*Csch[(a + b*x)/2]^2 - 24*b*x*Log[1 - E^(a + b*x)] - 4*b^3*x^3*Log[1 - E^(a + b*x)] + 24*b*x*Log[1 + E^(a + b*x)] + 4*b^3*x^3*Log[1 + E^(a + b*x)] + 12*(2 + b^2*x^2)*PolyLog[2, -E^(a + b*x)] - 12*(2 + b^2*x^2)*PolyLog[2, E^(a + b*x)] - 24*b*x*PolyLog[3, -E^(a + b*x)] + 24*b*x*PolyLog[3, E^(a + b*x)] + 24*PolyLog[4, -E^(a + b*x)] - 24*PolyLog[4, E^(a + b*x)] + b^3*x^3*Sech[(a + b*x)/2]^2 - 6*b^2*x^2*Csch[a/2]*Csch[(a + b*x)/2]*Sinh[(b*x)/2] - 6*b^2*x^2*Sech[a/2]*Sech[(a + b*x)/2]*Sinh[(b*x)/2])/b^4","A",1
454,1,222,123,4.1480192,"\int x^2 \coth ^2(a+b x) \text{csch}(a+b x) \, dx","Integrate[x^2*Coth[a + b*x]^2*Csch[a + b*x],x]","-\frac{-4 b^2 x^2 \log \left(1-e^{a+b x}\right)+4 b^2 x^2 \log \left(e^{a+b x}+1\right)+b^2 x^2 \text{csch}^2\left(\frac{1}{2} (a+b x)\right)+b^2 x^2 \text{sech}^2\left(\frac{1}{2} (a+b x)\right)+8 b x \text{Li}_2\left(-e^{a+b x}\right)-8 b x \text{Li}_2\left(e^{a+b x}\right)-8 \text{Li}_3\left(-e^{a+b x}\right)+8 \text{Li}_3\left(e^{a+b x}\right)-8 \log \left(1-e^{a+b x}\right)+8 \log \left(e^{a+b x}+1\right)+8 b x \text{csch}(a)-4 b x \text{csch}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{csch}\left(\frac{1}{2} (a+b x)\right)-4 b x \text{sech}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{sech}\left(\frac{1}{2} (a+b x)\right)}{8 b^3}","\frac{\text{Li}_3\left(-e^{a+b x}\right)}{b^3}-\frac{\text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{\tanh ^{-1}(\cosh (a+b x))}{b^3}-\frac{x \text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{x \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{x \text{csch}(a+b x)}{b^2}-\frac{x^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{x^2 \coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-1/8*(8*b*x*Csch[a] + b^2*x^2*Csch[(a + b*x)/2]^2 - 8*Log[1 - E^(a + b*x)] - 4*b^2*x^2*Log[1 - E^(a + b*x)] + 8*Log[1 + E^(a + b*x)] + 4*b^2*x^2*Log[1 + E^(a + b*x)] + 8*b*x*PolyLog[2, -E^(a + b*x)] - 8*b*x*PolyLog[2, E^(a + b*x)] - 8*PolyLog[3, -E^(a + b*x)] + 8*PolyLog[3, E^(a + b*x)] + b^2*x^2*Sech[(a + b*x)/2]^2 - 4*b*x*Csch[a/2]*Csch[(a + b*x)/2]*Sinh[(b*x)/2] - 4*b*x*Sech[a/2]*Sech[(a + b*x)/2]*Sinh[(b*x)/2])/b^3","A",1
455,1,144,82,2.0349605,"\int x \coth ^2(a+b x) \text{csch}(a+b x) \, dx","Integrate[x*Coth[a + b*x]^2*Csch[a + b*x],x]","-\frac{-4 \text{Li}_2\left(-e^{-a-b x}\right)+4 \text{Li}_2\left(e^{-a-b x}\right)-4 (a+b x) \left(\log \left(1-e^{-a-b x}\right)-\log \left(e^{-a-b x}+1\right)\right)-2 \tanh \left(\frac{1}{2} (a+b x)\right)+2 \coth \left(\frac{1}{2} (a+b x)\right)+b x \text{csch}^2\left(\frac{1}{2} (a+b x)\right)+b x \text{sech}^2\left(\frac{1}{2} (a+b x)\right)+4 a \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{8 b^2}","-\frac{\text{Li}_2\left(-e^{a+b x}\right)}{2 b^2}+\frac{\text{Li}_2\left(e^{a+b x}\right)}{2 b^2}-\frac{\text{csch}(a+b x)}{2 b^2}-\frac{x \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{x \coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-1/8*(2*Coth[(a + b*x)/2] + b*x*Csch[(a + b*x)/2]^2 - 4*(a + b*x)*(Log[1 - E^(-a - b*x)] - Log[1 + E^(-a - b*x)]) + 4*a*Log[Tanh[(a + b*x)/2]] - 4*PolyLog[2, -E^(-a - b*x)] + 4*PolyLog[2, E^(-a - b*x)] + b*x*Sech[(a + b*x)/2]^2 - 2*Tanh[(a + b*x)/2])/b^2","A",1
456,1,57,34,0.0346617,"\int \coth ^2(a+b x) \text{csch}(a+b x) \, dx","Integrate[Coth[a + b*x]^2*Csch[a + b*x],x]","-\frac{\text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{\text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}+\frac{\log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b}","-\frac{\tanh ^{-1}(\cosh (a+b x))}{2 b}-\frac{\coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-1/8*Csch[(a + b*x)/2]^2/b + Log[Tanh[(a + b*x)/2]]/(2*b) - Sech[(a + b*x)/2]^2/(8*b)","A",1
457,0,0,29,54.005001,"\int \frac{\coth ^2(a+b x) \text{csch}(a+b x)}{x} \, dx","Integrate[(Coth[a + b*x]^2*Csch[a + b*x])/x,x]","\int \frac{\coth ^2(a+b x) \text{csch}(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{csch}^3(a+b x)}{x},x\right)+\text{Int}\left(\frac{\text{csch}(a+b x)}{x},x\right)",0,"Integrate[(Coth[a + b*x]^2*Csch[a + b*x])/x, x]","A",-1
458,0,0,29,45.8796828,"\int \frac{\coth ^2(a+b x) \text{csch}(a+b x)}{x^2} \, dx","Integrate[(Coth[a + b*x]^2*Csch[a + b*x])/x^2,x]","\int \frac{\coth ^2(a+b x) \text{csch}(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{csch}^3(a+b x)}{x^2},x\right)+\text{Int}\left(\frac{\text{csch}(a+b x)}{x^2},x\right)",0,"Integrate[(Coth[a + b*x]^2*Csch[a + b*x])/x^2, x]","A",-1
459,0,0,15,122.971021,"\int x^m \coth ^3(a+b x) \, dx","Integrate[x^m*Coth[a + b*x]^3,x]","\int x^m \coth ^3(a+b x) \, dx","\text{Int}\left(x^m \coth ^3(a+b x),x\right)",0,"Integrate[x^m*Coth[a + b*x]^3, x]","A",-1
460,1,390,179,3.3427266,"\int x^3 \coth ^3(a+b x) \, dx","Integrate[x^3*Coth[a + b*x]^3,x]","\frac{1}{4} \left(\frac{6 x^2 \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b^2}-\frac{2 e^{2 a} \left(e^{-2 a} b^4 x^4-2 e^{-2 a} \left(e^{2 a}-1\right) b^3 x^3 \log \left(1-e^{-a-b x}\right)-2 e^{-2 a} \left(e^{2 a}-1\right) b^3 x^3 \log \left(e^{-a-b x}+1\right)+6 \left(1-e^{-2 a}\right) \left(b^2 x^2 \text{Li}_2\left(-e^{-a-b x}\right)+2 \left(b x \text{Li}_3\left(-e^{-a-b x}\right)+\text{Li}_4\left(-e^{-a-b x}\right)\right)\right)+6 \left(1-e^{-2 a}\right) \left(b^2 x^2 \text{Li}_2\left(e^{-a-b x}\right)+2 \left(b x \text{Li}_3\left(e^{-a-b x}\right)+\text{Li}_4\left(e^{-a-b x}\right)\right)\right)+6 e^{-2 a} b^2 x^2+6 \left(1-e^{-2 a}\right) \text{Li}_2\left(-e^{-a-b x}\right)+6 \left(1-e^{-2 a}\right) \text{Li}_2\left(e^{-a-b x}\right)-6 \left(1-e^{-2 a}\right) b x \log \left(1-e^{-a-b x}\right)-6 \left(1-e^{-2 a}\right) b x \log \left(e^{-a-b x}+1\right)\right)}{\left(e^{2 a}-1\right) b^4}-\frac{2 x^3 \text{csch}^2(a+b x)}{b}+x^4 \coth (a)\right)","\frac{3 \text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 \text{Li}_4\left(e^{2 (a+b x)}\right)}{4 b^4}-\frac{3 x \text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 x \log \left(1-e^{2 (a+b x)}\right)}{b^3}+\frac{3 x^2 \text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^2}-\frac{3 x^2 \coth (a+b x)}{2 b^2}+\frac{x^3 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^3 \coth ^2(a+b x)}{2 b}-\frac{3 x^2}{2 b^2}+\frac{x^3}{2 b}-\frac{x^4}{4}",1,"(x^4*Coth[a] - (2*x^3*Csch[a + b*x]^2)/b - (2*E^(2*a)*((6*b^2*x^2)/E^(2*a) + (b^4*x^4)/E^(2*a) - 6*b*(1 - E^(-2*a))*x*Log[1 - E^(-a - b*x)] - (2*b^3*(-1 + E^(2*a))*x^3*Log[1 - E^(-a - b*x)])/E^(2*a) - 6*b*(1 - E^(-2*a))*x*Log[1 + E^(-a - b*x)] - (2*b^3*(-1 + E^(2*a))*x^3*Log[1 + E^(-a - b*x)])/E^(2*a) + 6*(1 - E^(-2*a))*PolyLog[2, -E^(-a - b*x)] + 6*(1 - E^(-2*a))*PolyLog[2, E^(-a - b*x)] + 6*(1 - E^(-2*a))*(b^2*x^2*PolyLog[2, -E^(-a - b*x)] + 2*(b*x*PolyLog[3, -E^(-a - b*x)] + PolyLog[4, -E^(-a - b*x)])) + 6*(1 - E^(-2*a))*(b^2*x^2*PolyLog[2, E^(-a - b*x)] + 2*(b*x*PolyLog[3, E^(-a - b*x)] + PolyLog[4, E^(-a - b*x)]))))/(b^4*(-1 + E^(2*a))) + (6*x^2*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b^2)/4","B",1
461,1,295,114,2.2123677,"\int x^2 \coth ^3(a+b x) \, dx","Integrate[x^2*Coth[a + b*x]^3,x]","\frac{x \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b^2}-\frac{e^{2 a} \left(2 e^{-2 a} b^3 x^3-3 e^{-2 a} \left(e^{2 a}-1\right) b^2 x^2 \log \left(1-e^{-a-b x}\right)-3 e^{-2 a} \left(e^{2 a}-1\right) b^2 x^2 \log \left(e^{-a-b x}+1\right)+6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(-e^{-a-b x}\right)+\text{Li}_3\left(-e^{-a-b x}\right)\right)+6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(e^{-a-b x}\right)+\text{Li}_3\left(e^{-a-b x}\right)\right)+6 e^{-2 a} b x+3 \left(1-e^{-2 a}\right) \left(b x-\log \left(1-e^{a+b x}\right)\right)+3 \left(1-e^{-2 a}\right) \left(b x-\log \left(e^{a+b x}+1\right)\right)\right)}{3 \left(e^{2 a}-1\right) b^3}-\frac{x^2 \text{csch}^2(a+b x)}{2 b}+\frac{1}{3} x^3 \coth (a)","-\frac{\text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^3}+\frac{\log (\sinh (a+b x))}{b^3}+\frac{x \text{Li}_2\left(e^{2 (a+b x)}\right)}{b^2}-\frac{x \coth (a+b x)}{b^2}+\frac{x^2 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^2 \coth ^2(a+b x)}{2 b}+\frac{x^2}{2 b}-\frac{x^3}{3}",1,"(x^3*Coth[a])/3 - (x^2*Csch[a + b*x]^2)/(2*b) - (E^(2*a)*((6*b*x)/E^(2*a) + (2*b^3*x^3)/E^(2*a) - (3*b^2*(-1 + E^(2*a))*x^2*Log[1 - E^(-a - b*x)])/E^(2*a) - (3*b^2*(-1 + E^(2*a))*x^2*Log[1 + E^(-a - b*x)])/E^(2*a) + 3*(1 - E^(-2*a))*(b*x - Log[1 - E^(a + b*x)]) + 3*(1 - E^(-2*a))*(b*x - Log[1 + E^(a + b*x)]) + 6*(1 - E^(-2*a))*(b*x*PolyLog[2, -E^(-a - b*x)] + PolyLog[3, -E^(-a - b*x)]) + 6*(1 - E^(-2*a))*(b*x*PolyLog[2, E^(-a - b*x)] + PolyLog[3, E^(-a - b*x)])))/(3*b^3*(-1 + E^(2*a))) + (x*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b^2","B",1
462,1,231,82,6.1281643,"\int x \coth ^3(a+b x) \, dx","Integrate[x*Coth[a + b*x]^3,x]","-\frac{\text{csch}(a) \text{sech}(a) \left(b^2 x^2 e^{-\tanh ^{-1}(\tanh (a))}-\frac{i \tanh (a) \left(i \text{Li}_2\left(e^{2 i \left(i b x+i \tanh ^{-1}(\tanh (a))\right)}\right)-b x \left(-\pi +2 i \tanh ^{-1}(\tanh (a))\right)-2 \left(i \tanh ^{-1}(\tanh (a))+i b x\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}(\tanh (a))+i b x\right)}\right)+2 i \tanh ^{-1}(\tanh (a)) \log \left(i \sinh \left(\tanh ^{-1}(\tanh (a))+b x\right)\right)-\pi  \log \left(e^{2 b x}+1\right)+\pi  \log (\cosh (b x))\right)}{\sqrt{1-\tanh ^2(a)}}\right)}{2 b^2 \sqrt{\text{sech}^2(a) \left(\cosh ^2(a)-\sinh ^2(a)\right)}}+\frac{\text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{2 b^2}-\frac{x \text{csch}^2(a+b x)}{2 b}+\frac{1}{2} x^2 \coth (a)","\frac{\text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^2}-\frac{\coth (a+b x)}{2 b^2}+\frac{x \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x \coth ^2(a+b x)}{2 b}+\frac{x}{2 b}-\frac{x^2}{2}",1,"(x^2*Coth[a])/2 - (x*Csch[a + b*x]^2)/(2*b) + (Csch[a]*Csch[a + b*x]*Sinh[b*x])/(2*b^2) - (Csch[a]*Sech[a]*((b^2*x^2)/E^ArcTanh[Tanh[a]] - (I*(-(b*x*(-Pi + (2*I)*ArcTanh[Tanh[a]])) - Pi*Log[1 + E^(2*b*x)] - 2*(I*b*x + I*ArcTanh[Tanh[a]])*Log[1 - E^((2*I)*(I*b*x + I*ArcTanh[Tanh[a]]))] + Pi*Log[Cosh[b*x]] + (2*I)*ArcTanh[Tanh[a]]*Log[I*Sinh[b*x + ArcTanh[Tanh[a]]]] + I*PolyLog[2, E^((2*I)*(I*b*x + I*ArcTanh[Tanh[a]]))])*Tanh[a])/Sqrt[1 - Tanh[a]^2]))/(2*b^2*Sqrt[Sech[a]^2*(Cosh[a]^2 - Sinh[a]^2)])","C",0
463,1,34,27,0.079183,"\int \coth ^3(a+b x) \, dx","Integrate[Coth[a + b*x]^3,x]","-\frac{\coth ^2(a+b x)-2 \log (\tanh (a+b x))-2 \log (\cosh (a+b x))}{2 b}","\frac{\log (\sinh (a+b x))}{b}-\frac{\coth ^2(a+b x)}{2 b}",1,"-1/2*(Coth[a + b*x]^2 - 2*Log[Cosh[a + b*x]] - 2*Log[Tanh[a + b*x]])/b","A",1
464,0,0,15,0.7480096,"\int \frac{\coth ^3(a+b x)}{x} \, dx","Integrate[Coth[a + b*x]^3/x,x]","\int \frac{\coth ^3(a+b x)}{x} \, dx","\text{Int}\left(\frac{\coth ^3(a+b x)}{x},x\right)",0,"Integrate[Coth[a + b*x]^3/x, x]","A",-1
465,0,0,15,0.4291419,"\int \frac{\coth ^3(a+b x)}{x^2} \, dx","Integrate[Coth[a + b*x]^3/x^2,x]","\int \frac{\coth ^3(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\coth ^3(a+b x)}{x^2},x\right)",0,"Integrate[Coth[a + b*x]^3/x^2, x]","A",-1
466,0,0,19,9.551932,"\int x^m \text{csch}(a+b x) \text{sech}(a+b x) \, dx","Integrate[x^m*Csch[a + b*x]*Sech[a + b*x],x]","\int x^m \text{csch}(a+b x) \text{sech}(a+b x) \, dx","\text{Int}\left(x^m \text{csch}(a+b x) \text{sech}(a+b x),x\right)",0,"Integrate[x^m*Csch[a + b*x]*Sech[a + b*x], x]","A",-1
467,1,150,148,4.345371,"\int x^3 \text{csch}(a+b x) \text{sech}(a+b x) \, dx","Integrate[x^3*Csch[a + b*x]*Sech[a + b*x],x]","\frac{4 b^3 x^3 \log \left(1-e^{2 (a+b x)}\right)-4 b^3 x^3 \log \left(e^{2 (a+b x)}+1\right)-6 b^2 x^2 \text{Li}_2\left(-e^{2 (a+b x)}\right)+6 b^2 x^2 \text{Li}_2\left(e^{2 (a+b x)}\right)+6 b x \text{Li}_3\left(-e^{2 (a+b x)}\right)-6 b x \text{Li}_3\left(e^{2 (a+b x)}\right)-3 \text{Li}_4\left(-e^{2 (a+b x)}\right)+3 \text{Li}_4\left(e^{2 (a+b x)}\right)}{4 b^4}","-\frac{3 \text{Li}_4\left(-e^{2 a+2 b x}\right)}{4 b^4}+\frac{3 \text{Li}_4\left(e^{2 a+2 b x}\right)}{4 b^4}+\frac{3 x \text{Li}_3\left(-e^{2 a+2 b x}\right)}{2 b^3}-\frac{3 x \text{Li}_3\left(e^{2 a+2 b x}\right)}{2 b^3}-\frac{3 x^2 \text{Li}_2\left(-e^{2 a+2 b x}\right)}{2 b^2}+\frac{3 x^2 \text{Li}_2\left(e^{2 a+2 b x}\right)}{2 b^2}-\frac{2 x^3 \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}",1,"(4*b^3*x^3*Log[1 - E^(2*(a + b*x))] - 4*b^3*x^3*Log[1 + E^(2*(a + b*x))] - 6*b^2*x^2*PolyLog[2, -E^(2*(a + b*x))] + 6*b^2*x^2*PolyLog[2, E^(2*(a + b*x))] + 6*b*x*PolyLog[3, -E^(2*(a + b*x))] - 6*b*x*PolyLog[3, E^(2*(a + b*x))] - 3*PolyLog[4, -E^(2*(a + b*x))] + 3*PolyLog[4, E^(2*(a + b*x))])/(4*b^4)","A",1
468,1,108,97,4.3126468,"\int x^2 \text{csch}(a+b x) \text{sech}(a+b x) \, dx","Integrate[x^2*Csch[a + b*x]*Sech[a + b*x],x]","\frac{2 b^2 x^2 \log \left(1-e^{2 (a+b x)}\right)-2 b^2 x^2 \log \left(e^{2 (a+b x)}+1\right)-2 b x \text{Li}_2\left(-e^{2 (a+b x)}\right)+2 b x \text{Li}_2\left(e^{2 (a+b x)}\right)+\text{Li}_3\left(-e^{2 (a+b x)}\right)-\text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^3}","\frac{\text{Li}_3\left(-e^{2 a+2 b x}\right)}{2 b^3}-\frac{\text{Li}_3\left(e^{2 a+2 b x}\right)}{2 b^3}-\frac{x \text{Li}_2\left(-e^{2 a+2 b x}\right)}{b^2}+\frac{x \text{Li}_2\left(e^{2 a+2 b x}\right)}{b^2}-\frac{2 x^2 \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}",1,"(2*b^2*x^2*Log[1 - E^(2*(a + b*x))] - 2*b^2*x^2*Log[1 + E^(2*(a + b*x))] - 2*b*x*PolyLog[2, -E^(2*(a + b*x))] + 2*b*x*PolyLog[2, E^(2*(a + b*x))] + PolyLog[3, -E^(2*(a + b*x))] - PolyLog[3, E^(2*(a + b*x))])/(2*b^3)","A",1
469,1,110,58,0.0878307,"\int x \text{csch}(a+b x) \text{sech}(a+b x) \, dx","Integrate[x*Csch[a + b*x]*Sech[a + b*x],x]","\frac{\text{Li}_2\left(-e^{-2 (a+b x)}\right)-\text{Li}_2\left(e^{-2 (a+b x)}\right)+2 a \log \left(1-e^{-2 (a+b x)}\right)+2 b x \log \left(1-e^{-2 (a+b x)}\right)-2 a \log \left(e^{-2 (a+b x)}+1\right)-2 b x \log \left(e^{-2 (a+b x)}+1\right)-2 a \log (\tanh (a+b x))}{2 b^2}","-\frac{\text{Li}_2\left(-e^{2 a+2 b x}\right)}{2 b^2}+\frac{\text{Li}_2\left(e^{2 a+2 b x}\right)}{2 b^2}-\frac{2 x \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}",1,"(2*a*Log[1 - E^(-2*(a + b*x))] + 2*b*x*Log[1 - E^(-2*(a + b*x))] - 2*a*Log[1 + E^(-2*(a + b*x))] - 2*b*x*Log[1 + E^(-2*(a + b*x))] - 2*a*Log[Tanh[a + b*x]] + PolyLog[2, -E^(-2*(a + b*x))] - PolyLog[2, E^(-2*(a + b*x))])/(2*b^2)","A",1
470,1,31,11,0.01266,"\int \text{csch}(a+b x) \text{sech}(a+b x) \, dx","Integrate[Csch[a + b*x]*Sech[a + b*x],x]","2 \left(\frac{\log (\sinh (a+b x))}{2 b}-\frac{\log (\cosh (a+b x))}{2 b}\right)","\frac{\log (\tanh (a+b x))}{b}",1,"2*(-1/2*Log[Cosh[a + b*x]]/b + Log[Sinh[a + b*x]]/(2*b))","B",1
471,0,0,18,17.6097587,"\int \frac{\text{csch}(a+b x) \text{sech}(a+b x)}{x} \, dx","Integrate[(Csch[a + b*x]*Sech[a + b*x])/x,x]","\int \frac{\text{csch}(a+b x) \text{sech}(a+b x)}{x} \, dx","2 \text{Int}\left(\frac{\text{csch}(2 a+2 b x)}{x},x\right)",0,"Integrate[(Csch[a + b*x]*Sech[a + b*x])/x, x]","A",-1
472,0,0,18,16.0119684,"\int \frac{\text{csch}(a+b x) \text{sech}(a+b x)}{x^2} \, dx","Integrate[(Csch[a + b*x]*Sech[a + b*x])/x^2,x]","\int \frac{\text{csch}(a+b x) \text{sech}(a+b x)}{x^2} \, dx","2 \text{Int}\left(\frac{\text{csch}(2 a+2 b x)}{x^2},x\right)",0,"Integrate[(Csch[a + b*x]*Sech[a + b*x])/x^2, x]","A",-1
473,0,0,21,125.5985325,"\int x^m \text{csch}(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x^m*Csch[a + b*x]*Sech[a + b*x]^2,x]","\int x^m \text{csch}(a+b x) \text{sech}^2(a+b x) \, dx","\text{Int}\left(x^m \text{csch}(a+b x) \text{sech}^2(a+b x),x\right)",0,"Integrate[x^m*Csch[a + b*x]*Sech[a + b*x]^2, x]","A",-1
474,1,282,226,0.3953477,"\int x^3 \text{csch}(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x^3*Csch[a + b*x]*Sech[a + b*x]^2,x]","\frac{b^3 x^3 \text{sech}(a+b x)-2 b^3 x^3 \tanh ^{-1}(\sinh (a+b x)+\cosh (a+b x))-3 i \left(b^2 x^2 \log \left(1-i e^{a+b x}\right)-b^2 x^2 \log \left(1+i e^{a+b x}\right)-2 b x \text{Li}_2\left(-i e^{a+b x}\right)+2 b x \text{Li}_2\left(i e^{a+b x}\right)+2 \text{Li}_3\left(-i e^{a+b x}\right)-2 \text{Li}_3\left(i e^{a+b x}\right)\right)-3 b^2 x^2 \text{Li}_2(-\cosh (a+b x)-\sinh (a+b x))+3 b^2 x^2 \text{Li}_2(\cosh (a+b x)+\sinh (a+b x))+6 b x \text{Li}_3(-\cosh (a+b x)-\sinh (a+b x))-6 b x \text{Li}_3(\cosh (a+b x)+\sinh (a+b x))-6 \text{Li}_4(-\cosh (a+b x)-\sinh (a+b x))+6 \text{Li}_4(\cosh (a+b x)+\sinh (a+b x))}{b^4}","-\frac{6 i \text{Li}_3\left(-i e^{a+b x}\right)}{b^4}+\frac{6 i \text{Li}_3\left(i e^{a+b x}\right)}{b^4}-\frac{6 \text{Li}_4\left(-e^{a+b x}\right)}{b^4}+\frac{6 \text{Li}_4\left(e^{a+b x}\right)}{b^4}+\frac{6 i x \text{Li}_2\left(-i e^{a+b x}\right)}{b^3}-\frac{6 i x \text{Li}_2\left(i e^{a+b x}\right)}{b^3}+\frac{6 x \text{Li}_3\left(-e^{a+b x}\right)}{b^3}-\frac{6 x \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{3 x^2 \text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{3 x^2 \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{6 x^2 \tan ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{2 x^3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}+\frac{x^3 \text{sech}(a+b x)}{b}",1,"(-2*b^3*x^3*ArcTanh[Cosh[a + b*x] + Sinh[a + b*x]] - 3*b^2*x^2*PolyLog[2, -Cosh[a + b*x] - Sinh[a + b*x]] + 3*b^2*x^2*PolyLog[2, Cosh[a + b*x] + Sinh[a + b*x]] - (3*I)*(b^2*x^2*Log[1 - I*E^(a + b*x)] - b^2*x^2*Log[1 + I*E^(a + b*x)] - 2*b*x*PolyLog[2, (-I)*E^(a + b*x)] + 2*b*x*PolyLog[2, I*E^(a + b*x)] + 2*PolyLog[3, (-I)*E^(a + b*x)] - 2*PolyLog[3, I*E^(a + b*x)]) + 6*b*x*PolyLog[3, -Cosh[a + b*x] - Sinh[a + b*x]] - 6*b*x*PolyLog[3, Cosh[a + b*x] + Sinh[a + b*x]] - 6*PolyLog[4, -Cosh[a + b*x] - Sinh[a + b*x]] + 6*PolyLog[4, Cosh[a + b*x] + Sinh[a + b*x]] + b^3*x^3*Sech[a + b*x])/b^4","A",0
475,1,225,146,0.6464055,"\int x^2 \text{csch}(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x^2*Csch[a + b*x]*Sech[a + b*x]^2,x]","\frac{-2 \left(b^2 x^2 \tanh ^{-1}(\sinh (a+b x)+\cosh (a+b x))+b x \text{Li}_2(-\cosh (a+b x)-\sinh (a+b x))-b x \text{Li}_2(\cosh (a+b x)+\sinh (a+b x))-\text{Li}_3(-\cosh (a+b x)-\sinh (a+b x))+\text{Li}_3(\cosh (a+b x)+\sinh (a+b x))\right)+b^2 x^2 \text{sech}(a+b x)+2 i \left(\text{Li}_2\left(-i e^{a+b x}\right)-\text{Li}_2\left(i e^{a+b x}\right)\right)+(-2 i a-2 i b x+\pi ) \left(\log \left(1-i e^{a+b x}\right)-\log \left(1+i e^{a+b x}\right)\right)-(\pi -2 i a) \log \left(\cot \left(\frac{1}{4} (2 i a+2 i b x+\pi )\right)\right)}{b^3}","\frac{2 i \text{Li}_2\left(-i e^{a+b x}\right)}{b^3}-\frac{2 i \text{Li}_2\left(i e^{a+b x}\right)}{b^3}+\frac{2 \text{Li}_3\left(-e^{a+b x}\right)}{b^3}-\frac{2 \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{2 x \text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{2 x \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{4 x \tan ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{2 x^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}+\frac{x^2 \text{sech}(a+b x)}{b}",1,"(((-2*I)*a + Pi - (2*I)*b*x)*(Log[1 - I*E^(a + b*x)] - Log[1 + I*E^(a + b*x)]) - ((-2*I)*a + Pi)*Log[Cot[((2*I)*a + Pi + (2*I)*b*x)/4]] + (2*I)*(PolyLog[2, (-I)*E^(a + b*x)] - PolyLog[2, I*E^(a + b*x)]) - 2*(b^2*x^2*ArcTanh[Cosh[a + b*x] + Sinh[a + b*x]] + b*x*PolyLog[2, -Cosh[a + b*x] - Sinh[a + b*x]] - b*x*PolyLog[2, Cosh[a + b*x] + Sinh[a + b*x]] - PolyLog[3, -Cosh[a + b*x] - Sinh[a + b*x]] + PolyLog[3, Cosh[a + b*x] + Sinh[a + b*x]]) + b^2*x^2*Sech[a + b*x])/b^3","A",0
476,1,106,67,0.2897469,"\int x \text{csch}(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x*Csch[a + b*x]*Sech[a + b*x]^2,x]","\frac{\text{Li}_2\left(-e^{-a-b x}\right)-\text{Li}_2\left(e^{-a-b x}\right)+(a+b x) \left(\log \left(1-e^{-a-b x}\right)-\log \left(e^{-a-b x}+1\right)\right)+b x \text{sech}(a+b x)-a \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)-2 \tan ^{-1}\left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{b^2}","-\frac{\text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{\text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{\tan ^{-1}(\sinh (a+b x))}{b^2}-\frac{2 x \tanh ^{-1}\left(e^{a+b x}\right)}{b}+\frac{x \text{sech}(a+b x)}{b}",1,"(-2*ArcTan[Tanh[(a + b*x)/2]] + (a + b*x)*(Log[1 - E^(-a - b*x)] - Log[1 + E^(-a - b*x)]) - a*Log[Tanh[(a + b*x)/2]] + PolyLog[2, -E^(-a - b*x)] - PolyLog[2, E^(-a - b*x)] + b*x*Sech[a + b*x])/b^2","A",1
477,1,26,23,0.030172,"\int \text{csch}(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[Csch[a + b*x]*Sech[a + b*x]^2,x]","\frac{\text{sech}(a+b x)}{b}+\frac{\log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{b}","\frac{\text{sech}(a+b x)}{b}-\frac{\tanh ^{-1}(\cosh (a+b x))}{b}",1,"Log[Tanh[(a + b*x)/2]]/b + Sech[a + b*x]/b","A",1
478,0,0,21,35.9060764,"\int \frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{x} \, dx","Integrate[(Csch[a + b*x]*Sech[a + b*x]^2)/x,x]","\int \frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{x},x\right)",0,"Integrate[(Csch[a + b*x]*Sech[a + b*x]^2)/x, x]","A",-1
479,0,0,21,25.8996342,"\int \frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{x^2} \, dx","Integrate[(Csch[a + b*x]*Sech[a + b*x]^2)/x^2,x]","\int \frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{x^2},x\right)",0,"Integrate[(Csch[a + b*x]*Sech[a + b*x]^2)/x^2, x]","A",-1
480,0,0,21,82.1941801,"\int x^m \text{csch}(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[x^m*Csch[a + b*x]*Sech[a + b*x]^3,x]","\int x^m \text{csch}(a+b x) \text{sech}^3(a+b x) \, dx","\text{Int}\left(x^m \text{csch}(a+b x) \text{sech}^3(a+b x),x\right)",0,"Integrate[x^m*Csch[a + b*x]*Sech[a + b*x]^3, x]","A",-1
481,1,462,240,7.3925113,"\int x^3 \text{csch}(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[x^3*Csch[a + b*x]*Sech[a + b*x]^3,x]","-\frac{3 x^2 \text{sech}(a) \sinh (b x) \text{sech}(a+b x)}{2 b^2}-\frac{e^{2 a} \left(e^{-2 a} b^4 x^4-2 \left(1-e^{-2 a}\right) b^3 x^3 \log \left(1-e^{-a-b x}\right)-2 \left(1-e^{-2 a}\right) b^3 x^3 \log \left(e^{-a-b x}+1\right)+6 \left(1-e^{-2 a}\right) \left(b^2 x^2 \text{Li}_2\left(-e^{-a-b x}\right)+2 \left(b x \text{Li}_3\left(-e^{-a-b x}\right)+\text{Li}_4\left(-e^{-a-b x}\right)\right)\right)+6 \left(1-e^{-2 a}\right) \left(b^2 x^2 \text{Li}_2\left(e^{-a-b x}\right)+2 \left(b x \text{Li}_3\left(e^{-a-b x}\right)+\text{Li}_4\left(e^{-a-b x}\right)\right)\right)\right)}{2 \left(e^{2 a}-1\right) b^4}-\frac{e^{2 a} \left(2 e^{-2 a} b^4 x^4+4 \left(e^{-2 a}+1\right) b^3 x^3 \log \left(e^{-2 (a+b x)}+1\right)-3 e^{-2 a} \left(e^{2 a}+1\right) \left(2 b^2 x^2 \text{Li}_2\left(-e^{-2 (a+b x)}\right)+2 b x \text{Li}_3\left(-e^{-2 (a+b x)}\right)+\text{Li}_4\left(-e^{-2 (a+b x)}\right)\right)-12 e^{-2 a} b^2 x^2+6 \left(e^{-2 a}+1\right) \text{Li}_2\left(-e^{-2 (a+b x)}\right)-12 \left(e^{-2 a}+1\right) b x \log \left(e^{-2 (a+b x)}+1\right)\right)}{4 \left(e^{2 a}+1\right) b^4}+\frac{x^3 \text{sech}^2(a+b x)}{2 b}+\frac{1}{4} x^4 \text{csch}(a) \text{sech}(a)","\frac{3 \text{Li}_2\left(-e^{2 (a+b x)}\right)}{2 b^4}-\frac{3 \text{Li}_4\left(-e^{2 a+2 b x}\right)}{4 b^4}+\frac{3 \text{Li}_4\left(e^{2 a+2 b x}\right)}{4 b^4}+\frac{3 x \text{Li}_3\left(-e^{2 a+2 b x}\right)}{2 b^3}-\frac{3 x \text{Li}_3\left(e^{2 a+2 b x}\right)}{2 b^3}+\frac{3 x \log \left(e^{2 (a+b x)}+1\right)}{b^3}-\frac{3 x^2 \text{Li}_2\left(-e^{2 a+2 b x}\right)}{2 b^2}+\frac{3 x^2 \text{Li}_2\left(e^{2 a+2 b x}\right)}{2 b^2}-\frac{3 x^2 \tanh (a+b x)}{2 b^2}-\frac{2 x^3 \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}-\frac{x^3 \tanh ^2(a+b x)}{2 b}-\frac{3 x^2}{2 b^2}+\frac{x^3}{2 b}",1,"-1/2*(E^(2*a)*((b^4*x^4)/E^(2*a) - 2*b^3*(1 - E^(-2*a))*x^3*Log[1 - E^(-a - b*x)] - 2*b^3*(1 - E^(-2*a))*x^3*Log[1 + E^(-a - b*x)] + 6*(1 - E^(-2*a))*(b^2*x^2*PolyLog[2, -E^(-a - b*x)] + 2*(b*x*PolyLog[3, -E^(-a - b*x)] + PolyLog[4, -E^(-a - b*x)])) + 6*(1 - E^(-2*a))*(b^2*x^2*PolyLog[2, E^(-a - b*x)] + 2*(b*x*PolyLog[3, E^(-a - b*x)] + PolyLog[4, E^(-a - b*x)]))))/(b^4*(-1 + E^(2*a))) - (E^(2*a)*((-12*b^2*x^2)/E^(2*a) + (2*b^4*x^4)/E^(2*a) - 12*b*(1 + E^(-2*a))*x*Log[1 + E^(-2*(a + b*x))] + 4*b^3*(1 + E^(-2*a))*x^3*Log[1 + E^(-2*(a + b*x))] + 6*(1 + E^(-2*a))*PolyLog[2, -E^(-2*(a + b*x))] - (3*(1 + E^(2*a))*(2*b^2*x^2*PolyLog[2, -E^(-2*(a + b*x))] + 2*b*x*PolyLog[3, -E^(-2*(a + b*x))] + PolyLog[4, -E^(-2*(a + b*x))]))/E^(2*a)))/(4*b^4*(1 + E^(2*a))) + (x^4*Csch[a]*Sech[a])/4 + (x^3*Sech[a + b*x]^2)/(2*b) - (3*x^2*Sech[a]*Sech[a + b*x]*Sinh[b*x])/(2*b^2)","A",1
482,1,362,148,3.868338,"\int x^2 \text{csch}(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[x^2*Csch[a + b*x]*Sech[a + b*x]^3,x]","\frac{1}{6} \left(-\frac{6 x \text{sech}(a) \sinh (b x) \text{sech}(a+b x)}{b^2}-\frac{2 e^{2 a} \left(2 e^{-2 a} b^3 x^3-3 \left(1-e^{-2 a}\right) b^2 x^2 \log \left(1-e^{-a-b x}\right)-3 \left(1-e^{-2 a}\right) b^2 x^2 \log \left(e^{-a-b x}+1\right)+6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(-e^{-a-b x}\right)+\text{Li}_3\left(-e^{-a-b x}\right)\right)+6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(e^{-a-b x}\right)+\text{Li}_3\left(e^{-a-b x}\right)\right)\right)}{\left(e^{2 a}-1\right) b^3}+\frac{-6 \left(e^{2 a}+1\right) b^2 x^2 \log \left(e^{-2 (a+b x)}+1\right)+6 \left(e^{2 a}+1\right) b x \text{Li}_2\left(-e^{-2 (a+b x)}\right)+3 \left(e^{2 a}+1\right) \text{Li}_3\left(-e^{-2 (a+b x)}\right)-12 e^{2 a} b x+6 e^{2 a} \log \left(e^{2 (a+b x)}+1\right)+6 \log \left(e^{2 (a+b x)}+1\right)-4 b^3 x^3}{\left(e^{2 a}+1\right) b^3}+\frac{3 x^2 \text{sech}^2(a+b x)}{b}+2 x^3 \text{csch}(a) \text{sech}(a)\right)","\frac{\text{Li}_3\left(-e^{2 a+2 b x}\right)}{2 b^3}-\frac{\text{Li}_3\left(e^{2 a+2 b x}\right)}{2 b^3}+\frac{\log (\cosh (a+b x))}{b^3}-\frac{x \text{Li}_2\left(-e^{2 a+2 b x}\right)}{b^2}+\frac{x \text{Li}_2\left(e^{2 a+2 b x}\right)}{b^2}-\frac{x \tanh (a+b x)}{b^2}-\frac{2 x^2 \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}-\frac{x^2 \tanh ^2(a+b x)}{2 b}+\frac{x^2}{2 b}",1,"((-2*E^(2*a)*((2*b^3*x^3)/E^(2*a) - 3*b^2*(1 - E^(-2*a))*x^2*Log[1 - E^(-a - b*x)] - 3*b^2*(1 - E^(-2*a))*x^2*Log[1 + E^(-a - b*x)] + 6*(1 - E^(-2*a))*(b*x*PolyLog[2, -E^(-a - b*x)] + PolyLog[3, -E^(-a - b*x)]) + 6*(1 - E^(-2*a))*(b*x*PolyLog[2, E^(-a - b*x)] + PolyLog[3, E^(-a - b*x)])))/(b^3*(-1 + E^(2*a))) + (-12*b*E^(2*a)*x - 4*b^3*x^3 - 6*b^2*(1 + E^(2*a))*x^2*Log[1 + E^(-2*(a + b*x))] + 6*Log[1 + E^(2*(a + b*x))] + 6*E^(2*a)*Log[1 + E^(2*(a + b*x))] + 6*b*(1 + E^(2*a))*x*PolyLog[2, -E^(-2*(a + b*x))] + 3*(1 + E^(2*a))*PolyLog[3, -E^(-2*(a + b*x))])/(b^3*(1 + E^(2*a))) + 2*x^3*Csch[a]*Sech[a] + (3*x^2*Sech[a + b*x]^2)/b - (6*x*Sech[a]*Sech[a + b*x]*Sinh[b*x])/b^2)/6","B",1
483,1,139,95,0.4345523,"\int x \text{csch}(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[x*Csch[a + b*x]*Sech[a + b*x]^3,x]","\frac{\text{Li}_2\left(-e^{-2 (a+b x)}\right)-\text{Li}_2\left(e^{-2 (a+b x)}\right)+2 a \log \left(1-e^{-2 (a+b x)}\right)+2 b x \log \left(1-e^{-2 (a+b x)}\right)-2 a \log \left(e^{-2 (a+b x)}+1\right)-2 b x \log \left(e^{-2 (a+b x)}+1\right)-\tanh (a+b x)+b x \text{sech}^2(a+b x)-2 a \log (\sinh (a+b x))+2 a \log (\cosh (a+b x))}{2 b^2}","-\frac{\text{Li}_2\left(-e^{2 a+2 b x}\right)}{2 b^2}+\frac{\text{Li}_2\left(e^{2 a+2 b x}\right)}{2 b^2}-\frac{\tanh (a+b x)}{2 b^2}-\frac{2 x \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}-\frac{x \tanh ^2(a+b x)}{2 b}+\frac{x}{2 b}",1,"(2*a*Log[1 - E^(-2*(a + b*x))] + 2*b*x*Log[1 - E^(-2*(a + b*x))] - 2*a*Log[1 + E^(-2*(a + b*x))] - 2*b*x*Log[1 + E^(-2*(a + b*x))] + 2*a*Log[Cosh[a + b*x]] - 2*a*Log[Sinh[a + b*x]] + PolyLog[2, -E^(-2*(a + b*x))] - PolyLog[2, E^(-2*(a + b*x))] + b*x*Sech[a + b*x]^2 - Tanh[a + b*x])/(2*b^2)","A",1
484,1,36,27,0.0331848,"\int \text{csch}(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[Csch[a + b*x]*Sech[a + b*x]^3,x]","-\frac{-\text{sech}^2(a+b x)-2 \log (\sinh (a+b x))+2 \log (\cosh (a+b x))}{2 b}","\frac{\log (\tanh (a+b x))}{b}-\frac{\tanh ^2(a+b x)}{2 b}",1,"-1/2*(2*Log[Cosh[a + b*x]] - 2*Log[Sinh[a + b*x]] - Sech[a + b*x]^2)/b","A",1
485,0,0,21,57.7270597,"\int \frac{\text{csch}(a+b x) \text{sech}^3(a+b x)}{x} \, dx","Integrate[(Csch[a + b*x]*Sech[a + b*x]^3)/x,x]","\int \frac{\text{csch}(a+b x) \text{sech}^3(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{csch}(a+b x) \text{sech}^3(a+b x)}{x},x\right)",0,"Integrate[(Csch[a + b*x]*Sech[a + b*x]^3)/x, x]","A",-1
486,0,0,21,29.650865,"\int \frac{\text{csch}(a+b x) \text{sech}^3(a+b x)}{x^2} \, dx","Integrate[(Csch[a + b*x]*Sech[a + b*x]^3)/x^2,x]","\int \frac{\text{csch}(a+b x) \text{sech}^3(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{csch}(a+b x) \text{sech}^3(a+b x)}{x^2},x\right)",0,"Integrate[(Csch[a + b*x]*Sech[a + b*x]^3)/x^2, x]","A",-1
487,0,0,21,44.6758284,"\int x^m \text{csch}^2(a+b x) \text{sech}(a+b x) \, dx","Integrate[x^m*Csch[a + b*x]^2*Sech[a + b*x],x]","\int x^m \text{csch}^2(a+b x) \text{sech}(a+b x) \, dx","\text{Int}\left(x^m \text{csch}^2(a+b x) \text{sech}(a+b x),x\right)",0,"Integrate[x^m*Csch[a + b*x]^2*Sech[a + b*x], x]","A",-1
488,1,333,237,1.8135402,"\int x^3 \text{csch}^2(a+b x) \text{sech}(a+b x) \, dx","Integrate[x^3*Csch[a + b*x]^2*Sech[a + b*x],x]","\frac{-2 b^3 x^3 \text{csch}(a)+b^3 x^3 \text{csch}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{csch}\left(\frac{1}{2} (a+b x)\right)+b^3 x^3 \text{sech}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{sech}\left(\frac{1}{2} (a+b x)\right)-12 \left(b^2 x^2 \tanh ^{-1}(\sinh (a+b x)+\cosh (a+b x))+b x \text{Li}_2(-\cosh (a+b x)-\sinh (a+b x))-b x \text{Li}_2(\cosh (a+b x)+\sinh (a+b x))-\text{Li}_3(-\cosh (a+b x)-\sinh (a+b x))+\text{Li}_3(\cosh (a+b x)+\sinh (a+b x))\right)-2 i \left(b^3 x^3 \log \left(1-i e^{a+b x}\right)-b^3 x^3 \log \left(1+i e^{a+b x}\right)-3 b^2 x^2 \text{Li}_2\left(-i e^{a+b x}\right)+3 b^2 x^2 \text{Li}_2\left(i e^{a+b x}\right)+6 b x \text{Li}_3\left(-i e^{a+b x}\right)-6 b x \text{Li}_3\left(i e^{a+b x}\right)-6 \text{Li}_4\left(-i e^{a+b x}\right)+6 \text{Li}_4\left(i e^{a+b x}\right)\right)}{2 b^4}","\frac{6 \text{Li}_3\left(-e^{a+b x}\right)}{b^4}-\frac{6 \text{Li}_3\left(e^{a+b x}\right)}{b^4}+\frac{6 i \text{Li}_4\left(-i e^{a+b x}\right)}{b^4}-\frac{6 i \text{Li}_4\left(i e^{a+b x}\right)}{b^4}-\frac{6 x \text{Li}_2\left(-e^{a+b x}\right)}{b^3}+\frac{6 x \text{Li}_2\left(e^{a+b x}\right)}{b^3}-\frac{6 i x \text{Li}_3\left(-i e^{a+b x}\right)}{b^3}+\frac{6 i x \text{Li}_3\left(i e^{a+b x}\right)}{b^3}+\frac{3 i x^2 \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}-\frac{3 i x^2 \text{Li}_2\left(i e^{a+b x}\right)}{b^2}-\frac{6 x^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{2 x^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}-\frac{x^3 \text{csch}(a+b x)}{b}",1,"(-2*b^3*x^3*Csch[a] - 12*(b^2*x^2*ArcTanh[Cosh[a + b*x] + Sinh[a + b*x]] + b*x*PolyLog[2, -Cosh[a + b*x] - Sinh[a + b*x]] - b*x*PolyLog[2, Cosh[a + b*x] + Sinh[a + b*x]] - PolyLog[3, -Cosh[a + b*x] - Sinh[a + b*x]] + PolyLog[3, Cosh[a + b*x] + Sinh[a + b*x]]) - (2*I)*(b^3*x^3*Log[1 - I*E^(a + b*x)] - b^3*x^3*Log[1 + I*E^(a + b*x)] - 3*b^2*x^2*PolyLog[2, (-I)*E^(a + b*x)] + 3*b^2*x^2*PolyLog[2, I*E^(a + b*x)] + 6*b*x*PolyLog[3, (-I)*E^(a + b*x)] - 6*b*x*PolyLog[3, I*E^(a + b*x)] - 6*PolyLog[4, (-I)*E^(a + b*x)] + 6*PolyLog[4, I*E^(a + b*x)]) + b^3*x^3*Csch[a/2]*Csch[(a + b*x)/2]*Sinh[(b*x)/2] + b^3*x^3*Sech[a/2]*Sech[(a + b*x)/2]*Sinh[(b*x)/2])/(2*b^4)","A",0
489,1,312,157,1.9314581,"\int x^2 \text{csch}^2(a+b x) \text{sech}(a+b x) \, dx","Integrate[x^2*Csch[a + b*x]^2*Sech[a + b*x],x]","\frac{-2 i b^2 x^2 \log \left(1-i e^{a+b x}\right)+2 i b^2 x^2 \log \left(1+i e^{a+b x}\right)-2 b^2 x^2 \text{csch}(a)+b^2 x^2 \text{csch}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{csch}\left(\frac{1}{2} (a+b x)\right)+b^2 x^2 \text{sech}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{sech}\left(\frac{1}{2} (a+b x)\right)+4 i b x \text{Li}_2\left(-i e^{a+b x}\right)-4 i b x \text{Li}_2\left(i e^{a+b x}\right)+4 \text{Li}_2\left(-e^{-a-b x}\right)-4 \text{Li}_2\left(e^{-a-b x}\right)-4 i \text{Li}_3\left(-i e^{a+b x}\right)+4 i \text{Li}_3\left(i e^{a+b x}\right)+4 b x \log \left(1-e^{-a-b x}\right)-4 b x \log \left(e^{-a-b x}+1\right)+4 a \log \left(1-e^{-a-b x}\right)-4 a \log \left(e^{-a-b x}+1\right)-4 a \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b^3}","-\frac{2 \text{Li}_2\left(-e^{a+b x}\right)}{b^3}+\frac{2 \text{Li}_2\left(e^{a+b x}\right)}{b^3}-\frac{2 i \text{Li}_3\left(-i e^{a+b x}\right)}{b^3}+\frac{2 i \text{Li}_3\left(i e^{a+b x}\right)}{b^3}+\frac{2 i x \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}-\frac{2 i x \text{Li}_2\left(i e^{a+b x}\right)}{b^2}-\frac{4 x \tanh ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{2 x^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}-\frac{x^2 \text{csch}(a+b x)}{b}",1,"(-2*b^2*x^2*Csch[a] + 4*a*Log[1 - E^(-a - b*x)] + 4*b*x*Log[1 - E^(-a - b*x)] - 4*a*Log[1 + E^(-a - b*x)] - 4*b*x*Log[1 + E^(-a - b*x)] - (2*I)*b^2*x^2*Log[1 - I*E^(a + b*x)] + (2*I)*b^2*x^2*Log[1 + I*E^(a + b*x)] - 4*a*Log[Tanh[(a + b*x)/2]] + 4*PolyLog[2, -E^(-a - b*x)] - 4*PolyLog[2, E^(-a - b*x)] + (4*I)*b*x*PolyLog[2, (-I)*E^(a + b*x)] - (4*I)*b*x*PolyLog[2, I*E^(a + b*x)] - (4*I)*PolyLog[3, (-I)*E^(a + b*x)] + (4*I)*PolyLog[3, I*E^(a + b*x)] + b^2*x^2*Csch[a/2]*Csch[(a + b*x)/2]*Sinh[(b*x)/2] + b^2*x^2*Sech[a/2]*Sech[(a + b*x)/2]*Sinh[(b*x)/2])/(2*b^3)","A",1
490,1,112,79,0.8330453,"\int x \text{csch}^2(a+b x) \text{sech}(a+b x) \, dx","Integrate[x*Csch[a + b*x]^2*Sech[a + b*x],x]","\frac{2 i \text{Li}_2(-i (\cosh (a+b x)+\sinh (a+b x)))-2 i \text{Li}_2(i (\cosh (a+b x)+\sinh (a+b x)))+b x \tanh \left(\frac{1}{2} (a+b x)\right)-b x \coth \left(\frac{1}{2} (a+b x)\right)+2 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)-4 b x \tan ^{-1}(\sinh (a+b x)+\cosh (a+b x))}{2 b^2}","\frac{i \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}-\frac{i \text{Li}_2\left(i e^{a+b x}\right)}{b^2}-\frac{\tanh ^{-1}(\cosh (a+b x))}{b^2}-\frac{2 x \tan ^{-1}\left(e^{a+b x}\right)}{b}-\frac{x \text{csch}(a+b x)}{b}",1,"(-4*b*x*ArcTan[Cosh[a + b*x] + Sinh[a + b*x]] - b*x*Coth[(a + b*x)/2] + 2*Log[Tanh[(a + b*x)/2]] + (2*I)*PolyLog[2, (-I)*(Cosh[a + b*x] + Sinh[a + b*x])] - (2*I)*PolyLog[2, I*(Cosh[a + b*x] + Sinh[a + b*x])] + b*x*Tanh[(a + b*x)/2])/(2*b^2)","A",0
491,1,29,24,0.0162955,"\int \text{csch}^2(a+b x) \text{sech}(a+b x) \, dx","Integrate[Csch[a + b*x]^2*Sech[a + b*x],x]","-\frac{\text{csch}(a+b x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\sinh ^2(a+b x)\right)}{b}","-\frac{\text{csch}(a+b x)}{b}-\frac{\tan ^{-1}(\sinh (a+b x))}{b}",1,"-((Csch[a + b*x]*Hypergeometric2F1[-1/2, 1, 1/2, -Sinh[a + b*x]^2])/b)","C",1
492,0,0,21,23.4485424,"\int \frac{\text{csch}^2(a+b x) \text{sech}(a+b x)}{x} \, dx","Integrate[(Csch[a + b*x]^2*Sech[a + b*x])/x,x]","\int \frac{\text{csch}^2(a+b x) \text{sech}(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{csch}^2(a+b x) \text{sech}(a+b x)}{x},x\right)",0,"Integrate[(Csch[a + b*x]^2*Sech[a + b*x])/x, x]","A",-1
493,0,0,21,25.9997941,"\int \frac{\text{csch}^2(a+b x) \text{sech}(a+b x)}{x^2} \, dx","Integrate[(Csch[a + b*x]^2*Sech[a + b*x])/x^2,x]","\int \frac{\text{csch}^2(a+b x) \text{sech}(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{csch}^2(a+b x) \text{sech}(a+b x)}{x^2},x\right)",0,"Integrate[(Csch[a + b*x]^2*Sech[a + b*x])/x^2, x]","A",-1
494,0,0,23,7.3803897,"\int x^m \text{csch}^2(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x^m*Csch[a + b*x]^2*Sech[a + b*x]^2,x]","\int x^m \text{csch}^2(a+b x) \text{sech}^2(a+b x) \, dx","\text{Int}\left(x^m \text{csch}^2(a+b x) \text{sech}^2(a+b x),x\right)",0,"Integrate[x^m*Csch[a + b*x]^2*Sech[a + b*x]^2, x]","A",-1
495,1,284,85,5.7602575,"\int x^3 \text{csch}^2(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x^3*Csch[a + b*x]^2*Sech[a + b*x]^2,x]","4 \left(\frac{x^3 \text{csch}(2 a) \sinh (2 b x) \text{csch}(2 a+2 b x)}{2 b}-\frac{e^{4 a} \left(8 e^{-4 a} b^3 x^3-6 \left(1-e^{-4 a}\right) b^2 x^2 \log \left(1-e^{-a-b x}\right)-6 \left(1-e^{-4 a}\right) b^2 x^2 \log \left(e^{-a-b x}+1\right)-6 \left(1-e^{-4 a}\right) b^2 x^2 \log \left(e^{-2 (a+b x)}+1\right)+12 \left(1-e^{-4 a}\right) \left(b x \text{Li}_2\left(-e^{-a-b x}\right)+\text{Li}_3\left(-e^{-a-b x}\right)\right)+12 \left(1-e^{-4 a}\right) \left(b x \text{Li}_2\left(e^{-a-b x}\right)+\text{Li}_3\left(e^{-a-b x}\right)\right)+3 e^{-4 a} \left(e^{4 a}-1\right) \left(2 b x \text{Li}_2\left(-e^{-2 (a+b x)}\right)+\text{Li}_3\left(-e^{-2 (a+b x)}\right)\right)\right)}{8 \left(e^{4 a}-1\right) b^4}\right)","-\frac{3 \text{Li}_3\left(e^{4 (a+b x)}\right)}{8 b^4}+\frac{3 x \text{Li}_2\left(e^{4 (a+b x)}\right)}{2 b^3}+\frac{3 x^2 \log \left(1-e^{4 (a+b x)}\right)}{b^2}-\frac{2 x^3 \coth (2 a+2 b x)}{b}-\frac{2 x^3}{b}",1,"4*(-1/8*(E^(4*a)*((8*b^3*x^3)/E^(4*a) - 6*b^2*(1 - E^(-4*a))*x^2*Log[1 - E^(-a - b*x)] - 6*b^2*(1 - E^(-4*a))*x^2*Log[1 + E^(-a - b*x)] - 6*b^2*(1 - E^(-4*a))*x^2*Log[1 + E^(-2*(a + b*x))] + 12*(1 - E^(-4*a))*(b*x*PolyLog[2, -E^(-a - b*x)] + PolyLog[3, -E^(-a - b*x)]) + 12*(1 - E^(-4*a))*(b*x*PolyLog[2, E^(-a - b*x)] + PolyLog[3, E^(-a - b*x)]) + (3*(-1 + E^(4*a))*(2*b*x*PolyLog[2, -E^(-2*(a + b*x))] + PolyLog[3, -E^(-2*(a + b*x))]))/E^(4*a)))/(b^4*(-1 + E^(4*a))) + (x^3*Csch[2*a]*Csch[2*a + 2*b*x]*Sinh[2*b*x])/(2*b))","B",1
496,1,216,64,4.1892458,"\int x^2 \text{csch}^2(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x^2*Csch[a + b*x]^2*Sech[a + b*x]^2,x]","4 \left(\frac{x^2 \text{csch}(2 a) \sinh (2 b x) \text{csch}(2 a+2 b x)}{2 b}-\frac{e^{4 a} \left(4 e^{-4 a} b^2 x^2+2 \left(1-e^{-4 a}\right) \text{Li}_2\left(-e^{-a-b x}\right)+2 \left(1-e^{-4 a}\right) \text{Li}_2\left(e^{-a-b x}\right)+\left(1-e^{-4 a}\right) \text{Li}_2\left(-e^{-2 (a+b x)}\right)-2 \left(1-e^{-4 a}\right) b x \log \left(1-e^{-a-b x}\right)-2 \left(1-e^{-4 a}\right) b x \log \left(e^{-a-b x}+1\right)-2 \left(1-e^{-4 a}\right) b x \log \left(e^{-2 (a+b x)}+1\right)\right)}{4 \left(e^{4 a}-1\right) b^3}\right)","\frac{\text{Li}_2\left(e^{4 (a+b x)}\right)}{2 b^3}+\frac{2 x \log \left(1-e^{4 (a+b x)}\right)}{b^2}-\frac{2 x^2 \coth (2 a+2 b x)}{b}-\frac{2 x^2}{b}",1,"4*(-1/4*(E^(4*a)*((4*b^2*x^2)/E^(4*a) - 2*b*(1 - E^(-4*a))*x*Log[1 - E^(-a - b*x)] - 2*b*(1 - E^(-4*a))*x*Log[1 + E^(-a - b*x)] - 2*b*(1 - E^(-4*a))*x*Log[1 + E^(-2*(a + b*x))] + 2*(1 - E^(-4*a))*PolyLog[2, -E^(-a - b*x)] + 2*(1 - E^(-4*a))*PolyLog[2, E^(-a - b*x)] + (1 - E^(-4*a))*PolyLog[2, -E^(-2*(a + b*x))]))/(b^3*(-1 + E^(4*a))) + (x^2*Csch[2*a]*Csch[2*a + 2*b*x]*Sinh[2*b*x])/(2*b))","B",1
497,1,26,30,0.156706,"\int x \text{csch}^2(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x*Csch[a + b*x]^2*Sech[a + b*x]^2,x]","\frac{\log (\sinh (2 (a+b x)))-2 b x \coth (2 (a+b x))}{b^2}","\frac{\log (\sinh (2 a+2 b x))}{b^2}-\frac{2 x \coth (2 a+2 b x)}{b}",1,"(-2*b*x*Coth[2*(a + b*x)] + Log[Sinh[2*(a + b*x)]])/b^2","A",1
498,1,13,23,0.0104621,"\int \text{csch}^2(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[Csch[a + b*x]^2*Sech[a + b*x]^2,x]","-\frac{2 \coth (2 (a+b x))}{b}","-\frac{\tanh (a+b x)}{b}-\frac{\coth (a+b x)}{b}",1,"(-2*Coth[2*(a + b*x)])/b","A",1
499,0,0,20,23.9554404,"\int \frac{\text{csch}^2(a+b x) \text{sech}^2(a+b x)}{x} \, dx","Integrate[(Csch[a + b*x]^2*Sech[a + b*x]^2)/x,x]","\int \frac{\text{csch}^2(a+b x) \text{sech}^2(a+b x)}{x} \, dx","4 \text{Int}\left(\frac{\text{csch}^2(2 a+2 b x)}{x},x\right)",0,"Integrate[(Csch[a + b*x]^2*Sech[a + b*x]^2)/x, x]","A",-1
500,0,0,20,21.1213181,"\int \frac{\text{csch}^2(a+b x) \text{sech}^2(a+b x)}{x^2} \, dx","Integrate[(Csch[a + b*x]^2*Sech[a + b*x]^2)/x^2,x]","\int \frac{\text{csch}^2(a+b x) \text{sech}^2(a+b x)}{x^2} \, dx","4 \text{Int}\left(\frac{\text{csch}^2(2 a+2 b x)}{x^2},x\right)",0,"Integrate[(Csch[a + b*x]^2*Sech[a + b*x]^2)/x^2, x]","A",-1
501,0,0,23,56.0275254,"\int x^m \text{csch}^2(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[x^m*Csch[a + b*x]^2*Sech[a + b*x]^3,x]","\int x^m \text{csch}^2(a+b x) \text{sech}^3(a+b x) \, dx","\text{Int}\left(x^m \text{csch}^2(a+b x) \text{sech}^3(a+b x),x\right)",0,"Integrate[x^m*Csch[a + b*x]^2*Sech[a + b*x]^3, x]","A",-1
502,1,397,206,7.4209797,"\int x^2 \text{csch}^2(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[x^2*Csch[a + b*x]^2*Sech[a + b*x]^3,x]","\frac{2 \left(-a \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)-i \left(i \left(\text{Li}_2\left(-e^{i (i a+i b x)}\right)-\text{Li}_2\left(e^{i (i a+i b x)}\right)\right)+(i a+i b x) \left(\log \left(1-e^{i (i a+i b x)}\right)-\log \left(1+e^{i (i a+i b x)}\right)\right)\right)\right)}{b^3}-\frac{x \text{sech}(a) \text{sech}(a+b x) (b x \sinh (a)+2 \cosh (a))}{2 b^2}-\frac{i \left(3 b^2 x^2 \log \left(1-i e^{a+b x}\right)-3 b^2 x^2 \log \left(1+i e^{a+b x}\right)-6 b x \text{Li}_2\left(-i e^{a+b x}\right)+6 b x \text{Li}_2\left(i e^{a+b x}\right)+6 \text{Li}_3\left(-i e^{a+b x}\right)-6 \text{Li}_3\left(i e^{a+b x}\right)+4 i \tan ^{-1}\left(e^{a+b x}\right)\right)}{2 b^3}-\frac{x^2 \text{csch}(a)}{b}+\frac{x^2 \text{csch}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{csch}\left(\frac{a}{2}+\frac{b x}{2}\right)}{2 b}-\frac{x^2 \text{sech}(a) \sinh (b x) \text{sech}^2(a+b x)}{2 b}+\frac{x^2 \text{sech}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{sech}\left(\frac{a}{2}+\frac{b x}{2}\right)}{2 b}","-\frac{2 \text{Li}_2\left(-e^{a+b x}\right)}{b^3}+\frac{2 \text{Li}_2\left(e^{a+b x}\right)}{b^3}-\frac{3 i \text{Li}_3\left(-i e^{a+b x}\right)}{b^3}+\frac{3 i \text{Li}_3\left(i e^{a+b x}\right)}{b^3}+\frac{\tan ^{-1}(\sinh (a+b x))}{b^3}+\frac{3 i x \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}-\frac{3 i x \text{Li}_2\left(i e^{a+b x}\right)}{b^2}-\frac{4 x \tanh ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{x \text{sech}(a+b x)}{b^2}-\frac{3 x^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}-\frac{3 x^2 \text{csch}(a+b x)}{2 b}+\frac{x^2 \text{csch}(a+b x) \text{sech}^2(a+b x)}{2 b}",1,"-((x^2*Csch[a])/b) + (2*(-(a*Log[Tanh[(a + b*x)/2]]) - I*((I*a + I*b*x)*(Log[1 - E^(I*(I*a + I*b*x))] - Log[1 + E^(I*(I*a + I*b*x))]) + I*(PolyLog[2, -E^(I*(I*a + I*b*x))] - PolyLog[2, E^(I*(I*a + I*b*x))]))))/b^3 - ((I/2)*((4*I)*ArcTan[E^(a + b*x)] + 3*b^2*x^2*Log[1 - I*E^(a + b*x)] - 3*b^2*x^2*Log[1 + I*E^(a + b*x)] - 6*b*x*PolyLog[2, (-I)*E^(a + b*x)] + 6*b*x*PolyLog[2, I*E^(a + b*x)] + 6*PolyLog[3, (-I)*E^(a + b*x)] - 6*PolyLog[3, I*E^(a + b*x)]))/b^3 - (x*Sech[a]*Sech[a + b*x]*(2*Cosh[a] + b*x*Sinh[a]))/(2*b^2) + (x^2*Csch[a/2]*Csch[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(2*b) + (x^2*Sech[a/2]*Sech[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(2*b) - (x^2*Sech[a]*Sech[a + b*x]^2*Sinh[b*x])/(2*b)","A",1
503,1,209,120,2.49151,"\int x \text{csch}^2(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[x*Csch[a + b*x]^2*Sech[a + b*x]^3,x]","-\frac{-3 i \text{Li}_2\left(-i e^{-a-b x}\right)+3 i \text{Li}_2\left(i e^{-a-b x}\right)-3 i a \log \left(1-i e^{-a-b x}\right)-3 i b x \log \left(1-i e^{-a-b x}\right)+3 i a \log \left(1+i e^{-a-b x}\right)+3 i b x \log \left(1+i e^{-a-b x}\right)-b x \tanh \left(\frac{1}{2} (a+b x)\right)+b x \coth \left(\frac{1}{2} (a+b x)\right)+\text{sech}(a+b x)-2 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)-3 a \tan ^{-1}(\sinh (a+b x))+b x \tanh (a+b x) \text{sech}(a+b x)}{2 b^2}","\frac{3 i \text{Li}_2\left(-i e^{a+b x}\right)}{2 b^2}-\frac{3 i \text{Li}_2\left(i e^{a+b x}\right)}{2 b^2}-\frac{\text{sech}(a+b x)}{2 b^2}-\frac{\tanh ^{-1}(\cosh (a+b x))}{b^2}-\frac{3 x \tan ^{-1}\left(e^{a+b x}\right)}{b}-\frac{3 x \text{csch}(a+b x)}{2 b}+\frac{x \text{csch}(a+b x) \text{sech}^2(a+b x)}{2 b}",1,"-1/2*(-3*a*ArcTan[Sinh[a + b*x]] + b*x*Coth[(a + b*x)/2] - (3*I)*a*Log[1 - I*E^(-a - b*x)] - (3*I)*b*x*Log[1 - I*E^(-a - b*x)] + (3*I)*a*Log[1 + I*E^(-a - b*x)] + (3*I)*b*x*Log[1 + I*E^(-a - b*x)] - 2*Log[Tanh[(a + b*x)/2]] - (3*I)*PolyLog[2, (-I)*E^(-a - b*x)] + (3*I)*PolyLog[2, I*E^(-a - b*x)] + Sech[a + b*x] - b*x*Tanh[(a + b*x)/2] + b*x*Sech[a + b*x]*Tanh[a + b*x])/b^2","A",1
504,1,29,49,0.0147168,"\int \text{csch}^2(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[Csch[a + b*x]^2*Sech[a + b*x]^3,x]","-\frac{\text{csch}(a+b x) \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\sinh ^2(a+b x)\right)}{b}","-\frac{3 \text{csch}(a+b x)}{2 b}-\frac{3 \tan ^{-1}(\sinh (a+b x))}{2 b}+\frac{\text{csch}(a+b x) \text{sech}^2(a+b x)}{2 b}",1,"-((Csch[a + b*x]*Hypergeometric2F1[-1/2, 2, 1/2, -Sinh[a + b*x]^2])/b)","C",1
505,0,0,23,43.9748241,"\int \frac{\text{csch}^2(a+b x) \text{sech}^3(a+b x)}{x} \, dx","Integrate[(Csch[a + b*x]^2*Sech[a + b*x]^3)/x,x]","\int \frac{\text{csch}^2(a+b x) \text{sech}^3(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{csch}^2(a+b x) \text{sech}^3(a+b x)}{x},x\right)",0,"Integrate[(Csch[a + b*x]^2*Sech[a + b*x]^3)/x, x]","A",-1
506,0,0,23,35.3154474,"\int \frac{\text{csch}^2(a+b x) \text{sech}^3(a+b x)}{x^2} \, dx","Integrate[(Csch[a + b*x]^2*Sech[a + b*x]^3)/x^2,x]","\int \frac{\text{csch}^2(a+b x) \text{sech}^3(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{csch}^2(a+b x) \text{sech}^3(a+b x)}{x^2},x\right)",0,"Integrate[(Csch[a + b*x]^2*Sech[a + b*x]^3)/x^2, x]","A",-1
507,0,0,21,69.5778349,"\int x^m \text{csch}^3(a+b x) \text{sech}(a+b x) \, dx","Integrate[x^m*Csch[a + b*x]^3*Sech[a + b*x],x]","\int x^m \text{csch}^3(a+b x) \text{sech}(a+b x) \, dx","\text{Int}\left(x^m \text{csch}^3(a+b x) \text{sech}(a+b x),x\right)",0,"Integrate[x^m*Csch[a + b*x]^3*Sech[a + b*x], x]","A",-1
508,1,490,240,7.5563951,"\int x^3 \text{csch}^3(a+b x) \text{sech}(a+b x) \, dx","Integrate[x^3*Csch[a + b*x]^3*Sech[a + b*x],x]","\frac{3 x^2 \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{2 b^2}-\frac{3 \left(2 b^2 x^2 \text{Li}_2\left(-e^{-2 (a+b x)}\right)+2 b x \text{Li}_3\left(-e^{-2 (a+b x)}\right)+\text{Li}_4\left(-e^{-2 (a+b x)}\right)\right)}{4 b^4}+\frac{e^{2 a} \left(e^{-2 a} b^4 x^4-2 e^{-2 a} \left(e^{2 a}-1\right) b^3 x^3 \log \left(1-e^{-a-b x}\right)-2 e^{-2 a} \left(e^{2 a}-1\right) b^3 x^3 \log \left(e^{-a-b x}+1\right)+6 \left(1-e^{-2 a}\right) \left(b^2 x^2 \text{Li}_2\left(-e^{-a-b x}\right)+2 \left(b x \text{Li}_3\left(-e^{-a-b x}\right)+\text{Li}_4\left(-e^{-a-b x}\right)\right)\right)+6 \left(1-e^{-2 a}\right) \left(b^2 x^2 \text{Li}_2\left(e^{-a-b x}\right)+2 \left(b x \text{Li}_3\left(e^{-a-b x}\right)+\text{Li}_4\left(e^{-a-b x}\right)\right)\right)-6 e^{-2 a} b^2 x^2-6 \left(1-e^{-2 a}\right) \text{Li}_2\left(-e^{-a-b x}\right)-6 \left(1-e^{-2 a}\right) \text{Li}_2\left(e^{-a-b x}\right)+6 \left(1-e^{-2 a}\right) b x \log \left(1-e^{-a-b x}\right)+6 \left(1-e^{-2 a}\right) b x \log \left(e^{-a-b x}+1\right)\right)}{2 \left(e^{2 a}-1\right) b^4}+\frac{x^3 \log \left(e^{-2 (a+b x)}+1\right)}{b}-\frac{x^3 \text{csch}^2(a+b x)}{2 b}+\frac{x^4}{2 e^{2 a}+2}-\frac{1}{4} x^4 \text{csch}(a) \text{sech}(a)","\frac{3 \text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 \text{Li}_4\left(-e^{2 a+2 b x}\right)}{4 b^4}-\frac{3 \text{Li}_4\left(e^{2 a+2 b x}\right)}{4 b^4}-\frac{3 x \text{Li}_3\left(-e^{2 a+2 b x}\right)}{2 b^3}+\frac{3 x \text{Li}_3\left(e^{2 a+2 b x}\right)}{2 b^3}+\frac{3 x \log \left(1-e^{2 (a+b x)}\right)}{b^3}+\frac{3 x^2 \text{Li}_2\left(-e^{2 a+2 b x}\right)}{2 b^2}-\frac{3 x^2 \text{Li}_2\left(e^{2 a+2 b x}\right)}{2 b^2}-\frac{3 x^2 \coth (a+b x)}{2 b^2}+\frac{2 x^3 \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}-\frac{x^3 \coth ^2(a+b x)}{2 b}-\frac{3 x^2}{2 b^2}+\frac{x^3}{2 b}",1,"x^4/(2 + 2*E^(2*a)) - (x^3*Csch[a + b*x]^2)/(2*b) + (x^3*Log[1 + E^(-2*(a + b*x))])/b + (E^(2*a)*((-6*b^2*x^2)/E^(2*a) + (b^4*x^4)/E^(2*a) + 6*b*(1 - E^(-2*a))*x*Log[1 - E^(-a - b*x)] - (2*b^3*(-1 + E^(2*a))*x^3*Log[1 - E^(-a - b*x)])/E^(2*a) + 6*b*(1 - E^(-2*a))*x*Log[1 + E^(-a - b*x)] - (2*b^3*(-1 + E^(2*a))*x^3*Log[1 + E^(-a - b*x)])/E^(2*a) - 6*(1 - E^(-2*a))*PolyLog[2, -E^(-a - b*x)] - 6*(1 - E^(-2*a))*PolyLog[2, E^(-a - b*x)] + 6*(1 - E^(-2*a))*(b^2*x^2*PolyLog[2, -E^(-a - b*x)] + 2*(b*x*PolyLog[3, -E^(-a - b*x)] + PolyLog[4, -E^(-a - b*x)])) + 6*(1 - E^(-2*a))*(b^2*x^2*PolyLog[2, E^(-a - b*x)] + 2*(b*x*PolyLog[3, E^(-a - b*x)] + PolyLog[4, E^(-a - b*x)]))))/(2*b^4*(-1 + E^(2*a))) - (3*(2*b^2*x^2*PolyLog[2, -E^(-2*(a + b*x))] + 2*b*x*PolyLog[3, -E^(-2*(a + b*x))] + PolyLog[4, -E^(-2*(a + b*x))]))/(4*b^4) - (x^4*Csch[a]*Sech[a])/4 + (3*x^2*Csch[a]*Csch[a + b*x]*Sinh[b*x])/(2*b^2)","B",1
509,1,369,148,4.4676095,"\int x^2 \text{csch}^3(a+b x) \text{sech}(a+b x) \, dx","Integrate[x^2*Csch[a + b*x]^3*Sech[a + b*x],x]","\frac{1}{6} \left(\frac{6 x \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b^2}+\frac{2 b^2 x^2 \left(\frac{2 b x}{e^{2 a}+1}+3 \log \left(e^{-2 (a+b x)}+1\right)\right)-6 b x \text{Li}_2\left(-e^{-2 (a+b x)}\right)-3 \text{Li}_3\left(-e^{-2 (a+b x)}\right)}{b^3}-\frac{2 e^{2 a} \left(-2 e^{-2 a} b^3 x^3+3 e^{-2 a} \left(e^{2 a}-1\right) b^2 x^2 \log \left(1-e^{-a-b x}\right)+3 e^{-2 a} \left(e^{2 a}-1\right) b^2 x^2 \log \left(e^{-a-b x}+1\right)-6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(-e^{-a-b x}\right)+\text{Li}_3\left(-e^{-a-b x}\right)\right)-6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(e^{-a-b x}\right)+\text{Li}_3\left(e^{-a-b x}\right)\right)+6 e^{-2 a} b x+3 \left(1-e^{-2 a}\right) \left(b x-\log \left(1-e^{a+b x}\right)\right)+3 \left(1-e^{-2 a}\right) \left(b x-\log \left(e^{a+b x}+1\right)\right)\right)}{\left(e^{2 a}-1\right) b^3}-\frac{3 x^2 \text{csch}^2(a+b x)}{b}-2 x^3 \text{csch}(a) \text{sech}(a)\right)","-\frac{\text{Li}_3\left(-e^{2 a+2 b x}\right)}{2 b^3}+\frac{\text{Li}_3\left(e^{2 a+2 b x}\right)}{2 b^3}+\frac{\log (\sinh (a+b x))}{b^3}+\frac{x \text{Li}_2\left(-e^{2 a+2 b x}\right)}{b^2}-\frac{x \text{Li}_2\left(e^{2 a+2 b x}\right)}{b^2}-\frac{x \coth (a+b x)}{b^2}+\frac{2 x^2 \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}-\frac{x^2 \coth ^2(a+b x)}{2 b}+\frac{x^2}{2 b}",1,"((-3*x^2*Csch[a + b*x]^2)/b - (2*E^(2*a)*((6*b*x)/E^(2*a) - (2*b^3*x^3)/E^(2*a) + (3*b^2*(-1 + E^(2*a))*x^2*Log[1 - E^(-a - b*x)])/E^(2*a) + (3*b^2*(-1 + E^(2*a))*x^2*Log[1 + E^(-a - b*x)])/E^(2*a) + 3*(1 - E^(-2*a))*(b*x - Log[1 - E^(a + b*x)]) + 3*(1 - E^(-2*a))*(b*x - Log[1 + E^(a + b*x)]) - 6*(1 - E^(-2*a))*(b*x*PolyLog[2, -E^(-a - b*x)] + PolyLog[3, -E^(-a - b*x)]) - 6*(1 - E^(-2*a))*(b*x*PolyLog[2, E^(-a - b*x)] + PolyLog[3, E^(-a - b*x)])))/(b^3*(-1 + E^(2*a))) + (2*b^2*x^2*((2*b*x)/(1 + E^(2*a)) + 3*Log[1 + E^(-2*(a + b*x))]) - 6*b*x*PolyLog[2, -E^(-2*(a + b*x))] - 3*PolyLog[3, -E^(-2*(a + b*x))])/b^3 - 2*x^3*Csch[a]*Sech[a] + (6*x*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b^2)/6","B",1
510,1,137,95,0.6796737,"\int x \text{csch}^3(a+b x) \text{sech}(a+b x) \, dx","Integrate[x*Csch[a + b*x]^3*Sech[a + b*x],x]","-\frac{\text{Li}_2\left(-e^{-2 (a+b x)}\right)-\text{Li}_2\left(e^{-2 (a+b x)}\right)+2 a \log \left(1-e^{-2 (a+b x)}\right)+2 b x \log \left(1-e^{-2 (a+b x)}\right)-2 a \log \left(e^{-2 (a+b x)}+1\right)-2 b x \log \left(e^{-2 (a+b x)}+1\right)+\coth (a+b x)+b x \text{csch}^2(a+b x)-2 a \log (\sinh (a+b x))+2 a \log (\cosh (a+b x))}{2 b^2}","\frac{\text{Li}_2\left(-e^{2 a+2 b x}\right)}{2 b^2}-\frac{\text{Li}_2\left(e^{2 a+2 b x}\right)}{2 b^2}-\frac{\coth (a+b x)}{2 b^2}+\frac{2 x \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}-\frac{x \coth ^2(a+b x)}{2 b}+\frac{x}{2 b}",1,"-1/2*(Coth[a + b*x] + b*x*Csch[a + b*x]^2 + 2*a*Log[1 - E^(-2*(a + b*x))] + 2*b*x*Log[1 - E^(-2*(a + b*x))] - 2*a*Log[1 + E^(-2*(a + b*x))] - 2*b*x*Log[1 + E^(-2*(a + b*x))] + 2*a*Log[Cosh[a + b*x]] - 2*a*Log[Sinh[a + b*x]] + PolyLog[2, -E^(-2*(a + b*x))] - PolyLog[2, E^(-2*(a + b*x))])/b^2","A",1
511,1,34,28,0.0476072,"\int \text{csch}^3(a+b x) \text{sech}(a+b x) \, dx","Integrate[Csch[a + b*x]^3*Sech[a + b*x],x]","-\frac{\text{csch}^2(a+b x)+2 \log (\sinh (a+b x))-2 \log (\cosh (a+b x))}{2 b}","-\frac{\coth ^2(a+b x)}{2 b}-\frac{\log (\tanh (a+b x))}{b}",1,"-1/2*(Csch[a + b*x]^2 - 2*Log[Cosh[a + b*x]] + 2*Log[Sinh[a + b*x]])/b","A",1
512,0,0,21,57.3075361,"\int \frac{\text{csch}^3(a+b x) \text{sech}(a+b x)}{x} \, dx","Integrate[(Csch[a + b*x]^3*Sech[a + b*x])/x,x]","\int \frac{\text{csch}^3(a+b x) \text{sech}(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{csch}^3(a+b x) \text{sech}(a+b x)}{x},x\right)",0,"Integrate[(Csch[a + b*x]^3*Sech[a + b*x])/x, x]","A",-1
513,0,0,21,27.6218302,"\int \frac{\text{csch}^3(a+b x) \text{sech}(a+b x)}{x^2} \, dx","Integrate[(Csch[a + b*x]^3*Sech[a + b*x])/x^2,x]","\int \frac{\text{csch}^3(a+b x) \text{sech}(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{csch}^3(a+b x) \text{sech}(a+b x)}{x^2},x\right)",0,"Integrate[(Csch[a + b*x]^3*Sech[a + b*x])/x^2, x]","A",-1
514,0,0,23,69.1617068,"\int x^m \text{csch}^3(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x^m*Csch[a + b*x]^3*Sech[a + b*x]^2,x]","\int x^m \text{csch}^3(a+b x) \text{sech}^2(a+b x) \, dx","\text{Int}\left(x^m \text{csch}^3(a+b x) \text{sech}^2(a+b x),x\right)",0,"Integrate[x^m*Csch[a + b*x]^3*Sech[a + b*x]^2, x]","A",-1
515,1,433,317,8.4249408,"\int x^3 \text{csch}^3(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x^3*Csch[a + b*x]^3*Sech[a + b*x]^2,x]","-\frac{3 x^2 \text{csch}(a)}{2 b^2}+\frac{3 x^2 \text{csch}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{csch}\left(\frac{a}{2}+\frac{b x}{2}\right)}{4 b^2}+\frac{3 x^2 \text{sech}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{sech}\left(\frac{a}{2}+\frac{b x}{2}\right)}{4 b^2}+\frac{3 i \left(b^2 x^2 \log \left(1-i e^{a+b x}\right)-b^2 x^2 \log \left(1+i e^{a+b x}\right)-2 b x \text{Li}_2\left(-i e^{a+b x}\right)+2 b x \text{Li}_2\left(i e^{a+b x}\right)+2 \text{Li}_3\left(-i e^{a+b x}\right)-2 \text{Li}_3\left(i e^{a+b x}\right)\right)}{b^4}-\frac{3 \left(b^3 x^3 \log \left(1-e^{a+b x}\right)-b^3 x^3 \log \left(e^{a+b x}+1\right)+\left(2-3 b^2 x^2\right) \text{Li}_2\left(-e^{a+b x}\right)+\left(3 b^2 x^2-2\right) \text{Li}_2\left(e^{a+b x}\right)+6 b x \text{Li}_3\left(-e^{a+b x}\right)-6 b x \text{Li}_3\left(e^{a+b x}\right)-6 \text{Li}_4\left(-e^{a+b x}\right)+6 \text{Li}_4\left(e^{a+b x}\right)-2 b x \log \left(1-e^{a+b x}\right)+2 b x \log \left(e^{a+b x}+1\right)\right)}{2 b^4}-\frac{x^3 \text{csch}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}-\frac{x^3 \text{sech}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}-\frac{x^3 \text{sech}(a+b x)}{b}","-\frac{3 \text{Li}_2\left(-e^{a+b x}\right)}{b^4}+\frac{3 \text{Li}_2\left(e^{a+b x}\right)}{b^4}+\frac{6 i \text{Li}_3\left(-i e^{a+b x}\right)}{b^4}-\frac{6 i \text{Li}_3\left(i e^{a+b x}\right)}{b^4}+\frac{9 \text{Li}_4\left(-e^{a+b x}\right)}{b^4}-\frac{9 \text{Li}_4\left(e^{a+b x}\right)}{b^4}-\frac{6 i x \text{Li}_2\left(-i e^{a+b x}\right)}{b^3}+\frac{6 i x \text{Li}_2\left(i e^{a+b x}\right)}{b^3}-\frac{9 x \text{Li}_3\left(-e^{a+b x}\right)}{b^3}+\frac{9 x \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{6 x \tanh ^{-1}\left(e^{a+b x}\right)}{b^3}+\frac{9 x^2 \text{Li}_2\left(-e^{a+b x}\right)}{2 b^2}-\frac{9 x^2 \text{Li}_2\left(e^{a+b x}\right)}{2 b^2}+\frac{6 x^2 \tan ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{3 x^2 \text{csch}(a+b x)}{2 b^2}+\frac{3 x^3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{3 x^3 \text{sech}(a+b x)}{2 b}-\frac{x^3 \text{csch}^2(a+b x) \text{sech}(a+b x)}{2 b}",1,"(-3*x^2*Csch[a])/(2*b^2) - (x^3*Csch[a/2 + (b*x)/2]^2)/(8*b) + ((3*I)*(b^2*x^2*Log[1 - I*E^(a + b*x)] - b^2*x^2*Log[1 + I*E^(a + b*x)] - 2*b*x*PolyLog[2, (-I)*E^(a + b*x)] + 2*b*x*PolyLog[2, I*E^(a + b*x)] + 2*PolyLog[3, (-I)*E^(a + b*x)] - 2*PolyLog[3, I*E^(a + b*x)]))/b^4 - (3*(-2*b*x*Log[1 - E^(a + b*x)] + b^3*x^3*Log[1 - E^(a + b*x)] + 2*b*x*Log[1 + E^(a + b*x)] - b^3*x^3*Log[1 + E^(a + b*x)] + (2 - 3*b^2*x^2)*PolyLog[2, -E^(a + b*x)] + (-2 + 3*b^2*x^2)*PolyLog[2, E^(a + b*x)] + 6*b*x*PolyLog[3, -E^(a + b*x)] - 6*b*x*PolyLog[3, E^(a + b*x)] - 6*PolyLog[4, -E^(a + b*x)] + 6*PolyLog[4, E^(a + b*x)]))/(2*b^4) - (x^3*Sech[a/2 + (b*x)/2]^2)/(8*b) - (x^3*Sech[a + b*x])/b + (3*x^2*Csch[a/2]*Csch[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(4*b^2) + (3*x^2*Sech[a/2]*Sech[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(4*b^2)","A",1
516,1,441,197,8.067369,"\int x^2 \text{csch}^3(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x^2*Csch[a + b*x]^3*Sech[a + b*x]^2,x]","\frac{2 \left(-i \left(\text{Li}_2\left(-e^{i \left(-i a-i b x+\frac{\pi }{2}\right)}\right)-\text{Li}_2\left(e^{i \left(-i a-i b x+\frac{\pi }{2}\right)}\right)\right)-\left(\left(-i a-i b x+\frac{\pi }{2}\right) \left(\log \left(1-e^{i \left(-i a-i b x+\frac{\pi }{2}\right)}\right)-\log \left(1+e^{i \left(-i a-i b x+\frac{\pi }{2}\right)}\right)\right)\right)+\left(\frac{\pi }{2}-i a\right) \log \left(\tan \left(\frac{1}{2} \left(-i a-i b x+\frac{\pi }{2}\right)\right)\right)\right)}{b^3}-\frac{x \text{csch}(a)}{b^2}+\frac{x \text{csch}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{csch}\left(\frac{a}{2}+\frac{b x}{2}\right)}{2 b^2}+\frac{x \text{sech}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{sech}\left(\frac{a}{2}+\frac{b x}{2}\right)}{2 b^2}+\frac{-3 b^2 x^2 \log \left(1-e^{a+b x}\right)+3 b^2 x^2 \log \left(e^{a+b x}+1\right)+6 b x \text{Li}_2\left(-e^{a+b x}\right)-6 b x \text{Li}_2\left(e^{a+b x}\right)-6 \text{Li}_3\left(-e^{a+b x}\right)+6 \text{Li}_3\left(e^{a+b x}\right)+2 \log \left(1-e^{a+b x}\right)-2 \log \left(e^{a+b x}+1\right)}{2 b^3}-\frac{x^2 \text{csch}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}-\frac{x^2 \text{sech}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}-\frac{x^2 \text{sech}(a+b x)}{b}","-\frac{2 i \text{Li}_2\left(-i e^{a+b x}\right)}{b^3}+\frac{2 i \text{Li}_2\left(i e^{a+b x}\right)}{b^3}-\frac{3 \text{Li}_3\left(-e^{a+b x}\right)}{b^3}+\frac{3 \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{\tanh ^{-1}(\cosh (a+b x))}{b^3}+\frac{3 x \text{Li}_2\left(-e^{a+b x}\right)}{b^2}-\frac{3 x \text{Li}_2\left(e^{a+b x}\right)}{b^2}+\frac{4 x \tan ^{-1}\left(e^{a+b x}\right)}{b^2}-\frac{x \text{csch}(a+b x)}{b^2}+\frac{3 x^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{3 x^2 \text{sech}(a+b x)}{2 b}-\frac{x^2 \text{csch}^2(a+b x) \text{sech}(a+b x)}{2 b}",1,"-((x*Csch[a])/b^2) - (x^2*Csch[a/2 + (b*x)/2]^2)/(8*b) + (2*(-(((-I)*a + Pi/2 - I*b*x)*(Log[1 - E^(I*((-I)*a + Pi/2 - I*b*x))] - Log[1 + E^(I*((-I)*a + Pi/2 - I*b*x))])) + ((-I)*a + Pi/2)*Log[Tan[((-I)*a + Pi/2 - I*b*x)/2]] - I*(PolyLog[2, -E^(I*((-I)*a + Pi/2 - I*b*x))] - PolyLog[2, E^(I*((-I)*a + Pi/2 - I*b*x))])))/b^3 + (2*Log[1 - E^(a + b*x)] - 3*b^2*x^2*Log[1 - E^(a + b*x)] - 2*Log[1 + E^(a + b*x)] + 3*b^2*x^2*Log[1 + E^(a + b*x)] + 6*b*x*PolyLog[2, -E^(a + b*x)] - 6*b*x*PolyLog[2, E^(a + b*x)] - 6*PolyLog[3, -E^(a + b*x)] + 6*PolyLog[3, E^(a + b*x)])/(2*b^3) - (x^2*Sech[a/2 + (b*x)/2]^2)/(8*b) - (x^2*Sech[a + b*x])/b + (x*Csch[a/2]*Csch[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(2*b^2) + (x*Sech[a/2]*Sech[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(2*b^2)","B",1
517,1,168,109,2.9946693,"\int x \text{csch}^3(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[x*Csch[a + b*x]^3*Sech[a + b*x]^2,x]","-\frac{12 \left(\text{Li}_2\left(-e^{-a-b x}\right)-\text{Li}_2\left(e^{-a-b x}\right)\right)+12 (a+b x) \left(\log \left(1-e^{-a-b x}\right)-\log \left(e^{-a-b x}+1\right)\right)-2 \tanh \left(\frac{1}{2} (a+b x)\right)+2 \coth \left(\frac{1}{2} (a+b x)\right)+b x \text{csch}^2\left(\frac{1}{2} (a+b x)\right)+b x \text{sech}^2\left(\frac{1}{2} (a+b x)\right)+8 b x \text{sech}(a+b x)-12 a \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)-16 \tan ^{-1}\left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{8 b^2}","\frac{3 \text{Li}_2\left(-e^{a+b x}\right)}{2 b^2}-\frac{3 \text{Li}_2\left(e^{a+b x}\right)}{2 b^2}-\frac{\text{csch}(a+b x)}{2 b^2}+\frac{\tan ^{-1}(\sinh (a+b x))}{b^2}+\frac{3 x \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{3 x \text{sech}(a+b x)}{2 b}-\frac{x \text{csch}^2(a+b x) \text{sech}(a+b x)}{2 b}",1,"-1/8*(-16*ArcTan[Tanh[(a + b*x)/2]] + 2*Coth[(a + b*x)/2] + b*x*Csch[(a + b*x)/2]^2 + 12*(a + b*x)*(Log[1 - E^(-a - b*x)] - Log[1 + E^(-a - b*x)]) - 12*a*Log[Tanh[(a + b*x)/2]] + 12*(PolyLog[2, -E^(-a - b*x)] - PolyLog[2, E^(-a - b*x)]) + b*x*Sech[(a + b*x)/2]^2 + 8*b*x*Sech[a + b*x] - 2*Tanh[(a + b*x)/2])/b^2","A",1
518,1,68,49,0.0367167,"\int \text{csch}^3(a+b x) \text{sech}^2(a+b x) \, dx","Integrate[Csch[a + b*x]^3*Sech[a + b*x]^2,x]","-\frac{\text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{\text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{\text{sech}(a+b x)}{b}-\frac{3 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b}","-\frac{3 \text{sech}(a+b x)}{2 b}+\frac{3 \tanh ^{-1}(\cosh (a+b x))}{2 b}-\frac{\text{csch}^2(a+b x) \text{sech}(a+b x)}{2 b}",1,"-1/8*Csch[(a + b*x)/2]^2/b - (3*Log[Tanh[(a + b*x)/2]])/(2*b) - Sech[(a + b*x)/2]^2/(8*b) - Sech[a + b*x]/b","A",1
519,0,0,23,67.5512764,"\int \frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{x} \, dx","Integrate[(Csch[a + b*x]^3*Sech[a + b*x]^2)/x,x]","\int \frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{x},x\right)",0,"Integrate[(Csch[a + b*x]^3*Sech[a + b*x]^2)/x, x]","A",-1
520,0,0,23,46.1221014,"\int \frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{x^2} \, dx","Integrate[(Csch[a + b*x]^3*Sech[a + b*x]^2)/x^2,x]","\int \frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{csch}^3(a+b x) \text{sech}^2(a+b x)}{x^2},x\right)",0,"Integrate[(Csch[a + b*x]^3*Sech[a + b*x]^2)/x^2, x]","A",-1
521,-1,0,23,180.0012467,"\int x^m \text{csch}^3(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[x^m*Csch[a + b*x]^3*Sech[a + b*x]^3,x]","\text{\$Aborted}","\text{Int}\left(x^m \text{csch}^3(a+b x) \text{sech}^3(a+b x),x\right)",0,"$Aborted","F",-1
522,1,274,240,7.4157257,"\int x^3 \text{csch}^3(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[x^3*Csch[a + b*x]^3*Sech[a + b*x]^3,x]","\frac{-4 b^3 x^3 \log \left(1-e^{2 (a+b x)}\right)+4 b^3 x^3 \log \left(e^{2 (a+b x)}+1\right)-b^3 x^3 \text{csch}^2(a+b x)-b^3 x^3 \text{sech}^2(a+b x)+\left(6 b^2 x^2-3\right) \text{Li}_2\left(-e^{2 (a+b x)}\right)+\left(3-6 b^2 x^2\right) \text{Li}_2\left(e^{2 (a+b x)}\right)+3 b^2 x^2 \text{csch}(a) \sinh (b x) \text{csch}(a+b x)-3 b^2 x^2 \text{csch}(a) \text{sech}(a)+3 b^2 x^2 \text{sech}(a) \sinh (b x) \text{sech}(a+b x)-6 b x \text{Li}_3\left(-e^{2 (a+b x)}\right)+6 b x \text{Li}_3\left(e^{2 (a+b x)}\right)+3 \text{Li}_4\left(-e^{2 (a+b x)}\right)-3 \text{Li}_4\left(e^{2 (a+b x)}\right)+6 b x \log \left(1-e^{2 (a+b x)}\right)-6 b x \log \left(e^{2 (a+b x)}+1\right)}{2 b^4}","-\frac{3 \text{Li}_2\left(-e^{2 a+2 b x}\right)}{2 b^4}+\frac{3 \text{Li}_2\left(e^{2 a+2 b x}\right)}{2 b^4}+\frac{3 \text{Li}_4\left(-e^{2 a+2 b x}\right)}{2 b^4}-\frac{3 \text{Li}_4\left(e^{2 a+2 b x}\right)}{2 b^4}-\frac{3 x \text{Li}_3\left(-e^{2 a+2 b x}\right)}{b^3}+\frac{3 x \text{Li}_3\left(e^{2 a+2 b x}\right)}{b^3}-\frac{6 x \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b^3}+\frac{3 x^2 \text{Li}_2\left(-e^{2 a+2 b x}\right)}{b^2}-\frac{3 x^2 \text{Li}_2\left(e^{2 a+2 b x}\right)}{b^2}-\frac{3 x^2 \text{csch}(2 a+2 b x)}{b^2}+\frac{4 x^3 \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}-\frac{2 x^3 \coth (2 a+2 b x) \text{csch}(2 a+2 b x)}{b}",1,"(-(b^3*x^3*Csch[a + b*x]^2) + 6*b*x*Log[1 - E^(2*(a + b*x))] - 4*b^3*x^3*Log[1 - E^(2*(a + b*x))] - 6*b*x*Log[1 + E^(2*(a + b*x))] + 4*b^3*x^3*Log[1 + E^(2*(a + b*x))] + (-3 + 6*b^2*x^2)*PolyLog[2, -E^(2*(a + b*x))] + (3 - 6*b^2*x^2)*PolyLog[2, E^(2*(a + b*x))] - 6*b*x*PolyLog[3, -E^(2*(a + b*x))] + 6*b*x*PolyLog[3, E^(2*(a + b*x))] + 3*PolyLog[4, -E^(2*(a + b*x))] - 3*PolyLog[4, E^(2*(a + b*x))] - 3*b^2*x^2*Csch[a]*Sech[a] - b^3*x^3*Sech[a + b*x]^2 + 3*b^2*x^2*Csch[a]*Csch[a + b*x]*Sinh[b*x] + 3*b^2*x^2*Sech[a]*Sech[a + b*x]*Sinh[b*x])/(2*b^4)","A",1
523,1,192,149,6.3646202,"\int x^2 \text{csch}^3(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[x^2*Csch[a + b*x]^3*Sech[a + b*x]^3,x]","-\frac{4 b^2 x^2 \log \left(1-e^{2 (a+b x)}\right)-4 b^2 x^2 \log \left(e^{2 (a+b x)}+1\right)+b^2 x^2 \text{csch}^2(a+b x)+b^2 x^2 \text{sech}^2(a+b x)-4 b x \text{Li}_2\left(-e^{2 (a+b x)}\right)+4 b x \text{Li}_2\left(e^{2 (a+b x)}\right)+2 \text{Li}_3\left(-e^{2 (a+b x)}\right)-2 \text{Li}_3\left(e^{2 (a+b x)}\right)+4 \tanh ^{-1}\left(e^{2 (a+b x)}\right)-2 b x \text{csch}(a) \sinh (b x) \text{csch}(a+b x)+2 b x \text{csch}(a) \text{sech}(a)-2 b x \text{sech}(a) \sinh (b x) \text{sech}(a+b x)}{2 b^3}","-\frac{\text{Li}_3\left(-e^{2 a+2 b x}\right)}{b^3}+\frac{\text{Li}_3\left(e^{2 a+2 b x}\right)}{b^3}-\frac{\tanh ^{-1}(\cosh (2 a+2 b x))}{b^3}+\frac{2 x \text{Li}_2\left(-e^{2 a+2 b x}\right)}{b^2}-\frac{2 x \text{Li}_2\left(e^{2 a+2 b x}\right)}{b^2}-\frac{2 x \text{csch}(2 a+2 b x)}{b^2}+\frac{4 x^2 \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}-\frac{2 x^2 \coth (2 a+2 b x) \text{csch}(2 a+2 b x)}{b}",1,"-1/2*(4*ArcTanh[E^(2*(a + b*x))] + b^2*x^2*Csch[a + b*x]^2 + 4*b^2*x^2*Log[1 - E^(2*(a + b*x))] - 4*b^2*x^2*Log[1 + E^(2*(a + b*x))] - 4*b*x*PolyLog[2, -E^(2*(a + b*x))] + 4*b*x*PolyLog[2, E^(2*(a + b*x))] + 2*PolyLog[3, -E^(2*(a + b*x))] - 2*PolyLog[3, E^(2*(a + b*x))] + 2*b*x*Csch[a]*Sech[a] + b^2*x^2*Sech[a + b*x]^2 - 2*b*x*Csch[a]*Csch[a + b*x]*Sinh[b*x] - 2*b*x*Sech[a]*Sech[a + b*x]*Sinh[b*x])/b^3","A",1
524,1,148,91,1.3609547,"\int x \text{csch}^3(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[x*Csch[a + b*x]^3*Sech[a + b*x]^3,x]","-\frac{2 \text{Li}_2\left(-e^{-2 (a+b x)}\right)-2 \text{Li}_2\left(e^{-2 (a+b x)}\right)+4 a \log \left(1-e^{-2 (a+b x)}\right)+4 b x \log \left(1-e^{-2 (a+b x)}\right)-4 a \log \left(e^{-2 (a+b x)}+1\right)-4 b x \log \left(e^{-2 (a+b x)}+1\right)-\tanh (a+b x)+\coth (a+b x)+b x \text{csch}^2(a+b x)+b x \text{sech}^2(a+b x)-4 a \log (\tanh (a+b x))}{2 b^2}","\frac{\text{Li}_2\left(-e^{2 a+2 b x}\right)}{b^2}-\frac{\text{Li}_2\left(e^{2 a+2 b x}\right)}{b^2}-\frac{\text{csch}(2 a+2 b x)}{b^2}+\frac{4 x \tanh ^{-1}\left(e^{2 a+2 b x}\right)}{b}-\frac{2 x \coth (2 a+2 b x) \text{csch}(2 a+2 b x)}{b}",1,"-1/2*(Coth[a + b*x] + b*x*Csch[a + b*x]^2 + 4*a*Log[1 - E^(-2*(a + b*x))] + 4*b*x*Log[1 - E^(-2*(a + b*x))] - 4*a*Log[1 + E^(-2*(a + b*x))] - 4*b*x*Log[1 + E^(-2*(a + b*x))] - 4*a*Log[Tanh[a + b*x]] + 2*PolyLog[2, -E^(-2*(a + b*x))] - 2*PolyLog[2, E^(-2*(a + b*x))] + b*x*Sech[a + b*x]^2 - Tanh[a + b*x])/b^2","A",1
525,1,47,43,0.0116903,"\int \text{csch}^3(a+b x) \text{sech}^3(a+b x) \, dx","Integrate[Csch[a + b*x]^3*Sech[a + b*x]^3,x]","8 \left(-\frac{\text{csch}^2(a+b x)}{16 b}-\frac{\text{sech}^2(a+b x)}{16 b}-\frac{\log (\tanh (a+b x))}{4 b}\right)","\frac{\tanh ^2(a+b x)}{2 b}-\frac{\coth ^2(a+b x)}{2 b}-\frac{2 \log (\tanh (a+b x))}{b}",1,"8*(-1/16*Csch[a + b*x]^2/b - Log[Tanh[a + b*x]]/(4*b) - Sech[a + b*x]^2/(16*b))","A",1
526,0,0,20,60.7329054,"\int \frac{\text{csch}^3(a+b x) \text{sech}^3(a+b x)}{x} \, dx","Integrate[(Csch[a + b*x]^3*Sech[a + b*x]^3)/x,x]","\int \frac{\text{csch}^3(a+b x) \text{sech}^3(a+b x)}{x} \, dx","8 \text{Int}\left(\frac{\text{csch}^3(2 a+2 b x)}{x},x\right)",0,"Integrate[(Csch[a + b*x]^3*Sech[a + b*x]^3)/x, x]","A",-1
527,0,0,20,43.442535,"\int \frac{\text{csch}^3(a+b x) \text{sech}^3(a+b x)}{x^2} \, dx","Integrate[(Csch[a + b*x]^3*Sech[a + b*x]^3)/x^2,x]","\int \frac{\text{csch}^3(a+b x) \text{sech}^3(a+b x)}{x^2} \, dx","8 \text{Int}\left(\frac{\text{csch}^3(2 a+2 b x)}{x^2},x\right)",0,"Integrate[(Csch[a + b*x]^3*Sech[a + b*x]^3)/x^2, x]","A",-1
528,1,77,87,0.357606,"\int x \cosh ^{\frac{5}{2}}(a+b x) \sinh (a+b x) \, dx","Integrate[x*Cosh[a + b*x]^(5/2)*Sinh[a + b*x],x]","\frac{\sqrt{\cosh (a+b x)} (-46 \sinh (a+b x)-6 \sinh (3 (a+b x))+63 b x \cosh (a+b x)+21 b x \cosh (3 (a+b x)))+40 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{294 b^2}","\frac{20 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{147 b^2}-\frac{4 \sinh (a+b x) \cosh ^{\frac{5}{2}}(a+b x)}{49 b^2}-\frac{20 \sinh (a+b x) \sqrt{\cosh (a+b x)}}{147 b^2}+\frac{2 x \cosh ^{\frac{7}{2}}(a+b x)}{7 b}",1,"((40*I)*EllipticF[(I/2)*(a + b*x), 2] + Sqrt[Cosh[a + b*x]]*(63*b*x*Cosh[a + b*x] + 21*b*x*Cosh[3*(a + b*x)] - 46*Sinh[a + b*x] - 6*Sinh[3*(a + b*x)]))/(294*b^2)","A",1
529,1,142,64,2.0149955,"\int x \cosh ^{\frac{3}{2}}(a+b x) \sinh (a+b x) \, dx","Integrate[x*Cosh[a + b*x]^(3/2)*Sinh[a + b*x],x]","\frac{e^{-3 (a+b x)} \left(48 e^{2 (a+b x)} \sqrt{e^{2 (a+b x)}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-e^{2 (a+b x)}\right)+\left(e^{2 (a+b x)}+1\right) \left(2 (5 b x-12) e^{2 (a+b x)}+(5 b x-2) e^{4 (a+b x)}+5 b x+2\right)\right)}{50 \sqrt{2} b^2 \sqrt{e^{-a-b x}+e^{a+b x}}}","\frac{12 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{25 b^2}-\frac{4 \sinh (a+b x) \cosh ^{\frac{3}{2}}(a+b x)}{25 b^2}+\frac{2 x \cosh ^{\frac{5}{2}}(a+b x)}{5 b}",1,"((1 + E^(2*(a + b*x)))*(2 + 5*b*x + 2*E^(2*(a + b*x))*(-12 + 5*b*x) + E^(4*(a + b*x))*(-2 + 5*b*x)) + 48*E^(2*(a + b*x))*Sqrt[1 + E^(2*(a + b*x))]*Hypergeometric2F1[-1/4, 1/2, 3/4, -E^(2*(a + b*x))])/(50*Sqrt[2]*b^2*E^(3*(a + b*x))*Sqrt[E^(-a - b*x) + E^(a + b*x)])","C",1
530,1,56,64,0.1648443,"\int x \sqrt{\cosh (a+b x)} \sinh (a+b x) \, dx","Integrate[x*Sqrt[Cosh[a + b*x]]*Sinh[a + b*x],x]","\frac{2 \sqrt{\cosh (a+b x)} (3 b x \cosh (a+b x)-2 \sinh (a+b x))+4 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{9 b^2}","\frac{4 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{9 b^2}-\frac{4 \sinh (a+b x) \sqrt{\cosh (a+b x)}}{9 b^2}+\frac{2 x \cosh ^{\frac{3}{2}}(a+b x)}{3 b}",1,"((4*I)*EllipticF[(I/2)*(a + b*x), 2] + 2*Sqrt[Cosh[a + b*x]]*(3*b*x*Cosh[a + b*x] - 2*Sinh[a + b*x]))/(9*b^2)","A",1
531,1,190,37,1.5542535,"\int \frac{x \sinh (a+b x)}{\sqrt{\cosh (a+b x)}} \, dx","Integrate[(x*Sinh[a + b*x])/Sqrt[Cosh[a + b*x]],x]","\frac{\sqrt{2} e^{-a-b x} \sqrt{e^{2 (a+b x)}+1} \left(18 \, _3F_2\left(-\frac{1}{4},-\frac{1}{4},\frac{1}{2};\frac{3}{4},\frac{3}{4};-e^{2 (a+b x)}\right)-2 e^{2 (a+b x)} \, _3F_2\left(\frac{1}{2},\frac{3}{4},\frac{3}{4};\frac{7}{4},\frac{7}{4};-e^{2 (a+b x)}\right)+3 b x \left(3 \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-e^{2 (a+b x)}\right)+e^{2 (a+b x)} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-e^{2 (a+b x)}\right)\right)\right)}{9 b^2 \sqrt{e^{-a-b x}+e^{a+b x}}}","\frac{2 x \sqrt{\cosh (a+b x)}}{b}+\frac{4 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b^2}",1,"(Sqrt[2]*E^(-a - b*x)*Sqrt[1 + E^(2*(a + b*x))]*(3*b*x*(3*Hypergeometric2F1[-1/4, 1/2, 3/4, -E^(2*(a + b*x))] + E^(2*(a + b*x))*Hypergeometric2F1[1/2, 3/4, 7/4, -E^(2*(a + b*x))]) + 18*HypergeometricPFQ[{-1/4, -1/4, 1/2}, {3/4, 3/4}, -E^(2*(a + b*x))] - 2*E^(2*(a + b*x))*HypergeometricPFQ[{1/2, 3/4, 3/4}, {7/4, 7/4}, -E^(2*(a + b*x))]))/(9*b^2*Sqrt[E^(-a - b*x) + E^(a + b*x)])","C",0
532,1,37,37,0.1762288,"\int \frac{x \sinh (a+b x)}{\cosh ^{\frac{3}{2}}(a+b x)} \, dx","Integrate[(x*Sinh[a + b*x])/Cosh[a + b*x]^(3/2),x]","-\frac{2 x}{b \sqrt{\cosh (a+b x)}}-\frac{4 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b^2}","-\frac{2 x}{b \sqrt{\cosh (a+b x)}}-\frac{4 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b^2}",1,"(-2*x)/(b*Sqrt[Cosh[a + b*x]]) - ((4*I)*EllipticF[(I/2)*(a + b*x), 2])/b^2","A",1
533,1,57,64,0.196377,"\int \frac{x \sinh (a+b x)}{\cosh ^{\frac{5}{2}}(a+b x)} \, dx","Integrate[(x*Sinh[a + b*x])/Cosh[a + b*x]^(5/2),x]","\frac{2 \left(\sinh (2 (a+b x))+2 i \cosh ^{\frac{3}{2}}(a+b x) E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)-b x\right)}{3 b^2 \cosh ^{\frac{3}{2}}(a+b x)}","\frac{4 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{3 b^2}+\frac{4 \sinh (a+b x)}{3 b^2 \sqrt{\cosh (a+b x)}}-\frac{2 x}{3 b \cosh ^{\frac{3}{2}}(a+b x)}",1,"(2*(-(b*x) + (2*I)*Cosh[a + b*x]^(3/2)*EllipticE[(I/2)*(a + b*x), 2] + Sinh[2*(a + b*x)]))/(3*b^2*Cosh[a + b*x]^(3/2))","A",1
534,1,57,64,0.2471545,"\int \frac{x \sinh (a+b x)}{\cosh ^{\frac{7}{2}}(a+b x)} \, dx","Integrate[(x*Sinh[a + b*x])/Cosh[a + b*x]^(7/2),x]","\frac{2 \left(\sinh (2 (a+b x))-2 i \cosh ^{\frac{5}{2}}(a+b x) F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)-3 b x\right)}{15 b^2 \cosh ^{\frac{5}{2}}(a+b x)}","-\frac{4 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{15 b^2}+\frac{4 \sinh (a+b x)}{15 b^2 \cosh ^{\frac{3}{2}}(a+b x)}-\frac{2 x}{5 b \cosh ^{\frac{5}{2}}(a+b x)}",1,"(2*(-3*b*x - (2*I)*Cosh[a + b*x]^(5/2)*EllipticF[(I/2)*(a + b*x), 2] + Sinh[2*(a + b*x)]))/(15*b^2*Cosh[a + b*x]^(5/2))","A",1
535,1,69,87,0.2822156,"\int \frac{x \sinh (a+b x)}{\cosh ^{\frac{9}{2}}(a+b x)} \, dx","Integrate[(x*Sinh[a + b*x])/Cosh[a + b*x]^(9/2),x]","\frac{10 \sinh (2 (a+b x))+3 \sinh (4 (a+b x))+24 i \cosh ^{\frac{7}{2}}(a+b x) E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)-20 b x}{70 b^2 \cosh ^{\frac{7}{2}}(a+b x)}","\frac{12 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{35 b^2}+\frac{4 \sinh (a+b x)}{35 b^2 \cosh ^{\frac{5}{2}}(a+b x)}+\frac{12 \sinh (a+b x)}{35 b^2 \sqrt{\cosh (a+b x)}}-\frac{2 x}{7 b \cosh ^{\frac{7}{2}}(a+b x)}",1,"(-20*b*x + (24*I)*Cosh[a + b*x]^(7/2)*EllipticE[(I/2)*(a + b*x), 2] + 10*Sinh[2*(a + b*x)] + 3*Sinh[4*(a + b*x)])/(70*b^2*Cosh[a + b*x]^(7/2))","A",1
536,1,69,107,0.3328647,"\int x \text{sech}^{\frac{9}{2}}(a+b x) \sinh (a+b x) \, dx","Integrate[x*Sech[a + b*x]^(9/2)*Sinh[a + b*x],x]","\frac{\text{sech}^{\frac{7}{2}}(a+b x) \left(10 \sinh (2 (a+b x))+3 \sinh (4 (a+b x))+24 i \cosh ^{\frac{7}{2}}(a+b x) E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)-20 b x\right)}{70 b^2}","\frac{4 \sinh (a+b x) \text{sech}^{\frac{5}{2}}(a+b x)}{35 b^2}+\frac{12 \sinh (a+b x) \sqrt{\text{sech}(a+b x)}}{35 b^2}+\frac{12 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{35 b^2}-\frac{2 x \text{sech}^{\frac{7}{2}}(a+b x)}{7 b}",1,"(Sech[a + b*x]^(7/2)*(-20*b*x + (24*I)*Cosh[a + b*x]^(7/2)*EllipticE[(I/2)*(a + b*x), 2] + 10*Sinh[2*(a + b*x)] + 3*Sinh[4*(a + b*x)]))/(70*b^2)","A",1
537,1,65,84,0.2513046,"\int x \text{sech}^{\frac{7}{2}}(a+b x) \sinh (a+b x) \, dx","Integrate[x*Sech[a + b*x]^(7/2)*Sinh[a + b*x],x]","-\frac{2 \sqrt{\text{sech}(a+b x)} \left(-2 \tanh (a+b x)+3 b x \text{sech}^2(a+b x)+2 i \sqrt{\cosh (a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)\right)}{15 b^2}","\frac{4 \sinh (a+b x) \text{sech}^{\frac{3}{2}}(a+b x)}{15 b^2}-\frac{4 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{15 b^2}-\frac{2 x \text{sech}^{\frac{5}{2}}(a+b x)}{5 b}",1,"(-2*Sqrt[Sech[a + b*x]]*((2*I)*Sqrt[Cosh[a + b*x]]*EllipticF[(I/2)*(a + b*x), 2] + 3*b*x*Sech[a + b*x]^2 - 2*Tanh[a + b*x]))/(15*b^2)","A",1
538,1,57,84,0.1958381,"\int x \text{sech}^{\frac{5}{2}}(a+b x) \sinh (a+b x) \, dx","Integrate[x*Sech[a + b*x]^(5/2)*Sinh[a + b*x],x]","\frac{2 \text{sech}^{\frac{3}{2}}(a+b x) \left(\sinh (2 (a+b x))+2 i \cosh ^{\frac{3}{2}}(a+b x) E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)-b x\right)}{3 b^2}","\frac{4 \sinh (a+b x) \sqrt{\text{sech}(a+b x)}}{3 b^2}+\frac{4 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{3 b^2}-\frac{2 x \text{sech}^{\frac{3}{2}}(a+b x)}{3 b}",1,"(2*Sech[a + b*x]^(3/2)*(-(b*x) + (2*I)*Cosh[a + b*x]^(3/2)*EllipticE[(I/2)*(a + b*x), 2] + Sinh[2*(a + b*x)]))/(3*b^2)","A",1
539,1,46,57,0.1431988,"\int x \text{sech}^{\frac{3}{2}}(a+b x) \sinh (a+b x) \, dx","Integrate[x*Sech[a + b*x]^(3/2)*Sinh[a + b*x],x]","-\frac{2 \sqrt{\text{sech}(a+b x)} \left(b x+2 i \sqrt{\cosh (a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)\right)}{b^2}","-\frac{2 x \sqrt{\text{sech}(a+b x)}}{b}-\frac{4 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b^2}",1,"(-2*(b*x + (2*I)*Sqrt[Cosh[a + b*x]]*EllipticF[(I/2)*(a + b*x), 2])*Sqrt[Sech[a + b*x]])/b^2","A",1
540,1,100,57,1.1470134,"\int x \sqrt{\text{sech}(a+b x)} \sinh (a+b x) \, dx","Integrate[x*Sqrt[Sech[a + b*x]]*Sinh[a + b*x],x]","\frac{\sqrt{2} e^{-a-b x} \sqrt{\frac{e^{a+b x}}{e^{2 (a+b x)}+1}} \left(4 \sqrt{e^{2 (a+b x)}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-e^{2 (a+b x)}\right)+(b x-2) \left(e^{2 (a+b x)}+1\right)\right)}{b^2}","\frac{2 x}{b \sqrt{\text{sech}(a+b x)}}+\frac{4 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b^2}",1,"(Sqrt[2]*E^(-a - b*x)*Sqrt[E^(a + b*x)/(1 + E^(2*(a + b*x)))]*((1 + E^(2*(a + b*x)))*(-2 + b*x) + 4*Sqrt[1 + E^(2*(a + b*x))]*Hypergeometric2F1[-1/4, 1/2, 3/4, -E^(2*(a + b*x))]))/b^2","C",1
541,1,71,84,0.177433,"\int \frac{x \sinh (a+b x)}{\sqrt{\text{sech}(a+b x)}} \, dx","Integrate[(x*Sinh[a + b*x])/Sqrt[Sech[a + b*x]],x]","\frac{\sqrt{\text{sech}(a+b x)} \left(-2 \sinh (2 (a+b x))+3 b x \cosh (2 (a+b x))+4 i \sqrt{\cosh (a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)+3 b x\right)}{9 b^2}","-\frac{4 \sinh (a+b x)}{9 b^2 \sqrt{\text{sech}(a+b x)}}+\frac{4 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{9 b^2}+\frac{2 x}{3 b \text{sech}^{\frac{3}{2}}(a+b x)}",1,"(Sqrt[Sech[a + b*x]]*(3*b*x + 3*b*x*Cosh[2*(a + b*x)] + (4*I)*Sqrt[Cosh[a + b*x]]*EllipticF[(I/2)*(a + b*x), 2] - 2*Sinh[2*(a + b*x)]))/(9*b^2)","A",1
542,1,125,84,2.4305097,"\int \frac{x \sinh (a+b x)}{\text{sech}^{\frac{3}{2}}(a+b x)} \, dx","Integrate[(x*Sinh[a + b*x])/Sech[a + b*x]^(3/2),x]","\frac{e^{-3 (a+b x)} \left(48 e^{2 (a+b x)} \sqrt{e^{2 (a+b x)}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-e^{2 (a+b x)}\right)+\left(e^{2 (a+b x)}+1\right) \left(2 (5 b x-12) e^{2 (a+b x)}+(5 b x-2) e^{4 (a+b x)}+5 b x+2\right)\right) \sqrt{\text{sech}(a+b x)}}{100 b^2}","-\frac{4 \sinh (a+b x)}{25 b^2 \text{sech}^{\frac{3}{2}}(a+b x)}+\frac{12 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{25 b^2}+\frac{2 x}{5 b \text{sech}^{\frac{5}{2}}(a+b x)}",1,"(((1 + E^(2*(a + b*x)))*(2 + 5*b*x + 2*E^(2*(a + b*x))*(-12 + 5*b*x) + E^(4*(a + b*x))*(-2 + 5*b*x)) + 48*E^(2*(a + b*x))*Sqrt[1 + E^(2*(a + b*x))]*Hypergeometric2F1[-1/4, 1/2, 3/4, -E^(2*(a + b*x))])*Sqrt[Sech[a + b*x]])/(100*b^2*E^(3*(a + b*x)))","C",1
543,1,93,107,0.2913499,"\int \frac{x \sinh (a+b x)}{\text{sech}^{\frac{5}{2}}(a+b x)} \, dx","Integrate[(x*Sinh[a + b*x])/Sech[a + b*x]^(5/2),x]","\frac{\sqrt{\text{sech}(a+b x)} \left(-52 \sinh (2 (a+b x))-6 \sinh (4 (a+b x))+84 b x \cosh (2 (a+b x))+21 b x \cosh (4 (a+b x))+80 i \sqrt{\cosh (a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)+63 b x\right)}{588 b^2}","-\frac{4 \sinh (a+b x)}{49 b^2 \text{sech}^{\frac{5}{2}}(a+b x)}-\frac{20 \sinh (a+b x)}{147 b^2 \sqrt{\text{sech}(a+b x)}}+\frac{20 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{147 b^2}+\frac{2 x}{7 b \text{sech}^{\frac{7}{2}}(a+b x)}",1,"(Sqrt[Sech[a + b*x]]*(63*b*x + 84*b*x*Cosh[2*(a + b*x)] + 21*b*x*Cosh[4*(a + b*x)] + (80*I)*Sqrt[Cosh[a + b*x]]*EllipticF[(I/2)*(a + b*x), 2] - 52*Sinh[2*(a + b*x)] - 6*Sinh[4*(a + b*x)]))/(588*b^2)","A",1
544,1,103,121,0.3180729,"\int x \cosh (a+b x) \sinh ^{\frac{5}{2}}(a+b x) \, dx","Integrate[x*Cosh[a + b*x]*Sinh[a + b*x]^(5/2),x]","\frac{52 \sinh (2 (a+b x))-6 \sinh (4 (a+b x))-84 b x \cosh (2 (a+b x))+21 b x \cosh (4 (a+b x))-80 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)+63 b x}{588 b^2 \sqrt{\sinh (a+b x)}}","-\frac{4 \sinh ^{\frac{5}{2}}(a+b x) \cosh (a+b x)}{49 b^2}+\frac{20 \sqrt{\sinh (a+b x)} \cosh (a+b x)}{147 b^2}+\frac{20 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{147 b^2 \sqrt{\sinh (a+b x)}}+\frac{2 x \sinh ^{\frac{7}{2}}(a+b x)}{7 b}",1,"(63*b*x - 84*b*x*Cosh[2*(a + b*x)] + 21*b*x*Cosh[4*(a + b*x)] - (80*I)*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]] + 52*Sinh[2*(a + b*x)] - 6*Sinh[4*(a + b*x)])/(588*b^2*Sqrt[Sinh[a + b*x]])","A",1
545,1,143,98,2.3574341,"\int x \cosh (a+b x) \sinh ^{\frac{3}{2}}(a+b x) \, dx","Integrate[x*Cosh[a + b*x]*Sinh[a + b*x]^(3/2),x]","\frac{e^{-3 (a+b x)} \left(48 e^{2 (a+b x)} \sqrt{1-e^{2 (a+b x)}} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};e^{2 (a+b x)}\right)+\left(e^{2 (a+b x)}-1\right) \left((24-10 b x) e^{2 (a+b x)}+(5 b x-2) e^{4 (a+b x)}+5 b x+2\right)\right)}{50 \sqrt{2} b^2 \sqrt{e^{a+b x}-e^{-a-b x}}}","-\frac{4 \sinh ^{\frac{3}{2}}(a+b x) \cosh (a+b x)}{25 b^2}-\frac{12 i \sqrt{\sinh (a+b x)} E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{25 b^2 \sqrt{i \sinh (a+b x)}}+\frac{2 x \sinh ^{\frac{5}{2}}(a+b x)}{5 b}",1,"((-1 + E^(2*(a + b*x)))*(2 + 5*b*x + E^(2*(a + b*x))*(24 - 10*b*x) + E^(4*(a + b*x))*(-2 + 5*b*x)) + 48*E^(2*(a + b*x))*Sqrt[1 - E^(2*(a + b*x))]*Hypergeometric2F1[-1/4, 1/2, 3/4, E^(2*(a + b*x))])/(50*Sqrt[2]*b^2*E^(3*(a + b*x))*Sqrt[-E^(-a - b*x) + E^(a + b*x)])","C",1
546,1,77,98,0.2058784,"\int x \cosh (a+b x) \sqrt{\sinh (a+b x)} \, dx","Integrate[x*Cosh[a + b*x]*Sqrt[Sinh[a + b*x]],x]","\frac{2 \left(3 b x \sinh ^2(a+b x)-\sinh (2 (a+b x))+2 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)\right)}{9 b^2 \sqrt{\sinh (a+b x)}}","-\frac{4 \sqrt{\sinh (a+b x)} \cosh (a+b x)}{9 b^2}-\frac{4 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{9 b^2 \sqrt{\sinh (a+b x)}}+\frac{2 x \sinh ^{\frac{3}{2}}(a+b x)}{3 b}",1,"(2*((2*I)*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]] + 3*b*x*Sinh[a + b*x]^2 - Sinh[2*(a + b*x)]))/(9*b^2*Sqrt[Sinh[a + b*x]])","A",1
547,1,182,71,1.7725277,"\int \frac{x \cosh (a+b x)}{\sqrt{\sinh (a+b x)}} \, dx","Integrate[(x*Cosh[a + b*x])/Sqrt[Sinh[a + b*x]],x]","\frac{e^{-a-b x} \sqrt{2-2 e^{2 (a+b x)}} \left(-18 \, _3F_2\left(-\frac{1}{4},-\frac{1}{4},\frac{1}{2};\frac{3}{4},\frac{3}{4};e^{2 (a+b x)}\right)-2 e^{2 (a+b x)} \, _3F_2\left(\frac{1}{2},\frac{3}{4},\frac{3}{4};\frac{7}{4},\frac{7}{4};e^{2 (a+b x)}\right)-3 b x \left(3 \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};e^{2 (a+b x)}\right)-e^{2 (a+b x)} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};e^{2 (a+b x)}\right)\right)\right)}{9 b^2 \sqrt{e^{a+b x}-e^{-a-b x}}}","\frac{2 x \sqrt{\sinh (a+b x)}}{b}+\frac{4 i \sqrt{\sinh (a+b x)} E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{b^2 \sqrt{i \sinh (a+b x)}}",1,"(E^(-a - b*x)*Sqrt[2 - 2*E^(2*(a + b*x))]*(-3*b*x*(3*Hypergeometric2F1[-1/4, 1/2, 3/4, E^(2*(a + b*x))] - E^(2*(a + b*x))*Hypergeometric2F1[1/2, 3/4, 7/4, E^(2*(a + b*x))]) - 18*HypergeometricPFQ[{-1/4, -1/4, 1/2}, {3/4, 3/4}, E^(2*(a + b*x))] - 2*E^(2*(a + b*x))*HypergeometricPFQ[{1/2, 3/4, 3/4}, {7/4, 7/4}, E^(2*(a + b*x))]))/(9*b^2*Sqrt[-E^(-a - b*x) + E^(a + b*x)])","C",0
548,1,56,71,0.1699024,"\int \frac{x \cosh (a+b x)}{\sinh ^{\frac{3}{2}}(a+b x)} \, dx","Integrate[(x*Cosh[a + b*x])/Sinh[a + b*x]^(3/2),x]","\frac{-2 b x+4 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)}{b^2 \sqrt{\sinh (a+b x)}}","-\frac{2 x}{b \sqrt{\sinh (a+b x)}}-\frac{4 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{b^2 \sqrt{\sinh (a+b x)}}",1,"(-2*b*x + (4*I)*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]])/(b^2*Sqrt[Sinh[a + b*x]])","A",1
549,1,66,98,0.2147131,"\int \frac{x \cosh (a+b x)}{\sinh ^{\frac{5}{2}}(a+b x)} \, dx","Integrate[(x*Cosh[a + b*x])/Sinh[a + b*x]^(5/2),x]","-\frac{2 \left(\sinh (2 (a+b x))+2 i (i \sinh (a+b x))^{3/2} E\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)+b x\right)}{3 b^2 \sinh ^{\frac{3}{2}}(a+b x)}","-\frac{4 \cosh (a+b x)}{3 b^2 \sqrt{\sinh (a+b x)}}-\frac{4 i \sqrt{\sinh (a+b x)} E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{3 b^2 \sqrt{i \sinh (a+b x)}}-\frac{2 x}{3 b \sinh ^{\frac{3}{2}}(a+b x)}",1,"(-2*(b*x + (2*I)*EllipticE[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*(I*Sinh[a + b*x])^(3/2) + Sinh[2*(a + b*x)]))/(3*b^2*Sinh[a + b*x]^(3/2))","A",1
550,1,67,98,0.2806835,"\int \frac{x \cosh (a+b x)}{\sinh ^{\frac{7}{2}}(a+b x)} \, dx","Integrate[(x*Cosh[a + b*x])/Sinh[a + b*x]^(7/2),x]","-\frac{2 \left(\sinh (2 (a+b x))-2 i (i \sinh (a+b x))^{5/2} F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)+3 b x\right)}{15 b^2 \sinh ^{\frac{5}{2}}(a+b x)}","-\frac{4 \cosh (a+b x)}{15 b^2 \sinh ^{\frac{3}{2}}(a+b x)}+\frac{4 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{15 b^2 \sqrt{\sinh (a+b x)}}-\frac{2 x}{5 b \sinh ^{\frac{5}{2}}(a+b x)}",1,"(-2*(3*b*x - (2*I)*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*(I*Sinh[a + b*x])^(5/2) + Sinh[2*(a + b*x)]))/(15*b^2*Sinh[a + b*x]^(5/2))","A",1
551,1,89,121,0.2770699,"\int \frac{x \cosh (a+b x)}{\sinh ^{\frac{9}{2}}(a+b x)} \, dx","Integrate[(x*Cosh[a + b*x])/Sinh[a + b*x]^(9/2),x]","-\frac{2 \left(\sinh (2 (a+b x))-6 \sinh ^3(a+b x) \cosh (a+b x)+6 \sqrt{i \sinh (a+b x)} \sinh ^3(a+b x) E\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)+5 b x\right)}{35 b^2 \sinh ^{\frac{7}{2}}(a+b x)}","-\frac{4 \cosh (a+b x)}{35 b^2 \sinh ^{\frac{5}{2}}(a+b x)}+\frac{12 \cosh (a+b x)}{35 b^2 \sqrt{\sinh (a+b x)}}+\frac{12 i \sqrt{\sinh (a+b x)} E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{35 b^2 \sqrt{i \sinh (a+b x)}}-\frac{2 x}{7 b \sinh ^{\frac{7}{2}}(a+b x)}",1,"(-2*(5*b*x - 6*Cosh[a + b*x]*Sinh[a + b*x]^3 + 6*EllipticE[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]]*Sinh[a + b*x]^3 + Sinh[2*(a + b*x)]))/(35*b^2*Sinh[a + b*x]^(7/2))","A",1
552,1,83,121,0.5269701,"\int x \cosh (a+b x) \text{csch}^{\frac{9}{2}}(a+b x) \, dx","Integrate[x*Cosh[a + b*x]*Csch[a + b*x]^(9/2),x]","-\frac{2 \sqrt{\text{csch}(a+b x)} \left(-6 \cosh (a+b x)+(\sinh (2 (a+b x))+5 b x) \text{csch}^3(a+b x)+6 \sqrt{i \sinh (a+b x)} E\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)\right)}{35 b^2}","-\frac{4 \cosh (a+b x) \text{csch}^{\frac{5}{2}}(a+b x)}{35 b^2}+\frac{12 \cosh (a+b x) \sqrt{\text{csch}(a+b x)}}{35 b^2}+\frac{12 i E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{35 b^2 \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)}}-\frac{2 x \text{csch}^{\frac{7}{2}}(a+b x)}{7 b}",1,"(-2*Sqrt[Csch[a + b*x]]*(-6*Cosh[a + b*x] + 6*EllipticE[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]] + Csch[a + b*x]^3*(5*b*x + Sinh[2*(a + b*x)])))/(35*b^2)","A",1
553,1,75,98,0.3037537,"\int x \cosh (a+b x) \text{csch}^{\frac{7}{2}}(a+b x) \, dx","Integrate[x*Cosh[a + b*x]*Csch[a + b*x]^(7/2),x]","-\frac{2 \sqrt{\text{csch}(a+b x)} \left(2 \coth (a+b x)+3 b x \text{csch}^2(a+b x)+2 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)\right)}{15 b^2}","-\frac{4 \cosh (a+b x) \text{csch}^{\frac{3}{2}}(a+b x)}{15 b^2}+\frac{4 i \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{15 b^2}-\frac{2 x \text{csch}^{\frac{5}{2}}(a+b x)}{5 b}",1,"(-2*Sqrt[Csch[a + b*x]]*(2*Coth[a + b*x] + 3*b*x*Csch[a + b*x]^2 + (2*I)*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]]))/(15*b^2)","A",1
554,1,70,98,0.2166222,"\int x \cosh (a+b x) \text{csch}^{\frac{5}{2}}(a+b x) \, dx","Integrate[x*Cosh[a + b*x]*Csch[a + b*x]^(5/2),x]","-\frac{2 \sqrt{\text{csch}(a+b x)} \left(2 \cosh (a+b x)+b x \text{csch}(a+b x)-2 \sqrt{i \sinh (a+b x)} E\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)\right)}{3 b^2}","-\frac{4 \cosh (a+b x) \sqrt{\text{csch}(a+b x)}}{3 b^2}-\frac{4 i E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{3 b^2 \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)}}-\frac{2 x \text{csch}^{\frac{3}{2}}(a+b x)}{3 b}",1,"(-2*Sqrt[Csch[a + b*x]]*(2*Cosh[a + b*x] + b*x*Csch[a + b*x] - 2*EllipticE[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]]))/(3*b^2)","A",1
555,1,56,71,0.1513692,"\int x \cosh (a+b x) \text{csch}^{\frac{3}{2}}(a+b x) \, dx","Integrate[x*Cosh[a + b*x]*Csch[a + b*x]^(3/2),x]","-\frac{2 \sqrt{\text{csch}(a+b x)} \left(b x-2 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)\right)}{b^2}","-\frac{2 x \sqrt{\text{csch}(a+b x)}}{b}-\frac{4 i \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{b^2}",1,"(-2*Sqrt[Csch[a + b*x]]*(b*x - (2*I)*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]]))/b^2","A",1
556,1,183,71,1.0969171,"\int x \cosh (a+b x) \sqrt{\text{csch}(a+b x)} \, dx","Integrate[x*Cosh[a + b*x]*Sqrt[Csch[a + b*x]],x]","\frac{e^{-a-b x} \sqrt{2-2 e^{2 (a+b x)}} \sqrt{\frac{e^{a+b x}}{e^{2 (a+b x)}-1}} \left(-18 \, _3F_2\left(-\frac{1}{4},-\frac{1}{4},\frac{1}{2};\frac{3}{4},\frac{3}{4};e^{2 (a+b x)}\right)-2 e^{2 (a+b x)} \, _3F_2\left(\frac{1}{2},\frac{3}{4},\frac{3}{4};\frac{7}{4},\frac{7}{4};e^{2 (a+b x)}\right)-3 b x \left(3 \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};e^{2 (a+b x)}\right)-e^{2 (a+b x)} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};e^{2 (a+b x)}\right)\right)\right)}{9 b^2}","\frac{2 x}{b \sqrt{\text{csch}(a+b x)}}+\frac{4 i E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{b^2 \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)}}",1,"(E^(-a - b*x)*Sqrt[2 - 2*E^(2*(a + b*x))]*Sqrt[E^(a + b*x)/(-1 + E^(2*(a + b*x)))]*(-3*b*x*(3*Hypergeometric2F1[-1/4, 1/2, 3/4, E^(2*(a + b*x))] - E^(2*(a + b*x))*Hypergeometric2F1[1/2, 3/4, 7/4, E^(2*(a + b*x))]) - 18*HypergeometricPFQ[{-1/4, -1/4, 1/2}, {3/4, 3/4}, E^(2*(a + b*x))] - 2*E^(2*(a + b*x))*HypergeometricPFQ[{1/2, 3/4, 3/4}, {7/4, 7/4}, E^(2*(a + b*x))]))/(9*b^2)","C",0
557,1,67,98,0.4329669,"\int \frac{x \cosh (a+b x)}{\sqrt{\text{csch}(a+b x)}} \, dx","Integrate[(x*Cosh[a + b*x])/Sqrt[Csch[a + b*x]],x]","\frac{-4 \coth (a+b x)-\frac{4 i F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)}{(i \sinh (a+b x))^{3/2}}+6 b x}{9 b^2 \text{csch}^{\frac{3}{2}}(a+b x)}","-\frac{4 \cosh (a+b x)}{9 b^2 \sqrt{\text{csch}(a+b x)}}-\frac{4 i \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{9 b^2}+\frac{2 x}{3 b \text{csch}^{\frac{3}{2}}(a+b x)}",1,"(6*b*x - 4*Coth[a + b*x] - ((4*I)*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2])/(I*Sinh[a + b*x])^(3/2))/(9*b^2*Csch[a + b*x]^(3/2))","A",1
558,1,111,98,2.053818,"\int \frac{x \cosh (a+b x)}{\text{csch}^{\frac{3}{2}}(a+b x)} \, dx","Integrate[(x*Cosh[a + b*x])/Csch[a + b*x]^(3/2),x]","\frac{e^{-2 (a+b x)} \left(-\frac{48 e^{2 (a+b x)} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};e^{2 (a+b x)}\right)}{\sqrt{1-e^{2 (a+b x)}}}+(24-10 b x) e^{2 (a+b x)}+(5 b x-2) e^{4 (a+b x)}+5 b x+2\right)}{50 b^2 \sqrt{\text{csch}(a+b x)}}","-\frac{4 \cosh (a+b x)}{25 b^2 \text{csch}^{\frac{3}{2}}(a+b x)}-\frac{12 i E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{25 b^2 \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)}}+\frac{2 x}{5 b \text{csch}^{\frac{5}{2}}(a+b x)}",1,"(2 + 5*b*x + E^(2*(a + b*x))*(24 - 10*b*x) + E^(4*(a + b*x))*(-2 + 5*b*x) - (48*E^(2*(a + b*x))*Hypergeometric2F1[-1/4, 1/2, 3/4, E^(2*(a + b*x))])/Sqrt[1 - E^(2*(a + b*x))])/(50*b^2*E^(2*(a + b*x))*Sqrt[Csch[a + b*x]])","C",1
559,1,103,121,0.4095005,"\int \frac{x \cosh (a+b x)}{\text{csch}^{\frac{5}{2}}(a+b x)} \, dx","Integrate[(x*Cosh[a + b*x])/Csch[a + b*x]^(5/2),x]","\frac{\sqrt{\text{csch}(a+b x)} \left(52 \sinh (2 (a+b x))-6 \sinh (4 (a+b x))-84 b x \cosh (2 (a+b x))+21 b x \cosh (4 (a+b x))-80 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)+63 b x\right)}{588 b^2}","-\frac{4 \cosh (a+b x)}{49 b^2 \text{csch}^{\frac{5}{2}}(a+b x)}+\frac{20 \cosh (a+b x)}{147 b^2 \sqrt{\text{csch}(a+b x)}}+\frac{20 i \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{147 b^2}+\frac{2 x}{7 b \text{csch}^{\frac{7}{2}}(a+b x)}",1,"(Sqrt[Csch[a + b*x]]*(63*b*x - 84*b*x*Cosh[2*(a + b*x)] + 21*b*x*Cosh[4*(a + b*x)] - (80*I)*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]] + 52*Sinh[2*(a + b*x)] - 6*Sinh[4*(a + b*x)]))/(588*b^2)","A",1
560,1,13,13,0.0658119,"\int \sqrt{\sinh (x) \tanh (x)} \, dx","Integrate[Sqrt[Sinh[x]*Tanh[x]],x]","2 \coth (x) \sqrt{\sinh (x) \tanh (x)}","2 \coth (x) \sqrt{\sinh (x) \tanh (x)}",1,"2*Coth[x]*Sqrt[Sinh[x]*Tanh[x]]","A",1
561,1,23,31,0.0700412,"\int (\sinh (x) \tanh (x))^{3/2} \, dx","Integrate[(Sinh[x]*Tanh[x])^(3/2),x]","\frac{2}{3} \sinh (x) \left(4 \text{csch}^2(x)+1\right) \sqrt{\sinh (x) \tanh (x)}","\frac{2}{3} \sinh (x) \sqrt{\sinh (x) \tanh (x)}+\frac{8}{3} \text{csch}(x) \sqrt{\sinh (x) \tanh (x)}",1,"(2*(1 + 4*Csch[x]^2)*Sinh[x]*Sqrt[Sinh[x]*Tanh[x]])/3","A",1
562,1,29,50,0.1150057,"\int (\sinh (x) \tanh (x))^{5/2} \, dx","Integrate[(Sinh[x]*Tanh[x])^(5/2),x]","-\frac{2}{15} \tanh (x) \sqrt{\sinh (x) \tanh (x)} \left(-3 \cosh ^2(x)+32 \coth ^2(x)-5\right)","\frac{2}{5} \sinh ^2(x) \tanh (x) \sqrt{\sinh (x) \tanh (x)}+\frac{16}{15} \tanh (x) \sqrt{\sinh (x) \tanh (x)}-\frac{64}{15} \coth (x) \sqrt{\sinh (x) \tanh (x)}",1,"(-2*(-5 - 3*Cosh[x]^2 + 32*Coth[x]^2)*Tanh[x]*Sqrt[Sinh[x]*Tanh[x]])/15","A",1
563,1,35,13,0.0804119,"\int \sqrt{\cosh (x) \coth (x)} \, dx","Integrate[Sqrt[Cosh[x]*Coth[x]],x]","\frac{2 \left(\sqrt[4]{-\sinh ^2(x)}-1\right) \tanh (x) \sqrt{\cosh (x) \coth (x)}}{\sqrt[4]{-\sinh ^2(x)}}","2 \tanh (x) \sqrt{\cosh (x) \coth (x)}",1,"(2*Sqrt[Cosh[x]*Coth[x]]*(-1 + (-Sinh[x]^2)^(1/4))*Tanh[x])/(-Sinh[x]^2)^(1/4)","B",1
564,1,21,31,0.0511545,"\int (\cosh (x) \coth (x))^{3/2} \, dx","Integrate[(Cosh[x]*Coth[x])^(3/2),x]","\frac{2}{3} \left(\cosh ^2(x)-4\right) \text{sech}(x) \sqrt{\cosh (x) \coth (x)}","\frac{2}{3} \cosh (x) \sqrt{\cosh (x) \coth (x)}-\frac{8}{3} \text{sech}(x) \sqrt{\cosh (x) \coth (x)}",1,"(2*(-4 + Cosh[x]^2)*Sqrt[Cosh[x]*Coth[x]]*Sech[x])/3","A",1
565,1,44,50,0.323138,"\int (\cosh (x) \coth (x))^{5/2} \, dx","Integrate[(Cosh[x]*Coth[x])^(5/2),x]","\frac{1}{15} \sqrt{\cosh (x) \coth (x)} \left(64 \tanh (x)-10 \coth (x)+6 \sinh (x) \cosh (x)+57 \left(-\sinh ^2(x)\right)^{3/4} \text{csch}(x) \text{sech}(x)\right)","\frac{2}{5} \cosh ^2(x) \coth (x) \sqrt{\cosh (x) \coth (x)}-\frac{16}{15} \coth (x) \sqrt{\cosh (x) \coth (x)}+\frac{64}{15} \tanh (x) \sqrt{\cosh (x) \coth (x)}",1,"(Sqrt[Cosh[x]*Coth[x]]*(-10*Coth[x] + 6*Cosh[x]*Sinh[x] + 57*Csch[x]*Sech[x]*(-Sinh[x]^2)^(3/4) + 64*Tanh[x]))/15","A",1
566,1,60,52,0.1164023,"\int \frac{b+c+\cosh (x)}{a+b \sinh (x)} \, dx","Integrate[(b + c + Cosh[x])/(a + b*Sinh[x]),x]","\frac{2 (b+c) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\frac{\log (a+b \sinh (x))}{b}","\frac{\log (a+b \sinh (x))}{b}-\frac{2 (b+c) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}",1,"(2*(b + c)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + Log[a + b*Sinh[x]]/b","A",1
567,1,62,53,0.1130731,"\int \frac{b+c+\cosh (x)}{a-b \sinh (x)} \, dx","Integrate[(b + c + Cosh[x])/(a - b*Sinh[x]),x]","-\frac{2 (b+c) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-\frac{\log (b \sinh (x)-a)}{b}","\frac{2 (b+c) \tanh ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}-\frac{\log (a-b \sinh (x))}{b}",1,"(-2*(b + c)*ArcTan[(b + a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - Log[-a + b*Sinh[x]]/b","A",1
568,1,56,57,0.0955804,"\int \frac{b+c+\sinh (x)}{a+b \cosh (x)} \, dx","Integrate[(b + c + Sinh[x])/(a + b*Cosh[x]),x]","\frac{\log (a+b \cosh (x))}{b}-\frac{2 (b+c) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}","\frac{2 (b+c) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}+\frac{\log (a+b \cosh (x))}{b}",1,"(-2*(b + c)*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] + Log[a + b*Cosh[x]]/b","A",1
569,1,56,59,0.0988394,"\int \frac{b+c+\sinh (x)}{a-b \cosh (x)} \, dx","Integrate[(b + c + Sinh[x])/(a - b*Cosh[x]),x]","-\frac{2 (b+c) \tan ^{-1}\left(\frac{(a+b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}-\frac{\log (a-b \cosh (x))}{b}","\frac{2 (b+c) \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a-b}}\right)}{\sqrt{a-b} \sqrt{a+b}}-\frac{\log (a-b \cosh (x))}{b}",1,"(-2*(b + c)*ArcTan[((a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] - Log[a - b*Cosh[x]]/b","A",1
570,1,25,25,0.1765394,"\int \frac{x (b-a \sinh (x))}{(a+b \sinh (x))^2} \, dx","Integrate[(x*(b - a*Sinh[x]))/(a + b*Sinh[x])^2,x]","\frac{\log (a+b \sinh (x))}{b}-\frac{x \cosh (x)}{a+b \sinh (x)}","\frac{\log (a+b \sinh (x))}{b}-\frac{x \cosh (x)}{a+b \sinh (x)}",1,"Log[a + b*Sinh[x]]/b - (x*Cosh[x])/(a + b*Sinh[x])","A",1
571,1,25,25,0.1250073,"\int \frac{x (b+a \cosh (x))}{(a+b \cosh (x))^2} \, dx","Integrate[(x*(b + a*Cosh[x]))/(a + b*Cosh[x])^2,x]","\frac{x \sinh (x)}{a+b \cosh (x)}-\frac{\log (a+b \cosh (x))}{b}","\frac{x \sinh (x)}{a+b \cosh (x)}-\frac{\log (a+b \cosh (x))}{b}",1,"-(Log[a + b*Cosh[x]]/b) + (x*Sinh[x])/(a + b*Cosh[x])","A",1
572,1,63,62,0.1296239,"\int \frac{a+b \text{sech}(x)}{c+d \cosh (x)} \, dx","Integrate[(a + b*Sech[x])/(c + d*Cosh[x]),x]","\frac{2 \left(\frac{(b d-a c) \tan ^{-1}\left(\frac{(c-d) \tanh \left(\frac{x}{2}\right)}{\sqrt{d^2-c^2}}\right)}{\sqrt{d^2-c^2}}+b \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)}{c}","\frac{2 (a c-b d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tanh \left(\frac{x}{2}\right)}{\sqrt{c+d}}\right)}{c \sqrt{c-d} \sqrt{c+d}}+\frac{b \tan ^{-1}(\sinh (x))}{c}",1,"(2*(b*ArcTan[Tanh[x/2]] + ((-(a*c) + b*d)*ArcTan[((c - d)*Tanh[x/2])/Sqrt[-c^2 + d^2]])/Sqrt[-c^2 + d^2]))/c","A",1
573,1,67,58,0.1393578,"\int \frac{a+b \text{csch}(x)}{c+d \sinh (x)} \, dx","Integrate[(a + b*Csch[x])/(c + d*Sinh[x]),x]","\frac{\frac{2 (a c-b d) \tan ^{-1}\left(\frac{d-c \tanh \left(\frac{x}{2}\right)}{\sqrt{-c^2-d^2}}\right)}{\sqrt{-c^2-d^2}}+b \log \left(\tanh \left(\frac{x}{2}\right)\right)}{c}","-\frac{2 (a c-b d) \tanh ^{-1}\left(\frac{d-c \tanh \left(\frac{x}{2}\right)}{\sqrt{c^2+d^2}}\right)}{c \sqrt{c^2+d^2}}-\frac{b \tanh ^{-1}(\cosh (x))}{c}",1,"((2*(a*c - b*d)*ArcTan[(d - c*Tanh[x/2])/Sqrt[-c^2 - d^2]])/Sqrt[-c^2 - d^2] + b*Log[Tanh[x/2]])/c","A",1
574,1,24,19,0.0320634,"\int \frac{1+\sinh ^2(x)}{1-\sinh ^2(x)} \, dx","Integrate[(1 + Sinh[x]^2)/(1 - Sinh[x]^2),x]","-2 \left(\frac{x}{2}-\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{\sqrt{2}}\right)","\sqrt{2} \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)-x",1,"-2*(x/2 - ArcTanh[Sqrt[2]*Tanh[x]]/Sqrt[2])","A",1
575,1,8,8,0.0158799,"\int \frac{1-\sinh ^2(x)}{1+\sinh ^2(x)} \, dx","Integrate[(1 - Sinh[x]^2)/(1 + Sinh[x]^2),x]","2 \tanh (x)-x","2 \tanh (x)-x",1,"-x + 2*Tanh[x]","A",1
576,1,8,8,0.0066031,"\int \frac{1+\cosh ^2(x)}{1-\cosh ^2(x)} \, dx","Integrate[(1 + Cosh[x]^2)/(1 - Cosh[x]^2),x]","2 \coth (x)-x","2 \coth (x)-x",1,"-x + 2*Coth[x]","A",1
577,1,24,19,0.031216,"\int \frac{1-\cosh ^2(x)}{1+\cosh ^2(x)} \, dx","Integrate[(1 - Cosh[x]^2)/(1 + Cosh[x]^2),x]","-2 \left(\frac{x}{2}-\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{\sqrt{2}}\right)","\sqrt{2} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)-x",1,"-2*(x/2 - ArcTanh[Tanh[x]/Sqrt[2]]/Sqrt[2])","A",1
578,1,127,74,0.2231841,"\int \frac{a+b \text{sech}^2(x)}{c+d \cosh (x)} \, dx","Integrate[(a + b*Sech[x]^2)/(c + d*Cosh[x]),x]","-\frac{2 \text{sech}(x) \left(a \cosh ^2(x)+b\right) \left(2 \cosh (x) \left(\left(a c^2+b d^2\right) \tan ^{-1}\left(\frac{(c-d) \tanh \left(\frac{x}{2}\right)}{\sqrt{d^2-c^2}}\right)+b d \sqrt{d^2-c^2} \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)-b c \sqrt{d^2-c^2} \sinh (x)\right)}{c^2 \sqrt{d^2-c^2} (a \cosh (2 x)+a+2 b)}","\frac{2 \left(a c^2+b d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tanh \left(\frac{x}{2}\right)}{\sqrt{c+d}}\right)}{c^2 \sqrt{c-d} \sqrt{c+d}}-\frac{b d \tan ^{-1}(\sinh (x))}{c^2}+\frac{b \tanh (x)}{c}",1,"(-2*(b + a*Cosh[x]^2)*Sech[x]*(2*(b*d*Sqrt[-c^2 + d^2]*ArcTan[Tanh[x/2]] + (a*c^2 + b*d^2)*ArcTan[((c - d)*Tanh[x/2])/Sqrt[-c^2 + d^2]])*Cosh[x] - b*c*Sqrt[-c^2 + d^2]*Sinh[x]))/(c^2*Sqrt[-c^2 + d^2]*(a + 2*b + a*Cosh[2*x]))","A",1
579,1,125,69,0.419915,"\int \frac{a+b \text{csch}^2(x)}{c+d \sinh (x)} \, dx","Integrate[(a + b*Csch[x]^2)/(c + d*Sinh[x]),x]","-\frac{\text{csch}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \left(\sinh (x) \left(b d \sqrt{-c^2-d^2} \log \left(\tanh \left(\frac{x}{2}\right)\right)-2 \left(a c^2+b d^2\right) \tan ^{-1}\left(\frac{d-c \tanh \left(\frac{x}{2}\right)}{\sqrt{-c^2-d^2}}\right)\right)+b c \sqrt{-c^2-d^2} \cosh (x)\right)}{2 c^2 \sqrt{-c^2-d^2}}","-\frac{2 \left(a c^2+b d^2\right) \tanh ^{-1}\left(\frac{d-c \tanh \left(\frac{x}{2}\right)}{\sqrt{c^2+d^2}}\right)}{c^2 \sqrt{c^2+d^2}}+\frac{b d \tanh ^{-1}(\cosh (x))}{c^2}-\frac{b \coth (x)}{c}",1,"-1/2*(Csch[x/2]*Sech[x/2]*(b*c*Sqrt[-c^2 - d^2]*Cosh[x] + (-2*(a*c^2 + b*d^2)*ArcTan[(d - c*Tanh[x/2])/Sqrt[-c^2 - d^2]] + b*d*Sqrt[-c^2 - d^2]*Log[Tanh[x/2]])*Sinh[x]))/(c^2*Sqrt[-c^2 - d^2])","A",1
580,1,9,9,0.0042168,"\int (a \cosh (x)+b \sinh (x)) \, dx","Integrate[a*Cosh[x] + b*Sinh[x],x]","a \sinh (x)+b \cosh (x)","a \sinh (x)+b \cosh (x)",1,"b*Cosh[x] + a*Sinh[x]","A",1
581,1,36,37,0.058121,"\int (a \cosh (x)+b \sinh (x))^2 \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{1}{4} \left(\left(a^2+b^2\right) \sinh (2 x)+2 x (a-b) (a+b)+2 a b \cosh (2 x)\right)","\frac{1}{2} x \left(a^2-b^2\right)+\frac{1}{2} (a \sinh (x)+b \cosh (x)) (a \cosh (x)+b \sinh (x))",1,"(2*(a - b)*(a + b)*x + 2*a*b*Cosh[2*x] + (a^2 + b^2)*Sinh[2*x])/4","A",1
582,1,63,35,0.1364637,"\int (a \cosh (x)+b \sinh (x))^3 \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^3,x]","\frac{1}{12} \left(9 a \left(a^2-b^2\right) \sinh (x)+a \left(a^2+3 b^2\right) \sinh (3 x)+9 b \left(a^2-b^2\right) \cosh (x)+b \left(3 a^2+b^2\right) \cosh (3 x)\right)","\left(a^2-b^2\right) (a \sinh (x)+b \cosh (x))+\frac{1}{3} (a \sinh (x)+b \cosh (x))^3",1,"(9*b*(a^2 - b^2)*Cosh[x] + b*(3*a^2 + b^2)*Cosh[3*x] + 9*a*(a^2 - b^2)*Sinh[x] + a*(a^2 + 3*b^2)*Sinh[3*x])/12","A",1
583,1,87,72,0.1501178,"\int (a \cosh (x)+b \sinh (x))^4 \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^4,x]","\frac{1}{32} \left(8 \left(a^4-b^4\right) \sinh (2 x)+16 a b \left(a^2-b^2\right) \cosh (2 x)+4 a b \left(a^2+b^2\right) \cosh (4 x)+\left(a^4+6 a^2 b^2+b^4\right) \sinh (4 x)+12 x (a-b)^2 (a+b)^2\right)","\frac{3}{8} x \left(a^2-b^2\right)^2+\frac{3}{8} \left(a^2-b^2\right) (a \sinh (x)+b \cosh (x)) (a \cosh (x)+b \sinh (x))+\frac{1}{4} (a \sinh (x)+b \cosh (x)) (a \cosh (x)+b \sinh (x))^3",1,"(12*(a - b)^2*(a + b)^2*x + 16*a*b*(a^2 - b^2)*Cosh[2*x] + 4*a*b*(a^2 + b^2)*Cosh[4*x] + 8*(a^4 - b^4)*Sinh[2*x] + (a^4 + 6*a^2*b^2 + b^4)*Sinh[4*x])/32","A",1
584,1,133,61,0.2299598,"\int (a \cosh (x)+b \sinh (x))^5 \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^5,x]","\frac{1}{240} \left(150 a \left(a^2-b^2\right)^2 \sinh (x)+150 b \left(a^2-b^2\right)^2 \cosh (x)+25 a \left(a^4+2 a^2 b^2-3 b^4\right) \sinh (3 x)+3 a \left(a^4+10 a^2 b^2+5 b^4\right) \sinh (5 x)-25 b \left(-3 a^4+2 a^2 b^2+b^4\right) \cosh (3 x)+3 b \left(5 a^4+10 a^2 b^2+b^4\right) \cosh (5 x)\right)","\frac{2}{3} \left(a^2-b^2\right) (a \sinh (x)+b \cosh (x))^3+\left(a^2-b^2\right)^2 (a \sinh (x)+b \cosh (x))+\frac{1}{5} (a \sinh (x)+b \cosh (x))^5",1,"(150*b*(a^2 - b^2)^2*Cosh[x] - 25*b*(-3*a^4 + 2*a^2*b^2 + b^4)*Cosh[3*x] + 3*b*(5*a^4 + 10*a^2*b^2 + b^4)*Cosh[5*x] + 150*a*(a^2 - b^2)^2*Sinh[x] + 25*a*(a^4 + 2*a^2*b^2 - 3*b^4)*Sinh[3*x] + 3*a*(a^4 + 10*a^2*b^2 + 5*b^4)*Sinh[5*x])/240","B",1
585,1,46,38,0.0472777,"\int \frac{1}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}","\frac{\tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}",1,"(2*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/(Sqrt[a - b]*Sqrt[a + b])","A",1
586,1,17,17,0.0268783,"\int \frac{1}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^(-2),x]","\frac{\sinh (x)}{a (a \cosh (x)+b \sinh (x))}","\frac{\sinh (x)}{a (a \cosh (x)+b \sinh (x))}",1,"Sinh[x]/(a*(a*Cosh[x] + b*Sinh[x]))","A",1
587,1,96,77,0.4913705,"\int \frac{1}{(a \cosh (x)+b \sinh (x))^3} \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^(-3),x]","\frac{1}{2} \left(\frac{2 \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{3/2} (a+b)^{3/2}}+\frac{b}{a (a-b) (a+b) (a \cosh (x)+b \sinh (x))}+\frac{\sinh (x)}{a (a \cosh (x)+b \sinh (x))^2}\right)","\frac{a \sinh (x)+b \cosh (x)}{2 \left(a^2-b^2\right) (a \cosh (x)+b \sinh (x))^2}+\frac{\tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{2 \left(a^2-b^2\right)^{3/2}}",1,"((2*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(3/2)*(a + b)^(3/2)) + Sinh[x]/(a*(a*Cosh[x] + b*Sinh[x])^2) + b/(a*(a - b)*(a + b)*(a*Cosh[x] + b*Sinh[x])))/2","A",1
588,1,64,67,0.1434229,"\int \frac{1}{(a \cosh (x)+b \sinh (x))^4} \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^(-4),x]","\frac{\sinh (x) \left(\left(a^2+b^2\right) \cosh (2 x)+2 a^2-b^2\right)+a b \cosh (3 x)}{3 a (a-b) (a+b) (a \cosh (x)+b \sinh (x))^3}","\frac{2 \sinh (x)}{3 a \left(a^2-b^2\right) (a \cosh (x)+b \sinh (x))}+\frac{a \sinh (x)+b \cosh (x)}{3 \left(a^2-b^2\right) (a \cosh (x)+b \sinh (x))^3}",1,"(a*b*Cosh[3*x] + (2*a^2 - b^2 + (a^2 + b^2)*Cosh[2*x])*Sinh[x])/(3*a*(a - b)*(a + b)*(a*Cosh[x] + b*Sinh[x])^3)","A",1
589,1,147,112,1.0612377,"\int \frac{1}{(a \cosh (x)+b \sinh (x))^5} \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^(-5),x]","\frac{1}{8} \left(\frac{6 \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{5/2} (a+b)^{5/2}}+\frac{b \left(3 (a \cosh (x)+b \sinh (x))^2+2 (a-b) (a+b)\right)}{a (a-b)^2 (a+b)^2 (a \cosh (x)+b \sinh (x))^3}+\frac{\sinh (x) \left(\frac{3 (a \cosh (x)+b \sinh (x))^2}{(a-b) (a+b)}+2\right)}{a (a \cosh (x)+b \sinh (x))^4}\right)","\frac{3 (a \sinh (x)+b \cosh (x))}{8 \left(a^2-b^2\right)^2 (a \cosh (x)+b \sinh (x))^2}+\frac{a \sinh (x)+b \cosh (x)}{4 \left(a^2-b^2\right) (a \cosh (x)+b \sinh (x))^4}+\frac{3 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{8 \left(a^2-b^2\right)^{5/2}}",1,"((6*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(5/2)*(a + b)^(5/2)) + (b*(2*(a - b)*(a + b) + 3*(a*Cosh[x] + b*Sinh[x])^2))/(a*(a - b)^2*(a + b)^2*(a*Cosh[x] + b*Sinh[x])^3) + (Sinh[x]*(2 + (3*(a*Cosh[x] + b*Sinh[x])^2)/((a - b)*(a + b))))/(a*(a*Cosh[x] + b*Sinh[x])^4))/8","A",1
590,1,206,65,0.7584027,"\int \sqrt{a \cosh (x)+b \sinh (x)} \, dx","Integrate[Sqrt[a*Cosh[x] + b*Sinh[x]],x]","\frac{b \left(b^2-a^2\right) \sinh \left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right) \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{3}{4};\cosh ^2\left(x+\tanh ^{-1}\left(\frac{b}{a}\right)\right)\right)+\sqrt{-\sinh ^2\left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)} \left(2 a^2 b \sqrt{1-\frac{b^2}{a^2}} \sinh (x)-2 a \left(a^2-b^2\right) \cosh \left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)+a^2 b \sinh \left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)+2 a^3 \sqrt{1-\frac{b^2}{a^2}} \cosh (x)-b^3 \sinh \left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)\right)}{a b \sqrt{1-\frac{b^2}{a^2}} \sqrt{-\sinh ^2\left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)} \sqrt{a \cosh (x)+b \sinh (x)}}","-\frac{2 i \sqrt{a \cosh (x)+b \sinh (x)} E\left(\left.\frac{1}{2} \left(i x-\tan ^{-1}(a,-i b)\right)\right|2\right)}{\sqrt{\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}}}",1,"(b*(-a^2 + b^2)*HypergeometricPFQ[{-1/2, -1/4}, {3/4}, Cosh[x + ArcTanh[b/a]]^2]*Sinh[x + ArcTanh[b/a]] + Sqrt[-Sinh[x + ArcTanh[b/a]]^2]*(2*a^3*Sqrt[1 - b^2/a^2]*Cosh[x] - 2*a*(a^2 - b^2)*Cosh[x + ArcTanh[b/a]] + 2*a^2*b*Sqrt[1 - b^2/a^2]*Sinh[x] + a^2*b*Sinh[x + ArcTanh[b/a]] - b^3*Sinh[x + ArcTanh[b/a]]))/(a*b*Sqrt[1 - b^2/a^2]*Sqrt[a*Cosh[x] + b*Sinh[x]]*Sqrt[-Sinh[x + ArcTanh[b/a]]^2])","C",0
591,1,92,103,0.5980619,"\int (a \cosh (x)+b \sinh (x))^{3/2} \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^(3/2),x]","\frac{2}{3} \sqrt{a \cosh (x)+b \sinh (x)} \left(-b \sqrt{1-\frac{a^2}{b^2}} \sqrt{\cosh ^2\left(\tanh ^{-1}\left(\frac{a}{b}\right)+x\right)} \text{sech}\left(\tanh ^{-1}\left(\frac{a}{b}\right)+x\right) \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\sinh ^2\left(x+\tanh ^{-1}\left(\frac{a}{b}\right)\right)\right)+a \sinh (x)+b \cosh (x)\right)","\frac{2}{3} (a \sinh (x)+b \cosh (x)) \sqrt{a \cosh (x)+b \sinh (x)}-\frac{2 i \left(a^2-b^2\right) \sqrt{\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}} F\left(\left.\frac{1}{2} \left(i x-\tan ^{-1}(a,-i b)\right)\right|2\right)}{3 \sqrt{a \cosh (x)+b \sinh (x)}}",1,"(2*(b*Cosh[x] - Sqrt[1 - a^2/b^2]*b*Sqrt[Cosh[x + ArcTanh[a/b]]^2]*HypergeometricPFQ[{1/4, 1/2}, {5/4}, -Sinh[x + ArcTanh[a/b]]^2]*Sech[x + ArcTanh[a/b]] + a*Sinh[x])*Sqrt[a*Cosh[x] + b*Sinh[x]])/3","C",1
592,1,193,103,0.8568084,"\int (a \cosh (x)+b \sinh (x))^{5/2} \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^(5/2),x]","\frac{(a \cosh (x)+b \sinh (x)) \left(b \left(a^2+b^2\right) \sinh (2 x)+6 a \left(a^2-b^2\right)+2 a b^2 \cosh (2 x)\right)-\frac{3 (a-b)^2 (a+b)^2 \left(b \sinh \left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right) \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{3}{4};\cosh ^2\left(x+\tanh ^{-1}\left(\frac{b}{a}\right)\right)\right)+\sqrt{-\sinh ^2\left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)} \left(2 a \cosh \left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)-b \sinh \left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)\right)\right)}{a \sqrt{1-\frac{b^2}{a^2}} \sqrt{-\sinh ^2\left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)}}}{5 b \sqrt{a \cosh (x)+b \sinh (x)}}","\frac{2}{5} (a \sinh (x)+b \cosh (x)) (a \cosh (x)+b \sinh (x))^{3/2}-\frac{6 i \left(a^2-b^2\right) \sqrt{a \cosh (x)+b \sinh (x)} E\left(\left.\frac{1}{2} \left(i x-\tan ^{-1}(a,-i b)\right)\right|2\right)}{5 \sqrt{\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}}}",1,"((a*Cosh[x] + b*Sinh[x])*(6*a*(a^2 - b^2) + 2*a*b^2*Cosh[2*x] + b*(a^2 + b^2)*Sinh[2*x]) - (3*(a - b)^2*(a + b)^2*(b*HypergeometricPFQ[{-1/2, -1/4}, {3/4}, Cosh[x + ArcTanh[b/a]]^2]*Sinh[x + ArcTanh[b/a]] + Sqrt[-Sinh[x + ArcTanh[b/a]]^2]*(2*a*Cosh[x + ArcTanh[b/a]] - b*Sinh[x + ArcTanh[b/a]])))/(a*Sqrt[1 - b^2/a^2]*Sqrt[-Sinh[x + ArcTanh[b/a]]^2]))/(5*b*Sqrt[a*Cosh[x] + b*Sinh[x]])","C",0
593,1,81,65,0.0969378,"\int \frac{1}{\sqrt{a \cosh (x)+b \sinh (x)}} \, dx","Integrate[1/Sqrt[a*Cosh[x] + b*Sinh[x]],x]","\frac{2 \sqrt{a \cosh (x)+b \sinh (x)} \sqrt{\cosh ^2\left(\tanh ^{-1}\left(\frac{a}{b}\right)+x\right)} \text{sech}\left(\tanh ^{-1}\left(\frac{a}{b}\right)+x\right) \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\sinh ^2\left(x+\tanh ^{-1}\left(\frac{a}{b}\right)\right)\right)}{b \sqrt{1-\frac{a^2}{b^2}}}","-\frac{2 i \sqrt{\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}} F\left(\left.\frac{1}{2} \left(i x-\tan ^{-1}(a,-i b)\right)\right|2\right)}{\sqrt{a \cosh (x)+b \sinh (x)}}",1,"(2*Sqrt[Cosh[x + ArcTanh[a/b]]^2]*HypergeometricPFQ[{1/4, 1/2}, {5/4}, -Sinh[x + ArcTanh[a/b]]^2]*Sech[x + ArcTanh[a/b]]*Sqrt[a*Cosh[x] + b*Sinh[x]])/(Sqrt[1 - a^2/b^2]*b)","C",1
594,1,148,112,0.463602,"\int \frac{1}{(a \cosh (x)+b \sinh (x))^{3/2}} \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^(-3/2),x]","\frac{b \sinh \left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right) \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{3}{4};\cosh ^2\left(x+\tanh ^{-1}\left(\frac{b}{a}\right)\right)\right)-\sqrt{-\sinh ^2\left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)} \left(2 a \sqrt{1-\frac{b^2}{a^2}} \cosh (x)+b \sinh \left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)-2 a \cosh \left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)\right)}{a b \sqrt{1-\frac{b^2}{a^2}} \sqrt{-\sinh ^2\left(\tanh ^{-1}\left(\frac{b}{a}\right)+x\right)} \sqrt{a \cosh (x)+b \sinh (x)}}","\frac{2 (a \sinh (x)+b \cosh (x))}{\left(a^2-b^2\right) \sqrt{a \cosh (x)+b \sinh (x)}}+\frac{2 i \sqrt{a \cosh (x)+b \sinh (x)} E\left(\left.\frac{1}{2} \left(i x-\tan ^{-1}(a,-i b)\right)\right|2\right)}{\left(a^2-b^2\right) \sqrt{\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}}}",1,"(b*HypergeometricPFQ[{-1/2, -1/4}, {3/4}, Cosh[x + ArcTanh[b/a]]^2]*Sinh[x + ArcTanh[b/a]] - Sqrt[-Sinh[x + ArcTanh[b/a]]^2]*(2*a*Sqrt[1 - b^2/a^2]*Cosh[x] - 2*a*Cosh[x + ArcTanh[b/a]] + b*Sinh[x + ArcTanh[b/a]]))/(a*b*Sqrt[1 - b^2/a^2]*Sqrt[a*Cosh[x] + b*Sinh[x]]*Sqrt[-Sinh[x + ArcTanh[b/a]]^2])","C",0
595,1,133,116,0.5885948,"\int \frac{1}{(a \cosh (x)+b \sinh (x))^{5/2}} \, dx","Integrate[(a*Cosh[x] + b*Sinh[x])^(-5/2),x]","-\frac{2 \left((a \cosh (x)+b \sinh (x))^2 \sqrt{\cosh ^2\left(\tanh ^{-1}\left(\frac{a}{b}\right)+x\right)} \text{sech}\left(\tanh ^{-1}\left(\frac{a}{b}\right)+x\right) \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\sinh ^2\left(x+\tanh ^{-1}\left(\frac{a}{b}\right)\right)\right)+b \sqrt{1-\frac{a^2}{b^2}} (a \sinh (x)+b \cosh (x))\right)}{3 b \sqrt{1-\frac{a^2}{b^2}} (b-a) (a+b) (a \cosh (x)+b \sinh (x))^{3/2}}","\frac{2 (a \sinh (x)+b \cosh (x))}{3 \left(a^2-b^2\right) (a \cosh (x)+b \sinh (x))^{3/2}}-\frac{2 i \sqrt{\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}} F\left(\left.\frac{1}{2} \left(i x-\tan ^{-1}(a,-i b)\right)\right|2\right)}{3 \left(a^2-b^2\right) \sqrt{a \cosh (x)+b \sinh (x)}}",1,"(-2*(Sqrt[1 - a^2/b^2]*b*(b*Cosh[x] + a*Sinh[x]) + Sqrt[Cosh[x + ArcTanh[a/b]]^2]*HypergeometricPFQ[{1/4, 1/2}, {5/4}, -Sinh[x + ArcTanh[a/b]]^2]*Sech[x + ArcTanh[a/b]]*(a*Cosh[x] + b*Sinh[x])^2))/(3*Sqrt[1 - a^2/b^2]*b*(-a + b)*(a + b)*(a*Cosh[x] + b*Sinh[x])^(3/2))","C",1
596,1,45,23,0.0189839,"\int (a \cosh (c+d x)+a \sinh (c+d x)) \, dx","Integrate[a*Cosh[c + d*x] + a*Sinh[c + d*x],x]","\frac{a \sinh (c) \sinh (d x)}{d}+\frac{a \cosh (c) \cosh (d x)}{d}+\frac{a \sinh (c) \cosh (d x)}{d}+\frac{a \cosh (c) \sinh (d x)}{d}","\frac{a \sinh (c+d x)}{d}+\frac{a \cosh (c+d x)}{d}",1,"(a*Cosh[c]*Cosh[d*x])/d + (a*Cosh[d*x]*Sinh[c])/d + (a*Cosh[c]*Sinh[d*x])/d + (a*Sinh[c]*Sinh[d*x])/d","A",1
597,1,25,26,0.0536754,"\int (a \cosh (c+d x)+a \sinh (c+d x))^2 \, dx","Integrate[(a*Cosh[c + d*x] + a*Sinh[c + d*x])^2,x]","\frac{a^2 (\sinh (c+d x)+\cosh (c+d x))^2}{2 d}","\frac{(a \sinh (c+d x)+a \cosh (c+d x))^2}{2 d}",1,"(a^2*(Cosh[c + d*x] + Sinh[c + d*x])^2)/(2*d)","A",1
598,1,25,26,0.0816173,"\int (a \cosh (c+d x)+a \sinh (c+d x))^3 \, dx","Integrate[(a*Cosh[c + d*x] + a*Sinh[c + d*x])^3,x]","\frac{a^3 (\sinh (c+d x)+\cosh (c+d x))^3}{3 d}","\frac{(a \sinh (c+d x)+a \cosh (c+d x))^3}{3 d}",1,"(a^3*(Cosh[c + d*x] + Sinh[c + d*x])^3)/(3*d)","A",1
599,1,24,26,0.0812536,"\int (a \cosh (c+d x)+a \sinh (c+d x))^n \, dx","Integrate[(a*Cosh[c + d*x] + a*Sinh[c + d*x])^n,x]","\frac{(a (\sinh (c+d x)+\cosh (c+d x)))^n}{d n}","\frac{(a \sinh (c+d x)+a \cosh (c+d x))^n}{d n}",1,"(a*(Cosh[c + d*x] + Sinh[c + d*x]))^n/(d*n)","A",1
600,1,24,24,0.0417953,"\int \frac{1}{a \cosh (c+d x)+a \sinh (c+d x)} \, dx","Integrate[(a*Cosh[c + d*x] + a*Sinh[c + d*x])^(-1),x]","-\frac{1}{d (a \sinh (c+d x)+a \cosh (c+d x))}","-\frac{1}{d (a \sinh (c+d x)+a \cosh (c+d x))}",1,"-(1/(d*(a*Cosh[c + d*x] + a*Sinh[c + d*x])))","A",1
601,1,26,26,0.0448554,"\int \frac{1}{(a \cosh (c+d x)+a \sinh (c+d x))^2} \, dx","Integrate[(a*Cosh[c + d*x] + a*Sinh[c + d*x])^(-2),x]","-\frac{1}{2 d (a \sinh (c+d x)+a \cosh (c+d x))^2}","-\frac{1}{2 d (a \sinh (c+d x)+a \cosh (c+d x))^2}",1,"-1/2*1/(d*(a*Cosh[c + d*x] + a*Sinh[c + d*x])^2)","A",1
602,1,26,26,0.0480771,"\int \frac{1}{(a \cosh (c+d x)+a \sinh (c+d x))^3} \, dx","Integrate[(a*Cosh[c + d*x] + a*Sinh[c + d*x])^(-3),x]","-\frac{1}{3 d (a \sinh (c+d x)+a \cosh (c+d x))^3}","-\frac{1}{3 d (a \sinh (c+d x)+a \cosh (c+d x))^3}",1,"-1/3*1/(d*(a*Cosh[c + d*x] + a*Sinh[c + d*x])^3)","A",1
603,1,24,26,0.0236614,"\int \sqrt{a \cosh (c+d x)+a \sinh (c+d x)} \, dx","Integrate[Sqrt[a*Cosh[c + d*x] + a*Sinh[c + d*x]],x]","\frac{2 \sqrt{a (\sinh (c+d x)+\cosh (c+d x))}}{d}","\frac{2 \sqrt{a \sinh (c+d x)+a \cosh (c+d x)}}{d}",1,"(2*Sqrt[a*(Cosh[c + d*x] + Sinh[c + d*x])])/d","A",1
604,1,24,26,0.0363778,"\int \frac{1}{\sqrt{a \cosh (c+d x)+a \sinh (c+d x)}} \, dx","Integrate[1/Sqrt[a*Cosh[c + d*x] + a*Sinh[c + d*x]],x]","-\frac{2}{d \sqrt{a (\sinh (c+d x)+\cosh (c+d x))}}","-\frac{2}{d \sqrt{a \sinh (c+d x)+a \cosh (c+d x)}}",1,"-2/(d*Sqrt[a*(Cosh[c + d*x] + Sinh[c + d*x])])","A",1
605,1,47,24,0.0196984,"\int (a \cosh (c+d x)-a \sinh (c+d x)) \, dx","Integrate[a*Cosh[c + d*x] - a*Sinh[c + d*x],x]","-\frac{a \sinh (c) \sinh (d x)}{d}-\frac{a \cosh (c) \cosh (d x)}{d}+\frac{a \sinh (c) \cosh (d x)}{d}+\frac{a \cosh (c) \sinh (d x)}{d}","\frac{a \sinh (c+d x)}{d}-\frac{a \cosh (c+d x)}{d}",1,"-((a*Cosh[c]*Cosh[d*x])/d) + (a*Cosh[d*x]*Sinh[c])/d + (a*Cosh[c]*Sinh[d*x])/d - (a*Sinh[c]*Sinh[d*x])/d","A",1
606,1,27,27,0.029647,"\int (a \cosh (c+d x)-a \sinh (c+d x))^2 \, dx","Integrate[(a*Cosh[c + d*x] - a*Sinh[c + d*x])^2,x]","-\frac{(a \cosh (c+d x)-a \sinh (c+d x))^2}{2 d}","-\frac{(a \cosh (c+d x)-a \sinh (c+d x))^2}{2 d}",1,"-1/2*(a*Cosh[c + d*x] - a*Sinh[c + d*x])^2/d","A",1
607,1,27,27,0.024904,"\int (a \cosh (c+d x)-a \sinh (c+d x))^3 \, dx","Integrate[(a*Cosh[c + d*x] - a*Sinh[c + d*x])^3,x]","-\frac{(a \cosh (c+d x)-a \sinh (c+d x))^3}{3 d}","-\frac{(a \cosh (c+d x)-a \sinh (c+d x))^3}{3 d}",1,"-1/3*(a*Cosh[c + d*x] - a*Sinh[c + d*x])^3/d","A",1
608,1,27,28,0.0486169,"\int (a \cosh (c+d x)-a \sinh (c+d x))^n \, dx","Integrate[(a*Cosh[c + d*x] - a*Sinh[c + d*x])^n,x]","-\frac{(a (\cosh (c+d x)-\sinh (c+d x)))^n}{d n}","-\frac{(a \cosh (c+d x)-a \sinh (c+d x))^n}{d n}",1,"-((a*(Cosh[c + d*x] - Sinh[c + d*x]))^n/(d*n))","A",1
609,1,22,24,0.0080125,"\int \frac{1}{a \cosh (c+d x)-a \sinh (c+d x)} \, dx","Integrate[(a*Cosh[c + d*x] - a*Sinh[c + d*x])^(-1),x]","\frac{1}{a d \cosh (c+d x)-a d \sinh (c+d x)}","\frac{1}{d (a \cosh (c+d x)-a \sinh (c+d x))}",1,"(a*d*Cosh[c + d*x] - a*d*Sinh[c + d*x])^(-1)","A",1
610,1,27,27,0.0444452,"\int \frac{1}{(a \cosh (c+d x)-a \sinh (c+d x))^2} \, dx","Integrate[(a*Cosh[c + d*x] - a*Sinh[c + d*x])^(-2),x]","\frac{1}{2 d (a \cosh (c+d x)-a \sinh (c+d x))^2}","\frac{1}{2 d (a \cosh (c+d x)-a \sinh (c+d x))^2}",1,"1/(2*d*(a*Cosh[c + d*x] - a*Sinh[c + d*x])^2)","A",1
611,1,27,27,0.072432,"\int \frac{1}{(a \cosh (c+d x)-a \sinh (c+d x))^3} \, dx","Integrate[(a*Cosh[c + d*x] - a*Sinh[c + d*x])^(-3),x]","\frac{1}{3 d (a \cosh (c+d x)-a \sinh (c+d x))^3}","\frac{1}{3 d (a \cosh (c+d x)-a \sinh (c+d x))^3}",1,"1/(3*d*(a*Cosh[c + d*x] - a*Sinh[c + d*x])^3)","A",1
612,1,26,27,0.0224162,"\int \sqrt{a \cosh (c+d x)-a \sinh (c+d x)} \, dx","Integrate[Sqrt[a*Cosh[c + d*x] - a*Sinh[c + d*x]],x]","-\frac{2 \sqrt{a (\cosh (c+d x)-\sinh (c+d x))}}{d}","-\frac{2 \sqrt{a \cosh (c+d x)-a \sinh (c+d x)}}{d}",1,"(-2*Sqrt[a*(Cosh[c + d*x] - Sinh[c + d*x])])/d","A",1
613,1,26,27,0.0300525,"\int \frac{1}{\sqrt{a \cosh (c+d x)-a \sinh (c+d x)}} \, dx","Integrate[1/Sqrt[a*Cosh[c + d*x] - a*Sinh[c + d*x]],x]","\frac{2}{d \sqrt{a (\cosh (c+d x)-\sinh (c+d x))}}","\frac{2}{d \sqrt{a \cosh (c+d x)-a \sinh (c+d x)}}",1,"2/(d*Sqrt[a*(Cosh[c + d*x] - Sinh[c + d*x])])","A",1
614,1,355,124,1.9585993,"\int (a \text{sech}(x)+b \tanh (x))^5 \, dx","Integrate[(a*Sech[x] + b*Tanh[x])^5,x]","\frac{\frac{2 \text{sech}^2(x) \left(a \left(3 a^2-5 b^2\right) \sinh (x)+6 a^2 b-2 b^3\right) (a+b \sinh (x))^6}{a^2+b^2}+\frac{b \left(2 a b^5 \left(5 b^2-3 a^2\right) \sinh ^5(x)+4 b^4 \left(-9 a^4+12 a^2 b^2+b^4\right) \sinh ^4(x)+10 a b^3 \left(-9 a^4+8 a^2 b^2+b^4\right) \sinh ^3(x)-8 b^2 \left(15 a^6-4 a^4 b^2+2 a^2 b^4+b^6\right) \sinh ^2(x)-10 a b \left(9 a^6+6 a^4 b^2+8 a^2 b^4+3 b^6\right) \sinh (x)+\frac{\left(a^2+b^2\right)^2 \left(\left(3 a^5+10 a^3 b^2+15 a b^4+8 b^4 \sqrt{-b^2}\right) \log \left(\sqrt{-b^2}-b \sinh (x)\right)+\left(-3 a^5-10 a^3 b^2-15 a b^4+8 \left(-b^2\right)^{5/2}\right) \log \left(\sqrt{-b^2}+b \sinh (x)\right)\right)}{\sqrt{-b^2}}\right)}{a^2+b^2}+4 \text{sech}^4(x) (a \sinh (x)+b) (a+b \sinh (x))^6}{16 \left(a^2+b^2\right)}","-\frac{1}{8} a b^2 \left(3 a^2+7 b^2\right) \sinh (x)-\frac{1}{8} \text{sech}^2(x) (a+b \sinh (x))^2 \left(2 b \left(a^2+2 b^2\right)-a \left(3 a^2+5 b^2\right) \sinh (x)\right)+\frac{1}{8} a \left(3 a^4+10 a^2 b^2+15 b^4\right) \tan ^{-1}(\sinh (x))-\frac{1}{4} \text{sech}^4(x) (b-a \sinh (x)) (a+b \sinh (x))^4+b^5 \log (\cosh (x))",1,"(4*Sech[x]^4*(b + a*Sinh[x])*(a + b*Sinh[x])^6 + (2*Sech[x]^2*(a + b*Sinh[x])^6*(6*a^2*b - 2*b^3 + a*(3*a^2 - 5*b^2)*Sinh[x]))/(a^2 + b^2) + (b*(((a^2 + b^2)^2*((3*a^5 + 10*a^3*b^2 + 15*a*b^4 + 8*b^4*Sqrt[-b^2])*Log[Sqrt[-b^2] - b*Sinh[x]] + (-3*a^5 - 10*a^3*b^2 - 15*a*b^4 + 8*(-b^2)^(5/2))*Log[Sqrt[-b^2] + b*Sinh[x]]))/Sqrt[-b^2] - 10*a*b*(9*a^6 + 6*a^4*b^2 + 8*a^2*b^4 + 3*b^6)*Sinh[x] - 8*b^2*(15*a^6 - 4*a^4*b^2 + 2*a^2*b^4 + b^6)*Sinh[x]^2 + 10*a*b^3*(-9*a^4 + 8*a^2*b^2 + b^4)*Sinh[x]^3 + 4*b^4*(-9*a^4 + 12*a^2*b^2 + b^4)*Sinh[x]^4 + 2*a*b^5*(-3*a^2 + 5*b^2)*Sinh[x]^5))/(a^2 + b^2))/(16*(a^2 + b^2))","B",1
615,1,79,100,0.1855942,"\int (a \text{sech}(x)+b \tanh (x))^4 \, dx","Integrate[(a*Sech[x] + b*Tanh[x])^4,x]","\frac{1}{3} \left(-4 a b \left(a^2-b^2\right) \text{sech}^3(x)+2 \left(a^4+3 a^2 b^2-2 b^4\right) \tanh (x)+\left(a^4-6 a^2 b^2+b^4\right) \tanh (x) \text{sech}^2(x)-12 a b^3 \text{sech}(x)+3 b^4 x\right)","-\frac{4}{3} a b \left(a^2+2 b^2\right) \cosh (x)-\frac{1}{3} b^2 \left(2 a^2+3 b^2\right) \sinh (x) \cosh (x)+\frac{1}{3} \text{sech}(x) (a+b \sinh (x))^2 \left(\left(2 a^2+3 b^2\right) \sinh (x)+a b\right)-\frac{1}{3} \text{sech}^3(x) (b-a \sinh (x)) (a+b \sinh (x))^3+b^4 x",1,"(3*b^4*x - 12*a*b^3*Sech[x] - 4*a*b*(a^2 - b^2)*Sech[x]^3 + 2*(a^4 + 3*a^2*b^2 - 2*b^4)*Tanh[x] + (a^4 - 6*a^2*b^2 + b^4)*Sech[x]^2*Tanh[x])/3","A",1
616,1,194,58,1.9937505,"\int (a \text{sech}(x)+b \tanh (x))^3 \, dx","Integrate[(a*Sech[x] + b*Tanh[x])^3,x]","\frac{1}{4} \left(\frac{b \left(\left(a^3+3 a b^2-2 \left(-b^2\right)^{3/2}\right) \log \left(\sqrt{-b^2}-b \sinh (x)\right)-\left(a^3+3 a b^2+2 \left(-b^2\right)^{3/2}\right) \log \left(\sqrt{-b^2}+b \sinh (x)\right)\right)}{\sqrt{-b^2}}+\frac{2 a^4 b \text{sech}^2(x)}{a^2+b^2}+\frac{a \tanh (x) \text{sech}(x) \left(2 a^4-4 a^2 b^2+b^4 \cosh (2 x)-7 b^4\right)}{a^2+b^2}-\frac{2 b \tanh ^2(x) \left(-4 a^4-2 a^2 b^2+a b^3 \sinh (x)+b^4\right)}{a^2+b^2}\right)","\frac{1}{2} a \left(a^2+3 b^2\right) \tan ^{-1}(\sinh (x))-\frac{1}{2} a b^2 \sinh (x)-\frac{1}{2} \text{sech}^2(x) (b-a \sinh (x)) (a+b \sinh (x))^2+b^3 \log (\cosh (x))",1,"((b*((a^3 + 3*a*b^2 - 2*(-b^2)^(3/2))*Log[Sqrt[-b^2] - b*Sinh[x]] - (a^3 + 3*a*b^2 + 2*(-b^2)^(3/2))*Log[Sqrt[-b^2] + b*Sinh[x]]))/Sqrt[-b^2] + (2*a^4*b*Sech[x]^2)/(a^2 + b^2) + (a*(2*a^4 - 4*a^2*b^2 - 7*b^4 + b^4*Cosh[2*x])*Sech[x]*Tanh[x])/(a^2 + b^2) - (2*b*(-4*a^4 - 2*a^2*b^2 + b^4 + a*b^3*Sinh[x])*Tanh[x]^2)/(a^2 + b^2))/4","B",1
617,1,26,29,0.0504457,"\int (a \text{sech}(x)+b \tanh (x))^2 \, dx","Integrate[(a*Sech[x] + b*Tanh[x])^2,x]","\left(a^2-b^2\right) \tanh (x)-2 a b \text{sech}(x)+b^2 \tanh ^{-1}(\tanh (x))","-a b \cosh (x)-\text{sech}(x) (b-a \sinh (x)) (a+b \sinh (x))+b^2 x",1,"b^2*ArcTanh[Tanh[x]] - 2*a*b*Sech[x] + (a^2 - b^2)*Tanh[x]","A",1
618,1,16,11,0.0048325,"\int (a \text{sech}(x)+b \tanh (x)) \, dx","Integrate[a*Sech[x] + b*Tanh[x],x]","2 a \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+b \log (\cosh (x))","a \tan ^{-1}(\sinh (x))+b \log (\cosh (x))",1,"2*a*ArcTan[Tanh[x/2]] + b*Log[Cosh[x]]","A",1
619,1,11,11,0.0063709,"\int \frac{1}{a \text{sech}(x)+b \tanh (x)} \, dx","Integrate[(a*Sech[x] + b*Tanh[x])^(-1),x]","\frac{\log (a+b \sinh (x))}{b}","\frac{\log (a+b \sinh (x))}{b}",1,"Log[a + b*Sinh[x]]/b","A",1
620,1,502,62,2.0847902,"\int \frac{1}{(a \text{sech}(x)+b \tanh (x))^2} \, dx","Integrate[(a*Sech[x] + b*Tanh[x])^(-2),x]","-\frac{\cosh (x) \left(\sqrt{a+i b} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}} \left(\sqrt{a-i b} \left(a^2+b^2\right) \sqrt{1+i \sinh (x)} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}-2 \sqrt[4]{-1} b^{3/2} (b+i a) \sinh (x) \sin ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{b}}\right)-2 \sqrt[4]{-1} a \sqrt{b} (b+i a) \sin ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{b}}\right)\right)-2 a \sqrt{a-i b} \sqrt{a+i b} \sqrt{1+i \sinh (x)} (a+b \sinh (x)) \tanh ^{-1}\left(\frac{\sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)+2 a (a-i b) \sqrt{1+i \sinh (x)} (a+b \sinh (x)) \tanh ^{-1}\left(\frac{\sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{a+i b} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)\right)}{b (a-i b)^{3/2} (a+i b)^{3/2} \sqrt{1+i \sinh (x)} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}} (a+b \sinh (x))}","\frac{2 a \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^2 \sqrt{a^2+b^2}}-\frac{\cosh (x)}{b (a+b \sinh (x))}+\frac{x}{b^2}",1,"-((Cosh[x]*(-2*a*Sqrt[a - I*b]*Sqrt[a + I*b]*ArcTanh[Sqrt[-((b*(I + Sinh[x]))/(a - I*b))]/Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]]*Sqrt[1 + I*Sinh[x]]*(a + b*Sinh[x]) + 2*a*(a - I*b)*ArcTanh[(Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/(Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))])]*Sqrt[1 + I*Sinh[x]]*(a + b*Sinh[x]) + Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]*(-2*(-1)^(1/4)*a*Sqrt[b]*(I*a + b)*ArcSin[((1/2 + I/2)*Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/Sqrt[b]] - 2*(-1)^(1/4)*b^(3/2)*(I*a + b)*ArcSin[((1/2 + I/2)*Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/Sqrt[b]]*Sinh[x] + Sqrt[a - I*b]*(a^2 + b^2)*Sqrt[1 + I*Sinh[x]]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])))/((a - I*b)^(3/2)*(a + I*b)^(3/2)*b*Sqrt[1 + I*Sinh[x]]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))]*(a + b*Sinh[x])))","C",1
621,1,42,48,0.1374448,"\int \frac{1}{(a \text{sech}(x)+b \tanh (x))^3} \, dx","Integrate[(a*Sech[x] + b*Tanh[x])^(-3),x]","-\frac{\frac{-3 a^2-4 a b \sinh (x)+b^2}{2 (a+b \sinh (x))^2}-\log (a+b \sinh (x))}{b^3}","-\frac{a^2+b^2}{2 b^3 (a+b \sinh (x))^2}+\frac{2 a}{b^3 (a+b \sinh (x))}+\frac{\log (a+b \sinh (x))}{b^3}",1,"-((-Log[a + b*Sinh[x]] + (-3*a^2 + b^2 - 4*a*b*Sinh[x])/(2*(a + b*Sinh[x])^2))/b^3)","A",1
622,1,3430,146,6.4561217,"\int \frac{1}{(a \text{sech}(x)+b \tanh (x))^4} \, dx","Integrate[(a*Sech[x] + b*Tanh[x])^(-4),x]","\text{Result too large to show}","\frac{a \cosh ^3(x)}{2 b \left(a^2+b^2\right) (a+b \sinh (x))^2}+\frac{a \left(2 a^2+3 b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^4 \left(a^2+b^2\right)^{3/2}}-\frac{\cosh (x) \left(2 \left(a^2+b^2\right)+a b \sinh (x)\right)}{2 b^3 \left(a^2+b^2\right) (a+b \sinh (x))}-\frac{\cosh ^3(x)}{3 b (a+b \sinh (x))^3}+\frac{x}{b^4}",1,"((-I)*Sech[x]*(a + b*Sinh[x])^4*(((I/3)*b*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b))^(5/2)*((I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b))^(5/2))/((((-I)*a*b)/(a - I*b) - b^2/(a - I*b))*(((-I)*a*b)/(a + I*b) + b^2/(a + I*b))*(a + b*Sinh[x])^3) - (((I/2)*a*b^3*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b))^(5/2)*((I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b))^(5/2))/((a^2 + b^2)*(((-I)*a*b)/(a - I*b) - b^2/(a - I*b))*(((-I)*a*b)/(a + I*b) + b^2/(a + I*b))*(a + b*Sinh[x])^2) - (-(((((3*I)*a^2*b^5)/(a^2 + b^2)^2 - ((2*I)*b^5*(3*a^2 + 2*b^2))/(a^2 + b^2)^2)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b))^(5/2)*((I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b))^(5/2))/((((-I)*a*b)/(a - I*b) - b^2/(a - I*b))*(((-I)*a*b)/(a + I*b) + b^2/(a + I*b))*(a + b*Sinh[x]))) - ((16*Sqrt[2]*(a - I*b)*b^6*(3*a^2 + 4*b^2)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b))^(5/2)*Sqrt[(I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b)]*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^(5/2)*((5*(1/(2*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^2) + (1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^(-1)))/8 + (((15*I)/32)*b^3*(((-I)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b + ((a - I*b)^2*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b))^2)/(3*b^2) + ((-1)^(1/4)*Sqrt[2]*Sqrt[a - I*b]*ArcSin[((-1)^(1/4)*Sqrt[a - I*b]*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)])/(Sqrt[2]*Sqrt[b])]*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)])/(Sqrt[b]*Sqrt[1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b])))/((a - I*b)^3*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b))^3*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^2)))/(5*(a + I*b)*(a^2 + b^2)^3*Sqrt[((-I)*(a + I*b)*((I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b)))/b]) + (I*(((4*I)*a*b^7*(3*a^2 + 4*b^2))/(a^2 + b^2)^3 - (I*a*b^7*(6*a^2 + 7*b^2))/(a^2 + b^2)^3)*((-4*Sqrt[2]*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b))^(3/2)*Sqrt[(I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b)]*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^(5/2)*((3/(4*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^2) + (1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^(-1))/2 - (3*b^2*(((-I)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b + ((-1)^(1/4)*Sqrt[2]*Sqrt[a - I*b]*ArcSin[((-1)^(1/4)*Sqrt[a - I*b]*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)])/(Sqrt[2]*Sqrt[b])]*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)])/(Sqrt[b]*Sqrt[1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b])))/(8*(a - I*b)^2*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b))^2*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^2)))/(3*(a + I*b)*Sqrt[((-I)*(a + I*b)*((I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b)))/b]) - (I*((I*a*b)/(a - I*b) + b^2/(a - I*b))*(((-I)*((I*a*b)/(a - I*b) + b^2/(a - I*b))*(((-I)*((I*a*b)/(a + I*b) - b^2/(a + I*b))*(((2*I)*Sqrt[a - I*b]*ArcTanh[(Sqrt[a - I*b]*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)])/(Sqrt[a + I*b]*Sqrt[(I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b)])])/(Sqrt[a + I*b]*b) - ((2*I)*Sqrt[(I*a*b)/(a + I*b) - b^2/(a + I*b)]*ArcTanh[(Sqrt[(I*a*b)/(a + I*b) - b^2/(a + I*b)]*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)])/(Sqrt[(I*a*b)/(a - I*b) + b^2/(a - I*b)]*Sqrt[(I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b)])])/(b*Sqrt[(I*a*b)/(a - I*b) + b^2/(a - I*b)])))/b + ((2*I)*Sqrt[2]*(a - I*b)*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)]*Sqrt[(I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b)]*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^(3/2)*(-(((-1)^(3/4)*Sqrt[b]*ArcSin[((-1)^(1/4)*Sqrt[a - I*b]*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)])/(Sqrt[2]*Sqrt[b])])/(Sqrt[2]*Sqrt[a - I*b]*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)]*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^(3/2))) + 1/(2*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b))))/((a + I*b)*b*Sqrt[((-I)*(a + I*b)*((I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b)))/b])))/b - (4*Sqrt[2]*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)]*Sqrt[(I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b)]*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^(5/2)*((-3*(-1)^(3/4)*Sqrt[b]*ArcSin[((-1)^(1/4)*Sqrt[a - I*b]*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)])/(Sqrt[2]*Sqrt[b])])/(4*Sqrt[2]*Sqrt[a - I*b]*Sqrt[((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)]*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^(5/2)) + (3/(2*(1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^2) + (1 - ((I/2)*(a - I*b)*(((-I)*b)/(a - I*b) - (b*Sinh[x])/(a - I*b)))/b)^(-1))/4))/((a + I*b)*Sqrt[((-I)*(a + I*b)*((I*b)/(a + I*b) - (b*Sinh[x])/(a + I*b)))/b])))/b))/b)/((((-I)*a*b)/(a - I*b) - b^2/(a - I*b))*(((-I)*a*b)/(a + I*b) + b^2/(a + I*b))))/(2*(((-I)*a*b)/(a - I*b) - b^2/(a - I*b))*(((-I)*a*b)/(a + I*b) + b^2/(a + I*b))))/(3*(((-I)*a*b)/(a - I*b) - b^2/(a - I*b))*(((-I)*a*b)/(a + I*b) + b^2/(a + I*b)))))/((1 - (a + b*Sinh[x])/(a - I*b))^(3/2)*(1 - (a + b*Sinh[x])/(a + I*b))^(3/2)*(a*Sech[x] + b*Tanh[x])^4)","C",0
623,1,83,95,0.2508551,"\int \frac{1}{(a \text{sech}(x)+b \tanh (x))^5} \, dx","Integrate[(a*Sech[x] + b*Tanh[x])^(-5),x]","\frac{-\frac{\left(a^2+b^2\right)^2}{4 (a+b \sinh (x))^4}+\frac{4 a \left(a^2+b^2\right)}{3 (a+b \sinh (x))^3}-\frac{3 a^2+b^2}{(a+b \sinh (x))^2}+\frac{4 a}{a+b \sinh (x)}+\log (a+b \sinh (x))}{b^5}","-\frac{\left(a^2+b^2\right)^2}{4 b^5 (a+b \sinh (x))^4}+\frac{4 a \left(a^2+b^2\right)}{3 b^5 (a+b \sinh (x))^3}-\frac{3 a^2+b^2}{b^5 (a+b \sinh (x))^2}+\frac{4 a}{b^5 (a+b \sinh (x))}+\frac{\log (a+b \sinh (x))}{b^5}",1,"(Log[a + b*Sinh[x]] - (a^2 + b^2)^2/(4*(a + b*Sinh[x])^4) + (4*a*(a^2 + b^2))/(3*(a + b*Sinh[x])^3) - (3*a^2 + b^2)/(a + b*Sinh[x])^2 + (4*a)/(a + b*Sinh[x]))/b^5","A",1
624,1,62,40,0.1116023,"\int (\text{sech}(x)+i \tanh (x))^5 \, dx","Integrate[(Sech[x] + I*Tanh[x])^5,x]","-\frac{11}{4} i \tanh ^4(x)-\frac{1}{2} i \tanh ^2(x)-\frac{5}{4} i \text{sech}^4(x)+\tan ^{-1}(\sinh (x))+i \log (\cosh (x))-\tanh (x) \text{sech}^3(x)-5 \tanh ^3(x) \text{sech}(x)+\tanh (x) \text{sech}(x)","\frac{4 i}{1-i \sinh (x)}-\frac{2 i}{(1-i \sinh (x))^2}+i \log (\sinh (x)+i)",1,"ArcTan[Sinh[x]] + I*Log[Cosh[x]] - ((5*I)/4)*Sech[x]^4 + Sech[x]*Tanh[x] - Sech[x]^3*Tanh[x] - (I/2)*Tanh[x]^2 - 5*Sech[x]*Tanh[x]^3 - ((11*I)/4)*Tanh[x]^4","A",1
625,1,74,38,0.135239,"\int (\text{sech}(x)+i \tanh (x))^4 \, dx","Integrate[(Sech[x] + I*Tanh[x])^4,x]","\frac{3 (3 x-8 i) \cosh \left(\frac{x}{2}\right)+(-3 x+16 i) \cosh \left(\frac{3 x}{2}\right)-6 i \sinh \left(\frac{x}{2}\right) (2 x+x \cosh (x)-4 i)}{6 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^3}","x-\frac{2 i \cosh ^3(x)}{3 (1-i \sinh (x))^3}+\frac{2 i \cosh (x)}{1-i \sinh (x)}",1,"(3*(-8*I + 3*x)*Cosh[x/2] + (16*I - 3*x)*Cosh[(3*x)/2] - (6*I)*(-4*I + 2*x + x*Cosh[x])*Sinh[x/2])/(6*(Cosh[x/2] - I*Sinh[x/2])^3)","A",1
626,1,39,26,0.0305675,"\int (\text{sech}(x)+i \tanh (x))^3 \, dx","Integrate[(Sech[x] + I*Tanh[x])^3,x]","\frac{1}{2} i \tanh ^2(x)-\frac{3}{2} i \text{sech}^2(x)-\tan ^{-1}(\sinh (x))-i \log (\cosh (x))+2 \tanh (x) \text{sech}(x)","-\frac{2 i}{1-i \sinh (x)}-i \log (\sinh (x)+i)",1,"-ArcTan[Sinh[x]] - I*Log[Cosh[x]] - ((3*I)/2)*Sech[x]^2 + 2*Sech[x]*Tanh[x] + (I/2)*Tanh[x]^2","A",1
627,1,14,20,0.0052134,"\int (\text{sech}(x)+i \tanh (x))^2 \, dx","Integrate[(Sech[x] + I*Tanh[x])^2,x]","-x+2 \tanh (x)-2 i \text{sech}(x)","-x-\frac{2 i \cosh (x)}{1-i \sinh (x)}",1,"-x - (2*I)*Sech[x] + 2*Tanh[x]","A",1
628,1,17,11,0.0041134,"\int (\text{sech}(x)+i \tanh (x)) \, dx","Integrate[Sech[x] + I*Tanh[x],x]","2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+i \log (\cosh (x))","\tan ^{-1}(\sinh (x))+i \log (\cosh (x))",1,"2*ArcTan[Tanh[x/2]] + I*Log[Cosh[x]]","A",1
629,1,17,13,0.0165801,"\int \frac{1}{\text{sech}(x)+i \tanh (x)} \, dx","Integrate[(Sech[x] + I*Tanh[x])^(-1),x]","2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-i \log (\cosh (x))","-i \log (-\sinh (x)+i)",1,"2*ArcTan[Tanh[x/2]] - I*Log[Cosh[x]]","A",1
630,1,31,20,0.0274613,"\int \frac{1}{(\text{sech}(x)+i \tanh (x))^2} \, dx","Integrate[(Sech[x] + I*Tanh[x])^(-2),x]","-x+\frac{4 \sinh \left(\frac{x}{2}\right)}{\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)}","-x+\frac{2 i \cosh (x)}{1+i \sinh (x)}",1,"-x + (4*Sinh[x/2])/(Cosh[x/2] + I*Sinh[x/2])","A",1
631,1,40,28,0.0386337,"\int \frac{1}{(\text{sech}(x)+i \tanh (x))^3} \, dx","Integrate[(Sech[x] + I*Tanh[x])^(-3),x]","-2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+i \log (\cosh (x))+\frac{2 i}{\left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^2}","\frac{2 i}{1+i \sinh (x)}+i \log (-\sinh (x)+i)",1,"-2*ArcTan[Tanh[x/2]] + I*Log[Cosh[x]] + (2*I)/(Cosh[x/2] + I*Sinh[x/2])^2","A",1
632,1,75,38,0.0811983,"\int \frac{1}{(\text{sech}(x)+i \tanh (x))^4} \, dx","Integrate[(Sech[x] + I*Tanh[x])^(-4),x]","\frac{3 (3 x+8 i) \cosh \left(\frac{x}{2}\right)-(3 x+16 i) \cosh \left(\frac{3 x}{2}\right)+6 i \sinh \left(\frac{x}{2}\right) (2 x+x \cosh (x)+4 i)}{6 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^3}","x+\frac{2 i \cosh ^3(x)}{3 (1+i \sinh (x))^3}-\frac{2 i \cosh (x)}{1+i \sinh (x)}",1,"(3*(8*I + 3*x)*Cosh[x/2] - (16*I + 3*x)*Cosh[(3*x)/2] + (6*I)*(4*I + 2*x + x*Cosh[x])*Sinh[x/2])/(6*(Cosh[x/2] + I*Sinh[x/2])^3)","A",1
633,1,45,42,0.1077858,"\int \frac{1}{(\text{sech}(x)+i \tanh (x))^5} \, dx","Integrate[(Sech[x] + I*Tanh[x])^(-5),x]","2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-i \log (\cosh (x))+\frac{4 \sinh (x)-2 i}{\left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^4}","-\frac{4 i}{1+i \sinh (x)}+\frac{2 i}{(1+i \sinh (x))^2}-i \log (-\sinh (x)+i)",1,"2*ArcTan[Tanh[x/2]] - I*Log[Cosh[x]] + (-2*I + 4*Sinh[x])/(Cosh[x/2] + I*Sinh[x/2])^4","A",1
634,1,62,42,0.0599267,"\int (\text{sech}(x)-i \tanh (x))^5 \, dx","Integrate[(Sech[x] - I*Tanh[x])^5,x]","\frac{11}{4} i \tanh ^4(x)+\frac{1}{2} i \tanh ^2(x)+\frac{5}{4} i \text{sech}^4(x)+\tan ^{-1}(\sinh (x))-i \log (\cosh (x))-\tanh (x) \text{sech}^3(x)-5 \tanh ^3(x) \text{sech}(x)+\tanh (x) \text{sech}(x)","-\frac{4 i}{1+i \sinh (x)}+\frac{2 i}{(1+i \sinh (x))^2}-i \log (-\sinh (x)+i)",1,"ArcTan[Sinh[x]] - I*Log[Cosh[x]] + ((5*I)/4)*Sech[x]^4 + Sech[x]*Tanh[x] - Sech[x]^3*Tanh[x] + (I/2)*Tanh[x]^2 - 5*Sech[x]*Tanh[x]^3 + ((11*I)/4)*Tanh[x]^4","A",1
635,1,75,38,0.0538762,"\int (\text{sech}(x)-i \tanh (x))^4 \, dx","Integrate[(Sech[x] - I*Tanh[x])^4,x]","\frac{3 (3 x+8 i) \cosh \left(\frac{x}{2}\right)-(3 x+16 i) \cosh \left(\frac{3 x}{2}\right)+6 i \sinh \left(\frac{x}{2}\right) (2 x+x \cosh (x)+4 i)}{6 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^3}","x+\frac{2 i \cosh ^3(x)}{3 (1+i \sinh (x))^3}-\frac{2 i \cosh (x)}{1+i \sinh (x)}",1,"(3*(8*I + 3*x)*Cosh[x/2] - (16*I + 3*x)*Cosh[(3*x)/2] + (6*I)*(4*I + 2*x + x*Cosh[x])*Sinh[x/2])/(6*(Cosh[x/2] + I*Sinh[x/2])^3)","A",1
636,1,39,28,0.0286981,"\int (\text{sech}(x)-i \tanh (x))^3 \, dx","Integrate[(Sech[x] - I*Tanh[x])^3,x]","-\frac{1}{2} i \tanh ^2(x)+\frac{3}{2} i \text{sech}^2(x)-\tan ^{-1}(\sinh (x))+i \log (\cosh (x))+2 \tanh (x) \text{sech}(x)","\frac{2 i}{1+i \sinh (x)}+i \log (-\sinh (x)+i)",1,"-ArcTan[Sinh[x]] + I*Log[Cosh[x]] + ((3*I)/2)*Sech[x]^2 + 2*Sech[x]*Tanh[x] - (I/2)*Tanh[x]^2","A",1
637,1,14,20,0.0052302,"\int (\text{sech}(x)-i \tanh (x))^2 \, dx","Integrate[(Sech[x] - I*Tanh[x])^2,x]","-x+2 \tanh (x)+2 i \text{sech}(x)","-x+\frac{2 i \cosh (x)}{1+i \sinh (x)}",1,"-x + (2*I)*Sech[x] + 2*Tanh[x]","A",1
638,1,17,11,0.0043469,"\int (\text{sech}(x)-i \tanh (x)) \, dx","Integrate[Sech[x] - I*Tanh[x],x]","2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-i \log (\cosh (x))","\tan ^{-1}(\sinh (x))-i \log (\cosh (x))",1,"2*ArcTan[Tanh[x/2]] - I*Log[Cosh[x]]","A",1
639,1,17,11,0.0173243,"\int \frac{1}{\text{sech}(x)-i \tanh (x)} \, dx","Integrate[(Sech[x] - I*Tanh[x])^(-1),x]","2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+i \log (\cosh (x))","i \log (\sinh (x)+i)",1,"2*ArcTan[Tanh[x/2]] + I*Log[Cosh[x]]","A",1
640,1,31,20,0.0281713,"\int \frac{1}{(\text{sech}(x)-i \tanh (x))^2} \, dx","Integrate[(Sech[x] - I*Tanh[x])^(-2),x]","-x+\frac{4 \sinh \left(\frac{x}{2}\right)}{\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)}","-x-\frac{2 i \cosh (x)}{1-i \sinh (x)}",1,"-x + (4*Sinh[x/2])/(Cosh[x/2] - I*Sinh[x/2])","A",1
641,1,27,26,0.0394369,"\int \frac{1}{(\text{sech}(x)-i \tanh (x))^3} \, dx","Integrate[(Sech[x] - I*Tanh[x])^(-3),x]","\frac{2}{\sinh (x)+i}-2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-i \log (\cosh (x))","-\frac{2 i}{1-i \sinh (x)}-i \log (\sinh (x)+i)",1,"-2*ArcTan[Tanh[x/2]] - I*Log[Cosh[x]] + 2/(I + Sinh[x])","A",1
642,1,74,38,0.0663801,"\int \frac{1}{(\text{sech}(x)-i \tanh (x))^4} \, dx","Integrate[(Sech[x] - I*Tanh[x])^(-4),x]","\frac{3 (3 x-8 i) \cosh \left(\frac{x}{2}\right)+(-3 x+16 i) \cosh \left(\frac{3 x}{2}\right)-6 i \sinh \left(\frac{x}{2}\right) (2 x+x \cosh (x)-4 i)}{6 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^3}","x-\frac{2 i \cosh ^3(x)}{3 (1-i \sinh (x))^3}+\frac{2 i \cosh (x)}{1-i \sinh (x)}",1,"(3*(-8*I + 3*x)*Cosh[x/2] + (16*I - 3*x)*Cosh[(3*x)/2] - (6*I)*(-4*I + 2*x + x*Cosh[x])*Sinh[x/2])/(6*(Cosh[x/2] - I*Sinh[x/2])^3)","A",1
643,1,45,40,0.1041653,"\int \frac{1}{(\text{sech}(x)-i \tanh (x))^5} \, dx","Integrate[(Sech[x] - I*Tanh[x])^(-5),x]","2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+i \log (\cosh (x))+\frac{4 \sinh (x)+2 i}{\left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^4}","\frac{4 i}{1-i \sinh (x)}-\frac{2 i}{(1-i \sinh (x))^2}+i \log (\sinh (x)+i)",1,"2*ArcTan[Tanh[x/2]] + I*Log[Cosh[x]] + (2*I + 4*Sinh[x])/(Cosh[x/2] - I*Sinh[x/2])^4","A",1
644,1,244,124,0.4740213,"\int (a \coth (x)+b \text{csch}(x))^5 \, dx","Integrate[(a*Coth[x] + b*Csch[x])^5,x]","-\frac{1}{64} \text{csch}^4(x) \left(-24 a^5 \log (\sinh (x))-8 a^5 \cosh (4 x) \log (\sinh (x))-16 a^5+50 a^4 b \cosh (3 x)-45 a^4 b \log \left(\tanh \left(\frac{x}{2}\right)\right)-15 a^4 b \cosh (4 x) \log \left(\tanh \left(\frac{x}{2}\right)\right)+20 a^2 b^3 \cosh (3 x)+30 a^2 b^3 \log \left(\tanh \left(\frac{x}{2}\right)\right)+10 a^2 b^3 \cosh (4 x) \log \left(\tanh \left(\frac{x}{2}\right)\right)+2 b \left(15 a^4+70 a^2 b^2+11 b^4\right) \cosh (x)+4 \cosh (2 x) \left(8 a^5 \log (\sinh (x))+8 \left(a^5+5 a^3 b^2\right)+b \left(15 a^4-10 a^2 b^2+3 b^4\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)+80 a b^4-6 b^5 \cosh (3 x)-9 b^5 \log \left(\tanh \left(\frac{x}{2}\right)\right)-3 b^5 \cosh (4 x) \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)","a^5 \log (\sinh (x))+\frac{1}{8} a^2 b \left(7 a^2-3 b^2\right) \cosh (x)-\frac{1}{8} \text{csch}^2(x) (a \cosh (x)+b)^2 \left(b \left(5 a^2-3 b^2\right) \cosh (x)+2 a \left(2 a^2-b^2\right)\right)-\frac{1}{8} b \left(15 a^4-10 a^2 b^2+3 b^4\right) \tanh ^{-1}(\cosh (x))-\frac{1}{4} \text{csch}^4(x) (a \cosh (x)+b)^4 (a+b \cosh (x))",1,"-1/64*(Csch[x]^4*(-16*a^5 + 80*a*b^4 + 2*b*(15*a^4 + 70*a^2*b^2 + 11*b^4)*Cosh[x] + 50*a^4*b*Cosh[3*x] + 20*a^2*b^3*Cosh[3*x] - 6*b^5*Cosh[3*x] - 24*a^5*Log[Sinh[x]] - 8*a^5*Cosh[4*x]*Log[Sinh[x]] - 45*a^4*b*Log[Tanh[x/2]] + 30*a^2*b^3*Log[Tanh[x/2]] - 9*b^5*Log[Tanh[x/2]] - 15*a^4*b*Cosh[4*x]*Log[Tanh[x/2]] + 10*a^2*b^3*Cosh[4*x]*Log[Tanh[x/2]] - 3*b^5*Cosh[4*x]*Log[Tanh[x/2]] + 4*Cosh[2*x]*(8*(a^5 + 5*a^3*b^2) + 8*a^5*Log[Sinh[x]] + b*(15*a^4 - 10*a^2*b^2 + 3*b^4)*Log[Tanh[x/2]])))","A",1
645,1,95,101,0.2766848,"\int (a \coth (x)+b \text{csch}(x))^4 \, dx","Integrate[(a*Coth[x] + b*Csch[x])^4,x]","-\frac{1}{12} \text{csch}^3(x) \left(9 a^4 x \sinh (x)-3 a^4 x \sinh (3 x)+4 a^4 \cosh (3 x)+24 a^3 b \cosh (2 x)-8 a^3 b+6 a^2 b^2 \cosh (3 x)+6 b^2 \left(3 a^2+b^2\right) \cosh (x)+16 a b^3-2 b^4 \cosh (3 x)\right)","a^4 x+\frac{4}{3} a b \left(2 a^2-b^2\right) \sinh (x)+\frac{1}{3} a^2 \left(3 a^2-2 b^2\right) \sinh (x) \cosh (x)-\frac{1}{3} \text{csch}(x) (a \cosh (x)+b)^2 \left(\left(3 a^2-2 b^2\right) \cosh (x)+a b\right)-\frac{1}{3} \text{csch}^3(x) (a \cosh (x)+b)^3 (a+b \cosh (x))",1,"-1/12*(Csch[x]^3*(-8*a^3*b + 16*a*b^3 + 6*b^2*(3*a^2 + b^2)*Cosh[x] + 24*a^3*b*Cosh[2*x] + 4*a^4*Cosh[3*x] + 6*a^2*b^2*Cosh[3*x] - 2*b^4*Cosh[3*x] + 9*a^4*x*Sinh[x] - 3*a^4*x*Sinh[3*x]))","A",1
646,1,99,59,0.2531034,"\int (a \coth (x)+b \text{csch}(x))^3 \, dx","Integrate[(a*Coth[x] + b*Csch[x])^3,x]","-\frac{1}{4} \text{csch}^2(x) \left(2 a^3 \log (\sinh (x))+2 a^3+2 b \left(3 a^2+b^2\right) \cosh (x)+3 a^2 b \log \left(\tanh \left(\frac{x}{2}\right)\right)+\cosh (2 x) \left(b \left(b^2-3 a^2\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)-2 a^3 \log (\sinh (x))\right)+6 a b^2-b^3 \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)","a^3 \log (\sinh (x))-\frac{1}{2} b \left(3 a^2-b^2\right) \tanh ^{-1}(\cosh (x))+\frac{1}{2} a^2 b \cosh (x)-\frac{1}{2} \text{csch}^2(x) (a \cosh (x)+b)^2 (a+b \cosh (x))",1,"-1/4*(Csch[x]^2*(2*a^3 + 6*a*b^2 + 2*b*(3*a^2 + b^2)*Cosh[x] + 2*a^3*Log[Sinh[x]] + 3*a^2*b*Log[Tanh[x/2]] - b^3*Log[Tanh[x/2]] + Cosh[2*x]*(-2*a^3*Log[Sinh[x]] + b*(-3*a^2 + b^2)*Log[Tanh[x/2]])))","A",1
647,1,23,27,0.1281104,"\int (a \coth (x)+b \text{csch}(x))^2 \, dx","Integrate[(a*Coth[x] + b*Csch[x])^2,x]","a (a x-2 b \text{csch}(x))-\left(a^2+b^2\right) \coth (x)","a^2 x+a b \sinh (x)-\text{csch}(x) (a \cosh (x)+b) (a+b \cosh (x))",1,"-((a^2 + b^2)*Coth[x]) + a*(a*x - 2*b*Csch[x])","A",1
648,1,15,12,0.0040385,"\int (a \coth (x)+b \text{csch}(x)) \, dx","Integrate[a*Coth[x] + b*Csch[x],x]","a \log (\sinh (x))+b \log \left(\tanh \left(\frac{x}{2}\right)\right)","a \log (\sinh (x))-b \tanh ^{-1}(\cosh (x))",1,"a*Log[Sinh[x]] + b*Log[Tanh[x/2]]","A",1
649,1,11,11,0.0187306,"\int \frac{1}{a \coth (x)+b \text{csch}(x)} \, dx","Integrate[(a*Coth[x] + b*Csch[x])^(-1),x]","\frac{\log (a \cosh (x)+b)}{a}","\frac{\log (a \cosh (x)+b)}{a}",1,"Log[b + a*Cosh[x]]/a","A",1
650,1,61,67,0.3485939,"\int \frac{1}{(a \coth (x)+b \text{csch}(x))^2} \, dx","Integrate[(a*Coth[x] + b*Csch[x])^(-2),x]","\frac{\frac{2 b \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-\frac{a \sinh (x)}{a \cosh (x)+b}+x}{a^2}","-\frac{2 b \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^2 \sqrt{a-b} \sqrt{a+b}}+\frac{x}{a^2}-\frac{\sinh (x)}{a (a \cosh (x)+b)}",1,"(x + (2*b*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] - (a*Sinh[x])/(b + a*Cosh[x]))/a^2","A",1
651,1,77,50,0.1130128,"\int \frac{1}{(a \coth (x)+b \text{csch}(x))^3} \, dx","Integrate[(a*Coth[x] + b*Csch[x])^(-3),x]","\frac{a^2 \cosh (2 x) \log (a \cosh (x)+b)+a^2 \log (a \cosh (x)+b)+a^2+2 b^2 \log (a \cosh (x)+b)+4 a b \cosh (x) (\log (a \cosh (x)+b)+1)+3 b^2}{2 a^3 (a \cosh (x)+b)^2}","\frac{2 b}{a^3 (a \cosh (x)+b)}+\frac{\log (a \cosh (x)+b)}{a^3}+\frac{a^2-b^2}{2 a^3 (a \cosh (x)+b)^2}",1,"(a^2 + 3*b^2 + a^2*Log[b + a*Cosh[x]] + 2*b^2*Log[b + a*Cosh[x]] + a^2*Cosh[2*x]*Log[b + a*Cosh[x]] + 4*a*b*Cosh[x]*(1 + Log[b + a*Cosh[x]]))/(2*a^3*(b + a*Cosh[x])^2)","A",1
652,1,150,159,0.4683854,"\int \frac{1}{(a \coth (x)+b \text{csch}(x))^4} \, dx","Integrate[(a*Coth[x] + b*Csch[x])^(-4),x]","\frac{\sinh (x) \left(-\frac{a \left(8 a^2-11 b^2\right) (a \cosh (x)+b)^2}{(a-b) (a+b)}-\frac{6 b \left(2 b^2-3 a^2\right) \text{csch}(x) (a \cosh (x)+b)^3 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}+2 a \left(a^2-b^2\right)+7 a b (a \cosh (x)+b)+6 x \text{csch}(x) (a \cosh (x)+b)^3\right)}{6 a^4 (a \cosh (x)+b)^3}","\frac{x}{a^4}-\frac{b \sinh ^3(x)}{2 a \left(a^2-b^2\right) (a \cosh (x)+b)^2}-\frac{b \left(3 a^2-2 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^4 (a-b)^{3/2} (a+b)^{3/2}}-\frac{\sinh (x) \left(2 \left(a^2-b^2\right)-a b \cosh (x)\right)}{2 a^3 \left(a^2-b^2\right) (a \cosh (x)+b)}-\frac{\sinh ^3(x)}{3 a (a \cosh (x)+b)^3}",1,"((2*a*(a^2 - b^2) + 7*a*b*(b + a*Cosh[x]) - (a*(8*a^2 - 11*b^2)*(b + a*Cosh[x])^2)/((a - b)*(a + b)) + 6*x*(b + a*Cosh[x])^3*Csch[x] - (6*b*(-3*a^2 + 2*b^2)*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]]*(b + a*Cosh[x])^3*Csch[x])/(a^2 - b^2)^(3/2))*Sinh[x])/(6*a^4*(b + a*Cosh[x])^3)","A",1
653,1,138,98,0.3159516,"\int \frac{1}{(a \coth (x)+b \text{csch}(x))^5} \, dx","Integrate[(a*Coth[x] + b*Csch[x])^(-5),x]","\frac{12 a^4 \cosh ^4(x) \log (a \cosh (x)+b)-3 a^4+48 a^3 b \cosh ^3(x) (\log (a \cosh (x)+b)+1)+12 a^2 \cosh ^2(x) \left(a^2+6 b^2 \log (a \cosh (x)+b)+9 b^2\right)+8 a b \cosh (x) \left(a^2+6 b^2 \log (a \cosh (x)+b)+11 b^2\right)+2 a^2 b^2+12 b^4 \log (a \cosh (x)+b)+25 b^4}{12 a^5 (a \cosh (x)+b)^4}","\frac{4 b}{a^5 (a \cosh (x)+b)}+\frac{\log (a \cosh (x)+b)}{a^5}-\frac{\left(a^2-b^2\right)^2}{4 a^5 (a \cosh (x)+b)^4}-\frac{4 b \left(a^2-b^2\right)}{3 a^5 (a \cosh (x)+b)^3}+\frac{a^2-3 b^2}{a^5 (a \cosh (x)+b)^2}",1,"(-3*a^4 + 2*a^2*b^2 + 25*b^4 + 12*b^4*Log[b + a*Cosh[x]] + 12*a^4*Cosh[x]^4*Log[b + a*Cosh[x]] + 48*a^3*b*Cosh[x]^3*(1 + Log[b + a*Cosh[x]]) + 12*a^2*Cosh[x]^2*(a^2 + 9*b^2 + 6*b^2*Log[b + a*Cosh[x]]) + 8*a*b*Cosh[x]*(a^2 + 11*b^2 + 6*b^2*Log[b + a*Cosh[x]]))/(12*a^5*(b + a*Cosh[x])^4)","A",1
654,1,53,28,0.0910143,"\int (\coth (x)+\text{csch}(x))^5 \, dx","Integrate[(Coth[x] + Csch[x])^5,x]","-\frac{1}{2} \text{csch}^4\left(\frac{x}{2}\right)-2 \text{csch}^2\left(\frac{x}{2}\right)+6 \log \left(\sinh \left(\frac{x}{2}\right)\right)+\log (\sinh (x))-5 \log \left(\tanh \left(\frac{x}{2}\right)\right)-6 \log \left(\cosh \left(\frac{x}{2}\right)\right)","\frac{4}{1-\cosh (x)}-\frac{2}{(1-\cosh (x))^2}+\log (1-\cosh (x))",1,"-2*Csch[x/2]^2 - Csch[x/2]^4/2 - 6*Log[Cosh[x/2]] + 6*Log[Sinh[x/2]] + Log[Sinh[x]] - 5*Log[Tanh[x/2]]","A",1
655,1,30,30,0.0544366,"\int (\coth (x)+\text{csch}(x))^4 \, dx","Integrate[(Coth[x] + Csch[x])^4,x]","x-\frac{8}{3} \coth \left(\frac{x}{2}\right)-\frac{2}{3} \coth \left(\frac{x}{2}\right) \text{csch}^2\left(\frac{x}{2}\right)","x+\frac{2 \sinh ^3(x)}{3 (1-\cosh (x))^3}+\frac{2 \sinh (x)}{1-\cosh (x)}",1,"x - (8*Coth[x/2])/3 - (2*Coth[x/2]*Csch[x/2]^2)/3","A",1
656,1,41,18,0.0525695,"\int (\coth (x)+\text{csch}(x))^3 \, dx","Integrate[(Coth[x] + Csch[x])^3,x]","-\text{csch}^2\left(\frac{x}{2}\right)-2 \log \left(\sinh \left(\frac{x}{2}\right)\right)+\log (\sinh (x))+3 \log \left(\tanh \left(\frac{x}{2}\right)\right)+2 \log \left(\cosh \left(\frac{x}{2}\right)\right)","\frac{2}{1-\cosh (x)}+\log (1-\cosh (x))",1,"-Csch[x/2]^2 + 2*Log[Cosh[x/2]] - 2*Log[Sinh[x/2]] + Log[Sinh[x]] + 3*Log[Tanh[x/2]]","B",1
657,1,10,14,0.0257569,"\int (\coth (x)+\text{csch}(x))^2 \, dx","Integrate[(Coth[x] + Csch[x])^2,x]","x-2 \coth \left(\frac{x}{2}\right)","x+\frac{2 \sinh (x)}{1-\cosh (x)}",1,"x - 2*Coth[x/2]","A",1
658,1,11,9,0.003499,"\int (\coth (x)+\text{csch}(x)) \, dx","Integrate[Coth[x] + Csch[x],x]","\log (\sinh (x))+\log \left(\tanh \left(\frac{x}{2}\right)\right)","\log (\sinh (x))-\tanh ^{-1}(\cosh (x))",1,"Log[Sinh[x]] + Log[Tanh[x/2]]","A",1
659,1,9,5,0.0203021,"\int \frac{1}{\coth (x)+\text{csch}(x)} \, dx","Integrate[(Coth[x] + Csch[x])^(-1),x]","2 \log \left(\cosh \left(\frac{x}{2}\right)\right)","\log (\cosh (x)+1)",1,"2*Log[Cosh[x/2]]","A",1
660,1,10,12,0.0207692,"\int \frac{1}{(\coth (x)+\text{csch}(x))^2} \, dx","Integrate[(Coth[x] + Csch[x])^(-2),x]","x-2 \tanh \left(\frac{x}{2}\right)","x-\frac{2 \sinh (x)}{\cosh (x)+1}",1,"x - 2*Tanh[x/2]","A",1
661,1,18,14,0.0220936,"\int \frac{1}{(\coth (x)+\text{csch}(x))^3} \, dx","Integrate[(Coth[x] + Csch[x])^(-3),x]","\text{sech}^2\left(\frac{x}{2}\right)+2 \log \left(\cosh \left(\frac{x}{2}\right)\right)","\frac{2}{\cosh (x)+1}+\log (\cosh (x)+1)",1,"2*Log[Cosh[x/2]] + Sech[x/2]^2","A",1
662,1,30,26,0.0218202,"\int \frac{1}{(\coth (x)+\text{csch}(x))^4} \, dx","Integrate[(Coth[x] + Csch[x])^(-4),x]","x-\frac{8}{3} \tanh \left(\frac{x}{2}\right)+\frac{2}{3} \tanh \left(\frac{x}{2}\right) \text{sech}^2\left(\frac{x}{2}\right)","x-\frac{2 \sinh ^3(x)}{3 (\cosh (x)+1)^3}-\frac{2 \sinh (x)}{\cosh (x)+1}",1,"x - (8*Tanh[x/2])/3 + (2*Sech[x/2]^2*Tanh[x/2])/3","A",1
663,1,32,22,0.0214268,"\int \frac{1}{(\coth (x)+\text{csch}(x))^5} \, dx","Integrate[(Coth[x] + Csch[x])^(-5),x]","-\frac{1}{2} \text{sech}^4\left(\frac{x}{2}\right)+2 \text{sech}^2\left(\frac{x}{2}\right)+2 \log \left(\cosh \left(\frac{x}{2}\right)\right)","\frac{4}{\cosh (x)+1}-\frac{2}{(\cosh (x)+1)^2}+\log (\cosh (x)+1)",1,"2*Log[Cosh[x/2]] + 2*Sech[x/2]^2 - Sech[x/2]^4/2","A",1
664,1,55,24,0.0858342,"\int (-\coth (x)+\text{csch}(x))^5 \, dx","Integrate[(-Coth[x] + Csch[x])^5,x]","\frac{1}{2} \text{sech}^4\left(\frac{x}{2}\right)-2 \text{sech}^2\left(\frac{x}{2}\right)+6 \log \left(\sinh \left(\frac{x}{2}\right)\right)-\log (\sinh (x))-5 \log \left(\tanh \left(\frac{x}{2}\right)\right)-6 \log \left(\cosh \left(\frac{x}{2}\right)\right)","-\frac{4}{\cosh (x)+1}+\frac{2}{(\cosh (x)+1)^2}-\log (\cosh (x)+1)",1,"-6*Log[Cosh[x/2]] + 6*Log[Sinh[x/2]] - Log[Sinh[x]] - 5*Log[Tanh[x/2]] - 2*Sech[x/2]^2 + Sech[x/2]^4/2","B",1
665,1,30,26,0.0078205,"\int (-\coth (x)+\text{csch}(x))^4 \, dx","Integrate[(-Coth[x] + Csch[x])^4,x]","2 \tanh ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-\frac{2}{3} \tanh ^3\left(\frac{x}{2}\right)-2 \tanh \left(\frac{x}{2}\right)","x-\frac{2 \sinh ^3(x)}{3 (\cosh (x)+1)^3}-\frac{2 \sinh (x)}{\cosh (x)+1}",1,"2*ArcTanh[Tanh[x/2]] - 2*Tanh[x/2] - (2*Tanh[x/2]^3)/3","A",1
666,1,43,16,0.0545526,"\int (-\coth (x)+\text{csch}(x))^3 \, dx","Integrate[(-Coth[x] + Csch[x])^3,x]","-\text{sech}^2\left(\frac{x}{2}\right)-2 \log \left(\sinh \left(\frac{x}{2}\right)\right)-\log (\sinh (x))+3 \log \left(\tanh \left(\frac{x}{2}\right)\right)+2 \log \left(\cosh \left(\frac{x}{2}\right)\right)","-\frac{2}{\cosh (x)+1}-\log (\cosh (x)+1)",1,"2*Log[Cosh[x/2]] - 2*Log[Sinh[x/2]] - Log[Sinh[x]] + 3*Log[Tanh[x/2]] - Sech[x/2]^2","B",1
667,1,18,12,0.0054417,"\int (-\coth (x)+\text{csch}(x))^2 \, dx","Integrate[(-Coth[x] + Csch[x])^2,x]","2 \tanh ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-2 \tanh \left(\frac{x}{2}\right)","x-\frac{2 \sinh (x)}{\cosh (x)+1}",1,"2*ArcTanh[Tanh[x/2]] - 2*Tanh[x/2]","A",1
668,1,13,11,0.0052052,"\int (-\coth (x)+\text{csch}(x)) \, dx","Integrate[-Coth[x] + Csch[x],x]","\log \left(\tanh \left(\frac{x}{2}\right)\right)-\log (\sinh (x))","-\log (\sinh (x))-\tanh ^{-1}(\cosh (x))",1,"-Log[Sinh[x]] + Log[Tanh[x/2]]","A",1
669,1,9,9,0.0215877,"\int \frac{1}{-\coth (x)+\text{csch}(x)} \, dx","Integrate[(-Coth[x] + Csch[x])^(-1),x]","-2 \log \left(\sinh \left(\frac{x}{2}\right)\right)","-\log (1-\cosh (x))",1,"-2*Log[Sinh[x/2]]","A",1
670,1,24,14,0.0090904,"\int \frac{1}{(-\coth (x)+\text{csch}(x))^2} \, dx","Integrate[(-Coth[x] + Csch[x])^(-2),x]","-2 \coth \left(\frac{x}{2}\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\tanh ^2\left(\frac{x}{2}\right)\right)","x+\frac{2 \sinh (x)}{1-\cosh (x)}",1,"-2*Coth[x/2]*Hypergeometric2F1[-1/2, 1, 1/2, Tanh[x/2]^2]","C",1
671,1,18,20,0.0252279,"\int \frac{1}{(-\coth (x)+\text{csch}(x))^3} \, dx","Integrate[(-Coth[x] + Csch[x])^(-3),x]","\text{csch}^2\left(\frac{x}{2}\right)-2 \log \left(\sinh \left(\frac{x}{2}\right)\right)","-\frac{2}{1-\cosh (x)}-\log (1-\cosh (x))",1,"Csch[x/2]^2 - 2*Log[Sinh[x/2]]","A",1
672,1,28,30,0.0083147,"\int \frac{1}{(-\coth (x)+\text{csch}(x))^4} \, dx","Integrate[(-Coth[x] + Csch[x])^(-4),x]","-\frac{2}{3} \coth ^3\left(\frac{x}{2}\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\tanh ^2\left(\frac{x}{2}\right)\right)","x+\frac{2 \sinh ^3(x)}{3 (1-\cosh (x))^3}+\frac{2 \sinh (x)}{1-\cosh (x)}",1,"(-2*Coth[x/2]^3*Hypergeometric2F1[-3/2, 1, -1/2, Tanh[x/2]^2])/3","C",1
673,1,32,30,0.0243248,"\int \frac{1}{(-\coth (x)+\text{csch}(x))^5} \, dx","Integrate[(-Coth[x] + Csch[x])^(-5),x]","\frac{1}{2} \text{csch}^4\left(\frac{x}{2}\right)+2 \text{csch}^2\left(\frac{x}{2}\right)-2 \log \left(\sinh \left(\frac{x}{2}\right)\right)","-\frac{4}{1-\cosh (x)}+\frac{2}{(1-\cosh (x))^2}-\log (1-\cosh (x))",1,"2*Csch[x/2]^2 + Csch[x/2]^4/2 - 2*Log[Sinh[x/2]]","A",1
674,1,10,8,0.0040427,"\int (\text{csch}(x)+\sinh (x)) \, dx","Integrate[Csch[x] + Sinh[x],x]","\cosh (x)+\log \left(\tanh \left(\frac{x}{2}\right)\right)","\cosh (x)-\tanh ^{-1}(\cosh (x))",1,"Cosh[x] + Log[Tanh[x/2]]","A",1
675,1,18,22,0.0043488,"\int (\text{csch}(x)+\sinh (x))^2 \, dx","Integrate[(Csch[x] + Sinh[x])^2,x]","\frac{3 x}{2}+\frac{1}{4} \sinh (2 x)-\coth (x)","\frac{3 x}{2}-\frac{3 \coth (x)}{2}+\frac{1}{2} \cosh ^2(x) \coth (x)",1,"(3*x)/2 - Coth[x] + Sinh[2*x]/4","A",1
676,1,45,34,0.0713746,"\int (\text{csch}(x)+\sinh (x))^3 \, dx","Integrate[(Csch[x] + Sinh[x])^3,x]","\frac{1}{48} \text{csch}^2(x) \left(-50 \cosh (x)+25 \cosh (3 x)+\cosh (5 x)-60 \log \left(\tanh \left(\frac{x}{2}\right)\right)+60 \cosh (2 x) \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)","\frac{5 \cosh ^3(x)}{6}+\frac{5 \cosh (x)}{2}-\frac{1}{2} \cosh ^3(x) \coth ^2(x)-\frac{5}{2} \tanh ^{-1}(\cosh (x))",1,"(Csch[x]^2*(-50*Cosh[x] + 25*Cosh[3*x] + Cosh[5*x] - 60*Log[Tanh[x/2]] + 60*Cosh[2*x]*Log[Tanh[x/2]]))/48","A",1
677,1,35,13,0.0699127,"\int \sqrt{\text{csch}(x)+\sinh (x)} \, dx","Integrate[Sqrt[Csch[x] + Sinh[x]],x]","\frac{2 \left(\sqrt[4]{-\sinh ^2(x)}-1\right) \tanh (x) \sqrt{\cosh (x) \coth (x)}}{\sqrt[4]{-\sinh ^2(x)}}","2 \tanh (x) \sqrt{\cosh (x) \coth (x)}",1,"(2*Sqrt[Cosh[x]*Coth[x]]*(-1 + (-Sinh[x]^2)^(1/4))*Tanh[x])/(-Sinh[x]^2)^(1/4)","B",1
678,1,21,31,0.0518491,"\int (\text{csch}(x)+\sinh (x))^{3/2} \, dx","Integrate[(Csch[x] + Sinh[x])^(3/2),x]","\frac{2}{3} \left(\cosh ^2(x)-4\right) \text{sech}(x) \sqrt{\cosh (x) \coth (x)}","\frac{2}{3} \cosh (x) \sqrt{\cosh (x) \coth (x)}-\frac{8}{3} \text{sech}(x) \sqrt{\cosh (x) \coth (x)}",1,"(2*(-4 + Cosh[x]^2)*Sqrt[Cosh[x]*Coth[x]]*Sech[x])/3","A",1
679,1,44,50,0.324864,"\int (\text{csch}(x)+\sinh (x))^{5/2} \, dx","Integrate[(Csch[x] + Sinh[x])^(5/2),x]","\frac{1}{15} \sqrt{\cosh (x) \coth (x)} \left(64 \tanh (x)-10 \coth (x)+6 \sinh (x) \cosh (x)+57 \left(-\sinh ^2(x)\right)^{3/4} \text{csch}(x) \text{sech}(x)\right)","\frac{2}{5} \cosh ^2(x) \coth (x) \sqrt{\cosh (x) \coth (x)}-\frac{16}{15} \coth (x) \sqrt{\cosh (x) \coth (x)}+\frac{64}{15} \tanh (x) \sqrt{\cosh (x) \coth (x)}",1,"(Sqrt[Cosh[x]*Coth[x]]*(-10*Coth[x] + 6*Cosh[x]*Sinh[x] + 57*Csch[x]*Sech[x]*(-Sinh[x]^2)^(3/4) + 64*Tanh[x]))/15","A",1
680,1,14,8,0.0045588,"\int (-\cosh (x)+\text{sech}(x)) \, dx","Integrate[-Cosh[x] + Sech[x],x]","2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-\sinh (x)","\tan ^{-1}(\sinh (x))-\sinh (x)",1,"2*ArcTan[Tanh[x/2]] - Sinh[x]","A",1
681,1,16,22,0.0293918,"\int (-\cosh (x)+\text{sech}(x))^2 \, dx","Integrate[(-Cosh[x] + Sech[x])^2,x]","-\frac{3 x}{2}+\frac{1}{4} \sinh (2 x)+\tanh (x)","-\frac{3 x}{2}+\frac{3 \tanh (x)}{2}+\frac{1}{2} \sinh ^2(x) \tanh (x)",1,"(-3*x)/2 + Sinh[2*x]/4 + Tanh[x]","A",1
682,1,37,34,0.0286873,"\int (-\cosh (x)+\text{sech}(x))^3 \, dx","Integrate[(-Cosh[x] + Sech[x])^3,x]","-\frac{1}{48} \text{sech}^2(x) \left(-50 \sinh (x)-25 \sinh (3 x)+\sinh (5 x)+60 \tan ^{-1}(\sinh (x))+60 \cosh (2 x) \tan ^{-1}(\sinh (x))\right)","-\frac{5 \sinh ^3(x)}{6}+\frac{5 \sinh (x)}{2}+\frac{1}{2} \sinh ^3(x) \tanh ^2(x)-\frac{5}{2} \tan ^{-1}(\sinh (x))",1,"-1/48*(Sech[x]^2*(60*ArcTan[Sinh[x]] + 60*ArcTan[Sinh[x]]*Cosh[2*x] - 50*Sinh[x] - 25*Sinh[3*x] + Sinh[5*x]))","A",1
683,1,14,14,0.0555534,"\int \sqrt{-\cosh (x)+\text{sech}(x)} \, dx","Integrate[Sqrt[-Cosh[x] + Sech[x]],x]","2 \coth (x) \sqrt{-\sinh (x) \tanh (x)}","2 \coth (x) \sqrt{-\sinh (x) \tanh (x)}",1,"2*Coth[x]*Sqrt[-(Sinh[x]*Tanh[x])]","A",1
684,1,24,33,0.086278,"\int (-\cosh (x)+\text{sech}(x))^{3/2} \, dx","Integrate[(-Cosh[x] + Sech[x])^(3/2),x]","\frac{2}{3} \coth (x) \left(4 \text{csch}^2(x)+1\right) (-\sinh (x) \tanh (x))^{3/2}","-\frac{2}{3} \sinh (x) \sqrt{-\sinh (x) \tanh (x)}-\frac{8}{3} \text{csch}(x) \sqrt{-\sinh (x) \tanh (x)}",1,"(2*Coth[x]*(1 + 4*Csch[x]^2)*(-(Sinh[x]*Tanh[x]))^(3/2))/3","A",1
685,1,30,53,0.1362874,"\int (-\cosh (x)+\text{sech}(x))^{5/2} \, dx","Integrate[(-Cosh[x] + Sech[x])^(5/2),x]","\frac{2}{15} \text{csch}(x) (-\sinh (x) \tanh (x))^{3/2} \left(-3 \cosh ^2(x)+32 \coth ^2(x)-5\right)","\frac{2}{5} \sinh ^2(x) \tanh (x) \sqrt{-\sinh (x) \tanh (x)}+\frac{16}{15} \tanh (x) \sqrt{-\sinh (x) \tanh (x)}-\frac{64}{15} \coth (x) \sqrt{-\sinh (x) \tanh (x)}",1,"(2*(-5 - 3*Cosh[x]^2 + 32*Coth[x]^2)*Csch[x]*(-(Sinh[x]*Tanh[x]))^(3/2))/15","A",1
686,1,35,18,0.0266211,"\int \frac{1}{\sinh (x)+\tanh (x)} \, dx","Integrate[(Sinh[x] + Tanh[x])^(-1),x]","-\frac{1}{4} \text{sech}^2\left(\frac{x}{2}\right)+\frac{1}{2} \log \left(\sinh \left(\frac{x}{2}\right)\right)-\frac{1}{2} \log \left(\cosh \left(\frac{x}{2}\right)\right)","-\frac{1}{2 (\cosh (x)+1)}-\frac{1}{2} \tanh ^{-1}(\cosh (x))",1,"-1/2*Log[Cosh[x/2]] + Log[Sinh[x/2]]/2 - Sech[x/2]^2/4","A",1
687,1,50,20,0.055285,"\int \frac{1}{\sinh (x)-\tanh (x)} \, dx","Integrate[(Sinh[x] - Tanh[x])^(-1),x]","-\frac{1}{4} \text{csch}^2\left(\frac{x}{2}\right) \left(\log \left(\sinh \left(\frac{x}{2}\right)\right)-\log \left(\cosh \left(\frac{x}{2}\right)\right)+\cosh (x) \left(\log \left(\cosh \left(\frac{x}{2}\right)\right)-\log \left(\sinh \left(\frac{x}{2}\right)\right)\right)+1\right)","\frac{1}{2 (1-\cosh (x))}-\frac{1}{2} \tanh ^{-1}(\cosh (x))",1,"-1/4*(Csch[x/2]^2*(1 - Log[Cosh[x/2]] + Cosh[x]*(Log[Cosh[x/2]] - Log[Sinh[x/2]]) + Log[Sinh[x/2]]))","B",1
688,1,29,39,0.0745477,"\int \frac{\sinh (x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[Sinh[x]/(a*Cosh[x] + b*Sinh[x]),x]","\frac{a \log (a \cosh (x)+b \sinh (x))-b x}{a^2-b^2}","\frac{a \log (a \cosh (x)+b \sinh (x))}{a^2-b^2}-\frac{b x}{a^2-b^2}",1,"(-(b*x) + a*Log[a*Cosh[x] + b*Sinh[x]])/(a^2 - b^2)","A",1
689,1,89,74,0.2045444,"\int \frac{\sinh ^2(x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[Sinh[x]^2/(a*Cosh[x] + b*Sinh[x]),x]","\frac{a \left(\sqrt{a-b} (a+b) \sinh (x)-2 a \sqrt{a+b} \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)\right)-b \sqrt{a-b} (a+b) \cosh (x)}{(a-b)^{3/2} (a+b)^2}","\frac{a \sinh (x)}{a^2-b^2}-\frac{b \cosh (x)}{a^2-b^2}-\frac{a^2 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}",1,"(-(Sqrt[a - b]*b*(a + b)*Cosh[x]) + a*(-2*a*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])] + Sqrt[a - b]*(a + b)*Sinh[x]))/((a - b)^(3/2)*(a + b)^2)","A",1
690,1,75,101,0.1582773,"\int \frac{\sinh ^3(x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[Sinh[x]^3/(a*Cosh[x] + b*Sinh[x]),x]","\frac{-4 a^3 \log (a \cosh (x)+b \sinh (x))+\left(b^3-a^2 b\right) \sinh (2 x)+a \left(a^2-b^2\right) \cosh (2 x)+6 a^2 b x-2 b^3 x}{4 (a-b)^2 (a+b)^2}","\frac{a^2 b x}{\left(a^2-b^2\right)^2}+\frac{b x}{2 \left(a^2-b^2\right)}+\frac{a \sinh ^2(x)}{2 \left(a^2-b^2\right)}-\frac{b \sinh (x) \cosh (x)}{2 \left(a^2-b^2\right)}-\frac{a^3 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^2}",1,"(6*a^2*b*x - 2*b^3*x + a*(a^2 - b^2)*Cosh[2*x] - 4*a^3*Log[a*Cosh[x] + b*Sinh[x]] + (-(a^2*b) + b^3)*Sinh[2*x])/(4*(a - b)^2*(a + b)^2)","A",1
691,1,29,39,0.0519662,"\int \frac{\cosh (x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[Cosh[x]/(a*Cosh[x] + b*Sinh[x]),x]","\frac{a x-b \log (a \cosh (x)+b \sinh (x))}{a^2-b^2}","\frac{a x}{a^2-b^2}-\frac{b \log (a \cosh (x)+b \sinh (x))}{a^2-b^2}",1,"(a*x - b*Log[a*Cosh[x] + b*Sinh[x]])/(a^2 - b^2)","A",1
692,1,80,74,0.1652015,"\int \frac{\cosh ^2(x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[Cosh[x]^2/(a*Cosh[x] + b*Sinh[x]),x]","\frac{a \sinh (x)}{a^2-b^2}+\frac{b \cosh (x)}{b^2-a^2}-\frac{2 b^2 \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{3/2} (a+b)^{3/2}}","\frac{a \sinh (x)}{a^2-b^2}-\frac{b \cosh (x)}{a^2-b^2}-\frac{b^2 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}",1,"(-2*b^2*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(3/2)*(a + b)^(3/2)) + (b*Cosh[x])/(-a^2 + b^2) + (a*Sinh[x])/(a^2 - b^2)","A",1
693,1,75,101,0.1229719,"\int \frac{\cosh ^3(x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[Cosh[x]^3/(a*Cosh[x] + b*Sinh[x]),x]","\frac{2 a^3 x+\left(b^3-a^2 b\right) \cosh (2 x)+a \left(a^2-b^2\right) \sinh (2 x)+4 b^3 \log (a \cosh (x)+b \sinh (x))-6 a b^2 x}{4 (a-b)^2 (a+b)^2}","-\frac{a b^2 x}{\left(a^2-b^2\right)^2}+\frac{a x}{2 \left(a^2-b^2\right)}-\frac{b \cosh ^2(x)}{2 \left(a^2-b^2\right)}+\frac{a \sinh (x) \cosh (x)}{2 \left(a^2-b^2\right)}+\frac{b^3 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^2}",1,"(2*a^3*x - 6*a*b^2*x + (-(a^2*b) + b^3)*Cosh[2*x] + 4*b^3*Log[a*Cosh[x] + b*Sinh[x]] + a*(a^2 - b^2)*Sinh[2*x])/(4*(a - b)^2*(a + b)^2)","A",1
694,1,60,50,0.1347769,"\int \frac{\tanh (x)}{b \cosh (x)+a \sinh (x)} \, dx","Integrate[Tanh[x]/(b*Cosh[x] + a*Sinh[x]),x]","\frac{2 \left(\tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-\frac{b \tan ^{-1}\left(\frac{a+b \tanh \left(\frac{x}{2}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)}{a}","\frac{b \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{a \sqrt{a^2-b^2}}+\frac{\tan ^{-1}(\sinh (x))}{a}",1,"(2*(ArcTan[Tanh[x/2]] - (b*ArcTan[(a + b*Tanh[x/2])/(Sqrt[-a + b]*Sqrt[a + b])])/(Sqrt[-a + b]*Sqrt[a + b])))/a","A",1
695,1,59,51,0.0848419,"\int \frac{\coth (x)}{b \cosh (x)+a \sinh (x)} \, dx","Integrate[Coth[x]/(b*Cosh[x] + a*Sinh[x]),x]","\frac{\log \left(\tanh \left(\frac{x}{2}\right)\right)-\frac{2 a \tan ^{-1}\left(\frac{a+b \tanh \left(\frac{x}{2}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)}{\sqrt{b-a} \sqrt{a+b}}}{b}","\frac{a \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2}}-\frac{\tanh ^{-1}(\cosh (x))}{b}",1,"((-2*a*ArcTan[(a + b*Tanh[x/2])/(Sqrt[-a + b]*Sqrt[a + b])])/(Sqrt[-a + b]*Sqrt[a + b]) + Log[Tanh[x/2]])/b","A",1
696,1,125,66,0.1911223,"\int \frac{\sinh (x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[Sinh[x]/(a*Cosh[x] + b*Sinh[x])^2,x]","-\frac{2 b^2 \sqrt{a+b} \sinh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+2 a b \sqrt{a+b} \cosh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+a \sqrt{a-b} (a+b)}{(a-b)^{3/2} (a+b)^2 (a \cosh (x)+b \sinh (x))}","-\frac{a}{\left(a^2-b^2\right) (a \cosh (x)+b \sinh (x))}-\frac{b \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}",1,"-((a*Sqrt[a - b]*(a + b) + 2*a*b*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Cosh[x] + 2*b^2*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Sinh[x])/((a - b)^(3/2)*(a + b)^2*(a*Cosh[x] + b*Sinh[x])))","A",1
697,1,61,68,0.2784224,"\int \frac{\sinh ^2(x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[Sinh[x]^2/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{x \left(a^2+b^2\right)-\frac{a (a-b) (a+b) \sinh (x)}{a \cosh (x)+b \sinh (x)}-2 a b \log (a \cosh (x)+b \sinh (x))}{(a-b)^2 (a+b)^2}","\frac{x \left(a^2+b^2\right)}{\left(a^2-b^2\right)^2}-\frac{a}{\left(a^2-b^2\right) (a \coth (x)+b)}-\frac{2 a b \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^2}",1,"((a^2 + b^2)*x - 2*a*b*Log[a*Cosh[x] + b*Sinh[x]] - (a*(a - b)*(a + b)*Sinh[x])/(a*Cosh[x] + b*Sinh[x]))/((a - b)^2*(a + b)^2)","A",1
698,1,205,195,0.4565264,"\int \frac{\sinh ^3(x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[Sinh[x]^3/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{-b \cosh (x) \left((a-b)^{3/2} (a+b)^2 \sinh (x)-6 a^3 \sqrt{a+b} \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)\right)+a \left(a^2 \sqrt{a-b} (a+b)-2 b^2 \sqrt{a-b} (a+b) \sinh ^2(x)+6 a b^2 \sqrt{a+b} \sinh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)\right)+a \sqrt{a-b} \left(a^3+a^2 b+a b^2+b^3\right) \cosh ^2(x)}{(a-b)^{5/2} (a+b)^3 (a \cosh (x)+b \sinh (x))}","-\frac{a^3}{b^3 (a+b)^2 \left(1-\tanh \left(\frac{x}{2}\right)\right)}+\frac{a^3}{b^3 (a-b)^2 \left(\tanh \left(\frac{x}{2}\right)+1\right)}+\frac{2 a^2 \left(a+b \tanh \left(\frac{x}{2}\right)\right)}{\left(a^2-b^2\right)^2 \left(a \tanh ^2\left(\frac{x}{2}\right)+a+2 b \tanh \left(\frac{x}{2}\right)\right)}+\frac{3 a^2 b \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}+\frac{\left(2 a^2+b^2\right) \cosh (x)}{b^4-a^2 b^2}+\frac{a \left(a^2+2 b^2\right) \sinh (x)}{b^3 \left(a^2-b^2\right)}",1,"(a*Sqrt[a - b]*(a^3 + a^2*b + a*b^2 + b^3)*Cosh[x]^2 - b*Cosh[x]*(-6*a^3*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])] + (a - b)^(3/2)*(a + b)^2*Sinh[x]) + a*(a^2*Sqrt[a - b]*(a + b) + 6*a*b^2*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Sinh[x] - 2*Sqrt[a - b]*b^2*(a + b)*Sinh[x]^2))/((a - b)^(5/2)*(a + b)^3*(a*Cosh[x] + b*Sinh[x]))","A",1
699,1,124,64,0.1320707,"\int \frac{\cosh (x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[Cosh[x]/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{2 a^2 \sqrt{a+b} \cosh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+2 a b \sqrt{a+b} \sinh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+b \sqrt{a-b} (a+b)}{(a-b)^{3/2} (a+b)^2 (a \cosh (x)+b \sinh (x))}","\frac{b}{\left(a^2-b^2\right) (a \cosh (x)+b \sinh (x))}+\frac{a \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}",1,"(Sqrt[a - b]*b*(a + b) + 2*a^2*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Cosh[x] + 2*a*b*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Sinh[x])/((a - b)^(3/2)*(a + b)^2*(a*Cosh[x] + b*Sinh[x]))","A",1
700,1,66,67,0.3235169,"\int \frac{\cosh ^2(x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[Cosh[x]^2/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{x \left(a^2+b^2\right)+\frac{b^2 \left(b^2-a^2\right) \sinh (x)}{a (a \cosh (x)+b \sinh (x))}-2 a b \log (a \cosh (x)+b \sinh (x))}{(a-b)^2 (a+b)^2}","\frac{x \left(a^2+b^2\right)}{\left(a^2-b^2\right)^2}+\frac{b}{\left(a^2-b^2\right) (a+b \tanh (x))}-\frac{2 a b \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^2}",1,"((a^2 + b^2)*x - 2*a*b*Log[a*Cosh[x] + b*Sinh[x]] + (b^2*(-a^2 + b^2)*Sinh[x])/(a*(a*Cosh[x] + b*Sinh[x])))/((a - b)^2*(a + b)^2)","A",1
701,1,204,133,0.3695242,"\int \frac{\cosh ^3(x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[Cosh[x]^3/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{-2 a^2 b \sqrt{a-b} (a+b) \cosh ^2(x)+b \sqrt{a-b} \left(a^3+a^2 b+a b^2+b^3\right) \sinh ^2(x)-6 a b^3 \sqrt{a+b} \sinh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+b^3 \left(-\sqrt{a-b}\right) (a+b)+a \cosh (x) \left((a-b)^{3/2} (a+b)^2 \sinh (x)-6 a b^2 \sqrt{a+b} \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)\right)}{(a-b)^{5/2} (a+b)^3 (a \cosh (x)+b \sinh (x))}","-\frac{3 a b^2 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}-\frac{2 b^3 \left(a+b \tanh \left(\frac{x}{2}\right)\right)}{a \left(a^2-b^2\right)^2 \left(a \tanh ^2\left(\frac{x}{2}\right)+a+2 b \tanh \left(\frac{x}{2}\right)\right)}+\frac{1}{(a+b)^2 \left(1-\tanh \left(\frac{x}{2}\right)\right)}-\frac{1}{(a-b)^2 \left(\tanh \left(\frac{x}{2}\right)+1\right)}",1,"(-(Sqrt[a - b]*b^3*(a + b)) - 2*a^2*Sqrt[a - b]*b*(a + b)*Cosh[x]^2 - 6*a*b^3*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Sinh[x] + Sqrt[a - b]*b*(a^3 + a^2*b + a*b^2 + b^3)*Sinh[x]^2 + a*Cosh[x]*(-6*a*b^2*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])] + (a - b)^(3/2)*(a + b)^2*Sinh[x]))/((a - b)^(5/2)*(a + b)^3*(a*Cosh[x] + b*Sinh[x]))","A",1
702,1,54,19,0.121564,"\int \frac{\sinh (x)}{(a \cosh (x)+b \sinh (x))^3} \, dx","Integrate[Sinh[x]/(a*Cosh[x] + b*Sinh[x])^3,x]","-\frac{a^2+a b \sinh (2 x)+b^2 \cosh (2 x)-b^2}{2 a (a-b) (a+b) (a \cosh (x)+b \sinh (x))^2}","\frac{\tanh ^2(x)}{2 a (a+b \tanh (x))^2}",1,"-1/2*(a^2 - b^2 + b^2*Cosh[2*x] + a*b*Sinh[2*x])/(a*(a - b)*(a + b)*(a*Cosh[x] + b*Sinh[x])^2)","B",1
703,1,117,104,0.776066,"\int \frac{\sinh ^3(x)}{(a \cosh (x)+b \sinh (x))^3} \, dx","Integrate[Sinh[x]^3/(a*Cosh[x] + b*Sinh[x])^3,x]","\frac{a^3}{2 (a-b)^2 (a+b)^2 (a \cosh (x)+b \sinh (x))^2}-\frac{b x \left(3 a^2+b^2\right)}{(a-b)^3 (a+b)^3}+\frac{\left(a^3+3 a b^2\right) \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}+\frac{3 a b \sinh (x)}{(a-b)^2 (a+b)^2 (a \cosh (x)+b \sinh (x))}","-\frac{b x \left(3 a^2+b^2\right)}{\left(a^2-b^2\right)^3}+\frac{2 a b}{\left(a^2-b^2\right)^2 (a \coth (x)+b)}-\frac{a}{2 \left(a^2-b^2\right) (a \coth (x)+b)^2}+\frac{a \left(a^2+3 b^2\right) \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}",1,"-((b*(3*a^2 + b^2)*x)/((a - b)^3*(a + b)^3)) + ((a^3 + 3*a*b^2)*Log[a*Cosh[x] + b*Sinh[x]])/(a^2 - b^2)^3 + a^3/(2*(a - b)^2*(a + b)^2*(a*Cosh[x] + b*Sinh[x])^2) + (3*a*b*Sinh[x])/((a - b)^2*(a + b)^2*(a*Cosh[x] + b*Sinh[x]))","A",1
704,1,40,19,0.0621518,"\int \frac{\cosh (x)}{(a \cosh (x)+b \sinh (x))^3} \, dx","Integrate[Cosh[x]/(a*Cosh[x] + b*Sinh[x])^3,x]","\frac{a \sinh (2 x)+b \cosh (2 x)}{2 (a-b) (a+b) (a \cosh (x)+b \sinh (x))^2}","-\frac{\coth ^2(x)}{2 b (a \coth (x)+b)^2}",1,"(b*Cosh[2*x] + a*Sinh[2*x])/(2*(a - b)*(a + b)*(a*Cosh[x] + b*Sinh[x])^2)","B",1
705,1,119,104,1.0511717,"\int \frac{\cosh ^3(x)}{(a \cosh (x)+b \sinh (x))^3} \, dx","Integrate[Cosh[x]^3/(a*Cosh[x] + b*Sinh[x])^3,x]","\frac{a x \left(a^2+3 b^2\right)}{(a-b)^3 (a+b)^3}+\frac{\left(-3 a^2 b-b^3\right) \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}-\frac{b^3}{2 (a-b)^2 (a+b)^2 (a \cosh (x)+b \sinh (x))^2}-\frac{3 b^2 \sinh (x)}{(a-b)^2 (a+b)^2 (a \cosh (x)+b \sinh (x))}","\frac{a x \left(a^2+3 b^2\right)}{\left(a^2-b^2\right)^3}+\frac{2 a b}{\left(a^2-b^2\right)^2 (a+b \tanh (x))}+\frac{b}{2 \left(a^2-b^2\right) (a+b \tanh (x))^2}-\frac{b \left(3 a^2+b^2\right) \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}",1,"(a*(a^2 + 3*b^2)*x)/((a - b)^3*(a + b)^3) + ((-3*a^2*b - b^3)*Log[a*Cosh[x] + b*Sinh[x]])/(a^2 - b^2)^3 - b^3/(2*(a - b)^2*(a + b)^2*(a*Cosh[x] + b*Sinh[x])^2) - (3*b^2*Sinh[x])/((a - b)^2*(a + b)^2*(a*Cosh[x] + b*Sinh[x]))","A",1
706,1,79,72,0.2086777,"\int \frac{\cosh (x) \sinh (x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[(Cosh[x]*Sinh[x])/(a*Cosh[x] + b*Sinh[x]),x]","\frac{b \sinh (x)}{b^2-a^2}+\frac{a \cosh (x)}{a^2-b^2}+\frac{2 a b \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{3/2} (a+b)^{3/2}}","-\frac{b \sinh (x)}{a^2-b^2}+\frac{a \cosh (x)}{a^2-b^2}+\frac{a b \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}",1,"(2*a*b*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(3/2)*(a + b)^(3/2)) + (a*Cosh[x])/(a^2 - b^2) + (b*Sinh[x])/(-a^2 + b^2)","A",1
707,1,73,102,0.2539583,"\int \frac{\cosh (x) \sinh ^2(x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[(Cosh[x]*Sinh[x]^2)/(a*Cosh[x] + b*Sinh[x]),x]","\frac{\left(b^3-a^2 b\right) \cosh (2 x)+a \left(-2 x \left(a^2+b^2\right)+\left(a^2-b^2\right) \sinh (2 x)+4 a b \log (a \cosh (x)+b \sinh (x))\right)}{4 (a-b)^2 (a+b)^2}","-\frac{a x}{2 \left(a^2-b^2\right)}-\frac{a b^2 x}{\left(a^2-b^2\right)^2}-\frac{b \sinh ^2(x)}{2 \left(a^2-b^2\right)}+\frac{a \sinh (x) \cosh (x)}{2 \left(a^2-b^2\right)}+\frac{a^2 b \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^2}",1,"((-(a^2*b) + b^3)*Cosh[2*x] + a*(-2*(a^2 + b^2)*x + 4*a*b*Log[a*Cosh[x] + b*Sinh[x]] + (a^2 - b^2)*Sinh[2*x]))/(4*(a - b)^2*(a + b)^2)","A",1
708,1,180,137,1.1501843,"\int \frac{\cosh (x) \sinh ^3(x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[(Cosh[x]*Sinh[x]^3)/(a*Cosh[x] + b*Sinh[x]),x]","\frac{-3 a \sqrt{a-b} \sqrt{a+b} \left(3 a^2+b^2\right) \cosh (x)+a \sqrt{a-b} \sqrt{a+b} \left(a^2-b^2\right) \cosh (3 x)+b \left(-24 a^3 \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+3 \sqrt{a-b} \sqrt{a+b} \left(5 a^2-b^2\right) \sinh (x)-\sqrt{a-b} \sqrt{a+b} \left(a^2-b^2\right) \sinh (3 x)\right)}{12 (a-b)^{5/2} (a+b)^{5/2}}","-\frac{b \sinh ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a^2 b \sinh (x)}{\left(a^2-b^2\right)^2}+\frac{a \cosh ^3(x)}{3 \left(a^2-b^2\right)}-\frac{a \cosh (x)}{a^2-b^2}-\frac{a b^2 \cosh (x)}{\left(a^2-b^2\right)^2}-\frac{a^3 b \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}",1,"(-3*a*Sqrt[a - b]*Sqrt[a + b]*(3*a^2 + b^2)*Cosh[x] + a*Sqrt[a - b]*Sqrt[a + b]*(a^2 - b^2)*Cosh[3*x] + b*(-24*a^3*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])] + 3*Sqrt[a - b]*Sqrt[a + b]*(5*a^2 - b^2)*Sinh[x] - Sqrt[a - b]*Sqrt[a + b]*(a^2 - b^2)*Sinh[3*x]))/(12*(a - b)^(5/2)*(a + b)^(5/2))","A",1
709,1,73,102,0.2526239,"\int \frac{\cosh ^2(x) \sinh (x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[(Cosh[x]^2*Sinh[x])/(a*Cosh[x] + b*Sinh[x]),x]","\frac{a \left(a^2-b^2\right) \cosh (2 x)+b \left(2 x \left(a^2+b^2\right)+\left(b^2-a^2\right) \sinh (2 x)-4 a b \log (a \cosh (x)+b \sinh (x))\right)}{4 (a-b)^2 (a+b)^2}","\frac{a^2 b x}{\left(a^2-b^2\right)^2}-\frac{b x}{2 \left(a^2-b^2\right)}+\frac{a \sinh ^2(x)}{2 \left(a^2-b^2\right)}-\frac{b \sinh (x) \cosh (x)}{2 \left(a^2-b^2\right)}-\frac{a b^2 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^2}",1,"(a*(a^2 - b^2)*Cosh[2*x] + b*(2*(a^2 + b^2)*x - 4*a*b*Log[a*Cosh[x] + b*Sinh[x]] + (-a^2 + b^2)*Sinh[2*x]))/(4*(a - b)^2*(a + b)^2)","A",1
710,1,179,122,1.0111776,"\int \frac{\cosh ^2(x) \sinh ^2(x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[(Cosh[x]^2*Sinh[x]^2)/(a*Cosh[x] + b*Sinh[x]),x]","\frac{3 b \sqrt{a-b} \sqrt{a+b} \left(3 a^2+b^2\right) \cosh (x)-b \sqrt{a-b} \sqrt{a+b} \left(a^2-b^2\right) \cosh (3 x)+a \left(-3 \sqrt{a-b} \sqrt{a+b} \left(a^2+3 b^2\right) \sinh (x)+\sqrt{a-b} \sqrt{a+b} \left(a^2-b^2\right) \sinh (3 x)+24 a b^2 \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)\right)}{12 (a-b)^{5/2} (a+b)^{5/2}}","\frac{a \sinh ^3(x)}{3 \left(a^2-b^2\right)}-\frac{a b^2 \sinh (x)}{\left(a^2-b^2\right)^2}-\frac{b \cosh ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a^2 b \cosh (x)}{\left(a^2-b^2\right)^2}+\frac{a^2 b^2 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}",1,"(3*Sqrt[a - b]*b*Sqrt[a + b]*(3*a^2 + b^2)*Cosh[x] - Sqrt[a - b]*b*Sqrt[a + b]*(a^2 - b^2)*Cosh[3*x] + a*(24*a*b^2*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])] - 3*Sqrt[a - b]*Sqrt[a + b]*(a^2 + 3*b^2)*Sinh[x] + Sqrt[a - b]*Sqrt[a + b]*(a^2 - b^2)*Sinh[3*x]))/(12*(a - b)^(5/2)*(a + b)^(5/2))","A",1
711,1,128,194,0.6361392,"\int \frac{\cosh ^2(x) \sinh ^3(x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[(Cosh[x]^2*Sinh[x]^3)/(a*Cosh[x] + b*Sinh[x]),x]","\frac{-4 a \left(a^4-b^4\right) \cosh (2 x)+a \left(a^2-b^2\right)^2 \cosh (4 x)-b \left(-8 a^2 \left(a^2-b^2\right) \sinh (2 x)+\left(a^2-b^2\right)^2 \sinh (4 x)+4 \left(3 a^4 x-8 a^3 b \log (a \cosh (x)+b \sinh (x))+6 a^2 b^2 x-b^4 x\right)\right)}{32 (a-b)^3 (a+b)^3}","\frac{b x}{8 \left(a^2-b^2\right)}-\frac{a^2 b x}{2 \left(a^2-b^2\right)^2}+\frac{a \sinh ^4(x)}{4 \left(a^2-b^2\right)}-\frac{a b^2 \sinh ^2(x)}{2 \left(a^2-b^2\right)^2}-\frac{b \sinh (x) \cosh ^3(x)}{4 \left(a^2-b^2\right)}+\frac{b \sinh (x) \cosh (x)}{8 \left(a^2-b^2\right)}+\frac{a^2 b \sinh (x) \cosh (x)}{2 \left(a^2-b^2\right)^2}-\frac{a^2 b^3 x}{\left(a^2-b^2\right)^3}+\frac{a^3 b^2 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}",1,"(-4*a*(a^4 - b^4)*Cosh[2*x] + a*(a^2 - b^2)^2*Cosh[4*x] - b*(4*(3*a^4*x + 6*a^2*b^2*x - b^4*x - 8*a^3*b*Log[a*Cosh[x] + b*Sinh[x]]) - 8*a^2*(a^2 - b^2)*Sinh[2*x] + (a^2 - b^2)^2*Sinh[4*x]))/(32*(a - b)^3*(a + b)^3)","A",1
712,1,167,137,1.1773724,"\int \frac{\cosh ^3(x) \sinh (x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[(Cosh[x]^3*Sinh[x])/(a*Cosh[x] + b*Sinh[x]),x]","\frac{1}{12} \left(\frac{3 b \left(a^2+3 b^2\right) \sinh (x)}{(a-b)^2 (a+b)^2}+\frac{3 a \left(a^2-5 b^2\right) \cosh (x)}{(a-b)^2 (a+b)^2}-\frac{a^2 b \sinh (3 x)}{(a-b)^2 (a+b)^2}+\frac{b^3 \sinh (3 x)}{(a-b)^2 (a+b)^2}-\frac{24 a b^3 \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{5/2} (a+b)^{5/2}}+\frac{a \cosh (3 x)}{(a-b) (a+b)}\right)","-\frac{b \sinh ^3(x)}{3 \left(a^2-b^2\right)}-\frac{b \sinh (x)}{a^2-b^2}+\frac{a^2 b \sinh (x)}{\left(a^2-b^2\right)^2}+\frac{a \cosh ^3(x)}{3 \left(a^2-b^2\right)}-\frac{a b^2 \cosh (x)}{\left(a^2-b^2\right)^2}-\frac{a b^3 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}",1,"((-24*a*b^3*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(5/2)*(a + b)^(5/2)) + (3*a*(a^2 - 5*b^2)*Cosh[x])/((a - b)^2*(a + b)^2) + (a*Cosh[3*x])/((a - b)*(a + b)) + (3*b*(a^2 + 3*b^2)*Sinh[x])/((a - b)^2*(a + b)^2) - (a^2*b*Sinh[3*x])/((a - b)^2*(a + b)^2) + (b^3*Sinh[3*x])/((a - b)^2*(a + b)^2))/12","A",1
713,1,126,194,0.613053,"\int \frac{\cosh ^3(x) \sinh ^2(x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[(Cosh[x]^3*Sinh[x]^2)/(a*Cosh[x] + b*Sinh[x]),x]","\frac{4 b \left(a^4-b^4\right) \cosh (2 x)-b \left(a^2-b^2\right)^2 \cosh (4 x)+a \left(8 b^2 \left(b^2-a^2\right) \sinh (2 x)+\left(a^2-b^2\right)^2 \sinh (4 x)-4 \left(x \left(a^4-6 a^2 b^2-3 b^4\right)+8 a b^3 \log (a \cosh (x)+b \sinh (x))\right)\right)}{32 (a-b)^3 (a+b)^3}","-\frac{a x}{8 \left(a^2-b^2\right)}-\frac{a b^2 x}{2 \left(a^2-b^2\right)^2}+\frac{a^2 b \sinh ^2(x)}{2 \left(a^2-b^2\right)^2}-\frac{b \cosh ^4(x)}{4 \left(a^2-b^2\right)}+\frac{a \sinh (x) \cosh ^3(x)}{4 \left(a^2-b^2\right)}-\frac{a \sinh (x) \cosh (x)}{8 \left(a^2-b^2\right)}-\frac{a b^2 \sinh (x) \cosh (x)}{2 \left(a^2-b^2\right)^2}-\frac{a^2 b^3 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}+\frac{a^3 b^2 x}{\left(a^2-b^2\right)^3}",1,"(4*b*(a^4 - b^4)*Cosh[2*x] - b*(a^2 - b^2)^2*Cosh[4*x] + a*(-4*((a^4 - 6*a^2*b^2 - 3*b^4)*x + 8*a*b^3*Log[a*Cosh[x] + b*Sinh[x]]) + 8*b^2*(-a^2 + b^2)*Sinh[2*x] + (a^2 - b^2)^2*Sinh[4*x]))/(32*(a - b)^3*(a + b)^3)","A",1
714,1,325,212,2.2954709,"\int \frac{\cosh ^3(x) \sinh ^3(x)}{a \cosh (x)+b \sinh (x)} \, dx","Integrate[(Cosh[x]^3*Sinh[x]^3)/(a*Cosh[x] + b*Sinh[x]),x]","\frac{1}{32} \left(\frac{2 b \left(3 a^2+b^2\right) \sinh (3 x)}{3 (a-b)^2 (a+b)^2}-\frac{2 a \left(a^2+3 b^2\right) \cosh (3 x)}{3 (a-b)^2 (a+b)^2}-3 \left(\frac{2 b \sinh (x)}{b^2-a^2}+\frac{2 a \cosh (x)}{a^2-b^2}+\frac{4 a b \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{3/2} (a+b)^{3/2}}\right)+\frac{2 b \left(5 a^4+10 a^2 b^2+b^4\right) \sinh (x)}{(b-a)^3 (a+b)^3}+\frac{2 a \left(a^4+10 a^2 b^2+5 b^4\right) \cosh (x)}{(a-b)^3 (a+b)^3}+\frac{4 a b \left(3 a^4+10 a^2 b^2+3 b^4\right) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{7/2} (a+b)^{7/2}}-\frac{2 b \sinh (5 x)}{5 (a-b) (a+b)}+\frac{2 a \cosh (5 x)}{5 (a-b) (a+b)}\right)","-\frac{b \sinh ^5(x)}{5 \left(a^2-b^2\right)}-\frac{b \sinh ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a^2 b \sinh ^3(x)}{3 \left(a^2-b^2\right)^2}+\frac{a \cosh ^5(x)}{5 \left(a^2-b^2\right)}-\frac{a \cosh ^3(x)}{3 \left(a^2-b^2\right)}-\frac{a b^2 \cosh ^3(x)}{3 \left(a^2-b^2\right)^2}-\frac{a^2 b^3 \sinh (x)}{\left(a^2-b^2\right)^3}+\frac{a^3 b^2 \cosh (x)}{\left(a^2-b^2\right)^3}+\frac{a^3 b^3 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{7/2}}",1,"((4*a*b*(3*a^4 + 10*a^2*b^2 + 3*b^4)*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(7/2)*(a + b)^(7/2)) + (2*a*(a^4 + 10*a^2*b^2 + 5*b^4)*Cosh[x])/((a - b)^3*(a + b)^3) - (2*a*(a^2 + 3*b^2)*Cosh[3*x])/(3*(a - b)^2*(a + b)^2) + (2*a*Cosh[5*x])/(5*(a - b)*(a + b)) + (2*b*(5*a^4 + 10*a^2*b^2 + b^4)*Sinh[x])/((-a + b)^3*(a + b)^3) - 3*((4*a*b*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(3/2)*(a + b)^(3/2)) + (2*a*Cosh[x])/(a^2 - b^2) + (2*b*Sinh[x])/(-a^2 + b^2)) + (2*b*(3*a^2 + b^2)*Sinh[3*x])/(3*(a - b)^2*(a + b)^2) - (2*b*Sinh[5*x])/(5*(a - b)*(a + b)))/32","A",1
715,1,60,93,0.2355361,"\int \frac{\cosh (x) \sinh (x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[(Cosh[x]*Sinh[x])/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{\left(a^2+b^2\right) \log (a \cosh (x)+b \sinh (x))-2 a b x+\frac{b (a-b) (a+b) \sinh (x)}{a \cosh (x)+b \sinh (x)}}{(a-b)^2 (a+b)^2}","-\frac{2 a b x}{\left(a^2-b^2\right)^2}+\frac{b \sinh (x)}{\left(a^2-b^2\right) (a \cosh (x)+b \sinh (x))}+\frac{a^2 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^2}+\frac{b^2 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^2}",1,"(-2*a*b*x + (a^2 + b^2)*Log[a*Cosh[x] + b*Sinh[x]] + ((a - b)*b*(a + b)*Sinh[x])/(a*Cosh[x] + b*Sinh[x]))/((a - b)^2*(a + b)^2)","A",1
716,1,222,165,1.0982561,"\int \frac{\cosh (x) \sinh ^2(x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[(Cosh[x]*Sinh[x]^2)/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{b \left(\sqrt{a-b} \sqrt{a+b} \left(a^2+b^2\right) \sinh ^2(x)-2 a \left(a^2+2 b^2\right) \sinh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+a^2 \left(-\sqrt{a-b}\right) \sqrt{a+b}\right)+a \cosh (x) \left(\sqrt{a-b} \sqrt{a+b} \left(a^2-b^2\right) \sinh (x)-2 a \left(a^2+2 b^2\right) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)\right)-2 a^2 b \sqrt{a-b} \sqrt{a+b} \cosh ^2(x)}{(a-b)^{5/2} (a+b)^{5/2} (a \cosh (x)+b \sinh (x))}","\frac{a^2 \sinh (x)}{\left(a^2-b^2\right)^2}+\frac{b^2 \sinh (x)}{\left(a^2-b^2\right)^2}-\frac{2 a b \cosh (x)}{\left(a^2-b^2\right)^2}-\frac{a^2 b}{\left(a^2-b^2\right)^2 (a \cosh (x)+b \sinh (x))}-\frac{2 a b^2 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}-\frac{a^3 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}",1,"(-2*a^2*Sqrt[a - b]*b*Sqrt[a + b]*Cosh[x]^2 + a*Cosh[x]*(-2*a*(a^2 + 2*b^2)*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])] + Sqrt[a - b]*Sqrt[a + b]*(a^2 - b^2)*Sinh[x]) + b*(-(a^2*Sqrt[a - b]*Sqrt[a + b]) - 2*a*(a^2 + 2*b^2)*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Sinh[x] + Sqrt[a - b]*Sqrt[a + b]*(a^2 + b^2)*Sinh[x]^2))/((a - b)^(5/2)*(a + b)^(5/2)*(a*Cosh[x] + b*Sinh[x]))","A",1
717,1,176,215,1.0306133,"\int \frac{\cosh (x) \sinh ^3(x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[(Cosh[x]*Sinh[x]^3)/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{a \left(a^2-b^2\right)^2 \cosh (3 x)-2 b \sinh (x) \left(\left(a^2-b^2\right)^2 \cosh (2 x)+2 a \left(3 a^3+2 a \left(a^2+3 b^2\right) \log (a \cosh (x)+b \sinh (x))-6 a^2 b x-3 a b^2-2 b^3 x\right)\right)+a \cosh (x) \left(a^4+24 a^3 b x-8 a^2 \left(a^2+3 b^2\right) \log (a \cosh (x)+b \sinh (x))+2 a^2 b^2+8 a b^3 x-3 b^4\right)}{8 (a-b)^3 (a+b)^3 (a \cosh (x)+b \sinh (x))}","\frac{a b x \left(a^2+b^2\right)}{\left(a^2-b^2\right)^3}+\frac{a b x}{\left(a^2-b^2\right)^2}+\frac{a^2 \sinh ^2(x)}{2 \left(a^2-b^2\right)^2}+\frac{b^2 \sinh ^2(x)}{2 \left(a^2-b^2\right)^2}-\frac{a^2 b}{\left(a^2-b^2\right)^2 (a \coth (x)+b)}-\frac{a b \sinh (x) \cosh (x)}{\left(a^2-b^2\right)^2}-\frac{3 a^2 b^2 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}+\frac{a b^3 x}{\left(a^2-b^2\right)^3}-\frac{a^4 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}+\frac{a^3 b x}{\left(a^2-b^2\right)^3}",1,"(a*(a^2 - b^2)^2*Cosh[3*x] + a*Cosh[x]*(a^4 + 2*a^2*b^2 - 3*b^4 + 24*a^3*b*x + 8*a*b^3*x - 8*a^2*(a^2 + 3*b^2)*Log[a*Cosh[x] + b*Sinh[x]]) - 2*b*((a^2 - b^2)^2*Cosh[2*x] + 2*a*(3*a^3 - 3*a*b^2 - 6*a^2*b*x - 2*b^3*x + 2*a*(a^2 + 3*b^2)*Log[a*Cosh[x] + b*Sinh[x]]))*Sinh[x])/(8*(a - b)^3*(a + b)^3*(a*Cosh[x] + b*Sinh[x]))","A",1
718,1,264,163,0.9006616,"\int \frac{\cosh ^2(x) \sinh (x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[(Cosh[x]^2*Sinh[x])/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{1}{4} \left(\frac{4 \left(a^2+b^2\right) \cosh (x)}{(a-b)^2 (a+b)^2}+\frac{6 b \left(3 a^2+b^2\right) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{5/2} (a+b)^{5/2}}+\frac{a \left(a^2+3 b^2\right)}{(a-b)^2 (a+b)^2 (a \cosh (x)+b \sinh (x))}-\frac{8 a b \sinh (x)}{(a-b)^2 (a+b)^2}\right)-\frac{2 b^2 \sqrt{a+b} \sinh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+2 a b \sqrt{a+b} \cosh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+a \sqrt{a-b} (a+b)}{4 (a-b)^{3/2} (a+b)^2 (a \cosh (x)+b \sinh (x))}","-\frac{2 a b \sinh (x)}{\left(a^2-b^2\right)^2}+\frac{b^2 \cosh (x)}{\left(a^2-b^2\right)^2}+\frac{a^2 \cosh (x)}{\left(a^2-b^2\right)^2}+\frac{a b^2}{\left(a^2-b^2\right)^2 (a \cosh (x)+b \sinh (x))}+\frac{2 a^2 b \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}+\frac{b^3 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}",1,"-1/4*(a*Sqrt[a - b]*(a + b) + 2*a*b*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Cosh[x] + 2*b^2*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Sinh[x])/((a - b)^(3/2)*(a + b)^2*(a*Cosh[x] + b*Sinh[x])) + ((6*b*(3*a^2 + b^2)*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(5/2)*(a + b)^(5/2)) + (4*(a^2 + b^2)*Cosh[x])/((a - b)^2*(a + b)^2) - (8*a*b*Sinh[x])/((a - b)^2*(a + b)^2) + (a*(a^2 + 3*b^2))/((a - b)^2*(a + b)^2*(a*Cosh[x] + b*Sinh[x])))/4","A",1
719,1,174,205,2.0472464,"\int \frac{\cosh ^2(x) \sinh ^2(x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[(Cosh[x]^2*Sinh[x]^2)/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{1}{8} \left(\frac{2 \left(a^2+b^2\right) \sinh (2 x)}{(a-b)^2 (a+b)^2}+\frac{16 a b \left(a^2+b^2\right) \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}-\frac{\sinh (x)}{a^2 \cosh (x)+a b \sinh (x)}-\frac{4 x \left(a^4+6 a^2 b^2+b^4\right)}{(a-b)^3 (a+b)^3}+\frac{\left(a^4+6 a^2 b^2+b^4\right) \sinh (x)}{a (a-b)^2 (a+b)^2 (a \cosh (x)+b \sinh (x))}-\frac{4 a b \cosh (2 x)}{(a-b)^2 (a+b)^2}\right)","-\frac{a^2 x}{2 \left(a^2-b^2\right)^2}-\frac{4 a^2 b^2 x}{\left(a^2-b^2\right)^3}+\frac{b^2 x}{2 \left(a^2-b^2\right)^2}-\frac{a b \sinh ^2(x)}{\left(a^2-b^2\right)^2}+\frac{a^2 \sinh (x) \cosh (x)}{2 \left(a^2-b^2\right)^2}+\frac{a b^2 \sinh (x)}{\left(a^2-b^2\right)^2 (a \cosh (x)+b \sinh (x))}+\frac{b^2 \sinh (x) \cosh (x)}{2 \left(a^2-b^2\right)^2}+\frac{2 a b^3 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}+\frac{2 a^3 b \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}",1,"((-4*(a^4 + 6*a^2*b^2 + b^4)*x)/((a - b)^3*(a + b)^3) - (4*a*b*Cosh[2*x])/((a - b)^2*(a + b)^2) + (16*a*b*(a^2 + b^2)*Log[a*Cosh[x] + b*Sinh[x]])/(a^2 - b^2)^3 + ((a^4 + 6*a^2*b^2 + b^4)*Sinh[x])/(a*(a - b)^2*(a + b)^2*(a*Cosh[x] + b*Sinh[x])) - Sinh[x]/(a^2*Cosh[x] + a*b*Sinh[x]) + (2*(a^2 + b^2)*Sinh[2*x])/((a - b)^2*(a + b)^2))/8","A",1
720,1,474,261,3.9373264,"\int \frac{\cosh ^2(x) \sinh ^3(x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[(Cosh[x]^2*Sinh[x]^3)/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{1}{16} \left(\frac{32 a b \left(a^2+b^2\right) \sinh (x)}{(a-b)^3 (a+b)^3}-\frac{4 \left(a^2+b^2\right) \cosh (x)}{(a-b)^2 (a+b)^2}+\frac{4 \left(a^2+b^2\right) \cosh (3 x)}{3 (a-b)^2 (a+b)^2}-\frac{6 b \left(3 a^2+b^2\right) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{5/2} (a+b)^{5/2}}-\frac{a \left(a^2+3 b^2\right)}{(a-b)^2 (a+b)^2 (a \cosh (x)+b \sinh (x))}-\frac{8 \left(a^4+6 a^2 b^2+b^4\right) \cosh (x)}{(a-b)^3 (a+b)^3}-\frac{10 b \left(5 a^4+10 a^2 b^2+b^4\right) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{7/2} (a+b)^{7/2}}-\frac{a \left(a^4+10 a^2 b^2+5 b^4\right)}{(a-b)^3 (a+b)^3 (a \cosh (x)+b \sinh (x))}+\frac{2 \left(2 b^2 \sqrt{a+b} \sinh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+2 a b \sqrt{a+b} \cosh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+a \sqrt{a-b} (a+b)\right)}{(a-b)^{3/2} (a+b)^2 (a \cosh (x)+b \sinh (x))}+\frac{8 a b \sinh (x)}{(a-b)^2 (a+b)^2}-\frac{8 a b \sinh (3 x)}{3 (a-b)^2 (a+b)^2}\right)","-\frac{2 a b \sinh ^3(x)}{3 \left(a^2-b^2\right)^2}+\frac{a^2 \cosh ^3(x)}{3 \left(a^2-b^2\right)^2}+\frac{b^2 \cosh ^3(x)}{3 \left(a^2-b^2\right)^2}-\frac{a^2 \cosh (x)}{\left(a^2-b^2\right)^2}-\frac{4 a^2 b^2 \cosh (x)}{\left(a^2-b^2\right)^3}+\frac{2 a b^3 \sinh (x)}{\left(a^2-b^2\right)^3}-\frac{3 a^2 b^3 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{7/2}}-\frac{2 a^4 b \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{7/2}}+\frac{2 a^3 b \sinh (x)}{\left(a^2-b^2\right)^3}-\frac{a^3 b^2}{\left(a^2-b^2\right)^3 (a \cosh (x)+b \sinh (x))}",1,"((-6*b*(3*a^2 + b^2)*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(5/2)*(a + b)^(5/2)) - (10*b*(5*a^4 + 10*a^2*b^2 + b^4)*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(7/2)*(a + b)^(7/2)) - (4*(a^2 + b^2)*Cosh[x])/((a - b)^2*(a + b)^2) - (8*(a^4 + 6*a^2*b^2 + b^4)*Cosh[x])/((a - b)^3*(a + b)^3) + (4*(a^2 + b^2)*Cosh[3*x])/(3*(a - b)^2*(a + b)^2) + (8*a*b*Sinh[x])/((a - b)^2*(a + b)^2) + (32*a*b*(a^2 + b^2)*Sinh[x])/((a - b)^3*(a + b)^3) - (a*(a^2 + 3*b^2))/((a - b)^2*(a + b)^2*(a*Cosh[x] + b*Sinh[x])) - (a*(a^4 + 10*a^2*b^2 + 5*b^4))/((a - b)^3*(a + b)^3*(a*Cosh[x] + b*Sinh[x])) + (2*(a*Sqrt[a - b]*(a + b) + 2*a*b*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Cosh[x] + 2*b^2*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Sinh[x]))/((a - b)^(3/2)*(a + b)^2*(a*Cosh[x] + b*Sinh[x])) - (8*a*b*Sinh[3*x])/(3*(a - b)^2*(a + b)^2))/16","A",1
721,1,183,215,1.3176074,"\int \frac{\cosh ^3(x) \sinh (x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[(Cosh[x]^3*Sinh[x])/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{a \cosh (x) \left(\left(a^4-b^4\right) \cosh (2 x)-4 b \left(-a x \left(a^2+3 b^2\right)+a \left(a^2-b^2\right) \sinh (x) \cosh (x)+b \left(3 a^2+b^2\right) \log (a \cosh (x)+b \sinh (x))\right)\right)+b \sinh (x) \left(\left(a^4-b^4\right) \cosh (2 x)-2 a b \left(a^2-b^2\right) \sinh (2 x)+4 b \left(a^3 x-b \left(3 a^2+b^2\right) \log (a \cosh (x)+b \sinh (x))-a^2 b+3 a b^2 x+b^3\right)\right)}{4 (a-b)^3 (a+b)^3 (a \cosh (x)+b \sinh (x))}","\frac{a b x \left(a^2+b^2\right)}{\left(a^2-b^2\right)^3}-\frac{a b x}{\left(a^2-b^2\right)^2}+\frac{a^2 \sinh ^2(x)}{2 \left(a^2-b^2\right)^2}+\frac{b^2 \cosh ^2(x)}{2 \left(a^2-b^2\right)^2}+\frac{a b^2}{\left(a^2-b^2\right)^2 (a+b \tanh (x))}-\frac{a b \sinh (x) \cosh (x)}{\left(a^2-b^2\right)^2}-\frac{3 a^2 b^2 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}-\frac{b^4 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^3}+\frac{a b^3 x}{\left(a^2-b^2\right)^3}+\frac{a^3 b x}{\left(a^2-b^2\right)^3}",1,"(a*Cosh[x]*((a^4 - b^4)*Cosh[2*x] - 4*b*(-(a*(a^2 + 3*b^2)*x) + b*(3*a^2 + b^2)*Log[a*Cosh[x] + b*Sinh[x]] + a*(a^2 - b^2)*Cosh[x]*Sinh[x])) + b*Sinh[x]*((a^4 - b^4)*Cosh[2*x] + 4*b*(-(a^2*b) + b^3 + a^3*x + 3*a*b^2*x - b*(3*a^2 + b^2)*Log[a*Cosh[x] + b*Sinh[x]]) - 2*a*b*(a^2 - b^2)*Sinh[2*x]))/(4*(a - b)^3*(a + b)^3*(a*Cosh[x] + b*Sinh[x]))","A",1
722,1,481,259,2.1729289,"\int \frac{\cosh ^3(x) \sinh ^2(x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[(Cosh[x]^3*Sinh[x]^2)/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{1}{16} \left(\frac{4 \left(a^2+b^2\right) \sinh (x)}{(a-b)^2 (a+b)^2}-\frac{6 a \left(a^2+3 b^2\right) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{5/2} (a+b)^{5/2}}-\frac{b \left(3 a^2+b^2\right)}{(a-b)^2 (a+b)^2 (a \cosh (x)+b \sinh (x))}-\frac{8 a b \cosh (x)}{(a-b)^2 (a+b)^2}\right)-\frac{2 a^2 \sqrt{a+b} \cosh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+2 a b \sqrt{a+b} \sinh (x) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+b \sqrt{a-b} (a+b)}{8 (a-b)^{3/2} (a+b)^2 (a \cosh (x)+b \sinh (x))}+\frac{1}{16} \left(\frac{4 \left(a^2+b^2\right) \sinh (3 x)}{3 (a-b)^2 (a+b)^2}+\frac{32 a b \left(a^2+b^2\right) \cosh (x)}{(a-b)^3 (a+b)^3}-\frac{8 \left(a^4+6 a^2 b^2+b^4\right) \sinh (x)}{(a-b)^3 (a+b)^3}+\frac{10 a \left(a^4+10 a^2 b^2+5 b^4\right) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)}{(a-b)^{7/2} (a+b)^{7/2}}+\frac{b \left(5 a^4+10 a^2 b^2+b^4\right)}{(a-b)^3 (a+b)^3 (a \cosh (x)+b \sinh (x))}-\frac{8 a b \cosh (3 x)}{3 (a-b)^2 (a+b)^2}\right)","\frac{b^2 \sinh ^3(x)}{3 \left(a^2-b^2\right)^2}+\frac{a^2 \sinh ^3(x)}{3 \left(a^2-b^2\right)^2}+\frac{b^2 \sinh (x)}{\left(a^2-b^2\right)^2}-\frac{4 a^2 b^2 \sinh (x)}{\left(a^2-b^2\right)^3}-\frac{2 a b \cosh ^3(x)}{3 \left(a^2-b^2\right)^2}+\frac{2 a b^4 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{7/2}}+\frac{2 a b^3 \cosh (x)}{\left(a^2-b^2\right)^3}+\frac{a^2 b^3}{\left(a^2-b^2\right)^3 (a \cosh (x)+b \sinh (x))}+\frac{2 a^3 b \cosh (x)}{\left(a^2-b^2\right)^3}+\frac{3 a^3 b^2 \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{7/2}}",1,"-1/8*(Sqrt[a - b]*b*(a + b) + 2*a^2*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Cosh[x] + 2*a*b*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]*Sinh[x])/((a - b)^(3/2)*(a + b)^2*(a*Cosh[x] + b*Sinh[x])) + ((-6*a*(a^2 + 3*b^2)*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(5/2)*(a + b)^(5/2)) - (8*a*b*Cosh[x])/((a - b)^2*(a + b)^2) + (4*(a^2 + b^2)*Sinh[x])/((a - b)^2*(a + b)^2) - (b*(3*a^2 + b^2))/((a - b)^2*(a + b)^2*(a*Cosh[x] + b*Sinh[x])))/16 + ((10*a*(a^4 + 10*a^2*b^2 + 5*b^4)*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/((a - b)^(7/2)*(a + b)^(7/2)) + (32*a*b*(a^2 + b^2)*Cosh[x])/((a - b)^3*(a + b)^3) - (8*a*b*Cosh[3*x])/(3*(a - b)^2*(a + b)^2) - (8*(a^4 + 6*a^2*b^2 + b^4)*Sinh[x])/((a - b)^3*(a + b)^3) + (b*(5*a^4 + 10*a^2*b^2 + b^4))/((a - b)^3*(a + b)^3*(a*Cosh[x] + b*Sinh[x])) + (4*(a^2 + b^2)*Sinh[3*x])/(3*(a - b)^2*(a + b)^2))/16","A",1
723,1,366,314,1.4865733,"\int \frac{\cosh ^3(x) \sinh ^3(x)}{(a \cosh (x)+b \sinh (x))^2} \, dx","Integrate[(Cosh[x]^3*Sinh[x]^3)/(a*Cosh[x] + b*Sinh[x])^2,x]","\frac{a^7 \cosh (5 x)+20 a^6 b \sinh (x)+9 a^6 b \sinh (3 x)-a^6 b \sinh (5 x)-48 a^5 b^2 x \sinh (x)-3 a^5 b^2 \cosh (5 x)+84 a^4 b^3 \sinh (x)-15 a^4 b^3 \sinh (3 x)+3 a^4 b^3 \sinh (5 x)+192 a^4 b^3 \sinh (x) \log (a \cosh (x)+b \sinh (x))-288 a^3 b^4 x \sinh (x)+3 a^3 b^4 \cosh (5 x)-100 a^2 b^5 \sinh (x)+3 a^2 b^5 \sinh (3 x)-3 a^2 b^5 \sinh (5 x)+192 a^2 b^5 \sinh (x) \log (a \cosh (x)+b \sinh (x))-3 a \left(a^2-b^2\right)^2 \left(a^2+3 b^2\right) \cosh (3 x)-4 a \cosh (x) \left(a^6+12 a^5 b x+9 a^4 b^2+72 a^3 b^3 x-5 a^2 b^4-48 a^2 b^2 \left(a^2+b^2\right) \log (a \cosh (x)+b \sinh (x))+12 a b^5 x-5 b^6\right)-48 a b^6 x \sinh (x)-a b^6 \cosh (5 x)-4 b^7 \sinh (x)+3 b^7 \sinh (3 x)+b^7 \sinh (5 x)}{64 (a-b)^4 (a+b)^4 (a \cosh (x)+b \sinh (x))}","\frac{a b x}{4 \left(a^2-b^2\right)^2}+\frac{a^2 \sinh ^4(x)}{4 \left(a^2-b^2\right)^2}-\frac{2 a^2 b^2 \sinh ^2(x)}{\left(a^2-b^2\right)^3}+\frac{b^2 \cosh ^4(x)}{4 \left(a^2-b^2\right)^2}-\frac{a b \sinh (x) \cosh ^3(x)}{2 \left(a^2-b^2\right)^2}+\frac{a b \sinh (x) \cosh (x)}{4 \left(a^2-b^2\right)^2}+\frac{3 a^2 b^4 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^4}+\frac{a b^3 x}{\left(a^2-b^2\right)^3}+\frac{a^2 b^3 \sinh (x)}{\left(a^2-b^2\right)^3 (a \cosh (x)+b \sinh (x))}+\frac{a b^3 \sinh (x) \cosh (x)}{\left(a^2-b^2\right)^3}+\frac{3 a^4 b^2 \log (a \cosh (x)+b \sinh (x))}{\left(a^2-b^2\right)^4}-\frac{a^3 b x}{\left(a^2-b^2\right)^3}+\frac{a^3 b \sinh (x) \cosh (x)}{\left(a^2-b^2\right)^3}-\frac{6 a^3 b^3 x}{\left(a^2-b^2\right)^4}",1,"(-3*a*(a^2 - b^2)^2*(a^2 + 3*b^2)*Cosh[3*x] + a^7*Cosh[5*x] - 3*a^5*b^2*Cosh[5*x] + 3*a^3*b^4*Cosh[5*x] - a*b^6*Cosh[5*x] - 4*a*Cosh[x]*(a^6 + 9*a^4*b^2 - 5*a^2*b^4 - 5*b^6 + 12*a^5*b*x + 72*a^3*b^3*x + 12*a*b^5*x - 48*a^2*b^2*(a^2 + b^2)*Log[a*Cosh[x] + b*Sinh[x]]) + 20*a^6*b*Sinh[x] + 84*a^4*b^3*Sinh[x] - 100*a^2*b^5*Sinh[x] - 4*b^7*Sinh[x] - 48*a^5*b^2*x*Sinh[x] - 288*a^3*b^4*x*Sinh[x] - 48*a*b^6*x*Sinh[x] + 192*a^4*b^3*Log[a*Cosh[x] + b*Sinh[x]]*Sinh[x] + 192*a^2*b^5*Log[a*Cosh[x] + b*Sinh[x]]*Sinh[x] + 9*a^6*b*Sinh[3*x] - 15*a^4*b^3*Sinh[3*x] + 3*a^2*b^5*Sinh[3*x] + 3*b^7*Sinh[3*x] - a^6*b*Sinh[5*x] + 3*a^4*b^3*Sinh[5*x] - 3*a^2*b^5*Sinh[5*x] + b^7*Sinh[5*x])/(64*(a - b)^4*(a + b)^4*(a*Cosh[x] + b*Sinh[x]))","A",1
724,1,78,80,0.2393422,"\int \frac{A+C \sinh (x)}{b \cosh (x)+c \sinh (x)} \, dx","Integrate[(A + C*Sinh[x])/(b*Cosh[x] + c*Sinh[x]),x]","\frac{2 A \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)}{\sqrt{b-c} \sqrt{b+c}}+\frac{C (b \log (b \cosh (x)+c \sinh (x))-c x)}{b^2-c^2}","\frac{A \tan ^{-1}\left(\frac{b \sinh (x)+c \cosh (x)}{\sqrt{b^2-c^2}}\right)}{\sqrt{b^2-c^2}}-\frac{c C x}{b^2-c^2}+\frac{b C \log (b \cosh (x)+c \sinh (x))}{b^2-c^2}",1,"(2*A*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])])/(Sqrt[b - c]*Sqrt[b + c]) + (C*(-(c*x) + b*Log[b*Cosh[x] + c*Sinh[x]]))/(b^2 - c^2)","A",1
725,1,155,82,0.4604292,"\int \frac{A+C \sinh (x)}{(b \cosh (x)+c \sinh (x))^2} \, dx","Integrate[(A + C*Sinh[x])/(b*Cosh[x] + c*Sinh[x])^2,x]","-\frac{\sinh (x) \left(2 b c^2 C \sqrt{b+c} \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)-A (b-c)^{3/2} (b+c)^2\right)+2 b^2 c C \sqrt{b+c} \cosh (x) \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)+b^2 C \sqrt{b-c} (b+c)}{b (b-c)^{3/2} (b+c)^2 (b \cosh (x)+c \sinh (x))}","-\frac{-A b \sinh (x)-A c \cosh (x)+b C}{\left(b^2-c^2\right) (b \cosh (x)+c \sinh (x))}-\frac{c C \tan ^{-1}\left(\frac{b \sinh (x)+c \cosh (x)}{\sqrt{b^2-c^2}}\right)}{\left(b^2-c^2\right)^{3/2}}",1,"-((b^2*Sqrt[b - c]*(b + c)*C + 2*b^2*c*Sqrt[b + c]*C*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])]*Cosh[x] + (-(A*(b - c)^(3/2)*(b + c)^2) + 2*b*c^2*Sqrt[b + c]*C*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])])*Sinh[x])/(b*(b - c)^(3/2)*(b + c)^2*(b*Cosh[x] + c*Sinh[x])))","A",1
726,1,134,123,1.1930978,"\int \frac{A+C \sinh (x)}{(b \cosh (x)+c \sinh (x))^3} \, dx","Integrate[(A + C*Sinh[x])/(b*Cosh[x] + c*Sinh[x])^3,x]","\frac{1}{2} \left(\frac{A \left(b^2-c^2\right) \sinh (x)-b^2 C}{b (b-c) (b+c) (b \cosh (x)+c \sinh (x))^2}+\frac{c (A-2 C \sinh (x))}{b (b-c) (b+c) (b \cosh (x)+c \sinh (x))}+\frac{2 A \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)}{(b-c)^{3/2} (b+c)^{3/2}}\right)","-\frac{-A b \sinh (x)-A c \cosh (x)+b C}{2 \left(b^2-c^2\right) (b \cosh (x)+c \sinh (x))^2}+\frac{A \tan ^{-1}\left(\frac{b \sinh (x)+c \cosh (x)}{\sqrt{b^2-c^2}}\right)}{2 \left(b^2-c^2\right)^{3/2}}-\frac{b c C \sinh (x)+c^2 C \cosh (x)}{\left(b^2-c^2\right)^2 (b \cosh (x)+c \sinh (x))}",1,"((2*A*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])])/((b - c)^(3/2)*(b + c)^(3/2)) + (-(b^2*C) + A*(b^2 - c^2)*Sinh[x])/(b*(b - c)*(b + c)*(b*Cosh[x] + c*Sinh[x])^2) + (c*(A - 2*C*Sinh[x]))/(b*(b - c)*(b + c)*(b*Cosh[x] + c*Sinh[x])))/2","A",1
727,1,78,80,0.1790563,"\int \frac{A+B \cosh (x)}{b \cosh (x)+c \sinh (x)} \, dx","Integrate[(A + B*Cosh[x])/(b*Cosh[x] + c*Sinh[x]),x]","\frac{2 A \sqrt{b-c} \sqrt{b+c} \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)-B c \log (b \cosh (x)+c \sinh (x))+b B x}{b^2-c^2}","\frac{A \tan ^{-1}\left(\frac{b \sinh (x)+c \cosh (x)}{\sqrt{b^2-c^2}}\right)}{\sqrt{b^2-c^2}}+\frac{b B x}{b^2-c^2}-\frac{B c \log (b \cosh (x)+c \sinh (x))}{b^2-c^2}",1,"(b*B*x + 2*A*Sqrt[b - c]*Sqrt[b + c]*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])] - B*c*Log[b*Cosh[x] + c*Sinh[x]])/(b^2 - c^2)","A",1
728,1,151,78,0.3004322,"\int \frac{A+B \cosh (x)}{(b \cosh (x)+c \sinh (x))^2} \, dx","Integrate[(A + B*Cosh[x])/(b*Cosh[x] + c*Sinh[x])^2,x]","\frac{\sinh (x) \left(A (b-c)^{3/2} (b+c)^2+2 b^2 B c \sqrt{b+c} \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)\right)+2 b^3 B \sqrt{b+c} \cosh (x) \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)+b B c \sqrt{b-c} (b+c)}{b (b-c)^{3/2} (b+c)^2 (b \cosh (x)+c \sinh (x))}","\frac{A b \sinh (x)+A c \cosh (x)+B c}{\left(b^2-c^2\right) (b \cosh (x)+c \sinh (x))}+\frac{b B \tan ^{-1}\left(\frac{b \sinh (x)+c \cosh (x)}{\sqrt{b^2-c^2}}\right)}{\left(b^2-c^2\right)^{3/2}}",1,"(b*B*Sqrt[b - c]*c*(b + c) + 2*b^3*B*Sqrt[b + c]*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])]*Cosh[x] + (A*(b - c)^(3/2)*(b + c)^2 + 2*b^2*B*c*Sqrt[b + c]*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])])*Sinh[x])/(b*(b - c)^(3/2)*(b + c)^2*(b*Cosh[x] + c*Sinh[x]))","A",1
729,1,134,120,1.0910362,"\int \frac{A+B \cosh (x)}{(b \cosh (x)+c \sinh (x))^3} \, dx","Integrate[(A + B*Cosh[x])/(b*Cosh[x] + c*Sinh[x])^3,x]","\frac{1}{2} \left(\frac{A \left(b^2-c^2\right) \sinh (x)+b B c}{b (b-c) (b+c) (b \cosh (x)+c \sinh (x))^2}+\frac{A c+2 b B \sinh (x)}{b (b-c) (b+c) (b \cosh (x)+c \sinh (x))}+\frac{2 A \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)}{(b-c)^{3/2} (b+c)^{3/2}}\right)","\frac{A b \sinh (x)+A c \cosh (x)+B c}{2 \left(b^2-c^2\right) (b \cosh (x)+c \sinh (x))^2}+\frac{A \tan ^{-1}\left(\frac{b \sinh (x)+c \cosh (x)}{\sqrt{b^2-c^2}}\right)}{2 \left(b^2-c^2\right)^{3/2}}+\frac{b^2 B \sinh (x)+b B c \cosh (x)}{\left(b^2-c^2\right)^2 (b \cosh (x)+c \sinh (x))}",1,"((2*A*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])])/((b - c)^(3/2)*(b + c)^(3/2)) + (A*c + 2*b*B*Sinh[x])/(b*(b - c)*(b + c)*(b*Cosh[x] + c*Sinh[x])) + (b*B*c + A*(b^2 - c^2)*Sinh[x])/(b*(b - c)*(b + c)*(b*Cosh[x] + c*Sinh[x])^2))/2","A",1
730,1,17,11,0.004066,"\int \frac{\cosh (x)+\sinh (x)}{\cosh (x)-\sinh (x)} \, dx","Integrate[(Cosh[x] + Sinh[x])/(Cosh[x] - Sinh[x]),x]","\frac{1}{2} \sinh (2 x)+\frac{1}{2} \cosh (2 x)","\frac{1}{2} (\sinh (x)+\cosh (x))^2",1,"Cosh[2*x]/2 + Sinh[2*x]/2","A",1
731,1,17,11,0.004964,"\int \frac{\cosh (x)-\sinh (x)}{\cosh (x)+\sinh (x)} \, dx","Integrate[(Cosh[x] - Sinh[x])/(Cosh[x] + Sinh[x]),x]","\frac{1}{2} \sinh (2 x)-\frac{1}{2} \cosh (2 x)","-\frac{1}{2 (\sinh (x)+\cosh (x))^2}",1,"-1/2*Cosh[2*x] + Sinh[2*x]/2","A",1
732,1,15,14,0.0348602,"\int \frac{\cosh (x)-i \sinh (x)}{\cosh (x)+i \sinh (x)} \, dx","Integrate[(Cosh[x] - I*Sinh[x])/(Cosh[x] + I*Sinh[x]),x]","\tan ^{-1}(\tanh (x))-\frac{1}{2} i \log (\cosh (2 x))","-i \log (\cosh (x)+i \sinh (x))",1,"ArcTan[Tanh[x]] - (I/2)*Log[Cosh[2*x]]","A",1
733,1,43,53,0.1240132,"\int \frac{B \cosh (x)+C \sinh (x)}{b \cosh (x)+c \sinh (x)} \, dx","Integrate[(B*Cosh[x] + C*Sinh[x])/(b*Cosh[x] + c*Sinh[x]),x]","\frac{x (b B-c C)+(b C-B c) \log (b \cosh (x)+c \sinh (x))}{(b-c) (b+c)}","\frac{x (b B-c C)}{b^2-c^2}-\frac{(B c-b C) \log (b \cosh (x)+c \sinh (x))}{b^2-c^2}",1,"((b*B - c*C)*x + (-(B*c) + b*C)*Log[b*Cosh[x] + c*Sinh[x]])/((b - c)*(b + c))","A",1
734,1,87,78,0.2475626,"\int \frac{B \cosh (x)+C \sinh (x)}{(b \cosh (x)+c \sinh (x))^2} \, dx","Integrate[(B*Cosh[x] + C*Sinh[x])/(b*Cosh[x] + c*Sinh[x])^2,x]","\frac{2 (b B-c C) \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)}{(b-c)^{3/2} (b+c)^{3/2}}+\frac{B c-b C}{(b-c) (b+c) (b \cosh (x)+c \sinh (x))}","\frac{B c-b C}{\left(b^2-c^2\right) (b \cosh (x)+c \sinh (x))}+\frac{(b B-c C) \tan ^{-1}\left(\frac{b \sinh (x)+c \cosh (x)}{\sqrt{b^2-c^2}}\right)}{\left(b^2-c^2\right)^{3/2}}",1,"(2*(b*B - c*C)*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])])/((b - c)^(3/2)*(b + c)^(3/2)) + (B*c - b*C)/((b - c)*(b + c)*(b*Cosh[x] + c*Sinh[x]))","A",1
735,1,70,71,0.1708682,"\int \frac{B \cosh (x)+C \sinh (x)}{(b \cosh (x)+c \sinh (x))^3} \, dx","Integrate[(B*Cosh[x] + C*Sinh[x])/(b*Cosh[x] + c*Sinh[x])^3,x]","\frac{C \left(c^2-b^2\right)+b \sinh (2 x) (b B-c C)+c \cosh (2 x) (b B-c C)}{2 b (b-c) (b+c) (b \cosh (x)+c \sinh (x))^2}","\frac{B c-b C}{2 \left(b^2-c^2\right) (b \cosh (x)+c \sinh (x))^2}+\frac{\sinh (x) (b B-c C)}{b \left(b^2-c^2\right) (b \cosh (x)+c \sinh (x))}",1,"((-b^2 + c^2)*C + c*(b*B - c*C)*Cosh[2*x] + b*(b*B - c*C)*Sinh[2*x])/(2*b*(b - c)*(b + c)*(b*Cosh[x] + c*Sinh[x])^2)","A",1
736,1,90,92,0.2681424,"\int \frac{A+B \cosh (x)+C \sinh (x)}{b \cosh (x)+c \sinh (x)} \, dx","Integrate[(A + B*Cosh[x] + C*Sinh[x])/(b*Cosh[x] + c*Sinh[x]),x]","\frac{2 A \sqrt{b-c} \sqrt{b+c} \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)+x (b B-c C)+(b C-B c) \log (b \cosh (x)+c \sinh (x))}{(b-c) (b+c)}","\frac{A \tan ^{-1}\left(\frac{b \sinh (x)+c \cosh (x)}{\sqrt{b^2-c^2}}\right)}{\sqrt{b^2-c^2}}+\frac{x (b B-c C)}{b^2-c^2}-\frac{(B c-b C) \log (b \cosh (x)+c \sinh (x))}{b^2-c^2}",1,"((b*B - c*C)*x + 2*A*Sqrt[b - c]*Sqrt[b + c]*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])] + (-(B*c) + b*C)*Log[b*Cosh[x] + c*Sinh[x]])/((b - c)*(b + c))","A",1
737,1,106,88,0.2915956,"\int \frac{A+B \cosh (x)+C \sinh (x)}{(b \cosh (x)+c \sinh (x))^2} \, dx","Integrate[(A + B*Cosh[x] + C*Sinh[x])/(b*Cosh[x] + c*Sinh[x])^2,x]","\frac{A \left(b^2-c^2\right) \sinh (x)+b (B c-b C)}{b (b-c) (b+c) (b \cosh (x)+c \sinh (x))}+\frac{2 (b B-c C) \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)}{(b-c)^{3/2} (b+c)^{3/2}}","\frac{A b \sinh (x)+A c \cosh (x)-b C+B c}{\left(b^2-c^2\right) (b \cosh (x)+c \sinh (x))}+\frac{(b B-c C) \tan ^{-1}\left(\frac{b \sinh (x)+c \cosh (x)}{\sqrt{b^2-c^2}}\right)}{\left(b^2-c^2\right)^{3/2}}",1,"(2*(b*B - c*C)*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])])/((b - c)^(3/2)*(b + c)^(3/2)) + (b*(B*c - b*C) + A*(b^2 - c^2)*Sinh[x])/(b*(b - c)*(b + c)*(b*Cosh[x] + c*Sinh[x]))","A",1
738,1,146,135,0.8406449,"\int \frac{A+B \cosh (x)+C \sinh (x)}{(b \cosh (x)+c \sinh (x))^3} \, dx","Integrate[(A + B*Cosh[x] + C*Sinh[x])/(b*Cosh[x] + c*Sinh[x])^3,x]","\frac{1}{2} \left(\frac{A \left(b^2-c^2\right) \sinh (x)+b (B c-b C)}{b (b-c) (b+c) (b \cosh (x)+c \sinh (x))^2}+\frac{A c+2 \sinh (x) (b B-c C)}{b (b-c) (b+c) (b \cosh (x)+c \sinh (x))}+\frac{2 A \tan ^{-1}\left(\frac{b \tanh \left(\frac{x}{2}\right)+c}{\sqrt{b-c} \sqrt{b+c}}\right)}{(b-c)^{3/2} (b+c)^{3/2}}\right)","\frac{A b \sinh (x)+A c \cosh (x)-b C+B c}{2 \left(b^2-c^2\right) (b \cosh (x)+c \sinh (x))^2}+\frac{A \tan ^{-1}\left(\frac{b \sinh (x)+c \cosh (x)}{\sqrt{b^2-c^2}}\right)}{2 \left(b^2-c^2\right)^{3/2}}+\frac{b \sinh (x) (b B-c C)+c \cosh (x) (b B-c C)}{\left(b^2-c^2\right)^2 (b \cosh (x)+c \sinh (x))}",1,"((2*A*ArcTan[(c + b*Tanh[x/2])/(Sqrt[b - c]*Sqrt[b + c])])/((b - c)^(3/2)*(b + c)^(3/2)) + (b*(B*c - b*C) + A*(b^2 - c^2)*Sinh[x])/(b*(b - c)*(b + c)*(b*Cosh[x] + c*Sinh[x])^2) + (A*c + 2*(b*B - c*C)*Sinh[x])/(b*(b - c)*(b + c)*(b*Cosh[x] + c*Sinh[x])))/2","A",1
739,1,116,119,0.1991166,"\int (a+b \cosh (x)+c \sinh (x))^3 \, dx","Integrate[(a + b*Cosh[x] + c*Sinh[x])^3,x]","\frac{1}{12} \left(6 a x \left(2 a^2+3 b^2-3 c^2\right)+9 b \sinh (x) \left(4 a^2+b^2-c^2\right)+9 c \cosh (x) \left(4 a^2+b^2-c^2\right)+9 a \left(b^2+c^2\right) \sinh (2 x)+18 a b c \cosh (2 x)+b \left(b^2+3 c^2\right) \sinh (3 x)+c \left(3 b^2+c^2\right) \cosh (3 x)\right)","\frac{1}{2} a x \left(2 a^2+3 b^2-3 c^2\right)+\frac{1}{6} b \sinh (x) \left(11 a^2+4 b^2-4 c^2\right)+\frac{1}{6} c \cosh (x) \left(11 a^2+4 b^2-4 c^2\right)+\frac{1}{3} (b \sinh (x)+c \cosh (x)) (a+b \cosh (x)+c \sinh (x))^2+\frac{5}{6} (a b \sinh (x)+a c \cosh (x)) (a+b \cosh (x)+c \sinh (x))",1,"(6*a*(2*a^2 + 3*b^2 - 3*c^2)*x + 9*c*(4*a^2 + b^2 - c^2)*Cosh[x] + 18*a*b*c*Cosh[2*x] + c*(3*b^2 + c^2)*Cosh[3*x] + 9*b*(4*a^2 + b^2 - c^2)*Sinh[x] + 9*a*(b^2 + c^2)*Sinh[2*x] + b*(b^2 + 3*c^2)*Sinh[3*x])/12","A",1
740,1,54,59,0.0883742,"\int (a+b \cosh (x)+c \sinh (x))^2 \, dx","Integrate[(a + b*Cosh[x] + c*Sinh[x])^2,x]","\frac{1}{4} \left(2 x \left(2 a^2+b^2-c^2\right)+8 a b \sinh (x)+8 a c \cosh (x)+\left(b^2+c^2\right) \sinh (2 x)+2 b c \cosh (2 x)\right)","\frac{1}{2} x \left(2 a^2+b^2-c^2\right)+\frac{1}{2} (b \sinh (x)+c \cosh (x)) (a+b \cosh (x)+c \sinh (x))+\frac{3}{2} a b \sinh (x)+\frac{3}{2} a c \cosh (x)",1,"(2*(2*a^2 + b^2 - c^2)*x + 8*a*c*Cosh[x] + 2*b*c*Cosh[2*x] + 8*a*b*Sinh[x] + (b^2 + c^2)*Sinh[2*x])/4","A",1
741,1,12,12,0.002319,"\int (a+b \cosh (x)+c \sinh (x)) \, dx","Integrate[a + b*Cosh[x] + c*Sinh[x],x]","a x+b \sinh (x)+c \cosh (x)","a x+b \sinh (x)+c \cosh (x)",1,"a*x + c*Cosh[x] + b*Sinh[x]","A",1
742,1,54,51,0.0814239,"\int \frac{1}{a+b \cosh (x)+c \sinh (x)} \, dx","Integrate[(a + b*Cosh[x] + c*Sinh[x])^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\sqrt{-a^2+b^2-c^2}}","-\frac{2 \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\sqrt{a^2-b^2+c^2}}",1,"(2*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/Sqrt[-a^2 + b^2 - c^2]","A",1
743,1,105,90,0.2765839,"\int \frac{1}{(a+b \cosh (x)+c \sinh (x))^2} \, dx","Integrate[(a + b*Cosh[x] + c*Sinh[x])^(-2),x]","\frac{\left(b^2-c^2\right) \sinh (x)-a c}{b \left(-a^2+b^2-c^2\right) (a+b \cosh (x)+c \sinh (x))}-\frac{2 a \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\left(-a^2+b^2-c^2\right)^{3/2}}","-\frac{2 a \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(a^2-b^2+c^2\right)^{3/2}}-\frac{b \sinh (x)+c \cosh (x)}{\left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))}",1,"(-2*a*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/(-a^2 + b^2 - c^2)^(3/2) + (-(a*c) + (b^2 - c^2)*Sinh[x])/(b*(-a^2 + b^2 - c^2)*(a + b*Cosh[x] + c*Sinh[x]))","A",1
744,1,183,146,0.5302157,"\int \frac{1}{(a+b \cosh (x)+c \sinh (x))^3} \, dx","Integrate[(a + b*Cosh[x] + c*Sinh[x])^(-3),x]","\frac{1}{2} \left(\frac{2 \left(2 a^2+b^2-c^2\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\left(-a^2+b^2-c^2\right)^{5/2}}+\frac{\left(b^2-c^2\right) \sinh (x)-a c}{b \left(-a^2+b^2-c^2\right) (a+b \cosh (x)+c \sinh (x))^2}+\frac{c \left(2 a^2+b^2-c^2\right)-3 a \left(b^2-c^2\right) \sinh (x)}{b \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))}\right)","-\frac{\left(2 a^2+b^2-c^2\right) \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(a^2-b^2+c^2\right)^{5/2}}-\frac{3 (a b \sinh (x)+a c \cosh (x))}{2 \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))}-\frac{b \sinh (x)+c \cosh (x)}{2 \left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))^2}",1,"((2*(2*a^2 + b^2 - c^2)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/(-a^2 + b^2 - c^2)^(5/2) + (-(a*c) + (b^2 - c^2)*Sinh[x])/(b*(-a^2 + b^2 - c^2)*(a + b*Cosh[x] + c*Sinh[x])^2) + (c*(2*a^2 + b^2 - c^2) - 3*a*(b^2 - c^2)*Sinh[x])/(b*(a^2 - b^2 + c^2)^2*(a + b*Cosh[x] + c*Sinh[x])))/2","A",1
745,1,488,220,0.9614258,"\int \frac{1}{(a+b \cosh (x)+c \sinh (x))^4} \, dx","Integrate[(a + b*Cosh[x] + c*Sinh[x])^(-4),x]","-\frac{a \left(2 a^2+3 b^2-3 c^2\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\left(-a^2+b^2-c^2\right)^{7/2}}-\frac{-44 a^5 c+72 a^4 b^2 \sinh (x)-132 a^4 c^2 \sinh (x)+54 a^3 b^3 \sinh (2 x)-82 a^3 b^2 c-78 a^3 b c^2 \sinh (2 x)+82 a^3 c^3-9 a^2 b^4 \sinh (x)+11 a^2 b^4 \sinh (3 x)+22 a^2 b^3 c \cosh (3 x)-72 a^2 b^2 c^2 \sinh (x)-30 a^2 b c \cosh (x) \left(2 a^2+3 b^2-3 c^2\right)-6 a c \cosh (2 x) \left(a^2 \left(11 c^2-7 b^2\right)+2 \left(b^4+b^2 c^2-2 c^4\right)\right)-22 a^2 b c^3 \cosh (3 x)+81 a^2 c^4 \sinh (x)-11 a^2 c^4 \sinh (3 x)+6 a b^5 \sinh (2 x)-24 a b^4 c-48 a b^3 c^2 \sinh (2 x)+48 a b^2 c^3+42 a b c^4 \sinh (2 x)-24 a c^5+12 b^6 \sinh (x)+4 b^6 \sinh (3 x)+8 b^5 c \cosh (3 x)-36 b^4 c^2 \sinh (x)-4 b^4 c^2 \sinh (3 x)-16 b^3 c^3 \cosh (3 x)+36 b^2 c^4 \sinh (x)-4 b^2 c^4 \sinh (3 x)+8 b c^5 \cosh (3 x)-12 c^6 \sinh (x)+4 c^6 \sinh (3 x)}{24 b \left(a^2-b^2+c^2\right)^3 (a+b \cosh (x)+c \sinh (x))^3}","-\frac{a \left(2 a^2+3 b^2-3 c^2\right) \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(a^2-b^2+c^2\right)^{7/2}}-\frac{b \sinh (x) \left(11 a^2+4 b^2-4 c^2\right)+c \cosh (x) \left(11 a^2+4 b^2-4 c^2\right)}{6 \left(a^2-b^2+c^2\right)^3 (a+b \cosh (x)+c \sinh (x))}-\frac{5 (a b \sinh (x)+a c \cosh (x))}{6 \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))^2}-\frac{b \sinh (x)+c \cosh (x)}{3 \left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))^3}",1,"-((a*(2*a^2 + 3*b^2 - 3*c^2)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/(-a^2 + b^2 - c^2)^(7/2)) - (-44*a^5*c - 82*a^3*b^2*c - 24*a*b^4*c + 82*a^3*c^3 + 48*a*b^2*c^3 - 24*a*c^5 - 30*a^2*b*c*(2*a^2 + 3*b^2 - 3*c^2)*Cosh[x] - 6*a*c*(a^2*(-7*b^2 + 11*c^2) + 2*(b^4 + b^2*c^2 - 2*c^4))*Cosh[2*x] + 22*a^2*b^3*c*Cosh[3*x] + 8*b^5*c*Cosh[3*x] - 22*a^2*b*c^3*Cosh[3*x] - 16*b^3*c^3*Cosh[3*x] + 8*b*c^5*Cosh[3*x] + 72*a^4*b^2*Sinh[x] - 9*a^2*b^4*Sinh[x] + 12*b^6*Sinh[x] - 132*a^4*c^2*Sinh[x] - 72*a^2*b^2*c^2*Sinh[x] - 36*b^4*c^2*Sinh[x] + 81*a^2*c^4*Sinh[x] + 36*b^2*c^4*Sinh[x] - 12*c^6*Sinh[x] + 54*a^3*b^3*Sinh[2*x] + 6*a*b^5*Sinh[2*x] - 78*a^3*b*c^2*Sinh[2*x] - 48*a*b^3*c^2*Sinh[2*x] + 42*a*b*c^4*Sinh[2*x] + 11*a^2*b^4*Sinh[3*x] + 4*b^6*Sinh[3*x] - 4*b^4*c^2*Sinh[3*x] - 11*a^2*c^4*Sinh[3*x] - 4*b^2*c^4*Sinh[3*x] + 4*c^6*Sinh[3*x])/(24*b*(a^2 - b^2 + c^2)^3*(a + b*Cosh[x] + c*Sinh[x])^3)","B",1
746,1,112,105,0.1657873,"\int (a+a \cosh (x)+c \sinh (x))^3 \, dx","Integrate[(a + a*Cosh[x] + c*Sinh[x])^3,x]","\frac{1}{12} \left(30 a^3 x+45 a^3 \sinh (x)+9 a^3 \sinh (2 x)+a^3 \sinh (3 x)-9 c \left(c^2-5 a^2\right) \cosh (x)+18 a^2 c \cosh (2 x)+3 a^2 c \cosh (3 x)-18 a c^2 x-9 a c^2 \sinh (x)+9 a c^2 \sinh (2 x)+3 a c^2 \sinh (3 x)+c^3 \cosh (3 x)\right)","\frac{1}{2} a x \left(5 a^2-3 c^2\right)+\frac{1}{6} a \left(15 a^2-4 c^2\right) \sinh (x)+\frac{1}{6} c \left(15 a^2-4 c^2\right) \cosh (x)+\frac{5}{6} \left(a^2 \sinh (x)+a c \cosh (x)\right) (a \cosh (x)+a+c \sinh (x))+\frac{1}{3} (a \sinh (x)+c \cosh (x)) (a \cosh (x)+a+c \sinh (x))^2",1,"(30*a^3*x - 18*a*c^2*x - 9*c*(-5*a^2 + c^2)*Cosh[x] + 18*a^2*c*Cosh[2*x] + 3*a^2*c*Cosh[3*x] + c^3*Cosh[3*x] + 45*a^3*Sinh[x] - 9*a*c^2*Sinh[x] + 9*a^3*Sinh[2*x] + 9*a*c^2*Sinh[2*x] + a^3*Sinh[3*x] + 3*a*c^2*Sinh[3*x])/12","A",1
747,1,55,57,0.0711102,"\int (a+a \cosh (x)+c \sinh (x))^2 \, dx","Integrate[(a + a*Cosh[x] + c*Sinh[x])^2,x]","\frac{1}{2} x \left(3 a^2-c^2\right)+\frac{1}{4} \left(a^2+c^2\right) \sinh (2 x)+2 a^2 \sinh (x)+2 a c \cosh (x)+\frac{1}{2} a c \cosh (2 x)","\frac{1}{2} x \left(3 a^2-c^2\right)+\frac{3}{2} a^2 \sinh (x)+\frac{3}{2} a c \cosh (x)+\frac{1}{2} (a \sinh (x)+c \cosh (x)) (a \cosh (x)+a+c \sinh (x))",1,"((3*a^2 - c^2)*x)/2 + 2*a*c*Cosh[x] + (a*c*Cosh[2*x])/2 + 2*a^2*Sinh[x] + ((a^2 + c^2)*Sinh[2*x])/4","A",1
748,1,12,12,0.0020596,"\int (a+a \cosh (x)+c \sinh (x)) \, dx","Integrate[a + a*Cosh[x] + c*Sinh[x],x]","a x+a \sinh (x)+c \cosh (x)","a x+a \sinh (x)+c \cosh (x)",1,"a*x + c*Cosh[x] + a*Sinh[x]","A",1
749,1,35,15,0.0425203,"\int \frac{1}{a+a \cosh (x)+c \sinh (x)} \, dx","Integrate[(a + a*Cosh[x] + c*Sinh[x])^(-1),x]","\frac{\log \left(a \cosh \left(\frac{x}{2}\right)+c \sinh \left(\frac{x}{2}\right)\right)}{c}-\frac{\log \left(\cosh \left(\frac{x}{2}\right)\right)}{c}","\frac{\log \left(a+c \tanh \left(\frac{x}{2}\right)\right)}{c}",1,"-(Log[Cosh[x/2]]/c) + Log[a*Cosh[x/2] + c*Sinh[x/2]]/c","B",1
750,1,87,43,0.3205714,"\int \frac{1}{(a+a \cosh (x)+c \sinh (x))^2} \, dx","Integrate[(a + a*Cosh[x] + c*Sinh[x])^(-2),x]","\frac{\frac{c \left(c^2-a^2\right) \sinh \left(\frac{x}{2}\right)}{a \left(a \cosh \left(\frac{x}{2}\right)+c \sinh \left(\frac{x}{2}\right)\right)}+2 a \left(\log \left(a \cosh \left(\frac{x}{2}\right)+c \sinh \left(\frac{x}{2}\right)\right)-\log \left(\cosh \left(\frac{x}{2}\right)\right)\right)-c \tanh \left(\frac{x}{2}\right)}{2 c^3}","\frac{a \log \left(a+c \tanh \left(\frac{x}{2}\right)\right)}{c^3}-\frac{a \sinh (x)+c \cosh (x)}{c^2 (a \cosh (x)+a+c \sinh (x))}",1,"(2*a*(-Log[Cosh[x/2]] + Log[a*Cosh[x/2] + c*Sinh[x/2]]) + (c*(-a^2 + c^2)*Sinh[x/2])/(a*(a*Cosh[x/2] + c*Sinh[x/2])) - c*Tanh[x/2])/(2*c^3)","B",1
751,1,148,89,0.5501909,"\int \frac{1}{(a+a \cosh (x)+c \sinh (x))^3} \, dx","Integrate[(a + a*Cosh[x] + c*Sinh[x])^(-3),x]","\frac{4 \left(c^2-3 a^2\right) \log \left(\cosh \left(\frac{x}{2}\right)\right)+\frac{6 c \left(c^2-a^2\right) \sinh \left(\frac{x}{2}\right)}{a \cosh \left(\frac{x}{2}\right)+c \sinh \left(\frac{x}{2}\right)}+4 \left(3 a^2-c^2\right) \log \left(a \cosh \left(\frac{x}{2}\right)+c \sinh \left(\frac{x}{2}\right)\right)+\frac{c^2 (a-c) (a+c)}{\left(a \cosh \left(\frac{x}{2}\right)+c \sinh \left(\frac{x}{2}\right)\right)^2}-6 a c \tanh \left(\frac{x}{2}\right)+c^2 \left(-\text{sech}^2\left(\frac{x}{2}\right)\right)}{8 c^5}","-\frac{3 \left(a^2 \sinh (x)+a c \cosh (x)\right)}{2 c^4 (a \cosh (x)+a+c \sinh (x))}+\frac{\left(3 a^2-c^2\right) \log \left(a+c \tanh \left(\frac{x}{2}\right)\right)}{2 c^5}-\frac{a \sinh (x)+c \cosh (x)}{2 c^2 (a \cosh (x)+a+c \sinh (x))^2}",1,"(4*(-3*a^2 + c^2)*Log[Cosh[x/2]] + 4*(3*a^2 - c^2)*Log[a*Cosh[x/2] + c*Sinh[x/2]] - c^2*Sech[x/2]^2 + ((a - c)*c^2*(a + c))/(a*Cosh[x/2] + c*Sinh[x/2])^2 + (6*c*(-a^2 + c^2)*Sinh[x/2])/(a*Cosh[x/2] + c*Sinh[x/2]) - 6*a*c*Tanh[x/2])/(8*c^5)","A",1
752,1,300,140,0.634018,"\int \frac{1}{(a+a \cosh (x)+c \sinh (x))^4} \, dx","Integrate[(a + a*Cosh[x] + c*Sinh[x])^(-4),x]","\frac{192 \left(3 a c^2-5 a^3\right) \log \left(\cosh \left(\frac{x}{2}\right)\right)+192 a \left(5 a^2-3 c^2\right) \log \left(a \cosh \left(\frac{x}{2}\right)+c \sinh \left(\frac{x}{2}\right)\right)-\frac{c \text{sech}^6\left(\frac{x}{2}\right) \left(150 a^6 \sinh (x)+120 a^6 \sinh (2 x)+30 a^6 \sinh (3 x)+75 a^5 c \cosh (3 x)-150 a^5 c-255 a^4 c^2 \sinh (x)-72 a^4 c^2 \sinh (2 x)+37 a^4 c^2 \sinh (3 x)-35 a^3 c^3 \cosh (3 x)+130 a^3 c^3+129 a^2 c^4 \sinh (x)+36 a^2 c^4 \sinh (2 x)-27 a^2 c^4 \sinh (3 x)+\left(-75 a^5 c+75 a^3 c^3+12 a c^5\right) \cosh (x)+6 a c \left(25 a^4-15 a^2 c^2+4 c^4\right) \cosh (2 x)+4 a c^5 \cosh (3 x)-24 a c^5-12 c^6 \sinh (x)+4 c^6 \sinh (3 x)\right)}{a \left(a+c \tanh \left(\frac{x}{2}\right)\right)^3}}{384 c^7}","-\frac{5 \left(a^2 \sinh (x)+a c \cosh (x)\right)}{6 c^4 (a \cosh (x)+a+c \sinh (x))^2}+\frac{a \left(5 a^2-3 c^2\right) \log \left(a+c \tanh \left(\frac{x}{2}\right)\right)}{2 c^7}-\frac{a \left(15 a^2-4 c^2\right) \sinh (x)+c \left(15 a^2-4 c^2\right) \cosh (x)}{6 c^6 (a \cosh (x)+a+c \sinh (x))}-\frac{a \sinh (x)+c \cosh (x)}{3 c^2 (a \cosh (x)+a+c \sinh (x))^3}",1,"(192*(-5*a^3 + 3*a*c^2)*Log[Cosh[x/2]] + 192*a*(5*a^2 - 3*c^2)*Log[a*Cosh[x/2] + c*Sinh[x/2]] - (c*Sech[x/2]^6*(-150*a^5*c + 130*a^3*c^3 - 24*a*c^5 + (-75*a^5*c + 75*a^3*c^3 + 12*a*c^5)*Cosh[x] + 6*a*c*(25*a^4 - 15*a^2*c^2 + 4*c^4)*Cosh[2*x] + 75*a^5*c*Cosh[3*x] - 35*a^3*c^3*Cosh[3*x] + 4*a*c^5*Cosh[3*x] + 150*a^6*Sinh[x] - 255*a^4*c^2*Sinh[x] + 129*a^2*c^4*Sinh[x] - 12*c^6*Sinh[x] + 120*a^6*Sinh[2*x] - 72*a^4*c^2*Sinh[2*x] + 36*a^2*c^4*Sinh[2*x] + 30*a^6*Sinh[3*x] + 37*a^4*c^2*Sinh[3*x] - 27*a^2*c^4*Sinh[3*x] + 4*c^6*Sinh[3*x]))/(a*(a + c*Tanh[x/2])^3))/(384*c^7)","B",1
753,1,208,188,0.5141509,"\int \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^4 \, dx","Integrate[(Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^4,x]","\frac{7}{4} \left(b^4-c^4\right) \sinh (2 x)+7 b (b-c) \sqrt{b^2-c^2} (b+c) \sinh (x)+\frac{1}{3} b \sqrt{b^2-c^2} \left(b^2+3 c^2\right) \sinh (3 x)+7 c (b-c) \sqrt{b^2-c^2} (b+c) \cosh (x)+\frac{7}{2} b c \left(b^2-c^2\right) \cosh (2 x)+\frac{1}{3} c \sqrt{b^2-c^2} \left(3 b^2+c^2\right) \cosh (3 x)+\frac{1}{8} b c \left(b^2+c^2\right) \cosh (4 x)+\frac{1}{32} \left(b^4+6 b^2 c^2+c^4\right) \sinh (4 x)+\frac{35}{8} x (b-c)^2 (b+c)^2","\frac{35}{8} x \left(b^2-c^2\right)^2+\frac{35}{8} b \left(b^2-c^2\right)^{3/2} \sinh (x)+\frac{35}{8} c \left(b^2-c^2\right)^{3/2} \cosh (x)+\frac{1}{4} (b \sinh (x)+c \cosh (x)) \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^3+\frac{7}{12} \sqrt{b^2-c^2} (b \sinh (x)+c \cosh (x)) \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^2+\frac{35}{24} \left(b^2-c^2\right) (b \sinh (x)+c \cosh (x)) \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)",1,"(35*(b - c)^2*(b + c)^2*x)/8 + 7*(b - c)*c*(b + c)*Sqrt[b^2 - c^2]*Cosh[x] + (7*b*c*(b^2 - c^2)*Cosh[2*x])/2 + (c*Sqrt[b^2 - c^2]*(3*b^2 + c^2)*Cosh[3*x])/3 + (b*c*(b^2 + c^2)*Cosh[4*x])/8 + 7*b*(b - c)*(b + c)*Sqrt[b^2 - c^2]*Sinh[x] + (7*(b^4 - c^4)*Sinh[2*x])/4 + (b*Sqrt[b^2 - c^2]*(b^2 + 3*c^2)*Sinh[3*x])/3 + ((b^4 + 6*b^2*c^2 + c^4)*Sinh[4*x])/32","A",1
754,1,134,136,0.266724,"\int \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^3 \, dx","Integrate[(Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^3,x]","\frac{1}{12} \left(30 x (b-c) (b+c) \sqrt{b^2-c^2}+45 b \left(b^2-c^2\right) \sinh (x)+9 \sqrt{b^2-c^2} \left(b^2+c^2\right) \sinh (2 x)+b \left(b^2+3 c^2\right) \sinh (3 x)+45 c \left(b^2-c^2\right) \cosh (x)+18 b c \sqrt{b^2-c^2} \cosh (2 x)+c \left(3 b^2+c^2\right) \cosh (3 x)\right)","\frac{5}{2} x \left(b^2-c^2\right)^{3/2}+\frac{5}{2} b \left(b^2-c^2\right) \sinh (x)+\frac{5}{2} c \left(b^2-c^2\right) \cosh (x)+\frac{1}{3} (b \sinh (x)+c \cosh (x)) \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^2+\frac{5}{6} \sqrt{b^2-c^2} (b \sinh (x)+c \cosh (x)) \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)",1,"(30*(b - c)*(b + c)*Sqrt[b^2 - c^2]*x + 45*c*(b^2 - c^2)*Cosh[x] + 18*b*c*Sqrt[b^2 - c^2]*Cosh[2*x] + c*(3*b^2 + c^2)*Cosh[3*x] + 45*b*(b^2 - c^2)*Sinh[x] + 9*Sqrt[b^2 - c^2]*(b^2 + c^2)*Sinh[2*x] + b*(b^2 + 3*c^2)*Sinh[3*x])/12","A",1
755,1,72,90,0.1191718,"\int \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^2 \, dx","Integrate[(Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^2,x]","\frac{1}{4} \left(8 b \sqrt{b^2-c^2} \sinh (x)+\left(b^2+c^2\right) \sinh (2 x)+8 c \sqrt{b^2-c^2} \cosh (x)+6 x (b-c) (b+c)+2 b c \cosh (2 x)\right)","\frac{3}{2} x \left(b^2-c^2\right)+\frac{3}{2} b \sqrt{b^2-c^2} \sinh (x)+\frac{3}{2} c \sqrt{b^2-c^2} \cosh (x)+\frac{1}{2} (b \sinh (x)+c \cosh (x)) \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)",1,"(6*(b - c)*(b + c)*x + 8*c*Sqrt[b^2 - c^2]*Cosh[x] + 2*b*c*Cosh[2*x] + 8*b*Sqrt[b^2 - c^2]*Sinh[x] + (b^2 + c^2)*Sinh[2*x])/4","A",1
756,1,24,24,0.0080338,"\int \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right) \, dx","Integrate[Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x],x]","x \sqrt{b^2-c^2}+b \sinh (x)+c \cosh (x)","x \sqrt{b^2-c^2}+b \sinh (x)+c \cosh (x)",1,"Sqrt[b^2 - c^2]*x + c*Cosh[x] + b*Sinh[x]","A",1
757,1,36,34,0.084471,"\int \frac{1}{\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)} \, dx","Integrate[(Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(-1),x]","\frac{-\sqrt{b^2-c^2} \sinh (x)-c}{c (b \sinh (x)+c \cosh (x))}","-\frac{\sqrt{b^2-c^2} \sinh (x)+c}{c (b \sinh (x)+c \cosh (x))}",1,"(-c - Sqrt[b^2 - c^2]*Sinh[x])/(c*(c*Cosh[x] + b*Sinh[x]))","A",1
758,1,68,100,0.1652694,"\int \frac{1}{\left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^2} \, dx","Integrate[(Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(-2),x]","-\frac{-2 c \sqrt{b^2-c^2}+b^2 \sinh ^3(x)+2 b c \cosh ^3(x)+2 c^2 \sinh (x)+c^2 \sinh (x) \cosh ^2(x)}{3 c (b \sinh (x)+c \cosh (x))^3}","\frac{b \sinh (x)+c \cosh (x)}{3 \sqrt{b^2-c^2} \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^2}-\frac{\sqrt{b^2-c^2} \sinh (x)+c}{3 c \sqrt{b^2-c^2} (b \sinh (x)+c \cosh (x))}",1,"-1/3*(-2*c*Sqrt[b^2 - c^2] + 2*b*c*Cosh[x]^3 + 2*c^2*Sinh[x] + c^2*Cosh[x]^2*Sinh[x] + b^2*Sinh[x]^3)/(c*(c*Cosh[x] + b*Sinh[x])^3)","A",1
759,1,184,146,0.4017185,"\int \frac{1}{\left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^3} \, dx","Integrate[(Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(-3),x]","\frac{-12 \left(b^2-c^2\right) \left(\sqrt{b^2-c^2} \sinh (x)+c\right)-\frac{2 \sqrt{b^2-c^2} \sinh (x) (b \sinh (x)+c \cosh (x))^4}{(b-c) (b+c)}-\frac{b \sqrt{b^2-c^2} (b \sinh (x)+c \cosh (x))^3}{(b-c) (b+c)}+\left(\sqrt{b^2-c^2} \sinh (x)-5 c\right) (b \sinh (x)+c \cosh (x))^2+12 b \sqrt{b^2-c^2} (b \sinh (x)+c \cosh (x))}{15 c (b \sinh (x)+c \cosh (x))^5}","\frac{2 (b \sinh (x)+c \cosh (x))}{15 \left(b^2-c^2\right) \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^2}+\frac{b \sinh (x)+c \cosh (x)}{5 \sqrt{b^2-c^2} \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^3}-\frac{2 \left(\sqrt{b^2-c^2} \sinh (x)+c\right)}{15 c \left(b^2-c^2\right) (b \sinh (x)+c \cosh (x))}",1,"(12*b*Sqrt[b^2 - c^2]*(c*Cosh[x] + b*Sinh[x]) - (b*Sqrt[b^2 - c^2]*(c*Cosh[x] + b*Sinh[x])^3)/((b - c)*(b + c)) - (2*Sqrt[b^2 - c^2]*Sinh[x]*(c*Cosh[x] + b*Sinh[x])^4)/((b - c)*(b + c)) + (c*Cosh[x] + b*Sinh[x])^2*(-5*c + Sqrt[b^2 - c^2]*Sinh[x]) - 12*(b^2 - c^2)*(c + Sqrt[b^2 - c^2]*Sinh[x]))/(15*c*(c*Cosh[x] + b*Sinh[x])^5)","A",1
760,1,425,198,0.8289861,"\int \frac{1}{\left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^4} \, dx","Integrate[(Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(-4),x]","-\frac{-35 b^6 \sinh (x)+21 b^6 \sinh (3 x)-7 b^6 \sinh (5 x)+b^6 \sinh (7 x)+112 b^5 c \cosh (3 x)-28 b^5 c \cosh (5 x)+6 b^5 c \cosh (7 x)+1295 b^4 c^2 \sinh (x)+189 b^4 c^2 \sinh (3 x)-35 b^4 c^2 \sinh (5 x)+15 b^4 c^2 \sinh (7 x)+56 b^3 c^3 \cosh (3 x)+20 b^3 c^3 \cosh (7 x)-2485 b^2 c^4 \sinh (x)-161 b^2 c^4 \sinh (3 x)+35 b^2 c^4 \sinh (5 x)+15 b^2 c^4 \sinh (7 x)+1190 b c \left(b^2-c^2\right)^2 \cosh (x)-832 c^5 \sqrt{b^2-c^2}+896 b c^4 \sqrt{b^2-c^2} \sinh (2 x)+1664 b^2 c^3 \sqrt{b^2-c^2}-832 b^4 c \sqrt{b^2-c^2}+448 c \sqrt{b^2-c^2} \left(c^4-b^4\right) \cosh (2 x)-896 b^3 c^2 \sqrt{b^2-c^2} \sinh (2 x)-168 b c^5 \cosh (3 x)+28 b c^5 \cosh (5 x)+6 b c^5 \cosh (7 x)+1225 c^6 \sinh (x)-49 c^6 \sinh (3 x)+7 c^6 \sinh (5 x)+c^6 \sinh (7 x)}{1120 c (b-c) (b+c) (b \sinh (x)+c \cosh (x))^7}","\frac{2 (b \sinh (x)+c \cosh (x))}{35 \left(b^2-c^2\right)^{3/2} \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^2}+\frac{3 (b \sinh (x)+c \cosh (x))}{35 \left(b^2-c^2\right) \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^3}+\frac{b \sinh (x)+c \cosh (x)}{7 \sqrt{b^2-c^2} \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^4}-\frac{2 \left(\sqrt{b^2-c^2} \sinh (x)+c\right)}{35 c \left(b^2-c^2\right)^{3/2} (b \sinh (x)+c \cosh (x))}",1,"-1/1120*(-832*b^4*c*Sqrt[b^2 - c^2] + 1664*b^2*c^3*Sqrt[b^2 - c^2] - 832*c^5*Sqrt[b^2 - c^2] + 1190*b*c*(b^2 - c^2)^2*Cosh[x] + 448*c*Sqrt[b^2 - c^2]*(-b^4 + c^4)*Cosh[2*x] + 112*b^5*c*Cosh[3*x] + 56*b^3*c^3*Cosh[3*x] - 168*b*c^5*Cosh[3*x] - 28*b^5*c*Cosh[5*x] + 28*b*c^5*Cosh[5*x] + 6*b^5*c*Cosh[7*x] + 20*b^3*c^3*Cosh[7*x] + 6*b*c^5*Cosh[7*x] - 35*b^6*Sinh[x] + 1295*b^4*c^2*Sinh[x] - 2485*b^2*c^4*Sinh[x] + 1225*c^6*Sinh[x] - 896*b^3*c^2*Sqrt[b^2 - c^2]*Sinh[2*x] + 896*b*c^4*Sqrt[b^2 - c^2]*Sinh[2*x] + 21*b^6*Sinh[3*x] + 189*b^4*c^2*Sinh[3*x] - 161*b^2*c^4*Sinh[3*x] - 49*c^6*Sinh[3*x] - 7*b^6*Sinh[5*x] - 35*b^4*c^2*Sinh[5*x] + 35*b^2*c^4*Sinh[5*x] + 7*c^6*Sinh[5*x] + b^6*Sinh[7*x] + 15*b^4*c^2*Sinh[7*x] + 15*b^2*c^4*Sinh[7*x] + c^6*Sinh[7*x])/((b - c)*c*(b + c)*(c*Cosh[x] + b*Sinh[x])^7)","B",1
761,1,3775,294,6.3551713,"\int (a+b \cosh (x)+c \sinh (x))^{5/2} \, dx","Integrate[(a + b*Cosh[x] + c*Sinh[x])^(5/2),x]","\text{Result too large to show}","\frac{16 i a \left(a^2-b^2+c^2\right) \sqrt{\frac{a+b \cosh (x)+c \sinh (x)}{a+\sqrt{b^2-c^2}}} F\left(\frac{1}{2} \left(i x-\tan ^{-1}(b,-i c)\right)|\frac{2 \sqrt{b^2-c^2}}{a+\sqrt{b^2-c^2}}\right)}{15 \sqrt{a+b \cosh (x)+c \sinh (x)}}-\frac{2 i \left(23 a^2+9 b^2-9 c^2\right) \sqrt{a+b \cosh (x)+c \sinh (x)} E\left(\frac{1}{2} \left(i x-\tan ^{-1}(b,-i c)\right)|\frac{2 \sqrt{b^2-c^2}}{a+\sqrt{b^2-c^2}}\right)}{15 \sqrt{\frac{a+b \cosh (x)+c \sinh (x)}{a+\sqrt{b^2-c^2}}}}+\frac{2}{5} (b \sinh (x)+c \cosh (x)) (a+b \cosh (x)+c \sinh (x))^{3/2}+\frac{16}{15} (a b \sinh (x)+a c \cosh (x)) \sqrt{a+b \cosh (x)+c \sinh (x)}",1,"Sqrt[a + b*Cosh[x] + c*Sinh[x]]*((2*b*(23*a^2 + 9*b^2 - 9*c^2))/(15*c) + (22*a*c*Cosh[x])/15 + (2*b*c*Cosh[2*x])/5 + (22*a*b*Sinh[x])/15 + ((b^2 + c^2)*Sinh[2*x])/5) + (2*a^3*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(Sqrt[1 - b^2/c^2]*c*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) + (34*a*b^2*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(15*Sqrt[1 - b^2/c^2]*c*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) - (34*a*c*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(15*Sqrt[1 - b^2/c^2]*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) - (23*a^2*b^2*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(15*c) - (3*b^4*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(5*c) + (23*a^2*c*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/15 + (6*b^2*c*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/5 - (3*c^3*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/5","C",0
762,1,2292,249,6.1572259,"\int (a+b \cosh (x)+c \sinh (x))^{3/2} \, dx","Integrate[(a + b*Cosh[x] + c*Sinh[x])^(3/2),x]","\text{Result too large to show}","\frac{2 i \left(a^2-b^2+c^2\right) \sqrt{\frac{a+b \cosh (x)+c \sinh (x)}{a+\sqrt{b^2-c^2}}} F\left(\frac{1}{2} \left(i x-\tan ^{-1}(b,-i c)\right)|\frac{2 \sqrt{b^2-c^2}}{a+\sqrt{b^2-c^2}}\right)}{3 \sqrt{a+b \cosh (x)+c \sinh (x)}}-\frac{8 i a \sqrt{a+b \cosh (x)+c \sinh (x)} E\left(\frac{1}{2} \left(i x-\tan ^{-1}(b,-i c)\right)|\frac{2 \sqrt{b^2-c^2}}{a+\sqrt{b^2-c^2}}\right)}{3 \sqrt{\frac{a+b \cosh (x)+c \sinh (x)}{a+\sqrt{b^2-c^2}}}}+\frac{2}{3} (b \sinh (x)+c \cosh (x)) \sqrt{a+b \cosh (x)+c \sinh (x)}",1,"((8*a*b)/(3*c) + (2*c*Cosh[x])/3 + (2*b*Sinh[x])/3)*Sqrt[a + b*Cosh[x] + c*Sinh[x]] + (2*a^2*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(Sqrt[1 - b^2/c^2]*c*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) + (2*b^2*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(3*Sqrt[1 - b^2/c^2]*c*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) - (2*c*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(3*Sqrt[1 - b^2/c^2]*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) - (4*a*b^2*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(3*c) + (4*a*c*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/3","C",0
763,1,1401,102,6.1115712,"\int \sqrt{a+b \cosh (x)+c \sinh (x)} \, dx","Integrate[Sqrt[a + b*Cosh[x] + c*Sinh[x]],x]","-\frac{\left(\frac{c F_1\left(-\frac{1}{2};-\frac{1}{2},-\frac{1}{2};\frac{1}{2};\frac{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \left(\frac{a}{b \sqrt{1-\frac{c^2}{b^2}}}+1\right)},\frac{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \left(\frac{a}{b \sqrt{1-\frac{c^2}{b^2}}}-1\right)}\right) \sinh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \sqrt{\frac{b \sqrt{\frac{b^2-c^2}{b^2}}-b \sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{a+b \sqrt{\frac{b^2-c^2}{b^2}}}} \sqrt{a+b \sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)} \sqrt{\frac{\sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right) b+\sqrt{\frac{b^2-c^2}{b^2}} b}{b \sqrt{\frac{b^2-c^2}{b^2}}-a}}}-\frac{\frac{c \sinh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}}}-\frac{2 b \left(a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)\right)}{b^2-c^2}}{\sqrt{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}}\right) b^2}{c}+\frac{2 \sqrt{a+b \cosh (x)+c \sinh (x)} b}{c}+c \left(\frac{c F_1\left(-\frac{1}{2};-\frac{1}{2},-\frac{1}{2};\frac{1}{2};\frac{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \left(\frac{a}{b \sqrt{1-\frac{c^2}{b^2}}}+1\right)},\frac{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \left(\frac{a}{b \sqrt{1-\frac{c^2}{b^2}}}-1\right)}\right) \sinh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \sqrt{\frac{b \sqrt{\frac{b^2-c^2}{b^2}}-b \sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{a+b \sqrt{\frac{b^2-c^2}{b^2}}}} \sqrt{a+b \sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)} \sqrt{\frac{\sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right) b+\sqrt{\frac{b^2-c^2}{b^2}} b}{b \sqrt{\frac{b^2-c^2}{b^2}}-a}}}-\frac{\frac{c \sinh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}}}-\frac{2 b \left(a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)\right)}{b^2-c^2}}{\sqrt{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}}\right)+\frac{2 a F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{2};\frac{3}{2};-\frac{i \left(a+\sqrt{1-\frac{b^2}{c^2}} c \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)\right)}{\sqrt{1-\frac{b^2}{c^2}} \left(1-\frac{i a}{\sqrt{1-\frac{b^2}{c^2}} c}\right) c},-\frac{i \left(a+\sqrt{1-\frac{b^2}{c^2}} c \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)\right)}{\sqrt{1-\frac{b^2}{c^2}} \left(-\frac{i a}{\sqrt{1-\frac{b^2}{c^2}} c}-1\right) c}\right) \text{sech}\left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right) \sqrt{i \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)-1} \sqrt{\frac{c \sqrt{\frac{c^2-b^2}{c^2}}-i c \sqrt{\frac{c^2-b^2}{c^2}} \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)}{i a+c \sqrt{\frac{c^2-b^2}{c^2}}}} \sqrt{\frac{i \sqrt{\frac{c^2-b^2}{c^2}} \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right) c+\sqrt{\frac{c^2-b^2}{c^2}} c}{c \sqrt{\frac{c^2-b^2}{c^2}}-i a}} \sqrt{a+c \sqrt{\frac{c^2-b^2}{c^2}} \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)}}{\sqrt{1-\frac{b^2}{c^2}} c \sqrt{i \left(\sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)+i\right)}}","-\frac{2 i \sqrt{a+b \cosh (x)+c \sinh (x)} E\left(\frac{1}{2} \left(i x-\tan ^{-1}(b,-i c)\right)|\frac{2 \sqrt{b^2-c^2}}{a+\sqrt{b^2-c^2}}\right)}{\sqrt{\frac{a+b \cosh (x)+c \sinh (x)}{a+\sqrt{b^2-c^2}}}}",1,"(2*b*Sqrt[a + b*Cosh[x] + c*Sinh[x]])/c + (2*a*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(Sqrt[1 - b^2/c^2]*c*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) - (b^2*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/c + c*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]])","C",0
764,1,237,102,0.5197087,"\int \frac{1}{\sqrt{a+b \cosh (x)+c \sinh (x)}} \, dx","Integrate[1/Sqrt[a + b*Cosh[x] + c*Sinh[x]],x]","\frac{2 \text{sech}\left(\tanh ^{-1}\left(\frac{b}{c}\right)+x\right) \sqrt{a+b \cosh (x)+c \sinh (x)} \sqrt{-\frac{-i c \sqrt{1-\frac{b^2}{c^2}}+b \cosh (x)+c \sinh (x)}{a+i c \sqrt{1-\frac{b^2}{c^2}}}} \sqrt{-\frac{i c \sqrt{1-\frac{b^2}{c^2}}+b \cosh (x)+c \sinh (x)}{a-i c \sqrt{1-\frac{b^2}{c^2}}}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{2};\frac{3}{2};\frac{a+b \cosh (x)+c \sinh (x)}{a+i \sqrt{1-\frac{b^2}{c^2}} c},\frac{a+b \cosh (x)+c \sinh (x)}{a-i \sqrt{1-\frac{b^2}{c^2}} c}\right)}{c \sqrt{1-\frac{b^2}{c^2}}}","-\frac{2 i \sqrt{\frac{a+b \cosh (x)+c \sinh (x)}{a+\sqrt{b^2-c^2}}} F\left(\frac{1}{2} \left(i x-\tan ^{-1}(b,-i c)\right)|\frac{2 \sqrt{b^2-c^2}}{a+\sqrt{b^2-c^2}}\right)}{\sqrt{a+b \cosh (x)+c \sinh (x)}}",1,"(2*AppellF1[1/2, 1/2, 1/2, 3/2, (a + b*Cosh[x] + c*Sinh[x])/(a + I*Sqrt[1 - b^2/c^2]*c), (a + b*Cosh[x] + c*Sinh[x])/(a - I*Sqrt[1 - b^2/c^2]*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[a + b*Cosh[x] + c*Sinh[x]]*Sqrt[-(((-I)*Sqrt[1 - b^2/c^2]*c + b*Cosh[x] + c*Sinh[x])/(a + I*Sqrt[1 - b^2/c^2]*c))]*Sqrt[-((I*Sqrt[1 - b^2/c^2]*c + b*Cosh[x] + c*Sinh[x])/(a - I*Sqrt[1 - b^2/c^2]*c))])/(Sqrt[1 - b^2/c^2]*c)","C",0
765,1,1522,156,6.21023,"\int \frac{1}{(a+b \cosh (x)+c \sinh (x))^{3/2}} \, dx","Integrate[(a + b*Cosh[x] + c*Sinh[x])^(-3/2),x]","-\frac{\left(\frac{c F_1\left(-\frac{1}{2};-\frac{1}{2},-\frac{1}{2};\frac{1}{2};\frac{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \left(\frac{a}{b \sqrt{1-\frac{c^2}{b^2}}}+1\right)},\frac{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \left(\frac{a}{b \sqrt{1-\frac{c^2}{b^2}}}-1\right)}\right) \sinh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \sqrt{\frac{b \sqrt{\frac{b^2-c^2}{b^2}}-b \sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{a+b \sqrt{\frac{b^2-c^2}{b^2}}}} \sqrt{a+b \sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)} \sqrt{\frac{\sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right) b+\sqrt{\frac{b^2-c^2}{b^2}} b}{b \sqrt{\frac{b^2-c^2}{b^2}}-a}}}-\frac{\frac{c \sinh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}}}-\frac{2 b \left(a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)\right)}{b^2-c^2}}{\sqrt{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}}\right) b^2}{c \left(a^2-b^2+c^2\right)}+\sqrt{a+b \cosh (x)+c \sinh (x)} \left(-\frac{2 \left(b^2-c^2\right)}{b c \left(-a^2+b^2-c^2\right)}-\frac{2 \left(-\sinh (x) b^2+a c+c^2 \sinh (x)\right)}{b \left(-a^2+b^2-c^2\right) (a+b \cosh (x)+c \sinh (x))}\right)+\frac{c \left(\frac{c F_1\left(-\frac{1}{2};-\frac{1}{2},-\frac{1}{2};\frac{1}{2};\frac{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \left(\frac{a}{b \sqrt{1-\frac{c^2}{b^2}}}+1\right)},\frac{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \left(\frac{a}{b \sqrt{1-\frac{c^2}{b^2}}}-1\right)}\right) \sinh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}} \sqrt{\frac{b \sqrt{\frac{b^2-c^2}{b^2}}-b \sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{a+b \sqrt{\frac{b^2-c^2}{b^2}}}} \sqrt{a+b \sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)} \sqrt{\frac{\sqrt{\frac{b^2-c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right) b+\sqrt{\frac{b^2-c^2}{b^2}} b}{b \sqrt{\frac{b^2-c^2}{b^2}}-a}}}-\frac{\frac{c \sinh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}{b \sqrt{1-\frac{c^2}{b^2}}}-\frac{2 b \left(a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)\right)}{b^2-c^2}}{\sqrt{a+b \sqrt{1-\frac{c^2}{b^2}} \cosh \left(x+\tanh ^{-1}\left(\frac{c}{b}\right)\right)}}\right)}{a^2-b^2+c^2}+\frac{2 a F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{2};\frac{3}{2};-\frac{i \left(a+\sqrt{1-\frac{b^2}{c^2}} c \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)\right)}{\sqrt{1-\frac{b^2}{c^2}} \left(1-\frac{i a}{\sqrt{1-\frac{b^2}{c^2}} c}\right) c},-\frac{i \left(a+\sqrt{1-\frac{b^2}{c^2}} c \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)\right)}{\sqrt{1-\frac{b^2}{c^2}} \left(-\frac{i a}{\sqrt{1-\frac{b^2}{c^2}} c}-1\right) c}\right) \text{sech}\left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right) \sqrt{i \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)-1} \sqrt{\frac{c \sqrt{\frac{c^2-b^2}{c^2}}-i c \sqrt{\frac{c^2-b^2}{c^2}} \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)}{i a+c \sqrt{\frac{c^2-b^2}{c^2}}}} \sqrt{\frac{i \sqrt{\frac{c^2-b^2}{c^2}} \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right) c+\sqrt{\frac{c^2-b^2}{c^2}} c}{c \sqrt{\frac{c^2-b^2}{c^2}}-i a}} \sqrt{a+c \sqrt{\frac{c^2-b^2}{c^2}} \sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)}}{\sqrt{1-\frac{b^2}{c^2}} c \left(a^2-b^2+c^2\right) \sqrt{i \left(\sinh \left(x+\tanh ^{-1}\left(\frac{b}{c}\right)\right)+i\right)}}","-\frac{2 (b \sinh (x)+c \cosh (x))}{\left(a^2-b^2+c^2\right) \sqrt{a+b \cosh (x)+c \sinh (x)}}-\frac{2 i \sqrt{a+b \cosh (x)+c \sinh (x)} E\left(\frac{1}{2} \left(i x-\tan ^{-1}(b,-i c)\right)|\frac{2 \sqrt{b^2-c^2}}{a+\sqrt{b^2-c^2}}\right)}{\left(a^2-b^2+c^2\right) \sqrt{\frac{a+b \cosh (x)+c \sinh (x)}{a+\sqrt{b^2-c^2}}}}",1,"Sqrt[a + b*Cosh[x] + c*Sinh[x]]*((-2*(b^2 - c^2))/(b*c*(-a^2 + b^2 - c^2)) - (2*(a*c - b^2*Sinh[x] + c^2*Sinh[x]))/(b*(-a^2 + b^2 - c^2)*(a + b*Cosh[x] + c*Sinh[x]))) + (2*a*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(Sqrt[1 - b^2/c^2]*c*(a^2 - b^2 + c^2)*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) - (b^2*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(c*(a^2 - b^2 + c^2)) + (c*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(a^2 - b^2 + c^2)","C",0
766,1,2492,322,6.261033,"\int \frac{1}{(a+b \cosh (x)+c \sinh (x))^{5/2}} \, dx","Integrate[(a + b*Cosh[x] + c*Sinh[x])^(-5/2),x]","\text{Result too large to show}","\frac{2 i \sqrt{\frac{a+b \cosh (x)+c \sinh (x)}{a+\sqrt{b^2-c^2}}} F\left(\frac{1}{2} \left(i x-\tan ^{-1}(b,-i c)\right)|\frac{2 \sqrt{b^2-c^2}}{a+\sqrt{b^2-c^2}}\right)}{3 \left(a^2-b^2+c^2\right) \sqrt{a+b \cosh (x)+c \sinh (x)}}-\frac{8 i a \sqrt{a+b \cosh (x)+c \sinh (x)} E\left(\frac{1}{2} \left(i x-\tan ^{-1}(b,-i c)\right)|\frac{2 \sqrt{b^2-c^2}}{a+\sqrt{b^2-c^2}}\right)}{3 \left(a^2-b^2+c^2\right)^2 \sqrt{\frac{a+b \cosh (x)+c \sinh (x)}{a+\sqrt{b^2-c^2}}}}-\frac{8 (a b \sinh (x)+a c \cosh (x))}{3 \left(a^2-b^2+c^2\right)^2 \sqrt{a+b \cosh (x)+c \sinh (x)}}-\frac{2 (b \sinh (x)+c \cosh (x))}{3 \left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))^{3/2}}",1,"Sqrt[a + b*Cosh[x] + c*Sinh[x]]*((8*a*(b^2 - c^2))/(3*b*c*(a^2 - b^2 + c^2)^2) - (2*(a*c - b^2*Sinh[x] + c^2*Sinh[x]))/(3*b*(-a^2 + b^2 - c^2)*(a + b*Cosh[x] + c*Sinh[x])^2) - (2*(-3*a^2*c - b^2*c + c^3 + 4*a*b^2*Sinh[x] - 4*a*c^2*Sinh[x]))/(3*b*(-a^2 + b^2 - c^2)^2*(a + b*Cosh[x] + c*Sinh[x]))) + (2*a^2*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(Sqrt[1 - b^2/c^2]*c*(a^2 - b^2 + c^2)^2*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) + (2*b^2*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(3*Sqrt[1 - b^2/c^2]*c*(a^2 - b^2 + c^2)^2*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) - (2*c*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(3*Sqrt[1 - b^2/c^2]*(a^2 - b^2 + c^2)^2*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) - (4*a*b^2*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(3*c*(a^2 - b^2 + c^2)^2) + (4*a*c*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(3*(a^2 - b^2 + c^2)^2)","C",0
767,1,4093,411,6.5665879,"\int \frac{1}{(a+b \cosh (x)+c \sinh (x))^{7/2}} \, dx","Integrate[(a + b*Cosh[x] + c*Sinh[x])^(-7/2),x]","\text{Result too large to show}","\frac{16 i a \sqrt{\frac{a+b \cosh (x)+c \sinh (x)}{a+\sqrt{b^2-c^2}}} F\left(\frac{1}{2} \left(i x-\tan ^{-1}(b,-i c)\right)|\frac{2 \sqrt{b^2-c^2}}{a+\sqrt{b^2-c^2}}\right)}{15 \left(a^2-b^2+c^2\right)^2 \sqrt{a+b \cosh (x)+c \sinh (x)}}-\frac{2 i \left(23 a^2+9 b^2-9 c^2\right) \sqrt{a+b \cosh (x)+c \sinh (x)} E\left(\frac{1}{2} \left(i x-\tan ^{-1}(b,-i c)\right)|\frac{2 \sqrt{b^2-c^2}}{a+\sqrt{b^2-c^2}}\right)}{15 \left(a^2-b^2+c^2\right)^3 \sqrt{\frac{a+b \cosh (x)+c \sinh (x)}{a+\sqrt{b^2-c^2}}}}-\frac{2 \left(b \sinh (x) \left(23 a^2+9 b^2-9 c^2\right)+c \cosh (x) \left(23 a^2+9 b^2-9 c^2\right)\right)}{15 \left(a^2-b^2+c^2\right)^3 \sqrt{a+b \cosh (x)+c \sinh (x)}}-\frac{16 (a b \sinh (x)+a c \cosh (x))}{15 \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))^{3/2}}-\frac{2 (b \sinh (x)+c \cosh (x))}{5 \left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))^{5/2}}",1,"Sqrt[a + b*Cosh[x] + c*Sinh[x]]*((-2*(23*a^2 + 9*b^2 - 9*c^2)*(b^2 - c^2))/(15*b*c*(-a^2 + b^2 - c^2)^3) - (2*(a*c - b^2*Sinh[x] + c^2*Sinh[x]))/(5*b*(-a^2 + b^2 - c^2)*(a + b*Cosh[x] + c*Sinh[x])^3) - (2*(-5*a^2*c - 3*b^2*c + 3*c^3 + 8*a*b^2*Sinh[x] - 8*a*c^2*Sinh[x]))/(15*b*(-a^2 + b^2 - c^2)^2*(a + b*Cosh[x] + c*Sinh[x])^2) + (2*(-15*a^3*c - 17*a*b^2*c + 17*a*c^3 + 23*a^2*b^2*Sinh[x] + 9*b^4*Sinh[x] - 23*a^2*c^2*Sinh[x] - 18*b^2*c^2*Sinh[x] + 9*c^4*Sinh[x]))/(15*b*(-a^2 + b^2 - c^2)^3*(a + b*Cosh[x] + c*Sinh[x]))) + (2*a^3*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(Sqrt[1 - b^2/c^2]*c*(a^2 - b^2 + c^2)^3*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) + (34*a*b^2*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(15*Sqrt[1 - b^2/c^2]*c*(a^2 - b^2 + c^2)^3*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) - (34*a*c*AppellF1[1/2, 1/2, 1/2, 3/2, ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c), ((-I)*(a + Sqrt[1 - b^2/c^2]*c*Sinh[x + ArcTanh[b/c]]))/(Sqrt[1 - b^2/c^2]*(-1 - (I*a)/(Sqrt[1 - b^2/c^2]*c))*c)]*Sech[x + ArcTanh[b/c]]*Sqrt[-1 + I*Sinh[x + ArcTanh[b/c]]]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] - I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/(I*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[(c*Sqrt[(-b^2 + c^2)/c^2] + I*c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]])/((-I)*a + c*Sqrt[(-b^2 + c^2)/c^2])]*Sqrt[a + c*Sqrt[(-b^2 + c^2)/c^2]*Sinh[x + ArcTanh[b/c]]])/(15*Sqrt[1 - b^2/c^2]*(a^2 - b^2 + c^2)^3*Sqrt[I*(I + Sinh[x + ArcTanh[b/c]])]) - (23*a^2*b^2*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(15*c*(a^2 - b^2 + c^2)^3) - (3*b^4*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(5*c*(a^2 - b^2 + c^2)^3) + (23*a^2*c*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(15*(a^2 - b^2 + c^2)^3) + (6*b^2*c*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(5*(a^2 - b^2 + c^2)^3) - (3*c^3*((c*AppellF1[-1/2, -1/2, -1/2, 1/2, (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(1 + a/(b*Sqrt[1 - c^2/b^2]))), (a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*(-1 + a/(b*Sqrt[1 - c^2/b^2])))]*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] - b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(a + b*Sqrt[(b^2 - c^2)/b^2])]*Sqrt[a + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]]]*Sqrt[(b*Sqrt[(b^2 - c^2)/b^2] + b*Sqrt[(b^2 - c^2)/b^2]*Cosh[x + ArcTanh[c/b]])/(-a + b*Sqrt[(b^2 - c^2)/b^2])]) - ((-2*b*(a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]))/(b^2 - c^2) + (c*Sinh[x + ArcTanh[c/b]])/(b*Sqrt[1 - c^2/b^2]))/Sqrt[a + b*Sqrt[1 - c^2/b^2]*Cosh[x + ArcTanh[c/b]]]))/(5*(a^2 - b^2 + c^2)^3)","C",0
768,1,10223,140,75.5229359,"\int \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{5/2} \, dx","Integrate[(Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(5/2),x]","\text{Result too large to show}","\frac{2}{5} (b \sinh (x)+c \cosh (x)) \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{3/2}+\frac{16}{15} \sqrt{b^2-c^2} (b \sinh (x)+c \cosh (x)) \sqrt{\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}+\frac{64 \left(b^2-c^2\right) (b \sinh (x)+c \cosh (x))}{15 \sqrt{\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}}",1,"Result too large to show","C",0
769,1,10141,92,73.4139643,"\int \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{3/2} \, dx","Integrate[(Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(3/2),x]","\text{Result too large to show}","\frac{2}{3} \sqrt{\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)} (b \sinh (x)+c \cosh (x))+\frac{8 \sqrt{b^2-c^2} (b \sinh (x)+c \cosh (x))}{3 \sqrt{\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}}",1,"Result too large to show","C",0
770,1,10054,37,74.4648676,"\int \sqrt{\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)} \, dx","Integrate[Sqrt[Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x]],x]","\text{Result too large to show}","\frac{2 (b \sinh (x)+c \cosh (x))}{\sqrt{\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}}",1,"Result too large to show","C",0
771,1,211,99,32.6947076,"\int \frac{1}{\sqrt{\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}} \, dx","Integrate[1/Sqrt[Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x]],x]","-\frac{\sqrt{2} \left(c \sqrt{b^2-c^2} \sinh (x)+b \sqrt{b^2-c^2} \cosh (x)+b^2-c^2\right) \sqrt{-\frac{c \sqrt{b^2-c^2} \sinh (x)+b \sqrt{b^2-c^2} \cosh (x)-b^2+c^2}{b^2-c^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{\frac{-b \cosh (x)-c \sinh (x)+\sqrt{b^2-c^2}}{\sqrt{b^2-c^2}}}}{\sqrt{2}}\right)\right|1\right)}{\sqrt{b^2-c^2} (b \sinh (x)+c \cosh (x)) \sqrt{\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}}","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt[4]{b^2-c^2} \sinh \left(x+i \tan ^{-1}(b,-i c)\right)}{\sqrt{2} \sqrt{\sqrt{b^2-c^2}+\sqrt{b^2-c^2} \cosh \left(x+i \tan ^{-1}(b,-i c)\right)}}\right)}{\sqrt[4]{b^2-c^2}}",1,"-((Sqrt[2]*EllipticF[ArcSin[Sqrt[(Sqrt[b^2 - c^2] - b*Cosh[x] - c*Sinh[x])/Sqrt[b^2 - c^2]]/Sqrt[2]], 1]*(b^2 - c^2 + b*Sqrt[b^2 - c^2]*Cosh[x] + c*Sqrt[b^2 - c^2]*Sinh[x])*Sqrt[-((-b^2 + c^2 + b*Sqrt[b^2 - c^2]*Cosh[x] + c*Sqrt[b^2 - c^2]*Sinh[x])/(b^2 - c^2))])/(Sqrt[b^2 - c^2]*(c*Cosh[x] + b*Sinh[x])*Sqrt[Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x]]))","C",1
772,-1,0,155,180.0017,"\int \frac{1}{\left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{3/2}} \, dx","Integrate[(Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(-3/2),x]","\text{\$Aborted}","\frac{b \sinh (x)+c \cosh (x)}{2 \sqrt{b^2-c^2} \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b^2-c^2} \sinh \left(x+i \tan ^{-1}(b,-i c)\right)}{\sqrt{2} \sqrt{\sqrt{b^2-c^2}+\sqrt{b^2-c^2} \cosh \left(x+i \tan ^{-1}(b,-i c)\right)}}\right)}{2 \sqrt{2} \left(b^2-c^2\right)^{3/4}}",1,"$Aborted","F",-1
773,-1,0,205,180.0102292,"\int \frac{1}{\left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{5/2}} \, dx","Integrate[(Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(-5/2),x]","\text{\$Aborted}","\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{b^2-c^2} \sinh \left(x+i \tan ^{-1}(b,-i c)\right)}{\sqrt{2} \sqrt{\sqrt{b^2-c^2}+\sqrt{b^2-c^2} \cosh \left(x+i \tan ^{-1}(b,-i c)\right)}}\right)}{16 \sqrt{2} \left(b^2-c^2\right)^{5/4}}+\frac{3 (b \sinh (x)+c \cosh (x))}{16 \left(b^2-c^2\right) \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{3/2}}+\frac{b \sinh (x)+c \cosh (x)}{4 \sqrt{b^2-c^2} \left(\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{5/2}}",1,"$Aborted","F",-1
774,1,9943,146,76.2317175,"\int \left(-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{5/2} \, dx","Integrate[(-Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(5/2),x]","\text{Result too large to show}","\frac{2}{5} (b \sinh (x)+c \cosh (x)) \left(-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{3/2}-\frac{16}{15} \sqrt{b^2-c^2} (b \sinh (x)+c \cosh (x)) \sqrt{-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}+\frac{64 \left(b^2-c^2\right) (b \sinh (x)+c \cosh (x))}{15 \sqrt{-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}}",1,"Result too large to show","C",0
775,1,9861,96,73.7373714,"\int \left(-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{3/2} \, dx","Integrate[(-Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(3/2),x]","\text{Result too large to show}","\frac{2}{3} (b \sinh (x)+c \cosh (x)) \sqrt{-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}-\frac{8 \sqrt{b^2-c^2} (b \sinh (x)+c \cosh (x))}{3 \sqrt{-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}}",1,"Result too large to show","C",0
776,1,9771,39,74.7608553,"\int \sqrt{-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)} \, dx","Integrate[Sqrt[-Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x]],x]","\text{Result too large to show}","\frac{2 (b \sinh (x)+c \cosh (x))}{\sqrt{-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}}",1,"Result too large to show","C",0
777,1,52609,102,31.2900382,"\int \frac{1}{\sqrt{-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)}} \, dx","Integrate[1/Sqrt[-Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x]],x]","\text{Result too large to show}","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt[4]{b^2-c^2} \sinh \left(x+i \tan ^{-1}(b,-i c)\right)}{\sqrt{2} \sqrt{-\sqrt{b^2-c^2}+\sqrt{b^2-c^2} \cosh \left(x+i \tan ^{-1}(b,-i c)\right)}}\right)}{\sqrt[4]{b^2-c^2}}",1,"Result too large to show","C",0
778,-1,0,159,180.0012187,"\int \frac{1}{\left(-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{3/2}} \, dx","Integrate[(-Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(-3/2),x]","\text{\$Aborted}","-\frac{b \sinh (x)+c \cosh (x)}{2 \sqrt{b^2-c^2} \left(-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b^2-c^2} \sinh \left(x+i \tan ^{-1}(b,-i c)\right)}{\sqrt{2} \sqrt{-\sqrt{b^2-c^2}+\sqrt{b^2-c^2} \cosh \left(x+i \tan ^{-1}(b,-i c)\right)}}\right)}{2 \sqrt{2} \left(b^2-c^2\right)^{3/4}}",1,"$Aborted","F",-1
779,-1,0,211,180.0027242,"\int \frac{1}{\left(-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{5/2}} \, dx","Integrate[(-Sqrt[b^2 - c^2] + b*Cosh[x] + c*Sinh[x])^(-5/2),x]","\text{\$Aborted}","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{b^2-c^2} \sinh \left(x+i \tan ^{-1}(b,-i c)\right)}{\sqrt{2} \sqrt{-\sqrt{b^2-c^2}+\sqrt{b^2-c^2} \cosh \left(x+i \tan ^{-1}(b,-i c)\right)}}\right)}{16 \sqrt{2} \left(b^2-c^2\right)^{5/4}}+\frac{3 (b \sinh (x)+c \cosh (x))}{16 \left(b^2-c^2\right) \left(-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{3/2}}-\frac{b \sinh (x)+c \cosh (x)}{4 \sqrt{b^2-c^2} \left(-\sqrt{b^2-c^2}+b \cosh (x)+c \sinh (x)\right)^{5/2}}",1,"$Aborted","F",-1
780,1,86,107,0.2048471,"\int \frac{1}{a+c \text{sech}(x)+b \tanh (x)} \, dx","Integrate[(a + c*Sech[x] + b*Tanh[x])^(-1),x]","\frac{-\frac{2 a c \tan ^{-1}\left(\frac{(a-c) \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a^2-b^2-c^2}}\right)}{\sqrt{a^2-b^2-c^2}}-b \log (a \cosh (x)+b \sinh (x)+c)+a x}{a^2-b^2}","-\frac{2 a c \tan ^{-1}\left(\frac{(a-c) \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a^2-b^2-c^2}}\right)}{\left(a^2-b^2\right) \sqrt{a^2-b^2-c^2}}-\frac{b \log (a \cosh (x)+b \sinh (x)+c)}{a^2-b^2}+\frac{a x}{a^2-b^2}",1,"(a*x - (2*a*c*ArcTan[(b + (a - c)*Tanh[x/2])/Sqrt[a^2 - b^2 - c^2]])/Sqrt[a^2 - b^2 - c^2] - b*Log[c + a*Cosh[x] + b*Sinh[x]])/(a^2 - b^2)","A",1
781,1,86,113,0.2245496,"\int \frac{1}{a+b \coth (x)+c \text{csch}(x)} \, dx","Integrate[(a + b*Coth[x] + c*Csch[x])^(-1),x]","\frac{-\frac{2 a c \tan ^{-1}\left(\frac{a+(b-c) \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2+b^2-c^2}}\right)}{\sqrt{-a^2+b^2-c^2}}-b \log (a \sinh (x)+b \cosh (x)+c)+a x}{a^2-b^2}","\frac{2 a c \tanh ^{-1}\left(\frac{a+(b-c) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(a^2-b^2\right) \sqrt{a^2-b^2+c^2}}-\frac{b \log (i a \sinh (x)+i b \cosh (x)+i c)}{a^2-b^2}+\frac{a x}{a^2-b^2}",1,"(a*x - (2*a*c*ArcTan[(a + (b - c)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/Sqrt[-a^2 + b^2 - c^2] - b*Log[c + b*Cosh[x] + a*Sinh[x]])/(a^2 - b^2)","A",1
782,1,86,104,0.2143624,"\int \frac{\sinh (x)}{a+b \cosh (x)+c \sinh (x)} \, dx","Integrate[Sinh[x]/(a + b*Cosh[x] + c*Sinh[x]),x]","\frac{\frac{2 a c \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\sqrt{-a^2+b^2-c^2}}+b \log (a+b \cosh (x)+c \sinh (x))-c x}{b^2-c^2}","-\frac{2 a c \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(b^2-c^2\right) \sqrt{a^2-b^2+c^2}}+\frac{b \log (a+b \cosh (x)+c \sinh (x))}{b^2-c^2}-\frac{c x}{b^2-c^2}",1,"(-(c*x) + (2*a*c*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/Sqrt[-a^2 + b^2 - c^2] + b*Log[a + b*Cosh[x] + c*Sinh[x]])/(b^2 - c^2)","A",1
783,1,18,18,0.0463103,"\int \frac{\sinh (x)}{1+\cosh (x)+\sinh (x)} \, dx","Integrate[Sinh[x]/(1 + Cosh[x] + Sinh[x]),x]","\frac{x}{2}-\frac{\sinh (x)}{2}+\frac{\cosh (x)}{2}","\frac{x}{2}-\frac{\sinh (x)}{2}+\frac{\cosh (x)}{2}",1,"x/2 + Cosh[x]/2 - Sinh[x]/2","A",1
784,1,54,54,0.0624978,"\int \frac{\text{sech}(x)}{a+c \text{sech}(x)+b \tanh (x)} \, dx","Integrate[Sech[x]/(a + c*Sech[x] + b*Tanh[x]),x]","\frac{2 \tan ^{-1}\left(\frac{(a-c) \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a^2-b^2-c^2}}\right)}{\sqrt{a^2-b^2-c^2}}","\frac{2 \tan ^{-1}\left(\frac{(a-c) \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a^2-b^2-c^2}}\right)}{\sqrt{a^2-b^2-c^2}}",1,"(2*ArcTan[(b + (a - c)*Tanh[x/2])/Sqrt[a^2 - b^2 - c^2]])/Sqrt[a^2 - b^2 - c^2]","A",1
785,1,96,146,0.2657329,"\int \frac{\text{sech}^2(x)}{a+c \text{sech}(x)+b \tanh (x)} \, dx","Integrate[Sech[x]^2/(a + c*Sech[x] + b*Tanh[x]),x]","\frac{-\frac{2 a c \tan ^{-1}\left(\frac{(a-c) \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a^2-b^2-c^2}}\right)}{\sqrt{a^2-b^2-c^2}}+b (\log (a \cosh (x)+b \sinh (x)+c)-\log (\cosh (x)))+2 c \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{b^2+c^2}","-\frac{2 a c \tan ^{-1}\left(\frac{(a-c) \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a^2-b^2-c^2}}\right)}{\left(b^2+c^2\right) \sqrt{a^2-b^2-c^2}}+\frac{b \log \left((a-c) \tanh ^2\left(\frac{x}{2}\right)+a+2 b \tanh \left(\frac{x}{2}\right)+c\right)}{b^2+c^2}-\frac{b \log \left(\tanh ^2\left(\frac{x}{2}\right)+1\right)}{b^2+c^2}+\frac{2 c \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{b^2+c^2}",1,"(2*c*ArcTan[Tanh[x/2]] - (2*a*c*ArcTan[(b + (a - c)*Tanh[x/2])/Sqrt[a^2 - b^2 - c^2]])/Sqrt[a^2 - b^2 - c^2] + b*(-Log[Cosh[x]] + Log[c + a*Cosh[x] + b*Sinh[x]]))/(b^2 + c^2)","A",1
786,1,28,19,0.0729187,"\int \frac{\text{csch}(x)}{2+2 \coth (x)+3 \text{csch}(x)} \, dx","Integrate[Csch[x]/(2 + 2*Coth[x] + 3*Csch[x]),x]","\frac{x}{6}-\frac{1}{3} \log \left(5 \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)\right)","-\frac{2}{3} \tanh ^{-1}\left(\frac{1}{3} \left(2-\tanh \left(\frac{x}{2}\right)\right)\right)",1,"x/6 - Log[5*Cosh[x/2] - Sinh[x/2]]/3","A",1
787,1,54,50,0.0468032,"\int \frac{\text{csch}(x)}{a+b \coth (x)+c \text{csch}(x)} \, dx","Integrate[Csch[x]/(a + b*Coth[x] + c*Csch[x]),x]","\frac{2 \tan ^{-1}\left(\frac{a+(b-c) \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2+b^2-c^2}}\right)}{\sqrt{-a^2+b^2-c^2}}","-\frac{2 \tanh ^{-1}\left(\frac{a+(b-c) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\sqrt{a^2-b^2+c^2}}",1,"(2*ArcTan[(a + (b - c)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/Sqrt[-a^2 + b^2 - c^2]","A",1
788,1,97,118,0.2443904,"\int \frac{\text{csch}^2(x)}{a+b \coth (x)+c \text{csch}(x)} \, dx","Integrate[Csch[x]^2/(a + b*Coth[x] + c*Csch[x]),x]","\frac{-\frac{2 a c \tan ^{-1}\left(\frac{a+(b-c) \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2+b^2-c^2}}\right)}{\sqrt{-a^2+b^2-c^2}}+b \log (a \sinh (x)+b \cosh (x)+c)-b \log (\sinh (x))+c \log \left(\tanh \left(\frac{x}{2}\right)\right)}{c^2-b^2}","-\frac{2 a c \tanh ^{-1}\left(\frac{a+(b-c) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(b^2-c^2\right) \sqrt{a^2-b^2+c^2}}-\frac{b \log \left(2 a \tanh \left(\frac{x}{2}\right)+(b-c) \tanh ^2\left(\frac{x}{2}\right)+b+c\right)}{b^2-c^2}+\frac{\log \left(\tanh \left(\frac{x}{2}\right)\right)}{b+c}",1,"((-2*a*c*ArcTan[(a + (b - c)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/Sqrt[-a^2 + b^2 - c^2] - b*Log[Sinh[x]] + b*Log[c + b*Cosh[x] + a*Sinh[x]] + c*Log[Tanh[x/2]])/(-b^2 + c^2)","A",1
789,1,104,120,0.2581579,"\int \frac{A+C \sinh (x)}{a+b \cosh (x)+c \sinh (x)} \, dx","Integrate[(A + C*Sinh[x])/(a + b*Cosh[x] + c*Sinh[x]),x]","\frac{\frac{2 \left(a c C+A \left(b^2-c^2\right)\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\sqrt{-a^2+b^2-c^2}}+C (b \log (a+b \cosh (x)+c \sinh (x))-c x)}{(b-c) (b+c)}","-\frac{2 \left(a c C+A \left(b^2-c^2\right)\right) \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(b^2-c^2\right) \sqrt{a^2-b^2+c^2}}+\frac{b C \log (a+b \cosh (x)+c \sinh (x))}{b^2-c^2}-\frac{c C x}{b^2-c^2}",1,"((2*(A*(b^2 - c^2) + a*c*C)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/Sqrt[-a^2 + b^2 - c^2] + C*(-(c*x) + b*Log[a + b*Cosh[x] + c*Sinh[x]]))/((b - c)*(b + c))","A",1
790,1,130,108,0.331391,"\int \frac{A+C \sinh (x)}{(a+b \cosh (x)+c \sinh (x))^2} \, dx","Integrate[(A + C*Sinh[x])/(a + b*Cosh[x] + c*Sinh[x])^2,x]","\frac{a^2 C+\sinh (x) \left(a c C+A \left(b^2-c^2\right)\right)-a A c-b^2 C}{b \left(-a^2+b^2-c^2\right) (a+b \cosh (x)+c \sinh (x))}-\frac{2 (a A+c C) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\left(-a^2+b^2-c^2\right)^{3/2}}","\frac{-\cosh (x) (A c-a C)-A b \sinh (x)+b C}{\left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))}-\frac{2 (a A+c C) \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(a^2-b^2+c^2\right)^{3/2}}",1,"(-2*(a*A + c*C)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/(-a^2 + b^2 - c^2)^(3/2) + (-(a*A*c) + a^2*C - b^2*C + (A*(b^2 - c^2) + a*c*C)*Sinh[x])/(b*(-a^2 + b^2 - c^2)*(a + b*Cosh[x] + c*Sinh[x]))","A",1
791,1,373,198,0.8812457,"\int \frac{A+C \sinh (x)}{(a+b \cosh (x)+c \sinh (x))^3} \, dx","Integrate[(A + C*Sinh[x])/(a + b*Cosh[x] + c*Sinh[x])^3,x]","\frac{\left(2 a^2 A+3 a c C+A \left(b^2-c^2\right)\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\left(-a^2+b^2-c^2\right)^{5/2}}+\frac{-2 a^4 C+6 a^3 A c-4 a^3 c C \sinh (x)+2 b c \cosh (x) \left(2 a^2 A+3 a c C+A \left(b^2-c^2\right)\right)+c \cosh (2 x) \left(a^2 (-c) C+3 a A \left(c^2-b^2\right)+2 c C \left(c^2-b^2\right)\right)-8 a^2 A b^2 \sinh (x)+12 a^2 A c^2 \sinh (x)+4 a^2 b^2 C-a^2 b c C \sinh (2 x)+5 a^2 c^2 C-3 a A b^3 \sinh (2 x)+3 a A b^2 c+3 a A b c^2 \sinh (2 x)-3 a A c^3-2 a b^2 c C \sinh (x)+8 a c^3 C \sinh (x)+2 A b^4 \sinh (x)-2 A b^2 c^2 \sinh (x)-2 b^4 C-2 b^3 c C \sinh (2 x)+4 b^2 c^2 C+2 b c^3 C \sinh (2 x)-2 c^4 C}{4 b \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))^2}","-\frac{\left(2 a^2 A+3 a c C+A \left(b^2-c^2\right)\right) \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(a^2-b^2+c^2\right)^{5/2}}+\frac{-\cosh (x) \left(a^2 (-C)+3 a A c+2 c^2 C\right)-b \sinh (x) (3 a A+2 c C)+a b C}{2 \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))}+\frac{-\cosh (x) (A c-a C)-A b \sinh (x)+b C}{2 \left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))^2}",1,"((2*a^2*A + A*(b^2 - c^2) + 3*a*c*C)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/(-a^2 + b^2 - c^2)^(5/2) + (6*a^3*A*c + 3*a*A*b^2*c - 3*a*A*c^3 - 2*a^4*C + 4*a^2*b^2*C - 2*b^4*C + 5*a^2*c^2*C + 4*b^2*c^2*C - 2*c^4*C + 2*b*c*(2*a^2*A + A*(b^2 - c^2) + 3*a*c*C)*Cosh[x] + c*(3*a*A*(-b^2 + c^2) - a^2*c*C + 2*c*(-b^2 + c^2)*C)*Cosh[2*x] - 8*a^2*A*b^2*Sinh[x] + 2*A*b^4*Sinh[x] + 12*a^2*A*c^2*Sinh[x] - 2*A*b^2*c^2*Sinh[x] - 4*a^3*c*C*Sinh[x] - 2*a*b^2*c*C*Sinh[x] + 8*a*c^3*C*Sinh[x] - 3*a*A*b^3*Sinh[2*x] + 3*a*A*b*c^2*Sinh[2*x] - a^2*b*c*C*Sinh[2*x] - 2*b^3*c*C*Sinh[2*x] + 2*b*c^3*C*Sinh[2*x])/(4*b*(a^2 - b^2 + c^2)^2*(a + b*Cosh[x] + c*Sinh[x])^2)","A",1
792,1,104,121,0.2150647,"\int \frac{A+B \cosh (x)}{a+b \cosh (x)+c \sinh (x)} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Cosh[x] + c*Sinh[x]),x]","\frac{B (b x-c \log (a+b \cosh (x)+c \sinh (x)))-\frac{2 \left(a b B+A \left(c^2-b^2\right)\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\sqrt{-a^2+b^2-c^2}}}{(b-c) (b+c)}","\frac{2 \left(a b B-A \left(b^2-c^2\right)\right) \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(b^2-c^2\right) \sqrt{a^2-b^2+c^2}}-\frac{B c \log (a+b \cosh (x)+c \sinh (x))}{b^2-c^2}+\frac{b B x}{b^2-c^2}",1,"((-2*(a*b*B + A*(-b^2 + c^2))*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/Sqrt[-a^2 + b^2 - c^2] + B*(b*x - c*Log[a + b*Cosh[x] + c*Sinh[x]]))/((b - c)*(b + c))","A",1
793,1,125,108,0.2754409,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x)+c \sinh (x))^2} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Cosh[x] + c*Sinh[x])^2,x]","\frac{\sinh (x) \left(A \left(b^2-c^2\right)-a b B\right)-a A c+b B c}{b \left(-a^2+b^2-c^2\right) (a+b \cosh (x)+c \sinh (x))}-\frac{2 (a A-b B) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\left(-a^2+b^2-c^2\right)^{3/2}}","-\frac{2 (a A-b B) \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(a^2-b^2+c^2\right)^{3/2}}-\frac{\sinh (x) (A b-a B)+A c \cosh (x)+B c}{\left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))}",1,"(-2*(a*A - b*B)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/(-a^2 + b^2 - c^2)^(3/2) + (-(a*A*c) + b*B*c + (-(a*b*B) + A*(b^2 - c^2))*Sinh[x])/(b*(-a^2 + b^2 - c^2)*(a + b*Cosh[x] + c*Sinh[x]))","A",1
794,1,336,194,0.7292392,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x)+c \sinh (x))^3} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Cosh[x] + c*Sinh[x])^3,x]","\frac{\left(2 a^2 A-3 a b B+A \left(b^2-c^2\right)\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\left(-a^2+b^2-c^2\right)^{5/2}}+\frac{6 a^3 A c+4 a^3 b B \sinh (x)+2 b c \cosh (x) \left(2 a^2 A-3 a b B+A \left(b^2-c^2\right)\right)+c \cosh (2 x) \left(a^2 b B+3 a A \left(c^2-b^2\right)+2 b B \left(b^2-c^2\right)\right)-8 a^2 A b^2 \sinh (x)+12 a^2 A c^2 \sinh (x)+a^2 b^2 B \sinh (2 x)-9 a^2 b B c-3 a A b^3 \sinh (2 x)+3 a A b^2 c+3 a A b c^2 \sinh (2 x)-3 a A c^3+2 a b^3 B \sinh (x)-8 a b B c^2 \sinh (x)+2 A b^4 \sinh (x)-2 A b^2 c^2 \sinh (x)+2 b^4 B \sinh (2 x)-2 b^2 B c^2 \sinh (2 x)}{4 b \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))^2}","-\frac{\left(2 a^2 A-3 a b B+A \left(b^2-c^2\right)\right) \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(a^2-b^2+c^2\right)^{5/2}}-\frac{\sinh (x) \left(a^2 (-B)+3 a A b-2 b^2 B\right)+c \cosh (x) (3 a A-2 b B)+a B c}{2 \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))}-\frac{\sinh (x) (A b-a B)+A c \cosh (x)+B c}{2 \left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))^2}",1,"((2*a^2*A - 3*a*b*B + A*(b^2 - c^2))*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/(-a^2 + b^2 - c^2)^(5/2) + (6*a^3*A*c + 3*a*A*b^2*c - 9*a^2*b*B*c - 3*a*A*c^3 + 2*b*c*(2*a^2*A - 3*a*b*B + A*(b^2 - c^2))*Cosh[x] + c*(a^2*b*B + 2*b*B*(b^2 - c^2) + 3*a*A*(-b^2 + c^2))*Cosh[2*x] - 8*a^2*A*b^2*Sinh[x] + 2*A*b^4*Sinh[x] + 4*a^3*b*B*Sinh[x] + 2*a*b^3*B*Sinh[x] + 12*a^2*A*c^2*Sinh[x] - 2*A*b^2*c^2*Sinh[x] - 8*a*b*B*c^2*Sinh[x] - 3*a*A*b^3*Sinh[2*x] + a^2*b^2*B*Sinh[2*x] + 2*b^4*B*Sinh[2*x] + 3*a*A*b*c^2*Sinh[2*x] - 2*b^2*B*c^2*Sinh[2*x])/(4*b*(a^2 - b^2 + c^2)^2*(a + b*Cosh[x] + c*Sinh[x])^2)","A",1
795,1,107,125,0.3489366,"\int \frac{B \cosh (x)+C \sinh (x)}{a+b \cosh (x)+c \sinh (x)} \, dx","Integrate[(B*Cosh[x] + C*Sinh[x])/(a + b*Cosh[x] + c*Sinh[x]),x]","\frac{-\frac{2 a (b B-c C) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\sqrt{-a^2+b^2-c^2}}+(b C-B c) \log (a+b \cosh (x)+c \sinh (x))+x (b B-c C)}{(b-c) (b+c)}","\frac{2 a (b B-c C) \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(b^2-c^2\right) \sqrt{a^2-b^2+c^2}}-\frac{(B c-b C) \log (a+b \cosh (x)+c \sinh (x))}{b^2-c^2}+\frac{x (b B-c C)}{b^2-c^2}",1,"((b*B - c*C)*x - (2*a*(b*B - c*C)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/Sqrt[-a^2 + b^2 - c^2] + (-(B*c) + b*C)*Log[a + b*Cosh[x] + c*Sinh[x]])/((b - c)*(b + c))","A",1
796,1,123,108,0.3430345,"\int \frac{B \cosh (x)+C \sinh (x)}{(a+b \cosh (x)+c \sinh (x))^2} \, dx","Integrate[(B*Cosh[x] + C*Sinh[x])/(a + b*Cosh[x] + c*Sinh[x])^2,x]","\frac{2 (b B-c C) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\left(-a^2+b^2-c^2\right)^{3/2}}+\frac{a^2 C+a \sinh (x) (c C-b B)-b^2 C+b B c}{b \left(-a^2+b^2-c^2\right) (a+b \cosh (x)+c \sinh (x))}","\frac{2 (b B-c C) \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(a^2-b^2+c^2\right)^{3/2}}-\frac{-a B \sinh (x)-a C \cosh (x)-b C+B c}{\left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))}",1,"(2*(b*B - c*C)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/(-a^2 + b^2 - c^2)^(3/2) + (b*B*c + a^2*C - b^2*C + a*(-(b*B) + c*C)*Sinh[x])/(b*(-a^2 + b^2 - c^2)*(a + b*Cosh[x] + c*Sinh[x]))","A",1
797,1,319,194,0.7532851,"\int \frac{B \cosh (x)+C \sinh (x)}{(a+b \cosh (x)+c \sinh (x))^3} \, dx","Integrate[(B*Cosh[x] + C*Sinh[x])/(a + b*Cosh[x] + c*Sinh[x])^3,x]","\frac{-2 a^4 C+4 a^3 b B \sinh (x)-4 a^3 c C \sinh (x)+c \cosh (2 x) \left(a^2+2 b^2-2 c^2\right) (b B-c C)+a^2 b^2 B \sinh (2 x)+4 a^2 b^2 C-9 a^2 b B c-a^2 b c C \sinh (2 x)+5 a^2 c^2 C+2 a b^3 B \sinh (x)-2 a b^2 c C \sinh (x)-8 a b B c^2 \sinh (x)-6 a b c \cosh (x) (b B-c C)+8 a c^3 C \sinh (x)+2 b^4 B \sinh (2 x)-2 b^4 C-2 b^3 c C \sinh (2 x)-2 b^2 B c^2 \sinh (2 x)+4 b^2 c^2 C+2 b c^3 C \sinh (2 x)-2 c^4 C}{4 b \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))^2}-\frac{3 a (b B-c C) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\left(-a^2+b^2-c^2\right)^{5/2}}","\frac{3 a (b B-c C) \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right)}{\left(a^2-b^2+c^2\right)^{5/2}}-\frac{-\cosh (x) \left(C \left(a^2-2 c^2\right)+2 b B c\right)-\sinh (x) \left(a^2 B+2 b (b B-c C)\right)+a (B c-b C)}{2 \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))}-\frac{-a B \sinh (x)-a C \cosh (x)-b C+B c}{2 \left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))^2}",1,"(-3*a*(b*B - c*C)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/(-a^2 + b^2 - c^2)^(5/2) + (-9*a^2*b*B*c - 2*a^4*C + 4*a^2*b^2*C - 2*b^4*C + 5*a^2*c^2*C + 4*b^2*c^2*C - 2*c^4*C - 6*a*b*c*(b*B - c*C)*Cosh[x] + c*(a^2 + 2*b^2 - 2*c^2)*(b*B - c*C)*Cosh[2*x] + 4*a^3*b*B*Sinh[x] + 2*a*b^3*B*Sinh[x] - 8*a*b*B*c^2*Sinh[x] - 4*a^3*c*C*Sinh[x] - 2*a*b^2*c*C*Sinh[x] + 8*a*c^3*C*Sinh[x] + a^2*b^2*B*Sinh[2*x] + 2*b^4*B*Sinh[2*x] - 2*b^2*B*c^2*Sinh[2*x] - a^2*b*c*C*Sinh[2*x] - 2*b^3*c*C*Sinh[2*x] + 2*b*c^3*C*Sinh[2*x])/(4*b*(a^2 - b^2 + c^2)^2*(a + b*Cosh[x] + c*Sinh[x])^2)","A",1
798,1,119,137,0.3371665,"\int \frac{A+B \cosh (x)+C \sinh (x)}{a+b \cosh (x)+c \sinh (x)} \, dx","Integrate[(A + B*Cosh[x] + C*Sinh[x])/(a + b*Cosh[x] + c*Sinh[x]),x]","\frac{\frac{2 \left(-a b B+a c C+A b^2-A c^2\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\sqrt{-a^2+b^2-c^2}}+(b C-B c) \log (a+b \cosh (x)+c \sinh (x))+x (b B-c C)}{(b-c) (b+c)}","-\frac{2 \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right) \left(-a b B+a c C+A b^2-A c^2\right)}{\left(b^2-c^2\right) \sqrt{a^2-b^2+c^2}}-\frac{(B c-b C) \log (a+b \cosh (x)+c \sinh (x))}{b^2-c^2}+\frac{x (b B-c C)}{b^2-c^2}",1,"((b*B - c*C)*x + (2*(A*b^2 - a*b*B - A*c^2 + a*c*C)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/Sqrt[-a^2 + b^2 - c^2] + (-(B*c) + b*C)*Log[a + b*Cosh[x] + c*Sinh[x]])/((b - c)*(b + c))","A",1
799,1,143,121,0.4204775,"\int \frac{A+B \cosh (x)+C \sinh (x)}{(a+b \cosh (x)+c \sinh (x))^2} \, dx","Integrate[(A + B*Cosh[x] + C*Sinh[x])/(a + b*Cosh[x] + c*Sinh[x])^2,x]","\frac{a^2 C+\sinh (x) \left(-a b B+a c C+A \left(b^2-c^2\right)\right)-a A c+b (B c-b C)}{b \left(-a^2+b^2-c^2\right) (a+b \cosh (x)+c \sinh (x))}-\frac{2 (a A-b B+c C) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\left(-a^2+b^2-c^2\right)^{3/2}}","-\frac{2 \tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right) (a A-b B+c C)}{\left(a^2-b^2+c^2\right)^{3/2}}-\frac{\sinh (x) (A b-a B)+\cosh (x) (A c-a C)-b C+B c}{\left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))}",1,"(-2*(a*A - b*B + c*C)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/(-a^2 + b^2 - c^2)^(3/2) + (-(a*A*c) + a^2*C + b*(B*c - b*C) + (-(a*b*B) + A*(b^2 - c^2) + a*c*C)*Sinh[x])/(b*(-a^2 + b^2 - c^2)*(a + b*Cosh[x] + c*Sinh[x]))","A",1
800,1,465,233,1.1011863,"\int \frac{A+B \cosh (x)+C \sinh (x)}{(a+b \cosh (x)+c \sinh (x))^3} \, dx","Integrate[(A + B*Cosh[x] + C*Sinh[x])/(a + b*Cosh[x] + c*Sinh[x])^3,x]","\frac{\left(2 a^2 A-3 a b B+3 a c C+A b^2-A c^2\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)+c}{\sqrt{-a^2+b^2-c^2}}\right)}{\left(-a^2+b^2-c^2\right)^{5/2}}+\frac{-2 a^4 C+6 a^3 A c+4 a^3 b B \sinh (x)-4 a^3 c C \sinh (x)+2 b c \cosh (x) \left(2 a^2 A-3 a b B+3 a c C+A b^2-A c^2\right)+c \cosh (2 x) \left(a^2 (b B-c C)+3 a A \left(c^2-b^2\right)+2 \left(b^2-c^2\right) (b B-c C)\right)-8 a^2 A b^2 \sinh (x)+12 a^2 A c^2 \sinh (x)+a^2 b^2 B \sinh (2 x)+4 a^2 b^2 C-9 a^2 b B c-a^2 b c C \sinh (2 x)+5 a^2 c^2 C-3 a A b^3 \sinh (2 x)+3 a A b^2 c+3 a A b c^2 \sinh (2 x)-3 a A c^3+2 a b^3 B \sinh (x)-2 a b^2 c C \sinh (x)-8 a b B c^2 \sinh (x)+8 a c^3 C \sinh (x)+2 A b^4 \sinh (x)-2 A b^2 c^2 \sinh (x)+2 b^4 B \sinh (2 x)-2 b^4 C-2 b^3 c C \sinh (2 x)-2 b^2 B c^2 \sinh (2 x)+4 b^2 c^2 C+2 b c^3 C \sinh (2 x)-2 c^4 C}{4 b \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))^2}","-\frac{\tanh ^{-1}\left(\frac{c-(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2+c^2}}\right) \left(2 a^2 A-3 a b B+3 a c C+A b^2-A c^2\right)}{\left(a^2-b^2+c^2\right)^{5/2}}-\frac{\sinh (x) \left(a^2 (-B)+3 a A b-2 b (b B-c C)\right)+\cosh (x) \left(a^2 (-C)+3 a A c-2 c (b B-c C)\right)+a (B c-b C)}{2 \left(a^2-b^2+c^2\right)^2 (a+b \cosh (x)+c \sinh (x))}-\frac{\sinh (x) (A b-a B)+\cosh (x) (A c-a C)-b C+B c}{2 \left(a^2-b^2+c^2\right) (a+b \cosh (x)+c \sinh (x))^2}",1,"((2*a^2*A + A*b^2 - 3*a*b*B - A*c^2 + 3*a*c*C)*ArcTan[(c + (-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2 - c^2]])/(-a^2 + b^2 - c^2)^(5/2) + (6*a^3*A*c + 3*a*A*b^2*c - 9*a^2*b*B*c - 3*a*A*c^3 - 2*a^4*C + 4*a^2*b^2*C - 2*b^4*C + 5*a^2*c^2*C + 4*b^2*c^2*C - 2*c^4*C + 2*b*c*(2*a^2*A + A*b^2 - 3*a*b*B - A*c^2 + 3*a*c*C)*Cosh[x] + c*(3*a*A*(-b^2 + c^2) + a^2*(b*B - c*C) + 2*(b^2 - c^2)*(b*B - c*C))*Cosh[2*x] - 8*a^2*A*b^2*Sinh[x] + 2*A*b^4*Sinh[x] + 4*a^3*b*B*Sinh[x] + 2*a*b^3*B*Sinh[x] + 12*a^2*A*c^2*Sinh[x] - 2*A*b^2*c^2*Sinh[x] - 8*a*b*B*c^2*Sinh[x] - 4*a^3*c*C*Sinh[x] - 2*a*b^2*c*C*Sinh[x] + 8*a*c^3*C*Sinh[x] - 3*a*A*b^3*Sinh[2*x] + a^2*b^2*B*Sinh[2*x] + 2*b^4*B*Sinh[2*x] + 3*a*A*b*c^2*Sinh[2*x] - 2*b^2*B*c^2*Sinh[2*x] - a^2*b*c*C*Sinh[2*x] - 2*b^3*c*C*Sinh[2*x] + 2*b*c^3*C*Sinh[2*x])/(4*b*(a^2 - b^2 + c^2)^2*(a + b*Cosh[x] + c*Sinh[x])^2)","A",1
801,1,34,22,0.1060909,"\int \frac{b^2-c^2+a b \cosh (x)+a c \sinh (x)}{(a+b \cosh (x)+c \sinh (x))^2} \, dx","Integrate[(b^2 - c^2 + a*b*Cosh[x] + a*c*Sinh[x])/(a + b*Cosh[x] + c*Sinh[x])^2,x]","\frac{-a c+b^2 \sinh (x)-c^2 \sinh (x)}{b (a+b \cosh (x)+c \sinh (x))}","\frac{b \sinh (x)+c \cosh (x)}{a+b \cosh (x)+c \sinh (x)}",1,"(-(a*c) + b^2*Sinh[x] - c^2*Sinh[x])/(b*(a + b*Cosh[x] + c*Sinh[x]))","A",1
802,1,86,71,0.2359551,"\int \frac{A+C \sinh (x)}{a+b \cosh (x)+b \sinh (x)} \, dx","Integrate[(A + C*Sinh[x])/(a + b*Cosh[x] + b*Sinh[x]),x]","\frac{x \left(a^2 C+2 a A b+b^2 C\right)+2 \left(a^2 C-2 a A b-b^2 C\right) \log \left((b-a) \sinh \left(\frac{x}{2}\right)+(a+b) \cosh \left(\frac{x}{2}\right)\right)-2 a b C \sinh (x)+2 a b C \cosh (x)}{4 a^2 b}","\frac{x (2 a A+b C)}{2 a^2}-\frac{1}{2} \left(\frac{b C}{a^2}+\frac{2 A}{a}-\frac{C}{b}\right) \log (a+b \sinh (x)+b \cosh (x))-\frac{C \sinh (x)}{2 a}+\frac{C \cosh (x)}{2 a}",1,"((2*a*A*b + a^2*C + b^2*C)*x + 2*a*b*C*Cosh[x] + 2*(-2*a*A*b + a^2*C - b^2*C)*Log[(a + b)*Cosh[x/2] + (-a + b)*Sinh[x/2]] - 2*a*b*C*Sinh[x])/(4*a^2*b)","A",1
803,1,84,77,0.191354,"\int \frac{A+B \cosh (x)}{a+b \cosh (x)+b \sinh (x)} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Cosh[x] + b*Sinh[x]),x]","\frac{\frac{2 \left(a^2 B-2 a A b+b^2 B\right) \log \left((b-a) \sinh \left(\frac{x}{2}\right)+(a+b) \cosh \left(\frac{x}{2}\right)\right)}{b}+x \left(\frac{a^2 B}{b}+2 a A-b B\right)+2 a B \sinh (x)-2 a B \cosh (x)}{4 a^2}","-\frac{\left(a^2 (-B)+2 a A b-b^2 B\right) \log (a+b \sinh (x)+b \cosh (x))}{2 a^2 b}+\frac{x (2 a A-b B)}{2 a^2}+\frac{B \sinh (x)}{2 a}-\frac{B \cosh (x)}{2 a}",1,"((2*a*A + (a^2*B)/b - b*B)*x - 2*a*B*Cosh[x] + (2*(-2*a*A*b + a^2*B + b^2*B)*Log[(a + b)*Cosh[x/2] + (-a + b)*Sinh[x/2]])/b + 2*a*B*Sinh[x])/(4*a^2)","A",1
804,1,103,86,0.3121592,"\int \frac{A+B \cosh (x)+C \sinh (x)}{a+b \cosh (x)+b \sinh (x)} \, dx","Integrate[(A + B*Cosh[x] + C*Sinh[x])/(a + b*Cosh[x] + b*Sinh[x]),x]","\frac{\frac{2 \left(a^2 (B+C)-2 a A b+b^2 (B-C)\right) \log \left((b-a) \sinh \left(\frac{x}{2}\right)+(a+b) \cosh \left(\frac{x}{2}\right)\right)}{b}+x \left(\frac{a^2 (B+C)}{b}+2 a A+b (C-B)\right)+2 a (B-C) \sinh (x)-2 a (B-C) \cosh (x)}{4 a^2}","-\frac{\left(-\left(a^2 (B+C)\right)+2 a A b-b^2 (B-C)\right) \log (a+b \sinh (x)+b \cosh (x))}{2 a^2 b}+\frac{x (2 a A-b (B-C))}{2 a^2}-\frac{(B-C) (\cosh (x)-\sinh (x))}{2 a}",1,"((2*a*A + b*(-B + C) + (a^2*(B + C))/b)*x - 2*a*(B - C)*Cosh[x] + (2*(-2*a*A*b + b^2*(B - C) + a^2*(B + C))*Log[(a + b)*Cosh[x/2] + (-a + b)*Sinh[x/2]])/b + 2*a*(B - C)*Sinh[x])/(4*a^2)","A",1
805,1,86,77,0.2472352,"\int \frac{A+C \sinh (x)}{a+b \cosh (x)-b \sinh (x)} \, dx","Integrate[(A + C*Sinh[x])/(a + b*Cosh[x] - b*Sinh[x]),x]","\frac{\frac{2 \left(a^2 C+2 a A b-b^2 C\right) \log \left((a-b) \sinh \left(\frac{x}{2}\right)+(a+b) \cosh \left(\frac{x}{2}\right)\right)}{b}+x \left(-\frac{a^2 C}{b}+2 a A-b C\right)+2 a C \sinh (x)+2 a C \cosh (x)}{4 a^2}","\frac{\left(a^2 C+2 a A b-b^2 C\right) \log (a-b \sinh (x)+b \cosh (x))}{2 a^2 b}+\frac{x (2 a A-b C)}{2 a^2}+\frac{C \sinh (x)}{2 a}+\frac{C \cosh (x)}{2 a}",1,"((2*a*A - (a^2*C)/b - b*C)*x + 2*a*C*Cosh[x] + (2*(2*a*A*b + a^2*C - b^2*C)*Log[(a + b)*Cosh[x/2] + (a - b)*Sinh[x/2]])/b + 2*a*C*Sinh[x])/(4*a^2)","A",1
806,1,86,78,0.1637022,"\int \frac{A+B \cosh (x)}{a+b \cosh (x)-b \sinh (x)} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Cosh[x] - b*Sinh[x]),x]","\frac{x \left(a^2 B+2 a A b-b^2 B\right)-2 \left(a^2 B-2 a A b+b^2 B\right) \log \left((a-b) \sinh \left(\frac{x}{2}\right)+(a+b) \cosh \left(\frac{x}{2}\right)\right)+2 a b B \sinh (x)+2 a b B \cosh (x)}{4 a^2 b}","\frac{\left(a^2 (-B)+2 a A b-b^2 B\right) \log (a-b \sinh (x)+b \cosh (x))}{2 a^2 b}+\frac{x (2 a A-b B)}{2 a^2}+\frac{B \sinh (x)}{2 a}+\frac{B \cosh (x)}{2 a}",1,"((2*a*A*b + a^2*B - b^2*B)*x + 2*a*b*B*Cosh[x] - 2*(-2*a*A*b + a^2*B + b^2*B)*Log[(a + b)*Cosh[x/2] + (a - b)*Sinh[x/2]] + 2*a*b*B*Sinh[x])/(4*a^2*b)","A",1
807,1,102,81,0.2978703,"\int \frac{A+B \cosh (x)+C \sinh (x)}{a+b \cosh (x)-b \sinh (x)} \, dx","Integrate[(A + B*Cosh[x] + C*Sinh[x])/(a + b*Cosh[x] - b*Sinh[x]),x]","\frac{x \left(a^2 (B-C)+2 a A b-b^2 (B+C)\right)-2 \left(a^2 (B-C)-2 a A b+b^2 (B+C)\right) \log \left((a-b) \sinh \left(\frac{x}{2}\right)+(a+b) \cosh \left(\frac{x}{2}\right)\right)+2 a b (B+C) \sinh (x)+2 a b (B+C) \cosh (x)}{4 a^2 b}","\frac{\left(-\left(a^2 (B-C)\right)+2 a A b-b^2 (B+C)\right) \log (a-b \sinh (x)+b \cosh (x))}{2 a^2 b}+\frac{x (2 a A-b (B+C))}{2 a^2}+\frac{(B+C) (\sinh (x)+\cosh (x))}{2 a}",1,"((2*a*A*b + a^2*(B - C) - b^2*(B + C))*x + 2*a*b*(B + C)*Cosh[x] - 2*(-2*a*A*b + a^2*(B - C) + b^2*(B + C))*Log[(a + b)*Cosh[x/2] + (a - b)*Sinh[x/2]] + 2*a*b*(B + C)*Sinh[x])/(4*a^2*b)","A",1
808,1,3,3,0.0037175,"\int \frac{1}{\cosh ^2(x)+\sinh ^2(x)} \, dx","Integrate[(Cosh[x]^2 + Sinh[x]^2)^(-1),x]","\tan ^{-1}(\tanh (x))","\tan ^{-1}(\tanh (x))",1,"ArcTan[Tanh[x]]","A",1
809,1,8,11,0.0034153,"\int \frac{1}{\left(\cosh ^2(x)+\sinh ^2(x)\right)^2} \, dx","Integrate[(Cosh[x]^2 + Sinh[x]^2)^(-2),x]","\frac{1}{2} \tanh (2 x)","\frac{\tanh (x)}{\tanh ^2(x)+1}",1,"Tanh[2*x]/2","A",1
810,1,22,26,0.006525,"\int \frac{1}{\left(\cosh ^2(x)+\sinh ^2(x)\right)^3} \, dx","Integrate[(Cosh[x]^2 + Sinh[x]^2)^(-3),x]","\frac{1}{4} \tan ^{-1}(\sinh (2 x))+\frac{1}{4} \tanh (2 x) \text{sech}(2 x)","\frac{1}{2} \tan ^{-1}(\tanh (x))+\frac{\tanh (x) \text{sech}^2(x)}{2 \left(\tanh ^2(x)+1\right)^2}",1,"ArcTan[Sinh[2*x]]/4 + (Sech[2*x]*Tanh[2*x])/4","A",1
811,1,1,1,0.0004545,"\int \frac{1}{\cosh ^2(x)-\sinh ^2(x)} \, dx","Integrate[(Cosh[x]^2 - Sinh[x]^2)^(-1),x]","x","x",1,"x","A",1
812,1,1,1,0.0004475,"\int \frac{1}{\left(\cosh ^2(x)-\sinh ^2(x)\right)^2} \, dx","Integrate[(Cosh[x]^2 - Sinh[x]^2)^(-2),x]","x","x",1,"x","A",1
813,1,1,1,0.0004026,"\int \frac{1}{\left(\cosh ^2(x)-\sinh ^2(x)\right)^3} \, dx","Integrate[(Cosh[x]^2 - Sinh[x]^2)^(-3),x]","x","x",1,"x","A",1
814,1,1,1,0.0005066,"\int \frac{1}{\text{sech}^2(x)+\tanh ^2(x)} \, dx","Integrate[(Sech[x]^2 + Tanh[x]^2)^(-1),x]","x","x",1,"x","A",1
815,1,1,1,0.0004288,"\int \frac{1}{\left(\text{sech}^2(x)+\tanh ^2(x)\right)^2} \, dx","Integrate[(Sech[x]^2 + Tanh[x]^2)^(-2),x]","x","x",1,"x","A",1
816,1,1,1,0.0004656,"\int \frac{1}{\left(\text{sech}^2(x)+\tanh ^2(x)\right)^3} \, dx","Integrate[(Sech[x]^2 + Tanh[x]^2)^(-3),x]","x","x",1,"x","A",1
817,1,19,19,0.0432436,"\int \frac{1}{\text{sech}^2(x)-\tanh ^2(x)} \, dx","Integrate[(Sech[x]^2 - Tanh[x]^2)^(-1),x]","\sqrt{2} \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)-x","\sqrt{2} \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)-x",1,"-x + Sqrt[2]*ArcTanh[Sqrt[2]*Tanh[x]]","A",1
818,1,42,31,0.1209117,"\int \frac{1}{\left(\text{sech}^2(x)-\tanh ^2(x)\right)^2} \, dx","Integrate[(Sech[x]^2 - Tanh[x]^2)^(-2),x]","\frac{-3 x-\sinh (2 x)+x \cosh (2 x)}{\cosh (2 x)-3}-\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{\sqrt{2}}","x-\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{\sqrt{2}}+\frac{\tanh (x)}{1-2 \tanh ^2(x)}",1,"-(ArcTanh[Sqrt[2]*Tanh[x]]/Sqrt[2]) + (-3*x + x*Cosh[2*x] - Sinh[2*x])/(-3 + Cosh[2*x])","A",1
819,1,66,54,0.2125785,"\int \frac{1}{\left(\text{sech}^2(x)-\tanh ^2(x)\right)^3} \, dx","Integrate[(Sech[x]^2 - Tanh[x]^2)^(-3),x]","\frac{-76 x-2 \sinh (2 x)+3 \sinh (4 x)+48 x \cosh (2 x)-4 x \cosh (4 x)+7 \sqrt{2} (\cosh (2 x)-3)^2 \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{8 (\cosh (2 x)-3)^2}","-x+\frac{7 \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{4 \sqrt{2}}-\frac{\tanh (x)}{4 \left(1-2 \tanh ^2(x)\right)}+\frac{\tanh (x)}{2 \left(1-2 \tanh ^2(x)\right)^2}",1,"(-76*x + 7*Sqrt[2]*ArcTanh[Sqrt[2]*Tanh[x]]*(-3 + Cosh[2*x])^2 + 48*x*Cosh[2*x] - 4*x*Cosh[4*x] - 2*Sinh[2*x] + 3*Sinh[4*x])/(8*(-3 + Cosh[2*x])^2)","A",1
820,1,18,18,0.0420495,"\int \frac{1}{\coth ^2(x)+\text{csch}^2(x)} \, dx","Integrate[(Coth[x]^2 + Csch[x]^2)^(-1),x]","x-\sqrt{2} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)","x-\sqrt{2} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)",1,"x - Sqrt[2]*ArcTanh[Tanh[x]/Sqrt[2]]","A",1
821,1,64,32,0.0986049,"\int \frac{1}{\left(\coth ^2(x)+\text{csch}^2(x)\right)^2} \, dx","Integrate[(Coth[x]^2 + Csch[x]^2)^(-2),x]","\frac{(\cosh (2 x)+3) \text{csch}^4(x) \left(6 x-2 \sinh (2 x)+2 x \cosh (2 x)-\sqrt{2} (\cosh (2 x)+3) \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)\right)}{8 \left(\coth ^2(x)+\text{csch}^2(x)\right)^2}","x-\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\tanh (x)}{2-\tanh ^2(x)}",1,"((3 + Cosh[2*x])*Csch[x]^4*(6*x + 2*x*Cosh[2*x] - Sqrt[2]*ArcTanh[Tanh[x]/Sqrt[2]]*(3 + Cosh[2*x]) - 2*Sinh[2*x]))/(8*(Coth[x]^2 + Csch[x]^2)^2)","A",1
822,1,66,54,0.2063997,"\int \frac{1}{\left(\coth ^2(x)+\text{csch}^2(x)\right)^3} \, dx","Integrate[(Coth[x]^2 + Csch[x]^2)^(-3),x]","\frac{76 x-2 \sinh (2 x)-3 \sinh (4 x)+48 x \cosh (2 x)+4 x \cosh (4 x)-7 \sqrt{2} (\cosh (2 x)+3)^2 \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{8 (\cosh (2 x)+3)^2}","x-\frac{7 \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{4 \sqrt{2}}-\frac{\tanh (x)}{4 \left(2-\tanh ^2(x)\right)}-\frac{\tanh ^3(x)}{2 \left(2-\tanh ^2(x)\right)^2}",1,"(76*x + 48*x*Cosh[2*x] - 7*Sqrt[2]*ArcTanh[Tanh[x]/Sqrt[2]]*(3 + Cosh[2*x])^2 + 4*x*Cosh[4*x] - 2*Sinh[2*x] - 3*Sinh[4*x])/(8*(3 + Cosh[2*x])^2)","A",1
823,1,1,1,0.0005706,"\int \frac{1}{\coth ^2(x)-\text{csch}^2(x)} \, dx","Integrate[(Coth[x]^2 - Csch[x]^2)^(-1),x]","x","x",1,"x","A",1
824,1,1,1,0.0005254,"\int \frac{1}{\left(\coth ^2(x)-\text{csch}^2(x)\right)^2} \, dx","Integrate[(Coth[x]^2 - Csch[x]^2)^(-2),x]","x","x",1,"x","A",1
825,1,1,1,0.0005019,"\int \frac{1}{\left(\coth ^2(x)-\text{csch}^2(x)\right)^3} \, dx","Integrate[(Coth[x]^2 - Csch[x]^2)^(-3),x]","x","x",1,"x","A",1
826,1,217,271,0.7294094,"\int \frac{1}{a+b \sinh (x)+c \sinh ^2(x)} \, dx","Integrate[(a + b*Sinh[x] + c*Sinh[x]^2)^(-1),x]","\frac{2 \sqrt{2} c \left(\frac{\tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}-b\right)+2 c}{\sqrt{2 b \sqrt{b^2-4 a c}+4 c (a-c)-2 b^2}}\right)}{\sqrt{b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}-\frac{\tan ^{-1}\left(\frac{2 c-\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}+b\right)}{\sqrt{2} \sqrt{-b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}\right)}{\sqrt{-b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}\right)}{\sqrt{b^2-4 a c}}","\frac{2 \sqrt{2} c \tan ^{-1}\left(\frac{2 i c-\tanh \left(\frac{x}{2}\right) \left(\sqrt{4 a c-b^2}+i b\right)}{\sqrt{2} \sqrt{-i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}\right)}{\sqrt{4 a c-b^2} \sqrt{-i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}-\frac{2 \sqrt{2} c \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{4 a c-b^2}-i b \tanh \left(\frac{x}{2}\right)+2 i c}{\sqrt{2} \sqrt{i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}\right)}{\sqrt{4 a c-b^2} \sqrt{i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}",1,"(2*Sqrt[2]*c*(ArcTan[(2*c + (-b + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*(a - c)*c + 2*b*Sqrt[b^2 - 4*a*c]]]/Sqrt[-b^2 + 2*(a - c)*c + b*Sqrt[b^2 - 4*a*c]] - ArcTan[(2*c - (b + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/(Sqrt[2]*Sqrt[-b^2 + 2*(a - c)*c - b*Sqrt[b^2 - 4*a*c]])]/Sqrt[-b^2 + 2*(a - c)*c - b*Sqrt[b^2 - 4*a*c]]))/Sqrt[b^2 - 4*a*c]","A",1
827,1,244,280,0.5858827,"\int \frac{\sinh (x)}{a+b \sinh (x)+c \sinh ^2(x)} \, dx","Integrate[Sinh[x]/(a + b*Sinh[x] + c*Sinh[x]^2),x]","\frac{\sqrt{2} \left(\frac{\left(\sqrt{b^2-4 a c}-b\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}-b\right)+2 c}{\sqrt{2 b \sqrt{b^2-4 a c}+4 c (a-c)-2 b^2}}\right)}{\sqrt{b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}+\frac{\left(\sqrt{b^2-4 a c}+b\right) \tan ^{-1}\left(\frac{2 c-\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}+b\right)}{\sqrt{2} \sqrt{-b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}\right)}{\sqrt{-b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}\right)}{\sqrt{b^2-4 a c}}","\frac{\sqrt{2} \left(\frac{b}{\sqrt{4 a c-b^2}}+i\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{4 a c-b^2}-i b \tanh \left(\frac{x}{2}\right)+2 i c}{\sqrt{2} \sqrt{i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}\right)}{\sqrt{i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}+\frac{\sqrt{2} \left(-\frac{b}{\sqrt{4 a c-b^2}}+i\right) \tan ^{-1}\left(\frac{2 i c-\tanh \left(\frac{x}{2}\right) \left(\sqrt{4 a c-b^2}+i b\right)}{\sqrt{2} \sqrt{-i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}\right)}{\sqrt{-i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}",1,"(Sqrt[2]*(((-b + Sqrt[b^2 - 4*a*c])*ArcTan[(2*c + (-b + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*(a - c)*c + 2*b*Sqrt[b^2 - 4*a*c]]])/Sqrt[-b^2 + 2*(a - c)*c + b*Sqrt[b^2 - 4*a*c]] + ((b + Sqrt[b^2 - 4*a*c])*ArcTan[(2*c - (b + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/(Sqrt[2]*Sqrt[-b^2 + 2*(a - c)*c - b*Sqrt[b^2 - 4*a*c]])])/Sqrt[-b^2 + 2*(a - c)*c - b*Sqrt[b^2 - 4*a*c]]))/Sqrt[b^2 - 4*a*c]","A",1
828,1,283,309,0.6083969,"\int \frac{\sinh ^2(x)}{a+b \sinh (x)+c \sinh ^2(x)} \, dx","Integrate[Sinh[x]^2/(a + b*Sinh[x] + c*Sinh[x]^2),x]","\frac{-\frac{\sqrt{2} \left(b \sqrt{b^2-4 a c}+2 a c-b^2\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}-b\right)+2 c}{\sqrt{2 b \sqrt{b^2-4 a c}+4 c (a-c)-2 b^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}-\frac{\sqrt{2} \left(b \sqrt{b^2-4 a c}-2 a c+b^2\right) \tan ^{-1}\left(\frac{2 c-\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}+b\right)}{\sqrt{2} \sqrt{-b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{-b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}+x}{c}","-\frac{\sqrt{2} \left(\frac{b^2-2 a c}{\sqrt{4 a c-b^2}}+i b\right) \tan ^{-1}\left(\frac{2 i c-\tanh \left(\frac{x}{2}\right) \left(-\sqrt{4 a c-b^2}+i b\right)}{\sqrt{2} \sqrt{i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}\right)}{c \sqrt{i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}-\frac{\sqrt{2} \left(-\frac{b^2-2 a c}{\sqrt{4 a c-b^2}}+i b\right) \tan ^{-1}\left(\frac{2 i c-\tanh \left(\frac{x}{2}\right) \left(\sqrt{4 a c-b^2}+i b\right)}{\sqrt{2} \sqrt{-i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}\right)}{c \sqrt{-i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}+\frac{x}{c}",1,"(x - (Sqrt[2]*(-b^2 + 2*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(2*c + (-b + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*(a - c)*c + 2*b*Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[-b^2 + 2*(a - c)*c + b*Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*(b^2 - 2*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(2*c - (b + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/(Sqrt[2]*Sqrt[-b^2 + 2*(a - c)*c - b*Sqrt[b^2 - 4*a*c]])])/(Sqrt[b^2 - 4*a*c]*Sqrt[-b^2 + 2*(a - c)*c - b*Sqrt[b^2 - 4*a*c]]))/c","A",1
829,1,326,363,0.938136,"\int \frac{\sinh ^3(x)}{a+b \sinh (x)+c \sinh ^2(x)} \, dx","Integrate[Sinh[x]^3/(a + b*Sinh[x] + c*Sinh[x]^2),x]","\frac{\frac{\sqrt{2} \left(b^2 \sqrt{b^2-4 a c}-a c \sqrt{b^2-4 a c}+3 a b c-b^3\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}-b\right)+2 c}{\sqrt{2 b \sqrt{b^2-4 a c}+4 c (a-c)-2 b^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}+\frac{\sqrt{2} \left(b^2 \sqrt{b^2-4 a c}-a c \sqrt{b^2-4 a c}-3 a b c+b^3\right) \tan ^{-1}\left(\frac{2 c-\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}+b\right)}{\sqrt{2} \sqrt{-b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{-b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}-b x+c \cosh (x)}{c^2}","\frac{\sqrt{2} \left(\frac{b^3}{\sqrt{4 a c-b^2}}+i \left(\frac{3 i a b c}{\sqrt{4 a c-b^2}}-a c+b^2\right)\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{4 a c-b^2}-i b \tanh \left(\frac{x}{2}\right)+2 i c}{\sqrt{2} \sqrt{i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}\right)}{c^2 \sqrt{i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}-\frac{\sqrt{2} \left(\frac{b^3}{\sqrt{4 a c-b^2}}-i \left(-\frac{3 i a b c}{\sqrt{4 a c-b^2}}-a c+b^2\right)\right) \tan ^{-1}\left(\frac{2 i c-\tanh \left(\frac{x}{2}\right) \left(\sqrt{4 a c-b^2}+i b\right)}{\sqrt{2} \sqrt{-i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}\right)}{c^2 \sqrt{-i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}-\frac{b x}{c^2}+\frac{\cosh (x)}{c}",1,"(-(b*x) + (Sqrt[2]*(-b^3 + 3*a*b*c + b^2*Sqrt[b^2 - 4*a*c] - a*c*Sqrt[b^2 - 4*a*c])*ArcTan[(2*c + (-b + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*(a - c)*c + 2*b*Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[-b^2 + 2*(a - c)*c + b*Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*(b^3 - 3*a*b*c + b^2*Sqrt[b^2 - 4*a*c] - a*c*Sqrt[b^2 - 4*a*c])*ArcTan[(2*c - (b + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/(Sqrt[2]*Sqrt[-b^2 + 2*(a - c)*c - b*Sqrt[b^2 - 4*a*c]])])/(Sqrt[b^2 - 4*a*c]*Sqrt[-b^2 + 2*(a - c)*c - b*Sqrt[b^2 - 4*a*c]]) + c*Cosh[x])/c^2","A",1
830,1,14,12,0.038478,"\int \frac{a+b \sinh (x)}{b^2-2 a b \sinh (x)+a^2 \sinh ^2(x)} \, dx","Integrate[(a + b*Sinh[x])/(b^2 - 2*a*b*Sinh[x] + a^2*Sinh[x]^2),x]","-\frac{\cosh (x)}{a \sinh (x)-b}","\frac{\cosh (x)}{b-a \sinh (x)}",1,"-(Cosh[x]/(-b + a*Sinh[x]))","A",1
831,1,258,300,0.5865914,"\int \frac{d+e \sinh (x)}{a+b \sinh (x)+c \sinh ^2(x)} \, dx","Integrate[(d + e*Sinh[x])/(a + b*Sinh[x] + c*Sinh[x]^2),x]","\frac{\sqrt{2} \left(\frac{\left(e \left(\sqrt{b^2-4 a c}-b\right)+2 c d\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}-b\right)+2 c}{\sqrt{2 b \sqrt{b^2-4 a c}+4 c (a-c)-2 b^2}}\right)}{\sqrt{b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}+\frac{\left(e \left(\sqrt{b^2-4 a c}+b\right)-2 c d\right) \tan ^{-1}\left(\frac{2 c-\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}+b\right)}{\sqrt{2} \sqrt{-b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}\right)}{\sqrt{-b \sqrt{b^2-4 a c}+2 c (a-c)-b^2}}\right)}{\sqrt{b^2-4 a c}}","\frac{\sqrt{2} \left(-\frac{2 c d-b e}{\sqrt{4 a c-b^2}}+i e\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{4 a c-b^2}-i b \tanh \left(\frac{x}{2}\right)+2 i c}{\sqrt{2} \sqrt{i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}\right)}{\sqrt{i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}+\frac{\sqrt{2} \left(\frac{2 c d-b e}{\sqrt{4 a c-b^2}}+i e\right) \tan ^{-1}\left(\frac{2 i c-\tanh \left(\frac{x}{2}\right) \left(\sqrt{4 a c-b^2}+i b\right)}{\sqrt{2} \sqrt{-i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}\right)}{\sqrt{-i b \sqrt{4 a c-b^2}-2 c (a-c)+b^2}}",1,"(Sqrt[2]*(((2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e)*ArcTan[(2*c + (-b + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*(a - c)*c + 2*b*Sqrt[b^2 - 4*a*c]]])/Sqrt[-b^2 + 2*(a - c)*c + b*Sqrt[b^2 - 4*a*c]] + ((-2*c*d + (b + Sqrt[b^2 - 4*a*c])*e)*ArcTan[(2*c - (b + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/(Sqrt[2]*Sqrt[-b^2 + 2*(a - c)*c - b*Sqrt[b^2 - 4*a*c]])])/Sqrt[-b^2 + 2*(a - c)*c - b*Sqrt[b^2 - 4*a*c]]))/Sqrt[b^2 - 4*a*c]","A",1
832,1,198,223,0.6100021,"\int \frac{1}{a+b \cosh (x)+c \cosh ^2(x)} \, dx","Integrate[(a + b*Cosh[x] + c*Cosh[x]^2)^(-1),x]","\frac{2 \sqrt{2} c \left(\frac{\tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}+b-2 c\right)}{\sqrt{-2 b \sqrt{b^2-4 a c}+4 c (a+c)-2 b^2}}\right)}{\sqrt{-b \sqrt{b^2-4 a c}+2 c (a+c)-b^2}}+\frac{\tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}-b+2 c\right)}{\sqrt{2 b \sqrt{b^2-4 a c}+4 c (a+c)-2 b^2}}\right)}{\sqrt{b \sqrt{b^2-4 a c}+2 c (a+c)-b^2}}\right)}{\sqrt{b^2-4 a c}}","\frac{4 c \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{b^2-4 a c} \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{4 c \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}",1,"(2*Sqrt[2]*c*(ArcTan[((b - 2*c + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*c*(a + c) - 2*b*Sqrt[b^2 - 4*a*c]]]/Sqrt[-b^2 + 2*c*(a + c) - b*Sqrt[b^2 - 4*a*c]] + ArcTan[((-b + 2*c + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*c*(a + c) + 2*b*Sqrt[b^2 - 4*a*c]]]/Sqrt[-b^2 + 2*c*(a + c) + b*Sqrt[b^2 - 4*a*c]]))/Sqrt[b^2 - 4*a*c]","A",1
833,1,227,230,0.5458397,"\int \frac{\cosh (x)}{a+b \cosh (x)+c \cosh ^2(x)} \, dx","Integrate[Cosh[x]/(a + b*Cosh[x] + c*Cosh[x]^2),x]","\frac{\sqrt{2} \left(\frac{\left(\sqrt{b^2-4 a c}-b\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}-b+2 c\right)}{\sqrt{2 b \sqrt{b^2-4 a c}+4 c (a+c)-2 b^2}}\right)}{\sqrt{b \sqrt{b^2-4 a c}+2 c (a+c)-b^2}}-\frac{\left(\sqrt{b^2-4 a c}+b\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}+b-2 c\right)}{\sqrt{-2 b \sqrt{b^2-4 a c}+4 c (a+c)-2 b^2}}\right)}{\sqrt{-b \sqrt{b^2-4 a c}+2 c (a+c)-b^2}}\right)}{\sqrt{b^2-4 a c}}","\frac{2 \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}",1,"(Sqrt[2]*(-(((b + Sqrt[b^2 - 4*a*c])*ArcTan[((b - 2*c + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*c*(a + c) - 2*b*Sqrt[b^2 - 4*a*c]]])/Sqrt[-b^2 + 2*c*(a + c) - b*Sqrt[b^2 - 4*a*c]]) + ((-b + Sqrt[b^2 - 4*a*c])*ArcTan[((-b + 2*c + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*c*(a + c) + 2*b*Sqrt[b^2 - 4*a*c]]])/Sqrt[-b^2 + 2*c*(a + c) + b*Sqrt[b^2 - 4*a*c]]))/Sqrt[b^2 - 4*a*c]","A",1
834,1,264,255,0.5872652,"\int \frac{\cosh ^2(x)}{a+b \cosh (x)+c \cosh ^2(x)} \, dx","Integrate[Cosh[x]^2/(a + b*Cosh[x] + c*Cosh[x]^2),x]","\frac{\frac{\sqrt{2} \left(b \sqrt{b^2-4 a c}-2 a c+b^2\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}+b-2 c\right)}{\sqrt{-2 b \sqrt{b^2-4 a c}+4 c (a+c)-2 b^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{-b \sqrt{b^2-4 a c}+2 c (a+c)-b^2}}-\frac{\sqrt{2} \left(b \sqrt{b^2-4 a c}+2 a c-b^2\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}-b+2 c\right)}{\sqrt{2 b \sqrt{b^2-4 a c}+4 c (a+c)-2 b^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{b \sqrt{b^2-4 a c}+2 c (a+c)-b^2}}+x}{c}","-\frac{2 \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{2 \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{x}{c}",1,"(x + (Sqrt[2]*(b^2 - 2*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[((b - 2*c + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*c*(a + c) - 2*b*Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[-b^2 + 2*c*(a + c) - b*Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*(-b^2 + 2*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[((-b + 2*c + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*c*(a + c) + 2*b*Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[-b^2 + 2*c*(a + c) + b*Sqrt[b^2 - 4*a*c]]))/c","A",1
835,1,309,299,0.7993024,"\int \frac{\cosh ^3(x)}{a+b \cosh (x)+c \cosh ^2(x)} \, dx","Integrate[Cosh[x]^3/(a + b*Cosh[x] + c*Cosh[x]^2),x]","\frac{-\frac{\sqrt{2} \left(b^2 \sqrt{b^2-4 a c}-a c \sqrt{b^2-4 a c}-3 a b c+b^3\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}+b-2 c\right)}{\sqrt{-2 b \sqrt{b^2-4 a c}+4 c (a+c)-2 b^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{-b \sqrt{b^2-4 a c}+2 c (a+c)-b^2}}+\frac{\sqrt{2} \left(b^2 \sqrt{b^2-4 a c}-a c \sqrt{b^2-4 a c}+3 a b c-b^3\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}-b+2 c\right)}{\sqrt{2 b \sqrt{b^2-4 a c}+4 c (a+c)-2 b^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{b \sqrt{b^2-4 a c}+2 c (a+c)-b^2}}-b x+c \sinh (x)}{c^2}","\frac{2 \left(\frac{3 a b c}{\sqrt{b^2-4 a c}}-\frac{b^3}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^2 \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 \left(-\frac{3 a b c}{\sqrt{b^2-4 a c}}+\frac{b^3}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^2 \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{b x}{c^2}+\frac{\sinh (x)}{c}",1,"(-(b*x) - (Sqrt[2]*(b^3 - 3*a*b*c + b^2*Sqrt[b^2 - 4*a*c] - a*c*Sqrt[b^2 - 4*a*c])*ArcTan[((b - 2*c + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*c*(a + c) - 2*b*Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[-b^2 + 2*c*(a + c) - b*Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*(-b^3 + 3*a*b*c + b^2*Sqrt[b^2 - 4*a*c] - a*c*Sqrt[b^2 - 4*a*c])*ArcTan[((-b + 2*c + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*c*(a + c) + 2*b*Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[-b^2 + 2*c*(a + c) + b*Sqrt[b^2 - 4*a*c]]) + c*Sinh[x])/c^2","A",1
836,1,11,11,0.0558964,"\int \frac{a+b \cosh (x)}{b^2+2 a b \cosh (x)+a^2 \cosh ^2(x)} \, dx","Integrate[(a + b*Cosh[x])/(b^2 + 2*a*b*Cosh[x] + a^2*Cosh[x]^2),x]","\frac{\sinh (x)}{a \cosh (x)+b}","\frac{\sinh (x)}{a \cosh (x)+b}",1,"Sinh[x]/(b + a*Cosh[x])","A",1
837,1,241,246,0.4791956,"\int \frac{d+e \cosh (x)}{a+b \cosh (x)+c \cosh ^2(x)} \, dx","Integrate[(d + e*Cosh[x])/(a + b*Cosh[x] + c*Cosh[x]^2),x]","\frac{\sqrt{2} \left(\frac{\left(e \left(\sqrt{b^2-4 a c}-b\right)+2 c d\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}-b+2 c\right)}{\sqrt{2 b \sqrt{b^2-4 a c}+4 c (a+c)-2 b^2}}\right)}{\sqrt{b \sqrt{b^2-4 a c}+2 c (a+c)-b^2}}-\frac{\left(e \left(\sqrt{b^2-4 a c}+b\right)-2 c d\right) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \left(\sqrt{b^2-4 a c}+b-2 c\right)}{\sqrt{-2 b \sqrt{b^2-4 a c}+4 c (a+c)-2 b^2}}\right)}{\sqrt{-b \sqrt{b^2-4 a c}+2 c (a+c)-b^2}}\right)}{\sqrt{b^2-4 a c}}","\frac{2 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}",1,"(Sqrt[2]*(-(((-2*c*d + (b + Sqrt[b^2 - 4*a*c])*e)*ArcTan[((b - 2*c + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*c*(a + c) - 2*b*Sqrt[b^2 - 4*a*c]]])/Sqrt[-b^2 + 2*c*(a + c) - b*Sqrt[b^2 - 4*a*c]]) + ((2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e)*ArcTan[((-b + 2*c + Sqrt[b^2 - 4*a*c])*Tanh[x/2])/Sqrt[-2*b^2 + 4*c*(a + c) + 2*b*Sqrt[b^2 - 4*a*c]]])/Sqrt[-b^2 + 2*c*(a + c) + b*Sqrt[b^2 - 4*a*c]]))/Sqrt[b^2 - 4*a*c]","A",1
838,1,34,39,0.109206,"\int \frac{\sinh ^2(x)}{a \cosh ^2(x)+b \sinh ^2(x)} \, dx","Integrate[Sinh[x]^2/(a*Cosh[x]^2 + b*Sinh[x]^2),x]","\frac{x-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a}}\right)}{\sqrt{b}}}{a+b}","\frac{x}{a+b}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a}}\right)}{\sqrt{b} (a+b)}",1,"(x - (Sqrt[a]*ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a]])/Sqrt[b])/(a + b)","A",1
839,1,33,38,0.0590936,"\int \frac{\cosh ^2(x)}{a \cosh ^2(x)+b \sinh ^2(x)} \, dx","Integrate[Cosh[x]^2/(a*Cosh[x]^2 + b*Sinh[x]^2),x]","\frac{\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a}}\right)}{\sqrt{a}}+x}{a+b}","\frac{x}{a+b}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)}",1,"(x + (Sqrt[b]*ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a]])/Sqrt[a])/(a + b)","A",1
840,1,40,38,0.1394461,"\int \frac{\sinh ^3(x)}{\cosh ^3(x)+\sinh ^3(x)} \, dx","Integrate[Sinh[x]^3/(Cosh[x]^3 + Sinh[x]^3),x]","\frac{1}{36} \left(18 x-3 \sinh (2 x)+3 \cosh (2 x)-8 \sqrt{3} \tan ^{-1}\left(\frac{2 \tanh (x)-1}{\sqrt{3}}\right)\right)","\frac{x}{2}+\frac{1}{6 (\tanh (x)+1)}+\frac{2 \tan ^{-1}\left(\frac{1-2 \tanh (x)}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(18*x - 8*Sqrt[3]*ArcTan[(-1 + 2*Tanh[x])/Sqrt[3]] + 3*Cosh[2*x] - 3*Sinh[2*x])/36","A",1
841,1,40,38,0.1046399,"\int \frac{\cosh ^3(x)}{\cosh ^3(x)+\sinh ^3(x)} \, dx","Integrate[Cosh[x]^3/(Cosh[x]^3 + Sinh[x]^3),x]","\frac{1}{36} \left(18 x+3 \sinh (2 x)-3 \cosh (2 x)+8 \sqrt{3} \tan ^{-1}\left(\frac{2 \tanh (x)-1}{\sqrt{3}}\right)\right)","\frac{x}{2}-\frac{1}{6 (\tanh (x)+1)}-\frac{2 \tan ^{-1}\left(\frac{1-2 \tanh (x)}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(18*x + 8*Sqrt[3]*ArcTan[(-1 + 2*Tanh[x])/Sqrt[3]] - 3*Cosh[2*x] + 3*Sinh[2*x])/36","A",1
842,1,55,59,0.0575104,"\int \frac{x \text{csch}(x) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}} \, dx","Integrate[(x*Csch[x]*Sech[x])/Sqrt[a*Sech[x]^2],x]","\frac{\text{sech}(x) \left(\text{Li}_2\left(-e^{-x}\right)-\text{Li}_2\left(e^{-x}\right)+x \left(\log \left(1-e^{-x}\right)-\log \left(e^{-x}+1\right)\right)\right)}{\sqrt{a \text{sech}^2(x)}}","-\frac{\text{Li}_2\left(-e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}+\frac{\text{Li}_2\left(e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}-\frac{2 x \tanh ^{-1}\left(e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}",1,"((x*(Log[1 - E^(-x)] - Log[1 + E^(-x)]) + PolyLog[2, -E^(-x)] - PolyLog[2, E^(-x)])*Sech[x])/Sqrt[a*Sech[x]^2]","A",1
843,1,83,104,0.0708776,"\int \frac{x^2 \text{csch}(x) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}} \, dx","Integrate[(x^2*Csch[x]*Sech[x])/Sqrt[a*Sech[x]^2],x]","\frac{\text{sech}(x) \left(2 x \text{Li}_2\left(-e^{-x}\right)-2 x \text{Li}_2\left(e^{-x}\right)+2 \text{Li}_3\left(-e^{-x}\right)-2 \text{Li}_3\left(e^{-x}\right)+x^2 \log \left(1-e^{-x}\right)-x^2 \log \left(e^{-x}+1\right)\right)}{\sqrt{a \text{sech}^2(x)}}","-\frac{2 x \text{Li}_2\left(-e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}+\frac{2 x \text{Li}_2\left(e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}+\frac{2 \text{Li}_3\left(-e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}-\frac{2 \text{Li}_3\left(e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}-\frac{2 x^2 \tanh ^{-1}\left(e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}",1,"((x^2*Log[1 - E^(-x)] - x^2*Log[1 + E^(-x)] + 2*x*PolyLog[2, -E^(-x)] - 2*x*PolyLog[2, E^(-x)] + 2*PolyLog[3, -E^(-x)] - 2*PolyLog[3, E^(-x)])*Sech[x])/Sqrt[a*Sech[x]^2]","A",1
844,1,113,150,0.0896849,"\int \frac{x^3 \text{csch}(x) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}} \, dx","Integrate[(x^3*Csch[x]*Sech[x])/Sqrt[a*Sech[x]^2],x]","\frac{\text{sech}(x) \left(24 x^2 \text{Li}_2\left(-e^{-x}\right)+24 x^2 \text{Li}_2\left(e^x\right)+48 x \text{Li}_3\left(-e^{-x}\right)-48 x \text{Li}_3\left(e^x\right)+48 \text{Li}_4\left(-e^{-x}\right)+48 \text{Li}_4\left(e^x\right)-2 x^4-8 x^3 \log \left(e^{-x}+1\right)+8 x^3 \log \left(1-e^x\right)+\pi ^4\right)}{8 \sqrt{a \text{sech}^2(x)}}","-\frac{3 x^2 \text{Li}_2\left(-e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}+\frac{3 x^2 \text{Li}_2\left(e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}+\frac{6 x \text{Li}_3\left(-e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}-\frac{6 x \text{Li}_3\left(e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}-\frac{6 \text{Li}_4\left(-e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}+\frac{6 \text{Li}_4\left(e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}-\frac{2 x^3 \tanh ^{-1}\left(e^x\right) \text{sech}(x)}{\sqrt{a \text{sech}^2(x)}}",1,"((Pi^4 - 2*x^4 - 8*x^3*Log[1 + E^(-x)] + 8*x^3*Log[1 - E^x] + 24*x^2*PolyLog[2, -E^(-x)] + 24*x^2*PolyLog[2, E^x] + 48*x*PolyLog[3, -E^(-x)] - 48*x*PolyLog[3, E^x] + 48*PolyLog[4, -E^(-x)] + 48*PolyLog[4, E^x])*Sech[x])/(8*Sqrt[a*Sech[x]^2])","A",1
845,1,44,73,0.0510741,"\int \frac{x \text{csch}(x) \text{sech}(x)}{\sqrt{a \text{sech}^4(x)}} \, dx","Integrate[(x*Csch[x]*Sech[x])/Sqrt[a*Sech[x]^4],x]","\frac{\text{sech}^2(x) \left(x \left(x+2 \log \left(1-e^{-2 x}\right)\right)-\text{Li}_2\left(e^{-2 x}\right)\right)}{2 \sqrt{a \text{sech}^4(x)}}","\frac{\text{Li}_2\left(e^{2 x}\right) \text{sech}^2(x)}{2 \sqrt{a \text{sech}^4(x)}}-\frac{x^2 \text{sech}^2(x)}{2 \sqrt{a \text{sech}^4(x)}}+\frac{x \log \left(1-e^{2 x}\right) \text{sech}^2(x)}{\sqrt{a \text{sech}^4(x)}}",1,"((x*(x + 2*Log[1 - E^(-2*x)]) - PolyLog[2, E^(-2*x)])*Sech[x]^2)/(2*Sqrt[a*Sech[x]^4])","A",1
846,1,57,98,0.052019,"\int \frac{x^2 \text{csch}(x) \text{sech}(x)}{\sqrt{a \text{sech}^4(x)}} \, dx","Integrate[(x^2*Csch[x]*Sech[x])/Sqrt[a*Sech[x]^4],x]","\frac{\text{sech}^2(x) \left(6 x \text{Li}_2\left(e^{2 x}\right)-3 \text{Li}_3\left(e^{2 x}\right)-2 x^2 \left(x-3 \log \left(1-e^{2 x}\right)\right)\right)}{6 \sqrt{a \text{sech}^4(x)}}","\frac{x \text{Li}_2\left(e^{2 x}\right) \text{sech}^2(x)}{\sqrt{a \text{sech}^4(x)}}-\frac{\text{Li}_3\left(e^{2 x}\right) \text{sech}^2(x)}{2 \sqrt{a \text{sech}^4(x)}}-\frac{x^3 \text{sech}^2(x)}{3 \sqrt{a \text{sech}^4(x)}}+\frac{x^2 \log \left(1-e^{2 x}\right) \text{sech}^2(x)}{\sqrt{a \text{sech}^4(x)}}",1,"((-2*x^2*(x - 3*Log[1 - E^(2*x)]) + 6*x*PolyLog[2, E^(2*x)] - 3*PolyLog[3, E^(2*x)])*Sech[x]^2)/(6*Sqrt[a*Sech[x]^4])","A",1
847,1,68,129,0.0600127,"\int \frac{x^3 \text{csch}(x) \text{sech}(x)}{\sqrt{a \text{sech}^4(x)}} \, dx","Integrate[(x^3*Csch[x]*Sech[x])/Sqrt[a*Sech[x]^4],x]","-\frac{\text{sech}^2(x) \left(-6 x^2 \text{Li}_2\left(e^{2 x}\right)+6 x \text{Li}_3\left(e^{2 x}\right)-3 \text{Li}_4\left(e^{2 x}\right)+x^4-4 x^3 \log \left(1-e^{2 x}\right)\right)}{4 \sqrt{a \text{sech}^4(x)}}","\frac{3 x^2 \text{Li}_2\left(e^{2 x}\right) \text{sech}^2(x)}{2 \sqrt{a \text{sech}^4(x)}}-\frac{3 x \text{Li}_3\left(e^{2 x}\right) \text{sech}^2(x)}{2 \sqrt{a \text{sech}^4(x)}}+\frac{3 \text{Li}_4\left(e^{2 x}\right) \text{sech}^2(x)}{4 \sqrt{a \text{sech}^4(x)}}-\frac{x^4 \text{sech}^2(x)}{4 \sqrt{a \text{sech}^4(x)}}+\frac{x^3 \log \left(1-e^{2 x}\right) \text{sech}^2(x)}{\sqrt{a \text{sech}^4(x)}}",1,"-1/4*((x^4 - 4*x^3*Log[1 - E^(2*x)] - 6*x^2*PolyLog[2, E^(2*x)] + 6*x*PolyLog[3, E^(2*x)] - 3*PolyLog[4, E^(2*x)])*Sech[x]^2)/Sqrt[a*Sech[x]^4]","A",1
848,1,74,88,0.0609941,"\int x \text{csch}(x) \text{sech}(x) \sqrt{a \text{sech}^2(x)} \, dx","Integrate[x*Csch[x]*Sech[x]*Sqrt[a*Sech[x]^2],x]","\sqrt{a \text{sech}^2(x)} \left(\text{Li}_2\left(-e^{-x}\right) \cosh (x)-\text{Li}_2\left(e^{-x}\right) \cosh (x)+x+x \log \left(1-e^{-x}\right) \cosh (x)-x \log \left(e^{-x}+1\right) \cosh (x)-2 \cosh (x) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)","-\text{Li}_2\left(-e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+\text{Li}_2\left(e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+x \sqrt{a \text{sech}^2(x)}-2 x \cosh (x) \tanh ^{-1}\left(e^x\right) \sqrt{a \text{sech}^2(x)}-\cosh (x) \sqrt{a \text{sech}^2(x)} \tan ^{-1}(\sinh (x))",1,"(x - 2*ArcTan[Tanh[x/2]]*Cosh[x] + x*Cosh[x]*Log[1 - E^(-x)] - x*Cosh[x]*Log[1 + E^(-x)] + Cosh[x]*PolyLog[2, -E^(-x)] - Cosh[x]*PolyLog[2, E^(-x)])*Sqrt[a*Sech[x]^2]","A",1
849,1,154,187,0.2045814,"\int x^2 \text{csch}(x) \text{sech}(x) \sqrt{a \text{sech}^2(x)} \, dx","Integrate[x^2*Csch[x]*Sech[x]*Sqrt[a*Sech[x]^2],x]","\sqrt{a \text{sech}^2(x)} \left(2 x \left(\text{Li}_2\left(-e^{-x}\right)-\text{Li}_2\left(e^{-x}\right)\right) \cosh (x)+2 i \left(\text{Li}_2\left(-i e^{-x}\right)-\text{Li}_2\left(i e^{-x}\right)\right) \cosh (x)+2 \left(\text{Li}_3\left(-e^{-x}\right)-\text{Li}_3\left(e^{-x}\right)\right) \cosh (x)+x^2+x^2 \left(\log \left(1-e^{-x}\right)-\log \left(e^{-x}+1\right)\right) \cosh (x)+2 i x \left(\log \left(1-i e^{-x}\right)-\log \left(1+i e^{-x}\right)\right) \cosh (x)\right)","-2 x \text{Li}_2\left(-e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+2 x \text{Li}_2\left(e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+2 i \text{Li}_2\left(-i e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}-2 i \text{Li}_2\left(i e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+2 \text{Li}_3\left(-e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}-2 \text{Li}_3\left(e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+x^2 \sqrt{a \text{sech}^2(x)}-2 x^2 \cosh (x) \tanh ^{-1}\left(e^x\right) \sqrt{a \text{sech}^2(x)}-4 x \tan ^{-1}\left(e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}",1,"(x^2 + (2*I)*x*Cosh[x]*(Log[1 - I/E^x] - Log[1 + I/E^x]) + x^2*Cosh[x]*(Log[1 - E^(-x)] - Log[1 + E^(-x)]) + (2*I)*Cosh[x]*(PolyLog[2, (-I)/E^x] - PolyLog[2, I/E^x]) + 2*x*Cosh[x]*(PolyLog[2, -E^(-x)] - PolyLog[2, E^(-x)]) + 2*Cosh[x]*(PolyLog[3, -E^(-x)] - PolyLog[3, E^(-x)]))*Sqrt[a*Sech[x]^2]","A",1
850,1,249,287,0.6604878,"\int x^3 \text{csch}(x) \text{sech}(x) \sqrt{a \text{sech}^2(x)} \, dx","Integrate[x^3*Csch[x]*Sech[x]*Sqrt[a*Sech[x]^2],x]","\frac{1}{8} \sqrt{a \text{sech}^2(x)} \left(24 x^2 \text{Li}_2\left(-e^{-x}\right) \cosh (x)+24 x^2 \text{Li}_2\left(e^x\right) \cosh (x)+48 i x \text{Li}_2\left(-i e^{-x}\right) \cosh (x)-48 i x \text{Li}_2\left(i e^{-x}\right) \cosh (x)+48 x \text{Li}_3\left(-e^{-x}\right) \cosh (x)-48 x \text{Li}_3\left(e^x\right) \cosh (x)+48 i \text{Li}_3\left(-i e^{-x}\right) \cosh (x)-48 i \text{Li}_3\left(i e^{-x}\right) \cosh (x)+48 \text{Li}_4\left(-e^{-x}\right) \cosh (x)+48 \text{Li}_4\left(e^x\right) \cosh (x)-2 x^4 \cosh (x)+8 x^3-8 x^3 \log \left(e^{-x}+1\right) \cosh (x)+8 x^3 \log \left(1-e^x\right) \cosh (x)+24 i x^2 \log \left(1-i e^{-x}\right) \cosh (x)-24 i x^2 \log \left(1+i e^{-x}\right) \cosh (x)+\pi ^4 \cosh (x)\right)","-3 x^2 \text{Li}_2\left(-e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+3 x^2 \text{Li}_2\left(e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+6 i x \text{Li}_2\left(-i e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}-6 i x \text{Li}_2\left(i e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+6 x \text{Li}_3\left(-e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}-6 x \text{Li}_3\left(e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}-6 i \text{Li}_3\left(-i e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+6 i \text{Li}_3\left(i e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}-6 \text{Li}_4\left(-e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+6 \text{Li}_4\left(e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}+x^3 \sqrt{a \text{sech}^2(x)}-2 x^3 \cosh (x) \tanh ^{-1}\left(e^x\right) \sqrt{a \text{sech}^2(x)}-6 x^2 \tan ^{-1}\left(e^x\right) \cosh (x) \sqrt{a \text{sech}^2(x)}",1,"((8*x^3 + Pi^4*Cosh[x] - 2*x^4*Cosh[x] + (24*I)*x^2*Cosh[x]*Log[1 - I/E^x] - (24*I)*x^2*Cosh[x]*Log[1 + I/E^x] - 8*x^3*Cosh[x]*Log[1 + E^(-x)] + 8*x^3*Cosh[x]*Log[1 - E^x] + 24*x^2*Cosh[x]*PolyLog[2, -E^(-x)] + (48*I)*x*Cosh[x]*PolyLog[2, (-I)/E^x] - (48*I)*x*Cosh[x]*PolyLog[2, I/E^x] + 24*x^2*Cosh[x]*PolyLog[2, E^x] + 48*x*Cosh[x]*PolyLog[3, -E^(-x)] + (48*I)*Cosh[x]*PolyLog[3, (-I)/E^x] - (48*I)*Cosh[x]*PolyLog[3, I/E^x] - 48*x*Cosh[x]*PolyLog[3, E^x] + 48*Cosh[x]*PolyLog[4, -E^(-x)] + 48*Cosh[x]*PolyLog[4, E^x])*Sqrt[a*Sech[x]^2])/8","A",1
851,1,71,132,0.2303636,"\int x \text{csch}(x) \text{sech}(x) \sqrt{a \text{sech}^4(x)} \, dx","Integrate[x*Csch[x]*Sech[x]*Sqrt[a*Sech[x]^4],x]","\frac{1}{2} \cosh ^2(x) \sqrt{a \text{sech}^4(x)} \left(\text{Li}_2\left(-e^{-2 x}\right)-\text{Li}_2\left(e^{-2 x}\right)+2 x \log \left(1-e^{-2 x}\right)-2 x \log \left(e^{-2 x}+1\right)-\tanh (x)+x \text{sech}^2(x)\right)","-\frac{1}{2} \text{Li}_2\left(-e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}+\frac{1}{2} \text{Li}_2\left(e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}+\frac{1}{2} x \cosh ^2(x) \sqrt{a \text{sech}^4(x)}-\frac{1}{2} x \sinh ^2(x) \sqrt{a \text{sech}^4(x)}-2 x \cosh ^2(x) \tanh ^{-1}\left(e^{2 x}\right) \sqrt{a \text{sech}^4(x)}-\frac{1}{2} \sinh (x) \cosh (x) \sqrt{a \text{sech}^4(x)}",1,"(Cosh[x]^2*Sqrt[a*Sech[x]^4]*(2*x*Log[1 - E^(-2*x)] - 2*x*Log[1 + E^(-2*x)] + PolyLog[2, -E^(-2*x)] - PolyLog[2, E^(-2*x)] + x*Sech[x]^2 - Tanh[x]))/2","A",1
852,1,120,204,0.6455434,"\int x^2 \text{csch}(x) \text{sech}(x) \sqrt{a \text{sech}^4(x)} \, dx","Integrate[x^2*Csch[x]*Sech[x]*Sqrt[a*Sech[x]^4],x]","\frac{1}{24} \cosh ^2(x) \sqrt{a \text{sech}^4(x)} \left(24 x \text{Li}_2\left(-e^{-2 x}\right)+24 x \text{Li}_2\left(e^{2 x}\right)+12 \text{Li}_3\left(-e^{-2 x}\right)-12 \text{Li}_3\left(e^{2 x}\right)-16 x^3-24 x^2 \log \left(e^{-2 x}+1\right)+24 x^2 \log \left(1-e^{2 x}\right)+12 x^2 \text{sech}^2(x)-24 x \tanh (x)+24 \log (\cosh (x))+i \pi ^3\right)","-x \text{Li}_2\left(-e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}+x \text{Li}_2\left(e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}+\frac{1}{2} \text{Li}_3\left(-e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}-\frac{1}{2} \text{Li}_3\left(e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}+\frac{1}{2} x^2 \cosh ^2(x) \sqrt{a \text{sech}^4(x)}-\frac{1}{2} x^2 \sinh ^2(x) \sqrt{a \text{sech}^4(x)}-2 x^2 \cosh ^2(x) \tanh ^{-1}\left(e^{2 x}\right) \sqrt{a \text{sech}^4(x)}+\cosh ^2(x) \sqrt{a \text{sech}^4(x)} \log (\cosh (x))-x \sinh (x) \cosh (x) \sqrt{a \text{sech}^4(x)}",1,"(Cosh[x]^2*Sqrt[a*Sech[x]^4]*(I*Pi^3 - 16*x^3 - 24*x^2*Log[1 + E^(-2*x)] + 24*x^2*Log[1 - E^(2*x)] + 24*Log[Cosh[x]] + 24*x*PolyLog[2, -E^(-2*x)] + 24*x*PolyLog[2, E^(2*x)] + 12*PolyLog[3, -E^(-2*x)] - 12*PolyLog[3, E^(2*x)] + 12*x^2*Sech[x]^2 - 24*x*Tanh[x]))/24","C",1
853,1,157,326,1.0423147,"\int x^3 \text{csch}(x) \text{sech}(x) \sqrt{a \text{sech}^4(x)} \, dx","Integrate[x^3*Csch[x]*Sech[x]*Sqrt[a*Sech[x]^4],x]","\frac{1}{64} \cosh ^2(x) \sqrt{a \text{sech}^4(x)} \left(96 x^2 \text{Li}_2\left(e^{2 x}\right)+96 \left(x^2-1\right) \text{Li}_2\left(-e^{-2 x}\right)+96 x \text{Li}_3\left(-e^{-2 x}\right)-96 x \text{Li}_3\left(e^{2 x}\right)+48 \text{Li}_4\left(-e^{-2 x}\right)+48 \text{Li}_4\left(e^{2 x}\right)-32 x^4-64 x^3 \log \left(e^{-2 x}+1\right)+64 x^3 \log \left(1-e^{2 x}\right)+32 x^3 \text{sech}^2(x)+96 x^2-96 x^2 \tanh (x)+192 x \log \left(e^{-2 x}+1\right)+\pi ^4\right)","-\frac{3}{2} x^2 \text{Li}_2\left(-e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}+\frac{3}{2} x^2 \text{Li}_2\left(e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}+\frac{3}{2} x \text{Li}_3\left(-e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}-\frac{3}{2} x \text{Li}_3\left(e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}+\frac{3}{2} \text{Li}_2\left(-e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}-\frac{3}{4} \text{Li}_4\left(-e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}+\frac{3}{4} \text{Li}_4\left(e^{2 x}\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}+\frac{1}{2} x^3 \cosh ^2(x) \sqrt{a \text{sech}^4(x)}-\frac{1}{2} x^3 \sinh ^2(x) \sqrt{a \text{sech}^4(x)}-2 x^3 \cosh ^2(x) \tanh ^{-1}\left(e^{2 x}\right) \sqrt{a \text{sech}^4(x)}-\frac{3}{2} x^2 \cosh ^2(x) \sqrt{a \text{sech}^4(x)}-\frac{3}{2} x^2 \sinh (x) \cosh (x) \sqrt{a \text{sech}^4(x)}+3 x \log \left(e^{2 x}+1\right) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}",1,"(Cosh[x]^2*Sqrt[a*Sech[x]^4]*(Pi^4 + 96*x^2 - 32*x^4 + 192*x*Log[1 + E^(-2*x)] - 64*x^3*Log[1 + E^(-2*x)] + 64*x^3*Log[1 - E^(2*x)] + 96*(-1 + x^2)*PolyLog[2, -E^(-2*x)] + 96*x^2*PolyLog[2, E^(2*x)] + 96*x*PolyLog[3, -E^(-2*x)] - 96*x*PolyLog[3, E^(2*x)] + 48*PolyLog[4, -E^(-2*x)] + 48*PolyLog[4, E^(2*x)] + 32*x^3*Sech[x]^2 - 96*x^2*Tanh[x]))/64","A",1
854,1,162,147,0.688569,"\int (a+b \cosh (c+d x) \sinh (c+d x))^m \, dx","Integrate[(a + b*Cosh[c + d*x]*Sinh[c + d*x])^m,x]","\frac{\text{sech}(2 (c+d x)) \sqrt{\frac{b (1-i \sinh (2 (c+d x)))}{b+2 i a}} \sqrt{\frac{b (1+i \sinh (2 (c+d x)))}{b-2 i a}} \left(a+\frac{1}{2} b \sinh (2 (c+d x))\right)^{m+1} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;\frac{2 a+b \sinh (2 (c+d x))}{2 a+i b},\frac{2 a+b \sinh (2 (c+d x))}{2 a-i b}\right)}{b d (m+1)}","\frac{i \cosh (2 c+2 d x) \left(a+\frac{1}{2} b \sinh (2 c+2 d x)\right)^m \left(\frac{2 a+b \sinh (2 c+2 d x)}{2 a-i b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-i \sinh (2 c+2 d x)),\frac{b (1-i \sinh (2 c+2 d x))}{2 i a+b}\right)}{\sqrt{2} d \sqrt{1+i \sinh (2 c+2 d x)}}",1,"(AppellF1[1 + m, 1/2, 1/2, 2 + m, (2*a + b*Sinh[2*(c + d*x)])/(2*a + I*b), (2*a + b*Sinh[2*(c + d*x)])/(2*a - I*b)]*Sech[2*(c + d*x)]*Sqrt[(b*(1 - I*Sinh[2*(c + d*x)]))/((2*I)*a + b)]*Sqrt[(b*(1 + I*Sinh[2*(c + d*x)]))/((-2*I)*a + b)]*(a + (b*Sinh[2*(c + d*x)])/2)^(1 + m))/(b*d*(1 + m))","A",0
855,1,77,109,0.2710293,"\int (a+b \cosh (c+d x) \sinh (c+d x))^3 \, dx","Integrate[(a + b*Cosh[c + d*x]*Sinh[c + d*x])^3,x]","\frac{9 \left(16 a^2 b-b^3\right) \cosh (2 (c+d x))+6 a \left(4 \left(8 a^2-3 b^2\right) (c+d x)+3 b^2 \sinh (4 (c+d x))\right)+b^3 \cosh (6 (c+d x))}{192 d}","\frac{b \left(16 a^2-b^2\right) \cosh (2 c+2 d x)}{24 d}+\frac{1}{8} a x \left(8 a^2-3 b^2\right)+\frac{5 a b^2 \sinh (2 c+2 d x) \cosh (2 c+2 d x)}{48 d}+\frac{b \cosh (2 c+2 d x) (2 a+b \sinh (2 c+2 d x))^2}{48 d}",1,"(9*(16*a^2*b - b^3)*Cosh[2*(c + d*x)] + b^3*Cosh[6*(c + d*x)] + 6*a*(4*(8*a^2 - 3*b^2)*(c + d*x) + 3*b^2*Sinh[4*(c + d*x)]))/(192*d)","A",1
856,1,50,63,0.1164494,"\int (a+b \cosh (c+d x) \sinh (c+d x))^2 \, dx","Integrate[(a + b*Cosh[c + d*x]*Sinh[c + d*x])^2,x]","\frac{4 \left(8 a^2-b^2\right) (c+d x)+16 a b \cosh (2 (c+d x))+b^2 \sinh (4 (c+d x))}{32 d}","\frac{1}{8} x \left(8 a^2-b^2\right)+\frac{a b \cosh (2 c+2 d x)}{2 d}+\frac{b^2 \sinh (2 c+2 d x) \cosh (2 c+2 d x)}{16 d}",1,"(4*(8*a^2 - b^2)*(c + d*x) + 16*a*b*Cosh[2*(c + d*x)] + b^2*Sinh[4*(c + d*x)])/(32*d)","A",1
857,1,38,20,0.0085064,"\int (a+b \cosh (c+d x) \sinh (c+d x)) \, dx","Integrate[a + b*Cosh[c + d*x]*Sinh[c + d*x],x]","a x+\frac{b \sinh (2 c) \sinh (2 d x)}{4 d}+\frac{b \cosh (2 c) \cosh (2 d x)}{4 d}","a x+\frac{b \sinh ^2(c+d x)}{2 d}",1,"a*x + (b*Cosh[2*c]*Cosh[2*d*x])/(4*d) + (b*Sinh[2*c]*Sinh[2*d*x])/(4*d)","A",1
858,1,48,44,0.0784671,"\int \frac{1}{a+b \cosh (c+d x) \sinh (c+d x)} \, dx","Integrate[(a + b*Cosh[c + d*x]*Sinh[c + d*x])^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{b-2 a \tanh (c+d x)}{\sqrt{-4 a^2-b^2}}\right)}{d \sqrt{-4 a^2-b^2}}","-\frac{2 \tanh ^{-1}\left(\frac{b-2 a \tanh (c+d x)}{\sqrt{4 a^2+b^2}}\right)}{d \sqrt{4 a^2+b^2}}",1,"(2*ArcTan[(b - 2*a*Tanh[c + d*x])/Sqrt[-4*a^2 - b^2]])/(Sqrt[-4*a^2 - b^2]*d)","A",1
859,1,90,89,0.3508449,"\int \frac{1}{(a+b \cosh (c+d x) \sinh (c+d x))^2} \, dx","Integrate[(a + b*Cosh[c + d*x]*Sinh[c + d*x])^(-2),x]","\frac{2 \left(-\frac{4 a \tan ^{-1}\left(\frac{b-2 a \tanh (c+d x)}{\sqrt{-4 a^2-b^2}}\right)}{\left(-4 a^2-b^2\right)^{3/2}}-\frac{b \cosh (2 (c+d x))}{\left(4 a^2+b^2\right) (2 a+b \sinh (2 (c+d x)))}\right)}{d}","-\frac{8 a \tanh ^{-1}\left(\frac{b-2 a \tanh (c+d x)}{\sqrt{4 a^2+b^2}}\right)}{d \left(4 a^2+b^2\right)^{3/2}}-\frac{2 b \cosh (2 c+2 d x)}{d \left(4 a^2+b^2\right) (2 a+b \sinh (2 c+2 d x))}",1,"(2*((-4*a*ArcTan[(b - 2*a*Tanh[c + d*x])/Sqrt[-4*a^2 - b^2]])/(-4*a^2 - b^2)^(3/2) - (b*Cosh[2*(c + d*x)])/((4*a^2 + b^2)*(2*a + b*Sinh[2*(c + d*x)]))))/d","A",1
860,1,121,143,0.6642867,"\int \frac{1}{(a+b \cosh (c+d x) \sinh (c+d x))^3} \, dx","Integrate[(a + b*Cosh[c + d*x]*Sinh[c + d*x])^(-3),x]","\frac{2 \left(\frac{2 \left(8 a^2-b^2\right) \tan ^{-1}\left(\frac{b-2 a \tanh (c+d x)}{\sqrt{-4 a^2-b^2}}\right)}{\sqrt{-4 a^2-b^2}}-\frac{b \cosh (2 (c+d x)) \left(16 a^2+6 a b \sinh (2 (c+d x))+b^2\right)}{(2 a+b \sinh (2 (c+d x)))^2}\right)}{d \left(4 a^2+b^2\right)^2}","-\frac{4 \left(8 a^2-b^2\right) \tanh ^{-1}\left(\frac{b-2 a \tanh (c+d x)}{\sqrt{4 a^2+b^2}}\right)}{d \left(4 a^2+b^2\right)^{5/2}}-\frac{12 a b \cosh (2 c+2 d x)}{d \left(4 a^2+b^2\right)^2 (2 a+b \sinh (2 c+2 d x))}-\frac{2 b \cosh (2 c+2 d x)}{d \left(4 a^2+b^2\right) (2 a+b \sinh (2 c+2 d x))^2}",1,"(2*((2*(8*a^2 - b^2)*ArcTan[(b - 2*a*Tanh[c + d*x])/Sqrt[-4*a^2 - b^2]])/Sqrt[-4*a^2 - b^2] - (b*Cosh[2*(c + d*x)]*(16*a^2 + b^2 + 6*a*b*Sinh[2*(c + d*x)]))/(2*a + b*Sinh[2*(c + d*x)])^2))/((4*a^2 + b^2)^2*d)","A",1
861,1,239,301,1.4143704,"\int (a+b \cosh (c+d x) \sinh (c+d x))^{5/2} \, dx","Integrate[(a + b*Cosh[c + d*x]*Sinh[c + d*x])^(5/2),x]","\frac{-32 i a \left(4 a^2+b^2\right) \sqrt{\frac{2 a+b \sinh (2 (c+d x))}{2 a-i b}} F\left(\frac{1}{4} (-4 i c-4 i d x+\pi )|-\frac{2 i b}{2 a-i b}\right)+b \left(88 a^2 \cosh (2 (c+d x))+b \sinh (4 (c+d x)) (28 a+3 b \sinh (2 (c+d x)))\right)+2 \left(184 i a^3+92 a^2 b-18 i a b^2-9 b^3\right) \sqrt{\frac{2 a+b \sinh (2 (c+d x))}{2 a-i b}} E\left(\frac{1}{4} (-4 i c-4 i d x+\pi )|-\frac{2 i b}{2 a-i b}\right)}{120 d \sqrt{4 a+2 b \sinh (2 (c+d x))}}","\frac{2 i \sqrt{2} a \left(4 a^2+b^2\right) \sqrt{\frac{2 a+b \sinh (2 c+2 d x)}{2 a-i b}} F\left(\frac{1}{2} \left(2 i c+2 i d x-\frac{\pi }{2}\right)|\frac{2 b}{2 i a+b}\right)}{15 d \sqrt{2 a+b \sinh (2 c+2 d x)}}-\frac{i \left(92 a^2-9 b^2\right) \sqrt{2 a+b \sinh (2 c+2 d x)} E\left(\frac{1}{2} \left(2 i c+2 i d x-\frac{\pi }{2}\right)|\frac{2 b}{2 i a+b}\right)}{60 \sqrt{2} d \sqrt{\frac{2 a+b \sinh (2 c+2 d x)}{2 a-i b}}}+\frac{b \cosh (2 c+2 d x) (2 a+b \sinh (2 c+2 d x))^{3/2}}{20 \sqrt{2} d}+\frac{2 \sqrt{2} a b \cosh (2 c+2 d x) \sqrt{2 a+b \sinh (2 c+2 d x)}}{15 d}",1,"(2*((184*I)*a^3 + 92*a^2*b - (18*I)*a*b^2 - 9*b^3)*EllipticE[((-4*I)*c + Pi - (4*I)*d*x)/4, ((-2*I)*b)/(2*a - I*b)]*Sqrt[(2*a + b*Sinh[2*(c + d*x)])/(2*a - I*b)] - (32*I)*a*(4*a^2 + b^2)*EllipticF[((-4*I)*c + Pi - (4*I)*d*x)/4, ((-2*I)*b)/(2*a - I*b)]*Sqrt[(2*a + b*Sinh[2*(c + d*x)])/(2*a - I*b)] + b*(88*a^2*Cosh[2*(c + d*x)] + b*(28*a + 3*b*Sinh[2*(c + d*x)])*Sinh[4*(c + d*x)]))/(120*d*Sqrt[4*a + 2*b*Sinh[2*(c + d*x)]])","A",1
862,1,202,248,0.8536189,"\int (a+b \cosh (c+d x) \sinh (c+d x))^{3/2} \, dx","Integrate[(a + b*Cosh[c + d*x]*Sinh[c + d*x])^(3/2),x]","\frac{-2 i \left(4 a^2+b^2\right) \sqrt{\frac{2 a+b \sinh (2 (c+d x))}{2 a-i b}} F\left(\frac{1}{4} (-4 i c-4 i d x+\pi )|-\frac{2 i b}{2 a-i b}\right)+b (4 a \cosh (2 (c+d x))+b \sinh (4 (c+d x)))+16 a (b+2 i a) \sqrt{\frac{2 a+b \sinh (2 (c+d x))}{2 a-i b}} E\left(\frac{1}{4} (-4 i c-4 i d x+\pi )|-\frac{2 i b}{2 a-i b}\right)}{12 d \sqrt{4 a+2 b \sinh (2 (c+d x))}}","\frac{i \left(4 a^2+b^2\right) \sqrt{\frac{2 a+b \sinh (2 c+2 d x)}{2 a-i b}} F\left(\frac{1}{2} \left(2 i c+2 i d x-\frac{\pi }{2}\right)|\frac{2 b}{2 i a+b}\right)}{6 \sqrt{2} d \sqrt{2 a+b \sinh (2 c+2 d x)}}+\frac{b \cosh (2 c+2 d x) \sqrt{2 a+b \sinh (2 c+2 d x)}}{6 \sqrt{2} d}-\frac{2 i \sqrt{2} a \sqrt{2 a+b \sinh (2 c+2 d x)} E\left(\frac{1}{2} \left(2 i c+2 i d x-\frac{\pi }{2}\right)|\frac{2 b}{2 i a+b}\right)}{3 d \sqrt{\frac{2 a+b \sinh (2 c+2 d x)}{2 a-i b}}}",1,"(16*a*((2*I)*a + b)*EllipticE[((-4*I)*c + Pi - (4*I)*d*x)/4, ((-2*I)*b)/(2*a - I*b)]*Sqrt[(2*a + b*Sinh[2*(c + d*x)])/(2*a - I*b)] - (2*I)*(4*a^2 + b^2)*EllipticF[((-4*I)*c + Pi - (4*I)*d*x)/4, ((-2*I)*b)/(2*a - I*b)]*Sqrt[(2*a + b*Sinh[2*(c + d*x)])/(2*a - I*b)] + b*(4*a*Cosh[2*(c + d*x)] + b*Sinh[4*(c + d*x)]))/(12*d*Sqrt[4*a + 2*b*Sinh[2*(c + d*x)]])","A",1
863,1,94,96,0.1170583,"\int \sqrt{a+b \cosh (c+d x) \sinh (c+d x)} \, dx","Integrate[Sqrt[a + b*Cosh[c + d*x]*Sinh[c + d*x]],x]","\frac{(b+2 i a) \sqrt{\frac{2 a+b \sinh (2 (c+d x))}{2 a-i b}} E\left(\frac{1}{4} (-4 i c-4 i d x+\pi )|-\frac{2 i b}{2 a-i b}\right)}{d \sqrt{4 a+2 b \sinh (2 (c+d x))}}","-\frac{i \sqrt{2 a+b \sinh (2 c+2 d x)} E\left(\frac{1}{2} \left(2 i c+2 i d x-\frac{\pi }{2}\right)|\frac{2 b}{2 i a+b}\right)}{\sqrt{2} d \sqrt{\frac{2 a+b \sinh (2 c+2 d x)}{2 a-i b}}}",1,"(((2*I)*a + b)*EllipticE[((-4*I)*c + Pi - (4*I)*d*x)/4, ((-2*I)*b)/(2*a - I*b)]*Sqrt[(2*a + b*Sinh[2*(c + d*x)])/(2*a - I*b)])/(d*Sqrt[4*a + 2*b*Sinh[2*(c + d*x)]])","A",1
864,1,90,96,0.1390764,"\int \frac{1}{\sqrt{a+b \cosh (c+d x) \sinh (c+d x)}} \, dx","Integrate[1/Sqrt[a + b*Cosh[c + d*x]*Sinh[c + d*x]],x]","\frac{i \sqrt{\frac{2 a+b \sinh (2 (c+d x))}{2 a-i b}} F\left(\frac{1}{4} (-4 i c-4 i d x+\pi )|-\frac{2 i b}{2 a-i b}\right)}{d \sqrt{a+\frac{1}{2} b \sinh (2 (c+d x))}}","-\frac{i \sqrt{2} \sqrt{\frac{2 a+b \sinh (2 c+2 d x)}{2 a-i b}} F\left(\frac{1}{2} \left(2 i c+2 i d x-\frac{\pi }{2}\right)|\frac{2 b}{2 i a+b}\right)}{d \sqrt{2 a+b \sinh (2 c+2 d x)}}",1,"(I*EllipticF[((-4*I)*c + Pi - (4*I)*d*x)/4, ((-2*I)*b)/(2*a - I*b)]*Sqrt[(2*a + b*Sinh[2*(c + d*x)])/(2*a - I*b)])/(d*Sqrt[a + (b*Sinh[2*(c + d*x)])/2])","A",1
865,1,119,158,0.4447261,"\int \frac{1}{(a+b \cosh (c+d x) \sinh (c+d x))^{3/2}} \, dx","Integrate[(a + b*Cosh[c + d*x]*Sinh[c + d*x])^(-3/2),x]","\frac{2 \left(-b \cosh (2 (c+d x))+(b+2 i a) \sqrt{\frac{2 a+b \sinh (2 (c+d x))}{2 a-i b}} E\left(\frac{1}{4} (-4 i c-4 i d x+\pi )|-\frac{2 i b}{2 a-i b}\right)\right)}{d \left(4 a^2+b^2\right) \sqrt{a+\frac{1}{2} b \sinh (2 (c+d x))}}","-\frac{2 \sqrt{2} b \cosh (2 c+2 d x)}{d \left(4 a^2+b^2\right) \sqrt{2 a+b \sinh (2 c+2 d x)}}-\frac{2 i \sqrt{2} \sqrt{2 a+b \sinh (2 c+2 d x)} E\left(\frac{1}{2} \left(2 i c+2 i d x-\frac{\pi }{2}\right)|\frac{2 b}{2 i a+b}\right)}{d \left(4 a^2+b^2\right) \sqrt{\frac{2 a+b \sinh (2 c+2 d x)}{2 a-i b}}}",1,"(2*(-(b*Cosh[2*(c + d*x)]) + ((2*I)*a + b)*EllipticE[((-4*I)*c + Pi - (4*I)*d*x)/4, ((-2*I)*b)/(2*a - I*b)]*Sqrt[(2*a + b*Sinh[2*(c + d*x)])/(2*a - I*b)]))/((4*a^2 + b^2)*d*Sqrt[a + (b*Sinh[2*(c + d*x)])/2])","A",1
866,1,237,325,1.6540931,"\int \frac{1}{(a+b \cosh (c+d x) \sinh (c+d x))^{5/2}} \, dx","Integrate[(a + b*Cosh[c + d*x]*Sinh[c + d*x])^(-5/2),x]","\frac{4 \sqrt{2} \left(-b \cosh (2 (c+d x)) \left(20 a^2+8 a b \sinh (2 (c+d x))+b^2\right)+(b-2 i a) (2 a-i b)^2 \left(\frac{2 a+b \sinh (2 (c+d x))}{2 a-i b}\right)^{3/2} F\left(\frac{1}{4} (-4 i c-4 i d x+\pi )|-\frac{2 i b}{2 a-i b}\right)+8 i a (2 a-i b)^2 \left(\frac{2 a+b \sinh (2 (c+d x))}{2 a-i b}\right)^{3/2} E\left(\frac{1}{4} (-4 i c-4 i d x+\pi )|-\frac{2 i b}{2 a-i b}\right)\right)}{3 d \left(4 a^2+b^2\right)^2 (2 a+b \sinh (2 (c+d x)))^{3/2}}","-\frac{32 \sqrt{2} a b \cosh (2 c+2 d x)}{3 d \left(4 a^2+b^2\right)^2 \sqrt{2 a+b \sinh (2 c+2 d x)}}-\frac{4 \sqrt{2} b \cosh (2 c+2 d x)}{3 d \left(4 a^2+b^2\right) (2 a+b \sinh (2 c+2 d x))^{3/2}}+\frac{4 i \sqrt{2} \sqrt{\frac{2 a+b \sinh (2 c+2 d x)}{2 a-i b}} F\left(\frac{1}{2} \left(2 i c+2 i d x-\frac{\pi }{2}\right)|\frac{2 b}{2 i a+b}\right)}{3 d \left(4 a^2+b^2\right) \sqrt{2 a+b \sinh (2 c+2 d x)}}-\frac{32 i \sqrt{2} a \sqrt{2 a+b \sinh (2 c+2 d x)} E\left(\frac{1}{2} \left(2 i c+2 i d x-\frac{\pi }{2}\right)|\frac{2 b}{2 i a+b}\right)}{3 d \left(4 a^2+b^2\right)^2 \sqrt{\frac{2 a+b \sinh (2 c+2 d x)}{2 a-i b}}}",1,"(4*Sqrt[2]*((8*I)*a*(2*a - I*b)^2*EllipticE[((-4*I)*c + Pi - (4*I)*d*x)/4, ((-2*I)*b)/(2*a - I*b)]*((2*a + b*Sinh[2*(c + d*x)])/(2*a - I*b))^(3/2) + (2*a - I*b)^2*((-2*I)*a + b)*EllipticF[((-4*I)*c + Pi - (4*I)*d*x)/4, ((-2*I)*b)/(2*a - I*b)]*((2*a + b*Sinh[2*(c + d*x)])/(2*a - I*b))^(3/2) - b*Cosh[2*(c + d*x)]*(20*a^2 + b^2 + 8*a*b*Sinh[2*(c + d*x)])))/(3*(4*a^2 + b^2)^2*d*(2*a + b*Sinh[2*(c + d*x)])^(3/2))","A",1
867,1,279,386,0.4066052,"\int \frac{x^3}{a+b \cosh (x) \sinh (x)} \, dx","Integrate[x^3/(a + b*Cosh[x]*Sinh[x]),x]","\frac{6 x^2 \text{Li}_2\left(\frac{b e^{2 x}}{\sqrt{4 a^2+b^2}-2 a}\right)-6 x^2 \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+\sqrt{4 a^2+b^2}}\right)-6 x \text{Li}_3\left(\frac{b e^{2 x}}{\sqrt{4 a^2+b^2}-2 a}\right)+6 x \text{Li}_3\left(-\frac{b e^{2 x}}{2 a+\sqrt{4 a^2+b^2}}\right)+3 \text{Li}_4\left(\frac{b e^{2 x}}{\sqrt{4 a^2+b^2}-2 a}\right)-3 \text{Li}_4\left(-\frac{b e^{2 x}}{2 a+\sqrt{4 a^2+b^2}}\right)+4 x^3 \log \left(\frac{b e^{2 x}}{2 a-\sqrt{4 a^2+b^2}}+1\right)-4 x^3 \log \left(\frac{b e^{2 x}}{\sqrt{4 a^2+b^2}+2 a}+1\right)}{4 \sqrt{4 a^2+b^2}}","\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{2 x}}{2 a-\sqrt{4 a^2+b^2}}\right)}{2 \sqrt{4 a^2+b^2}}-\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+\sqrt{4 a^2+b^2}}\right)}{2 \sqrt{4 a^2+b^2}}-\frac{3 x \text{Li}_3\left(-\frac{b e^{2 x}}{2 a-\sqrt{4 a^2+b^2}}\right)}{2 \sqrt{4 a^2+b^2}}+\frac{3 x \text{Li}_3\left(-\frac{b e^{2 x}}{2 a+\sqrt{4 a^2+b^2}}\right)}{2 \sqrt{4 a^2+b^2}}+\frac{3 \text{Li}_4\left(-\frac{b e^{2 x}}{2 a-\sqrt{4 a^2+b^2}}\right)}{4 \sqrt{4 a^2+b^2}}-\frac{3 \text{Li}_4\left(-\frac{b e^{2 x}}{2 a+\sqrt{4 a^2+b^2}}\right)}{4 \sqrt{4 a^2+b^2}}+\frac{x^3 \log \left(\frac{b e^{2 x}}{2 a-\sqrt{4 a^2+b^2}}+1\right)}{\sqrt{4 a^2+b^2}}-\frac{x^3 \log \left(\frac{b e^{2 x}}{\sqrt{4 a^2+b^2}+2 a}+1\right)}{\sqrt{4 a^2+b^2}}",1,"(4*x^3*Log[1 + (b*E^(2*x))/(2*a - Sqrt[4*a^2 + b^2])] - 4*x^3*Log[1 + (b*E^(2*x))/(2*a + Sqrt[4*a^2 + b^2])] + 6*x^2*PolyLog[2, (b*E^(2*x))/(-2*a + Sqrt[4*a^2 + b^2])] - 6*x^2*PolyLog[2, -((b*E^(2*x))/(2*a + Sqrt[4*a^2 + b^2]))] - 6*x*PolyLog[3, (b*E^(2*x))/(-2*a + Sqrt[4*a^2 + b^2])] + 6*x*PolyLog[3, -((b*E^(2*x))/(2*a + Sqrt[4*a^2 + b^2]))] + 3*PolyLog[4, (b*E^(2*x))/(-2*a + Sqrt[4*a^2 + b^2])] - 3*PolyLog[4, -((b*E^(2*x))/(2*a + Sqrt[4*a^2 + b^2]))])/(4*Sqrt[4*a^2 + b^2])","A",1
868,1,210,281,0.2821647,"\int \frac{x^2}{a+b \cosh (x) \sinh (x)} \, dx","Integrate[x^2/(a + b*Cosh[x]*Sinh[x]),x]","\frac{2 x \text{Li}_2\left(\frac{b e^{2 x}}{\sqrt{4 a^2+b^2}-2 a}\right)-2 x \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+\sqrt{4 a^2+b^2}}\right)-\text{Li}_3\left(\frac{b e^{2 x}}{\sqrt{4 a^2+b^2}-2 a}\right)+\text{Li}_3\left(-\frac{b e^{2 x}}{2 a+\sqrt{4 a^2+b^2}}\right)+2 x^2 \log \left(\frac{b e^{2 x}}{2 a-\sqrt{4 a^2+b^2}}+1\right)-2 x^2 \log \left(\frac{b e^{2 x}}{\sqrt{4 a^2+b^2}+2 a}+1\right)}{2 \sqrt{4 a^2+b^2}}","\frac{x \text{Li}_2\left(-\frac{b e^{2 x}}{2 a-\sqrt{4 a^2+b^2}}\right)}{\sqrt{4 a^2+b^2}}-\frac{x \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+\sqrt{4 a^2+b^2}}\right)}{\sqrt{4 a^2+b^2}}-\frac{\text{Li}_3\left(-\frac{b e^{2 x}}{2 a-\sqrt{4 a^2+b^2}}\right)}{2 \sqrt{4 a^2+b^2}}+\frac{\text{Li}_3\left(-\frac{b e^{2 x}}{2 a+\sqrt{4 a^2+b^2}}\right)}{2 \sqrt{4 a^2+b^2}}+\frac{x^2 \log \left(\frac{b e^{2 x}}{2 a-\sqrt{4 a^2+b^2}}+1\right)}{\sqrt{4 a^2+b^2}}-\frac{x^2 \log \left(\frac{b e^{2 x}}{\sqrt{4 a^2+b^2}+2 a}+1\right)}{\sqrt{4 a^2+b^2}}",1,"(2*x^2*Log[1 + (b*E^(2*x))/(2*a - Sqrt[4*a^2 + b^2])] - 2*x^2*Log[1 + (b*E^(2*x))/(2*a + Sqrt[4*a^2 + b^2])] + 2*x*PolyLog[2, (b*E^(2*x))/(-2*a + Sqrt[4*a^2 + b^2])] - 2*x*PolyLog[2, -((b*E^(2*x))/(2*a + Sqrt[4*a^2 + b^2]))] - PolyLog[3, (b*E^(2*x))/(-2*a + Sqrt[4*a^2 + b^2])] + PolyLog[3, -((b*E^(2*x))/(2*a + Sqrt[4*a^2 + b^2]))])/(2*Sqrt[4*a^2 + b^2])","A",1
869,1,956,186,1.8679236,"\int \frac{x}{a+b \cosh (x) \sinh (x)} \, dx","Integrate[x/(a + b*Cosh[x]*Sinh[x]),x]","\frac{1}{2} \left(-\frac{i \pi  \tanh ^{-1}\left(\frac{2 a \tanh (x)-b}{\sqrt{4 a^2+b^2}}\right)}{\sqrt{4 a^2+b^2}}-\frac{2 \cos ^{-1}\left(-\frac{2 i a}{b}\right) \tanh ^{-1}\left(\frac{(2 a+i b) \cot \left(\frac{1}{4} (4 i x+\pi )\right)}{\sqrt{-4 a^2-b^2}}\right)+(\pi -4 i x) \tanh ^{-1}\left(\frac{(2 a-i b) \tan \left(\frac{1}{4} (4 i x+\pi )\right)}{\sqrt{-4 a^2-b^2}}\right)-\left(\cos ^{-1}\left(-\frac{2 i a}{b}\right)+2 i \tanh ^{-1}\left(\frac{(2 a+i b) \cot \left(\frac{1}{4} (4 i x+\pi )\right)}{\sqrt{-4 a^2-b^2}}\right)\right) \log \left(\frac{(2 i a+b) \left(-2 i a+b+\sqrt{-4 a^2-b^2}\right) \left(i \cot \left(\frac{1}{4} (4 i x+\pi )\right)+1\right)}{b \left(2 i a+b+i \sqrt{-4 a^2-b^2} \cot \left(\frac{1}{4} (4 i x+\pi )\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{2 i a}{b}\right)-2 i \tanh ^{-1}\left(\frac{(2 a+i b) \cot \left(\frac{1}{4} (4 i x+\pi )\right)}{\sqrt{-4 a^2-b^2}}\right)\right) \log \left(\frac{(2 i a+b) \left(2 i a-b+\sqrt{-4 a^2-b^2}\right) \left(\cot \left(\frac{1}{4} (4 i x+\pi )\right)+i\right)}{b \left(2 a-i b+\sqrt{-4 a^2-b^2} \cot \left(\frac{1}{4} (4 i x+\pi )\right)\right)}\right)+\left(\cos ^{-1}\left(-\frac{2 i a}{b}\right)-2 i \tanh ^{-1}\left(\frac{(2 a+i b) \cot \left(\frac{1}{4} (4 i x+\pi )\right)}{\sqrt{-4 a^2-b^2}}\right)-2 i \tanh ^{-1}\left(\frac{(2 a-i b) \tan \left(\frac{1}{4} (4 i x+\pi )\right)}{\sqrt{-4 a^2-b^2}}\right)\right) \log \left(-\frac{(-1)^{3/4} \sqrt{-4 a^2-b^2} e^{-x}}{2 \sqrt{-i b} \sqrt{a+b \cosh (x) \sinh (x)}}\right)+\left(\cos ^{-1}\left(-\frac{2 i a}{b}\right)+2 i \left(\tanh ^{-1}\left(\frac{(2 a+i b) \cot \left(\frac{1}{4} (4 i x+\pi )\right)}{\sqrt{-4 a^2-b^2}}\right)+\tanh ^{-1}\left(\frac{(2 a-i b) \tan \left(\frac{1}{4} (4 i x+\pi )\right)}{\sqrt{-4 a^2-b^2}}\right)\right)\right) \log \left(\frac{\sqrt[4]{-1} \sqrt{-4 a^2-b^2} e^x}{2 \sqrt{-i b} \sqrt{a+b \cosh (x) \sinh (x)}}\right)+i \left(\text{Li}_2\left(\frac{\left(2 i a+\sqrt{-4 a^2-b^2}\right) \left(2 i a+b-i \sqrt{-4 a^2-b^2} \cot \left(\frac{1}{4} (4 i x+\pi )\right)\right)}{b \left(2 i a+b+i \sqrt{-4 a^2-b^2} \cot \left(\frac{1}{4} (4 i x+\pi )\right)\right)}\right)-\text{Li}_2\left(\frac{\left(2 a+i \sqrt{-4 a^2-b^2}\right) \left(-2 a+i b+\sqrt{-4 a^2-b^2} \cot \left(\frac{1}{4} (4 i x+\pi )\right)\right)}{b \left(2 i a+b+i \sqrt{-4 a^2-b^2} \cot \left(\frac{1}{4} (4 i x+\pi )\right)\right)}\right)\right)}{\sqrt{-4 a^2-b^2}}\right)","\frac{\text{Li}_2\left(-\frac{b e^{2 x}}{2 a-\sqrt{4 a^2+b^2}}\right)}{2 \sqrt{4 a^2+b^2}}-\frac{\text{Li}_2\left(-\frac{b e^{2 x}}{2 a+\sqrt{4 a^2+b^2}}\right)}{2 \sqrt{4 a^2+b^2}}+\frac{x \log \left(\frac{b e^{2 x}}{2 a-\sqrt{4 a^2+b^2}}+1\right)}{\sqrt{4 a^2+b^2}}-\frac{x \log \left(\frac{b e^{2 x}}{\sqrt{4 a^2+b^2}+2 a}+1\right)}{\sqrt{4 a^2+b^2}}",1,"(((-I)*Pi*ArcTanh[(-b + 2*a*Tanh[x])/Sqrt[4*a^2 + b^2]])/Sqrt[4*a^2 + b^2] - (2*ArcCos[((-2*I)*a)/b]*ArcTanh[((2*a + I*b)*Cot[(Pi + (4*I)*x)/4])/Sqrt[-4*a^2 - b^2]] + (Pi - (4*I)*x)*ArcTanh[((2*a - I*b)*Tan[(Pi + (4*I)*x)/4])/Sqrt[-4*a^2 - b^2]] - (ArcCos[((-2*I)*a)/b] + (2*I)*ArcTanh[((2*a + I*b)*Cot[(Pi + (4*I)*x)/4])/Sqrt[-4*a^2 - b^2]])*Log[(((2*I)*a + b)*((-2*I)*a + b + Sqrt[-4*a^2 - b^2])*(1 + I*Cot[(Pi + (4*I)*x)/4]))/(b*((2*I)*a + b + I*Sqrt[-4*a^2 - b^2]*Cot[(Pi + (4*I)*x)/4]))] - (ArcCos[((-2*I)*a)/b] - (2*I)*ArcTanh[((2*a + I*b)*Cot[(Pi + (4*I)*x)/4])/Sqrt[-4*a^2 - b^2]])*Log[(((2*I)*a + b)*((2*I)*a - b + Sqrt[-4*a^2 - b^2])*(I + Cot[(Pi + (4*I)*x)/4]))/(b*(2*a - I*b + Sqrt[-4*a^2 - b^2]*Cot[(Pi + (4*I)*x)/4]))] + (ArcCos[((-2*I)*a)/b] - (2*I)*ArcTanh[((2*a + I*b)*Cot[(Pi + (4*I)*x)/4])/Sqrt[-4*a^2 - b^2]] - (2*I)*ArcTanh[((2*a - I*b)*Tan[(Pi + (4*I)*x)/4])/Sqrt[-4*a^2 - b^2]])*Log[-1/2*((-1)^(3/4)*Sqrt[-4*a^2 - b^2])/(Sqrt[(-I)*b]*E^x*Sqrt[a + b*Cosh[x]*Sinh[x]])] + (ArcCos[((-2*I)*a)/b] + (2*I)*(ArcTanh[((2*a + I*b)*Cot[(Pi + (4*I)*x)/4])/Sqrt[-4*a^2 - b^2]] + ArcTanh[((2*a - I*b)*Tan[(Pi + (4*I)*x)/4])/Sqrt[-4*a^2 - b^2]]))*Log[((-1)^(1/4)*Sqrt[-4*a^2 - b^2]*E^x)/(2*Sqrt[(-I)*b]*Sqrt[a + b*Cosh[x]*Sinh[x]])] + I*(PolyLog[2, (((2*I)*a + Sqrt[-4*a^2 - b^2])*((2*I)*a + b - I*Sqrt[-4*a^2 - b^2]*Cot[(Pi + (4*I)*x)/4]))/(b*((2*I)*a + b + I*Sqrt[-4*a^2 - b^2]*Cot[(Pi + (4*I)*x)/4]))] - PolyLog[2, ((2*a + I*Sqrt[-4*a^2 - b^2])*(-2*a + I*b + Sqrt[-4*a^2 - b^2]*Cot[(Pi + (4*I)*x)/4]))/(b*((2*I)*a + b + I*Sqrt[-4*a^2 - b^2]*Cot[(Pi + (4*I)*x)/4]))]))/Sqrt[-4*a^2 - b^2])/2","C",1
870,0,0,20,1.082367,"\int \frac{1}{x (a+b \cosh (x) \sinh (x))} \, dx","Integrate[1/(x*(a + b*Cosh[x]*Sinh[x])),x]","\int \frac{1}{x (a+b \cosh (x) \sinh (x))} \, dx","\text{Int}\left(\frac{1}{x \left(a+\frac{1}{2} b \sinh (2 x)\right)},x\right)",0,"Integrate[1/(x*(a + b*Cosh[x]*Sinh[x])), x]","A",-1
871,1,96,95,0.0726666,"\int F^{c (a+b x)} \sinh ^n(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sinh[d + e*x]^n,x]","\frac{\left(1-e^{2 (d+e x)}\right)^{-n} F^{c (a+b x)} \sinh ^n(d+e x) \, _2F_1\left(-n,\frac{b c \log (F)-e n}{2 e};\frac{b c \log (F)-e n}{2 e}+1;e^{2 (d+e x)}\right)}{b c \log (F)-e n}","-\frac{\left(1-e^{2 (d+e x)}\right)^{-n} F^{c (a+b x)} \sinh ^n(d+e x) \, _2F_1\left(-n,-\frac{e n-b c \log (F)}{2 e};\frac{1}{2} \left(-n+\frac{b c \log (F)}{e}+2\right);e^{2 (d+e x)}\right)}{e n-b c \log (F)}",1,"(F^(c*(a + b*x))*Hypergeometric2F1[-n, (-(e*n) + b*c*Log[F])/(2*e), 1 + (-(e*n) + b*c*Log[F])/(2*e), E^(2*(d + e*x))]*Sinh[d + e*x]^n)/((1 - E^(2*(d + e*x)))^n*(-(e*n) + b*c*Log[F]))","A",1
872,1,50,66,0.034333,"\int e^{2 (a+b x)} \sinh ^3(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Sinh[a + b*x]^3,x]","\frac{e^{-a-b x} \left(15 e^{2 (a+b x)}-5 e^{4 (a+b x)}+e^{6 (a+b x)}+5\right)}{40 b}","\frac{e^{-a-b x}}{8 b}+\frac{3 e^{a+b x}}{8 b}-\frac{e^{3 a+3 b x}}{8 b}+\frac{e^{5 a+5 b x}}{40 b}",1,"(E^(-a - b*x)*(5 + 15*E^(2*(a + b*x)) - 5*E^(4*(a + b*x)) + E^(6*(a + b*x))))/(40*b)","A",1
873,1,32,40,0.0176973,"\int e^{2 (a+b x)} \sinh ^2(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Sinh[a + b*x]^2,x]","\frac{-4 e^{2 (a+b x)}+e^{4 (a+b x)}+4 b x}{16 b}","-\frac{e^{2 a+2 b x}}{4 b}+\frac{e^{4 a+4 b x}}{16 b}+\frac{x}{4}",1,"(-4*E^(2*(a + b*x)) + E^(4*(a + b*x)) + 4*b*x)/(16*b)","A",1
874,1,25,32,0.013648,"\int e^{2 (a+b x)} \sinh (a+b x) \, dx","Integrate[E^(2*(a + b*x))*Sinh[a + b*x],x]","\frac{e^{a+b x} \left(e^{2 (a+b x)}-3\right)}{6 b}","\frac{e^{3 a+3 b x}}{6 b}-\frac{e^{a+b x}}{2 b}",1,"(E^(a + b*x)*(-3 + E^(2*(a + b*x))))/(6*b)","A",1
875,1,23,26,0.0153015,"\int e^{2 (a+b x)} \text{csch}(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Csch[a + b*x],x]","\frac{2 \left(e^{a+b x}-\tanh ^{-1}\left(e^{a+b x}\right)\right)}{b}","\frac{2 e^{a+b x}}{b}-\frac{2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(2*(E^(a + b*x) - ArcTanh[E^(a + b*x)]))/b","A",1
876,1,37,42,0.0516743,"\int e^{2 (a+b x)} \text{csch}^2(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Csch[a + b*x]^2,x]","\frac{2 \left(\frac{1}{1-e^{2 a+2 b x}}+\log \left(1-e^{2 a+2 b x}\right)\right)}{b}","\frac{2}{b \left(1-e^{2 a+2 b x}\right)}+\frac{2 \log \left(1-e^{2 a+2 b x}\right)}{b}",1,"(2*((1 - E^(2*a + 2*b*x))^(-1) + Log[1 - E^(2*a + 2*b*x)]))/b","A",1
877,1,61,73,0.0593642,"\int e^{2 (a+b x)} \text{csch}^3(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Csch[a + b*x]^3,x]","\frac{3 e^{a+b x}-5 e^{3 (a+b x)}-3 \left(e^{2 (a+b x)}-1\right)^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b \left(e^{2 (a+b x)}-1\right)^2}","\frac{3 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)}-\frac{2 e^{3 a+3 b x}}{b \left(1-e^{2 a+2 b x}\right)^2}-\frac{3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(3*E^(a + b*x) - 5*E^(3*(a + b*x)) - 3*(-1 + E^(2*(a + b*x)))^2*ArcTanh[E^(a + b*x)])/(b*(-1 + E^(2*(a + b*x)))^2)","A",1
878,1,108,139,0.4970032,"\int e^{a+b x} \sinh ^3(c+d x) \, dx","Integrate[E^(a + b*x)*Sinh[c + d*x]^3,x]","\frac{e^{a+b x} \left(\left(3 d^3-3 b^2 d\right) \cosh (3 (c+d x))+3 d \left(b^2-9 d^2\right) \cosh (c+d x)+2 b \sinh (c+d x) \left(\left(b^2-d^2\right) \cosh (2 (c+d x))-b^2+13 d^2\right)\right)}{4 \left(b^4-10 b^2 d^2+9 d^4\right)}","\frac{b e^{a+b x} \sinh ^3(c+d x)}{b^2-9 d^2}-\frac{3 d e^{a+b x} \sinh ^2(c+d x) \cosh (c+d x)}{b^2-9 d^2}+\frac{6 b d^2 e^{a+b x} \sinh (c+d x)}{b^4-10 b^2 d^2+9 d^4}-\frac{6 d^3 e^{a+b x} \cosh (c+d x)}{b^4-10 b^2 d^2+9 d^4}",1,"(E^(a + b*x)*(3*d*(b^2 - 9*d^2)*Cosh[c + d*x] + (-3*b^2*d + 3*d^3)*Cosh[3*(c + d*x)] + 2*b*(-b^2 + 13*d^2 + (b^2 - d^2)*Cosh[2*(c + d*x)])*Sinh[c + d*x]))/(4*(b^4 - 10*b^2*d^2 + 9*d^4))","A",1
879,1,58,88,0.1575866,"\int e^{a+b x} \sinh ^2(c+d x) \, dx","Integrate[E^(a + b*x)*Sinh[c + d*x]^2,x]","\frac{e^{a+b x} \left(b^2 \cosh (2 (c+d x))-b^2-2 b d \sinh (2 (c+d x))+4 d^2\right)}{2 \left(b^3-4 b d^2\right)}","\frac{b e^{a+b x} \sinh ^2(c+d x)}{b^2-4 d^2}-\frac{2 d e^{a+b x} \sinh (c+d x) \cosh (c+d x)}{b^2-4 d^2}+\frac{2 d^2 e^{a+b x}}{b \left(b^2-4 d^2\right)}",1,"(E^(a + b*x)*(-b^2 + 4*d^2 + b^2*Cosh[2*(c + d*x)] - 2*b*d*Sinh[2*(c + d*x)]))/(2*(b^3 - 4*b*d^2))","A",1
880,1,38,54,0.0786554,"\int e^{a+b x} \sinh (c+d x) \, dx","Integrate[E^(a + b*x)*Sinh[c + d*x],x]","\frac{e^{a+b x} (b \sinh (c+d x)-d \cosh (c+d x))}{(b-d) (b+d)}","\frac{b e^{a+b x} \sinh (c+d x)}{b^2-d^2}-\frac{d e^{a+b x} \cosh (c+d x)}{b^2-d^2}",1,"(E^(a + b*x)*(-(d*Cosh[c + d*x]) + b*Sinh[c + d*x]))/((b - d)*(b + d))","A",1
881,1,59,50,0.1271189,"\int e^{a+b x} \text{csch}(c+d x) \, dx","Integrate[E^(a + b*x)*Csch[c + d*x],x]","-\frac{2 (\sinh (c)+\cosh (c)) e^{a+x (b+d)} \, _2F_1\left(1,\frac{b+d}{2 d};\frac{b+3 d}{2 d};e^{2 d x} (\cosh (c)+\sinh (c))^2\right)}{b+d}","-\frac{2 e^{a+b x+c+d x} \, _2F_1\left(1,\frac{b+d}{2 d};\frac{1}{2} \left(\frac{b}{d}+3\right);e^{2 (c+d x)}\right)}{b+d}",1,"(-2*E^(a + (b + d)*x)*Hypergeometric2F1[1, (b + d)/(2*d), (b + 3*d)/(2*d), E^(2*d*x)*(Cosh[c] + Sinh[c])^2]*(Cosh[c] + Sinh[c]))/(b + d)","A",1
882,1,131,54,3.3682777,"\int e^{c+d x} \text{csch}^2(a+b x) \, dx","Integrate[E^(c + d*x)*Csch[a + b*x]^2,x]","\frac{e^c \left(\text{csch}(a) e^{d x} \sinh (b x) \text{csch}(a+b x)-\frac{2 e^{2 a} d \left(\frac{e^{d x} \, _2F_1\left(1,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)}{d}-\frac{e^{x (2 b+d)} \, _2F_1\left(1,\frac{d}{2 b}+1;\frac{d}{2 b}+2;e^{2 (a+b x)}\right)}{2 b+d}\right)}{e^{2 a}-1}\right)}{b}","\frac{4 e^{2 (a+b x)+c+d x} \, _2F_1\left(2,\frac{d}{2 b}+1;\frac{d}{2 b}+2;e^{2 (a+b x)}\right)}{2 b+d}",1,"(E^c*((-2*d*E^(2*a)*((E^(d*x)*Hypergeometric2F1[1, d/(2*b), 1 + d/(2*b), E^(2*(a + b*x))])/d - (E^((2*b + d)*x)*Hypergeometric2F1[1, 1 + d/(2*b), 2 + d/(2*b), E^(2*(a + b*x))])/(2*b + d)))/(-1 + E^(2*a)) + E^(d*x)*Csch[a]*Csch[a + b*x]*Sinh[b*x]))/b","B",1
883,1,94,100,2.4859278,"\int e^{c+d x} \text{csch}^3(a+b x) \, dx","Integrate[E^(c + d*x)*Csch[a + b*x]^3,x]","\frac{e^c \left(\frac{2 \text{csch}(a) (b-d) e^{x (b+d)} \, _2F_1\left(1,\frac{b+d}{2 b};\frac{3 b+d}{2 b};e^{2 b x} (\cosh (a)+\sinh (a))^2\right)}{\coth (a)-1}-e^{d x} \text{csch}(a+b x) (b \coth (a+b x)+d)\right)}{2 b^2}","\frac{(b-d) e^{a+b x+c+d x} \, _2F_1\left(1,\frac{b+d}{2 b};\frac{1}{2} \left(\frac{d}{b}+3\right);e^{2 (a+b x)}\right)}{b^2}-\frac{d e^{c+d x} \text{csch}(a+b x)}{2 b^2}-\frac{e^{c+d x} \coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"(E^c*(-(E^(d*x)*(d + b*Coth[a + b*x])*Csch[a + b*x]) + (2*(b - d)*E^((b + d)*x)*Csch[a]*Hypergeometric2F1[1, (b + d)/(2*b), (3*b + d)/(2*b), E^(2*b*x)*(Cosh[a] + Sinh[a])^2])/(-1 + Coth[a])))/(2*b^2)","A",1
884,1,96,95,0.0708523,"\int F^{c (a+b x)} \cosh ^n(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Cosh[d + e*x]^n,x]","\frac{\left(e^{2 (d+e x)}+1\right)^{-n} F^{c (a+b x)} \cosh ^n(d+e x) \, _2F_1\left(-n,\frac{b c \log (F)-e n}{2 e};\frac{b c \log (F)-e n}{2 e}+1;-e^{2 (d+e x)}\right)}{b c \log (F)-e n}","-\frac{\left(e^{2 (d+e x)}+1\right)^{-n} F^{c (a+b x)} \cosh ^n(d+e x) \, _2F_1\left(-n,-\frac{e n-b c \log (F)}{2 e};\frac{1}{2} \left(-n+\frac{b c \log (F)}{e}+2\right);-e^{2 (d+e x)}\right)}{e n-b c \log (F)}",1,"(F^(c*(a + b*x))*Cosh[d + e*x]^n*Hypergeometric2F1[-n, (-(e*n) + b*c*Log[F])/(2*e), 1 + (-(e*n) + b*c*Log[F])/(2*e), -E^(2*(d + e*x))])/((1 + E^(2*(d + e*x)))^n*(-(e*n) + b*c*Log[F]))","A",1
885,1,106,139,0.5069843,"\int e^{a+b x} \cosh ^3(c+d x) \, dx","Integrate[E^(a + b*x)*Cosh[c + d*x]^3,x]","\frac{e^{a+b x} \left(\left(b^3-b d^2\right) \cosh (3 (c+d x))+3 b \left(b^2-9 d^2\right) \cosh (c+d x)+6 d \sinh (c+d x) \left(\left(d^2-b^2\right) \cosh (2 (c+d x))-b^2+5 d^2\right)\right)}{4 \left(b^4-10 b^2 d^2+9 d^4\right)}","\frac{b e^{a+b x} \cosh ^3(c+d x)}{b^2-9 d^2}-\frac{3 d e^{a+b x} \sinh (c+d x) \cosh ^2(c+d x)}{b^2-9 d^2}-\frac{6 b d^2 e^{a+b x} \cosh (c+d x)}{b^4-10 b^2 d^2+9 d^4}+\frac{6 d^3 e^{a+b x} \sinh (c+d x)}{b^4-10 b^2 d^2+9 d^4}",1,"(E^(a + b*x)*(3*b*(b^2 - 9*d^2)*Cosh[c + d*x] + (b^3 - b*d^2)*Cosh[3*(c + d*x)] + 6*d*(-b^2 + 5*d^2 + (-b^2 + d^2)*Cosh[2*(c + d*x)])*Sinh[c + d*x]))/(4*(b^4 - 10*b^2*d^2 + 9*d^4))","A",1
886,1,56,88,0.1629488,"\int e^{a+b x} \cosh ^2(c+d x) \, dx","Integrate[E^(a + b*x)*Cosh[c + d*x]^2,x]","\frac{e^{a+b x} \left(b^2 \cosh (2 (c+d x))+b^2-2 b d \sinh (2 (c+d x))-4 d^2\right)}{2 \left(b^3-4 b d^2\right)}","\frac{b e^{a+b x} \cosh ^2(c+d x)}{b^2-4 d^2}-\frac{2 d e^{a+b x} \sinh (c+d x) \cosh (c+d x)}{b^2-4 d^2}-\frac{2 d^2 e^{a+b x}}{b \left(b^2-4 d^2\right)}",1,"(E^(a + b*x)*(b^2 - 4*d^2 + b^2*Cosh[2*(c + d*x)] - 2*b*d*Sinh[2*(c + d*x)]))/(2*(b^3 - 4*b*d^2))","A",1
887,1,38,54,0.0763836,"\int e^{a+b x} \cosh (c+d x) \, dx","Integrate[E^(a + b*x)*Cosh[c + d*x],x]","\frac{e^{a+b x} (b \cosh (c+d x)-d \sinh (c+d x))}{(b-d) (b+d)}","\frac{b e^{a+b x} \cosh (c+d x)}{b^2-d^2}-\frac{d e^{a+b x} \sinh (c+d x)}{b^2-d^2}",1,"(E^(a + b*x)*(b*Cosh[c + d*x] - d*Sinh[c + d*x]))/((b - d)*(b + d))","A",1
888,1,51,52,0.0199916,"\int e^{a+b x} \text{sech}(c+d x) \, dx","Integrate[E^(a + b*x)*Sech[c + d*x],x]","\frac{2 e^{a+x (b+d)+c} \, _2F_1\left(1,\frac{b+d}{2 d};\frac{1}{2} \left(\frac{b}{d}+3\right);-e^{2 (c+d x)}\right)}{b+d}","\frac{2 e^{a+b x+c+d x} \, _2F_1\left(1,\frac{b+d}{2 d};\frac{1}{2} \left(\frac{b}{d}+3\right);-e^{2 (c+d x)}\right)}{b+d}",1,"(2*E^(a + c + (b + d)*x)*Hypergeometric2F1[1, (b + d)/(2*d), (3 + b/d)/2, -E^(2*(c + d*x))])/(b + d)","A",1
889,1,56,56,0.0175314,"\int e^{a+b x} \text{sech}^2(c+d x) \, dx","Integrate[E^(a + b*x)*Sech[c + d*x]^2,x]","\frac{4 e^{a+b x+2 (c+d x)} \, _2F_1\left(2,\frac{b}{2 d}+1;\frac{b}{2 d}+2;-e^{2 (c+d x)}\right)}{b+2 d}","\frac{4 e^{a+b x+2 (c+d x)} \, _2F_1\left(2,\frac{b}{2 d}+1;\frac{b}{2 d}+2;-e^{2 (c+d x)}\right)}{b+2 d}",1,"(4*E^(a + b*x + 2*(c + d*x))*Hypergeometric2F1[2, 1 + b/(2*d), 2 + b/(2*d), -E^(2*(c + d*x))])/(b + 2*d)","A",1
890,1,80,103,0.1514962,"\int e^{a+b x} \text{sech}^3(c+d x) \, dx","Integrate[E^(a + b*x)*Sech[c + d*x]^3,x]","\frac{e^{a+b x} \left(\text{sech}(c+d x) (b+d \tanh (c+d x))-2 (b-d) e^{c+d x} \, _2F_1\left(1,\frac{b+d}{2 d};\frac{1}{2} \left(\frac{b}{d}+3\right);-e^{2 (c+d x)}\right)\right)}{2 d^2}","-\frac{(b-d) e^{a+b x+c+d x} \, _2F_1\left(1,\frac{b+d}{2 d};\frac{1}{2} \left(\frac{b}{d}+3\right);-e^{2 (c+d x)}\right)}{d^2}+\frac{b e^{a+b x} \text{sech}(c+d x)}{2 d^2}+\frac{e^{a+b x} \tanh (c+d x) \text{sech}(c+d x)}{2 d}",1,"(E^(a + b*x)*(-2*(b - d)*E^(c + d*x)*Hypergeometric2F1[1, (b + d)/(2*d), (3 + b/d)/2, -E^(2*(c + d*x))] + Sech[c + d*x]*(b + d*Tanh[c + d*x])))/(2*d^2)","A",1
891,1,89,90,0.0753882,"\int F^{c (a+b x)} \text{sech}^n(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sech[d + e*x]^n,x]","\frac{\left(e^{2 (d+e x)}+1\right)^n F^{c (a+b x)} \text{sech}^n(d+e x) \, _2F_1\left(n,\frac{e n+b c \log (F)}{2 e};\frac{e n+b c \log (F)}{2 e}+1;-e^{2 (d+e x)}\right)}{b c \log (F)+e n}","\frac{\left(e^{2 (d+e x)}+1\right)^n F^{a c+b c x} \text{sech}^n(d+e x) \, _2F_1\left(n,\frac{e n+b c \log (F)}{2 e};\frac{e n+b c \log (F)}{2 e}+1;-e^{2 (d+e x)}\right)}{b c \log (F)+e n}",1,"((1 + E^(2*(d + e*x)))^n*F^(c*(a + b*x))*Hypergeometric2F1[n, (e*n + b*c*Log[F])/(2*e), 1 + (e*n + b*c*Log[F])/(2*e), -E^(2*(d + e*x))]*Sech[d + e*x]^n)/(e*n + b*c*Log[F])","A",1
892,1,90,91,0.1036679,"\int F^{c (a+b x)} \text{csch}^n(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Csch[d + e*x]^n,x]","-\frac{\left(1-e^{-2 (d+e x)}\right)^n F^{c (a+b x)} \text{csch}^n(d+e x) \, _2F_1\left(n,\frac{e n-b c \log (F)}{2 e};\frac{1}{2} \left(n-\frac{b c \log (F)}{e}+2\right);e^{-2 (d+e x)}\right)}{e n-b c \log (F)}","-\frac{\left(1-e^{-2 (d+e x)}\right)^n F^{a c+b c x} \text{csch}^n(d+e x) \, _2F_1\left(n,\frac{e n-b c \log (F)}{2 e};\frac{1}{2} \left(n-\frac{b c \log (F)}{e}+2\right);e^{-2 (d+e x)}\right)}{e n-b c \log (F)}",1,"-(((1 - E^(-2*(d + e*x)))^n*F^(c*(a + b*x))*Csch[d + e*x]^n*Hypergeometric2F1[n, (e*n - b*c*Log[F])/(2*e), (2 + n - (b*c*Log[F])/e)/2, E^(-2*(d + e*x))])/(e*n - b*c*Log[F]))","A",1
893,1,196,254,1.9152993,"\int F^{c (a+b x)} (f+i f \sinh (d+e x))^2 \, dx","Integrate[F^(c*(a + b*x))*(f + I*f*Sinh[d + e*x])^2,x]","\frac{F^{c (a+b x)} (f+i f \sinh (d+e x))^2 \left(-\frac{2 e \sinh (2 (d+e x))}{4 e^2-b^2 c^2 \log ^2(F)}-\frac{b c \log (F) \cosh (2 (d+e x))}{b^2 c^2 \log ^2(F)-4 e^2}+\frac{4 i b c \log (F) \sinh (d+e x)}{(b c \log (F)-e) (b c \log (F)+e)}+\frac{4 i e \cosh (d+e x)}{(e-b c \log (F)) (b c \log (F)+e)}+\frac{3}{b c \log (F)}\right)}{2 \left(\cosh \left(\frac{1}{2} (d+e x)\right)+i \sinh \left(\frac{1}{2} (d+e x)\right)\right)^4}","\frac{b c f^2 \log (F) \sinh ^2(d+e x) F^{a c+b c x}}{4 e^2-b^2 c^2 \log ^2(F)}-\frac{2 i b c f^2 \log (F) \sinh (d+e x) F^{a c+b c x}}{e^2-b^2 c^2 \log ^2(F)}+\frac{2 i e f^2 \cosh (d+e x) F^{a c+b c x}}{e^2-b^2 c^2 \log ^2(F)}-\frac{2 e f^2 \sinh (d+e x) \cosh (d+e x) F^{a c+b c x}}{4 e^2-b^2 c^2 \log ^2(F)}+\frac{2 e^2 f^2 F^{a c+b c x}}{b c \log (F) \left(4 e^2-b^2 c^2 \log ^2(F)\right)}+\frac{f^2 F^{a c+b c x}}{b c \log (F)}",1,"(F^(c*(a + b*x))*(f + I*f*Sinh[d + e*x])^2*(3/(b*c*Log[F]) + ((4*I)*e*Cosh[d + e*x])/((e - b*c*Log[F])*(e + b*c*Log[F])) - (b*c*Cosh[2*(d + e*x)]*Log[F])/(-4*e^2 + b^2*c^2*Log[F]^2) + ((4*I)*b*c*Log[F]*Sinh[d + e*x])/((-e + b*c*Log[F])*(e + b*c*Log[F])) - (2*e*Sinh[2*(d + e*x)])/(4*e^2 - b^2*c^2*Log[F]^2)))/(2*(Cosh[(d + e*x)/2] + I*Sinh[(d + e*x)/2])^4)","A",1
894,1,93,106,0.6643607,"\int F^{c (a+b x)} (f+i f \sinh (d+e x)) \, dx","Integrate[F^(c*(a + b*x))*(f + I*f*Sinh[d + e*x]),x]","\frac{f F^{c (a+b x)} \left(i b^2 c^2 \log ^2(F) \sinh (d+e x)+b^2 c^2 \log ^2(F)-i b c e \log (F) \cosh (d+e x)-e^2\right)}{b c \log (F) (b c \log (F)-e) (b c \log (F)+e)}","-\frac{i b c f \log (F) \sinh (d+e x) F^{a c+b c x}}{e^2-b^2 c^2 \log ^2(F)}+\frac{i e f \cosh (d+e x) F^{a c+b c x}}{e^2-b^2 c^2 \log ^2(F)}+\frac{f F^{a c+b c x}}{b c \log (F)}",1,"(f*F^(c*(a + b*x))*(-e^2 - I*b*c*e*Cosh[d + e*x]*Log[F] + b^2*c^2*Log[F]^2 + I*b^2*c^2*Log[F]^2*Sinh[d + e*x]))/(b*c*Log[F]*(-e + b*c*Log[F])*(e + b*c*Log[F]))","A",1
895,1,104,85,3.7357518,"\int \frac{F^{c (a+b x)}}{f+i f \sinh (d+e x)} \, dx","Integrate[F^(c*(a + b*x))/(f + I*f*Sinh[d + e*x]),x]","\frac{2 F^{c (a+b x)} \left(\, _2F_1\left(1,\frac{b c \log (F)}{e};\frac{b c \log (F)}{e}+1;-i e^{d+e x}\right)+\frac{\cosh \left(\frac{e x}{2}\right)-\sinh \left(\frac{e x}{2}\right)}{\left(1-i e^d\right) \sinh \left(\frac{e x}{2}\right)+\left(-1-i e^d\right) \cosh \left(\frac{e x}{2}\right)}\right)}{e f}","\frac{2 e^{\frac{1}{2} (2 d+2 e x+i \pi )} F^{c (a+b x)} \, _2F_1\left(2,\frac{b c \log (F)}{e}+1;\frac{b c \log (F)}{e}+2;-e^{\frac{1}{2} (2 d+2 e x+i \pi )}\right)}{f (b c \log (F)+e)}",1,"(2*F^(c*(a + b*x))*(Hypergeometric2F1[1, (b*c*Log[F])/e, 1 + (b*c*Log[F])/e, (-I)*E^(d + e*x)] + (Cosh[(e*x)/2] - Sinh[(e*x)/2])/((-1 - I*E^d)*Cosh[(e*x)/2] + (1 - I*E^d)*Sinh[(e*x)/2])))/(e*f)","A",1
896,1,255,196,3.3429476,"\int \frac{F^{c (a+b x)}}{(f+i f \sinh (d+e x))^2} \, dx","Integrate[F^(c*(a + b*x))/(f + I*f*Sinh[d + e*x])^2,x]","\frac{F^{c (a+b x)} \left(\cosh \left(\frac{1}{2} (d+e x)\right)+i \sinh \left(\frac{1}{2} (d+e x)\right)\right) \left((1-i) \left(e^2-b^2 c^2 \log ^2(F)\right) \left(\cosh \left(\frac{1}{2} (d+e x)\right)+i \sinh \left(\frac{1}{2} (d+e x)\right)\right)^3 \left(-1+(1+i) \, _2F_1\left(1,\frac{b c \log (F)}{e};\frac{b c \log (F)}{e}+1;-i (\cosh (d+e x)+\sinh (d+e x))\right)\right)+2 \sinh \left(\frac{1}{2} (d+e x)\right) \left(e^2-b^2 c^2 \log ^2(F)\right) \left(\cosh \left(\frac{1}{2} (d+e x)\right)+i \sinh \left(\frac{1}{2} (d+e x)\right)\right)^2+e (b c \log (F)+i e) \left(\cosh \left(\frac{1}{2} (d+e x)\right)+i \sinh \left(\frac{1}{2} (d+e x)\right)\right)+2 e^2 \sinh \left(\frac{1}{2} (d+e x)\right)\right)}{3 e^3 (f+i f \sinh (d+e x))^2}","\frac{2 e^{\frac{1}{2} (2 d+2 e x+i \pi )} F^{c (a+b x)} (e-b c \log (F)) \, _2F_1\left(2,\frac{b c \log (F)}{e}+1;\frac{b c \log (F)}{e}+2;-e^{\frac{1}{2} (2 d+2 e x+i \pi )}\right)}{3 e^2 f^2}+\frac{b c \log (F) \text{sech}^2\left(\frac{d}{2}+\frac{e x}{2}+\frac{i \pi }{4}\right) F^{c (a+b x)}}{6 e^2 f^2}+\frac{\tanh \left(\frac{d}{2}+\frac{e x}{2}+\frac{i \pi }{4}\right) \text{sech}^2\left(\frac{d}{2}+\frac{e x}{2}+\frac{i \pi }{4}\right) F^{c (a+b x)}}{6 e f^2}",1,"(F^(c*(a + b*x))*(Cosh[(d + e*x)/2] + I*Sinh[(d + e*x)/2])*(e*(I*e + b*c*Log[F])*(Cosh[(d + e*x)/2] + I*Sinh[(d + e*x)/2]) + (1 - I)*(-1 + (1 + I)*Hypergeometric2F1[1, (b*c*Log[F])/e, 1 + (b*c*Log[F])/e, (-I)*(Cosh[d + e*x] + Sinh[d + e*x])])*(e^2 - b^2*c^2*Log[F]^2)*(Cosh[(d + e*x)/2] + I*Sinh[(d + e*x)/2])^3 + 2*e^2*Sinh[(d + e*x)/2] + 2*(e^2 - b^2*c^2*Log[F]^2)*(Cosh[(d + e*x)/2] + I*Sinh[(d + e*x)/2])^2*Sinh[(d + e*x)/2]))/(3*e^3*(f + I*f*Sinh[d + e*x])^2)","A",1
897,1,230,251,0.5953541,"\int F^{c (a+b x)} (f+f \cosh (d+e x))^2 \, dx","Integrate[F^(c*(a + b*x))*(f + f*Cosh[d + e*x])^2,x]","\frac{f^2 F^{c (a+b x)} \left(3 b^4 c^4 \log ^4(F)-4 b^3 c^3 e \log ^3(F) \sinh (d+e x)-2 b^3 c^3 e \log ^3(F) \sinh (2 (d+e x))-15 b^2 c^2 e^2 \log ^2(F)+4 \cosh (d+e x) \left(b^4 c^4 \log ^4(F)-4 b^2 c^2 e^2 \log ^2(F)\right)+\cosh (2 (d+e x)) \left(b^4 c^4 \log ^4(F)-b^2 c^2 e^2 \log ^2(F)\right)+16 b c e^3 \log (F) \sinh (d+e x)+2 b c e^3 \log (F) \sinh (2 (d+e x))+12 e^4\right)}{2 \left(b^5 c^5 \log ^5(F)-5 b^3 c^3 e^2 \log ^3(F)+4 b c e^4 \log (F)\right)}","\frac{2 e f^2 \sinh (d+e x) F^{a c+b c x}}{e^2-b^2 c^2 \log ^2(F)}-\frac{b c f^2 \log (F) \cosh ^2(d+e x) F^{a c+b c x}}{4 e^2-b^2 c^2 \log ^2(F)}-\frac{2 b c f^2 \log (F) \cosh (d+e x) F^{a c+b c x}}{e^2-b^2 c^2 \log ^2(F)}+\frac{2 e f^2 \sinh (d+e x) \cosh (d+e x) F^{a c+b c x}}{4 e^2-b^2 c^2 \log ^2(F)}+\frac{2 e^2 f^2 F^{a c+b c x}}{b c \log (F) \left(4 e^2-b^2 c^2 \log ^2(F)\right)}+\frac{f^2 F^{a c+b c x}}{b c \log (F)}",1,"(f^2*F^(c*(a + b*x))*(12*e^4 - 15*b^2*c^2*e^2*Log[F]^2 + 3*b^4*c^4*Log[F]^4 + 4*Cosh[d + e*x]*(-4*b^2*c^2*e^2*Log[F]^2 + b^4*c^4*Log[F]^4) + Cosh[2*(d + e*x)]*(-(b^2*c^2*e^2*Log[F]^2) + b^4*c^4*Log[F]^4) + 16*b*c*e^3*Log[F]*Sinh[d + e*x] - 4*b^3*c^3*e*Log[F]^3*Sinh[d + e*x] + 2*b*c*e^3*Log[F]*Sinh[2*(d + e*x)] - 2*b^3*c^3*e*Log[F]^3*Sinh[2*(d + e*x)]))/(2*(4*b*c*e^4*Log[F] - 5*b^3*c^3*e^2*Log[F]^3 + b^5*c^5*Log[F]^5))","A",1
898,1,88,101,0.2362681,"\int F^{c (a+b x)} (f+f \cosh (d+e x)) \, dx","Integrate[F^(c*(a + b*x))*(f + f*Cosh[d + e*x]),x]","\frac{f F^{c (a+b x)} \left(b^2 c^2 \log ^2(F) \cosh (d+e x)+b^2 c^2 \log ^2(F)-b c e \log (F) \sinh (d+e x)-e^2\right)}{b c \log (F) (b c \log (F)-e) (b c \log (F)+e)}","\frac{e f \sinh (d+e x) F^{a c+b c x}}{e^2-b^2 c^2 \log ^2(F)}-\frac{b c f \log (F) \cosh (d+e x) F^{a c+b c x}}{e^2-b^2 c^2 \log ^2(F)}+\frac{f F^{a c+b c x}}{b c \log (F)}",1,"(f*F^(c*(a + b*x))*(-e^2 + b^2*c^2*Log[F]^2 + b^2*c^2*Cosh[d + e*x]*Log[F]^2 - b*c*e*Log[F]*Sinh[d + e*x]))/(b*c*Log[F]*(-e + b*c*Log[F])*(e + b*c*Log[F]))","A",1
899,1,61,61,0.0469706,"\int \frac{F^{c (a+b x)}}{f+f \cosh (d+e x)} \, dx","Integrate[F^(c*(a + b*x))/(f + f*Cosh[d + e*x]),x]","\frac{2 e^{d+e x} F^{c (a+b x)} \, _2F_1\left(2,\frac{b c \log (F)}{e}+1;\frac{b c \log (F)}{e}+2;-e^{d+e x}\right)}{b c f \log (F)+e f}","\frac{2 e^{d+e x} F^{c (a+b x)} \, _2F_1\left(2,\frac{b c \log (F)}{e}+1;\frac{b c \log (F)}{e}+2;-e^{d+e x}\right)}{f (b c \log (F)+e)}",1,"(2*E^(d + e*x)*F^(c*(a + b*x))*Hypergeometric2F1[2, 1 + (b*c*Log[F])/e, 2 + (b*c*Log[F])/e, -E^(d + e*x)])/(e*f + b*c*f*Log[F])","A",1
900,1,127,151,0.3459541,"\int \frac{F^{c (a+b x)}}{(f+f \cosh (d+e x))^2} \, dx","Integrate[F^(c*(a + b*x))/(f + f*Cosh[d + e*x])^2,x]","\frac{2 \cosh \left(\frac{1}{2} (d+e x)\right) F^{c (a+b x)} \left(4 e^{d+e x} \cosh ^3\left(\frac{1}{2} (d+e x)\right) (e-b c \log (F)) \, _2F_1\left(2,\frac{b c \log (F)}{e}+1;\frac{b c \log (F)}{e}+2;-e^{d+e x}\right)+b c \log (F) \cosh \left(\frac{1}{2} (d+e x)\right)+e \sinh \left(\frac{1}{2} (d+e x)\right)\right)}{3 e^2 f^2 (\cosh (d+e x)+1)^2}","\frac{2 e^{d+e x} F^{c (a+b x)} (e-b c \log (F)) \, _2F_1\left(2,\frac{b c \log (F)}{e}+1;\frac{b c \log (F)}{e}+2;-e^{d+e x}\right)}{3 e^2 f^2}+\frac{b c \log (F) \text{sech}^2\left(\frac{d}{2}+\frac{e x}{2}\right) F^{c (a+b x)}}{6 e^2 f^2}+\frac{\tanh \left(\frac{d}{2}+\frac{e x}{2}\right) \text{sech}^2\left(\frac{d}{2}+\frac{e x}{2}\right) F^{c (a+b x)}}{6 e f^2}",1,"(2*F^(c*(a + b*x))*Cosh[(d + e*x)/2]*(b*c*Cosh[(d + e*x)/2]*Log[F] + 4*E^(d + e*x)*Cosh[(d + e*x)/2]^3*Hypergeometric2F1[2, 1 + (b*c*Log[F])/e, 2 + (b*c*Log[F])/e, -E^(d + e*x)]*(e - b*c*Log[F]) + e*Sinh[(d + e*x)/2]))/(3*e^2*f^2*(1 + Cosh[d + e*x])^2)","A",1
901,1,51,69,0.0660505,"\int e^{a+b x} \cosh (a+b x) \sinh ^3(a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]*Sinh[a + b*x]^3,x]","\frac{e^{-3 (a+b x)} \left(-30 e^{2 (a+b x)}-10 e^{6 (a+b x)}+3 e^{8 (a+b x)}+5\right)}{240 b}","\frac{e^{-3 a-3 b x}}{48 b}-\frac{e^{-a-b x}}{8 b}-\frac{e^{3 a+3 b x}}{24 b}+\frac{e^{5 a+5 b x}}{80 b}",1,"(5 - 30*E^(2*(a + b*x)) - 10*E^(6*(a + b*x)) + 3*E^(8*(a + b*x)))/(240*b*E^(3*(a + b*x)))","A",1
902,1,45,57,0.0639361,"\int e^{a+b x} \cosh (a+b x) \sinh ^2(a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]*Sinh[a + b*x]^2,x]","-\frac{2 e^{-2 (a+b x)}+2 e^{2 (a+b x)}-e^{4 (a+b x)}+4 b x}{32 b}","-\frac{e^{-2 a-2 b x}}{16 b}-\frac{e^{2 a+2 b x}}{16 b}+\frac{e^{4 a+4 b x}}{32 b}-\frac{x}{8}",1,"-1/32*(2/E^(2*(a + b*x)) + 2*E^(2*(a + b*x)) - E^(4*(a + b*x)) + 4*b*x)/b","A",1
903,1,28,35,0.009874,"\int e^{a+b x} \cosh (a+b x) \sinh (a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]*Sinh[a + b*x],x]","\frac{e^{-a-b x} \left(e^{4 (a+b x)}+3\right)}{12 b}","\frac{e^{-a-b x}}{4 b}+\frac{e^{3 a+3 b x}}{12 b}",1,"(E^(-a - b*x)*(3 + E^(4*(a + b*x))))/(12*b)","A",1
904,1,22,25,0.0176503,"\int e^{a+b x} \coth (a+b x) \, dx","Integrate[E^(a + b*x)*Coth[a + b*x],x]","\frac{e^{a+b x}-2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}","\frac{e^{a+b x}}{b}-\frac{2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(E^(a + b*x) - 2*ArcTanh[E^(a + b*x)])/b","A",1
905,1,34,41,0.0519858,"\int e^{a+b x} \coth (a+b x) \text{csch}(a+b x) \, dx","Integrate[E^(a + b*x)*Coth[a + b*x]*Csch[a + b*x],x]","\frac{\log \left(1-e^{2 (a+b x)}\right)-\frac{2}{e^{2 (a+b x)}-1}}{b}","\frac{2}{b \left(1-e^{2 a+2 b x}\right)}+\frac{\log \left(1-e^{2 a+2 b x}\right)}{b}",1,"(-2/(-1 + E^(2*(a + b*x))) + Log[1 - E^(2*(a + b*x))])/b","A",1
906,1,59,70,0.0819095,"\int e^{a+b x} \coth (a+b x) \text{csch}^2(a+b x) \, dx","Integrate[E^(a + b*x)*Coth[a + b*x]*Csch[a + b*x]^2,x]","\frac{e^{a+b x}-3 e^{3 (a+b x)}+\left(e^{2 (a+b x)}-1\right)^2 \left(-\tanh ^{-1}\left(e^{a+b x}\right)\right)}{b \left(e^{2 (a+b x)}-1\right)^2}","\frac{3 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)}-\frac{2 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)^2}-\frac{\tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(E^(a + b*x) - 3*E^(3*(a + b*x)) - (-1 + E^(2*(a + b*x)))^2*ArcTanh[E^(a + b*x)])/(b*(-1 + E^(2*(a + b*x)))^2)","A",1
907,1,67,91,0.0964443,"\int e^{a+b x} \cosh ^2(a+b x) \sinh ^3(a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]^2*Sinh[a + b*x]^3,x]","\frac{3 e^{-4 (a+b x)}-6 e^{-2 (a+b x)}-12 e^{2 (a+b x)}-3 e^{4 (a+b x)}+2 e^{6 (a+b x)}+24 b x}{384 b}","\frac{e^{-4 a-4 b x}}{128 b}-\frac{e^{-2 a-2 b x}}{64 b}-\frac{e^{2 a+2 b x}}{32 b}-\frac{e^{4 a+4 b x}}{128 b}+\frac{e^{6 a+6 b x}}{192 b}+\frac{x}{16}",1,"(3/E^(4*(a + b*x)) - 6/E^(2*(a + b*x)) - 12*E^(2*(a + b*x)) - 3*E^(4*(a + b*x)) + 2*E^(6*(a + b*x)) + 24*b*x)/(384*b)","A",1
908,1,40,49,0.0281182,"\int e^{a+b x} \cosh ^2(a+b x) \sinh ^2(a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]^2*Sinh[a + b*x]^2,x]","\frac{e^{-3 (a+b x)} \left(-30 e^{4 (a+b x)}+3 e^{8 (a+b x)}-5\right)}{240 b}","-\frac{e^{-3 a-3 b x}}{48 b}-\frac{e^{a+b x}}{8 b}+\frac{e^{5 a+5 b x}}{80 b}",1,"(-5 - 30*E^(4*(a + b*x)) + 3*E^(8*(a + b*x)))/(240*b*E^(3*(a + b*x)))","A",1
909,1,43,57,0.0465623,"\int e^{a+b x} \cosh ^2(a+b x) \sinh (a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]^2*Sinh[a + b*x],x]","\frac{2 e^{-2 (a+b x)}+2 e^{2 (a+b x)}+e^{4 (a+b x)}-4 b x}{32 b}","\frac{e^{-2 a-2 b x}}{16 b}+\frac{e^{2 a+2 b x}}{16 b}+\frac{e^{4 a+4 b x}}{32 b}-\frac{x}{8}",1,"(2/E^(2*(a + b*x)) + 2*E^(2*(a + b*x)) + E^(4*(a + b*x)) - 4*b*x)/(32*b)","A",1
910,1,39,42,0.0304544,"\int e^{a+b x} \cosh (a+b x) \coth (a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]*Coth[a + b*x],x]","\frac{e^{2 a+2 b x}+4 \log \left(1-e^{2 a+2 b x}\right)-2 b x}{4 b}","\frac{e^{2 a+2 b x}}{4 b}+\frac{\log \left(1-e^{2 a+2 b x}\right)}{b}-\frac{x}{2}",1,"(E^(2*a + 2*b*x) - 2*b*x + 4*Log[1 - E^(2*a + 2*b*x)])/(4*b)","A",1
911,1,179,53,1.7560125,"\int e^{a+b x} \coth ^2(a+b x) \, dx","Integrate[E^(a + b*x)*Coth[a + b*x]^2,x]","\frac{e^{a+b x} \left(\frac{4}{105} \left(e^{a+b x}+e^{3 (a+b x)}\right)^2 \, _4F_3\left(\frac{3}{2},2,2,2;1,1,\frac{9}{2};e^{2 (a+b x)}\right)+\frac{1}{48} e^{-4 (a+b x)} \left(-713 e^{2 (a+b x)}-181 e^{4 (a+b x)}+61 e^{6 (a+b x)}+\frac{3 \left(196 e^{2 (a+b x)}-14 e^{4 (a+b x)}-52 e^{6 (a+b x)}+e^{8 (a+b x)}+125\right) \tanh ^{-1}\left(\sqrt{e^{2 (a+b x)}}\right)}{\sqrt{e^{2 (a+b x)}}}-375\right)\right)}{b}","\frac{e^{a+b x}}{b}+\frac{2 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)}-\frac{2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(E^(a + b*x)*((-375 - 713*E^(2*(a + b*x)) - 181*E^(4*(a + b*x)) + 61*E^(6*(a + b*x)) + (3*(125 + 196*E^(2*(a + b*x)) - 14*E^(4*(a + b*x)) - 52*E^(6*(a + b*x)) + E^(8*(a + b*x)))*ArcTanh[Sqrt[E^(2*(a + b*x))]])/Sqrt[E^(2*(a + b*x))])/(48*E^(4*(a + b*x))) + (4*(E^(a + b*x) + E^(3*(a + b*x)))^2*HypergeometricPFQ[{3/2, 2, 2, 2}, {1, 1, 9/2}, E^(2*(a + b*x))])/105))/b","C",0
912,1,46,62,0.0879274,"\int e^{a+b x} \coth ^2(a+b x) \text{csch}(a+b x) \, dx","Integrate[E^(a + b*x)*Coth[a + b*x]^2*Csch[a + b*x],x]","\frac{\frac{2-4 e^{2 (a+b x)}}{\left(e^{2 (a+b x)}-1\right)^2}+\log \left(1-e^{2 (a+b x)}\right)}{b}","\frac{4}{b \left(1-e^{2 a+2 b x}\right)}-\frac{2}{b \left(1-e^{2 a+2 b x}\right)^2}+\frac{\log \left(1-e^{2 a+2 b x}\right)}{b}",1,"((2 - 4*E^(2*(a + b*x)))/(-1 + E^(2*(a + b*x)))^2 + Log[1 - E^(2*(a + b*x))])/b","A",1
913,1,51,69,0.0388692,"\int e^{a+b x} \cosh ^3(a+b x) \sinh ^3(a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]^3*Sinh[a + b*x]^3,x]","\frac{e^{-5 (a+b x)} \left(-105 e^{4 (a+b x)}-35 e^{8 (a+b x)}+5 e^{12 (a+b x)}+7\right)}{2240 b}","\frac{e^{-5 a-5 b x}}{320 b}-\frac{3 e^{-a-b x}}{64 b}-\frac{e^{3 a+3 b x}}{64 b}+\frac{e^{7 a+7 b x}}{448 b}",1,"(7 - 105*E^(4*(a + b*x)) - 35*E^(8*(a + b*x)) + 5*E^(12*(a + b*x)))/(2240*b*E^(5*(a + b*x)))","A",1
914,1,67,91,0.112865,"\int e^{a+b x} \cosh ^3(a+b x) \sinh ^2(a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]^3*Sinh[a + b*x]^2,x]","-\frac{3 e^{-4 (a+b x)}+6 e^{-2 (a+b x)}+12 e^{2 (a+b x)}-3 e^{4 (a+b x)}-2 e^{6 (a+b x)}+24 b x}{384 b}","-\frac{e^{-4 a-4 b x}}{128 b}-\frac{e^{-2 a-2 b x}}{64 b}-\frac{e^{2 a+2 b x}}{32 b}+\frac{e^{4 a+4 b x}}{128 b}+\frac{e^{6 a+6 b x}}{192 b}-\frac{x}{16}",1,"-1/384*(3/E^(4*(a + b*x)) + 6/E^(2*(a + b*x)) + 12*E^(2*(a + b*x)) - 3*E^(4*(a + b*x)) - 2*E^(6*(a + b*x)) + 24*b*x)/b","A",1
915,1,51,69,0.0573673,"\int e^{a+b x} \cosh ^3(a+b x) \sinh (a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]^3*Sinh[a + b*x],x]","\frac{e^{-3 (a+b x)} \left(30 e^{2 (a+b x)}+10 e^{6 (a+b x)}+3 e^{8 (a+b x)}+5\right)}{240 b}","\frac{e^{-3 a-3 b x}}{48 b}+\frac{e^{-a-b x}}{8 b}+\frac{e^{3 a+3 b x}}{24 b}+\frac{e^{5 a+5 b x}}{80 b}",1,"(5 + 30*E^(2*(a + b*x)) + 10*E^(6*(a + b*x)) + 3*E^(8*(a + b*x)))/(240*b*E^(3*(a + b*x)))","A",1
916,1,68,59,0.0788974,"\int e^{a+b x} \cosh ^2(a+b x) \coth (a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]^2*Coth[a + b*x],x]","\frac{e^{-a-b x} \left(12 e^{2 (a+b x)}+e^{4 (a+b x)}-24 \sqrt{e^{2 (a+b x)}} \tanh ^{-1}\left(\sqrt{e^{2 (a+b x)}}\right)+3\right)}{12 b}","\frac{e^{-a-b x}}{4 b}+\frac{e^{a+b x}}{b}+\frac{e^{3 a+3 b x}}{12 b}-\frac{2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(E^(-a - b*x)*(3 + 12*E^(2*(a + b*x)) + E^(4*(a + b*x)) - 24*Sqrt[E^(2*(a + b*x))]*ArcTanh[Sqrt[E^(2*(a + b*x))]]))/(12*b)","A",1
917,1,52,63,0.0835956,"\int e^{a+b x} \cosh (a+b x) \coth ^2(a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]*Coth[a + b*x]^2,x]","\frac{e^{2 (a+b x)}-\frac{8}{e^{2 (a+b x)}-1}+4 \log \left(1-e^{2 (a+b x)}\right)+2 b x}{4 b}","\frac{e^{2 a+2 b x}}{4 b}+\frac{2}{b \left(1-e^{2 a+2 b x}\right)}+\frac{\log \left(1-e^{2 a+2 b x}\right)}{b}+\frac{x}{2}",1,"(E^(2*(a + b*x)) - 8/(-1 + E^(2*(a + b*x))) + 2*b*x + 4*Log[1 - E^(2*(a + b*x))])/(4*b)","A",1
918,1,286,81,2.5350524,"\int e^{a+b x} \coth ^3(a+b x) \, dx","Integrate[E^(a + b*x)*Coth[a + b*x]^3,x]","-\frac{e^{-5 (a+b x)} \left(256 e^{8 (a+b x)} \left(e^{2 (a+b x)}+1\right)^3 \, _6F_5\left(\frac{3}{2},2,2,2,2,2;1,1,1,1,\frac{11}{2};e^{2 (a+b x)}\right)+384 e^{8 (a+b x)} \left(5 e^{2 (a+b x)}+7\right) \left(e^{2 (a+b x)}+1\right)^2 \, _5F_4\left(\frac{3}{2},2,2,2,2;1,1,1,\frac{11}{2};e^{2 (a+b x)}\right)-21 \left(507305 e^{2 (a+b x)}+173916 e^{4 (a+b x)}-154296 e^{6 (a+b x)}-73885 e^{8 (a+b x)}+4887 e^{10 (a+b x)}+252105\right)-\frac{315 \left(-28218 e^{2 (a+b x)}+1173 e^{4 (a+b x)}+17748 e^{6 (a+b x)}+4299 e^{8 (a+b x)}-1434 e^{10 (a+b x)}+7 e^{12 (a+b x)}-16807\right) \tanh ^{-1}\left(\sqrt{e^{2 (a+b x)}}\right)}{\sqrt{e^{2 (a+b x)}}}\right)}{60480 b}","\frac{e^{a+b x}}{b}+\frac{3 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)}-\frac{2 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)^2}-\frac{3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"-1/60480*(-21*(252105 + 507305*E^(2*(a + b*x)) + 173916*E^(4*(a + b*x)) - 154296*E^(6*(a + b*x)) - 73885*E^(8*(a + b*x)) + 4887*E^(10*(a + b*x))) - (315*(-16807 - 28218*E^(2*(a + b*x)) + 1173*E^(4*(a + b*x)) + 17748*E^(6*(a + b*x)) + 4299*E^(8*(a + b*x)) - 1434*E^(10*(a + b*x)) + 7*E^(12*(a + b*x)))*ArcTanh[Sqrt[E^(2*(a + b*x))]])/Sqrt[E^(2*(a + b*x))] + 384*E^(8*(a + b*x))*(1 + E^(2*(a + b*x)))^2*(7 + 5*E^(2*(a + b*x)))*HypergeometricPFQ[{3/2, 2, 2, 2, 2}, {1, 1, 1, 11/2}, E^(2*(a + b*x))] + 256*E^(8*(a + b*x))*(1 + E^(2*(a + b*x)))^3*HypergeometricPFQ[{3/2, 2, 2, 2, 2, 2}, {1, 1, 1, 1, 11/2}, E^(2*(a + b*x))])/(b*E^(5*(a + b*x)))","C",0
919,1,43,57,0.0793212,"\int e^{2 (a+b x)} \cosh (a+b x) \sinh ^3(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]*Sinh[a + b*x]^3,x]","\frac{3 e^{-2 (a+b x)}-3 e^{4 (a+b x)}+e^{6 (a+b x)}+12 b x}{96 b}","\frac{e^{-2 a-2 b x}}{32 b}-\frac{e^{4 a+4 b x}}{32 b}+\frac{e^{6 a+6 b x}}{96 b}+\frac{x}{8}",1,"(3/E^(2*(a + b*x)) - 3*E^(4*(a + b*x)) + E^(6*(a + b*x)) + 12*b*x)/(96*b)","A",1
920,1,51,66,0.0772083,"\int e^{2 (a+b x)} \cosh (a+b x) \sinh ^2(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]*Sinh[a + b*x]^2,x]","\frac{3 e^{-a-b x} \left(e^{6 (a+b x)}-5\right)-5 e^{a+b x} \left(e^{2 (a+b x)}+3\right)}{120 b}","-\frac{e^{-a-b x}}{8 b}-\frac{e^{a+b x}}{8 b}-\frac{e^{3 a+3 b x}}{24 b}+\frac{e^{5 a+5 b x}}{40 b}",1,"(-5*E^(a + b*x)*(3 + E^(2*(a + b*x))) + 3*E^(-a - b*x)*(-5 + E^(6*(a + b*x))))/(120*b)","A",1
921,1,25,23,0.0139672,"\int e^{2 (a+b x)} \cosh (a+b x) \sinh (a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]*Sinh[a + b*x],x]","\frac{1}{4} \left(\frac{e^{4 a+4 b x}}{4 b}-x\right)","\frac{e^{4 a+4 b x}}{16 b}-\frac{x}{4}",1,"(E^(4*a + 4*b*x)/(4*b) - x)/4","A",1
922,1,35,37,0.0285187,"\int e^{2 (a+b x)} \coth (a+b x) \, dx","Integrate[E^(2*(a + b*x))*Coth[a + b*x],x]","\frac{e^{2 a+2 b x}+2 \log \left(1-e^{2 a+2 b x}\right)}{2 b}","\frac{e^{2 a+2 b x}}{2 b}+\frac{\log \left(1-e^{2 a+2 b x}\right)}{b}",1,"(E^(2*a + 2*b*x) + 2*Log[1 - E^(2*a + 2*b*x)])/(2*b)","A",1
923,1,62,54,0.1203126,"\int e^{2 (a+b x)} \coth (a+b x) \text{csch}(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Coth[a + b*x]*Csch[a + b*x],x]","\frac{2 \left(\frac{e^{a+b x} \left(e^{2 (a+b x)}-2\right)}{e^{2 (a+b x)}-1}+\log \left(1-e^{a+b x}\right)-\log \left(e^{a+b x}+1\right)\right)}{b}","\frac{2 e^{a+b x}}{b}+\frac{2 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)}-\frac{4 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(2*((E^(a + b*x)*(-2 + E^(2*(a + b*x))))/(-1 + E^(2*(a + b*x))) + Log[1 - E^(a + b*x)] - Log[1 + E^(a + b*x)]))/b","A",1
924,1,47,63,0.0793263,"\int e^{2 (a+b x)} \coth (a+b x) \text{csch}^2(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Coth[a + b*x]*Csch[a + b*x]^2,x]","\frac{2 \left(\frac{2-3 e^{2 (a+b x)}}{\left(e^{2 (a+b x)}-1\right)^2}+\log \left(1-e^{2 (a+b x)}\right)\right)}{b}","\frac{6}{b \left(1-e^{2 a+2 b x}\right)}-\frac{2}{b \left(1-e^{2 a+2 b x}\right)^2}+\frac{2 \log \left(1-e^{2 a+2 b x}\right)}{b}",1,"(2*((2 - 3*E^(2*(a + b*x)))/(-1 + E^(2*(a + b*x)))^2 + Log[1 - E^(2*(a + b*x))]))/b","A",1
925,1,73,100,0.107603,"\int e^{2 (a+b x)} \cosh ^2(a+b x) \sinh ^3(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]^2*Sinh[a + b*x]^3,x]","\frac{e^{-3 (a+b x)} \left(-105 e^{2 (a+b x)}+210 e^{4 (a+b x)}-70 e^{6 (a+b x)}-21 e^{8 (a+b x)}+15 e^{10 (a+b x)}+35\right)}{3360 b}","\frac{e^{-3 a-3 b x}}{96 b}-\frac{e^{-a-b x}}{32 b}+\frac{e^{a+b x}}{16 b}-\frac{e^{3 a+3 b x}}{48 b}-\frac{e^{5 a+5 b x}}{160 b}+\frac{e^{7 a+7 b x}}{224 b}",1,"(35 - 105*E^(2*(a + b*x)) + 210*E^(4*(a + b*x)) - 70*E^(6*(a + b*x)) - 21*E^(8*(a + b*x)) + 15*E^(10*(a + b*x)))/(3360*b*E^(3*(a + b*x)))","A",1
926,1,38,52,0.0338349,"\int e^{2 (a+b x)} \cosh ^2(a+b x) \sinh ^2(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]^2*Sinh[a + b*x]^2,x]","\frac{e^{-2 (a+b x)} \left(-6 e^{4 (a+b x)}+e^{8 (a+b x)}-3\right)}{96 b}","-\frac{e^{-2 a-2 b x}}{32 b}-\frac{e^{2 a+2 b x}}{16 b}+\frac{e^{6 a+6 b x}}{96 b}",1,"(-3 - 6*E^(4*(a + b*x)) + E^(8*(a + b*x)))/(96*b*E^(2*(a + b*x)))","A",1
927,1,54,66,0.0473699,"\int e^{2 (a+b x)} \cosh ^2(a+b x) \sinh (a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]^2*Sinh[a + b*x],x]","\frac{e^{a+b x} \left(e^{2 (a+b x)}-3\right)}{24 b}+\frac{e^{-a-b x} \left(e^{6 (a+b x)}+5\right)}{40 b}","\frac{e^{-a-b x}}{8 b}-\frac{e^{a+b x}}{8 b}+\frac{e^{3 a+3 b x}}{24 b}+\frac{e^{5 a+5 b x}}{40 b}",1,"(E^(a + b*x)*(-3 + E^(2*(a + b*x))))/(24*b) + (E^(-a - b*x)*(5 + E^(6*(a + b*x))))/(40*b)","A",1
928,1,58,45,0.1335076,"\int e^{2 (a+b x)} \cosh (a+b x) \coth (a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]*Coth[a + b*x],x]","-\frac{e^{a+b x} \left(-\frac{1}{3} e^{2 (a+b x)}+\frac{4 \tanh ^{-1}\left(\sqrt{e^{2 (a+b x)}}\right)}{\sqrt{e^{2 (a+b x)}}}-3\right)}{2 b}","\frac{3 e^{a+b x}}{2 b}+\frac{e^{3 a+3 b x}}{6 b}-\frac{2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"-1/2*(E^(a + b*x)*(-3 - E^(2*(a + b*x))/3 + (4*ArcTanh[Sqrt[E^(2*(a + b*x))]])/Sqrt[E^(2*(a + b*x))]))/b","A",1
929,1,48,59,0.0707411,"\int e^{2 (a+b x)} \coth ^2(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Coth[a + b*x]^2,x]","\frac{e^{2 (a+b x)}-\frac{4}{e^{2 (a+b x)}-1}+4 \log \left(1-e^{2 (a+b x)}\right)}{2 b}","\frac{e^{2 a+2 b x}}{2 b}+\frac{2}{b \left(1-e^{2 a+2 b x}\right)}+\frac{2 \log \left(1-e^{2 a+2 b x}\right)}{b}",1,"(E^(2*(a + b*x)) - 4/(-1 + E^(2*(a + b*x))) + 4*Log[1 - E^(2*(a + b*x))])/(2*b)","A",1
930,1,247,85,4.5077121,"\int e^{2 (a+b x)} \coth ^2(a+b x) \text{csch}(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Coth[a + b*x]^2*Csch[a + b*x],x]","-\frac{e^{-3 (a+b x)} \left(128 e^{8 (a+b x)} \left(e^{2 (a+b x)}+1\right)^2 \, _5F_4\left(2,2,2,2,\frac{5}{2};1,1,1,\frac{11}{2};e^{2 (a+b x)}\right)+128 e^{8 (a+b x)} \left(16 e^{2 (a+b x)}+7 e^{4 (a+b x)}+9\right) \, _4F_3\left(2,2,2,\frac{5}{2};1,1,\frac{11}{2};e^{2 (a+b x)}\right)-21 \left(62725 e^{2 (a+b x)}-12071 e^{4 (a+b x)}-19353 e^{6 (a+b x)}+768 e^{8 (a+b x)}+56595\right)+\frac{315 \left(2924 e^{2 (a+b x)}-2534 e^{4 (a+b x)}-1548 e^{6 (a+b x)}+297 e^{8 (a+b x)}+3773\right) \tanh ^{-1}\left(\sqrt{e^{2 (a+b x)}}\right)}{\sqrt{e^{2 (a+b x)}}}\right)}{10080 b}","\frac{2 e^{a+b x}}{b}+\frac{3 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)}-\frac{2 e^{3 a+3 b x}}{b \left(1-e^{2 a+2 b x}\right)^2}-\frac{5 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"-1/10080*(-21*(56595 + 62725*E^(2*(a + b*x)) - 12071*E^(4*(a + b*x)) - 19353*E^(6*(a + b*x)) + 768*E^(8*(a + b*x))) + (315*(3773 + 2924*E^(2*(a + b*x)) - 2534*E^(4*(a + b*x)) - 1548*E^(6*(a + b*x)) + 297*E^(8*(a + b*x)))*ArcTanh[Sqrt[E^(2*(a + b*x))]])/Sqrt[E^(2*(a + b*x))] + 128*E^(8*(a + b*x))*(9 + 16*E^(2*(a + b*x)) + 7*E^(4*(a + b*x)))*HypergeometricPFQ[{2, 2, 2, 5/2}, {1, 1, 11/2}, E^(2*(a + b*x))] + 128*E^(8*(a + b*x))*(1 + E^(2*(a + b*x)))^2*HypergeometricPFQ[{2, 2, 2, 2, 5/2}, {1, 1, 1, 11/2}, E^(2*(a + b*x))])/(b*E^(3*(a + b*x)))","C",0
931,1,45,57,0.0519239,"\int e^{2 (a+b x)} \cosh ^3(a+b x) \sinh ^3(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]^3*Sinh[a + b*x]^3,x]","\frac{e^{-4 (a+b x)}-3 e^{4 (a+b x)}+\frac{1}{2} e^{8 (a+b x)}+12 b x}{256 b}","\frac{e^{-4 a-4 b x}}{256 b}-\frac{3 e^{4 a+4 b x}}{256 b}+\frac{e^{8 a+8 b x}}{512 b}+\frac{3 x}{64}",1,"(E^(-4*(a + b*x)) - 3*E^(4*(a + b*x)) + E^(8*(a + b*x))/2 + 12*b*x)/(256*b)","A",1
932,1,73,100,0.1079537,"\int e^{2 (a+b x)} \cosh ^3(a+b x) \sinh ^2(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]^3*Sinh[a + b*x]^2,x]","\frac{e^{-3 (a+b x)} \left(-105 e^{2 (a+b x)}-210 e^{4 (a+b x)}-70 e^{6 (a+b x)}+21 e^{8 (a+b x)}+15 e^{10 (a+b x)}-35\right)}{3360 b}","-\frac{e^{-3 a-3 b x}}{96 b}-\frac{e^{-a-b x}}{32 b}-\frac{e^{a+b x}}{16 b}-\frac{e^{3 a+3 b x}}{48 b}+\frac{e^{5 a+5 b x}}{160 b}+\frac{e^{7 a+7 b x}}{224 b}",1,"(-35 - 105*E^(2*(a + b*x)) - 210*E^(4*(a + b*x)) - 70*E^(6*(a + b*x)) + 21*E^(8*(a + b*x)) + 15*E^(10*(a + b*x)))/(3360*b*E^(3*(a + b*x)))","A",1
933,1,43,57,0.0689494,"\int e^{2 (a+b x)} \cosh ^3(a+b x) \sinh (a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]^3*Sinh[a + b*x],x]","\frac{3 e^{-2 (a+b x)}+3 e^{4 (a+b x)}+e^{6 (a+b x)}-12 b x}{96 b}","\frac{e^{-2 a-2 b x}}{32 b}+\frac{e^{4 a+4 b x}}{32 b}+\frac{e^{6 a+6 b x}}{96 b}-\frac{x}{8}",1,"(3/E^(2*(a + b*x)) + 3*E^(4*(a + b*x)) + E^(6*(a + b*x)) - 12*b*x)/(96*b)","A",1
934,1,48,59,0.0489532,"\int e^{2 (a+b x)} \cosh ^2(a+b x) \coth (a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]^2*Coth[a + b*x],x]","\frac{8 e^{2 (a+b x)}+e^{4 (a+b x)}+16 \log \left(1-e^{2 (a+b x)}\right)-4 b x}{16 b}","\frac{e^{2 a+2 b x}}{2 b}+\frac{e^{4 a+4 b x}}{16 b}+\frac{\log \left(1-e^{2 a+2 b x}\right)}{b}-\frac{x}{4}",1,"(8*E^(2*(a + b*x)) + E^(4*(a + b*x)) - 4*b*x + 16*Log[1 - E^(2*(a + b*x))])/(16*b)","A",1
935,1,220,73,0.9614829,"\int e^{2 (a+b x)} \cosh (a+b x) \coth ^2(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Cosh[a + b*x]*Coth[a + b*x]^2,x]","\frac{e^{-5 (a+b x)} \left(256 e^{8 (a+b x)} \left(e^{2 (a+b x)}+1\right)^3 \, _5F_4\left(\frac{3}{2},2,2,2,2;1,1,1,\frac{11}{2};e^{2 (a+b x)}\right)-21 \left(91925 e^{2 (a+b x)}+61158 e^{4 (a+b x)}-20166 e^{6 (a+b x)}-15061 e^{8 (a+b x)}+753 e^{10 (a+b x)}+36015\right)-\frac{315 \left(-5328 e^{2 (a+b x)}-1821 e^{4 (a+b x)}+3264 e^{6 (a+b x)}+1149 e^{8 (a+b x)}-240 e^{10 (a+b x)}+e^{12 (a+b x)}-2401\right) \tanh ^{-1}\left(\sqrt{e^{2 (a+b x)}}\right)}{\sqrt{e^{2 (a+b x)}}}\right)}{60480 b}","\frac{5 e^{a+b x}}{2 b}+\frac{e^{3 a+3 b x}}{6 b}+\frac{2 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)}-\frac{4 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(-21*(36015 + 91925*E^(2*(a + b*x)) + 61158*E^(4*(a + b*x)) - 20166*E^(6*(a + b*x)) - 15061*E^(8*(a + b*x)) + 753*E^(10*(a + b*x))) - (315*(-2401 - 5328*E^(2*(a + b*x)) - 1821*E^(4*(a + b*x)) + 3264*E^(6*(a + b*x)) + 1149*E^(8*(a + b*x)) - 240*E^(10*(a + b*x)) + E^(12*(a + b*x)))*ArcTanh[Sqrt[E^(2*(a + b*x))]])/Sqrt[E^(2*(a + b*x))] + 256*E^(8*(a + b*x))*(1 + E^(2*(a + b*x)))^3*HypergeometricPFQ[{3/2, 2, 2, 2, 2}, {1, 1, 1, 11/2}, E^(2*(a + b*x))])/(60480*b*E^(5*(a + b*x)))","C",0
936,1,60,80,0.1237909,"\int e^{2 (a+b x)} \coth ^3(a+b x) \, dx","Integrate[E^(2*(a + b*x))*Coth[a + b*x]^3,x]","\frac{\frac{8-12 e^{2 (a+b x)}}{\left(e^{2 (a+b x)}-1\right)^2}+e^{2 (a+b x)}+6 \log \left(1-e^{2 (a+b x)}\right)}{2 b}","\frac{e^{2 a+2 b x}}{2 b}+\frac{6}{b \left(1-e^{2 a+2 b x}\right)}-\frac{2}{b \left(1-e^{2 a+2 b x}\right)^2}+\frac{3 \log \left(1-e^{2 a+2 b x}\right)}{b}",1,"(E^(2*(a + b*x)) + (8 - 12*E^(2*(a + b*x)))/(-1 + E^(2*(a + b*x)))^2 + 6*Log[1 - E^(2*(a + b*x))])/(2*b)","A",1
937,1,42,113,0.0303899,"\int e^x \text{sech}(2 x) \tanh (2 x) \, dx","Integrate[E^x*Sech[2*x]*Tanh[2*x],x]","\frac{2}{3} e^{3 x} \left(\, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-e^{4 x}\right)-2 \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};-e^{4 x}\right)\right)","-\frac{e^{3 x}}{e^{4 x}+1}+\frac{\log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{4 \sqrt{2}}-\frac{\log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} e^x\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} e^x+1\right)}{2 \sqrt{2}}",1,"(2*E^(3*x)*(Hypergeometric2F1[3/4, 1, 7/4, -E^(4*x)] - 2*Hypergeometric2F1[3/4, 2, 7/4, -E^(4*x)]))/3","C",1
938,1,120,129,0.1262604,"\int e^x \text{sech}^2(2 x) \tanh (2 x) \, dx","Integrate[E^x*Sech[2*x]^2*Tanh[2*x],x]","\frac{1}{32} \left(-\frac{40 e^x}{e^{4 x}+1}+\frac{32 e^x}{\left(e^{4 x}+1\right)^2}-\sqrt{2} \log \left(-\sqrt{2} e^x+e^{2 x}+1\right)+\sqrt{2} \log \left(\sqrt{2} e^x+e^{2 x}+1\right)-2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} e^x\right)+2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} e^x+1\right)\right)","-\frac{e^x}{4 \left(e^{4 x}+1\right)}-\frac{e^{5 x}}{\left(e^{4 x}+1\right)^2}-\frac{\log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{16 \sqrt{2}}+\frac{\log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{16 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} e^x\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} e^x+1\right)}{8 \sqrt{2}}",1,"((32*E^x)/(1 + E^(4*x))^2 - (40*E^x)/(1 + E^(4*x)) - 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*E^x] + 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*E^x] - Sqrt[2]*Log[1 - Sqrt[2]*E^x + E^(2*x)] + Sqrt[2]*Log[1 + Sqrt[2]*E^x + E^(2*x)])/32","A",1
939,1,58,130,0.0646254,"\int e^x \text{sech}(2 x) \tanh ^2(2 x) \, dx","Integrate[E^x*Sech[2*x]*Tanh[2*x]^2,x]","\frac{e^{3 x}-3 e^{7 x}}{4 \left(e^{4 x}+1\right)^2}-\frac{5}{16} \text{RootSum}\left[\text{$\#$1}^4+1\&,\frac{x-\log \left(e^x-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]","-\frac{3 e^{3 x}}{4 \left(e^{4 x}+1\right)}+\frac{e^{3 x}}{\left(e^{4 x}+1\right)^2}+\frac{5 \log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{16 \sqrt{2}}-\frac{5 \log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{16 \sqrt{2}}-\frac{5 \tan ^{-1}\left(1-\sqrt{2} e^x\right)}{8 \sqrt{2}}+\frac{5 \tan ^{-1}\left(\sqrt{2} e^x+1\right)}{8 \sqrt{2}}",1,"(E^(3*x) - 3*E^(7*x))/(4*(1 + E^(4*x))^2) - (5*RootSum[1 + #1^4 & , (x - Log[E^x - #1])/#1 & ])/16","C",1
940,1,64,149,0.0655457,"\int e^x \text{sech}^2(2 x) \tanh ^2(2 x) \, dx","Integrate[E^x*Sech[2*x]^2*Tanh[2*x]^2,x]","\frac{1}{96} \left(-9 \text{RootSum}\left[\text{$\#$1}^4+1\&,\frac{x-\log \left(e^x-\text{$\#$1}\right)}{\text{$\#$1}^3}\&\right]-\frac{4 e^x \left(6 e^{4 x}+29 e^{8 x}+9\right)}{\left(e^{4 x}+1\right)^3}\right)","-\frac{3 e^x}{8 \left(e^{4 x}+1\right)}-\frac{5 e^{5 x}}{6 \left(e^{4 x}+1\right)^2}+\frac{4 e^{5 x}}{3 \left(e^{4 x}+1\right)^3}-\frac{3 \log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{32 \sqrt{2}}+\frac{3 \log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{32 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} e^x\right)}{16 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} e^x+1\right)}{16 \sqrt{2}}",1,"((-4*E^x*(9 + 6*E^(4*x) + 29*E^(8*x)))/(1 + E^(4*x))^3 - 9*RootSum[1 + #1^4 & , (x - Log[E^x - #1])/#1^3 & ])/96","C",1
941,1,31,34,0.0580399,"\int e^x \coth (2 x) \text{csch}(2 x) \, dx","Integrate[E^x*Coth[2*x]*Csch[2*x],x]","\frac{1}{2} \left(-\frac{2 e^{3 x}}{e^{4 x}-1}+\tan ^{-1}\left(e^x\right)-\tanh ^{-1}\left(e^x\right)\right)","\frac{e^{3 x}}{1-e^{4 x}}+\frac{1}{2} \tan ^{-1}\left(e^x\right)-\frac{1}{2} \tanh ^{-1}\left(e^x\right)",1,"((-2*E^(3*x))/(-1 + E^(4*x)) + ArcTan[E^x] - ArcTanh[E^x])/2","A",1
942,1,54,53,0.0956342,"\int e^x \coth (2 x) \text{csch}^2(2 x) \, dx","Integrate[E^x*Coth[2*x]*Csch[2*x]^2,x]","-\frac{-2 e^x+10 e^{5 x}+\left(e^{4 x}-1\right)^2 \tan ^{-1}\left(e^x\right)+\left(e^{4 x}-1\right)^2 \tanh ^{-1}\left(e^x\right)}{8 \left(e^{4 x}-1\right)^2}","\frac{e^x}{4 \left(1-e^{4 x}\right)}-\frac{e^{5 x}}{\left(1-e^{4 x}\right)^2}-\frac{1}{8} \tan ^{-1}\left(e^x\right)-\frac{1}{8} \tanh ^{-1}\left(e^x\right)",1,"-1/8*(-2*E^x + 10*E^(5*x) + (-1 + E^(4*x))^2*ArcTan[E^x] + (-1 + E^(4*x))^2*ArcTanh[E^x])/(-1 + E^(4*x))^2","A",1
943,1,161,55,3.3414976,"\int e^x \coth ^2(2 x) \text{csch}(2 x) \, dx","Integrate[E^x*Coth[2*x]^2*Csch[2*x],x]","-\frac{16 e^{7 x} \left(e^{4 x}+1\right)^2 \, _5F_4\left(\frac{7}{4},2,2,2,2;1,1,1,\frac{19}{4};e^{4 x}\right)}{1155}-\frac{8 e^{7 x} \left(26 e^{4 x}+11 e^{8 x}+15\right) \, _4F_3\left(\frac{7}{4},2,2,2;1,1,\frac{19}{4};e^{4 x}\right)}{1155}+\frac{e^{-5 x} \left(-7 \left(24152 e^{4 x}-10058 e^{8 x}-9048 e^{12 x}+513 e^{16 x}+25289\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};e^{4 x}\right)+244931 e^{4 x}+43161 e^{8 x}-26091 e^{12 x}+177023\right)}{10752}","\frac{3 e^{3 x}}{4 \left(1-e^{4 x}\right)}-\frac{e^{3 x}}{\left(1-e^{4 x}\right)^2}+\frac{5}{8} \tan ^{-1}\left(e^x\right)-\frac{5}{8} \tanh ^{-1}\left(e^x\right)",1,"(177023 + 244931*E^(4*x) + 43161*E^(8*x) - 26091*E^(12*x) - 7*(25289 + 24152*E^(4*x) - 10058*E^(8*x) - 9048*E^(12*x) + 513*E^(16*x))*Hypergeometric2F1[3/4, 1, 7/4, E^(4*x)])/(10752*E^(5*x)) - (8*E^(7*x)*(15 + 26*E^(4*x) + 11*E^(8*x))*HypergeometricPFQ[{7/4, 2, 2, 2}, {1, 1, 19/4}, E^(4*x)])/1155 - (16*E^(7*x)*(1 + E^(4*x))^2*HypergeometricPFQ[{7/4, 2, 2, 2, 2}, {1, 1, 1, 19/4}, E^(4*x)])/1155","C",0
944,1,310,75,5.5416117,"\int e^x \coth ^2(2 x) \text{csch}^2(2 x) \, dx","Integrate[E^x*Coth[2*x]^2*Csch[2*x]^2,x]","\frac{e^{-7 x} \left(1280 e^{16 x} \left(1346 e^{4 x}+557 e^{8 x}+821\right) \, _4F_3\left(2,2,2,\frac{9}{4};1,1,\frac{21}{4};e^{4 x}\right)+10240 e^{16 x} \left(42 e^{4 x}+19 e^{8 x}+23\right) \, _5F_4\left(2,2,2,2,\frac{9}{4};1,1,1,\frac{21}{4};e^{4 x}\right)+20480 e^{16 x} \, _6F_5\left(2,2,2,2,2,\frac{9}{4};1,1,1,1,\frac{21}{4};e^{4 x}\right)+40960 e^{20 x} \, _6F_5\left(2,2,2,2,2,\frac{9}{4};1,1,1,1,\frac{21}{4};e^{4 x}\right)+20480 e^{24 x} \, _6F_5\left(2,2,2,2,2,\frac{9}{4};1,1,1,1,\frac{21}{4};e^{4 x}\right)+732349800 e^{4 x} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};e^{4 x}\right)-635067810 e^{8 x} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};e^{4 x}\right)-384831720 e^{12 x} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};e^{4 x}\right)+60913125 e^{16 x} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};e^{4 x}\right)+1070609085 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};e^{4 x}\right)-946471617 e^{4 x}+369641285 e^{8 x}+351173641 e^{12 x}-23818496 e^{16 x}-1070609085\right)}{3818880}","\frac{3 e^x}{8 \left(1-e^{4 x}\right)}-\frac{5 e^{5 x}}{6 \left(1-e^{4 x}\right)^2}+\frac{4 e^{5 x}}{3 \left(1-e^{4 x}\right)^3}-\frac{3}{16} \tan ^{-1}\left(e^x\right)-\frac{3}{16} \tanh ^{-1}\left(e^x\right)",1,"(-1070609085 - 946471617*E^(4*x) + 369641285*E^(8*x) + 351173641*E^(12*x) - 23818496*E^(16*x) + 1070609085*Hypergeometric2F1[1/4, 1, 5/4, E^(4*x)] + 732349800*E^(4*x)*Hypergeometric2F1[1/4, 1, 5/4, E^(4*x)] - 635067810*E^(8*x)*Hypergeometric2F1[1/4, 1, 5/4, E^(4*x)] - 384831720*E^(12*x)*Hypergeometric2F1[1/4, 1, 5/4, E^(4*x)] + 60913125*E^(16*x)*Hypergeometric2F1[1/4, 1, 5/4, E^(4*x)] + 1280*E^(16*x)*(821 + 1346*E^(4*x) + 557*E^(8*x))*HypergeometricPFQ[{2, 2, 2, 9/4}, {1, 1, 21/4}, E^(4*x)] + 10240*E^(16*x)*(23 + 42*E^(4*x) + 19*E^(8*x))*HypergeometricPFQ[{2, 2, 2, 2, 9/4}, {1, 1, 1, 21/4}, E^(4*x)] + 20480*E^(16*x)*HypergeometricPFQ[{2, 2, 2, 2, 2, 9/4}, {1, 1, 1, 1, 21/4}, E^(4*x)] + 40960*E^(20*x)*HypergeometricPFQ[{2, 2, 2, 2, 2, 9/4}, {1, 1, 1, 1, 21/4}, E^(4*x)] + 20480*E^(24*x)*HypergeometricPFQ[{2, 2, 2, 2, 2, 9/4}, {1, 1, 1, 1, 21/4}, E^(4*x)])/(3818880*E^(7*x))","C",0
945,1,86,137,1.2074337,"\int e^{c+d x} \cosh (a+b x) \sinh ^3(a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]*Sinh[a + b*x]^3,x]","\frac{1}{8} e^{c+d x} \left(\frac{2 d \sinh (2 (a+b x))-4 b \cosh (2 (a+b x))}{4 b^2-d^2}+\frac{4 b \cosh (4 (a+b x))-d \sinh (4 (a+b x))}{16 b^2-d^2}\right)","\frac{d e^{c+d x} \sinh (2 a+2 b x)}{4 \left(4 b^2-d^2\right)}-\frac{d e^{c+d x} \sinh (4 a+4 b x)}{8 \left(16 b^2-d^2\right)}-\frac{b e^{c+d x} \cosh (2 a+2 b x)}{2 \left(4 b^2-d^2\right)}+\frac{b e^{c+d x} \cosh (4 a+4 b x)}{2 \left(16 b^2-d^2\right)}",1,"(E^(c + d*x)*((-4*b*Cosh[2*(a + b*x)] + 2*d*Sinh[2*(a + b*x)])/(4*b^2 - d^2) + (4*b*Cosh[4*(a + b*x)] - d*Sinh[4*(a + b*x)])/(16*b^2 - d^2)))/8","A",1
946,1,80,127,0.9850818,"\int e^{c+d x} \cosh (a+b x) \sinh ^2(a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]*Sinh[a + b*x]^2,x]","\frac{1}{4} e^{c+d x} \left(\frac{3 b \sinh (3 (a+b x))-d \cosh (3 (a+b x))}{9 b^2-d^2}+\frac{d \cosh (a+b x)-b \sinh (a+b x)}{(b-d) (b+d)}\right)","-\frac{b e^{c+d x} \sinh (a+b x)}{4 \left(b^2-d^2\right)}+\frac{3 b e^{c+d x} \sinh (3 a+3 b x)}{4 \left(9 b^2-d^2\right)}+\frac{d e^{c+d x} \cosh (a+b x)}{4 \left(b^2-d^2\right)}-\frac{d e^{c+d x} \cosh (3 a+3 b x)}{4 \left(9 b^2-d^2\right)}",1,"(E^(c + d*x)*((d*Cosh[a + b*x] - b*Sinh[a + b*x])/((b - d)*(b + d)) + (-(d*Cosh[3*(a + b*x)]) + 3*b*Sinh[3*(a + b*x)])/(9*b^2 - d^2)))/4","A",1
947,1,47,66,0.0522106,"\int e^{c+d x} \cosh (a+b x) \sinh (a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]*Sinh[a + b*x],x]","\frac{e^{c+d x} (2 b \cosh (2 (a+b x))-d \sinh (2 (a+b x)))}{2 \left(4 b^2-d^2\right)}","\frac{b e^{c+d x} \cosh (2 a+2 b x)}{4 b^2-d^2}-\frac{d e^{c+d x} \sinh (2 a+2 b x)}{2 \left(4 b^2-d^2\right)}",1,"(E^(c + d*x)*(2*b*Cosh[2*(a + b*x)] - d*Sinh[2*(a + b*x)]))/(2*(4*b^2 - d^2))","A",1
948,1,38,54,0.0471022,"\int e^{c+d x} \cosh (a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x],x]","\frac{e^{c+d x} (b \sinh (a+b x)-d \cosh (a+b x))}{(b-d) (b+d)}","\frac{b e^{c+d x} \sinh (a+b x)}{b^2-d^2}-\frac{d e^{c+d x} \cosh (a+b x)}{b^2-d^2}",1,"(E^(c + d*x)*(-(d*Cosh[a + b*x]) + b*Sinh[a + b*x]))/((b - d)*(b + d))","A",1
949,1,120,53,1.9433443,"\int e^{c+d x} \coth (a+b x) \, dx","Integrate[E^(c + d*x)*Coth[a + b*x],x]","\frac{\coth (a) e^{c+d x}}{d}-\frac{2 e^{2 a+c} \left(\frac{e^{d x} \, _2F_1\left(1,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)}{d}-\frac{e^{x (2 b+d)} \, _2F_1\left(1,\frac{d}{2 b}+1;\frac{d}{2 b}+2;e^{2 (a+b x)}\right)}{2 b+d}\right)}{e^{2 a}-1}","\frac{e^{c+d x}}{d}-\frac{2 e^{c+d x} \, _2F_1\left(1,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)}{d}",1,"(E^(c + d*x)*Coth[a])/d - (2*E^(2*a + c)*((E^(d*x)*Hypergeometric2F1[1, d/(2*b), 1 + d/(2*b), E^(2*(a + b*x))])/d - (E^((2*b + d)*x)*Hypergeometric2F1[1, 1 + d/(2*b), 2 + d/(2*b), E^(2*(a + b*x))])/(2*b + d)))/(-1 + E^(2*a))","B",1
950,1,92,101,0.6675867,"\int e^{c+d x} \coth (a+b x) \text{csch}(a+b x) \, dx","Integrate[E^(c + d*x)*Coth[a + b*x]*Csch[a + b*x],x]","\frac{e^c \text{csch}(a) \left(-2 d e^{x (b+d)} \, _2F_1\left(1,\frac{b+d}{2 b};\frac{3 b+d}{2 b};e^{2 b x} (\cosh (a)+\sinh (a))^2\right)-(b+d) e^{d x} (\cosh (a)-\sinh (a)) \text{csch}(a+b x)\right)}{b (\coth (a)-1) (b+d)}","\frac{4 e^{a+x (b+d)+c} \, _2F_1\left(2,\frac{b+d}{2 b};\frac{3 b+d}{2 b};e^{2 (a+b x)}\right)}{b+d}-\frac{2 e^{a+x (b+d)+c} \, _2F_1\left(1,\frac{b+d}{2 b};\frac{3 b+d}{2 b};e^{2 (a+b x)}\right)}{b+d}",1,"(E^c*Csch[a]*(-2*d*E^((b + d)*x)*Hypergeometric2F1[1, (b + d)/(2*b), (3*b + d)/(2*b), E^(2*b*x)*(Cosh[a] + Sinh[a])^2] - (b + d)*E^(d*x)*Csch[a + b*x]*(Cosh[a] - Sinh[a])))/(b*(b + d)*(-1 + Coth[a]))","A",1
951,1,159,113,1.5480411,"\int e^{c+d x} \coth (a+b x) \text{csch}^2(a+b x) \, dx","Integrate[E^(c + d*x)*Coth[a + b*x]*Csch[a + b*x]^2,x]","-\frac{e^{c-\frac{a d}{b}} \left(d^2 e^{\left(\frac{d}{b}+2\right) (a+b x)} \, _2F_1\left(1,\frac{d}{2 b}+1;\frac{d}{2 b}+2;e^{2 (a+b x)}\right)+d (2 b+d) e^{d \left(\frac{a}{b}+x\right)} \, _2F_1\left(1,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)+(2 b+d) e^{d \left(\frac{a}{b}+x\right)} \left(d \coth (a+b x)+b \text{csch}^2(a+b x)\right)\right)}{2 b^2 (2 b+d)}","\frac{4 e^{2 a+x (2 b+d)+c} \, _2F_1\left(2,\frac{1}{2} \left(\frac{d}{b}+2\right);\frac{1}{2} \left(\frac{d}{b}+4\right);e^{2 (a+b x)}\right)}{2 b+d}-\frac{8 e^{2 a+x (2 b+d)+c} \, _2F_1\left(3,\frac{1}{2} \left(\frac{d}{b}+2\right);\frac{1}{2} \left(\frac{d}{b}+4\right);e^{2 (a+b x)}\right)}{2 b+d}",1,"-1/2*(E^(c - (a*d)/b)*((2*b + d)*E^(d*(a/b + x))*(d*Coth[a + b*x] + b*Csch[a + b*x]^2) + d*(2*b + d)*E^(d*(a/b + x))*Hypergeometric2F1[1, d/(2*b), 1 + d/(2*b), E^(2*(a + b*x))] + d^2*E^((2 + d/b)*(a + b*x))*Hypergeometric2F1[1, 1 + d/(2*b), 2 + d/(2*b), E^(2*(a + b*x))]))/(b^2*(2*b + d))","A",1
952,1,117,195,1.1744748,"\int e^{c+d x} \cosh ^2(a+b x) \sinh ^3(a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]^2*Sinh[a + b*x]^3,x]","\frac{1}{16} e^{c+d x} \left(\frac{d \sinh (3 (a+b x))-3 b \cosh (3 (a+b x))}{9 b^2-d^2}+\frac{5 b \cosh (5 (a+b x))-d \sinh (5 (a+b x))}{25 b^2-d^2}+\frac{2 d \sinh (a+b x)-2 b \cosh (a+b x)}{(b-d) (b+d)}\right)","\frac{d e^{c+d x} \sinh (a+b x)}{8 \left(b^2-d^2\right)}+\frac{d e^{c+d x} \sinh (3 a+3 b x)}{16 \left(9 b^2-d^2\right)}-\frac{d e^{c+d x} \sinh (5 a+5 b x)}{16 \left(25 b^2-d^2\right)}-\frac{b e^{c+d x} \cosh (a+b x)}{8 \left(b^2-d^2\right)}-\frac{3 b e^{c+d x} \cosh (3 a+3 b x)}{16 \left(9 b^2-d^2\right)}+\frac{5 b e^{c+d x} \cosh (5 a+5 b x)}{16 \left(25 b^2-d^2\right)}",1,"(E^(c + d*x)*((-2*b*Cosh[a + b*x] + 2*d*Sinh[a + b*x])/((b - d)*(b + d)) + (-3*b*Cosh[3*(a + b*x)] + d*Sinh[3*(a + b*x)])/(9*b^2 - d^2) + (5*b*Cosh[5*(a + b*x)] - d*Sinh[5*(a + b*x)])/(25*b^2 - d^2)))/16","A",1
953,1,58,83,0.389151,"\int e^{c+d x} \cosh ^2(a+b x) \sinh ^2(a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]^2*Sinh[a + b*x]^2,x]","\frac{e^{c+d x} \left(d^2 \cosh (4 (a+b x))-4 b d \sinh (4 (a+b x))+16 b^2-d^2\right)}{8 \left(d^3-16 b^2 d\right)}","\frac{b e^{c+d x} \sinh (4 a+4 b x)}{2 \left(16 b^2-d^2\right)}-\frac{d e^{c+d x} \cosh (4 a+4 b x)}{8 \left(16 b^2-d^2\right)}-\frac{e^{c+d x}}{8 d}",1,"(E^(c + d*x)*(16*b^2 - d^2 + d^2*Cosh[4*(a + b*x)] - 4*b*d*Sinh[4*(a + b*x)]))/(8*(-16*b^2*d + d^3))","A",1
954,1,80,127,0.5634365,"\int e^{c+d x} \cosh ^2(a+b x) \sinh (a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]^2*Sinh[a + b*x],x]","\frac{1}{4} e^{c+d x} \left(\frac{3 b \cosh (3 (a+b x))-d \sinh (3 (a+b x))}{9 b^2-d^2}+\frac{b \cosh (a+b x)-d \sinh (a+b x)}{(b-d) (b+d)}\right)","-\frac{d e^{c+d x} \sinh (a+b x)}{4 \left(b^2-d^2\right)}-\frac{d e^{c+d x} \sinh (3 a+3 b x)}{4 \left(9 b^2-d^2\right)}+\frac{b e^{c+d x} \cosh (a+b x)}{4 \left(b^2-d^2\right)}+\frac{3 b e^{c+d x} \cosh (3 a+3 b x)}{4 \left(9 b^2-d^2\right)}",1,"(E^(c + d*x)*((b*Cosh[a + b*x] - d*Sinh[a + b*x])/((b - d)*(b + d)) + (3*b*Cosh[3*(a + b*x)] - d*Sinh[3*(a + b*x)])/(9*b^2 - d^2)))/4","A",1
955,1,55,95,0.1528401,"\int e^{c+d x} \cosh ^2(a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]^2,x]","\frac{e^{c+d x} \left(d^2 \cosh (2 (a+b x))-2 b d \sinh (2 (a+b x))-4 b^2+d^2\right)}{2 d^3-8 b^2 d}","-\frac{d e^{c+d x} \cosh ^2(a+b x)}{4 b^2-d^2}+\frac{2 b e^{c+d x} \sinh (a+b x) \cosh (a+b x)}{4 b^2-d^2}+\frac{2 b^2 e^{c+d x}}{d \left(4 b^2-d^2\right)}",1,"(E^(c + d*x)*(-4*b^2 + d^2 + d^2*Cosh[2*(a + b*x)] - 2*b*d*Sinh[2*(a + b*x)]))/(-8*b^2*d + 2*d^3)","A",1
956,1,93,103,0.5767401,"\int e^{c+d x} \cosh (a+b x) \coth (a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]*Coth[a + b*x],x]","\frac{e^c \left(\frac{e^{d x} (b \cosh (a+b x)-d \sinh (a+b x))}{b-d}-2 (\sinh (a)+\cosh (a)) e^{x (b+d)} \, _2F_1\left(1,\frac{b+d}{2 b};\frac{3 b+d}{2 b};e^{2 b x} (\cosh (a)+\sinh (a))^2\right)\right)}{b+d}","\frac{2 e^{-a-x (b-d)+c} \, _2F_1\left(1,-\frac{b-d}{2 b};\frac{b+d}{2 b};e^{2 (a+b x)}\right)}{b-d}-\frac{3 e^{-a-x (b-d)+c}}{2 (b-d)}+\frac{e^{a+x (b+d)+c}}{2 (b+d)}",1,"(E^c*(-2*E^((b + d)*x)*Hypergeometric2F1[1, (b + d)/(2*b), (3*b + d)/(2*b), E^(2*b*x)*(Cosh[a] + Sinh[a])^2]*(Cosh[a] + Sinh[a]) + (E^(d*x)*(b*Cosh[a + b*x] - d*Sinh[a + b*x]))/(b - d)))/(b + d)","A",1
957,1,145,94,0.8996609,"\int e^{c+d x} \coth ^2(a+b x) \, dx","Integrate[E^(c + d*x)*Coth[a + b*x]^2,x]","-\frac{2 d e^{2 a+c} \left(\frac{e^{d x} \, _2F_1\left(1,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)}{d}-\frac{e^{x (2 b+d)} \, _2F_1\left(1,\frac{d}{2 b}+1;\frac{d}{2 b}+2;e^{2 (a+b x)}\right)}{2 b+d}\right)}{\left(e^{2 a}-1\right) b}+\frac{\text{csch}(a) \sinh (b x) e^{c+d x} \text{csch}(a+b x)}{b}+\frac{e^{c+d x}}{d}","-\frac{4 e^{c+d x} \, _2F_1\left(1,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)}{d}+\frac{4 e^{c+d x} \, _2F_1\left(2,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)}{d}+\frac{e^{c+d x}}{d}",1,"E^(c + d*x)/d - (2*d*E^(2*a + c)*((E^(d*x)*Hypergeometric2F1[1, d/(2*b), 1 + d/(2*b), E^(2*(a + b*x))])/d - (E^((2*b + d)*x)*Hypergeometric2F1[1, 1 + d/(2*b), 2 + d/(2*b), E^(2*(a + b*x))])/(2*b + d)))/(b*(-1 + E^(2*a))) + (E^(c + d*x)*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b","A",1
958,1,111,151,1.3321265,"\int e^{c+d x} \coth ^2(a+b x) \text{csch}(a+b x) \, dx","Integrate[E^(c + d*x)*Coth[a + b*x]^2*Csch[a + b*x],x]","-\frac{e^{c-\frac{a d}{b}} \left(2 \left(b^2+d^2\right) e^{\frac{(b+d) (a+b x)}{b}} \, _2F_1\left(1,\frac{b+d}{2 b};\frac{3 b+d}{2 b};e^{2 (a+b x)}\right)+(b+d) e^{d \left(\frac{a}{b}+x\right)} \text{csch}(a+b x) (b \coth (a+b x)+d)\right)}{2 b^2 (b+d)}","-\frac{2 e^{a+x (b+d)+c} \, _2F_1\left(1,\frac{b+d}{2 b};\frac{3 b+d}{2 b};e^{2 (a+b x)}\right)}{b+d}+\frac{8 e^{a+x (b+d)+c} \, _2F_1\left(2,\frac{b+d}{2 b};\frac{3 b+d}{2 b};e^{2 (a+b x)}\right)}{b+d}-\frac{8 e^{a+x (b+d)+c} \, _2F_1\left(3,\frac{b+d}{2 b};\frac{3 b+d}{2 b};e^{2 (a+b x)}\right)}{b+d}",1,"-1/2*(E^(c - (a*d)/b)*((b + d)*E^(d*(a/b + x))*(d + b*Coth[a + b*x])*Csch[a + b*x] + 2*(b^2 + d^2)*E^(((b + d)*(a + b*x))/b)*Hypergeometric2F1[1, (b + d)/(2*b), (3*b + d)/(2*b), E^(2*(a + b*x))]))/(b^2*(b + d))","A",1
959,1,113,137,1.0149426,"\int e^{c+d x} \cosh ^3(a+b x) \sinh ^3(a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]^3*Sinh[a + b*x]^3,x]","\frac{e^{c+d x} \left(6 \left(4 b^3-b d^2\right) \cosh (6 (a+b x))+6 b \left(d^2-36 b^2\right) \cosh (2 (a+b x))+2 d \sinh (2 (a+b x)) \left(\left(d^2-4 b^2\right) \cosh (4 (a+b x))+52 b^2-d^2\right)\right)}{32 \left(144 b^4-40 b^2 d^2+d^4\right)}","\frac{3 d e^{c+d x} \sinh (2 a+2 b x)}{32 \left(4 b^2-d^2\right)}-\frac{d e^{c+d x} \sinh (6 a+6 b x)}{32 \left(36 b^2-d^2\right)}-\frac{3 b e^{c+d x} \cosh (2 a+2 b x)}{16 \left(4 b^2-d^2\right)}+\frac{3 b e^{c+d x} \cosh (6 a+6 b x)}{16 \left(36 b^2-d^2\right)}",1,"(E^(c + d*x)*(6*b*(-36*b^2 + d^2)*Cosh[2*(a + b*x)] + 6*(4*b^3 - b*d^2)*Cosh[6*(a + b*x)] + 2*d*(52*b^2 - d^2 + (-4*b^2 + d^2)*Cosh[4*(a + b*x)])*Sinh[2*(a + b*x)]))/(32*(144*b^4 - 40*b^2*d^2 + d^4))","A",1
960,1,118,195,1.2921297,"\int e^{c+d x} \cosh ^3(a+b x) \sinh ^2(a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]^3*Sinh[a + b*x]^2,x]","\frac{1}{16} e^{c+d x} \left(\frac{3 b \sinh (3 (a+b x))-d \cosh (3 (a+b x))}{9 b^2-d^2}+\frac{5 b \sinh (5 (a+b x))-d \cosh (5 (a+b x))}{25 b^2-d^2}+\frac{2 d \cosh (a+b x)-2 b \sinh (a+b x)}{(b-d) (b+d)}\right)","-\frac{b e^{c+d x} \sinh (a+b x)}{8 \left(b^2-d^2\right)}+\frac{3 b e^{c+d x} \sinh (3 a+3 b x)}{16 \left(9 b^2-d^2\right)}+\frac{5 b e^{c+d x} \sinh (5 a+5 b x)}{16 \left(25 b^2-d^2\right)}+\frac{d e^{c+d x} \cosh (a+b x)}{8 \left(b^2-d^2\right)}-\frac{d e^{c+d x} \cosh (3 a+3 b x)}{16 \left(9 b^2-d^2\right)}-\frac{d e^{c+d x} \cosh (5 a+5 b x)}{16 \left(25 b^2-d^2\right)}",1,"(E^(c + d*x)*((2*d*Cosh[a + b*x] - 2*b*Sinh[a + b*x])/((b - d)*(b + d)) + (-(d*Cosh[3*(a + b*x)]) + 3*b*Sinh[3*(a + b*x)])/(9*b^2 - d^2) + (-(d*Cosh[5*(a + b*x)]) + 5*b*Sinh[5*(a + b*x)])/(25*b^2 - d^2)))/16","A",1
961,1,86,137,1.0227382,"\int e^{c+d x} \cosh ^3(a+b x) \sinh (a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]^3*Sinh[a + b*x],x]","\frac{1}{8} e^{c+d x} \left(\frac{4 b \cosh (2 (a+b x))-2 d \sinh (2 (a+b x))}{4 b^2-d^2}+\frac{4 b \cosh (4 (a+b x))-d \sinh (4 (a+b x))}{16 b^2-d^2}\right)","-\frac{d e^{c+d x} \sinh (2 a+2 b x)}{4 \left(4 b^2-d^2\right)}-\frac{d e^{c+d x} \sinh (4 a+4 b x)}{8 \left(16 b^2-d^2\right)}+\frac{b e^{c+d x} \cosh (2 a+2 b x)}{2 \left(4 b^2-d^2\right)}+\frac{b e^{c+d x} \cosh (4 a+4 b x)}{2 \left(16 b^2-d^2\right)}",1,"(E^(c + d*x)*((4*b*Cosh[2*(a + b*x)] - 2*d*Sinh[2*(a + b*x)])/(4*b^2 - d^2) + (4*b*Cosh[4*(a + b*x)] - d*Sinh[4*(a + b*x)])/(16*b^2 - d^2)))/8","A",1
962,1,106,144,0.4845316,"\int e^{c+d x} \cosh ^3(a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]^3,x]","\frac{e^{c+d x} \left(\left(d^3-b^2 d\right) \cosh (3 (a+b x))+3 d \left(d^2-9 b^2\right) \cosh (a+b x)+6 b \sinh (a+b x) \left(\left(b^2-d^2\right) \cosh (2 (a+b x))+5 b^2-d^2\right)\right)}{4 \left(9 b^4-10 b^2 d^2+d^4\right)}","-\frac{d e^{c+d x} \cosh ^3(a+b x)}{9 b^2-d^2}+\frac{3 b e^{c+d x} \sinh (a+b x) \cosh ^2(a+b x)}{9 b^2-d^2}-\frac{6 b^2 d e^{c+d x} \cosh (a+b x)}{9 b^4-10 b^2 d^2+d^4}+\frac{6 b^3 e^{c+d x} \sinh (a+b x)}{9 b^4-10 b^2 d^2+d^4}",1,"(E^(c + d*x)*(3*d*(-9*b^2 + d^2)*Cosh[a + b*x] + (-(b^2*d) + d^3)*Cosh[3*(a + b*x)] + 6*b*(5*b^2 - d^2 + (b^2 - d^2)*Cosh[2*(a + b*x)])*Sinh[a + b*x]))/(4*(9*b^4 - 10*b^2*d^2 + d^4))","A",1
963,1,172,125,1.1005579,"\int e^{c+d x} \cosh ^2(a+b x) \coth (a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]^2*Coth[a + b*x],x]","-\frac{e^{c-\frac{a d}{b}} \left(2 \left(4 b^2-d^2\right) e^{d \left(\frac{a}{b}+x\right)} \, _2F_1\left(1,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)+2 d (2 b-d) e^{\left(\frac{d}{b}+2\right) (a+b x)} \, _2F_1\left(1,\frac{d}{2 b}+1;\frac{d}{2 b}+2;e^{2 (a+b x)}\right)+d e^{d \left(\frac{a}{b}+x\right)} (d \sinh (2 (a+b x))-2 b \cosh (2 (a+b x)))\right)}{8 b^2 d-2 d^3}","\frac{2 e^{-2 a-x (2 b-d)+c} \, _2F_1\left(1,\frac{1}{2} \left(\frac{d}{b}-2\right);\frac{d}{2 b};e^{2 (a+b x)}\right)}{2 b-d}-\frac{7 e^{-2 a-x (2 b-d)+c}}{4 (2 b-d)}+\frac{e^{2 a+x (2 b+d)+c}}{4 (2 b+d)}+\frac{e^{c+d x}}{d}",1,"-((E^(c - (a*d)/b)*(2*(4*b^2 - d^2)*E^(d*(a/b + x))*Hypergeometric2F1[1, d/(2*b), 1 + d/(2*b), E^(2*(a + b*x))] + 2*(2*b - d)*d*E^((2 + d/b)*(a + b*x))*Hypergeometric2F1[1, 1 + d/(2*b), 2 + d/(2*b), E^(2*(a + b*x))] + d*E^(d*(a/b + x))*(-2*b*Cosh[2*(a + b*x)] + d*Sinh[2*(a + b*x)])))/(8*b^2*d - 2*d^3))","A",1
964,1,145,160,1.2567773,"\int e^{c+d x} \cosh (a+b x) \coth ^2(a+b x) \, dx","Integrate[E^(c + d*x)*Cosh[a + b*x]*Coth[a + b*x]^2,x]","\frac{e^{c-\frac{a d}{b}} \text{csch}(a+b x) \left(e^{d \left(\frac{a}{b}+x\right)} \left(b^2 \cosh (2 (a+b x))-b d \sinh (2 (a+b x))-3 b^2+2 d^2\right)-4 d (b-d) e^{\frac{(b+d) (a+b x)}{b}} \sinh (a+b x) \, _2F_1\left(1,\frac{b+d}{2 b};\frac{3 b+d}{2 b};e^{2 (a+b x)}\right)\right)}{2 b (b-d) (b+d)}","\frac{6 e^{-a-x (b-d)+c} \, _2F_1\left(1,-\frac{b-d}{2 b};\frac{b+d}{2 b};e^{2 (a+b x)}\right)}{b-d}-\frac{4 e^{-a-x (b-d)+c} \, _2F_1\left(2,-\frac{b-d}{2 b};\frac{b+d}{2 b};e^{2 (a+b x)}\right)}{b-d}-\frac{5 e^{-a-x (b-d)+c}}{2 (b-d)}+\frac{e^{a+x (b+d)+c}}{2 (b+d)}",1,"(E^(c - (a*d)/b)*Csch[a + b*x]*(-4*(b - d)*d*E^(((b + d)*(a + b*x))/b)*Hypergeometric2F1[1, (b + d)/(2*b), (3*b + d)/(2*b), E^(2*(a + b*x))]*Sinh[a + b*x] + E^(d*(a/b + x))*(-3*b^2 + 2*d^2 + b^2*Cosh[2*(a + b*x)] - b*d*Sinh[2*(a + b*x)])))/(2*b*(b - d)*(b + d))","A",1
965,1,176,135,3.8107724,"\int e^{c+d x} \coth ^3(a+b x) \, dx","Integrate[E^(c + d*x)*Coth[a + b*x]^3,x]","\frac{1}{2} e^c \left(-\frac{2 e^{2 a} \left(2 b^2+d^2\right) \left(\frac{e^{d x} \, _2F_1\left(1,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)}{d}-\frac{e^{x (2 b+d)} \, _2F_1\left(1,\frac{d}{2 b}+1;\frac{d}{2 b}+2;e^{2 (a+b x)}\right)}{2 b+d}\right)}{\left(e^{2 a}-1\right) b^2}+\frac{d \text{csch}(a) e^{d x} \sinh (b x) \text{csch}(a+b x)}{b^2}-\frac{e^{d x} \text{csch}^2(a+b x)}{b}+\frac{2 \coth (a) e^{d x}}{d}\right)","-\frac{6 e^{c+d x} \, _2F_1\left(1,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)}{d}+\frac{12 e^{c+d x} \, _2F_1\left(2,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)}{d}-\frac{8 e^{c+d x} \, _2F_1\left(3,\frac{d}{2 b};\frac{d}{2 b}+1;e^{2 (a+b x)}\right)}{d}+\frac{e^{c+d x}}{d}",1,"(E^c*((2*E^(d*x)*Coth[a])/d - (E^(d*x)*Csch[a + b*x]^2)/b - (2*(2*b^2 + d^2)*E^(2*a)*((E^(d*x)*Hypergeometric2F1[1, d/(2*b), 1 + d/(2*b), E^(2*(a + b*x))])/d - (E^((2*b + d)*x)*Hypergeometric2F1[1, 1 + d/(2*b), 2 + d/(2*b), E^(2*(a + b*x))])/(2*b + d)))/(b^2*(-1 + E^(2*a))) + (d*E^(d*x)*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b^2))/2","A",1
966,1,155,73,1.321418,"\int \left(-\frac{3 d^2 e^{a+b x}}{4 \left(b^2-\frac{9 d^2}{4}\right) \sqrt{\sinh (c+d x)}}+e^{a+b x} \sinh ^{\frac{3}{2}}(c+d x)\right) \, dx","Integrate[(-3*d^2*E^(a + b*x))/(4*(b^2 - (9*d^2)/4)*Sqrt[Sinh[c + d*x]]) + E^(a + b*x)*Sinh[c + d*x]^(3/2),x]","\frac{2 e^{a+b x} \left(e^{2 (c+d x)}-1\right) \left(\left(4 b^2+8 b d+3 d^2\right) \sinh ^2(c+d x) \, _2F_1\left(1,\frac{1}{4} \left(\frac{2 b}{d}+7\right);\frac{2 b+d}{4 d};e^{2 (c+d x)}\right)-3 d^2 \, _2F_1\left(1,\frac{1}{4} \left(\frac{2 b}{d}+3\right);\frac{1}{4} \left(\frac{2 b}{d}+5\right);e^{2 (c+d x)}\right)\right)}{(2 b+d) (3 d-2 b) (2 b+3 d) \sqrt{\sinh (c+d x)}}","\frac{4 b e^{a+b x} \sinh ^{\frac{3}{2}}(c+d x)}{4 b^2-9 d^2}-\frac{6 d e^{a+b x} \sqrt{\sinh (c+d x)} \cosh (c+d x)}{4 b^2-9 d^2}",1,"(2*E^(a + b*x)*(-1 + E^(2*(c + d*x)))*(-3*d^2*Hypergeometric2F1[1, (3 + (2*b)/d)/4, (5 + (2*b)/d)/4, E^(2*(c + d*x))] + (4*b^2 + 8*b*d + 3*d^2)*Hypergeometric2F1[1, (7 + (2*b)/d)/4, (2*b + d)/(4*d), E^(2*(c + d*x))]*Sinh[c + d*x]^2))/((2*b + d)*(-2*b + 3*d)*(2*b + 3*d)*Sqrt[Sinh[c + d*x]])","C",0
967,1,17,17,0.043934,"\int e^{n \cosh (a+b x)} \sinh (a+b x) \, dx","Integrate[E^(n*Cosh[a + b*x])*Sinh[a + b*x],x]","\frac{e^{n \cosh (a+b x)}}{b n}","\frac{e^{n \cosh (a+b x)}}{b n}",1,"E^(n*Cosh[a + b*x])/(b*n)","A",1
968,1,22,22,0.2191563,"\int e^{n \cosh (a c+b c x)} \sinh (c (a+b x)) \, dx","Integrate[E^(n*Cosh[a*c + b*c*x])*Sinh[c*(a + b*x)],x]","\frac{e^{n \cosh (c (a+b x))}}{b c n}","\frac{e^{n \cosh (c (a+b x))}}{b c n}",1,"E^(n*Cosh[c*(a + b*x)])/(b*c*n)","A",1
969,1,22,23,0.0441991,"\int e^{n \cosh (c (a+b x))} \sinh (a c+b c x) \, dx","Integrate[E^(n*Cosh[c*(a + b*x)])*Sinh[a*c + b*c*x],x]","\frac{e^{n \cosh (c (a+b x))}}{b c n}","\frac{e^{n \cosh (a c+b c x)}}{b c n}",1,"E^(n*Cosh[c*(a + b*x)])/(b*c*n)","A",1
970,1,13,13,0.0642622,"\int e^{n \cosh (a+b x)} \tanh (a+b x) \, dx","Integrate[E^(n*Cosh[a + b*x])*Tanh[a + b*x],x]","\frac{\text{Ei}(n \cosh (a+b x))}{b}","\frac{\text{Ei}(n \cosh (a+b x))}{b}",1,"ExpIntegralEi[n*Cosh[a + b*x]]/b","A",1
971,1,18,18,0.1838088,"\int e^{n \cosh (a c+b c x)} \tanh (c (a+b x)) \, dx","Integrate[E^(n*Cosh[a*c + b*c*x])*Tanh[c*(a + b*x)],x]","\frac{\text{Ei}(n \cosh (c (a+b x)))}{b c}","\frac{\text{Ei}(n \cosh (c (a+b x)))}{b c}",1,"ExpIntegralEi[n*Cosh[c*(a + b*x)]]/(b*c)","A",1
972,1,18,19,0.0629333,"\int e^{n \cosh (c (a+b x))} \tanh (a c+b c x) \, dx","Integrate[E^(n*Cosh[c*(a + b*x)])*Tanh[a*c + b*c*x],x]","\frac{\text{Ei}(n \cosh (c (a+b x)))}{b c}","\frac{\text{Ei}(n \cosh (a c+b x c))}{b c}",1,"ExpIntegralEi[n*Cosh[c*(a + b*x)]]/(b*c)","A",1
973,1,17,17,0.0158822,"\int e^{n \sinh (a+b x)} \cosh (a+b x) \, dx","Integrate[E^(n*Sinh[a + b*x])*Cosh[a + b*x],x]","\frac{e^{n \sinh (a+b x)}}{b n}","\frac{e^{n \sinh (a+b x)}}{b n}",1,"E^(n*Sinh[a + b*x])/(b*n)","A",1
974,1,23,22,0.127682,"\int e^{n \sinh (a c+b c x)} \cosh (c (a+b x)) \, dx","Integrate[E^(n*Sinh[a*c + b*c*x])*Cosh[c*(a + b*x)],x]","\frac{e^{n \sinh (a c+b c x)}}{b c n}","\frac{e^{n \sinh (c (a+b x))}}{b c n}",1,"E^(n*Sinh[a*c + b*c*x])/(b*c*n)","A",1
975,1,23,23,0.0422021,"\int e^{n \sinh (c (a+b x))} \cosh (a c+b c x) \, dx","Integrate[E^(n*Sinh[c*(a + b*x)])*Cosh[a*c + b*c*x],x]","\frac{e^{n \sinh (a c+b c x)}}{b c n}","\frac{e^{n \sinh (a c+b c x)}}{b c n}",1,"E^(n*Sinh[a*c + b*c*x])/(b*c*n)","A",1
976,1,13,13,0.0366974,"\int e^{n \sinh (a+b x)} \coth (a+b x) \, dx","Integrate[E^(n*Sinh[a + b*x])*Coth[a + b*x],x]","\frac{\text{Ei}(n \sinh (a+b x))}{b}","\frac{\text{Ei}(n \sinh (a+b x))}{b}",1,"ExpIntegralEi[n*Sinh[a + b*x]]/b","A",1
977,1,18,18,0.0613139,"\int e^{n \sinh (a c+b c x)} \coth (c (a+b x)) \, dx","Integrate[E^(n*Sinh[a*c + b*c*x])*Coth[c*(a + b*x)],x]","\frac{\text{Ei}(n \sinh (c (a+b x)))}{b c}","\frac{\text{Ei}(n \sinh (c (a+b x)))}{b c}",1,"ExpIntegralEi[n*Sinh[c*(a + b*x)]]/(b*c)","A",1
978,1,18,19,0.0577421,"\int e^{n \sinh (c (a+b x))} \coth (a c+b c x) \, dx","Integrate[E^(n*Sinh[c*(a + b*x)])*Coth[a*c + b*c*x],x]","\frac{\text{Ei}(n \sinh (c (a+b x)))}{b c}","\frac{\text{Ei}(n \sinh (a c+b x c))}{b c}",1,"ExpIntegralEi[n*Sinh[c*(a + b*x)]]/(b*c)","A",1
979,1,20,11,0.0634663,"\int \frac{\text{sech}^2(x)}{a+b \tanh (x)} \, dx","Integrate[Sech[x]^2/(a + b*Tanh[x]),x]","\frac{\log (a \cosh (x)+b \sinh (x))-\log (\cosh (x))}{b}","\frac{\log (a+b \tanh (x))}{b}",1,"(-Log[Cosh[x]] + Log[a*Cosh[x] + b*Sinh[x]])/b","A",1
980,1,3,3,0.0037385,"\int \frac{\text{sech}^2(x)}{1+\tanh ^2(x)} \, dx","Integrate[Sech[x]^2/(1 + Tanh[x]^2),x]","\tan ^{-1}(\tanh (x))","\tan ^{-1}(\tanh (x))",1,"ArcTan[Tanh[x]]","A",1
981,0,0,11,0.0227668,"\int \frac{\text{sech}^2(x)}{9+\tanh ^2(x)} \, dx","Integrate[Sech[x]^2/(9 + Tanh[x]^2),x]","\int \frac{\text{sech}^2(x)}{9+\tanh ^2(x)} \, dx","\frac{1}{3} \tan ^{-1}\left(\frac{\tanh (x)}{3}\right)",1,"Integrate[Sech[x]^2/(9 + Tanh[x]^2), x]","F",-1
982,1,18,19,0.1905373,"\int \text{sech}^2(x) (a+b \tanh (x))^n \, dx","Integrate[Sech[x]^2*(a + b*Tanh[x])^n,x]","\frac{(a+b \tanh (x))^{n+1}}{b n+b}","\frac{(a+b \tanh (x))^{n+1}}{b (n+1)}",1,"(a + b*Tanh[x])^(1 + n)/(b + b*n)","A",1
983,1,4,4,0.0071368,"\int \text{sech}^2(x) \left(1+\frac{1}{1-\tanh ^2(x)}\right) \, dx","Integrate[Sech[x]^2*(1 + (1 - Tanh[x]^2)^(-1)),x]","x+\tanh (x)","x+\tanh (x)",1,"x + Tanh[x]","A",1
984,1,4,4,0.0031346,"\int \frac{\text{sech}^2(x) \left(2-\tanh ^2(x)\right)}{1-\tanh ^2(x)} \, dx","Integrate[(Sech[x]^2*(2 - Tanh[x]^2))/(1 - Tanh[x]^2),x]","x+\tanh (x)","x+\tanh (x)",1,"x + Tanh[x]","A",1
985,0,0,5,0.0422943,"\int \frac{\text{sech}^2(x)}{2+2 \tanh (x)+\tanh ^2(x)} \, dx","Integrate[Sech[x]^2/(2 + 2*Tanh[x] + Tanh[x]^2),x]","\int \frac{\text{sech}^2(x)}{2+2 \tanh (x)+\tanh ^2(x)} \, dx","\tan ^{-1}(\tanh (x)+1)",1,"Integrate[Sech[x]^2/(2 + 2*Tanh[x] + Tanh[x]^2), x]","F",-1
986,1,11,15,0.034256,"\int \frac{\text{sech}^2(x)}{\tanh ^2(x)+\tanh ^3(x)} \, dx","Integrate[Sech[x]^2/(Tanh[x]^2 + Tanh[x]^3),x]","x-\coth (x)-\log (\sinh (x))","-\coth (x)-\log (\tanh (x))+\log (\tanh (x)+1)",1,"x - Coth[x] - Log[Sinh[x]]","A",1
987,1,11,15,0.0262248,"\int \frac{\text{sech}^2(x)}{-\tanh ^2(x)+\tanh ^3(x)} \, dx","Integrate[Sech[x]^2/(-Tanh[x]^2 + Tanh[x]^3),x]","-x+\coth (x)-\log (\sinh (x))","\coth (x)+\log (1-\tanh (x))-\log (\tanh (x))",1,"-x + Coth[x] - Log[Sinh[x]]","A",1
988,1,74,102,0.1141306,"\int \frac{\text{sech}^2(x)}{3-4 \tanh ^3(x)} \, dx","Integrate[Sech[x]^2/(3 - 4*Tanh[x]^3),x]","\frac{\log \left(2 \sqrt[3]{6} \tanh ^2(x)+6^{2/3} \tanh (x)+3\right)-2 \log \left(3-6^{2/3} \tanh (x)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2\ 6^{2/3} \tanh (x)+3}{3 \sqrt{3}}\right)}{6\ 6^{2/3}}","\frac{\log \left(2 \sqrt[3]{2} \tanh ^2(x)+2^{2/3} \sqrt[3]{3} \tanh (x)+3^{2/3}\right)}{6\ 6^{2/3}}-\frac{\log \left(\sqrt[3]{3}-2^{2/3} \tanh (x)\right)}{3\ 6^{2/3}}+\frac{\tan ^{-1}\left(\frac{2\ 2^{2/3} \tanh (x)+\sqrt[3]{3}}{3^{5/6}}\right)}{3\ 2^{2/3} \sqrt[6]{3}}",1,"(2*Sqrt[3]*ArcTan[(3 + 2*6^(2/3)*Tanh[x])/(3*Sqrt[3])] - 2*Log[3 - 6^(2/3)*Tanh[x]] + Log[3 + 6^(2/3)*Tanh[x] + 2*6^(1/3)*Tanh[x]^2])/(6*6^(2/3))","A",1
989,0,0,22,0.0349037,"\int \frac{\text{sech}^2(x)}{11-5 \tanh (x)+5 \tanh ^2(x)} \, dx","Integrate[Sech[x]^2/(11 - 5*Tanh[x] + 5*Tanh[x]^2),x]","\int \frac{\text{sech}^2(x)}{11-5 \tanh (x)+5 \tanh ^2(x)} \, dx","-\frac{2 \tan ^{-1}\left(\sqrt{\frac{5}{39}} (1-2 \tanh (x))\right)}{\sqrt{195}}",1,"Integrate[Sech[x]^2/(11 - 5*Tanh[x] + 5*Tanh[x]^2), x]","F",-1
990,1,54,28,0.3609344,"\int \frac{\text{sech}^2(x) (a+b \tanh (x))}{c+d \tanh (x)} \, dx","Integrate[(Sech[x]^2*(a + b*Tanh[x]))/(c + d*Tanh[x]),x]","\frac{\cosh (x) (a+b \tanh (x)) ((b c-a d) (\log (\cosh (x))-\log (c \cosh (x)+d \sinh (x)))+b d \tanh (x))}{d^2 (a \cosh (x)+b \sinh (x))}","\frac{b \tanh (x)}{d}-\frac{(b c-a d) \log (c+d \tanh (x))}{d^2}",1,"(Cosh[x]*(a + b*Tanh[x])*((b*c - a*d)*(Log[Cosh[x]] - Log[c*Cosh[x] + d*Sinh[x]]) + b*d*Tanh[x]))/(d^2*(a*Cosh[x] + b*Sinh[x]))","A",1
991,1,61,53,0.6153704,"\int \frac{\text{sech}^2(x) (a+b \tanh (x))^2}{c+d \tanh (x)} \, dx","Integrate[(Sech[x]^2*(a + b*Tanh[x])^2)/(c + d*Tanh[x]),x]","-\frac{2 b d \tanh (x) (b c-2 a d)+2 (b c-a d)^2 (\log (\cosh (x))-\log (c \cosh (x)+d \sinh (x)))+b^2 d^2 \text{sech}^2(x)}{2 d^3}","\frac{(b c-a d)^2 \log (c+d \tanh (x))}{d^3}-\frac{b \tanh (x) (b c-a d)}{d^2}+\frac{(a+b \tanh (x))^2}{2 d}",1,"-1/2*(2*(b*c - a*d)^2*(Log[Cosh[x]] - Log[c*Cosh[x] + d*Sinh[x]]) + b^2*d^2*Sech[x]^2 + 2*b*d*(b*c - 2*a*d)*Tanh[x])/d^3","A",1
992,1,134,78,0.8719329,"\int \frac{\text{sech}^2(x) (a+b \tanh (x))^3}{c+d \tanh (x)} \, dx","Integrate[(Sech[x]^2*(a + b*Tanh[x])^3)/(c + d*Tanh[x]),x]","\frac{(a+b \tanh (x))^3 (c \cosh (x)+d \sinh (x)) \left(b d^2 \left(\sinh (2 x) \left(9 a^2 d-9 a b c+b^2 d\right)+b (-9 a d+3 b c-2 b d \tanh (x))\right)+6 \cosh ^2(x) (b c-a d)^3 (\log (\cosh (x))-\log (c \cosh (x)+d \sinh (x)))+6 b^3 c^2 d \sinh (x) \cosh (x)\right)}{6 d^4 (c+d \tanh (x)) (a \cosh (x)+b \sinh (x))^3}","-\frac{(b c-a d)^3 \log (c+d \tanh (x))}{d^4}+\frac{b \tanh (x) (b c-a d)^2}{d^3}-\frac{(b c-a d) (a+b \tanh (x))^2}{2 d^2}+\frac{(a+b \tanh (x))^3}{3 d}",1,"((c*Cosh[x] + d*Sinh[x])*(a + b*Tanh[x])^3*(6*(b*c - a*d)^3*Cosh[x]^2*(Log[Cosh[x]] - Log[c*Cosh[x] + d*Sinh[x]]) + 6*b^3*c^2*d*Cosh[x]*Sinh[x] + b*d^2*((-9*a*b*c + 9*a^2*d + b^2*d)*Sinh[2*x] + b*(3*b*c - 9*a*d - 2*b*d*Tanh[x]))))/(6*d^4*(a*Cosh[x] + b*Sinh[x])^3*(c + d*Tanh[x]))","A",1
993,1,12,12,0.0431166,"\int \frac{\text{sech}^2(x) \tanh ^2(x)}{\left(2+\tanh ^3(x)\right)^2} \, dx","Integrate[(Sech[x]^2*Tanh[x]^2)/(2 + Tanh[x]^3)^2,x]","-\frac{1}{3 \left(\tanh ^3(x)+2\right)}","-\frac{1}{3 \left(\tanh ^3(x)+2\right)}",1,"-1/3*1/(2 + Tanh[x]^3)","A",1
994,1,67,33,0.0264947,"\int \text{sech}^2(x) \tanh ^6(x) \left(1-\tanh ^2(x)\right)^3 \, dx","Integrate[Sech[x]^2*Tanh[x]^6*(1 - Tanh[x]^2)^3,x]","\frac{16 \tanh (x)}{3003}-\frac{1}{13} \tanh (x) \text{sech}^{12}(x)+\frac{27}{143} \tanh (x) \text{sech}^{10}(x)-\frac{53}{429} \tanh (x) \text{sech}^8(x)+\frac{5 \tanh (x) \text{sech}^6(x)}{3003}+\frac{2 \tanh (x) \text{sech}^4(x)}{1001}+\frac{8 \tanh (x) \text{sech}^2(x)}{3003}","-\frac{1}{13} \tanh ^{13}(x)+\frac{3 \tanh ^{11}(x)}{11}-\frac{\tanh ^9(x)}{3}+\frac{\tanh ^7(x)}{7}",1,"(16*Tanh[x])/3003 + (8*Sech[x]^2*Tanh[x])/3003 + (2*Sech[x]^4*Tanh[x])/1001 + (5*Sech[x]^6*Tanh[x])/3003 - (53*Sech[x]^8*Tanh[x])/429 + (27*Sech[x]^10*Tanh[x])/143 - (Sech[x]^12*Tanh[x])/13","B",1
995,1,27,26,0.2249418,"\int \frac{\text{sech}^2(x) \left(2+\tanh ^2(x)\right)}{1+\tanh ^3(x)} \, dx","Integrate[(Sech[x]^2*(2 + Tanh[x]^2))/(1 + Tanh[x]^3),x]","x+\frac{2 \tan ^{-1}\left(\frac{2 \tanh (x)-1}{\sqrt{3}}\right)}{\sqrt{3}}-\log (\cosh (x))","\log (\tanh (x)+1)-\frac{2 \tan ^{-1}\left(\frac{1-2 \tanh (x)}{\sqrt{3}}\right)}{\sqrt{3}}",1,"x + (2*ArcTan[(-1 + 2*Tanh[x])/Sqrt[3]])/Sqrt[3] - Log[Cosh[x]]","A",1
996,1,4,4,0.0024465,"\int \left(1+\cosh ^2(x)\right) \text{sech}^2(x) \, dx","Integrate[(1 + Cosh[x]^2)*Sech[x]^2,x]","x+\tanh (x)","x+\tanh (x)",1,"x + Tanh[x]","A",1
997,0,0,20,0.0304042,"\int \frac{\text{sech}^2(x)}{1+\text{sech}^2(x)-3 \tanh (x)} \, dx","Integrate[Sech[x]^2/(1 + Sech[x]^2 - 3*Tanh[x]),x]","\int \frac{\text{sech}^2(x)}{1+\text{sech}^2(x)-3 \tanh (x)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{2 \tanh (x)+3}{\sqrt{17}}\right)}{\sqrt{17}}",1,"Integrate[Sech[x]^2/(1 + Sech[x]^2 - 3*Tanh[x]), x]","F",-1
998,1,43,9,0.043383,"\int \frac{\text{sech}^2(x)}{\sqrt{4-\text{sech}^2(x)}} \, dx","Integrate[Sech[x]^2/Sqrt[4 - Sech[x]^2],x]","\frac{\sqrt{2 \cosh (2 x)+1} \text{sech}(x) \tanh ^{-1}\left(\frac{\sinh (x)}{\sqrt{4 \sinh ^2(x)+3}}\right)}{\sqrt{4-\text{sech}^2(x)}}","\sinh ^{-1}\left(\frac{\tanh (x)}{\sqrt{3}}\right)",1,"(ArcTanh[Sinh[x]/Sqrt[3 + 4*Sinh[x]^2]]*Sqrt[1 + 2*Cosh[2*x]]*Sech[x])/Sqrt[4 - Sech[x]^2]","B",1
999,1,47,9,0.0550918,"\int \frac{\text{sech}^2(x)}{\sqrt{1-4 \tanh ^2(x)}} \, dx","Integrate[Sech[x]^2/Sqrt[1 - 4*Tanh[x]^2],x]","\frac{\sqrt{3 \cosh (2 x)-5} \text{sech}(x) \tanh ^{-1}\left(\frac{2 \sinh (x)}{\sqrt{3 \sinh ^2(x)-1}}\right)}{2 \sqrt{2-8 \tanh ^2(x)}}","\frac{1}{2} \sin ^{-1}(2 \tanh (x))",1,"(ArcTanh[(2*Sinh[x])/Sqrt[-1 + 3*Sinh[x]^2]]*Sqrt[-5 + 3*Cosh[2*x]]*Sech[x])/(2*Sqrt[2 - 8*Tanh[x]^2])","B",1
1000,1,46,14,0.0415045,"\int \frac{\text{sech}^2(x)}{\sqrt{-4+\tanh ^2(x)}} \, dx","Integrate[Sech[x]^2/Sqrt[-4 + Tanh[x]^2],x]","\frac{\sqrt{3 \cosh (2 x)+5} \text{sech}(x) \tan ^{-1}\left(\frac{\sinh (x)}{\sqrt{3 \sinh ^2(x)+4}}\right)}{\sqrt{2} \sqrt{\tanh ^2(x)-4}}","\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{\tanh ^2(x)-4}}\right)",1,"(ArcTan[Sinh[x]/Sqrt[4 + 3*Sinh[x]^2]]*Sqrt[5 + 3*Cosh[2*x]]*Sech[x])/(Sqrt[2]*Sqrt[-4 + Tanh[x]^2])","B",1
1001,1,51,19,0.2259779,"\int \sqrt{1+\coth ^2(x)} \text{sech}^2(x) \, dx","Integrate[Sqrt[1 + Coth[x]^2]*Sech[x]^2,x]","\sinh (x) \sqrt{\coth ^2(x)+1} \text{sech}(2 x) \left(\cosh (x)+\sinh (x) \tanh (x)-\sqrt{-\cosh (2 x)} \tan ^{-1}\left(\frac{\cosh (x)}{\sqrt{-\cosh (2 x)}}\right)\right)","\tanh (x) \sqrt{\coth ^2(x)+1}-\sinh ^{-1}(\coth (x))",1,"Sqrt[1 + Coth[x]^2]*Sech[2*x]*Sinh[x]*(Cosh[x] - ArcTan[Cosh[x]/Sqrt[-Cosh[2*x]]]*Sqrt[-Cosh[2*x]] + Sinh[x]*Tanh[x])","B",1
1002,1,55,24,0.0969099,"\int \text{sech}^2(x) \sqrt{1+\tanh ^2(x)} \, dx","Integrate[Sech[x]^2*Sqrt[1 + Tanh[x]^2],x]","\frac{1}{4} \sqrt{\tanh ^2(x)+1} \text{sech}(x) \text{sech}(2 x) \left(-\sinh (x)+\sinh (3 x)+2 \sqrt{\cosh (2 x)} \cosh ^2(x) \tanh ^{-1}\left(\frac{\sinh (x)}{\sqrt{\cosh (2 x)}}\right)\right)","\frac{1}{2} \tanh (x) \sqrt{\tanh ^2(x)+1}+\frac{1}{2} \sinh ^{-1}(\tanh (x))",1,"(Sech[x]*Sech[2*x]*(2*ArcTanh[Sinh[x]/Sqrt[Cosh[2*x]]]*Cosh[x]^2*Sqrt[Cosh[2*x]] - Sinh[x] + Sinh[3*x])*Sqrt[1 + Tanh[x]^2])/4","B",1
1003,1,25,17,0.0165455,"\int \text{sech}^4(x) \left(-1+\text{sech}^2(x)\right)^2 \tanh (x) \, dx","Integrate[Sech[x]^4*(-1 + Sech[x]^2)^2*Tanh[x],x]","-\frac{1}{8} \text{sech}^8(x)+\frac{\text{sech}^6(x)}{3}-\frac{\text{sech}^4(x)}{4}","\frac{\tanh ^6(x)}{6}-\frac{\tanh ^8(x)}{8}",1,"-1/4*Sech[x]^4 + Sech[x]^6/3 - Sech[x]^8/8","A",1
1004,1,28,43,0.0598865,"\int e^{n \sinh (a+b x)} \sinh (2 a+2 b x) \, dx","Integrate[E^(n*Sinh[a + b*x])*Sinh[2*a + 2*b*x],x]","\frac{2 e^{n \sinh (a+b x)} (n \sinh (a+b x)-1)}{b n^2}","\frac{2 \sinh (a+b x) e^{n \sinh (a+b x)}}{b n}-\frac{2 e^{n \sinh (a+b x)}}{b n^2}",1,"(2*E^(n*Sinh[a + b*x])*(-1 + n*Sinh[a + b*x]))/(b*n^2)","A",1
1005,1,28,43,0.0288154,"\int e^{n \sinh (a+b x)} \sinh (2 (a+b x)) \, dx","Integrate[E^(n*Sinh[a + b*x])*Sinh[2*(a + b*x)],x]","\frac{2 e^{n \sinh (a+b x)} (n \sinh (a+b x)-1)}{b n^2}","\frac{2 \sinh (a+b x) e^{n \sinh (a+b x)}}{b n}-\frac{2 e^{n \sinh (a+b x)}}{b n^2}",1,"(2*E^(n*Sinh[a + b*x])*(-1 + n*Sinh[a + b*x]))/(b*n^2)","A",1
1006,1,36,64,0.0642312,"\int e^{n \sinh \left(\frac{a}{2}+\frac{b x}{2}\right)} \sinh (a+b x) \, dx","Integrate[E^(n*Sinh[a/2 + (b*x)/2])*Sinh[a + b*x],x]","\frac{4 e^{n \sinh \left(\frac{1}{2} (a+b x)\right)} \left(n \sinh \left(\frac{1}{2} (a+b x)\right)-1\right)}{b n^2}","\frac{4 \sinh \left(\frac{a}{2}+\frac{b x}{2}\right) e^{n \sinh \left(\frac{a}{2}+\frac{b x}{2}\right)}}{b n}-\frac{4 e^{n \sinh \left(\frac{a}{2}+\frac{b x}{2}\right)}}{b n^2}",1,"(4*E^(n*Sinh[(a + b*x)/2])*(-1 + n*Sinh[(a + b*x)/2]))/(b*n^2)","A",1
1007,1,36,64,0.0288333,"\int e^{n \sinh \left(\frac{1}{2} (a+b x)\right)} \sinh (a+b x) \, dx","Integrate[E^(n*Sinh[(a + b*x)/2])*Sinh[a + b*x],x]","\frac{4 e^{n \sinh \left(\frac{1}{2} (a+b x)\right)} \left(n \sinh \left(\frac{1}{2} (a+b x)\right)-1\right)}{b n^2}","\frac{4 \sinh \left(\frac{a}{2}+\frac{b x}{2}\right) e^{n \sinh \left(\frac{a}{2}+\frac{b x}{2}\right)}}{b n}-\frac{4 e^{n \sinh \left(\frac{a}{2}+\frac{b x}{2}\right)}}{b n^2}",1,"(4*E^(n*Sinh[(a + b*x)/2])*(-1 + n*Sinh[(a + b*x)/2]))/(b*n^2)","A",1
1008,1,28,43,0.1354595,"\int e^{n \cosh (a+b x)} \sinh (2 a+2 b x) \, dx","Integrate[E^(n*Cosh[a + b*x])*Sinh[2*a + 2*b*x],x]","\frac{2 e^{n \cosh (a+b x)} (n \cosh (a+b x)-1)}{b n^2}","\frac{2 \cosh (a+b x) e^{n \cosh (a+b x)}}{b n}-\frac{2 e^{n \cosh (a+b x)}}{b n^2}",1,"(2*E^(n*Cosh[a + b*x])*(-1 + n*Cosh[a + b*x]))/(b*n^2)","A",1
1009,1,28,43,0.0331957,"\int e^{n \cosh (a+b x)} \sinh (2 (a+b x)) \, dx","Integrate[E^(n*Cosh[a + b*x])*Sinh[2*(a + b*x)],x]","\frac{2 e^{n \cosh (a+b x)} (n \cosh (a+b x)-1)}{b n^2}","\frac{2 \cosh (a+b x) e^{n \cosh (a+b x)}}{b n}-\frac{2 e^{n \cosh (a+b x)}}{b n^2}",1,"(2*E^(n*Cosh[a + b*x])*(-1 + n*Cosh[a + b*x]))/(b*n^2)","A",1
1010,1,36,64,0.1658673,"\int e^{n \cosh \left(\frac{a}{2}+\frac{b x}{2}\right)} \sinh (a+b x) \, dx","Integrate[E^(n*Cosh[a/2 + (b*x)/2])*Sinh[a + b*x],x]","\frac{4 e^{n \cosh \left(\frac{1}{2} (a+b x)\right)} \left(n \cosh \left(\frac{1}{2} (a+b x)\right)-1\right)}{b n^2}","\frac{4 \cosh \left(\frac{a}{2}+\frac{b x}{2}\right) e^{n \cosh \left(\frac{a}{2}+\frac{b x}{2}\right)}}{b n}-\frac{4 e^{n \cosh \left(\frac{a}{2}+\frac{b x}{2}\right)}}{b n^2}",1,"(4*E^(n*Cosh[(a + b*x)/2])*(-1 + n*Cosh[(a + b*x)/2]))/(b*n^2)","A",1
1011,1,36,64,0.044084,"\int e^{n \cosh \left(\frac{1}{2} (a+b x)\right)} \sinh (a+b x) \, dx","Integrate[E^(n*Cosh[(a + b*x)/2])*Sinh[a + b*x],x]","\frac{4 e^{n \cosh \left(\frac{1}{2} (a+b x)\right)} \left(n \cosh \left(\frac{1}{2} (a+b x)\right)-1\right)}{b n^2}","\frac{4 \cosh \left(\frac{a}{2}+\frac{b x}{2}\right) e^{n \cosh \left(\frac{a}{2}+\frac{b x}{2}\right)}}{b n}-\frac{4 e^{n \cosh \left(\frac{a}{2}+\frac{b x}{2}\right)}}{b n^2}",1,"(4*E^(n*Cosh[(a + b*x)/2])*(-1 + n*Cosh[(a + b*x)/2]))/(b*n^2)","A",1
1012,1,9,9,0.0054294,"\int \text{csch}(x) \log (\tanh (x)) \text{sech}(x) \, dx","Integrate[Csch[x]*Log[Tanh[x]]*Sech[x],x]","\frac{1}{2} \log ^2(\tanh (x))","\frac{1}{2} \log ^2(\tanh (x))",1,"Log[Tanh[x]]^2/2","A",1
1013,1,9,9,0.0094039,"\int \text{csch}(2 x) \log (\tanh (x)) \, dx","Integrate[Csch[2*x]*Log[Tanh[x]],x]","\frac{1}{4} \log ^2(\tanh (x))","\frac{1}{4} \log ^2(\tanh (x))",1,"Log[Tanh[x]]^2/4","A",1
1014,0,0,21,0.0358175,"\int \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx","Integrate[Cosh[a + b*x]*F[c, d, Sinh[a + b*x], r, s],x]","\int \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx","\text{Int}(\cosh (a+b x) F(c,d,\sinh (a+b x),r,s),x)",0,"Integrate[Cosh[a + b*x]*F[c, d, Sinh[a + b*x], r, s], x]","A",-1
1015,0,0,21,0.0407338,"\int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx","Integrate[F[c, d, Cosh[a + b*x], r, s]*Sinh[a + b*x],x]","\int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx","\text{Int}(\sinh (a+b x) F(c,d,\cosh (a+b x),r,s),x)",0,"Integrate[F[c, d, Cosh[a + b*x], r, s]*Sinh[a + b*x], x]","A",-1
1016,0,0,23,0.0837403,"\int F(c,d,\tanh (a+b x),r,s) \text{sech}^2(a+b x) \, dx","Integrate[F[c, d, Tanh[a + b*x], r, s]*Sech[a + b*x]^2,x]","\int F(c,d,\tanh (a+b x),r,s) \text{sech}^2(a+b x) \, dx","\text{Int}\left(\text{sech}^2(a+b x) F(c,d,\tanh (a+b x),r,s),x\right)",0,"Integrate[F[c, d, Tanh[a + b*x], r, s]*Sech[a + b*x]^2, x]","A",-1
1017,0,0,23,0.0788297,"\int \text{csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx","Integrate[Csch[a + b*x]^2*F[c, d, Coth[a + b*x], r, s],x]","\int \text{csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx","\text{Int}\left(\text{csch}^2(a+b x) F(c,d,\coth (a+b x),r,s),x\right)",0,"Integrate[Csch[a + b*x]^2*F[c, d, Coth[a + b*x], r, s], x]","A",-1
1018,1,13,13,0.0076966,"\int \text{sech}(x) \left(5-11 \text{sech}^2(x)\right) \tanh (x) \, dx","Integrate[Sech[x]*(5 - 11*Sech[x]^2)*Tanh[x],x]","\frac{11 \text{sech}^3(x)}{3}-5 \text{sech}(x)","\frac{11 \text{sech}^3(x)}{3}-5 \text{sech}(x)",1,"-5*Sech[x] + (11*Sech[x]^3)/3","A",1
1019,1,20,12,0.0693248,"\int \frac{\text{csch}^2(x)}{a+b \coth (x)} \, dx","Integrate[Csch[x]^2/(a + b*Coth[x]),x]","\frac{\log (\sinh (x))-\log (a \sinh (x)+b \cosh (x))}{b}","-\frac{\log (a+b \coth (x))}{b}",1,"(Log[Sinh[x]] - Log[b*Cosh[x] + a*Sinh[x]])/b","A",1
1020,1,19,20,0.2368763,"\int (a+b \coth (x))^n \text{csch}^2(x) \, dx","Integrate[(a + b*Coth[x])^n*Csch[x]^2,x]","-\frac{(a+b \coth (x))^{n+1}}{b n+b}","-\frac{(a+b \coth (x))^{n+1}}{b (n+1)}",1,"-((a + b*Coth[x])^(1 + n)/(b + b*n))","A",1
1021,1,4,4,0.0035029,"\int \text{csch}^2(x) \left(-1+\sinh ^2(x)\right) \, dx","Integrate[Csch[x]^2*(-1 + Sinh[x]^2),x]","x+\coth (x)","x+\coth (x)",1,"x + Coth[x]","A",1
1022,1,4,4,0.0066514,"\int \left(-1-\frac{1}{1-\coth ^2(x)}\right) \text{csch}^2(x) \, dx","Integrate[(-1 - (1 - Coth[x]^2)^(-1))*Csch[x]^2,x]","x+\coth (x)","x+\coth (x)",1,"x + Coth[x]","A",1
1023,1,56,28,0.3473016,"\int \frac{(a+b \coth (x)) \text{csch}^2(x)}{c+d \coth (x)} \, dx","Integrate[((a + b*Coth[x])*Csch[x]^2)/(c + d*Coth[x]),x]","\frac{\sinh (x) (a+b \coth (x)) (-(b c-a d) (\log (\sinh (x))-\log (c \sinh (x)+d \cosh (x)))-b d \coth (x))}{d^2 (a \sinh (x)+b \cosh (x))}","\frac{(b c-a d) \log (c+d \coth (x))}{d^2}-\frac{b \coth (x)}{d}",1,"((a + b*Coth[x])*(-(b*d*Coth[x]) - (b*c - a*d)*(Log[Sinh[x]] - Log[d*Cosh[x] + c*Sinh[x]]))*Sinh[x])/(d^2*(b*Cosh[x] + a*Sinh[x]))","A",1
1024,1,62,53,0.5283509,"\int \frac{(a+b \coth (x))^2 \text{csch}^2(x)}{c+d \coth (x)} \, dx","Integrate[((a + b*Coth[x])^2*Csch[x]^2)/(c + d*Coth[x]),x]","\frac{2 b d \coth (x) (b c-2 a d)+2 (b c-a d)^2 (\log (\sinh (x))-\log (c \sinh (x)+d \cosh (x)))-b^2 d^2 \text{csch}^2(x)}{2 d^3}","-\frac{(b c-a d)^2 \log (c+d \coth (x))}{d^3}+\frac{b \coth (x) (b c-a d)}{d^2}-\frac{(a+b \coth (x))^2}{2 d}",1,"(2*b*d*(b*c - 2*a*d)*Coth[x] - b^2*d^2*Csch[x]^2 + 2*(b*c - a*d)^2*(Log[Sinh[x]] - Log[d*Cosh[x] + c*Sinh[x]]))/(2*d^3)","A",1
1025,1,136,78,1.2799079,"\int \frac{(a+b \coth (x))^3 \text{csch}^2(x)}{c+d \coth (x)} \, dx","Integrate[((a + b*Coth[x])^3*Csch[x]^2)/(c + d*Coth[x]),x]","\frac{(a+b \coth (x))^3 (c \sinh (x)+d \cosh (x)) \left(-b d \left(\sinh (2 x) \left(9 a^2 d^2-9 a b c d+b^2 \left(3 c^2+d^2\right)\right)-3 b d (b c-3 a d)\right)-6 \sinh ^2(x) (b c-a d)^3 (\log (\sinh (x))-\log (c \sinh (x)+d \cosh (x)))-2 b^3 d^3 \coth (x)\right)}{6 d^4 (c+d \coth (x)) (a \sinh (x)+b \cosh (x))^3}","\frac{(b c-a d)^3 \log (c+d \coth (x))}{d^4}-\frac{b \coth (x) (b c-a d)^2}{d^3}+\frac{(b c-a d) (a+b \coth (x))^2}{2 d^2}-\frac{(a+b \coth (x))^3}{3 d}",1,"((a + b*Coth[x])^3*(d*Cosh[x] + c*Sinh[x])*(-2*b^3*d^3*Coth[x] - 6*(b*c - a*d)^3*(Log[Sinh[x]] - Log[d*Cosh[x] + c*Sinh[x]])*Sinh[x]^2 - b*d*(-3*b*d*(b*c - 3*a*d) + (-9*a*b*c*d + 9*a^2*d^2 + b^2*(3*c^2 + d^2))*Sinh[2*x])))/(6*d^4*(c + d*Coth[x])*(b*Cosh[x] + a*Sinh[x])^3)","A",1
1026,1,136,36,0.2574051,"\int \cosh ^3(x) \left(a+b \cosh ^2(x)\right)^3 \sinh (x) \, dx","Integrate[Cosh[x]^3*(a + b*Cosh[x]^2)^3*Sinh[x],x]","\frac{1}{32} \left(4 a^3 \cosh (2 x)+a^3 \cosh (4 x)+12 a^2 b \cosh ^4(x)+4 a^2 b \cosh (3 x) \cosh ^3(x)+8 a b^2 \cosh ^6(x)+\frac{1}{32} a b^2 (48 \cosh (2 x)+36 \cosh (4 x)+16 \cosh (6 x)+3 \cosh (8 x))+2 b^3 \cosh ^8(x)+\frac{1}{320} b^3 (140 \cosh (2 x)+100 \cosh (4 x)+50 \cosh (6 x)+15 \cosh (8 x)+2 \cosh (10 x))\right)","\frac{\left(a+b \cosh ^2(x)\right)^5}{10 b^2}-\frac{a \left(a+b \cosh ^2(x)\right)^4}{8 b^2}",1,"(12*a^2*b*Cosh[x]^4 + 8*a*b^2*Cosh[x]^6 + 2*b^3*Cosh[x]^8 + 4*a^3*Cosh[2*x] + 4*a^2*b*Cosh[x]^3*Cosh[3*x] + a^3*Cosh[4*x] + (a*b^2*(48*Cosh[2*x] + 36*Cosh[4*x] + 16*Cosh[6*x] + 3*Cosh[8*x]))/32 + (b^3*(140*Cosh[2*x] + 100*Cosh[4*x] + 50*Cosh[6*x] + 15*Cosh[8*x] + 2*Cosh[10*x]))/320)/32","B",1
1027,1,114,36,0.6150387,"\int \cosh (x) \sinh ^3(x) \left(a+b \sinh ^2(x)\right)^3 \, dx","Integrate[Cosh[x]*Sinh[x]^3*(a + b*Sinh[x]^2)^3,x]","\frac{-20 \left(64 a^3+24 a b^2-7 b^3\right) \cosh (2 x)+20 \left(16 a^3+18 a b^2-5 b^3\right) \cosh (4 x)+b \left(320 \sinh ^6(x) \left((b-4 a)^2-b^2 \cosh (2 x)\right)-10 b (16 a-5 b) \cosh (6 x)+15 b (2 a-b) \cosh (8 x)+2 b^2 \cosh (10 x)\right)}{10240}","\frac{\left(a+b \sinh ^2(x)\right)^5}{10 b^2}-\frac{a \left(a+b \sinh ^2(x)\right)^4}{8 b^2}",1,"(-20*(64*a^3 + 24*a*b^2 - 7*b^3)*Cosh[2*x] + 20*(16*a^3 + 18*a*b^2 - 5*b^3)*Cosh[4*x] + b*(-10*(16*a - 5*b)*b*Cosh[6*x] + 15*(2*a - b)*b*Cosh[8*x] + 2*b^2*Cosh[10*x] + 320*((-4*a + b)^2 - b^2*Cosh[2*x])*Sinh[x]^6))/10240","B",1
1028,1,19,19,0.0130178,"\int \cosh (x) \sinh (x) \sqrt{a+b \sinh ^2(x)} \, dx","Integrate[Cosh[x]*Sinh[x]*Sqrt[a + b*Sinh[x]^2],x]","\frac{\left(a+b \sinh ^2(x)\right)^{3/2}}{3 b}","\frac{\left(a+b \sinh ^2(x)\right)^{3/2}}{3 b}",1,"(a + b*Sinh[x]^2)^(3/2)/(3*b)","A",1
1029,1,27,27,0.0348082,"\int \text{csch}(x) \sqrt{1+\log ^2(\coth (x))} \text{sech}(x) \, dx","Integrate[Csch[x]*Sqrt[1 + Log[Coth[x]]^2]*Sech[x],x]","-\frac{1}{2} \log (\coth (x)) \sqrt{\log ^2(\coth (x))+1}-\frac{1}{2} \sinh ^{-1}(\log (\coth (x)))","-\frac{1}{2} \log (\coth (x)) \sqrt{\log ^2(\coth (x))+1}-\frac{1}{2} \sinh ^{-1}(\log (\coth (x)))",1,"-1/2*ArcSinh[Log[Coth[x]]] - (Log[Coth[x]]*Sqrt[1 + Log[Coth[x]]^2])/2","A",1
1030,1,8,8,0.0174953,"\int \frac{\coth \left(\sqrt{x}\right) \text{csch}\left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[(Coth[Sqrt[x]]*Csch[Sqrt[x]])/Sqrt[x],x]","-2 \text{csch}\left(\sqrt{x}\right)","-2 \text{csch}\left(\sqrt{x}\right)",1,"-2*Csch[Sqrt[x]]","A",1
1031,1,12,8,0.0042449,"\int \frac{\cosh \left(\sqrt{x}\right) \sinh \left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[(Cosh[Sqrt[x]]*Sinh[Sqrt[x]])/Sqrt[x],x]","\frac{1}{2} \cosh \left(2 \sqrt{x}\right)","\sinh ^2\left(\sqrt{x}\right)",1,"Cosh[2*Sqrt[x]]/2","A",1
1032,1,8,8,0.0168385,"\int \frac{\text{sech}\left(\sqrt{x}\right) \tanh \left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[(Sech[Sqrt[x]]*Tanh[Sqrt[x]])/Sqrt[x],x]","-2 \text{sech}\left(\sqrt{x}\right)","-2 \text{sech}\left(\sqrt{x}\right)",1,"-2*Sech[Sqrt[x]]","A",1
1033,1,59,52,0.0891491,"\int \frac{\sinh ^2(x)}{a+b \sinh (2 x)} \, dx","Integrate[Sinh[x]^2/(a + b*Sinh[2*x]),x]","\frac{1}{4} \left(\frac{\log (a+b \sinh (2 x))}{b}-\frac{2 \tan ^{-1}\left(\frac{b-a \tanh (x)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}\right)","\frac{\tanh ^{-1}\left(\frac{b-a \tanh (x)}{\sqrt{a^2+b^2}}\right)}{2 \sqrt{a^2+b^2}}+\frac{\log (a+b \sinh (2 x))}{4 b}",1,"((-2*ArcTan[(b - a*Tanh[x])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + Log[a + b*Sinh[2*x]]/b)/4","A",1
1034,1,59,52,0.063454,"\int \frac{\cosh ^2(x)}{a+b \sinh (2 x)} \, dx","Integrate[Cosh[x]^2/(a + b*Sinh[2*x]),x]","\frac{1}{4} \left(\frac{2 \tan ^{-1}\left(\frac{b-a \tanh (x)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\frac{\log (a+b \sinh (2 x))}{b}\right)","\frac{\log (a+b \sinh (2 x))}{4 b}-\frac{\tanh ^{-1}\left(\frac{b-a \tanh (x)}{\sqrt{a^2+b^2}}\right)}{2 \sqrt{a^2+b^2}}",1,"((2*ArcTan[(b - a*Tanh[x])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + Log[a + b*Sinh[2*x]]/b)/4","A",1
1035,1,48,52,0.0827039,"\int \frac{\sinh ^2(x)}{a+b \cosh (2 x)} \, dx","Integrate[Sinh[x]^2/(a + b*Cosh[2*x]),x]","\frac{\frac{(a+b) \tan ^{-1}\left(\frac{(a-b) \tanh (x)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}+x}{2 b}","\frac{x}{2 b}-\frac{\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (x)}{\sqrt{a+b}}\right)}{2 b \sqrt{a-b}}",1,"(x + ((a + b)*ArcTan[((a - b)*Tanh[x])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2])/(2*b)","A",1
1036,1,50,52,0.0624606,"\int \frac{\cosh ^2(x)}{a+b \cosh (2 x)} \, dx","Integrate[Cosh[x]^2/(a + b*Cosh[2*x]),x]","\frac{\frac{(a-b) \tan ^{-1}\left(\frac{(a-b) \tanh (x)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}+x}{2 b}","\frac{x}{2 b}-\frac{\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (x)}{\sqrt{a+b}}\right)}{2 b \sqrt{a+b}}",1,"(x + ((a - b)*ArcTan[((a - b)*Tanh[x])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2])/(2*b)","A",1
1037,1,31,30,0.0362285,"\int \frac{\tanh (c+d x)}{\sqrt{a \sinh ^2(c+d x)}} \, dx","Integrate[Tanh[c + d*x]/Sqrt[a*Sinh[c + d*x]^2],x]","\frac{\sinh (c+d x) \tan ^{-1}(\sinh (c+d x))}{d \sqrt{a \sinh ^2(c+d x)}}","\frac{\tan ^{-1}\left(\frac{\sqrt{a \sinh ^2(c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"(ArcTan[Sinh[c + d*x]]*Sinh[c + d*x])/(d*Sqrt[a*Sinh[c + d*x]^2])","A",1
1038,1,49,31,0.0608644,"\int \frac{\coth (c+d x)}{\sqrt{a \cosh ^2(c+d x)}} \, dx","Integrate[Coth[c + d*x]/Sqrt[a*Cosh[c + d*x]^2],x]","\frac{\cosh (c+d x) \left(\log \left(\sinh \left(\frac{1}{2} (c+d x)\right)\right)-\log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)\right)}{d \sqrt{a \cosh ^2(c+d x)}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"(Cosh[c + d*x]*(-Log[Cosh[(c + d*x)/2]] + Log[Sinh[(c + d*x)/2]]))/(d*Sqrt[a*Cosh[c + d*x]^2])","A",1
1039,1,71,43,0.0322845,"\int x \cosh (2 x) \text{sech}(x) \, dx","Integrate[x*Cosh[2*x]*Sech[x],x]","i \left(\text{Li}_2\left(-i e^{-x}\right)-\text{Li}_2\left(i e^{-x}\right)\right)+i x \left(\log \left(1-i e^{-x}\right)-\log \left(1+i e^{-x}\right)\right)+2 x \sinh (x)-2 \cosh (x)","i \text{Li}_2\left(-i e^x\right)-i \text{Li}_2\left(i e^x\right)-2 x \tan ^{-1}\left(e^x\right)+2 x \sinh (x)-2 \cosh (x)",1,"-2*Cosh[x] + I*x*(Log[1 - I/E^x] - Log[1 + I/E^x]) + I*(PolyLog[2, (-I)/E^x] - PolyLog[2, I/E^x]) + 2*x*Sinh[x]","A",1
1040,1,12,12,0.020149,"\int x \cosh (2 x) \text{sech}^2(x) \, dx","Integrate[x*Cosh[2*x]*Sech[x]^2,x]","x^2-x \tanh (x)+\log (\cosh (x))","x^2-x \tanh (x)+\log (\cosh (x))",1,"x^2 + Log[Cosh[x]] - x*Tanh[x]","A",1
1041,1,78,53,0.0706084,"\int x \cosh (2 x) \text{sech}^3(x) \, dx","Integrate[x*Cosh[2*x]*Sech[x]^3,x]","-\frac{1}{2} i \left(3 \text{Li}_2\left(-i e^{-x}\right)-3 \text{Li}_2\left(i e^{-x}\right)+3 x \log \left(1-i e^{-x}\right)-3 x \log \left(1+i e^{-x}\right)-i \text{sech}(x)-i x \tanh (x) \text{sech}(x)\right)","-\frac{3}{2} i \text{Li}_2\left(-i e^x\right)+\frac{3}{2} i \text{Li}_2\left(i e^x\right)+3 x \tan ^{-1}\left(e^x\right)-\frac{\text{sech}(x)}{2}-\frac{1}{2} x \tanh (x) \text{sech}(x)",1,"(-1/2*I)*(3*x*Log[1 - I/E^x] - 3*x*Log[1 + I/E^x] + 3*PolyLog[2, (-I)/E^x] - 3*PolyLog[2, I/E^x] - I*Sech[x] - I*x*Sech[x]*Tanh[x])","A",1
1042,1,17,20,1.1386671,"\int \sqrt{\text{csch}(x)} (x \cosh (x)-4 \text{sech}(x) \tanh (x)) \, dx","Integrate[Sqrt[Csch[x]]*(x*Cosh[x] - 4*Sech[x]*Tanh[x]),x]","\frac{2 (x \text{csch}(x)-2 \text{sech}(x))}{\text{csch}^{\frac{3}{2}}(x)}","\frac{2 x}{\sqrt{\text{csch}(x)}}-\frac{4 \text{sech}(x)}{\text{csch}^{\frac{3}{2}}(x)}",1,"(2*(x*Csch[x] - 2*Sech[x]))/Csch[x]^(3/2)","A",1
1043,1,22,22,0.003986,"\int \sinh (x) (\cosh (x)+\sinh (x)) \, dx","Integrate[Sinh[x]*(Cosh[x] + Sinh[x]),x]","-\frac{x}{2}+\frac{1}{4} \sinh (2 x)+\frac{\cosh ^2(x)}{2}","-\frac{x}{2}+\frac{\sinh ^2(x)}{2}+\frac{1}{2} \sinh (x) \cosh (x)",1,"-1/2*x + Cosh[x]^2/2 + Sinh[2*x]/4","A",1
1044,1,37,69,0.0286692,"\int \frac{1+\sinh ^2(x)}{1+\cosh (x)+\sinh (x)} \, dx","Integrate[(1 + Sinh[x]^2)/(1 + Cosh[x] + Sinh[x]),x]","\frac{x}{4}+\frac{1}{8} \sinh (2 x)+\frac{\cosh (x)}{2}-\frac{1}{8} \cosh (2 x)-\log \left(\cosh \left(\frac{x}{2}\right)\right)","\frac{1}{2 \left(1-\tanh \left(\frac{x}{2}\right)\right)}+\frac{1}{\tanh \left(\frac{x}{2}\right)+1}-\frac{1}{2 \left(\tanh \left(\frac{x}{2}\right)+1\right)^2}+\frac{1}{4} \log \left(1-\tanh \left(\frac{x}{2}\right)\right)+\frac{3}{4} \log \left(\tanh \left(\frac{x}{2}\right)+1\right)",1,"x/4 + Cosh[x]/2 - Cosh[2*x]/8 - Log[Cosh[x/2]] + Sinh[2*x]/8","A",1
1045,1,120,129,0.481105,"\int x^5 \cosh ^7\left(a+b x^3\right) \sinh \left(a+b x^3\right) \, dx","Integrate[x^5*Cosh[a + b*x^3]^7*Sinh[a + b*x^3],x]","\frac{-672 \sinh \left(2 \left(a+b x^3\right)\right)-168 \sinh \left(4 \left(a+b x^3\right)\right)-32 \sinh \left(6 \left(a+b x^3\right)\right)-3 \sinh \left(8 \left(a+b x^3\right)\right)+1344 b x^3 \cosh \left(2 \left(a+b x^3\right)\right)+672 b x^3 \cosh \left(4 \left(a+b x^3\right)\right)+192 b x^3 \cosh \left(6 \left(a+b x^3\right)\right)+24 b x^3 \cosh \left(8 \left(a+b x^3\right)\right)}{73728 b^2}","-\frac{\sinh \left(a+b x^3\right) \cosh ^7\left(a+b x^3\right)}{192 b^2}-\frac{7 \sinh \left(a+b x^3\right) \cosh ^5\left(a+b x^3\right)}{1152 b^2}-\frac{35 \sinh \left(a+b x^3\right) \cosh ^3\left(a+b x^3\right)}{4608 b^2}-\frac{35 \sinh \left(a+b x^3\right) \cosh \left(a+b x^3\right)}{3072 b^2}+\frac{x^3 \cosh ^8\left(a+b x^3\right)}{24 b}-\frac{35 x^3}{3072 b}",1,"(1344*b*x^3*Cosh[2*(a + b*x^3)] + 672*b*x^3*Cosh[4*(a + b*x^3)] + 192*b*x^3*Cosh[6*(a + b*x^3)] + 24*b*x^3*Cosh[8*(a + b*x^3)] - 672*Sinh[2*(a + b*x^3)] - 168*Sinh[4*(a + b*x^3)] - 32*Sinh[6*(a + b*x^3)] - 3*Sinh[8*(a + b*x^3)])/(73728*b^2)","A",1
1046,1,33,39,0.0274168,"\int \frac{\cosh ^2(x)}{1+e^x} \, dx","Integrate[Cosh[x]^2/(1 + E^x),x]","\frac{1}{4} \left(3 x-\frac{e^{-2 x}}{2}+e^{-x}+e^x-4 \log \left(e^x+1\right)\right)","\frac{3 x}{4}-\frac{e^{-2 x}}{8}+\frac{e^{-x}}{4}+\frac{e^x}{4}-\log \left(e^x+1\right)",1,"(-1/2*1/E^(2*x) + E^(-x) + E^x + 3*x - 4*Log[1 + E^x])/4","A",1
1047,1,30,25,0.1868141,"\int \text{sech}(x) \sqrt{1+\text{sech}(x)} \tanh ^3(x) \, dx","Integrate[Sech[x]*Sqrt[1 + Sech[x]]*Tanh[x]^3,x]","-\frac{8}{35} \cosh ^4\left(\frac{x}{2}\right) (9 \cosh (x)-5) \text{sech}^3(x) \sqrt{\text{sech}(x)+1}","\frac{2}{7} (\text{sech}(x)+1)^{7/2}-\frac{4}{5} (\text{sech}(x)+1)^{5/2}",1,"(-8*Cosh[x/2]^4*(-5 + 9*Cosh[x])*Sech[x]^3*Sqrt[1 + Sech[x]])/35","A",1
1048,1,34,37,0.0516944,"\int \coth ^3(x) \text{csch}(x) \sqrt{1+\text{csch}(x)} \, dx","Integrate[Coth[x]^3*Csch[x]*Sqrt[1 + Csch[x]],x]","-\frac{1}{210} \text{csch}^3(x) \sqrt{\text{csch}(x)+1} (-117 \sinh (x)+43 \sinh (3 x)+62 \cosh (2 x)-2)","-\frac{2}{7} (\text{csch}(x)+1)^{7/2}+\frac{4}{5} (\text{csch}(x)+1)^{5/2}-\frac{4}{3} (\text{csch}(x)+1)^{3/2}",1,"-1/210*(Csch[x]^3*Sqrt[1 + Csch[x]]*(-2 + 62*Cosh[2*x] - 117*Sinh[x] + 43*Sinh[3*x]))","A",1
1049,1,4,4,0.0750867,"\int \cosh ^x(x) (\log (\cosh (x))+x \tanh (x)) \, dx","Integrate[Cosh[x]^x*(Log[Cosh[x]] + x*Tanh[x]),x]","\cosh ^x(x)","\cosh ^x(x)",1,"Cosh[x]^x","A",1
1050,1,33,27,0.0855811,"\int F^{a+b x} (\cosh (c+d x)+\sinh (c+d x))^n \, dx","Integrate[F^(a + b*x)*(Cosh[c + d*x] + Sinh[c + d*x])^n,x]","\frac{F^{a+b x} (\sinh (c+d x)+\cosh (c+d x))^n}{b \log (F)+d n}","\frac{F^{a+b x} \left(e^{c+d x}\right)^n}{b \log (F)+d n}",1,"(F^(a + b*x)*(Cosh[c + d*x] + Sinh[c + d*x])^n)/(d*n + b*Log[F])","A",1
1051,1,37,32,0.0727779,"\int F^{a+b x} (\cosh (c+d x)-\sinh (c+d x))^n \, dx","Integrate[F^(a + b*x)*(Cosh[c + d*x] - Sinh[c + d*x])^n,x]","-\frac{F^{a+b x} (\cosh (c+d x)-\sinh (c+d x))^n}{d n-b \log (F)}","-\frac{F^{a+b x} \left(e^{-c-d x}\right)^n}{d n-b \log (F)}",1,"-((F^(a + b*x)*(Cosh[c + d*x] - Sinh[c + d*x])^n)/(d*n - b*Log[F]))","A",1
1052,1,25,51,0.0315076,"\int \frac{\cosh ^4(a+b x)-\sinh ^4(a+b x)}{\cosh ^4(a+b x)+\sinh ^4(a+b x)} \, dx","Integrate[(Cosh[a + b*x]^4 - Sinh[a + b*x]^4)/(Cosh[a + b*x]^4 + Sinh[a + b*x]^4),x]","\frac{\tan ^{-1}\left(\frac{\sinh (2 a+2 b x)}{\sqrt{2}}\right)}{\sqrt{2} b}","\frac{\tan ^{-1}\left(\sqrt{2} \tanh (a+b x)+1\right)}{\sqrt{2} b}-\frac{\tan ^{-1}\left(1-\sqrt{2} \tanh (a+b x)\right)}{\sqrt{2} b}",1,"ArcTan[Sinh[2*a + 2*b*x]/Sqrt[2]]/(Sqrt[2]*b)","A",1
1053,1,115,47,1.3523273,"\int \frac{\cosh ^3(a+b x)-\sinh ^3(a+b x)}{\cosh ^3(a+b x)+\sinh ^3(a+b x)} \, dx","Integrate[(Cosh[a + b*x]^3 - Sinh[a + b*x]^3)/(Cosh[a + b*x]^3 + Sinh[a + b*x]^3),x]","\frac{(\sinh (a+b x)-\cosh (a+b x)) \left(\cosh (a+b x) \left(8 \sqrt{3} \tan ^{-1}\left(\frac{\text{sech}(b x) (\cosh (2 a+b x)-2 \sinh (2 a+b x))}{\sqrt{3}}\right)+3\right)+\sinh (a+b x) \left(8 \sqrt{3} \tan ^{-1}\left(\frac{\text{sech}(b x) (\cosh (2 a+b x)-2 \sinh (2 a+b x))}{\sqrt{3}}\right)-3\right)\right)}{18 b}","-\frac{1}{3 b (\tanh (a+b x)+1)}-\frac{4 \tan ^{-1}\left(\frac{1-2 \tanh (a+b x)}{\sqrt{3}}\right)}{3 \sqrt{3} b}",1,"((-Cosh[a + b*x] + Sinh[a + b*x])*((3 + 8*Sqrt[3]*ArcTan[(Sech[b*x]*(Cosh[2*a + b*x] - 2*Sinh[2*a + b*x]))/Sqrt[3]])*Cosh[a + b*x] + (-3 + 8*Sqrt[3]*ArcTan[(Sech[b*x]*(Cosh[2*a + b*x] - 2*Sinh[2*a + b*x]))/Sqrt[3]])*Sinh[a + b*x]))/(18*b)","B",1
1054,1,17,11,0.0041998,"\int \frac{\cosh ^2(a+b x)-\sinh ^2(a+b x)}{\cosh ^2(a+b x)+\sinh ^2(a+b x)} \, dx","Integrate[(Cosh[a + b*x]^2 - Sinh[a + b*x]^2)/(Cosh[a + b*x]^2 + Sinh[a + b*x]^2),x]","\frac{\tan ^{-1}(\sinh (2 a+2 b x))}{2 b}","\frac{\tan ^{-1}(\tanh (a+b x))}{b}",1,"ArcTan[Sinh[2*a + 2*b*x]]/(2*b)","A",1
1055,1,65,22,0.0239394,"\int \frac{\cosh (a+b x)-\sinh (a+b x)}{\cosh (a+b x)+\sinh (a+b x)} \, dx","Integrate[(Cosh[a + b*x] - Sinh[a + b*x])/(Cosh[a + b*x] + Sinh[a + b*x]),x]","-\frac{\sinh (2 a) \sinh (2 b x)}{2 b}-\frac{\cosh (2 a) \cosh (2 b x)}{2 b}+\frac{\sinh (2 a) \cosh (2 b x)}{2 b}+\frac{\cosh (2 a) \sinh (2 b x)}{2 b}","-\frac{1}{2 b (\sinh (a+b x)+\cosh (a+b x))^2}",1,"-1/2*(Cosh[2*a]*Cosh[2*b*x])/b + (Cosh[2*b*x]*Sinh[2*a])/(2*b) + (Cosh[2*a]*Sinh[2*b*x])/(2*b) - (Sinh[2*a]*Sinh[2*b*x])/(2*b)","B",1
1056,1,65,14,0.0248971,"\int \frac{-\text{csch}(a+b x)+\text{sech}(a+b x)}{\text{csch}(a+b x)+\text{sech}(a+b x)} \, dx","Integrate[(-Csch[a + b*x] + Sech[a + b*x])/(Csch[a + b*x] + Sech[a + b*x]),x]","\frac{\sinh (2 a) \sinh (2 b x)}{2 b}+\frac{\cosh (2 a) \cosh (2 b x)}{2 b}-\frac{\sinh (2 a) \cosh (2 b x)}{2 b}-\frac{\cosh (2 a) \sinh (2 b x)}{2 b}","\frac{1}{b (\tanh (a+b x)+1)}",1,"(Cosh[2*a]*Cosh[2*b*x])/(2*b) - (Cosh[2*b*x]*Sinh[2*a])/(2*b) - (Cosh[2*a]*Sinh[2*b*x])/(2*b) + (Sinh[2*a]*Sinh[2*b*x])/(2*b)","B",1
1057,1,17,12,0.0079979,"\int \frac{-\text{csch}^2(a+b x)+\text{sech}^2(a+b x)}{\text{csch}^2(a+b x)+\text{sech}^2(a+b x)} \, dx","Integrate[(-Csch[a + b*x]^2 + Sech[a + b*x]^2)/(Csch[a + b*x]^2 + Sech[a + b*x]^2),x]","-\frac{\tan ^{-1}(\sinh (2 a+2 b x))}{2 b}","-\frac{\tan ^{-1}(\tanh (a+b x))}{b}",1,"-1/2*ArcTan[Sinh[2*a + 2*b*x]]/b","A",1
1058,1,52,47,0.3311478,"\int \frac{-\text{csch}^3(a+b x)+\text{sech}^3(a+b x)}{\text{csch}^3(a+b x)+\text{sech}^3(a+b x)} \, dx","Integrate[(-Csch[a + b*x]^3 + Sech[a + b*x]^3)/(Csch[a + b*x]^3 + Sech[a + b*x]^3),x]","\frac{-3 \sinh (2 (a+b x))+3 \cosh (2 (a+b x))-8 \sqrt{3} \tan ^{-1}\left(\frac{2 \tanh (a+b x)-1}{\sqrt{3}}\right)}{18 b}","\frac{1}{3 b (\tanh (a+b x)+1)}+\frac{4 \tan ^{-1}\left(\frac{1-2 \tanh (a+b x)}{\sqrt{3}}\right)}{3 \sqrt{3} b}",1,"(-8*Sqrt[3]*ArcTan[(-1 + 2*Tanh[a + b*x])/Sqrt[3]] + 3*Cosh[2*(a + b*x)] - 3*Sinh[2*(a + b*x)])/(18*b)","A",1
1059,1,26,51,0.0313723,"\int \frac{-\text{csch}^4(a+b x)+\text{sech}^4(a+b x)}{\text{csch}^4(a+b x)+\text{sech}^4(a+b x)} \, dx","Integrate[(-Csch[a + b*x]^4 + Sech[a + b*x]^4)/(Csch[a + b*x]^4 + Sech[a + b*x]^4),x]","-\frac{\tan ^{-1}\left(\frac{\sinh (2 a+2 b x)}{\sqrt{2}}\right)}{\sqrt{2} b}","\frac{\tan ^{-1}\left(1-\sqrt{2} \tanh (a+b x)\right)}{\sqrt{2} b}-\frac{\tan ^{-1}\left(\sqrt{2} \tanh (a+b x)+1\right)}{\sqrt{2} b}",1,"-(ArcTan[Sinh[2*a + 2*b*x]/Sqrt[2]]/(Sqrt[2]*b))","A",1