1,1,53,43,0.0216011,"\int \tanh ^6(a+b x) \, dx","Integrate[Tanh[a + b*x]^6,x]","\frac{\tanh ^{-1}(\tanh (a+b x))}{b}-\frac{\tanh ^5(a+b x)}{5 b}-\frac{\tanh ^3(a+b x)}{3 b}-\frac{\tanh (a+b x)}{b}","-\frac{\tanh ^5(a+b x)}{5 b}-\frac{\tanh ^3(a+b x)}{3 b}-\frac{\tanh (a+b x)}{b}+x",1,"ArcTanh[Tanh[a + b*x]]/b - Tanh[a + b*x]/b - Tanh[a + b*x]^3/(3*b) - Tanh[a + b*x]^5/(5*b)","A",1
2,1,37,42,0.0947235,"\int \tanh ^5(a+b x) \, dx","Integrate[Tanh[a + b*x]^5,x]","\frac{-\tanh ^4(a+b x)-2 \tanh ^2(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)}{2 b}+\frac{\log (\cosh (a+b x))}{b}",1,"(4*Log[Cosh[a + b*x]] - 2*Tanh[a + b*x]^2 - Tanh[a + b*x]^4)/(4*b)","A",1
3,1,38,28,0.010276,"\int \tanh ^4(a+b x) \, dx","Integrate[Tanh[a + b*x]^4,x]","\frac{\tanh ^{-1}(\tanh (a+b x))}{b}-\frac{\tanh ^3(a+b x)}{3 b}-\frac{\tanh (a+b x)}{b}","-\frac{\tanh ^3(a+b x)}{3 b}-\frac{\tanh (a+b x)}{b}+x",1,"ArcTanh[Tanh[a + b*x]]/b - Tanh[a + b*x]/b - Tanh[a + b*x]^3/(3*b)","A",1
4,1,27,27,0.0125448,"\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
5,1,23,13,0.0076559,"\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
6,1,11,11,0.0059424,"\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
7,1,19,11,0.0113676,"\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
8,1,27,13,0.0099609,"\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
9,1,34,27,0.0789438,"\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
10,1,31,28,0.0105364,"\int \coth ^4(a+b x) \, dx","Integrate[Coth[a + b*x]^4,x]","-\frac{\coth ^3(a+b x) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\tanh ^2(a+b x)\right)}{3 b}","-\frac{\coth ^3(a+b x)}{3 b}-\frac{\coth (a+b x)}{b}+x",1,"-1/3*(Coth[a + b*x]^3*Hypergeometric2F1[-3/2, 1, -1/2, Tanh[a + b*x]^2])/b","C",1
11,1,44,42,0.1757793,"\int \coth ^5(a+b x) \, dx","Integrate[Coth[a + b*x]^5,x]","-\frac{\coth ^4(a+b x)+2 \coth ^2(a+b x)-4 \log (\tanh (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)}{2 b}+\frac{\log (\sinh (a+b x))}{b}",1,"-1/4*(2*Coth[a + b*x]^2 + Coth[a + b*x]^4 - 4*Log[Cosh[a + b*x]] - 4*Log[Tanh[a + b*x]])/b","A",1
12,1,31,43,0.0095388,"\int \coth ^6(a+b x) \, dx","Integrate[Coth[a + b*x]^6,x]","-\frac{\coth ^5(a+b x) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\tanh ^2(a+b x)\right)}{5 b}","-\frac{\coth ^5(a+b x)}{5 b}-\frac{\coth ^3(a+b x)}{3 b}-\frac{\coth (a+b x)}{b}+x",1,"-1/5*(Coth[a + b*x]^5*Hypergeometric2F1[-5/2, 1, -3/2, Tanh[a + b*x]^2])/b","C",1
13,1,83,97,0.2446921,"\int (b \tanh (c+d x))^{7/2} \, dx","Integrate[(b*Tanh[c + d*x])^(7/2),x]","\frac{b^3 \sqrt{b \tanh (c+d x)} \left(5 \tanh ^{-1}\left(\sqrt{\tanh (c+d x)}\right)-2 \tanh ^{\frac{5}{2}}(c+d x)-10 \sqrt{\tanh (c+d x)}+5 \tan ^{-1}\left(\sqrt{\tanh (c+d x)}\right)\right)}{5 d \sqrt{\tanh (c+d x)}}","\frac{b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{d}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b^3 \sqrt{b \tanh (c+d x)}}{d}-\frac{2 b (b \tanh (c+d x))^{5/2}}{5 d}",1,"(b^3*Sqrt[b*Tanh[c + d*x]]*(5*ArcTan[Sqrt[Tanh[c + d*x]]] + 5*ArcTanh[Sqrt[Tanh[c + d*x]]] - 10*Sqrt[Tanh[c + d*x]] - 2*Tanh[c + d*x]^(5/2)))/(5*d*Sqrt[Tanh[c + d*x]])","A",1
14,1,68,78,0.2228657,"\int (b \tanh (c+d x))^{5/2} \, dx","Integrate[(b*Tanh[c + d*x])^(5/2),x]","-\frac{(b \tanh (c+d x))^{5/2} \left(-3 \tanh ^{-1}\left(\sqrt{\tanh (c+d x)}\right)+2 \tanh ^{\frac{3}{2}}(c+d x)+3 \tan ^{-1}\left(\sqrt{\tanh (c+d x)}\right)\right)}{3 d \tanh ^{\frac{5}{2}}(c+d x)}","\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b (b \tanh (c+d x))^{3/2}}{3 d}",1,"-1/3*((b*Tanh[c + d*x])^(5/2)*(3*ArcTan[Sqrt[Tanh[c + d*x]]] - 3*ArcTanh[Sqrt[Tanh[c + d*x]]] + 2*Tanh[c + d*x]^(3/2)))/(d*Tanh[c + d*x]^(5/2))","A",1
15,1,61,75,0.0899976,"\int (b \tanh (c+d x))^{3/2} \, dx","Integrate[(b*Tanh[c + d*x])^(3/2),x]","\frac{(b \tanh (c+d x))^{3/2} \left(\tanh ^{-1}\left(\sqrt{\tanh (c+d x)}\right)-2 \sqrt{\tanh (c+d x)}+\tan ^{-1}\left(\sqrt{\tanh (c+d x)}\right)\right)}{d \tanh ^{\frac{3}{2}}(c+d x)}","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{d}+\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b \sqrt{b \tanh (c+d x)}}{d}",1,"((ArcTan[Sqrt[Tanh[c + d*x]]] + ArcTanh[Sqrt[Tanh[c + d*x]]] - 2*Sqrt[Tanh[c + d*x]])*(b*Tanh[c + d*x])^(3/2))/(d*Tanh[c + d*x]^(3/2))","A",1
16,1,51,58,0.041958,"\int \sqrt{b \tanh (c+d x)} \, dx","Integrate[Sqrt[b*Tanh[c + d*x]],x]","\frac{\sqrt{b \tanh (c+d x)} \left(\tanh ^{-1}\left(\sqrt{\tanh (c+d x)}\right)-\tan ^{-1}\left(\sqrt{\tanh (c+d x)}\right)\right)}{d \sqrt{\tanh (c+d x)}}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{d}",1,"((-ArcTan[Sqrt[Tanh[c + d*x]]] + ArcTanh[Sqrt[Tanh[c + d*x]]])*Sqrt[b*Tanh[c + d*x]])/(d*Sqrt[Tanh[c + d*x]])","A",1
17,1,49,57,0.0364505,"\int \frac{1}{\sqrt{b \tanh (c+d x)}} \, dx","Integrate[1/Sqrt[b*Tanh[c + d*x]],x]","\frac{\sqrt{\tanh (c+d x)} \left(\tanh ^{-1}\left(\sqrt{\tanh (c+d x)}\right)+\tan ^{-1}\left(\sqrt{\tanh (c+d x)}\right)\right)}{d \sqrt{b \tanh (c+d x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}",1,"((ArcTan[Sqrt[Tanh[c + d*x]]] + ArcTanh[Sqrt[Tanh[c + d*x]]])*Sqrt[Tanh[c + d*x]])/(d*Sqrt[b*Tanh[c + d*x]])","A",1
18,1,36,78,0.0786824,"\int \frac{1}{(b \tanh (c+d x))^{3/2}} \, dx","Integrate[(b*Tanh[c + d*x])^(-3/2),x]","-\frac{2 \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};\tanh ^2(c+d x)\right)}{b d \sqrt{b \tanh (c+d x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{\tan ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2}{b d \sqrt{b \tanh (c+d x)}}",1,"(-2*Hypergeometric2F1[-1/4, 1, 3/4, Tanh[c + d*x]^2])/(b*d*Sqrt[b*Tanh[c + d*x]])","C",1
19,1,38,79,0.0806274,"\int \frac{1}{(b \tanh (c+d x))^{5/2}} \, dx","Integrate[(b*Tanh[c + d*x])^(-5/2),x]","-\frac{2 \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};\tanh ^2(c+d x)\right)}{3 b d (b \tanh (c+d x))^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}-\frac{2}{3 b d (b \tanh (c+d x))^{3/2}}",1,"(-2*Hypergeometric2F1[-3/4, 1, 1/4, Tanh[c + d*x]^2])/(3*b*d*(b*Tanh[c + d*x])^(3/2))","C",1
20,1,38,100,0.1223979,"\int \frac{1}{(b \tanh (c+d x))^{7/2}} \, dx","Integrate[(b*Tanh[c + d*x])^(-7/2),x]","-\frac{2 \, _2F_1\left(-\frac{5}{4},1;-\frac{1}{4};\tanh ^2(c+d x)\right)}{5 b d (b \tanh (c+d x))^{5/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{b^{7/2} d}-\frac{\tan ^{-1}\left(\frac{\sqrt{b \tanh (c+d x)}}{\sqrt{b}}\right)}{b^{7/2} d}-\frac{2}{b^3 d \sqrt{b \tanh (c+d x)}}-\frac{2}{5 b d (b \tanh (c+d x))^{5/2}}",1,"(-2*Hypergeometric2F1[-5/4, 1, -1/4, Tanh[c + d*x]^2])/(5*b*d*(b*Tanh[c + d*x])^(5/2))","C",1
21,1,26,69,0.0274644,"\int \sqrt[3]{\tanh (8 x)} \, dx","Integrate[Tanh[8*x]^(1/3),x]","\frac{3}{32} \tanh ^{\frac{4}{3}}(8 x) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\tanh ^2(8 x)\right)","-\frac{1}{16} \log \left(1-\tanh ^{\frac{2}{3}}(8 x)\right)+\frac{1}{32} \log \left(\tanh ^{\frac{4}{3}}(8 x)+\tanh ^{\frac{2}{3}}(8 x)+1\right)-\frac{1}{16} \sqrt{3} \tan ^{-1}\left(\frac{2 \tanh ^{\frac{2}{3}}(8 x)+1}{\sqrt{3}}\right)",1,"(3*Hypergeometric2F1[2/3, 1, 5/3, Tanh[8*x]^2]*Tanh[8*x]^(4/3))/32","C",1
22,1,45,43,0.0499937,"\int \tanh ^n(a+b x) \, dx","Integrate[Tanh[a + b*x]^n,x]","\frac{\tanh ^{n+1}(a+b x) \, _2F_1\left(1,\frac{n+1}{2};\frac{n+1}{2}+1;\tanh ^2(a+b x)\right)}{b (n+1)}","\frac{\tanh ^{n+1}(a+b x) \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\tanh ^2(a+b x)\right)}{b (n+1)}",1,"(Hypergeometric2F1[1, (1 + n)/2, 1 + (1 + n)/2, Tanh[a + b*x]^2]*Tanh[a + b*x]^(1 + n))/(b*(1 + n))","A",1
23,1,51,48,0.0468841,"\int (b \tanh (c+d x))^n \, dx","Integrate[(b*Tanh[c + d*x])^n,x]","\frac{\tanh (c+d x) (b \tanh (c+d x))^n \, _2F_1\left(1,\frac{n+1}{2};\frac{n+1}{2}+1;\tanh ^2(c+d x)\right)}{d (n+1)}","\frac{(b \tanh (c+d x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\tanh ^2(c+d x)\right)}{b d (n+1)}",1,"(Hypergeometric2F1[1, (1 + n)/2, 1 + (1 + n)/2, Tanh[c + d*x]^2]*Tanh[c + d*x]*(b*Tanh[c + d*x])^n)/(d*(1 + n))","A",1
24,1,28,35,0.0259661,"\int \left(a \tanh ^2(x)\right)^{3/2} \, dx","Integrate[(a*Tanh[x]^2)^(3/2),x]","\frac{1}{2} a \sqrt{a \tanh ^2(x)} (\text{csch}(x) \text{sech}(x)+2 \coth (x) \log (\cosh (x)))","a \coth (x) \sqrt{a \tanh ^2(x)} \log (\cosh (x))-\frac{1}{2} a \tanh (x) \sqrt{a \tanh ^2(x)}",1,"(a*(2*Coth[x]*Log[Cosh[x]] + Csch[x]*Sech[x])*Sqrt[a*Tanh[x]^2])/2","A",1
25,1,16,16,0.0075684,"\int \sqrt{a \tanh ^2(x)} \, dx","Integrate[Sqrt[a*Tanh[x]^2],x]","\coth (x) \sqrt{a \tanh ^2(x)} \log (\cosh (x))","\coth (x) \sqrt{a \tanh ^2(x)} \log (\cosh (x))",1,"Coth[x]*Log[Cosh[x]]*Sqrt[a*Tanh[x]^2]","A",1
26,1,16,16,0.0081727,"\int \frac{1}{\sqrt{a \tanh ^2(x)}} \, dx","Integrate[1/Sqrt[a*Tanh[x]^2],x]","\frac{\tanh (x) \log (\sinh (x))}{\sqrt{a \tanh ^2(x)}}","\frac{\tanh (x) \log (\sinh (x))}{\sqrt{a \tanh ^2(x)}}",1,"(Log[Sinh[x]]*Tanh[x])/Sqrt[a*Tanh[x]^2]","A",1
27,1,56,88,0.3053539,"\int \left(-\tanh ^2(c+d x)\right)^{5/2} \, dx","Integrate[(-Tanh[c + d*x]^2)^(5/2),x]","\frac{\left(-\tanh ^2(c+d x)\right)^{5/2} \coth (c+d x) \left(-2 \coth ^2(c+d x)+4 \coth ^4(c+d x) \log (\cosh (c+d x))-1\right)}{4 d}","-\frac{\sqrt{-\tanh ^2(c+d x)} \tanh (c+d x)}{2 d}-\frac{\sqrt{-\tanh ^2(c+d x)} \tanh ^3(c+d x)}{4 d}+\frac{\sqrt{-\tanh ^2(c+d x)} \coth (c+d x) \log (\cosh (c+d x))}{d}",1,"(Coth[c + d*x]*(-1 - 2*Coth[c + d*x]^2 + 4*Coth[c + d*x]^4*Log[Cosh[c + d*x]])*(-Tanh[c + d*x]^2)^(5/2))/(4*d)","A",1
28,1,46,60,0.1017799,"\int \left(-\tanh ^2(c+d x)\right)^{3/2} \, dx","Integrate[(-Tanh[c + d*x]^2)^(3/2),x]","\frac{\left(-\tanh ^2(c+d x)\right)^{3/2} \coth (c+d x) \left(2 \coth ^2(c+d x) \log (\cosh (c+d x))-1\right)}{2 d}","\frac{\tanh (c+d x) \sqrt{-\tanh ^2(c+d x)}}{2 d}-\frac{\sqrt{-\tanh ^2(c+d x)} \coth (c+d x) \log (\cosh (c+d x))}{d}",1,"(Coth[c + d*x]*(-1 + 2*Coth[c + d*x]^2*Log[Cosh[c + d*x]])*(-Tanh[c + d*x]^2)^(3/2))/(2*d)","A",1
29,1,31,31,0.0343767,"\int \sqrt{-\tanh ^2(c+d x)} \, dx","Integrate[Sqrt[-Tanh[c + d*x]^2],x]","\frac{\sqrt{-\tanh ^2(c+d x)} \coth (c+d x) \log (\cosh (c+d x))}{d}","\frac{\sqrt{-\tanh ^2(c+d x)} \coth (c+d x) \log (\cosh (c+d x))}{d}",1,"(Coth[c + d*x]*Log[Cosh[c + d*x]]*Sqrt[-Tanh[c + d*x]^2])/d","A",1
30,1,39,31,0.0847628,"\int \frac{1}{\sqrt{-\tanh ^2(c+d x)}} \, dx","Integrate[1/Sqrt[-Tanh[c + d*x]^2],x]","\frac{\tanh (c+d x) (\log (\tanh (c+d x))+\log (\cosh (c+d x)))}{d \sqrt{-\tanh ^2(c+d x)}}","\frac{\tanh (c+d x) \log (\sinh (c+d x))}{d \sqrt{-\tanh ^2(c+d x)}}",1,"((Log[Cosh[c + d*x]] + Log[Tanh[c + d*x]])*Tanh[c + d*x])/(d*Sqrt[-Tanh[c + d*x]^2])","A",1
31,1,51,60,0.1472068,"\int \frac{1}{\left(-\tanh ^2(c+d x)\right)^{3/2}} \, dx","Integrate[(-Tanh[c + d*x]^2)^(-3/2),x]","\frac{\coth (c+d x)-2 \tanh (c+d x) (\log (\tanh (c+d x))+\log (\cosh (c+d x)))}{2 d \sqrt{-\tanh ^2(c+d x)}}","\frac{\coth (c+d x)}{2 d \sqrt{-\tanh ^2(c+d x)}}-\frac{\tanh (c+d x) \log (\sinh (c+d x))}{d \sqrt{-\tanh ^2(c+d x)}}",1,"(Coth[c + d*x] - 2*(Log[Cosh[c + d*x]] + Log[Tanh[c + d*x]])*Tanh[c + d*x])/(2*d*Sqrt[-Tanh[c + d*x]^2])","A",1
32,1,63,88,0.251794,"\int \frac{1}{\left(-\tanh ^2(c+d x)\right)^{5/2}} \, dx","Integrate[(-Tanh[c + d*x]^2)^(-5/2),x]","\frac{-\coth ^3(c+d x)-2 \coth (c+d x)+4 \tanh (c+d x) (\log (\tanh (c+d x))+\log (\cosh (c+d x)))}{4 d \sqrt{-\tanh ^2(c+d x)}}","-\frac{\coth ^3(c+d x)}{4 d \sqrt{-\tanh ^2(c+d x)}}-\frac{\coth (c+d x)}{2 d \sqrt{-\tanh ^2(c+d x)}}+\frac{\tanh (c+d x) \log (\sinh (c+d x))}{d \sqrt{-\tanh ^2(c+d x)}}",1,"(-2*Coth[c + d*x] - Coth[c + d*x]^3 + 4*(Log[Cosh[c + d*x]] + Log[Tanh[c + d*x]])*Tanh[c + d*x])/(4*d*Sqrt[-Tanh[c + d*x]^2])","A",1
33,1,38,57,0.0408584,"\int \sqrt{\tanh ^3(x)} \, dx","Integrate[Sqrt[Tanh[x]^3],x]","\frac{\sqrt{\tanh ^3(x)} \left(\tanh ^{-1}\left(\sqrt{\tanh (x)}\right)-2 \sqrt{\tanh (x)}+\tan ^{-1}\left(\sqrt{\tanh (x)}\right)\right)}{\tanh ^{\frac{3}{2}}(x)}","\frac{\tanh ^{-1}\left(\sqrt{\tanh (x)}\right) \sqrt{\tanh ^3(x)}}{\tanh ^{\frac{3}{2}}(x)}+\frac{\sqrt{\tanh ^3(x)} \tan ^{-1}\left(\sqrt{\tanh (x)}\right)}{\tanh ^{\frac{3}{2}}(x)}-2 \sqrt{\tanh ^3(x)} \coth (x)",1,"((ArcTan[Sqrt[Tanh[x]]] + ArcTanh[Sqrt[Tanh[x]]] - 2*Sqrt[Tanh[x]])*Sqrt[Tanh[x]^3])/Tanh[x]^(3/2)","A",1
34,1,55,86,0.0631513,"\int \left(a \tanh ^3(x)\right)^{3/2} \, dx","Integrate[(a*Tanh[x]^3)^(3/2),x]","-\frac{\left(a \tanh ^3(x)\right)^{3/2} \left(-21 \tanh ^{-1}\left(\sqrt{\tanh (x)}\right)+6 \tanh ^{\frac{7}{2}}(x)+14 \tanh ^{\frac{3}{2}}(x)+21 \tan ^{-1}\left(\sqrt{\tanh (x)}\right)\right)}{21 \tanh ^{\frac{9}{2}}(x)}","-\frac{2}{3} a \sqrt{a \tanh ^3(x)}-\frac{2}{7} a \tanh ^2(x) \sqrt{a \tanh ^3(x)}+\frac{a \tanh ^{-1}\left(\sqrt{\tanh (x)}\right) \sqrt{a \tanh ^3(x)}}{\tanh ^{\frac{3}{2}}(x)}-\frac{a \sqrt{a \tanh ^3(x)} \tan ^{-1}\left(\sqrt{\tanh (x)}\right)}{\tanh ^{\frac{3}{2}}(x)}",1,"-1/21*((a*Tanh[x]^3)^(3/2)*(21*ArcTan[Sqrt[Tanh[x]]] - 21*ArcTanh[Sqrt[Tanh[x]]] + 14*Tanh[x]^(3/2) + 6*Tanh[x]^(7/2)))/Tanh[x]^(9/2)","A",1
35,1,40,63,0.03473,"\int \sqrt{a \tanh ^3(x)} \, dx","Integrate[Sqrt[a*Tanh[x]^3],x]","\frac{\sqrt{a \tanh ^3(x)} \left(\tanh ^{-1}\left(\sqrt{\tanh (x)}\right)-2 \sqrt{\tanh (x)}+\tan ^{-1}\left(\sqrt{\tanh (x)}\right)\right)}{\tanh ^{\frac{3}{2}}(x)}","\frac{\tanh ^{-1}\left(\sqrt{\tanh (x)}\right) \sqrt{a \tanh ^3(x)}}{\tanh ^{\frac{3}{2}}(x)}+\frac{\sqrt{a \tanh ^3(x)} \tan ^{-1}\left(\sqrt{\tanh (x)}\right)}{\tanh ^{\frac{3}{2}}(x)}-2 \coth (x) \sqrt{a \tanh ^3(x)}",1,"((ArcTan[Sqrt[Tanh[x]]] + ArcTanh[Sqrt[Tanh[x]]] - 2*Sqrt[Tanh[x]])*Sqrt[a*Tanh[x]^3])/Tanh[x]^(3/2)","A",1
36,1,26,64,0.0176443,"\int \frac{1}{\sqrt{a \tanh ^3(x)}} \, dx","Integrate[1/Sqrt[a*Tanh[x]^3],x]","-\frac{2 \tanh (x) \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};\tanh ^2(x)\right)}{\sqrt{a \tanh ^3(x)}}","-\frac{2 \tanh (x)}{\sqrt{a \tanh ^3(x)}}+\frac{\tanh ^{-1}\left(\sqrt{\tanh (x)}\right) \tanh ^{\frac{3}{2}}(x)}{\sqrt{a \tanh ^3(x)}}-\frac{\tanh ^{\frac{3}{2}}(x) \tan ^{-1}\left(\sqrt{\tanh (x)}\right)}{\sqrt{a \tanh ^3(x)}}",1,"(-2*Hypergeometric2F1[-1/4, 1, 3/4, Tanh[x]^2]*Tanh[x])/Sqrt[a*Tanh[x]^3]","C",1
37,1,56,69,0.1554482,"\int \left(a \tanh ^4(x)\right)^{3/2} \, dx","Integrate[(a*Tanh[x]^4)^(3/2),x]","\frac{1}{240} \coth (x) \text{csch}^5(x) \left(a \tanh ^4(x)\right)^{3/2} (-50 \sinh (x)-25 \sinh (3 x)-23 \sinh (5 x)+150 x \cosh (x)+75 x \cosh (3 x)+15 x \cosh (5 x))","-\frac{1}{3} a \tanh (x) \sqrt{a \tanh ^4(x)}-\frac{1}{5} a \tanh ^3(x) \sqrt{a \tanh ^4(x)}+a x \coth ^2(x) \sqrt{a \tanh ^4(x)}-a \coth (x) \sqrt{a \tanh ^4(x)}",1,"(Coth[x]*Csch[x]^5*(150*x*Cosh[x] + 75*x*Cosh[3*x] + 15*x*Cosh[5*x] - 50*Sinh[x] - 25*Sinh[3*x] - 23*Sinh[5*x])*(a*Tanh[x]^4)^(3/2))/240","A",1
38,1,19,31,0.0175693,"\int \sqrt{a \tanh ^4(x)} \, dx","Integrate[Sqrt[a*Tanh[x]^4],x]","\coth (x) (x \coth (x)-1) \sqrt{a \tanh ^4(x)}","x \coth ^2(x) \sqrt{a \tanh ^4(x)}-\coth (x) \sqrt{a \tanh ^4(x)}",1,"Coth[x]*(-1 + x*Coth[x])*Sqrt[a*Tanh[x]^4]","A",1
39,1,19,31,0.034787,"\int \frac{1}{\sqrt{a \tanh ^4(x)}} \, dx","Integrate[1/Sqrt[a*Tanh[x]^4],x]","\frac{\tanh (x) (x \tanh (x)-1)}{\sqrt{a \tanh ^4(x)}}","\frac{x \tanh ^2(x)}{\sqrt{a \tanh ^4(x)}}-\frac{\tanh (x)}{\sqrt{a \tanh ^4(x)}}",1,"(Tanh[x]*(-1 + x*Tanh[x]))/Sqrt[a*Tanh[x]^4]","A",1
40,1,55,57,0.0530546,"\int \left(b \tanh ^m(c+d x)\right)^n \, dx","Integrate[(b*Tanh[c + d*x]^m)^n,x]","\frac{\tanh (c+d x) \left(b \tanh ^m(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (m n+1);\frac{1}{2} (m n+3);\tanh ^2(c+d x)\right)}{d m n+d}","\frac{\tanh (c+d x) \left(b \tanh ^m(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (m n+1);\frac{1}{2} (m n+3);\tanh ^2(c+d x)\right)}{d (m n+1)}",1,"(Hypergeometric2F1[1, (1 + m*n)/2, (3 + m*n)/2, Tanh[c + d*x]^2]*Tanh[c + d*x]*(b*Tanh[c + d*x]^m)^n)/(d + d*m*n)","A",1
41,1,202,100,1.6720224,"\int (a+a \tanh (c+d x))^5 \, dx","Integrate[(a + a*Tanh[c + d*x])^5,x]","\frac{a^5 \text{sech}(c) \text{sech}^4(c+d x) (-70 \sinh (c+2 d x)+30 \sinh (3 c+2 d x)-25 \sinh (3 c+4 d x)+48 d x \cosh (3 c+2 d x)+18 \cosh (3 c+2 d x)+12 d x \cosh (3 c+4 d x)+12 d x \cosh (5 c+4 d x)+48 \cosh (3 c+2 d x) \log (\cosh (c+d x))+12 \cosh (3 c+4 d x) \log (\cosh (c+d x))+12 \cosh (5 c+4 d x) \log (\cosh (c+d x))+6 \cosh (c+2 d x) (8 \log (\cosh (c+d x))+8 d x+3)+\cosh (c) (72 \log (\cosh (c+d x))+72 d x+33)+75 \sinh (c))}{12 d}","-\frac{8 a^5 \tanh (c+d x)}{d}+\frac{16 a^5 \log (\cosh (c+d x))}{d}+16 a^5 x-\frac{2 a^2 (a \tanh (c+d x)+a)^3}{3 d}-\frac{2 a \left(a^2 \tanh (c+d x)+a^2\right)^2}{d}-\frac{a (a \tanh (c+d x)+a)^4}{4 d}",1,"(a^5*Sech[c]*Sech[c + d*x]^4*(18*Cosh[3*c + 2*d*x] + 48*d*x*Cosh[3*c + 2*d*x] + 12*d*x*Cosh[3*c + 4*d*x] + 12*d*x*Cosh[5*c + 4*d*x] + 48*Cosh[3*c + 2*d*x]*Log[Cosh[c + d*x]] + 12*Cosh[3*c + 4*d*x]*Log[Cosh[c + d*x]] + 12*Cosh[5*c + 4*d*x]*Log[Cosh[c + d*x]] + 6*Cosh[c + 2*d*x]*(3 + 8*d*x + 8*Log[Cosh[c + d*x]]) + Cosh[c]*(33 + 72*d*x + 72*Log[Cosh[c + d*x]]) + 75*Sinh[c] - 70*Sinh[c + 2*d*x] + 30*Sinh[3*c + 2*d*x] - 25*Sinh[3*c + 4*d*x]))/(12*d)","B",1
42,1,178,77,1.1458807,"\int (a+a \tanh (c+d x))^4 \, dx","Integrate[(a + a*Tanh[c + d*x])^4,x]","\frac{a^4 \text{sech}(c) \text{sech}^3(c+d x) (\sinh (4 d x)+\cosh (4 d x)) (12 \sinh (2 c+d x)-11 \sinh (2 c+3 d x)+6 d x \cosh (2 c+3 d x)+6 d x \cosh (4 c+3 d x)+6 \cosh (2 c+3 d x) \log (\cosh (c+d x))+6 \cosh (4 c+3 d x) \log (\cosh (c+d x))+6 \cosh (d x) (3 \log (\cosh (c+d x))+3 d x+1)+6 \cosh (2 c+d x) (3 \log (\cosh (c+d x))+3 d x+1)-21 \sinh (d x))}{6 d (\sinh (d x)+\cosh (d x))^4}","-\frac{4 a^4 \tanh (c+d x)}{d}+\frac{8 a^4 \log (\cosh (c+d x))}{d}+8 a^4 x-\frac{\left(a^2 \tanh (c+d x)+a^2\right)^2}{d}-\frac{a (a \tanh (c+d x)+a)^3}{3 d}",1,"(a^4*Sech[c]*Sech[c + d*x]^3*(Cosh[4*d*x] + Sinh[4*d*x])*(6*d*x*Cosh[2*c + 3*d*x] + 6*d*x*Cosh[4*c + 3*d*x] + 6*Cosh[2*c + 3*d*x]*Log[Cosh[c + d*x]] + 6*Cosh[4*c + 3*d*x]*Log[Cosh[c + d*x]] + 6*Cosh[d*x]*(1 + 3*d*x + 3*Log[Cosh[c + d*x]]) + 6*Cosh[2*c + d*x]*(1 + 3*d*x + 3*Log[Cosh[c + d*x]]) - 21*Sinh[d*x] + 12*Sinh[2*c + d*x] - 11*Sinh[2*c + 3*d*x]))/(6*d*(Cosh[d*x] + Sinh[d*x])^4)","B",1
43,1,103,56,0.9662782,"\int (a+a \tanh (c+d x))^3 \, dx","Integrate[(a + a*Tanh[c + d*x])^3,x]","\frac{a^3 \text{sech}(c) \text{sech}^2(c+d x) (-3 \sinh (c+2 d x)+2 d x \cosh (3 c+2 d x)+2 \cosh (3 c+2 d x) \log (\cosh (c+d x))+2 \cosh (c+2 d x) (\log (\cosh (c+d x))+d x)+\cosh (c) (4 \log (\cosh (c+d x))+4 d x+1)+3 \sinh (c))}{2 d}","-\frac{2 a^3 \tanh (c+d x)}{d}+\frac{4 a^3 \log (\cosh (c+d x))}{d}+4 a^3 x-\frac{a (a \tanh (c+d x)+a)^2}{2 d}",1,"(a^3*Sech[c]*Sech[c + d*x]^2*(2*d*x*Cosh[3*c + 2*d*x] + 2*Cosh[3*c + 2*d*x]*Log[Cosh[c + d*x]] + 2*Cosh[c + 2*d*x]*(d*x + Log[Cosh[c + d*x]]) + Cosh[c]*(1 + 4*d*x + 4*Log[Cosh[c + d*x]]) + 3*Sinh[c] - 3*Sinh[c + 2*d*x]))/(2*d)","A",1
44,1,58,36,0.5350913,"\int (a+a \tanh (c+d x))^2 \, dx","Integrate[(a + a*Tanh[c + d*x])^2,x]","\frac{a^2 \text{sech}(c) \text{sech}(c+d x) (\cosh (d x) (\log (\cosh (c+d x))+d x)+\cosh (2 c+d x) (\log (\cosh (c+d x))+d x)-\sinh (d x))}{d}","-\frac{a^2 \tanh (c+d x)}{d}+\frac{2 a^2 \log (\cosh (c+d x))}{d}+2 a^2 x",1,"(a^2*Sech[c]*Sech[c + d*x]*(Cosh[d*x]*(d*x + Log[Cosh[c + d*x]]) + Cosh[2*c + d*x]*(d*x + Log[Cosh[c + d*x]]) - Sinh[d*x]))/d","A",1
45,1,39,28,0.1065564,"\int \frac{1}{a+a \tanh (c+d x)} \, dx","Integrate[(a + a*Tanh[c + d*x])^(-1),x]","\frac{(2 d x+1) \tanh (c+d x)+2 d x-1}{4 a d (\tanh (c+d x)+1)}","\frac{x}{2 a}-\frac{1}{2 d (a \tanh (c+d x)+a)}",1,"(-1 + 2*d*x + (1 + 2*d*x)*Tanh[c + d*x])/(4*a*d*(1 + Tanh[c + d*x]))","A",1
46,1,60,51,0.1806562,"\int \frac{1}{(a+a \tanh (c+d x))^2} \, dx","Integrate[(a + a*Tanh[c + d*x])^(-2),x]","\frac{\text{sech}^2(c+d x) ((4 d x+1) \sinh (2 (c+d x))+(4 d x-1) \cosh (2 (c+d x))-4)}{16 a^2 d (\tanh (c+d x)+1)^2}","-\frac{1}{4 d \left(a^2 \tanh (c+d x)+a^2\right)}+\frac{x}{4 a^2}-\frac{1}{4 d (a \tanh (c+d x)+a)^2}",1,"(Sech[c + d*x]^2*(-4 + (-1 + 4*d*x)*Cosh[2*(c + d*x)] + (1 + 4*d*x)*Sinh[2*(c + d*x)]))/(16*a^2*d*(1 + Tanh[c + d*x])^2)","A",1
47,1,83,73,0.2623379,"\int \frac{1}{(a+a \tanh (c+d x))^3} \, dx","Integrate[(a + a*Tanh[c + d*x])^(-3),x]","\frac{\text{sech}^3(c+d x) (-9 \sinh (c+d x)+12 d x \sinh (3 (c+d x))+2 \sinh (3 (c+d x))-27 \cosh (c+d x)+2 (6 d x-1) \cosh (3 (c+d x)))}{96 a^3 d (\tanh (c+d x)+1)^3}","-\frac{1}{8 d \left(a^3 \tanh (c+d x)+a^3\right)}+\frac{x}{8 a^3}-\frac{1}{8 a d (a \tanh (c+d x)+a)^2}-\frac{1}{6 d (a \tanh (c+d x)+a)^3}",1,"(Sech[c + d*x]^3*(-27*Cosh[c + d*x] + 2*(-1 + 6*d*x)*Cosh[3*(c + d*x)] - 9*Sinh[c + d*x] + 2*Sinh[3*(c + d*x)] + 12*d*x*Sinh[3*(c + d*x)]))/(96*a^3*d*(1 + Tanh[c + d*x])^3)","A",1
48,1,88,96,0.2585085,"\int \frac{1}{(a+a \tanh (c+d x))^4} \, dx","Integrate[(a + a*Tanh[c + d*x])^(-4),x]","\frac{\text{sech}^4(c+d x) (-32 \sinh (2 (c+d x))+24 d x \sinh (4 (c+d x))+3 \sinh (4 (c+d x))-64 \cosh (2 (c+d x))+3 (8 d x-1) \cosh (4 (c+d x))-36)}{384 a^4 d (\tanh (c+d x)+1)^4}","-\frac{1}{16 d \left(a^4 \tanh (c+d x)+a^4\right)}+\frac{x}{16 a^4}-\frac{1}{16 d \left(a^2 \tanh (c+d x)+a^2\right)^2}-\frac{1}{12 a d (a \tanh (c+d x)+a)^3}-\frac{1}{8 d (a \tanh (c+d x)+a)^4}",1,"(Sech[c + d*x]^4*(-36 - 64*Cosh[2*(c + d*x)] + 3*(-1 + 8*d*x)*Cosh[4*(c + d*x)] - 32*Sinh[2*(c + d*x)] + 3*Sinh[4*(c + d*x)] + 24*d*x*Sinh[4*(c + d*x)]))/(384*a^4*d*(1 + Tanh[c + d*x])^4)","A",1
49,1,109,121,0.2952962,"\int \frac{1}{(a+a \tanh (c+d x))^5} \, dx","Integrate[(a + a*Tanh[c + d*x])^(-5),x]","\frac{\text{sech}^5(c+d x) (-100 \sinh (c+d x)-225 \sinh (3 (c+d x))+120 d x \sinh (5 (c+d x))+12 \sinh (5 (c+d x))-500 \cosh (c+d x)-375 \cosh (3 (c+d x))+120 d x \cosh (5 (c+d x))-12 \cosh (5 (c+d x)))}{3840 a^5 d (\tanh (c+d x)+1)^5}","-\frac{1}{32 d \left(a^5 \tanh (c+d x)+a^5\right)}+\frac{x}{32 a^5}-\frac{1}{32 a d \left(a^2 \tanh (c+d x)+a^2\right)^2}-\frac{1}{24 a^2 d (a \tanh (c+d x)+a)^3}-\frac{1}{16 a d (a \tanh (c+d x)+a)^4}-\frac{1}{10 d (a \tanh (c+d x)+a)^5}",1,"(Sech[c + d*x]^5*(-500*Cosh[c + d*x] - 375*Cosh[3*(c + d*x)] - 12*Cosh[5*(c + d*x)] + 120*d*x*Cosh[5*(c + d*x)] - 100*Sinh[c + d*x] - 225*Sinh[3*(c + d*x)] + 12*Sinh[5*(c + d*x)] + 120*d*x*Sinh[5*(c + d*x)]))/(3840*a^5*d*(1 + Tanh[c + d*x])^5)","A",1
50,1,65,57,0.2073891,"\int (1+\tanh (x))^{7/2} \, dx","Integrate[(1 + Tanh[x])^(7/2),x]","\frac{\cosh ^3(x) \left(8 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right) (\tanh (x)+1)^3-\frac{2}{15} (\tanh (x)+1)^{7/2} \left(16 \tanh (x)-3 \text{sech}^2(x)+76\right)\right)}{(\sinh (x)+\cosh (x))^3}","8 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-\frac{2}{5} (\tanh (x)+1)^{5/2}-\frac{4}{3} (\tanh (x)+1)^{3/2}-8 \sqrt{\tanh (x)+1}",1,"(Cosh[x]^3*(8*Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]]*(1 + Tanh[x])^3 - (2*(1 + Tanh[x])^(7/2)*(76 - 3*Sech[x]^2 + 16*Tanh[x]))/15))/(Cosh[x] + Sinh[x])^3","A",1
51,1,39,45,0.1767433,"\int (1+\tanh (x))^{5/2} \, dx","Integrate[(1 + Tanh[x])^(5/2),x]","4 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-\frac{2}{3} \sqrt{\tanh (x)+1} (\tanh (x)+7)","4 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-\frac{2}{3} (\tanh (x)+1)^{3/2}-4 \sqrt{\tanh (x)+1}",1,"4*Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]] - (2*Sqrt[1 + Tanh[x]]*(7 + Tanh[x]))/3","A",1
52,1,33,33,0.0694441,"\int (1+\tanh (x))^{3/2} \, dx","Integrate[(1 + Tanh[x])^(3/2),x]","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-2 \sqrt{\tanh (x)+1}","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-2 \sqrt{\tanh (x)+1}",1,"2*Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]] - 2*Sqrt[1 + Tanh[x]]","A",1
53,1,21,21,0.049346,"\int \sqrt{1+\tanh (x)} \, dx","Integrate[Sqrt[1 + Tanh[x]],x]","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)",1,"Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]]","A",1
54,1,32,32,0.0777961,"\int \frac{1}{\sqrt{1+\tanh (x)}} \, dx","Integrate[1/Sqrt[1 + Tanh[x]],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{1}{\sqrt{\tanh (x)+1}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{1}{\sqrt{\tanh (x)+1}}",1,"ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]]/Sqrt[2] - 1/Sqrt[1 + Tanh[x]]","A",1
55,1,53,49,0.1486895,"\int \frac{1}{(1+\tanh (x))^{3/2}} \, dx","Integrate[(1 + Tanh[x])^(-3/2),x]","\frac{1}{12} \left(3 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-\frac{2 (\cosh (x)-\sinh (x)) (3 \sinh (x)+5 \cosh (x))}{\sqrt{\tanh (x)+1}}\right)","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}-\frac{1}{2 \sqrt{\tanh (x)+1}}-\frac{1}{3 (\tanh (x)+1)^{3/2}}",1,"(3*Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]] - (2*(Cosh[x] - Sinh[x])*(5*Cosh[x] + 3*Sinh[x]))/Sqrt[1 + Tanh[x]])/12","A",1
56,1,62,61,0.2344305,"\int \frac{1}{(1+\tanh (x))^{5/2}} \, dx","Integrate[(1 + Tanh[x])^(-5/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{4 \sqrt{2}}+\frac{(\sinh (2 x)-\cosh (2 x)) (20 \sinh (2 x)+26 \cosh (2 x)+11)}{60 \sqrt{\tanh (x)+1}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{4 \sqrt{2}}-\frac{1}{4 \sqrt{\tanh (x)+1}}-\frac{1}{6 (\tanh (x)+1)^{3/2}}-\frac{1}{5 (\tanh (x)+1)^{5/2}}",1,"ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]]/(4*Sqrt[2]) + ((-Cosh[2*x] + Sinh[2*x])*(11 + 26*Cosh[2*x] + 20*Sinh[2*x]))/(60*Sqrt[1 + Tanh[x]])","A",1
57,1,114,142,0.6829868,"\int (a+b \tanh (c+d x))^5 \, dx","Integrate[(a + b*Tanh[c + d*x])^5,x]","-\frac{60 a b^2 \left(2 a^2+b^2\right) \tanh (c+d x)+6 b^3 \left(10 a^2+b^2\right) \tanh ^2(c+d x)+20 a b^4 \tanh ^3(c+d x)-6 (a-b)^5 \log (\tanh (c+d x)+1)+6 (a+b)^5 \log (1-\tanh (c+d x))+3 b^5 \tanh ^4(c+d x)}{12 d}","-\frac{b \left(3 a^2+b^2\right) (a+b \tanh (c+d x))^2}{2 d}-\frac{4 a b^2 \left(a^2+b^2\right) \tanh (c+d x)}{d}+\frac{b \left(5 a^4+10 a^2 b^2+b^4\right) \log (\cosh (c+d x))}{d}+a x \left(a^4+10 a^2 b^2+5 b^4\right)-\frac{b (a+b \tanh (c+d x))^4}{4 d}-\frac{2 a b (a+b \tanh (c+d x))^3}{3 d}",1,"-1/12*(6*(a + b)^5*Log[1 - Tanh[c + d*x]] - 6*(a - b)^5*Log[1 + Tanh[c + d*x]] + 60*a*b^2*(2*a^2 + b^2)*Tanh[c + d*x] + 6*b^3*(10*a^2 + b^2)*Tanh[c + d*x]^2 + 20*a*b^4*Tanh[c + d*x]^3 + 3*b^5*Tanh[c + d*x]^4)/d","A",1
58,1,91,101,0.3635452,"\int (a+b \tanh (c+d x))^4 \, dx","Integrate[(a + b*Tanh[c + d*x])^4,x]","-\frac{6 b^2 \left(6 a^2+b^2\right) \tanh (c+d x)+12 a b^3 \tanh ^2(c+d x)-3 (a-b)^4 \log (\tanh (c+d x)+1)+3 (a+b)^4 \log (1-\tanh (c+d x))+2 b^4 \tanh ^3(c+d x)}{6 d}","-\frac{b^2 \left(3 a^2+b^2\right) \tanh (c+d x)}{d}+\frac{4 a b \left(a^2+b^2\right) \log (\cosh (c+d x))}{d}+x \left(a^4+6 a^2 b^2+b^4\right)-\frac{b (a+b \tanh (c+d x))^3}{3 d}-\frac{a b (a+b \tanh (c+d x))^2}{d}",1,"-1/6*(3*(a + b)^4*Log[1 - Tanh[c + d*x]] - 3*(a - b)^4*Log[1 + Tanh[c + d*x]] + 6*b^2*(6*a^2 + b^2)*Tanh[c + d*x] + 12*a*b^3*Tanh[c + d*x]^2 + 2*b^4*Tanh[c + d*x]^3)/d","A",1
59,1,67,69,0.3543126,"\int (a+b \tanh (c+d x))^3 \, dx","Integrate[(a + b*Tanh[c + d*x])^3,x]","-\frac{6 a b^2 \tanh (c+d x)+(a-b)^3 (-\log (\tanh (c+d x)+1))+(a+b)^3 \log (1-\tanh (c+d x))+b^3 \tanh ^2(c+d x)}{2 d}","\frac{b \left(3 a^2+b^2\right) \log (\cosh (c+d x))}{d}+a x \left(a^2+3 b^2\right)-\frac{2 a b^2 \tanh (c+d x)}{d}-\frac{b (a+b \tanh (c+d x))^2}{2 d}",1,"-1/2*((a + b)^3*Log[1 - Tanh[c + d*x]] - (a - b)^3*Log[1 + Tanh[c + d*x]] + 6*a*b^2*Tanh[c + d*x] + b^3*Tanh[c + d*x]^2)/d","A",1
60,1,54,38,0.1115718,"\int (a+b \tanh (c+d x))^2 \, dx","Integrate[(a + b*Tanh[c + d*x])^2,x]","\frac{(a-b)^2 \log (\tanh (c+d x)+1)-(a+b)^2 \log (1-\tanh (c+d x))-2 b^2 \tanh (c+d x)}{2 d}","x \left(a^2+b^2\right)+\frac{2 a b \log (\cosh (c+d x))}{d}-\frac{b^2 \tanh (c+d x)}{d}",1,"(-((a + b)^2*Log[1 - Tanh[c + d*x]]) + (a - b)^2*Log[1 + Tanh[c + d*x]] - 2*b^2*Tanh[c + d*x])/(2*d)","A",1
61,1,64,50,0.0902531,"\int \frac{1}{a+b \tanh (c+d x)} \, dx","Integrate[(a + b*Tanh[c + d*x])^(-1),x]","\frac{(b-a) \log (1-\tanh (c+d x))+(a+b) \log (\tanh (c+d x)+1)-2 b \log (a+b \tanh (c+d x))}{2 d (a-b) (a+b)}","\frac{a x}{a^2-b^2}-\frac{b \log (a \cosh (c+d x)+b \sinh (c+d x))}{d \left(a^2-b^2\right)}",1,"((-a + b)*Log[1 - Tanh[c + d*x]] + (a + b)*Log[1 + Tanh[c + d*x]] - 2*b*Log[a + b*Tanh[c + d*x]])/(2*(a - b)*(a + b)*d)","A",1
62,1,94,85,1.1761014,"\int \frac{1}{(a+b \tanh (c+d x))^2} \, dx","Integrate[(a + b*Tanh[c + d*x])^(-2),x]","\frac{\frac{2 b \left(\frac{a^2-b^2}{a+b \tanh (c+d x)}-2 a \log (a+b \tanh (c+d x))\right)}{\left(a^2-b^2\right)^2}-\frac{\log (1-\tanh (c+d x))}{(a+b)^2}+\frac{\log (\tanh (c+d x)+1)}{(a-b)^2}}{2 d}","\frac{b}{d \left(a^2-b^2\right) (a+b \tanh (c+d x))}-\frac{2 a b \log (a \cosh (c+d x)+b \sinh (c+d x))}{d \left(a^2-b^2\right)^2}+\frac{x \left(a^2+b^2\right)}{\left(a^2-b^2\right)^2}",1,"(-(Log[1 - Tanh[c + d*x]]/(a + b)^2) + Log[1 + Tanh[c + d*x]]/(a - b)^2 + (2*b*(-2*a*Log[a + b*Tanh[c + d*x]] + (a^2 - b^2)/(a + b*Tanh[c + d*x])))/(a^2 - b^2)^2)/(2*d)","A",1
63,1,122,129,2.4609045,"\int \frac{1}{(a+b \tanh (c+d x))^3} \, dx","Integrate[(a + b*Tanh[c + d*x])^(-3),x]","\frac{\frac{b \left(\frac{\left(a^2-b^2\right) \left(5 a^2+4 a b \tanh (c+d x)-b^2\right)}{(a+b \tanh (c+d x))^2}-2 \left(3 a^2+b^2\right) \log (a+b \tanh (c+d x))\right)}{\left(a^2-b^2\right)^3}-\frac{\log (1-\tanh (c+d x))}{(a+b)^3}+\frac{\log (\tanh (c+d x)+1)}{(a-b)^3}}{2 d}","\frac{2 a b}{d \left(a^2-b^2\right)^2 (a+b \tanh (c+d x))}+\frac{b}{2 d \left(a^2-b^2\right) (a+b \tanh (c+d x))^2}-\frac{b \left(3 a^2+b^2\right) \log (a \cosh (c+d x)+b \sinh (c+d x))}{d \left(a^2-b^2\right)^3}+\frac{a x \left(a^2+3 b^2\right)}{\left(a^2-b^2\right)^3}",1,"(-(Log[1 - Tanh[c + d*x]]/(a + b)^3) + Log[1 + Tanh[c + d*x]]/(a - b)^3 + (b*(-2*(3*a^2 + b^2)*Log[a + b*Tanh[c + d*x]] + ((a^2 - b^2)*(5*a^2 - b^2 + 4*a*b*Tanh[c + d*x]))/(a + b*Tanh[c + d*x])^2))/(a^2 - b^2)^3)/(2*d)","A",1
64,1,160,169,3.4297609,"\int \frac{1}{(a+b \tanh (c+d x))^4} \, dx","Integrate[(a + b*Tanh[c + d*x])^(-4),x]","\frac{\frac{2 b \left(\frac{\left(a^2-b^2\right) \left(13 a^4+3 b^2 \left(3 a^2+b^2\right) \tanh ^2(c+d x)+3 a b \left(7 a^2+b^2\right) \tanh (c+d x)-2 a^2 b^2+b^4\right)}{(a+b \tanh (c+d x))^3}-12 a \left(a^2+b^2\right) \log (a+b \tanh (c+d x))\right)}{\left(a^2-b^2\right)^4}-\frac{3 \log (1-\tanh (c+d x))}{(a+b)^4}+\frac{3 \log (\tanh (c+d x)+1)}{(a-b)^4}}{6 d}","\frac{b \left(3 a^2+b^2\right)}{d \left(a^2-b^2\right)^3 (a+b \tanh (c+d x))}+\frac{a b}{d \left(a^2-b^2\right)^2 (a+b \tanh (c+d x))^2}+\frac{b}{3 d \left(a^2-b^2\right) (a+b \tanh (c+d x))^3}-\frac{4 a b \left(a^2+b^2\right) \log (a \cosh (c+d x)+b \sinh (c+d x))}{d \left(a^2-b^2\right)^4}+\frac{x \left(a^4+6 a^2 b^2+b^4\right)}{\left(a^2-b^2\right)^4}",1,"((-3*Log[1 - Tanh[c + d*x]])/(a + b)^4 + (3*Log[1 + Tanh[c + d*x]])/(a - b)^4 + (2*b*(-12*a*(a^2 + b^2)*Log[a + b*Tanh[c + d*x]] + ((a^2 - b^2)*(13*a^4 - 2*a^2*b^2 + b^4 + 3*a*b*(7*a^2 + b^2)*Tanh[c + d*x] + 3*b^2*(3*a^2 + b^2)*Tanh[c + d*x]^2))/(a + b*Tanh[c + d*x])^3))/(a^2 - b^2)^4)/(6*d)","A",1
65,1,53,31,0.0344041,"\int \frac{1}{4+6 \tanh (c+d x)} \, dx","Integrate[(4 + 6*Tanh[c + d*x])^(-1),x]","-\frac{\log (1-\tanh (c+d x))}{20 d}-\frac{\log (\tanh (c+d x)+1)}{4 d}+\frac{3 \log (3 \tanh (c+d x)+2)}{10 d}","\frac{3 \log (3 \sinh (c+d x)+2 \cosh (c+d x))}{10 d}-\frac{x}{5}",1,"-1/20*Log[1 - Tanh[c + d*x]]/d - Log[1 + Tanh[c + d*x]]/(4*d) + (3*Log[2 + 3*Tanh[c + d*x]])/(10*d)","A",1
66,1,53,31,0.0325052,"\int \frac{1}{4-6 \tanh (c+d x)} \, dx","Integrate[(4 - 6*Tanh[c + d*x])^(-1),x]","-\frac{3 \log (2-3 \tanh (c+d x))}{10 d}+\frac{\log (1-\tanh (c+d x))}{4 d}+\frac{\log (\tanh (c+d x)+1)}{20 d}","-\frac{3 \log (2 \cosh (c+d x)-3 \sinh (c+d x))}{10 d}-\frac{x}{5}",1,"(-3*Log[2 - 3*Tanh[c + d*x]])/(10*d) + Log[1 - Tanh[c + d*x]]/(4*d) + Log[1 + Tanh[c + d*x]]/(20*d)","A",1
67,1,74,74,0.0871749,"\int \sqrt{a+b \tanh (c+d x)} \, dx","Integrate[Sqrt[a + b*Tanh[c + d*x]],x]","\frac{\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh (c+d x)}}{\sqrt{a+b}}\right)}{d}-\frac{\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh (c+d x)}}{\sqrt{a-b}}\right)}{d}","\frac{\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh (c+d x)}}{\sqrt{a+b}}\right)}{d}-\frac{\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh (c+d x)}}{\sqrt{a-b}}\right)}{d}",1,"-((Sqrt[a - b]*ArcTanh[Sqrt[a + b*Tanh[c + d*x]]/Sqrt[a - b]])/d) + (Sqrt[a + b]*ArcTanh[Sqrt[a + b*Tanh[c + d*x]]/Sqrt[a + b]])/d","A",1
68,1,74,74,0.0719269,"\int \frac{1}{\sqrt{a+b \tanh (c+d x)}} \, dx","Integrate[1/Sqrt[a + b*Tanh[c + d*x]],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh (c+d x)}}{\sqrt{a+b}}\right)}{d \sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh (c+d x)}}{\sqrt{a-b}}\right)}{d \sqrt{a-b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh (c+d x)}}{\sqrt{a+b}}\right)}{d \sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh (c+d x)}}{\sqrt{a-b}}\right)}{d \sqrt{a-b}}",1,"-(ArcTanh[Sqrt[a + b*Tanh[c + d*x]]/Sqrt[a - b]]/(Sqrt[a - b]*d)) + ArcTanh[Sqrt[a + b*Tanh[c + d*x]]/Sqrt[a + b]]/(Sqrt[a + b]*d)","A",1
69,1,42,60,0.0796509,"\int \frac{\sinh ^4(x)}{1+\tanh (x)} \, dx","Integrate[Sinh[x]^4/(1 + Tanh[x]),x]","\frac{1}{192} (12 x-3 \sinh (2 x)-3 \sinh (4 x)+\sinh (6 x)-15 \cosh (2 x)+6 \cosh (4 x)-\cosh (6 x))","\frac{x}{16}-\frac{1}{8 (1-\tanh (x))}-\frac{3}{16 (\tanh (x)+1)}+\frac{1}{32 (1-\tanh (x))^2}+\frac{5}{32 (\tanh (x)+1)^2}-\frac{1}{24 (\tanh (x)+1)^3}",1,"(12*x - 15*Cosh[2*x] + 6*Cosh[4*x] - Cosh[6*x] - 3*Sinh[2*x] - 3*Sinh[4*x] + Sinh[6*x])/192","A",1
70,1,34,25,0.063401,"\int \frac{\sinh ^3(x)}{1+\tanh (x)} \, dx","Integrate[Sinh[x]^3/(1 + Tanh[x]),x]","\frac{1}{120} (\cosh (x)-\sinh (x)) (-10 \sinh (2 x)+\sinh (4 x)-20 \cosh (2 x)+4 \cosh (4 x))","-\frac{\sinh ^5(x)}{5}+\frac{\cosh ^5(x)}{5}-\frac{\cosh ^3(x)}{3}",1,"((Cosh[x] - Sinh[x])*(-20*Cosh[2*x] + 4*Cosh[4*x] - 10*Sinh[2*x] + Sinh[4*x]))/120","A",1
71,1,24,38,0.0386037,"\int \frac{\sinh ^2(x)}{1+\tanh (x)} \, dx","Integrate[Sinh[x]^2/(1 + Tanh[x]),x]","\frac{1}{32} (-4 x+\sinh (4 x)+4 \cosh (2 x)-\cosh (4 x))","-\frac{x}{8}+\frac{1}{8 (1-\tanh (x))}+\frac{1}{4 (\tanh (x)+1)}-\frac{1}{8 (\tanh (x)+1)^2}",1,"(-4*x + 4*Cosh[2*x] - Cosh[4*x] + Sinh[4*x])/32","A",1
72,1,19,17,0.018943,"\int \frac{\sinh (x)}{1+\tanh (x)} \, dx","Integrate[Sinh[x]/(1 + Tanh[x]),x]","\frac{1}{12} \left(-4 \sinh ^3(x)+3 \cosh (x)+\cosh (3 x)\right)","\frac{\cosh ^3(x)}{3}-\frac{\sinh ^3(x)}{3}",1,"(3*Cosh[x] + Cosh[3*x] - 4*Sinh[x]^3)/12","A",1
73,1,14,12,0.0224388,"\int \frac{\text{csch}(x)}{1+\tanh (x)} \, dx","Integrate[Csch[x]/(1 + Tanh[x]),x]","-\sinh (x)+\cosh (x)+\log \left(\tanh \left(\frac{x}{2}\right)\right)","-\sinh (x)+\cosh (x)-\tanh ^{-1}(\cosh (x))",1,"Cosh[x] + Log[Tanh[x/2]] - Sinh[x]","A",1
74,1,11,15,0.030679,"\int \frac{\text{csch}^2(x)}{1+\tanh (x)} \, dx","Integrate[Csch[x]^2/(1 + Tanh[x]),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
75,1,20,18,0.0831316,"\int \frac{\text{csch}^3(x)}{1+\tanh (x)} \, dx","Integrate[Csch[x]^3/(1 + Tanh[x]),x]","\frac{1}{2} \left(\log \left(\tanh \left(\frac{x}{2}\right)\right)-(\coth (x)-2) \text{csch}(x)\right)","\text{csch}(x)-\frac{1}{2} \tanh ^{-1}(\cosh (x))-\frac{1}{2} \coth (x) \text{csch}(x)",1,"(-((-2 + Coth[x])*Csch[x]) + Log[Tanh[x/2]])/2","A",1
76,1,20,17,0.0506774,"\int \frac{\text{csch}^4(x)}{1+\tanh (x)} \, dx","Integrate[Csch[x]^4/(1 + Tanh[x]),x]","-\frac{1}{6} \text{csch}(x) (2 \cosh (x)+(2 \coth (x)-3) \text{csch}(x))","\frac{\coth ^2(x)}{2}-\frac{\coth ^3(x)}{3}",1,"-1/6*(Csch[x]*(2*Cosh[x] + (-3 + 2*Coth[x])*Csch[x]))","A",1
77,1,49,34,0.1244143,"\int \frac{\text{csch}^5(x)}{1+\tanh (x)} \, dx","Integrate[Csch[x]^5/(1 + Tanh[x]),x]","-\frac{1}{192} \text{csch}^4(x) \left(42 \cosh (x)+6 \cosh (3 x)+2 \sinh (x) \left(-9 \sinh (x) \log \left(\tanh \left(\frac{x}{2}\right)\right)+3 \sinh (3 x) \log \left(\tanh \left(\frac{x}{2}\right)\right)-32\right)\right)","\frac{\text{csch}^3(x)}{3}+\frac{1}{8} \tanh ^{-1}(\cosh (x))-\frac{1}{4} \coth (x) \text{csch}^3(x)-\frac{1}{8} \coth (x) \text{csch}(x)",1,"-1/192*(Csch[x]^4*(42*Cosh[x] + 6*Cosh[3*x] + 2*Sinh[x]*(-32 - 9*Log[Tanh[x/2]]*Sinh[x] + 3*Log[Tanh[x/2]]*Sinh[3*x])))","A",1
78,1,27,33,0.0536578,"\int \frac{\text{csch}^6(x)}{1+\tanh (x)} \, dx","Integrate[Csch[x]^6/(1 + Tanh[x]),x]","\frac{1}{120} \text{csch}^5(x) (30 \sinh (x)-20 \cosh (x)-5 \cosh (3 x)+\cosh (5 x))","-\frac{1}{5} \coth ^5(x)+\frac{\coth ^4(x)}{4}+\frac{\coth ^3(x)}{3}-\frac{\coth ^2(x)}{2}",1,"(Csch[x]^5*(-20*Cosh[x] - 5*Cosh[3*x] + Cosh[5*x] + 30*Sinh[x]))/120","A",1
79,1,68,44,0.2823031,"\int \frac{\text{csch}^7(x)}{1+\tanh (x)} \, dx","Integrate[Csch[x]^7/(1 + Tanh[x]),x]","\frac{\text{csch}^6(x) \left(-1140 \cosh (x)-170 \cosh (3 x)+30 \cosh (5 x)+6 \sinh (x) \left(50 \sinh (x) \log \left(\tanh \left(\frac{x}{2}\right)\right)-25 \sinh (3 x) \log \left(\tanh \left(\frac{x}{2}\right)\right)+5 \sinh (5 x) \log \left(\tanh \left(\frac{x}{2}\right)\right)+256\right)\right)}{7680}","\frac{\text{csch}^5(x)}{5}-\frac{1}{16} \tanh ^{-1}(\cosh (x))-\frac{1}{6} \coth (x) \text{csch}^5(x)-\frac{1}{24} \coth (x) \text{csch}^3(x)+\frac{1}{16} \coth (x) \text{csch}(x)",1,"(Csch[x]^6*(-1140*Cosh[x] - 170*Cosh[3*x] + 30*Cosh[5*x] + 6*Sinh[x]*(256 + 50*Log[Tanh[x/2]]*Sinh[x] - 25*Log[Tanh[x/2]]*Sinh[3*x] + 5*Log[Tanh[x/2]]*Sinh[5*x])))/7680","A",1
80,1,144,147,0.5963961,"\int \frac{\sinh ^4(x)}{a+b \tanh (x)} \, dx","Integrate[Sinh[x]^4/(a + b*Tanh[x]),x]","\frac{12 a^5 x+a^5 \sinh (4 x)-32 a^4 b \log (a \cosh (x)+b \sinh (x))+24 a^3 b^2 x-2 a^3 b^2 \sinh (4 x)-b \left(a^2-b^2\right)^2 \cosh (4 x)+4 b \left(3 a^4-4 a^2 b^2+b^4\right) \cosh (2 x)-8 a^3 \left(a^2-b^2\right) \sinh (2 x)-4 a b^4 x+a b^4 \sinh (4 x)}{32 (a-b)^3 (a+b)^3}","-\frac{\cosh ^4(x) (b-a \tanh (x))}{4 \left(a^2-b^2\right)}+\frac{\cosh ^2(x) \left(4 b \left(2 a^2-b^2\right)-a \left(5 a^2-b^2\right) \tanh (x)\right)}{8 \left(a^2-b^2\right)^2}-\frac{a^4 b \log (a+b \tanh (x))}{\left(a^2-b^2\right)^3}-\frac{a (3 a+b) \log (1-\tanh (x))}{16 (a+b)^3}+\frac{a (3 a-b) \log (\tanh (x)+1)}{16 (a-b)^3}",1,"(12*a^5*x + 24*a^3*b^2*x - 4*a*b^4*x + 4*b*(3*a^4 - 4*a^2*b^2 + b^4)*Cosh[2*x] - b*(a^2 - b^2)^2*Cosh[4*x] - 32*a^4*b*Log[a*Cosh[x] + b*Sinh[x]] - 8*a^3*(a^2 - b^2)*Sinh[2*x] + a^5*Sinh[4*x] - 2*a^3*b^2*Sinh[4*x] + a*b^4*Sinh[4*x])/(32*(a - b)^3*(a + b)^3)","A",1
81,1,180,137,1.2342534,"\int \frac{\sinh ^3(x)}{a+b \tanh (x)} \, dx","Integrate[Sinh[x]^3/(a + b*Tanh[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
82,1,73,84,0.2671846,"\int \frac{\sinh ^2(x)}{a+b \tanh (x)} \, dx","Integrate[Sinh[x]^2/(a + b*Tanh[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^2 b \log (a+b \tanh (x))}{\left(a^2-b^2\right)^2}-\frac{\cosh ^2(x) (b-a \tanh (x))}{2 \left(a^2-b^2\right)}+\frac{a \log (1-\tanh (x))}{4 (a+b)^2}-\frac{a \log (\tanh (x)+1)}{4 (a-b)^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
83,1,79,72,0.2356762,"\int \frac{\sinh (x)}{a+b \tanh (x)} \, dx","Integrate[Sinh[x]/(a + b*Tanh[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
84,1,59,52,0.1007192,"\int \frac{\text{csch}(x)}{a+b \tanh (x)} \, dx","Integrate[Csch[x]/(a + b*Tanh[x]),x]","\frac{\log \left(\tanh \left(\frac{x}{2}\right)\right)-\frac{2 b \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}}}{a}","-\frac{b \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{a \sqrt{a^2-b^2}}-\frac{\tanh ^{-1}(\cosh (x))}{a}",1,"((-2*b*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])])/(Sqrt[a - b]*Sqrt[a + b]) + Log[Tanh[x/2]])/a","A",1
85,1,28,29,0.0988938,"\int \frac{\text{csch}^2(x)}{a+b \tanh (x)} \, dx","Integrate[Csch[x]^2/(a + b*Tanh[x]),x]","-\frac{-b \log (a \cosh (x)+b \sinh (x))+a \coth (x)+b \log (\sinh (x))}{a^2}","-\frac{b \log (\tanh (x))}{a^2}+\frac{b \log (a+b \tanh (x))}{a^2}-\frac{\coth (x)}{a}",1,"-((a*Coth[x] + b*Log[Sinh[x]] - b*Log[a*Cosh[x] + b*Sinh[x]])/a^2)","A",1
86,1,123,82,0.3722054,"\int \frac{\text{csch}^3(x)}{a+b \tanh (x)} \, dx","Integrate[Csch[x]^3/(a + b*Tanh[x]),x]","-\frac{a^2 \text{csch}^2\left(\frac{x}{2}\right)+a^2 \text{sech}^2\left(\frac{x}{2}\right)+4 a^2 \log \left(\tanh \left(\frac{x}{2}\right)\right)+4 a b \tanh \left(\frac{x}{2}\right)-4 a b \coth \left(\frac{x}{2}\right)-16 b \sqrt{a-b} \sqrt{a+b} \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)-8 b^2 \log \left(\tanh \left(\frac{x}{2}\right)\right)}{8 a^3}","-\frac{b^2 \tanh ^{-1}(\cosh (x))}{a^3}+\frac{b \text{csch}(x)}{a^2}+\frac{b \sqrt{a^2-b^2} \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{a^3}+\frac{\tanh ^{-1}(\cosh (x))}{2 a}-\frac{\coth (x) \text{csch}(x)}{2 a}",1,"-1/8*(-16*Sqrt[a - b]*b*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])] - 4*a*b*Coth[x/2] + a^2*Csch[x/2]^2 + 4*a^2*Log[Tanh[x/2]] - 8*b^2*Log[Tanh[x/2]] + a^2*Sech[x/2]^2 + 4*a*b*Tanh[x/2])/a^3","A",1
87,1,70,78,0.2895766,"\int \frac{\text{csch}^4(x)}{a+b \tanh (x)} \, dx","Integrate[Csch[x]^4/(a + b*Tanh[x]),x]","\frac{-2 \coth (x) \left(a^3 \text{csch}^2(x)-2 a^3+3 a b^2\right)+6 b \left(a^2-b^2\right) (\log (\sinh (x))-\log (a \cosh (x)+b \sinh (x)))+3 a^2 b \text{csch}^2(x)}{6 a^4}","\frac{b \coth ^2(x)}{2 a^2}+\frac{b \left(a^2-b^2\right) \log (\tanh (x))}{a^4}-\frac{b \left(a^2-b^2\right) \log (a+b \tanh (x))}{a^4}+\frac{\left(a^2-b^2\right) \coth (x)}{a^3}-\frac{\coth ^3(x)}{3 a}",1,"(3*a^2*b*Csch[x]^2 - 2*Coth[x]*(-2*a^3 + 3*a*b^2 + a^3*Csch[x]^2) + 6*b*(a^2 - b^2)*(Log[Sinh[x]] - Log[a*Cosh[x] + b*Sinh[x]]))/(6*a^4)","A",1
88,1,296,255,0.8902196,"\int \frac{\text{csch}^5(x)}{a+b \tanh (x)} \, dx","Integrate[Csch[x]^5/(a + b*Tanh[x]),x]","\frac{3 a^4 \text{sech}^4\left(\frac{x}{2}\right)+18 a^4 \text{sech}^2\left(\frac{x}{2}\right)+72 a^4 \log \left(\tanh \left(\frac{x}{2}\right)\right)+112 a^3 b \tanh \left(\frac{x}{2}\right)+a^3 \text{csch}^4\left(\frac{x}{2}\right) (4 b \sinh (x)-3 a)+64 a^3 b \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)-16 a b \left(7 a^2-6 b^2\right) \coth \left(\frac{x}{2}\right)+6 a^2 \left(3 a^2-4 b^2\right) \text{csch}^2\left(\frac{x}{2}\right)-24 a^2 b^2 \text{sech}^2\left(\frac{x}{2}\right)-288 a^2 b^2 \log \left(\tanh \left(\frac{x}{2}\right)\right)-384 a^2 b \sqrt{a-b} \sqrt{a+b} \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)-96 a b^3 \tanh \left(\frac{x}{2}\right)+384 b^3 \sqrt{a-b} \sqrt{a+b} \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+192 b^4 \log \left(\tanh \left(\frac{x}{2}\right)\right)}{192 a^5}","\frac{b^4 \text{sech}(x)}{a^5}-\frac{b^4 \tanh ^{-1}(\cosh (x))}{a^5}+\frac{3 b^3 \text{csch}(x)}{2 a^4}+\frac{b^3 \tan ^{-1}(\sinh (x))}{a^4}-\frac{b^3 \text{csch}(x) \text{sech}^2(x)}{2 a^4}-\frac{b^3 \tanh (x) \text{sech}(x)}{2 a^4}-\frac{3 b^2 \text{sech}(x)}{2 a^3}+\frac{3 b^2 \tanh ^{-1}(\cosh (x))}{2 a^3}-\frac{b^2 \text{csch}^2(x) \text{sech}(x)}{2 a^3}+\frac{b \text{csch}^3(x)}{3 a^2}-\frac{b \text{csch}(x)}{a^2}-\frac{b \tan ^{-1}(\sinh (x))}{a^2}+\frac{b^2 \left(a^2-b^2\right) \text{sech}(x)}{a^5}-\frac{b \left(a^2-b^2\right)^{3/2} \tan ^{-1}\left(\frac{a \sinh (x)+b \cosh (x)}{\sqrt{a^2-b^2}}\right)}{a^5}+\frac{b \left(a^2-b^2\right) \tan ^{-1}(\sinh (x))}{a^4}-\frac{3 \tanh ^{-1}(\cosh (x))}{8 a}-\frac{\coth (x) \text{csch}^3(x)}{4 a}+\frac{3 \coth (x) \text{csch}(x)}{8 a}",1,"(-384*a^2*Sqrt[a - b]*b*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])] + 384*Sqrt[a - b]*b^3*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])] - 16*a*b*(7*a^2 - 6*b^2)*Coth[x/2] + 6*a^2*(3*a^2 - 4*b^2)*Csch[x/2]^2 + 72*a^4*Log[Tanh[x/2]] - 288*a^2*b^2*Log[Tanh[x/2]] + 192*b^4*Log[Tanh[x/2]] + 18*a^4*Sech[x/2]^2 - 24*a^2*b^2*Sech[x/2]^2 + 3*a^4*Sech[x/2]^4 + 64*a^3*b*Csch[x]^3*Sinh[x/2]^4 + a^3*Csch[x/2]^4*(-3*a + 4*b*Sinh[x]) + 112*a^3*b*Tanh[x/2] - 96*a*b^3*Tanh[x/2])/(192*a^5)","A",1
89,1,119,130,0.6877221,"\int \frac{\text{csch}^6(x)}{a+b \tanh (x)} \, dx","Integrate[Csch[x]^6/(a + b*Tanh[x]),x]","\frac{15 b \left(a^4 \text{csch}^4(x)-2 a^2 \left(a^2-b^2\right) \text{csch}^2(x)-4 \left(a^2-b^2\right)^2 (\log (\sinh (x))-\log (a \cosh (x)+b \sinh (x)))\right)-4 \coth (x) \left(3 a^5 \text{csch}^4(x)+8 a^5-25 a^3 b^2+\left(5 a^3 b^2-4 a^5\right) \text{csch}^2(x)+15 a b^4\right)}{60 a^6}","\frac{b \coth ^4(x)}{4 a^2}-\frac{b \left(a^2-b^2\right)^2 \log (\tanh (x))}{a^6}+\frac{b \left(a^2-b^2\right)^2 \log (a+b \tanh (x))}{a^6}-\frac{\left(a^2-b^2\right)^2 \coth (x)}{a^5}-\frac{b \left(2 a^2-b^2\right) \coth ^2(x)}{2 a^4}+\frac{\left(2 a^2-b^2\right) \coth ^3(x)}{3 a^3}-\frac{\coth ^5(x)}{5 a}",1,"(-4*Coth[x]*(8*a^5 - 25*a^3*b^2 + 15*a*b^4 + (-4*a^5 + 5*a^3*b^2)*Csch[x]^2 + 3*a^5*Csch[x]^4) + 15*b*(-2*a^2*(a^2 - b^2)*Csch[x]^2 + a^4*Csch[x]^4 - 4*(a^2 - b^2)^2*(Log[Sinh[x]] - Log[a*Cosh[x] + b*Sinh[x]])))/(60*a^6)","A",1
90,1,46,33,0.0719662,"\int \frac{\text{csch}(x)}{i+\tanh (x)} \, dx","Integrate[Csch[x]/(I + Tanh[x]),x]","-i \left(\sqrt{2} \tanh ^{-1}\left(\frac{1+i \tanh \left(\frac{x}{2}\right)}{\sqrt{2}}\right)+\log \left(\sinh \left(\frac{x}{2}\right)\right)-\log \left(\cosh \left(\frac{x}{2}\right)\right)\right)","i \tanh ^{-1}(\cosh (x))-\frac{i \tanh ^{-1}\left(\frac{\cosh (x)+i \sinh (x)}{\sqrt{2}}\right)}{\sqrt{2}}",1,"(-I)*(Sqrt[2]*ArcTanh[(1 + I*Tanh[x/2])/Sqrt[2]] - Log[Cosh[x/2]] + Log[Sinh[x/2]])","A",1
91,1,42,60,0.0503156,"\int \frac{\cosh ^4(x)}{1+\tanh (x)} \, dx","Integrate[Cosh[x]^4/(1 + Tanh[x]),x]","\frac{1}{192} (60 x+45 \sinh (2 x)+9 \sinh (4 x)+\sinh (6 x)-15 \cosh (2 x)-6 \cosh (4 x)-\cosh (6 x))","\frac{5 x}{16}+\frac{1}{8 (1-\tanh (x))}-\frac{3}{16 (\tanh (x)+1)}+\frac{1}{32 (1-\tanh (x))^2}-\frac{3}{32 (\tanh (x)+1)^2}-\frac{1}{24 (\tanh (x)+1)^3}",1,"(60*x - 15*Cosh[2*x] - 6*Cosh[4*x] - Cosh[6*x] + 45*Sinh[2*x] + 9*Sinh[4*x] + Sinh[6*x])/192","A",1
92,1,36,29,0.0495482,"\int \frac{\cosh ^3(x)}{1+\tanh (x)} \, dx","Integrate[Cosh[x]^3/(1 + Tanh[x]),x]","\frac{\text{sech}(x) (40 \sinh (2 x)+4 \sinh (4 x)+20 \cosh (2 x)+\cosh (4 x)-45)}{120 (\tanh (x)+1)}","\frac{4 \sinh ^3(x)}{15}+\frac{4 \sinh (x)}{5}-\frac{\cosh ^3(x)}{5 (\tanh (x)+1)}",1,"(Sech[x]*(-45 + 20*Cosh[2*x] + Cosh[4*x] + 40*Sinh[2*x] + 4*Sinh[4*x]))/(120*(1 + Tanh[x]))","A",1
93,1,30,38,0.0341528,"\int \frac{\cosh ^2(x)}{1+\tanh (x)} \, dx","Integrate[Cosh[x]^2/(1 + Tanh[x]),x]","\frac{1}{32} (12 x+8 \sinh (2 x)+\sinh (4 x)-4 \cosh (2 x)-\cosh (4 x))","\frac{3 x}{8}+\frac{1}{8 (1-\tanh (x))}-\frac{1}{4 (\tanh (x)+1)}-\frac{1}{8 (\tanh (x)+1)^2}",1,"(12*x - 4*Cosh[2*x] - Cosh[4*x] + 8*Sinh[2*x] + Sinh[4*x])/32","A",1
94,1,23,19,0.0303522,"\int \frac{\cosh (x)}{1+\tanh (x)} \, dx","Integrate[Cosh[x]/(1 + Tanh[x]),x]","\frac{1}{12} (9 \sinh (x)+\sinh (3 x)-3 \cosh (x)-\cosh (3 x))","\frac{2 \sinh (x)}{3}-\frac{\cosh (x)}{3 (\tanh (x)+1)}",1,"(-3*Cosh[x] - Cosh[3*x] + 9*Sinh[x] + Sinh[3*x])/12","A",1
95,1,7,10,0.0037824,"\int \frac{\text{sech}(x)}{1+\tanh (x)} \, dx","Integrate[Sech[x]/(1 + Tanh[x]),x]","\sinh (x)-\cosh (x)","-\frac{\text{sech}(x)}{\tanh (x)+1}",1,"-Cosh[x] + Sinh[x]","A",1
96,1,7,5,0.0042469,"\int \frac{\text{sech}^2(x)}{1+\tanh (x)} \, dx","Integrate[Sech[x]^2/(1 + Tanh[x]),x]","x-\log (\cosh (x))","\log (\tanh (x)+1)",1,"x - Log[Cosh[x]]","A",1
97,1,12,6,0.0264511,"\int \frac{\text{sech}^3(x)}{1+\tanh (x)} \, dx","Integrate[Sech[x]^3/(1 + Tanh[x]),x]","\text{sech}(x)+2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)","\text{sech}(x)+\tan ^{-1}(\sinh (x))",1,"2*ArcTan[Tanh[x/2]] + Sech[x]","A",1
98,1,11,11,0.0261845,"\int \frac{\text{sech}^4(x)}{1+\tanh (x)} \, dx","Integrate[Sech[x]^4/(1 + Tanh[x]),x]","\tanh (x)+\frac{\text{sech}^2(x)}{2}","\tanh (x)-\frac{\tanh ^2(x)}{2}",1,"Sech[x]^2/2 + Tanh[x]","A",1
99,1,24,24,0.0299647,"\int \frac{\text{sech}^5(x)}{1+\tanh (x)} \, dx","Integrate[Sech[x]^5/(1 + Tanh[x]),x]","\frac{\text{sech}^3(x)}{3}+\tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+\frac{1}{2} \tanh (x) \text{sech}(x)","\frac{\text{sech}^3(x)}{3}+\frac{1}{2} \tan ^{-1}(\sinh (x))+\frac{1}{2} \tanh (x) \text{sech}(x)",1,"ArcTan[Tanh[x/2]] + Sech[x]^3/3 + (Sech[x]*Tanh[x])/2","A",1
100,1,20,25,0.0310833,"\int \frac{\text{sech}^6(x)}{1+\tanh (x)} \, dx","Integrate[Sech[x]^6/(1 + Tanh[x]),x]","\frac{1}{12} (4 \sinh (2 x)+\sinh (4 x)+3) \text{sech}^4(x)","\frac{1}{4} (1-\tanh (x))^4-\frac{2}{3} (1-\tanh (x))^3",1,"(Sech[x]^4*(3 + 4*Sinh[2*x] + Sinh[4*x]))/12","A",1
101,1,34,34,0.0363298,"\int \frac{\text{sech}^7(x)}{1+\tanh (x)} \, dx","Integrate[Sech[x]^7/(1 + Tanh[x]),x]","\frac{1}{40} \left(8 \text{sech}^5(x)+30 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+10 \tanh (x) \text{sech}^3(x)+15 \tanh (x) \text{sech}(x)\right)","\frac{\text{sech}^5(x)}{5}+\frac{3}{8} \tan ^{-1}(\sinh (x))+\frac{1}{4} \tanh (x) \text{sech}^3(x)+\frac{3}{8} \tanh (x) \text{sech}(x)",1,"(30*ArcTan[Tanh[x/2]] + 8*Sech[x]^5 + 15*Sech[x]*Tanh[x] + 10*Sech[x]^3*Tanh[x])/40","A",1
102,1,137,140,0.6428502,"\int \frac{\text{sech}^8(x)}{a+b \tanh (x)} \, dx","Integrate[Sech[x]^8/(a + b*Tanh[x]),x]","\frac{2 b^2 \text{sech}^2(x) \left(15 \left(a^2-b^2\right)^2-2 a b \left(5 a^2-9 b^2\right) \tanh (x)\right)+60 \left(a^2-b^2\right)^3 (\log (\cosh (x))-\log (a \cosh (x)+b \sinh (x)))+3 b^4 \text{sech}^4(x) \left(-5 a^2+4 a b \tanh (x)+5 b^2\right)+4 a b \left(15 a^4-40 a^2 b^2+33 b^4\right) \tanh (x)+10 b^6 \text{sech}^6(x)}{60 b^7}","-\frac{\left(a^2-b^2\right)^3 \log (a+b \tanh (x))}{b^7}+\frac{a \left(a^2-3 b^2\right) \tanh ^3(x)}{3 b^4}-\frac{\left(a^2-3 b^2\right) \tanh ^4(x)}{4 b^3}+\frac{a \left(a^4-3 a^2 b^2+3 b^4\right) \tanh (x)}{b^6}-\frac{\left(a^4-3 a^2 b^2+3 b^4\right) \tanh ^2(x)}{2 b^5}+\frac{a \tanh ^5(x)}{5 b^2}-\frac{\tanh ^6(x)}{6 b}",1,"(60*(a^2 - b^2)^3*(Log[Cosh[x]] - Log[a*Cosh[x] + b*Sinh[x]]) + 10*b^6*Sech[x]^6 + 4*a*b*(15*a^4 - 40*a^2*b^2 + 33*b^4)*Tanh[x] + 3*b^4*Sech[x]^4*(-5*a^2 + 5*b^2 + 4*a*b*Tanh[x]) + 2*b^2*Sech[x]^2*(15*(a^2 - b^2)^2 - 2*a*b*(5*a^2 - 9*b^2)*Tanh[x]))/(60*b^7)","A",1
103,1,92,83,0.4056537,"\int \frac{\text{sech}^6(x)}{a+b \tanh (x)} \, dx","Integrate[Sech[x]^6/(a + b*Tanh[x]),x]","\frac{-4 \left(a b \left(3 a^2-5 b^2\right) \tanh (x)+3 \left(a^2-b^2\right)^2 (\log (\cosh (x))-\log (a \cosh (x)+b \sinh (x)))\right)+\text{sech}^2(x) \left(-6 a^2 b^2+4 a b^3 \tanh (x)+6 b^4\right)+3 b^4 \text{sech}^4(x)}{12 b^5}","\frac{\left(a^2-b^2\right)^2 \log (a+b \tanh (x))}{b^5}-\frac{a \left(a^2-2 b^2\right) \tanh (x)}{b^4}+\frac{\left(a^2-2 b^2\right) \tanh ^2(x)}{2 b^3}-\frac{a \tanh ^3(x)}{3 b^2}+\frac{\tanh ^4(x)}{4 b}",1,"(3*b^4*Sech[x]^4 + Sech[x]^2*(-6*a^2*b^2 + 6*b^4 + 4*a*b^3*Tanh[x]) - 4*(3*(a^2 - b^2)^2*(Log[Cosh[x]] - Log[a*Cosh[x] + b*Sinh[x]]) + a*b*(3*a^2 - 5*b^2)*Tanh[x]))/(12*b^5)","A",1
104,1,49,40,0.1897196,"\int \frac{\text{sech}^4(x)}{a+b \tanh (x)} \, dx","Integrate[Sech[x]^4/(a + b*Tanh[x]),x]","\frac{2 \left(a^2-b^2\right) (\log (\cosh (x))-\log (a \cosh (x)+b \sinh (x)))+2 a b \tanh (x)+b^2 \text{sech}^2(x)}{2 b^3}","-\frac{\left(a^2-b^2\right) \log (a+b \tanh (x))}{b^3}+\frac{a \tanh (x)}{b^2}-\frac{\tanh ^2(x)}{2 b}",1,"(2*(a^2 - b^2)*(Log[Cosh[x]] - Log[a*Cosh[x] + b*Sinh[x]]) + b^2*Sech[x]^2 + 2*a*b*Tanh[x])/(2*b^3)","A",1
105,1,20,11,0.0504918,"\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
106,1,29,39,0.0573815,"\int \frac{1}{a+b \tanh (x)} \, dx","Integrate[(a + b*Tanh[x])^(-1),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
107,1,75,91,0.1311074,"\int \frac{\cosh ^2(x)}{a+b \tanh (x)} \, dx","Integrate[Cosh[x]^2/(a + b*Tanh[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{\cosh ^2(x) (b-a \tanh (x))}{2 \left(a^2-b^2\right)}+\frac{b^3 \log (a+b \tanh (x))}{\left(a^2-b^2\right)^2}-\frac{(a+2 b) \log (1-\tanh (x))}{4 (a+b)^2}+\frac{(a-2 b) \log (\tanh (x)+1)}{4 (a-b)^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
108,1,156,155,0.2154696,"\int \frac{\cosh ^4(x)}{a+b \tanh (x)} \, dx","Integrate[Cosh[x]^4/(a + b*Tanh[x]),x]","\frac{12 a^5 x+8 a^5 \sinh (2 x)+a^5 \sinh (4 x)-40 a^3 b^2 x-24 a^3 b^2 \sinh (2 x)-2 a^3 b^2 \sinh (4 x)-b \left(a^2-b^2\right)^2 \cosh (4 x)-4 b \left(a^4-4 a^2 b^2+3 b^4\right) \cosh (2 x)-32 b^5 \log (a \cosh (x)+b \sinh (x))+60 a b^4 x+16 a b^4 \sinh (2 x)+a b^4 \sinh (4 x)}{32 (a-b)^3 (a+b)^3}","-\frac{\left(3 a^2+9 a b+8 b^2\right) \log (1-\tanh (x))}{16 (a+b)^3}+\frac{\left(3 a^2-9 a b+8 b^2\right) \log (\tanh (x)+1)}{16 (a-b)^3}-\frac{\cosh ^4(x) (b-a \tanh (x))}{4 \left(a^2-b^2\right)}-\frac{b^5 \log (a+b \tanh (x))}{\left(a^2-b^2\right)^3}+\frac{\cosh ^2(x) \left(4 b^3-a b^2 \left(7-\frac{3 a^2}{b^2}\right) \tanh (x)\right)}{8 \left(a^2-b^2\right)^2}",1,"(12*a^5*x - 40*a^3*b^2*x + 60*a*b^4*x - 4*b*(a^4 - 4*a^2*b^2 + 3*b^4)*Cosh[2*x] - b*(a^2 - b^2)^2*Cosh[4*x] - 32*b^5*Log[a*Cosh[x] + b*Sinh[x]] + 8*a^5*Sinh[2*x] - 24*a^3*b^2*Sinh[2*x] + 16*a*b^4*Sinh[2*x] + a^5*Sinh[4*x] - 2*a^3*b^2*Sinh[4*x] + a*b^4*Sinh[4*x])/(32*(a - b)^3*(a + b)^3)","A",1
109,1,166,157,0.5274404,"\int \frac{\text{sech}^7(x)}{a+b \tanh (x)} \, dx","Integrate[Sech[x]^7/(a + b*Tanh[x]),x]","\frac{10 b^3 \text{sech}^3(x) \left(-4 a^2+3 a b \tanh (x)+4 b^2\right)+30 \left(a \left(8 a^4-20 a^2 b^2+15 b^4\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-8 \sqrt{a-b} \sqrt{a+b} \left(a^2-b^2\right)^2 \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)\right)+15 b \text{sech}(x) \left(\left(7 a b^3-4 a^3 b\right) \tanh (x)+8 \left(a^2-b^2\right)^2\right)+24 b^5 \text{sech}^5(x)}{120 b^6}","-\frac{\left(a^2-b^2\right)^{5/2} \tan ^{-1}\left(\frac{\cosh (x) (a \tanh (x)+b)}{\sqrt{a^2-b^2}}\right)}{b^6}+\frac{\left(a^2-b^2\right)^2 \text{sech}(x)}{b^5}-\frac{a \left(4 a^2-7 b^2\right) \tanh (x) \text{sech}(x)}{8 b^4}-\frac{\left(a^2-b^2\right) \text{sech}^3(x)}{3 b^3}+\frac{a \left(8 a^4-20 a^2 b^2+15 b^4\right) \tan ^{-1}(\sinh (x))}{8 b^6}+\frac{a \tanh (x) \text{sech}^3(x)}{4 b^2}+\frac{\text{sech}^5(x)}{5 b}",1,"(30*(a*(8*a^4 - 20*a^2*b^2 + 15*b^4)*ArcTan[Tanh[x/2]] - 8*Sqrt[a - b]*Sqrt[a + b]*(a^2 - b^2)^2*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]) + 24*b^5*Sech[x]^5 + 10*b^3*Sech[x]^3*(-4*a^2 + 4*b^2 + 3*a*b*Tanh[x]) + 15*b*Sech[x]*(8*(a^2 - b^2)^2 + (-4*a^3*b + 7*a*b^3)*Tanh[x]))/(120*b^6)","A",1
110,1,116,102,0.2787744,"\int \frac{\text{sech}^5(x)}{a+b \tanh (x)} \, dx","Integrate[Sech[x]^5/(a + b*Tanh[x]),x]","\frac{-6 \left(a \left(2 a^2-3 b^2\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+2 \sqrt{a-b} \sqrt{a+b} \left(b^2-a^2\right) \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)\right)+3 b \text{sech}(x) \left(-2 a^2+a b \tanh (x)+2 b^2\right)+2 b^3 \text{sech}^3(x)}{6 b^4}","-\frac{a \left(2 a^2-3 b^2\right) \tan ^{-1}(\sinh (x))}{2 b^4}+\frac{\left(a^2-b^2\right)^{3/2} \tan ^{-1}\left(\frac{\cosh (x) (a \tanh (x)+b)}{\sqrt{a^2-b^2}}\right)}{b^4}-\frac{\left(a^2-b^2\right) \text{sech}(x)}{b^3}+\frac{a \tanh (x) \text{sech}(x)}{2 b^2}+\frac{\text{sech}^3(x)}{3 b}",1,"(-6*(a*(2*a^2 - 3*b^2)*ArcTan[Tanh[x/2]] + 2*Sqrt[a - b]*Sqrt[a + b]*(-a^2 + b^2)*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])]) + 2*b^3*Sech[x]^3 + 3*b*Sech[x]*(-2*a^2 + 2*b^2 + a*b*Tanh[x]))/(6*b^4)","A",1
111,1,65,56,0.0883802,"\int \frac{\text{sech}^3(x)}{a+b \tanh (x)} \, dx","Integrate[Sech[x]^3/(a + b*Tanh[x]),x]","\frac{-2 \sqrt{a-b} \sqrt{a+b} \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)+2 a \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+b \text{sech}(x)}{b^2}","-\frac{\sqrt{a^2-b^2} \tan ^{-1}\left(\frac{\cosh (x) (a \tanh (x)+b)}{\sqrt{a^2-b^2}}\right)}{b^2}+\frac{a \tan ^{-1}(\sinh (x))}{b^2}+\frac{\text{sech}(x)}{b}",1,"(2*a*ArcTan[Tanh[x/2]] - 2*Sqrt[a - b]*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])] + b*Sech[x])/b^2","A",1
112,1,46,37,0.0320065,"\int \frac{\text{sech}(x)}{a+b \tanh (x)} \, dx","Integrate[Sech[x]/(a + b*Tanh[x]),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{\cosh (x) (a \tanh (x)+b)}{\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
113,1,80,73,0.2386385,"\int \frac{\cosh (x)}{a+b \tanh (x)} \, dx","Integrate[Cosh[x]/(a + b*Tanh[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{\cosh (x) (a \tanh (x)+b)}{\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
114,1,258,132,0.4767134,"\int \frac{\cosh ^3(x)}{a+b \tanh (x)} \, dx","Integrate[Cosh[x]^3/(a + b*Tanh[x]),x]","\frac{9 a^4 \sqrt{a-b} \sinh (x)+a^4 \sqrt{a-b} \sinh (3 x)+9 a^3 b \sqrt{a-b} \sinh (x)+a^3 b \sqrt{a-b} \sinh (3 x)-21 a^2 b^2 \sqrt{a-b} \sinh (x)-a^2 b^2 \sqrt{a-b} \sinh (3 x)-3 b \sqrt{a-b} \left(a^3+a^2 b-5 a b^2-5 b^3\right) \cosh (x)+24 b^4 \sqrt{a+b} \tan ^{-1}\left(\frac{a \tanh \left(\frac{x}{2}\right)+b}{\sqrt{a-b} \sqrt{a+b}}\right)-21 a b^3 \sqrt{a-b} \sinh (x)-a b^3 \sqrt{a-b} \sinh (3 x)-b (a-b)^{3/2} (a+b)^2 \cosh (3 x)}{12 (a-b)^{5/2} (a+b)^3}","\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{a \sinh (x)}{a^2-b^2}-\frac{b \cosh ^3(x)}{3 \left(a^2-b^2\right)}+\frac{b^4 \tan ^{-1}\left(\frac{\cosh (x) (a \tanh (x)+b)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}+\frac{b^3 \cosh (x)}{\left(a^2-b^2\right)^2}",1,"(24*b^4*Sqrt[a + b]*ArcTan[(b + a*Tanh[x/2])/(Sqrt[a - b]*Sqrt[a + b])] - 3*Sqrt[a - b]*b*(a^3 + a^2*b - 5*a*b^2 - 5*b^3)*Cosh[x] - (a - b)^(3/2)*b*(a + b)^2*Cosh[3*x] + 9*a^4*Sqrt[a - b]*Sinh[x] + 9*a^3*Sqrt[a - b]*b*Sinh[x] - 21*a^2*Sqrt[a - b]*b^2*Sinh[x] - 21*a*Sqrt[a - b]*b^3*Sinh[x] + a^4*Sqrt[a - b]*Sinh[3*x] + a^3*Sqrt[a - b]*b*Sinh[3*x] - a^2*Sqrt[a - b]*b^2*Sinh[3*x] - a*Sqrt[a - b]*b^3*Sinh[3*x])/(12*(a - b)^(5/2)*(a + b)^3)","A",1
115,1,40,43,0.1041363,"\int \frac{\tanh ^5(x)}{1+\tanh (x)} \, dx","Integrate[Tanh[x]^5/(1 + Tanh[x]),x]","\frac{1}{12} \left(30 x-3 \sinh (2 x)+3 \cosh (2 x)-28 \tanh (x)-24 \log (\cosh (x))+(4 \tanh (x)-6) \text{sech}^2(x)\right)","\frac{5 x}{2}+\frac{\tanh ^4(x)}{2 (\tanh (x)+1)}-\frac{5 \tanh ^3(x)}{6}+\tanh ^2(x)-\frac{5 \tanh (x)}{2}-2 \log (\cosh (x))",1,"(30*x + 3*Cosh[2*x] - 24*Log[Cosh[x]] - 3*Sinh[2*x] - 28*Tanh[x] + Sech[x]^2*(-6 + 4*Tanh[x]))/12","A",1
116,1,33,37,0.0572719,"\int \frac{\tanh ^4(x)}{1+\tanh (x)} \, dx","Integrate[Tanh[x]^4/(1 + Tanh[x]),x]","\frac{1}{4} \left(-6 x+\sinh (2 x)-\cosh (2 x)+4 \tanh (x)+2 \text{sech}^2(x)+8 \log (\cosh (x))\right)","-\frac{3 x}{2}+\frac{\tanh ^3(x)}{2 (\tanh (x)+1)}-\tanh ^2(x)+\frac{3 \tanh (x)}{2}+2 \log (\cosh (x))",1,"(-6*x - Cosh[2*x] + 8*Log[Cosh[x]] + 2*Sech[x]^2 + Sinh[2*x] + 4*Tanh[x])/4","A",1
117,1,27,31,0.0508506,"\int \frac{\tanh ^3(x)}{1+\tanh (x)} \, dx","Integrate[Tanh[x]^3/(1 + Tanh[x]),x]","\frac{1}{4} (6 x-\sinh (2 x)+\cosh (2 x)-4 \tanh (x)-4 \log (\cosh (x)))","\frac{3 x}{2}+\frac{\tanh ^2(x)}{2 (\tanh (x)+1)}-\frac{3 \tanh (x)}{2}-\log (\cosh (x))",1,"(6*x + Cosh[2*x] - 4*Log[Cosh[x]] - Sinh[2*x] - 4*Tanh[x])/4","A",1
118,1,23,19,0.0300324,"\int \frac{\tanh ^2(x)}{1+\tanh (x)} \, dx","Integrate[Tanh[x]^2/(1 + Tanh[x]),x]","\frac{1}{4} (-2 x+\sinh (2 x)-\cosh (2 x)+4 \log (\cosh (x)))","-\frac{x}{2}-\frac{1}{2 (\tanh (x)+1)}+\log (\cosh (x))",1,"(-2*x - Cosh[2*x] + 4*Log[Cosh[x]] + Sinh[2*x])/4","A",1
119,1,18,16,0.0272232,"\int \frac{\tanh (x)}{1+\tanh (x)} \, dx","Integrate[Tanh[x]/(1 + Tanh[x]),x]","\frac{1}{4} (2 x-\sinh (2 x)+\cosh (2 x))","\frac{x}{2}+\frac{1}{2 (\tanh (x)+1)}",1,"(2*x + Cosh[2*x] - Sinh[2*x])/4","A",1
120,1,18,16,0.0163646,"\int \frac{1}{1+\tanh (x)} \, dx","Integrate[(1 + Tanh[x])^(-1),x]","\frac{1}{4} (2 x+\sinh (2 x)-\cosh (2 x))","\frac{x}{2}-\frac{1}{2 (\tanh (x)+1)}",1,"(2*x - Cosh[2*x] + Sinh[2*x])/4","A",1
121,1,23,19,0.0314531,"\int \frac{\coth (x)}{1+\tanh (x)} \, dx","Integrate[Coth[x]/(1 + Tanh[x]),x]","\frac{1}{4} (-2 x-\sinh (2 x)+\cosh (2 x)+4 \log (\sinh (x)))","-\frac{x}{2}+\frac{1}{2 (\tanh (x)+1)}+\log (\sinh (x))",1,"(-2*x + Cosh[2*x] + 4*Log[Sinh[x]] - Sinh[2*x])/4","A",1
122,1,27,29,0.0476112,"\int \frac{\coth ^2(x)}{1+\tanh (x)} \, dx","Integrate[Coth[x]^2/(1 + Tanh[x]),x]","\frac{1}{4} (6 x+\sinh (2 x)-\cosh (2 x)-4 \coth (x)-4 \log (\sinh (x)))","\frac{3 x}{2}-\frac{3 \coth (x)}{2}-\log (\sinh (x))+\frac{\coth (x)}{2 (\tanh (x)+1)}",1,"(6*x - Cosh[2*x] - 4*Coth[x] - 4*Log[Sinh[x]] + Sinh[2*x])/4","A",1
123,1,33,37,0.067129,"\int \frac{\coth ^3(x)}{1+\tanh (x)} \, dx","Integrate[Coth[x]^3/(1 + Tanh[x]),x]","\frac{1}{4} \left(-6 x-\sinh (2 x)+\cosh (2 x)+4 \coth (x)-2 \text{csch}^2(x)+8 \log (\sinh (x))\right)","-\frac{3 x}{2}-\coth ^2(x)+\frac{3 \coth (x)}{2}+2 \log (\sinh (x))+\frac{\coth ^2(x)}{2 (\tanh (x)+1)}",1,"(-6*x + Cosh[2*x] + 4*Coth[x] - 2*Csch[x]^2 + 8*Log[Sinh[x]] - Sinh[2*x])/4","A",1
124,1,42,43,0.1401189,"\int \frac{\coth ^4(x)}{1+\tanh (x)} \, dx","Integrate[Coth[x]^4/(1 + Tanh[x]),x]","\frac{1}{12} \left(-3 \cosh (2 x)-4 \coth (x) \left(\text{csch}^2(x)+7\right)+3 \left(10 x+\sinh (2 x)+2 \text{csch}^2(x)-8 \log (\sinh (x))\right)\right)","\frac{5 x}{2}-\frac{5 \coth ^3(x)}{6}+\coth ^2(x)-\frac{5 \coth (x)}{2}-2 \log (\sinh (x))+\frac{\coth ^3(x)}{2 (\tanh (x)+1)}",1,"(-3*Cosh[2*x] - 4*Coth[x]*(7 + Csch[x]^2) + 3*(10*x + 2*Csch[x]^2 - 8*Log[Sinh[x]] + Sinh[2*x]))/12","A",1
125,1,39,45,0.1954946,"\int \tanh (x) (1+\tanh (x))^{3/2} \, dx","Integrate[Tanh[x]*(1 + Tanh[x])^(3/2),x]","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-\frac{2}{3} \sqrt{\tanh (x)+1} (\tanh (x)+4)","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-\frac{2}{3} (\tanh (x)+1)^{3/2}-2 \sqrt{\tanh (x)+1}",1,"2*Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]] - (2*Sqrt[1 + Tanh[x]]*(4 + Tanh[x]))/3","A",1
126,1,32,32,0.049267,"\int \tanh (x) \sqrt{1+\tanh (x)} \, dx","Integrate[Tanh[x]*Sqrt[1 + Tanh[x]],x]","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-2 \sqrt{\tanh (x)+1}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-2 \sqrt{\tanh (x)+1}",1,"Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]] - 2*Sqrt[1 + Tanh[x]]","A",1
127,1,30,30,0.0600454,"\int \frac{\tanh (x)}{\sqrt{1+\tanh (x)}} \, dx","Integrate[Tanh[x]/Sqrt[1 + Tanh[x]],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}+\frac{1}{\sqrt{\tanh (x)+1}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}+\frac{1}{\sqrt{\tanh (x)+1}}",1,"ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]]/Sqrt[2] + 1/Sqrt[1 + Tanh[x]]","A",1
128,1,51,49,0.1317457,"\int \frac{\tanh (x)}{(1+\tanh (x))^{3/2}} \, dx","Integrate[Tanh[x]/(1 + Tanh[x])^(3/2),x]","\frac{1}{12} \left(3 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-\frac{2 (\cosh (x)-\sinh (x)) (3 \sinh (x)+\cosh (x))}{\sqrt{\tanh (x)+1}}\right)","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}-\frac{1}{2 \sqrt{\tanh (x)+1}}+\frac{1}{3 (\tanh (x)+1)^{3/2}}",1,"(3*Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]] - (2*(Cosh[x] - Sinh[x])*(Cosh[x] + 3*Sinh[x]))/Sqrt[1 + Tanh[x]])/12","A",1
129,1,53,45,0.2099799,"\int \tanh ^2(x) (1+\tanh (x))^{3/2} \, dx","Integrate[Tanh[x]^2*(1 + Tanh[x])^(3/2),x]","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-\frac{1}{5} \sqrt{\tanh (x)+1} \text{sech}^2(x) (2 \sinh (2 x)+7 \cosh (2 x)+5)","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-\frac{2}{5} (\tanh (x)+1)^{5/2}-2 \sqrt{\tanh (x)+1}",1,"2*Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]] - (Sech[x]^2*(5 + 7*Cosh[2*x] + 2*Sinh[2*x])*Sqrt[1 + Tanh[x]])/5","A",1
130,1,34,34,0.0735704,"\int \tanh ^2(x) \sqrt{1+\tanh (x)} \, dx","Integrate[Tanh[x]^2*Sqrt[1 + Tanh[x]],x]","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-\frac{2}{3} (\tanh (x)+1)^{3/2}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)-\frac{2}{3} (\tanh (x)+1)^{3/2}",1,"Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]] - (2*(1 + Tanh[x])^(3/2))/3","A",1
131,1,37,42,0.0954422,"\int \frac{\tanh ^2(x)}{\sqrt{1+\tanh (x)}} \, dx","Integrate[Tanh[x]^2/Sqrt[1 + Tanh[x]],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}+\frac{-2 \tanh (x)-3}{\sqrt{\tanh (x)+1}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}-2 \sqrt{\tanh (x)+1}-\frac{1}{\sqrt{\tanh (x)+1}}",1,"ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]]/Sqrt[2] + (-3 - 2*Tanh[x])/Sqrt[1 + Tanh[x]]","A",1
132,1,53,49,0.1042259,"\int \frac{\tanh ^2(x)}{(1+\tanh (x))^{3/2}} \, dx","Integrate[Tanh[x]^2/(1 + Tanh[x])^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}+\frac{(\cosh (x)-\sinh (x)) (9 \sinh (x)+7 \cosh (x))}{6 \sqrt{\tanh (x)+1}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}+\frac{3}{2 \sqrt{\tanh (x)+1}}-\frac{1}{3 (\tanh (x)+1)^{3/2}}",1,"ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]]/(2*Sqrt[2]) + ((Cosh[x] - Sinh[x])*(7*Cosh[x] + 9*Sinh[x]))/(6*Sqrt[1 + Tanh[x]])","A",1
133,1,105,94,0.5163791,"\int \frac{\tanh ^5(x)}{a+b \tanh (x)} \, dx","Integrate[Tanh[x]^5/(a + b*Tanh[x]),x]","-\frac{-6 a^5 \log (a \cosh (x)+b \sinh (x))+6 a \left(a^4-b^4\right) \log (\cosh (x))+b^2 \left(b^2-a^2\right) \text{sech}^2(x) (2 b \tanh (x)-3 a)+2 b \left(3 a^4+a^2 b^2-4 b^4\right) \tanh (x)+6 b^5 x}{6 b^4 (a-b) (a+b)}","-\frac{b x}{a^2-b^2}+\frac{a \log (\cosh (x))}{a^2-b^2}-\frac{\left(a^2+b^2\right) \tanh (x)}{b^3}+\frac{a^5 \log (a+b \tanh (x))}{b^4 \left(a^2-b^2\right)}+\frac{a \tanh ^2(x)}{2 b^2}-\frac{\tanh ^3(x)}{3 b}",1,"-1/6*(6*b^5*x + 6*a*(a^4 - b^4)*Log[Cosh[x]] - 6*a^5*Log[a*Cosh[x] + b*Sinh[x]] + 2*b*(3*a^4 + a^2*b^2 - 4*b^4)*Tanh[x] + b^2*(-a^2 + b^2)*Sech[x]^2*(-3*a + 2*b*Tanh[x]))/((a - b)*b^4*(a + b))","A",1
134,1,88,76,0.3177767,"\int \frac{\tanh ^4(x)}{a+b \tanh (x)} \, dx","Integrate[Tanh[x]^4/(a + b*Tanh[x]),x]","\frac{b^2 \left(a^2-b^2\right) \text{sech}^2(x)+2 \left(\left(a^4-b^4\right) \log (\cosh (x))+a^4 (-\log (a \cosh (x)+b \sinh (x)))+a b \left(a^2-b^2\right) \tanh (x)+a b^3 x\right)}{2 b^3 (a-b) (a+b)}","\frac{a x}{a^2-b^2}-\frac{b \log (\cosh (x))}{a^2-b^2}-\frac{a^4 \log (a+b \tanh (x))}{b^3 \left(a^2-b^2\right)}+\frac{a \tanh (x)}{b^2}-\frac{\tanh ^2(x)}{2 b}",1,"(b^2*(a^2 - b^2)*Sech[x]^2 + 2*(a*b^3*x + (a^4 - b^4)*Log[Cosh[x]] - a^4*Log[a*Cosh[x] + b*Sinh[x]] + a*b*(a^2 - b^2)*Tanh[x]))/(2*(a - b)*b^3*(a + b))","A",1
135,1,65,64,0.1472995,"\int \frac{\tanh ^3(x)}{a+b \tanh (x)} \, dx","Integrate[Tanh[x]^3/(a + b*Tanh[x]),x]","\frac{\left(a b^2-a^3\right) \log (\cosh (x))+a^3 \log (a \cosh (x)+b \sinh (x))+\left(b^3-a^2 b\right) \tanh (x)-b^3 x}{b^2 (a-b) (a+b)}","-\frac{b x}{a^2-b^2}+\frac{a \log (\cosh (x))}{a^2-b^2}+\frac{a^3 \log (a+b \tanh (x))}{b^2 \left(a^2-b^2\right)}-\frac{\tanh (x)}{b}",1,"(-(b^3*x) + (-a^3 + a*b^2)*Log[Cosh[x]] + a^3*Log[a*Cosh[x] + b*Sinh[x]] + (-(a^2*b) + b^3)*Tanh[x])/((a - b)*b^2*(a + b))","A",1
136,1,49,63,0.0940929,"\int \frac{\tanh ^2(x)}{a+b \tanh (x)} \, dx","Integrate[Tanh[x]^2/(a + b*Tanh[x]),x]","\frac{-a^2 \log (a \cosh (x)+b \sinh (x))+a^2 \log (\cosh (x))+a b x-b^2 \log (\cosh (x))}{a^2 b-b^3}","-\frac{a^2 \log (a \cosh (x)+b \sinh (x))}{b \left(a^2-b^2\right)}+\frac{a^3 x}{b^2 \left(a^2-b^2\right)}-\frac{a x}{b^2}+\frac{\log (\cosh (x))}{b}",1,"(a*b*x + a^2*Log[Cosh[x]] - b^2*Log[Cosh[x]] - a^2*Log[a*Cosh[x] + b*Sinh[x]])/(a^2*b - b^3)","A",1
137,1,29,39,0.0642327,"\int \frac{\tanh (x)}{a+b \tanh (x)} \, dx","Integrate[Tanh[x]/(a + b*Tanh[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
138,1,29,39,0.0501403,"\int \frac{1}{a+b \tanh (x)} \, dx","Integrate[(a + b*Tanh[x])^(-1),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
139,1,46,51,0.0910447,"\int \frac{\coth (x)}{a+b \tanh (x)} \, dx","Integrate[Coth[x]/(a + b*Tanh[x]),x]","\frac{\left(a^2-b^2\right) \log (\sinh (x))+b (b \log (a \cosh (x)+b \sinh (x))-a x)}{a^3-a b^2}","-\frac{b x}{a^2-b^2}+\frac{b^2 \log (a \cosh (x)+b \sinh (x))}{a \left(a^2-b^2\right)}+\frac{\log (\sinh (x))}{a}",1,"((a^2 - b^2)*Log[Sinh[x]] + b*(-(a*x) + b*Log[a*Cosh[x] + b*Sinh[x]]))/(a^3 - a*b^2)","A",1
140,1,64,60,0.1403667,"\int \frac{\coth ^2(x)}{a+b \tanh (x)} \, dx","Integrate[Coth[x]^2/(a + b*Tanh[x]),x]","\frac{\left(a b^2-a^3\right) \coth (x)+a^3 x+\left(b^3-a^2 b\right) \log (\sinh (x))-b^3 \log (a \cosh (x)+b \sinh (x))}{a^4-a^2 b^2}","\frac{a x}{a^2-b^2}-\frac{b^3 \log (a \cosh (x)+b \sinh (x))}{a^2 \left(a^2-b^2\right)}-\frac{b \log (\sinh (x))}{a^2}-\frac{\coth (x)}{a}",1,"(a^3*x + (-a^3 + a*b^2)*Coth[x] + (-(a^2*b) + b^3)*Log[Sinh[x]] - b^3*Log[a*Cosh[x] + b*Sinh[x]])/(a^4 - a^2*b^2)","A",1
141,1,91,76,0.2049157,"\int \frac{\coth ^3(x)}{a+b \tanh (x)} \, dx","Integrate[Coth[x]^3/(a + b*Tanh[x]),x]","\frac{2 a^4 \log (\sinh (x))-2 a^3 b x+2 a b \left(a^2-b^2\right) \coth (x)+\left(a^2 b^2-a^4\right) \text{csch}^2(x)+2 b^4 \log (a \cosh (x)+b \sinh (x))-2 b^4 \log (\sinh (x))}{2 a^3 (a-b) (a+b)}","-\frac{b x}{a^2-b^2}+\frac{b \coth (x)}{a^2}+\frac{\left(a^2+b^2\right) \log (\sinh (x))}{a^3}+\frac{b^4 \log (a \cosh (x)+b \sinh (x))}{a^3 \left(a^2-b^2\right)}-\frac{\coth ^2(x)}{2 a}",1,"(-2*a^3*b*x + 2*a*b*(a^2 - b^2)*Coth[x] + (-a^4 + a^2*b^2)*Csch[x]^2 + 2*a^4*Log[Sinh[x]] - 2*b^4*Log[Sinh[x]] + 2*b^4*Log[a*Cosh[x] + b*Sinh[x]])/(2*a^3*(a - b)*(a + b))","A",1
142,1,108,97,0.31668,"\int \frac{\coth ^4(x)}{a+b \tanh (x)} \, dx","Integrate[Coth[x]^4/(a + b*Tanh[x]),x]","\frac{6 a^5 x+6 \left(b^5-a^4 b\right) \log (\sinh (x))+3 a^2 b \left(a^2-b^2\right) \text{csch}^2(x)-2 a \left(a^2-b^2\right) \coth (x) \left(a^2 \text{csch}^2(x)+4 a^2+3 b^2\right)-6 b^5 \log (a \cosh (x)+b \sinh (x))}{6 a^4 (a-b) (a+b)}","\frac{a x}{a^2-b^2}+\frac{b \coth ^2(x)}{2 a^2}-\frac{b \left(a^2+b^2\right) \log (\sinh (x))}{a^4}-\frac{b^5 \log (a \cosh (x)+b \sinh (x))}{a^4 \left(a^2-b^2\right)}-\frac{\left(a^2+b^2\right) \coth (x)}{a^3}-\frac{\coth ^3(x)}{3 a}",1,"(6*a^5*x + 3*a^2*b*(a^2 - b^2)*Csch[x]^2 - 2*a*(a^2 - b^2)*Coth[x]*(4*a^2 + 3*b^2 + a^2*Csch[x]^2) + 6*(-(a^4*b) + b^5)*Log[Sinh[x]] - 6*b^5*Log[a*Cosh[x] + b*Sinh[x]])/(6*a^4*(a - b)*(a + b))","A",1
143,1,49,55,0.190749,"\int \frac{x \text{sech}^2(x)}{(a+b \tanh (x))^2} \, dx","Integrate[(x*Sech[x]^2)/(a + b*Tanh[x])^2,x]","\frac{b x-a \log (a \cosh (x)+b \sinh (x))}{a^3-a b^2}+\frac{x \sinh (x)}{a^2 \cosh (x)+a b \sinh (x)}","\frac{a x}{b \left(a^2-b^2\right)}-\frac{\log (a \cosh (x)+b \sinh (x))}{a^2-b^2}-\frac{x}{b (a+b \tanh (x))}",1,"(b*x - a*Log[a*Cosh[x] + b*Sinh[x]])/(a^3 - a*b^2) + (x*Sinh[x])/(a^2*Cosh[x] + a*b*Sinh[x])","A",1
144,1,250,231,2.7903704,"\int \frac{x \text{sech}^2(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Integrate[(x*Sech[c + d*x]^2)/(a + b*Tanh[c + d*x]^2),x]","\frac{\sqrt{a} \text{Li}_2\left(-\frac{(a+b) e^{2 (c+d x)}}{a-b-2 \sqrt{-a} \sqrt{b}}\right)-\sqrt{a} \text{Li}_2\left(-\frac{(a+b) e^{2 (c+d x)}}{a-b+2 \sqrt{-a} \sqrt{b}}\right)+2 \sqrt{a} (c+d x) \log \left(\frac{(a+b) e^{2 (c+d x)}}{-2 \sqrt{-a} \sqrt{b}+a-b}+1\right)-2 \sqrt{a} (c+d x) \log \left(\frac{(a+b) e^{2 (c+d x)}}{2 \sqrt{-a} \sqrt{b}+a-b}+1\right)-4 \sqrt{-a} c \tan ^{-1}\left(\frac{(a+b) e^{2 (c+d x)}+a-b}{2 \sqrt{a} \sqrt{b}}\right)}{4 \sqrt{-a^2} \sqrt{b} d^2}","\frac{\text{Li}_2\left(-\frac{(a+b) e^{2 c+2 d x}}{a-b-2 \sqrt{-a} \sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b} d^2}-\frac{\text{Li}_2\left(-\frac{(a+b) e^{2 c+2 d x}}{a-b+2 \sqrt{-a} \sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b} d^2}+\frac{x \log \left(\frac{(a+b) e^{2 c+2 d x}}{-2 \sqrt{-a} \sqrt{b}+a-b}+1\right)}{2 \sqrt{-a} \sqrt{b} d}-\frac{x \log \left(\frac{(a+b) e^{2 c+2 d x}}{2 \sqrt{-a} \sqrt{b}+a-b}+1\right)}{2 \sqrt{-a} \sqrt{b} d}",1,"(-4*Sqrt[-a]*c*ArcTan[(a - b + (a + b)*E^(2*(c + d*x)))/(2*Sqrt[a]*Sqrt[b])] + 2*Sqrt[a]*(c + d*x)*Log[1 + ((a + b)*E^(2*(c + d*x)))/(a - 2*Sqrt[-a]*Sqrt[b] - b)] - 2*Sqrt[a]*(c + d*x)*Log[1 + ((a + b)*E^(2*(c + d*x)))/(a + 2*Sqrt[-a]*Sqrt[b] - b)] + Sqrt[a]*PolyLog[2, -(((a + b)*E^(2*(c + d*x)))/(a - 2*Sqrt[-a]*Sqrt[b] - b))] - Sqrt[a]*PolyLog[2, -(((a + b)*E^(2*(c + d*x)))/(a + 2*Sqrt[-a]*Sqrt[b] - b))])/(4*Sqrt[-a^2]*Sqrt[b]*d^2)","A",1
145,1,316,351,2.5397035,"\int \frac{x^2 \text{sech}^2(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Integrate[(x^2*Sech[c + d*x]^2)/(a + b*Tanh[c + d*x]^2),x]","\frac{i \left(2 d^2 x^2 \log \left(1+\frac{\left(\sqrt{a}-i \sqrt{b}\right) e^{2 (c+d x)}}{\sqrt{a}+i \sqrt{b}}\right)-2 d^2 x^2 \log \left(1+\frac{\left(\sqrt{a}+i \sqrt{b}\right) e^{2 (c+d x)}}{\sqrt{a}-i \sqrt{b}}\right)+2 d x \text{Li}_2\left(-\frac{\left(\sqrt{a}-i \sqrt{b}\right) e^{2 (c+d x)}}{\sqrt{a}+i \sqrt{b}}\right)-2 d x \text{Li}_2\left(-\frac{\left(\sqrt{a}+i \sqrt{b}\right) e^{2 (c+d x)}}{\sqrt{a}-i \sqrt{b}}\right)-\text{Li}_3\left(-\frac{\left(\sqrt{a}-i \sqrt{b}\right) e^{2 (c+d x)}}{\sqrt{a}+i \sqrt{b}}\right)+\text{Li}_3\left(-\frac{\left(\sqrt{a}+i \sqrt{b}\right) e^{2 (c+d x)}}{\sqrt{a}-i \sqrt{b}}\right)\right)}{4 \sqrt{a} \sqrt{b} d^3}","-\frac{\text{Li}_3\left(-\frac{(a+b) e^{2 c+2 d x}}{a-b-2 \sqrt{-a} \sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b} d^3}+\frac{\text{Li}_3\left(-\frac{(a+b) e^{2 c+2 d x}}{a-b+2 \sqrt{-a} \sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b} d^3}+\frac{x \text{Li}_2\left(-\frac{(a+b) e^{2 c+2 d x}}{a-b-2 \sqrt{-a} \sqrt{b}}\right)}{2 \sqrt{-a} \sqrt{b} d^2}-\frac{x \text{Li}_2\left(-\frac{(a+b) e^{2 c+2 d x}}{a-b+2 \sqrt{-a} \sqrt{b}}\right)}{2 \sqrt{-a} \sqrt{b} d^2}+\frac{x^2 \log \left(\frac{(a+b) e^{2 c+2 d x}}{-2 \sqrt{-a} \sqrt{b}+a-b}+1\right)}{2 \sqrt{-a} \sqrt{b} d}-\frac{x^2 \log \left(\frac{(a+b) e^{2 c+2 d x}}{2 \sqrt{-a} \sqrt{b}+a-b}+1\right)}{2 \sqrt{-a} \sqrt{b} d}",1,"((I/4)*(2*d^2*x^2*Log[1 + ((Sqrt[a] - I*Sqrt[b])*E^(2*(c + d*x)))/(Sqrt[a] + I*Sqrt[b])] - 2*d^2*x^2*Log[1 + ((Sqrt[a] + I*Sqrt[b])*E^(2*(c + d*x)))/(Sqrt[a] - I*Sqrt[b])] + 2*d*x*PolyLog[2, -(((Sqrt[a] - I*Sqrt[b])*E^(2*(c + d*x)))/(Sqrt[a] + I*Sqrt[b]))] - 2*d*x*PolyLog[2, -(((Sqrt[a] + I*Sqrt[b])*E^(2*(c + d*x)))/(Sqrt[a] - I*Sqrt[b]))] - PolyLog[3, -(((Sqrt[a] - I*Sqrt[b])*E^(2*(c + d*x)))/(Sqrt[a] + I*Sqrt[b]))] + PolyLog[3, -(((Sqrt[a] + I*Sqrt[b])*E^(2*(c + d*x)))/(Sqrt[a] - I*Sqrt[b]))]))/(Sqrt[a]*Sqrt[b]*d^3)","C",1
146,1,64,29,0.0315333,"\int x^3 \tanh (a+2 \log (x)) \, dx","Integrate[x^3*Tanh[a + 2*Log[x]],x]","-\frac{1}{2} \cosh (2 a) \log \left(x^4 \sinh (a)+x^4 \cosh (a)-\sinh (a)+\cosh (a)\right)+\frac{1}{2} \sinh (2 a) \log \left(x^4 \sinh (a)+x^4 \cosh (a)-\sinh (a)+\cosh (a)\right)+\frac{x^4}{4}","\frac{x^4}{4}-\frac{1}{2} e^{-2 a} \log \left(e^{2 a} x^4+1\right)",1,"x^4/4 - (Cosh[2*a]*Log[Cosh[a] + x^4*Cosh[a] - Sinh[a] + x^4*Sinh[a]])/2 + (Log[Cosh[a] + x^4*Cosh[a] - Sinh[a] + x^4*Sinh[a]]*Sinh[2*a])/2","B",1
147,1,64,151,0.2647977,"\int x^2 \tanh (a+2 \log (x)) \, dx","Integrate[x^2*Tanh[a + 2*Log[x]],x]","\frac{1}{6} \left(3 (\cosh (2 a)-\sinh (2 a)) \text{RootSum}\left[\text{$\#$1}^4 \sinh (a)+\text{$\#$1}^4 \cosh (a)-\sinh (a)+\cosh (a)\&,\frac{\log (x)-\log (x-\text{$\#$1})}{\text{$\#$1}}\&\right]+2 x^3\right)","-\frac{e^{-3 a/2} \log \left(e^a x^2-\sqrt{2} e^{a/2} x+1\right)}{2 \sqrt{2}}+\frac{e^{-3 a/2} \log \left(e^a x^2+\sqrt{2} e^{a/2} x+1\right)}{2 \sqrt{2}}+\frac{e^{-3 a/2} \tan ^{-1}\left(1-\sqrt{2} e^{a/2} x\right)}{\sqrt{2}}-\frac{e^{-3 a/2} \tan ^{-1}\left(\sqrt{2} e^{a/2} x+1\right)}{\sqrt{2}}+\frac{x^3}{3}",1,"(2*x^3 + 3*RootSum[Cosh[a] - Sinh[a] + Cosh[a]*#1^4 + Sinh[a]*#1^4 & , (Log[x] - Log[x - #1])/#1 & ]*(Cosh[2*a] - Sinh[2*a]))/6","C",1
148,1,35,23,0.1869207,"\int x \tanh (a+2 \log (x)) \, dx","Integrate[x*Tanh[a + 2*Log[x]],x]","-\cosh (a) \tan ^{-1}\left(x^2 (\sinh (a)+\cosh (a))\right)+\sinh (a) \tan ^{-1}\left(x^2 (\sinh (a)+\cosh (a))\right)+\frac{x^2}{2}","\frac{x^2}{2}-e^{-a} \tan ^{-1}\left(e^a x^2\right)",1,"x^2/2 - ArcTan[x^2*(Cosh[a] + Sinh[a])]*Cosh[a] + ArcTan[x^2*(Cosh[a] + Sinh[a])]*Sinh[a]","A",1
149,1,58,145,0.182494,"\int \tanh (a+2 \log (x)) \, dx","Integrate[Tanh[a + 2*Log[x]],x]","\frac{1}{2} (\cosh (2 a)-\sinh (2 a)) \text{RootSum}\left[\text{$\#$1}^4 \sinh (a)+\text{$\#$1}^4 \cosh (a)-\sinh (a)+\cosh (a)\&,\frac{\log (x)-\log (x-\text{$\#$1})}{\text{$\#$1}^3}\&\right]+x","\frac{e^{-a/2} \log \left(e^a x^2-\sqrt{2} e^{a/2} x+1\right)}{2 \sqrt{2}}-\frac{e^{-a/2} \log \left(e^a x^2+\sqrt{2} e^{a/2} x+1\right)}{2 \sqrt{2}}+\frac{e^{-a/2} \tan ^{-1}\left(1-\sqrt{2} e^{a/2} x\right)}{\sqrt{2}}-\frac{e^{-a/2} \tan ^{-1}\left(\sqrt{2} e^{a/2} x+1\right)}{\sqrt{2}}+x",1,"x + (RootSum[Cosh[a] - Sinh[a] + Cosh[a]*#1^4 + Sinh[a]*#1^4 & , (Log[x] - Log[x - #1])/#1^3 & ]*(Cosh[2*a] - Sinh[2*a]))/2","C",1
150,1,12,12,0.0249393,"\int \frac{\tanh (a+2 \log (x))}{x} \, dx","Integrate[Tanh[a + 2*Log[x]]/x,x]","\frac{1}{2} \log (\cosh (a+2 \log (x)))","\frac{1}{2} \log (\cosh (a+2 \log (x)))",1,"Log[Cosh[a + 2*Log[x]]]/2","A",1
151,1,59,147,0.1708331,"\int \frac{\tanh (a+2 \log (x))}{x^2} \, dx","Integrate[Tanh[a + 2*Log[x]]/x^2,x]","\frac{2-x (\sinh (a)+\cosh (a))^2 \text{RootSum}\left[-\text{$\#$1}^4 \sinh (a)+\text{$\#$1}^4 \cosh (a)+\sinh (a)+\cosh (a)\&,\frac{\log \left(\frac{1}{x}-\text{$\#$1}\right)+\log (x)}{\text{$\#$1}^3}\&\right]}{2 x}","\frac{e^{a/2} \log \left(e^a x^2-\sqrt{2} e^{a/2} x+1\right)}{2 \sqrt{2}}-\frac{e^{a/2} \log \left(e^a x^2+\sqrt{2} e^{a/2} x+1\right)}{2 \sqrt{2}}-\frac{e^{a/2} \tan ^{-1}\left(1-\sqrt{2} e^{a/2} x\right)}{\sqrt{2}}+\frac{e^{a/2} \tan ^{-1}\left(\sqrt{2} e^{a/2} x+1\right)}{\sqrt{2}}+\frac{1}{x}",1,"(2 - x*RootSum[Cosh[a] + Sinh[a] + Cosh[a]*#1^4 - Sinh[a]*#1^4 & , (Log[x] + Log[x^(-1) - #1])/#1^3 & ]*(Cosh[a] + Sinh[a])^2)/(2*x)","C",1
152,1,40,20,0.1619126,"\int \frac{\tanh (a+2 \log (x))}{x^3} \, dx","Integrate[Tanh[a + 2*Log[x]]/x^3,x]","\cosh (a) \left(-\tan ^{-1}\left(\frac{\cosh (a)-\sinh (a)}{x^2}\right)\right)-\sinh (a) \tan ^{-1}\left(\frac{\cosh (a)-\sinh (a)}{x^2}\right)+\frac{1}{2 x^2}","e^a \tan ^{-1}\left(e^a x^2\right)+\frac{1}{2 x^2}",1,"1/(2*x^2) - ArcTan[(Cosh[a] - Sinh[a])/x^2]*Cosh[a] - ArcTan[(Cosh[a] - Sinh[a])/x^2]*Sinh[a]","A",1
153,1,86,47,0.1159527,"\int x^3 \tanh ^2(a+2 \log (x)) \, dx","Integrate[x^3*Tanh[a + 2*Log[x]]^2,x]","\frac{\sinh (3 a)-\cosh (3 a)}{\left(x^4-1\right) \sinh (a)+\left(x^4+1\right) \cosh (a)}-\cosh (2 a) \log \left(\left(x^4-1\right) \sinh (a)+\left(x^4+1\right) \cosh (a)\right)+\sinh (2 a) \log \left(\left(x^4-1\right) \sinh (a)+\left(x^4+1\right) \cosh (a)\right)+\frac{x^4}{4}","-\frac{e^{-2 a}}{e^{2 a} x^4+1}-e^{-2 a} \log \left(e^{2 a} x^4+1\right)+\frac{x^4}{4}",1,"x^4/4 - Cosh[2*a]*Log[(1 + x^4)*Cosh[a] + (-1 + x^4)*Sinh[a]] + Log[(1 + x^4)*Cosh[a] + (-1 + x^4)*Sinh[a]]*Sinh[2*a] + (-Cosh[3*a] + Sinh[3*a])/((1 + x^4)*Cosh[a] + (-1 + x^4)*Sinh[a])","A",1
154,1,174,173,0.708458,"\int x^2 \tanh ^2(a+2 \log (x)) \, dx","Integrate[x^2*Tanh[a + 2*Log[x]]^2,x]","\frac{1}{12} \left(\frac{12 x^3}{e^{2 a} x^4+1}+9 (-1)^{3/4} e^{-3 a/2} \log \left(\sqrt[4]{-1} e^{-3 a/2}-e^{-a} x\right)+9 \sqrt[4]{-1} e^{-3 a/2} \log \left((-1)^{3/4} e^{-3 a/2}-e^{-a} x\right)-9 (-1)^{3/4} e^{-3 a/2} \log \left(e^{-a} x+\sqrt[4]{-1} e^{-3 a/2}\right)-9 \sqrt[4]{-1} e^{-3 a/2} \log \left(e^{-a} x+(-1)^{3/4} e^{-3 a/2}\right)+4 x^3\right)","-\frac{3 e^{-3 a/2} \log \left(e^a x^2-\sqrt{2} e^{a/2} x+1\right)}{4 \sqrt{2}}+\frac{3 e^{-3 a/2} \log \left(e^a x^2+\sqrt{2} e^{a/2} x+1\right)}{4 \sqrt{2}}+\frac{x^3}{e^{2 a} x^4+1}+\frac{3 e^{-3 a/2} \tan ^{-1}\left(1-\sqrt{2} e^{a/2} x\right)}{2 \sqrt{2}}-\frac{3 e^{-3 a/2} \tan ^{-1}\left(\sqrt{2} e^{a/2} x+1\right)}{2 \sqrt{2}}+\frac{x^3}{3}",1,"(4*x^3 + (12*x^3)/(1 + E^(2*a)*x^4) + (9*(-1)^(3/4)*Log[(-1)^(1/4)/E^((3*a)/2) - x/E^a])/E^((3*a)/2) + (9*(-1)^(1/4)*Log[(-1)^(3/4)/E^((3*a)/2) - x/E^a])/E^((3*a)/2) - (9*(-1)^(3/4)*Log[(-1)^(1/4)/E^((3*a)/2) + x/E^a])/E^((3*a)/2) - (9*(-1)^(1/4)*Log[(-1)^(3/4)/E^((3*a)/2) + x/E^a])/E^((3*a)/2))/12","A",1
155,1,41,40,0.4066121,"\int x \tanh ^2(a+2 \log (x)) \, dx","Integrate[x*Tanh[a + 2*Log[x]]^2,x]","\frac{x^2}{e^{2 (a+2 \log (x))}+1}-e^{-a} \tan ^{-1}\left(e^a x^2\right)+\frac{x^2}{2}","-e^{-a} \tan ^{-1}\left(e^a x^2\right)+\frac{x^2}{e^{2 a} x^4+1}+\frac{x^2}{2}",1,"x^2/2 + x^2/(1 + E^(2*(a + 2*Log[x]))) - ArcTan[E^a*x^2]/E^a","A",1
156,1,146,165,0.5838062,"\int \tanh ^2(a+2 \log (x)) \, dx","Integrate[Tanh[a + 2*Log[x]]^2,x]","\frac{1}{4} \left(\frac{4 x}{e^{2 a} x^4+1}+\sqrt[4]{-1} e^{-a/2} \log \left(\sqrt[4]{-1} e^{-a/2}-x\right)+(-1)^{3/4} e^{-a/2} \log \left((-1)^{3/4} e^{-a/2}-x\right)-\sqrt[4]{-1} e^{-a/2} \log \left(\sqrt[4]{-1} e^{-a/2}+x\right)-(-1)^{3/4} e^{-a/2} \log \left((-1)^{3/4} e^{-a/2}+x\right)+4 x\right)","\frac{x}{e^{2 a} x^4+1}+\frac{e^{-a/2} \log \left(e^a x^2-\sqrt{2} e^{a/2} x+1\right)}{4 \sqrt{2}}-\frac{e^{-a/2} \log \left(e^a x^2+\sqrt{2} e^{a/2} x+1\right)}{4 \sqrt{2}}+\frac{e^{-a/2} \tan ^{-1}\left(1-\sqrt{2} e^{a/2} x\right)}{2 \sqrt{2}}-\frac{e^{-a/2} \tan ^{-1}\left(\sqrt{2} e^{a/2} x+1\right)}{2 \sqrt{2}}+x",1,"(4*x + (4*x)/(1 + E^(2*a)*x^4) + ((-1)^(1/4)*Log[(-1)^(1/4)/E^(a/2) - x])/E^(a/2) + ((-1)^(3/4)*Log[(-1)^(3/4)/E^(a/2) - x])/E^(a/2) - ((-1)^(1/4)*Log[(-1)^(1/4)/E^(a/2) + x])/E^(a/2) - ((-1)^(3/4)*Log[(-1)^(3/4)/E^(a/2) + x])/E^(a/2))/4","A",1
157,1,24,14,0.0384943,"\int \frac{\tanh ^2(a+2 \log (x))}{x} \, dx","Integrate[Tanh[a + 2*Log[x]]^2/x,x]","\frac{1}{2} \tanh ^{-1}(\tanh (a+2 \log (x)))-\frac{1}{2} \tanh (a+2 \log (x))","\log (x)-\frac{1}{2} \tanh (a+2 \log (x))",1,"ArcTanh[Tanh[a + 2*Log[x]]]/2 - Tanh[a + 2*Log[x]]/2","A",1
158,1,181,190,0.800153,"\int \frac{\tanh ^2(a+2 \log (x))}{x^2} \, dx","Integrate[Tanh[a + 2*Log[x]]^2/x^2,x]","\frac{1}{4} \left((-1)^{3/4} e^{a/2} \log \left(\frac{e^{-2 a} \left(\sqrt[4]{-1}-e^{a/2} x\right)}{x^4}\right)+\sqrt[4]{-1} e^{a/2} \log \left(\frac{e^{-2 a} \left((-1)^{3/4}-e^{a/2} x\right)}{x^4}\right)-(-1)^{3/4} e^{a/2} \log \left(\frac{e^{-2 a} \left(e^{a/2} x+\sqrt[4]{-1}\right)}{x^4}\right)-\sqrt[4]{-1} e^{a/2} \log \left(\frac{e^{-2 a} \left(e^{a/2} x+(-1)^{3/4}\right)}{x^4}\right)-\frac{4}{\frac{e^{-2 a}}{x^3}+x}-\frac{4}{x}\right)","-\frac{1}{x \left(e^{2 a} x^4+1\right)}-\frac{e^{a/2} \log \left(e^a x^2-\sqrt{2} e^{a/2} x+1\right)}{4 \sqrt{2}}+\frac{e^{a/2} \log \left(e^a x^2+\sqrt{2} e^{a/2} x+1\right)}{4 \sqrt{2}}-\frac{2 e^{2 a} x^3}{e^{2 a} x^4+1}+\frac{e^{a/2} \tan ^{-1}\left(1-\sqrt{2} e^{a/2} x\right)}{2 \sqrt{2}}-\frac{e^{a/2} \tan ^{-1}\left(\sqrt{2} e^{a/2} x+1\right)}{2 \sqrt{2}}",1,"(-4/x - 4/(1/(E^(2*a)*x^3) + x) + (-1)^(3/4)*E^(a/2)*Log[((-1)^(1/4) - E^(a/2)*x)/(E^(2*a)*x^4)] + (-1)^(1/4)*E^(a/2)*Log[((-1)^(3/4) - E^(a/2)*x)/(E^(2*a)*x^4)] - (-1)^(3/4)*E^(a/2)*Log[((-1)^(1/4) + E^(a/2)*x)/(E^(2*a)*x^4)] - (-1)^(1/4)*E^(a/2)*Log[((-1)^(3/4) + E^(a/2)*x)/(E^(2*a)*x^4)])/4","A",1
159,1,40,59,0.3979352,"\int \frac{\tanh ^2(a+2 \log (x))}{x^3} \, dx","Integrate[Tanh[a + 2*Log[x]]^2/x^3,x]","\frac{-\frac{2}{e^{-2 (a+2 \log (x))}+1}-1}{2 x^2}+e^a \tan ^{-1}\left(\frac{e^{-a}}{x^2}\right)","-e^a \tan ^{-1}\left(e^a x^2\right)-\frac{3 e^{2 a} x^2}{2 \left(e^{2 a} x^4+1\right)}-\frac{1}{2 x^2 \left(e^{2 a} x^4+1\right)}",1,"(-1 - 2/(1 + E^(-2*(a + 2*Log[x]))))/(2*x^2) + E^a*ArcTan[1/(E^a*x^2)]","A",1
160,1,47,60,0.1018368,"\int (e x)^m \tanh (a+2 \log (x)) \, dx","Integrate[(e*x)^m*Tanh[a + 2*Log[x]],x]","-\frac{x (e x)^m \left(2 \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-x^4 (\cosh (2 a)+\sinh (2 a))\right)-1\right)}{m+1}","\frac{(e x)^{m+1}}{e (m+1)}-\frac{2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-e^{2 a} x^4\right)}{e (m+1)}",1,"-((x*(e*x)^m*(-1 + 2*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, -(x^4*(Cosh[2*a] + Sinh[2*a]))]))/(1 + m))","A",1
161,1,79,79,0.1834339,"\int (e x)^m \tanh ^2(a+2 \log (x)) \, dx","Integrate[(e*x)^m*Tanh[a + 2*Log[x]]^2,x]","-\frac{x (e x)^m \left(4 \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-x^4 (\cosh (2 a)+\sinh (2 a))\right)-4 \, _2F_1\left(2,\frac{m+1}{4};\frac{m+5}{4};-x^4 (\cosh (2 a)+\sinh (2 a))\right)-1\right)}{m+1}","-\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-e^{2 a} x^4\right)}{e}+\frac{(e x)^{m+1}}{e \left(e^{2 a} x^4+1\right)}+\frac{(e x)^{m+1}}{e (m+1)}",1,"-((x*(e*x)^m*(-1 + 4*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, -(x^4*(Cosh[2*a] + Sinh[2*a]))] - 4*Hypergeometric2F1[2, (1 + m)/4, (5 + m)/4, -(x^4*(Cosh[2*a] + Sinh[2*a]))]))/(1 + m))","A",1
162,1,111,176,0.2463893,"\int (e x)^m \tanh ^3(a+2 \log (x)) \, dx","Integrate[(e*x)^m*Tanh[a + 2*Log[x]]^3,x]","-\frac{x (e x)^m \left(6 \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-x^4 (\cosh (2 a)+\sinh (2 a))\right)-12 \, _2F_1\left(2,\frac{m+1}{4};\frac{m+5}{4};-x^4 (\cosh (2 a)+\sinh (2 a))\right)+8 \, _2F_1\left(3,\frac{m+1}{4};\frac{m+5}{4};-x^4 (\cosh (2 a)+\sinh (2 a))\right)-1\right)}{m+1}","-\frac{\left(m^2+2 m+9\right) (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-e^{2 a} x^4\right)}{4 e (m+1)}-\frac{e^{-2 a} \left(e^{4 a} (m+5) x^4+e^{2 a} (3-m)\right) (e x)^{m+1}}{8 e \left(e^{2 a} x^4+1\right)}-\frac{\left(1-e^{2 a} x^4\right)^2 (e x)^{m+1}}{4 e \left(e^{2 a} x^4+1\right)^2}+\frac{(m+3) (m+5) (e x)^{m+1}}{8 e (m+1)}",1,"-((x*(e*x)^m*(-1 + 6*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, -(x^4*(Cosh[2*a] + Sinh[2*a]))] - 12*Hypergeometric2F1[2, (1 + m)/4, (5 + m)/4, -(x^4*(Cosh[2*a] + Sinh[2*a]))] + 8*Hypergeometric2F1[3, (1 + m)/4, (5 + m)/4, -(x^4*(Cosh[2*a] + Sinh[2*a]))]))/(1 + m))","A",1
163,1,259,79,2.2350624,"\int \tanh ^p(a+b \log (x)) \, dx","Integrate[Tanh[a + b*Log[x]]^p,x]","\frac{(2 b+1) x \left(\frac{e^{2 a} x^{2 b}-1}{e^{2 a} x^{2 b}+1}\right)^p F_1\left(\frac{1}{2 b};-p,p;1+\frac{1}{2 b};e^{2 a} x^{2 b},-e^{2 a} x^{2 b}\right)}{-2 e^{2 a} b p x^{2 b} F_1\left(1+\frac{1}{2 b};1-p,p;2+\frac{1}{2 b};e^{2 a} x^{2 b},-e^{2 a} x^{2 b}\right)-2 e^{2 a} b p x^{2 b} F_1\left(1+\frac{1}{2 b};-p,p+1;2+\frac{1}{2 b};e^{2 a} x^{2 b},-e^{2 a} x^{2 b}\right)+(2 b+1) F_1\left(\frac{1}{2 b};-p,p;1+\frac{1}{2 b};e^{2 a} x^{2 b},-e^{2 a} x^{2 b}\right)}","x \left(1-e^{2 a} x^{2 b}\right)^{-p} \left(e^{2 a} x^{2 b}-1\right)^p F_1\left(\frac{1}{2 b};-p,p;\frac{1}{2} \left(2+\frac{1}{b}\right);e^{2 a} x^{2 b},-e^{2 a} x^{2 b}\right)",1,"((1 + 2*b)*x*((-1 + E^(2*a)*x^(2*b))/(1 + E^(2*a)*x^(2*b)))^p*AppellF1[1/(2*b), -p, p, 1 + 1/(2*b), E^(2*a)*x^(2*b), -(E^(2*a)*x^(2*b))])/(-2*b*E^(2*a)*p*x^(2*b)*AppellF1[1 + 1/(2*b), 1 - p, p, 2 + 1/(2*b), E^(2*a)*x^(2*b), -(E^(2*a)*x^(2*b))] - 2*b*E^(2*a)*p*x^(2*b)*AppellF1[1 + 1/(2*b), -p, 1 + p, 2 + 1/(2*b), E^(2*a)*x^(2*b), -(E^(2*a)*x^(2*b))] + (1 + 2*b)*AppellF1[1/(2*b), -p, p, 1 + 1/(2*b), E^(2*a)*x^(2*b), -(E^(2*a)*x^(2*b))])","B",0
164,1,126,99,3.1927697,"\int (e x)^m \tanh ^p(a+b \log (x)) \, dx","Integrate[(e*x)^m*Tanh[a + b*Log[x]]^p,x]","\frac{x (e x)^m \left(1-e^{2 a} x^{2 b}\right)^{-p} \left(\frac{e^{2 a} x^{2 b}-1}{e^{2 a} x^{2 b}+1}\right)^p \left(e^{2 a} x^{2 b}+1\right)^p F_1\left(\frac{m+1}{2 b};-p,p;\frac{m+1}{2 b}+1;e^{2 a} x^{2 b},-e^{2 a} x^{2 b}\right)}{m+1}","\frac{(e x)^{m+1} \left(1-e^{2 a} x^{2 b}\right)^{-p} \left(e^{2 a} x^{2 b}-1\right)^p F_1\left(\frac{m+1}{2 b};-p,p;\frac{m+1}{2 b}+1;e^{2 a} x^{2 b},-e^{2 a} x^{2 b}\right)}{e (m+1)}",1,"(x*(e*x)^m*((-1 + E^(2*a)*x^(2*b))/(1 + E^(2*a)*x^(2*b)))^p*(1 + E^(2*a)*x^(2*b))^p*AppellF1[(1 + m)/(2*b), -p, p, 1 + (1 + m)/(2*b), E^(2*a)*x^(2*b), -(E^(2*a)*x^(2*b))])/((1 + m)*(1 - E^(2*a)*x^(2*b))^p)","A",0
165,1,76,51,3.1417199,"\int \tanh ^p\left(a+\frac{\log (x)}{2}\right) \, dx","Integrate[Tanh[a + Log[x]/2]^p,x]","\frac{e^{-2 a} 2^{-p} \left(\frac{e^{2 a} x-1}{e^{2 a} x+1}\right)^{p+1} \left(e^{2 a} x+1\right)^{p+1} \, _2F_1\left(p,p+1;p+2;\frac{1}{2} \left(1-e^{2 a} x\right)\right)}{p+1}","\frac{e^{-2 a} 2^{-p} \left(e^{2 a} x-1\right)^{p+1} \, _2F_1\left(p,p+1;p+2;\frac{1}{2} \left(1-e^{2 a} x\right)\right)}{p+1}",1,"(((-1 + E^(2*a)*x)/(1 + E^(2*a)*x))^(1 + p)*(1 + E^(2*a)*x)^(1 + p)*Hypergeometric2F1[p, 1 + p, 2 + p, (1 - E^(2*a)*x)/2])/(2^p*E^(2*a)*(1 + p))","A",0
166,1,121,106,3.1025367,"\int \tanh ^p\left(a+\frac{\log (x)}{4}\right) \, dx","Integrate[Tanh[a + Log[x]/4]^p,x]","\frac{e^{-4 a} \left(e^{2 a} \sqrt{x}-1\right) \left(\frac{e^{2 a} \sqrt{x}-1}{2 e^{2 a} \sqrt{x}+2}\right)^p \left(2^p (p+1) \left(e^{2 a} \sqrt{x}+1\right)-2 p \left(e^{2 a} \sqrt{x}+1\right)^p \, _2F_1\left(p,p+1;p+2;\frac{1}{2} \left(1-e^{2 a} \sqrt{x}\right)\right)\right)}{p+1}","e^{-4 a} \left(e^{2 a} \sqrt{x}-1\right)^{p+1} \left(e^{2 a} \sqrt{x}+1\right)^{1-p}-\frac{e^{-4 a} 2^{1-p} p \left(e^{2 a} \sqrt{x}-1\right)^{p+1} \, _2F_1\left(p,p+1;p+2;\frac{1}{2} \left(1-e^{2 a} \sqrt{x}\right)\right)}{p+1}",1,"((-1 + E^(2*a)*Sqrt[x])*((-1 + E^(2*a)*Sqrt[x])/(2 + 2*E^(2*a)*Sqrt[x]))^p*(2^p*(1 + p)*(1 + E^(2*a)*Sqrt[x]) - 2*p*(1 + E^(2*a)*Sqrt[x])^p*Hypergeometric2F1[p, 1 + p, 2 + p, (1 - E^(2*a)*Sqrt[x])/2]))/(E^(4*a)*(1 + p))","A",1
167,1,177,158,4.2798392,"\int \tanh ^p\left(a+\frac{\log (x)}{6}\right) \, dx","Integrate[Tanh[a + Log[x]/6]^p,x]","\frac{4 x \left(\frac{e^{2 a} \sqrt[3]{x}-1}{e^{2 a} \sqrt[3]{x}+1}\right)^p F_1\left(3;-p,p;4;e^{2 a} \sqrt[3]{x},-e^{2 a} \sqrt[3]{x}\right)}{4 F_1\left(3;-p,p;4;e^{2 a} \sqrt[3]{x},-e^{2 a} \sqrt[3]{x}\right)-e^{2 a} p \sqrt[3]{x} \left(F_1\left(4;1-p,p;5;e^{2 a} \sqrt[3]{x},-e^{2 a} \sqrt[3]{x}\right)+F_1\left(4;-p,p+1;5;e^{2 a} \sqrt[3]{x},-e^{2 a} \sqrt[3]{x}\right)\right)}","\frac{e^{-6 a} 2^{-p} \left(2 p^2+1\right) \left(e^{2 a} \sqrt[3]{x}-1\right)^{p+1} \, _2F_1\left(p,p+1;p+2;\frac{1}{2} \left(1-e^{2 a} \sqrt[3]{x}\right)\right)}{p+1}-e^{-6 a} p \left(e^{2 a} \sqrt[3]{x}-1\right)^{p+1} \left(e^{2 a} \sqrt[3]{x}+1\right)^{1-p}+e^{-4 a} \sqrt[3]{x} \left(e^{2 a} \sqrt[3]{x}-1\right)^{p+1} \left(e^{2 a} \sqrt[3]{x}+1\right)^{1-p}",1,"(4*((-1 + E^(2*a)*x^(1/3))/(1 + E^(2*a)*x^(1/3)))^p*x*AppellF1[3, -p, p, 4, E^(2*a)*x^(1/3), -(E^(2*a)*x^(1/3))])/(4*AppellF1[3, -p, p, 4, E^(2*a)*x^(1/3), -(E^(2*a)*x^(1/3))] - E^(2*a)*p*x^(1/3)*(AppellF1[4, 1 - p, p, 5, E^(2*a)*x^(1/3), -(E^(2*a)*x^(1/3))] + AppellF1[4, -p, 1 + p, 5, E^(2*a)*x^(1/3), -(E^(2*a)*x^(1/3))]))","C",0
168,1,177,190,3.4067686,"\int \tanh ^p\left(a+\frac{\log (x)}{8}\right) \, dx","Integrate[Tanh[a + Log[x]/8]^p,x]","\frac{5 x \left(\frac{e^{2 a} \sqrt[4]{x}-1}{e^{2 a} \sqrt[4]{x}+1}\right)^p F_1\left(4;-p,p;5;e^{2 a} \sqrt[4]{x},-e^{2 a} \sqrt[4]{x}\right)}{5 F_1\left(4;-p,p;5;e^{2 a} \sqrt[4]{x},-e^{2 a} \sqrt[4]{x}\right)-e^{2 a} p \sqrt[4]{x} \left(F_1\left(5;1-p,p;6;e^{2 a} \sqrt[4]{x},-e^{2 a} \sqrt[4]{x}\right)+F_1\left(5;-p,p+1;6;e^{2 a} \sqrt[4]{x},-e^{2 a} \sqrt[4]{x}\right)\right)}","-\frac{e^{-8 a} 2^{2-p} p \left(p^2+2\right) \left(e^{2 a} \sqrt[4]{x}-1\right)^{p+1} \, _2F_1\left(p,p+1;p+2;\frac{1}{2} \left(1-e^{2 a} \sqrt[4]{x}\right)\right)}{3 (p+1)}+\frac{1}{3} e^{-12 a} \left(e^{2 a} \sqrt[4]{x}-1\right)^{p+1} \left(e^{4 a} \left(2 p^2+3\right)-2 e^{6 a} p \sqrt[4]{x}\right) \left(e^{2 a} \sqrt[4]{x}+1\right)^{1-p}+e^{-4 a} \sqrt{x} \left(e^{2 a} \sqrt[4]{x}-1\right)^{p+1} \left(e^{2 a} \sqrt[4]{x}+1\right)^{1-p}",1,"(5*((-1 + E^(2*a)*x^(1/4))/(1 + E^(2*a)*x^(1/4)))^p*x*AppellF1[4, -p, p, 5, E^(2*a)*x^(1/4), -(E^(2*a)*x^(1/4))])/(5*AppellF1[4, -p, p, 5, E^(2*a)*x^(1/4), -(E^(2*a)*x^(1/4))] - E^(2*a)*p*x^(1/4)*(AppellF1[5, 1 - p, p, 6, E^(2*a)*x^(1/4), -(E^(2*a)*x^(1/4))] + AppellF1[5, -p, 1 + p, 6, E^(2*a)*x^(1/4), -(E^(2*a)*x^(1/4))]))","C",0
169,1,171,61,1.7402426,"\int \tanh ^p(a+\log (x)) \, dx","Integrate[Tanh[a + Log[x]]^p,x]","\frac{3 x \left(\frac{e^{2 a} x^2-1}{e^{2 a} x^2+1}\right)^p F_1\left(\frac{1}{2};-p,p;\frac{3}{2};e^{2 a} x^2,-e^{2 a} x^2\right)}{3 F_1\left(\frac{1}{2};-p,p;\frac{3}{2};e^{2 a} x^2,-e^{2 a} x^2\right)-2 e^{2 a} p x^2 \left(F_1\left(\frac{3}{2};1-p,p;\frac{5}{2};e^{2 a} x^2,-e^{2 a} x^2\right)+F_1\left(\frac{3}{2};-p,p+1;\frac{5}{2};e^{2 a} x^2,-e^{2 a} x^2\right)\right)}","x \left(1-e^{2 a} x^2\right)^{-p} \left(e^{2 a} x^2-1\right)^p F_1\left(\frac{1}{2};-p,p;\frac{3}{2};e^{2 a} x^2,-e^{2 a} x^2\right)",1,"(3*x*((-1 + E^(2*a)*x^2)/(1 + E^(2*a)*x^2))^p*AppellF1[1/2, -p, p, 3/2, E^(2*a)*x^2, -(E^(2*a)*x^2)])/(3*AppellF1[1/2, -p, p, 3/2, E^(2*a)*x^2, -(E^(2*a)*x^2)] - 2*E^(2*a)*p*x^2*(AppellF1[3/2, 1 - p, p, 5/2, E^(2*a)*x^2, -(E^(2*a)*x^2)] + AppellF1[3/2, -p, 1 + p, 5/2, E^(2*a)*x^2, -(E^(2*a)*x^2)]))","B",0
170,1,171,61,1.9786857,"\int \tanh ^p(a+2 \log (x)) \, dx","Integrate[Tanh[a + 2*Log[x]]^p,x]","\frac{5 x \left(\frac{e^{2 a} x^4-1}{e^{2 a} x^4+1}\right)^p F_1\left(\frac{1}{4};-p,p;\frac{5}{4};e^{2 a} x^4,-e^{2 a} x^4\right)}{5 F_1\left(\frac{1}{4};-p,p;\frac{5}{4};e^{2 a} x^4,-e^{2 a} x^4\right)-4 e^{2 a} p x^4 \left(F_1\left(\frac{5}{4};1-p,p;\frac{9}{4};e^{2 a} x^4,-e^{2 a} x^4\right)+F_1\left(\frac{5}{4};-p,p+1;\frac{9}{4};e^{2 a} x^4,-e^{2 a} x^4\right)\right)}","x \left(1-e^{2 a} x^4\right)^{-p} \left(e^{2 a} x^4-1\right)^p F_1\left(\frac{1}{4};-p,p;\frac{5}{4};e^{2 a} x^4,-e^{2 a} x^4\right)",1,"(5*x*((-1 + E^(2*a)*x^4)/(1 + E^(2*a)*x^4))^p*AppellF1[1/4, -p, p, 5/4, E^(2*a)*x^4, -(E^(2*a)*x^4)])/(5*AppellF1[1/4, -p, p, 5/4, E^(2*a)*x^4, -(E^(2*a)*x^4)] - 4*E^(2*a)*p*x^4*(AppellF1[5/4, 1 - p, p, 9/4, E^(2*a)*x^4, -(E^(2*a)*x^4)] + AppellF1[5/4, -p, 1 + p, 9/4, E^(2*a)*x^4, -(E^(2*a)*x^4)]))","B",0
171,1,171,61,2.080976,"\int \tanh ^p(a+3 \log (x)) \, dx","Integrate[Tanh[a + 3*Log[x]]^p,x]","\frac{7 x \left(\frac{e^{2 a} x^6-1}{e^{2 a} x^6+1}\right)^p F_1\left(\frac{1}{6};-p,p;\frac{7}{6};e^{2 a} x^6,-e^{2 a} x^6\right)}{7 F_1\left(\frac{1}{6};-p,p;\frac{7}{6};e^{2 a} x^6,-e^{2 a} x^6\right)-6 e^{2 a} p x^6 \left(F_1\left(\frac{7}{6};1-p,p;\frac{13}{6};e^{2 a} x^6,-e^{2 a} x^6\right)+F_1\left(\frac{7}{6};-p,p+1;\frac{13}{6};e^{2 a} x^6,-e^{2 a} x^6\right)\right)}","x \left(1-e^{2 a} x^6\right)^{-p} \left(e^{2 a} x^6-1\right)^p F_1\left(\frac{1}{6};-p,p;\frac{7}{6};e^{2 a} x^6,-e^{2 a} x^6\right)",1,"(7*x*((-1 + E^(2*a)*x^6)/(1 + E^(2*a)*x^6))^p*AppellF1[1/6, -p, p, 7/6, E^(2*a)*x^6, -(E^(2*a)*x^6)])/(7*AppellF1[1/6, -p, p, 7/6, E^(2*a)*x^6, -(E^(2*a)*x^6)] - 6*E^(2*a)*p*x^6*(AppellF1[7/6, 1 - p, p, 13/6, E^(2*a)*x^6, -(E^(2*a)*x^6)] + AppellF1[7/6, -p, 1 + p, 13/6, E^(2*a)*x^6, -(E^(2*a)*x^6)]))","B",0
172,1,127,59,7.9058635,"\int x^3 \tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^3*Tanh[d*(a + b*Log[c*x^n])],x]","\frac{x^4 \left(2 e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1+\frac{2}{b d n};2+\frac{2}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)-(b d n+2) \, _2F_1\left(1,\frac{2}{b d n};1+\frac{2}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)\right)}{4 b d n+8}","\frac{x^4}{4}-\frac{1}{2} x^4 \, _2F_1\left(1,\frac{2}{b d n};1+\frac{2}{b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)",1,"(x^4*(2*E^(2*d*(a + b*Log[c*x^n]))*Hypergeometric2F1[1, 1 + 2/(b*d*n), 2 + 2/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] - (2 + b*d*n)*Hypergeometric2F1[1, 2/(b*d*n), 1 + 2/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))]))/(8 + 4*b*d*n)","B",1
173,1,136,63,7.711499,"\int x^2 \tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^2*Tanh[d*(a + b*Log[c*x^n])],x]","\frac{x^3 \left(3 e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1+\frac{3}{2 b d n};2+\frac{3}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)-(2 b d n+3) \, _2F_1\left(1,\frac{3}{2 b d n};1+\frac{3}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)\right)}{6 b d n+9}","\frac{x^3}{3}-\frac{2}{3} x^3 \, _2F_1\left(1,\frac{3}{2 b d n};1+\frac{3}{2 b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)",1,"(x^3*(3*E^(2*d*(a + b*Log[c*x^n]))*Hypergeometric2F1[1, 1 + 3/(2*b*d*n), 2 + 3/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] - (3 + 2*b*d*n)*Hypergeometric2F1[1, 3/(2*b*d*n), 1 + 3/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))]))/(9 + 6*b*d*n)","B",1
174,1,122,55,7.8078789,"\int x \tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x*Tanh[d*(a + b*Log[c*x^n])],x]","\frac{x^2 \left(e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1+\frac{1}{b d n};2+\frac{1}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)-(b d n+1) \, _2F_1\left(1,\frac{1}{b d n};1+\frac{1}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)\right)}{2 b d n+2}","\frac{x^2}{2}-x^2 \, _2F_1\left(1,\frac{1}{b d n};1+\frac{1}{b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)",1,"(x^2*(E^(2*d*(a + b*Log[c*x^n]))*Hypergeometric2F1[1, 1 + 1/(b*d*n), 2 + 1/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] - (1 + b*d*n)*Hypergeometric2F1[1, 1/(b*d*n), 1 + 1/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))]))/(2 + 2*b*d*n)","B",1
175,1,126,53,8.7260025,"\int \tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[Tanh[d*(a + b*Log[c*x^n])],x]","\frac{x e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1+\frac{1}{2 b d n};2+\frac{1}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)}{2 b d n+1}-x \, _2F_1\left(1,\frac{1}{2 b d n};1+\frac{1}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)","x-2 x \, _2F_1\left(1,\frac{1}{2 b d n};1+\frac{1}{2 b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)",1,"(E^(2*d*(a + b*Log[c*x^n]))*x*Hypergeometric2F1[1, 1 + 1/(2*b*d*n), 2 + 1/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))])/(1 + 2*b*d*n) - x*Hypergeometric2F1[1, 1/(2*b*d*n), 1 + 1/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))]","B",1
176,1,24,25,0.0518658,"\int \frac{\tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Integrate[Tanh[d*(a + b*Log[c*x^n])]/x,x]","\frac{\log \left(\cosh \left(d \left(a+b \log \left(c x^n\right)\right)\right)\right)}{b d n}","\frac{\log \left(\cosh \left(a d+b d \log \left(c x^n\right)\right)\right)}{b d n}",1,"Log[Cosh[d*(a + b*Log[c*x^n])]]/(b*d*n)","A",1
177,1,126,59,3.3091256,"\int \frac{\tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Integrate[Tanh[d*(a + b*Log[c*x^n])]/x^2,x]","\frac{\frac{e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1-\frac{1}{2 b d n};2-\frac{1}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)}{2 b d n-1}+\, _2F_1\left(1,-\frac{1}{2 b d n};1-\frac{1}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)}{x}","\frac{2 \, _2F_1\left(1,-\frac{1}{2 b d n};1-\frac{1}{2 b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{x}-\frac{1}{x}",1,"((E^(2*d*(a + b*Log[c*x^n]))*Hypergeometric2F1[1, 1 - 1/(2*b*d*n), 2 - 1/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))])/(-1 + 2*b*d*n) + Hypergeometric2F1[1, -1/2*1/(b*d*n), 1 - 1/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))])/x","B",1
178,1,120,56,3.2940027,"\int \frac{\tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Integrate[Tanh[d*(a + b*Log[c*x^n])]/x^3,x]","\frac{\frac{e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1-\frac{1}{b d n};2-\frac{1}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)}{b d n-1}+\, _2F_1\left(1,-\frac{1}{b d n};1-\frac{1}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)}{2 x^2}","\frac{\, _2F_1\left(1,-\frac{1}{b d n};1-\frac{1}{b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{x^2}-\frac{1}{2 x^2}",1,"((E^(2*d*(a + b*Log[c*x^n]))*Hypergeometric2F1[1, 1 - 1/(b*d*n), 2 - 1/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))])/(-1 + b*d*n) + Hypergeometric2F1[1, -(1/(b*d*n)), 1 - 1/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))])/(2*x^2)","B",1
179,1,159,133,8.2660409,"\int x^3 \tanh ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^3*Tanh[d*(a + b*Log[c*x^n])]^2,x]","\frac{x^4 \left(8 e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1+\frac{2}{b d n};2+\frac{2}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)+(b d n+2) \left(-4 \, _2F_1\left(1,\frac{2}{b d n};1+\frac{2}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)-4 \tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right)+b d n\right)\right)}{4 b d n (b d n+2)}","-\frac{2 x^4 \, _2F_1\left(1,\frac{2}{b d n};1+\frac{2}{b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n}+\frac{x^4 \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}+\frac{1}{4} x^4 \left(\frac{4}{b d n}+1\right)",1,"(x^4*(8*E^(2*d*(a + b*Log[c*x^n]))*Hypergeometric2F1[1, 1 + 2/(b*d*n), 2 + 2/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] + (2 + b*d*n)*(b*d*n - 4*Hypergeometric2F1[1, 2/(b*d*n), 1 + 2/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] - 4*Tanh[d*(a + b*Log[c*x^n])])))/(4*b*d*n*(2 + b*d*n))","A",1
180,1,169,137,8.171797,"\int x^2 \tanh ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^2*Tanh[d*(a + b*Log[c*x^n])]^2,x]","\frac{x^3 \left(9 e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1+\frac{3}{2 b d n};2+\frac{3}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)+(2 b d n+3) \left(-3 \, _2F_1\left(1,\frac{3}{2 b d n};1+\frac{3}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)-3 \tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right)+b d n\right)\right)}{3 b d n (2 b d n+3)}","-\frac{2 x^3 \, _2F_1\left(1,\frac{3}{2 b d n};1+\frac{3}{2 b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n}+\frac{x^3 \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}+\frac{1}{3} x^3 \left(\frac{3}{b d n}+1\right)",1,"(x^3*(9*E^(2*d*(a + b*Log[c*x^n]))*Hypergeometric2F1[1, 1 + 3/(2*b*d*n), 2 + 3/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] + (3 + 2*b*d*n)*(b*d*n - 3*Hypergeometric2F1[1, 3/(2*b*d*n), 1 + 3/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] - 3*Tanh[d*(a + b*Log[c*x^n])])))/(3*b*d*n*(3 + 2*b*d*n))","A",1
181,1,155,131,8.3367537,"\int x \tanh ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x*Tanh[d*(a + b*Log[c*x^n])]^2,x]","\frac{x^2 \left(2 e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1+\frac{1}{b d n};2+\frac{1}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)+(b d n+1) \left(-2 \, _2F_1\left(1,\frac{1}{b d n};1+\frac{1}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)-2 \tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right)+b d n\right)\right)}{2 b d n (b d n+1)}","-\frac{2 x^2 \, _2F_1\left(1,\frac{1}{b d n};1+\frac{1}{b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n}+\frac{x^2 \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}+\frac{1}{2} x^2 \left(\frac{2}{b d n}+1\right)",1,"(x^2*(2*E^(2*d*(a + b*Log[c*x^n]))*Hypergeometric2F1[1, 1 + 1/(b*d*n), 2 + 1/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] + (1 + b*d*n)*(b*d*n - 2*Hypergeometric2F1[1, 1/(b*d*n), 1 + 1/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] - 2*Tanh[d*(a + b*Log[c*x^n])])))/(2*b*d*n*(1 + b*d*n))","A",1
182,1,163,127,9.0962487,"\int \tanh ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[Tanh[d*(a + b*Log[c*x^n])]^2,x]","\frac{x \left(e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1+\frac{1}{2 b d n};2+\frac{1}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)+(2 b d n+1) \left(-\, _2F_1\left(1,\frac{1}{2 b d n};1+\frac{1}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)-\tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right)+b d n\right)\right)}{b d n (2 b d n+1)}","-\frac{2 x \, _2F_1\left(1,\frac{1}{2 b d n};1+\frac{1}{2 b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n}+\frac{x \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}+x \left(\frac{1}{b d n}+1\right)",1,"(x*(E^(2*d*(a + b*Log[c*x^n]))*Hypergeometric2F1[1, 1 + 1/(2*b*d*n), 2 + 1/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] + (1 + 2*b*d*n)*(b*d*n - Hypergeometric2F1[1, 1/(2*b*d*n), 1 + 1/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] - Tanh[d*(a + b*Log[c*x^n])])))/(b*d*n*(1 + 2*b*d*n))","A",1
183,1,51,28,0.0846735,"\int \frac{\tanh ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Integrate[Tanh[d*(a + b*Log[c*x^n])]^2/x,x]","\frac{\tanh ^{-1}\left(\tanh \left(a d+b d \log \left(c x^n\right)\right)\right)}{b d n}-\frac{\tanh \left(a d+b d \log \left(c x^n\right)\right)}{b d n}","\log (x)-\frac{\tanh \left(a d+b d \log \left(c x^n\right)\right)}{b d n}",1,"ArcTanh[Tanh[a*d + b*d*Log[c*x^n]]]/(b*d*n) - Tanh[a*d + b*d*Log[c*x^n]]/(b*d*n)","A",1
184,1,162,135,3.5377561,"\int \frac{\tanh ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Integrate[Tanh[d*(a + b*Log[c*x^n])]^2/x^2,x]","-\frac{e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1-\frac{1}{2 b d n};2-\frac{1}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)+(2 b d n-1) \left(\, _2F_1\left(1,-\frac{1}{2 b d n};1-\frac{1}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)+\tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right)+b d n\right)}{b d n x (2 b d n-1)}","-\frac{2 \, _2F_1\left(1,-\frac{1}{2 b d n};1-\frac{1}{2 b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n x}+\frac{1-e^{2 a d} \left(c x^n\right)^{2 b d}}{b d n x \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}-\frac{1-\frac{1}{b d n}}{x}",1,"-((E^(2*d*(a + b*Log[c*x^n]))*Hypergeometric2F1[1, 1 - 1/(2*b*d*n), 2 - 1/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] + (-1 + 2*b*d*n)*(b*d*n + Hypergeometric2F1[1, -1/2*1/(b*d*n), 1 - 1/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] + Tanh[d*(a + b*Log[c*x^n])]))/(b*d*n*(-1 + 2*b*d*n)*x))","A",1
185,1,159,136,3.5865697,"\int \frac{\tanh ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Integrate[Tanh[d*(a + b*Log[c*x^n])]^2/x^3,x]","-\frac{2 e^{2 d \left(a+b \log \left(c x^n\right)\right)} \, _2F_1\left(1,1-\frac{1}{b d n};2-\frac{1}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)+(b d n-1) \left(2 \, _2F_1\left(1,-\frac{1}{b d n};1-\frac{1}{b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)+2 \tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right)+b d n\right)}{2 b d n x^2 (b d n-1)}","-\frac{2 \, _2F_1\left(1,-\frac{1}{b d n};1-\frac{1}{b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n x^2}+\frac{1-e^{2 a d} \left(c x^n\right)^{2 b d}}{b d n x^2 \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}+\frac{2-b d n}{2 b d n x^2}",1,"-1/2*(2*E^(2*d*(a + b*Log[c*x^n]))*Hypergeometric2F1[1, 1 - 1/(b*d*n), 2 - 1/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] + (-1 + b*d*n)*(b*d*n + 2*Hypergeometric2F1[1, -(1/(b*d*n)), 1 - 1/(b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] + 2*Tanh[d*(a + b*Log[c*x^n])]))/(b*d*n*(-1 + b*d*n)*x^2)","A",1
186,1,43,43,0.1458739,"\int \frac{\tanh ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Tanh[a + b*Log[c*x^n]]^3/x,x]","\frac{\log \left(\cosh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\tanh ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}","\frac{\log \left(\cosh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\tanh ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"Log[Cosh[a + b*Log[c*x^n]]]/(b*n) - Tanh[a + b*Log[c*x^n]]^2/(2*b*n)","A",1
187,1,62,45,0.1106636,"\int \frac{\tanh ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Tanh[a + b*Log[c*x^n]]^4/x,x]","\frac{\tanh ^{-1}\left(\tanh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\tanh ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\tanh \left(a+b \log \left(c x^n\right)\right)}{b n}","-\frac{\tanh ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\tanh \left(a+b \log \left(c x^n\right)\right)}{b n}+\log (x)",1,"ArcTanh[Tanh[a + b*Log[c*x^n]]]/(b*n) - Tanh[a + b*Log[c*x^n]]/(b*n) - Tanh[a + b*Log[c*x^n]]^3/(3*b*n)","A",1
188,1,55,66,0.2222329,"\int \frac{\tanh ^5\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Tanh[a + b*Log[c*x^n]]^5/x,x]","\frac{-\tanh ^4\left(a+b \log \left(c x^n\right)\right)-2 \tanh ^2\left(a+b \log \left(c x^n\right)\right)+4 \log \left(\cosh \left(a+b \log \left(c x^n\right)\right)\right)}{4 b n}","-\frac{\tanh ^4\left(a+b \log \left(c x^n\right)\right)}{4 b n}-\frac{\tanh ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}+\frac{\log \left(\cosh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}",1,"(4*Log[Cosh[a + b*Log[c*x^n]]] - 2*Tanh[a + b*Log[c*x^n]]^2 - Tanh[a + b*Log[c*x^n]]^4)/(4*b*n)","A",1
189,1,160,88,14.3270244,"\int (e x)^m \tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Tanh[d*(a + b*Log[c*x^n])],x]","\frac{x (e x)^m \left(\frac{(m+1) e^{2 a d} \left(c x^n\right)^{2 b d} \, _2F_1\left(1,\frac{m+2 b d n+1}{2 b d n};\frac{m+4 b d n+1}{2 b d n};-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{2 b d n+m+1}-\, _2F_1\left(1,\frac{m+1}{2 b d n};\frac{m+1}{2 b d n}+1;-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)\right)}{m+1}","\frac{(e x)^{m+1}}{e (m+1)}-\frac{2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2 b d n};\frac{m+1}{2 b d n}+1;-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{e (m+1)}",1,"(x*(e*x)^m*(-Hypergeometric2F1[1, (1 + m)/(2*b*d*n), 1 + (1 + m)/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] + (E^(2*a*d)*(1 + m)*(c*x^n)^(2*b*d)*Hypergeometric2F1[1, (1 + m + 2*b*d*n)/(2*b*d*n), (1 + m + 4*b*d*n)/(2*b*d*n), -(E^(2*a*d)*(c*x^n)^(2*b*d))])/(1 + m + 2*b*d*n)))/(1 + m)","A",1
190,1,516,169,16.8037796,"\int (e x)^m \tanh ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Tanh[d*(a + b*Log[c*x^n])]^2,x]","\frac{(m+1) x^{-m} (e x)^m \text{sech}\left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)\right) \left(\frac{x^{m+1} \sinh (b d n \log (x)) \text{sech}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{m+1}-\frac{\cosh \left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)\right) \exp \left(-\frac{(2 m+1) \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)}{b n}\right) \left((2 b d n+m+1) \exp \left(\frac{2 a m+a+b (2 m+1) \left(\log \left(c x^n\right)-n \log (x)\right)+b (m+1) n \log (x)}{b n}\right) \, _2F_1\left(1,\frac{m+1}{2 b d n};\frac{m+1}{2 b d n}+1;-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)-(m+1) \exp \left(\frac{a (2 b d n+2 m+1)}{b n}+\frac{(2 b d n+2 m+1) \left(\log \left(c x^n\right)-n \log (x)\right)}{n}+\log (x) (2 b d n+m+1)\right) \, _2F_1\left(1,\frac{m+2 b d n+1}{2 b d n};\frac{m+4 b d n+1}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)+(2 b d n+m+1) \tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right) \exp \left(\frac{2 a m+a+b (2 m+1) \left(\log \left(c x^n\right)-n \log (x)\right)+b (m+1) n \log (x)}{b n}\right)\right)}{(m+1) (2 b d n+m+1)}\right)}{b d n}-\frac{x (e x)^m \sinh (b d n \log (x)) \text{sech}\left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)\right) \text{sech}\left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)+b d n \log (x)\right)}{b d n}+\frac{x (e x)^m}{m+1}","-\frac{2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2 b d n};\frac{m+1}{2 b d n}+1;-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d e n}+\frac{(e x)^{m+1} \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d e n \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}+\frac{(e x)^{m+1} (b d n+m+1)}{b d e (m+1) n}",1,"(x*(e*x)^m)/(1 + m) - (x*(e*x)^m*Sech[d*(a + b*(-(n*Log[x]) + Log[c*x^n]))]*Sech[b*d*n*Log[x] + d*(a + b*(-(n*Log[x]) + Log[c*x^n]))]*Sinh[b*d*n*Log[x]])/(b*d*n) + ((1 + m)*(e*x)^m*Sech[d*(a + b*(-(n*Log[x]) + Log[c*x^n]))]*((x^(1 + m)*Sech[d*(a + b*Log[c*x^n])]*Sinh[b*d*n*Log[x]])/(1 + m) - (Cosh[d*(a + b*(-(n*Log[x]) + Log[c*x^n]))]*(E^((a + 2*a*m + b*(1 + m)*n*Log[x] + b*(1 + 2*m)*(-(n*Log[x]) + Log[c*x^n]))/(b*n))*(1 + m + 2*b*d*n)*Hypergeometric2F1[1, (1 + m)/(2*b*d*n), 1 + (1 + m)/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] - E^((a*(1 + 2*m + 2*b*d*n))/(b*n) + (1 + m + 2*b*d*n)*Log[x] + ((1 + 2*m + 2*b*d*n)*(-(n*Log[x]) + Log[c*x^n]))/n)*(1 + m)*Hypergeometric2F1[1, (1 + m + 2*b*d*n)/(2*b*d*n), (1 + m + 4*b*d*n)/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] + E^((a + 2*a*m + b*(1 + m)*n*Log[x] + b*(1 + 2*m)*(-(n*Log[x]) + Log[c*x^n]))/(b*n))*(1 + m + 2*b*d*n)*Tanh[d*(a + b*Log[c*x^n])]))/(E^(((1 + 2*m)*(a + b*(-(n*Log[x]) + Log[c*x^n])))/(b*n))*(1 + m)*(1 + m + 2*b*d*n))))/(b*d*n*x^m)","B",1
191,1,606,307,17.364636,"\int (e x)^m \tanh ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Tanh[d*(a + b*Log[c*x^n])]^3,x]","\frac{x^{-m} (e x)^m \left(2 b^2 d^2 n^2+m^2+2 m+1\right) \text{sech}\left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)\right) \left(\frac{x^{m+1} \sinh (b d n \log (x)) \text{sech}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{m+1}-\frac{\cosh \left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)\right) \exp \left(-\frac{(2 m+1) \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)}{b n}\right) \left((2 b d n+m+1) \exp \left(\frac{2 a m+a+b (2 m+1) \left(\log \left(c x^n\right)-n \log (x)\right)+b (m+1) n \log (x)}{b n}\right) \, _2F_1\left(1,\frac{m+1}{2 b d n};\frac{m+1}{2 b d n}+1;-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)-(m+1) \exp \left(\frac{a (2 b d n+2 m+1)}{b n}+\frac{(2 b d n+2 m+1) \left(\log \left(c x^n\right)-n \log (x)\right)}{n}+\log (x) (2 b d n+m+1)\right) \, _2F_1\left(1,\frac{m+2 b d n+1}{2 b d n};\frac{m+4 b d n+1}{2 b d n};-e^{2 d \left(a+b \log \left(c x^n\right)\right)}\right)+(2 b d n+m+1) \tanh \left(d \left(a+b \log \left(c x^n\right)\right)\right) \exp \left(\frac{2 a m+a+b (2 m+1) \left(\log \left(c x^n\right)-n \log (x)\right)+b (m+1) n \log (x)}{b n}\right)\right)}{(m+1) (2 b d n+m+1)}\right)}{2 b^2 d^2 n^2}-\frac{(m+1) x (e x)^m \sinh (b d n \log (x)) \text{sech}\left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)\right) \text{sech}\left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)+b d n \log (x)\right)}{2 b^2 d^2 n^2}+\frac{x (e x)^m \tanh \left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)\right)}{m+1}+\frac{x (e x)^m \text{sech}^2\left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)+b d n \log (x)\right)}{2 b d n}","-\frac{(e x)^{m+1} \left(2 b^2 d^2 n^2+m^2+2 m+1\right) \, _2F_1\left(1,\frac{m+1}{2 b d n};\frac{m+1}{2 b d n}+1;-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b^2 d^2 e (m+1) n^2}+\frac{e^{-2 a d} (e x)^{m+1} \left(\frac{e^{2 a d} (-2 b d n+m+1)}{n}-\frac{e^{4 a d} (2 b d n+m+1) \left(c x^n\right)^{2 b d}}{n}\right)}{2 b^2 d^2 e n \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}-\frac{(e x)^{m+1} \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)^2}{2 b d e n \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)^2}+\frac{(e x)^{m+1} (b d n+m+1) (2 b d n+m+1)}{2 b^2 d^2 e (m+1) n^2}",1,"(x*(e*x)^m*Sech[b*d*n*Log[x] + d*(a + b*(-(n*Log[x]) + Log[c*x^n]))]^2)/(2*b*d*n) - ((1 + m)*x*(e*x)^m*Sech[d*(a + b*(-(n*Log[x]) + Log[c*x^n]))]*Sech[b*d*n*Log[x] + d*(a + b*(-(n*Log[x]) + Log[c*x^n]))]*Sinh[b*d*n*Log[x]])/(2*b^2*d^2*n^2) + ((1 + 2*m + m^2 + 2*b^2*d^2*n^2)*(e*x)^m*Sech[d*(a + b*(-(n*Log[x]) + Log[c*x^n]))]*((x^(1 + m)*Sech[d*(a + b*Log[c*x^n])]*Sinh[b*d*n*Log[x]])/(1 + m) - (Cosh[d*(a + b*(-(n*Log[x]) + Log[c*x^n]))]*(E^((a + 2*a*m + b*(1 + m)*n*Log[x] + b*(1 + 2*m)*(-(n*Log[x]) + Log[c*x^n]))/(b*n))*(1 + m + 2*b*d*n)*Hypergeometric2F1[1, (1 + m)/(2*b*d*n), 1 + (1 + m)/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] - E^((a*(1 + 2*m + 2*b*d*n))/(b*n) + (1 + m + 2*b*d*n)*Log[x] + ((1 + 2*m + 2*b*d*n)*(-(n*Log[x]) + Log[c*x^n]))/n)*(1 + m)*Hypergeometric2F1[1, (1 + m + 2*b*d*n)/(2*b*d*n), (1 + m + 4*b*d*n)/(2*b*d*n), -E^(2*d*(a + b*Log[c*x^n]))] + E^((a + 2*a*m + b*(1 + m)*n*Log[x] + b*(1 + 2*m)*(-(n*Log[x]) + Log[c*x^n]))/(b*n))*(1 + m + 2*b*d*n)*Tanh[d*(a + b*Log[c*x^n])]))/(E^(((1 + 2*m)*(a + b*(-(n*Log[x]) + Log[c*x^n])))/(b*n))*(1 + m)*(1 + m + 2*b*d*n))))/(2*b^2*d^2*n^2*x^m) + (x*(e*x)^m*Tanh[d*(a + b*(-(n*Log[x]) + Log[c*x^n]))])/(1 + m)","A",0
192,1,387,115,4.1286577,"\int \tanh ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[Tanh[d*(a + b*Log[c*x^n])]^p,x]","\frac{x (2 b d n+1) \left(\frac{e^{2 a d} \left(c x^n\right)^{2 b d}-1}{e^{2 a d} \left(c x^n\right)^{2 b d}+1}\right)^p F_1\left(\frac{1}{2 b d n};-p,p;1+\frac{1}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d},-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{-2 b d n p e^{2 a d} \left(c x^n\right)^{2 b d} F_1\left(1+\frac{1}{2 b d n};1-p,p;2+\frac{1}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d},-e^{2 a d} \left(c x^n\right)^{2 b d}\right)-2 b d n p e^{2 a d} \left(c x^n\right)^{2 b d} F_1\left(1+\frac{1}{2 b d n};-p,p+1;2+\frac{1}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d},-e^{2 a d} \left(c x^n\right)^{2 b d}\right)+(2 b d n+1) F_1\left(\frac{1}{2 b d n};-p,p;1+\frac{1}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d},-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}","x \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)^{-p} \left(e^{2 a d} \left(c x^n\right)^{2 b d}-1\right)^p F_1\left(\frac{1}{2 b d n};-p,p;1+\frac{1}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d},-e^{2 a d} \left(c x^n\right)^{2 b d}\right)",1,"((1 + 2*b*d*n)*x*((-1 + E^(2*a*d)*(c*x^n)^(2*b*d))/(1 + E^(2*a*d)*(c*x^n)^(2*b*d)))^p*AppellF1[1/(2*b*d*n), -p, p, 1 + 1/(2*b*d*n), E^(2*a*d)*(c*x^n)^(2*b*d), -(E^(2*a*d)*(c*x^n)^(2*b*d))])/(-2*b*d*E^(2*a*d)*n*p*(c*x^n)^(2*b*d)*AppellF1[1 + 1/(2*b*d*n), 1 - p, p, 2 + 1/(2*b*d*n), E^(2*a*d)*(c*x^n)^(2*b*d), -(E^(2*a*d)*(c*x^n)^(2*b*d))] - 2*b*d*E^(2*a*d)*n*p*(c*x^n)^(2*b*d)*AppellF1[1 + 1/(2*b*d*n), -p, 1 + p, 2 + 1/(2*b*d*n), E^(2*a*d)*(c*x^n)^(2*b*d), -(E^(2*a*d)*(c*x^n)^(2*b*d))] + (1 + 2*b*d*n)*AppellF1[1/(2*b*d*n), -p, p, 1 + 1/(2*b*d*n), E^(2*a*d)*(c*x^n)^(2*b*d), -(E^(2*a*d)*(c*x^n)^(2*b*d))])","B",0
193,1,174,135,5.6026929,"\int (e x)^m \tanh ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Tanh[d*(a + b*Log[c*x^n])]^p,x]","\frac{x (e x)^m \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)^{-p} \left(\frac{e^{2 a d} \left(c x^n\right)^{2 b d}-1}{e^{2 a d} \left(c x^n\right)^{2 b d}+1}\right)^p \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)^p F_1\left(\frac{m+1}{2 b d n};-p,p;\frac{m+1}{2 b d n}+1;e^{2 a d} \left(c x^n\right)^{2 b d},-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{m+1}","\frac{(e x)^{m+1} \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)^{-p} \left(e^{2 a d} \left(c x^n\right)^{2 b d}-1\right)^p F_1\left(\frac{m+1}{2 b d n};-p,p;\frac{m+1}{2 b d n}+1;e^{2 a d} \left(c x^n\right)^{2 b d},-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{e (m+1)}",1,"(x*(e*x)^m*((-1 + E^(2*a*d)*(c*x^n)^(2*b*d))/(1 + E^(2*a*d)*(c*x^n)^(2*b*d)))^p*(1 + E^(2*a*d)*(c*x^n)^(2*b*d))^p*AppellF1[(1 + m)/(2*b*d*n), -p, p, 1 + (1 + m)/(2*b*d*n), E^(2*a*d)*(c*x^n)^(2*b*d), -(E^(2*a*d)*(c*x^n)^(2*b*d))])/((1 + m)*(1 - E^(2*a*d)*(c*x^n)^(2*b*d))^p)","A",0
194,1,64,73,0.2904592,"\int \frac{\tanh ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Tanh[a + b*Log[c*x^n]]^(5/2)/x,x]","-\frac{-3 \tanh ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)+2 \tanh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)+3 \tan ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{3 b n}","\frac{\tanh ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}-\frac{2 \tanh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\tan ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"-1/3*(3*ArcTan[Sqrt[Tanh[a + b*Log[c*x^n]]]] - 3*ArcTanh[Sqrt[Tanh[a + b*Log[c*x^n]]]] + 2*Tanh[a + b*Log[c*x^n]]^(3/2))/(b*n)","A",1
195,1,57,70,0.1391607,"\int \frac{\tanh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Tanh[a + b*Log[c*x^n]]^(3/2)/x,x]","\frac{\tanh ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)-2 \sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}+\tan ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","\frac{\tanh ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}-\frac{2 \sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}}{b n}+\frac{\tan ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"(ArcTan[Sqrt[Tanh[a + b*Log[c*x^n]]]] + ArcTanh[Sqrt[Tanh[a + b*Log[c*x^n]]]] - 2*Sqrt[Tanh[a + b*Log[c*x^n]]])/(b*n)","A",1
196,1,48,48,0.0800076,"\int \frac{\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Integrate[Sqrt[Tanh[a + b*Log[c*x^n]]]/x,x]","\frac{\tanh ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}-\frac{\tan ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","\frac{\tanh ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}-\frac{\tan ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"-(ArcTan[Sqrt[Tanh[a + b*Log[c*x^n]]]]/(b*n)) + ArcTanh[Sqrt[Tanh[a + b*Log[c*x^n]]]]/(b*n)","A",1
197,1,47,47,0.1199228,"\int \frac{1}{x \sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}} \, dx","Integrate[1/(x*Sqrt[Tanh[a + b*Log[c*x^n]]]),x]","\frac{\tanh ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tan ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","\frac{\tanh ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tan ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"ArcTan[Sqrt[Tanh[a + b*Log[c*x^n]]]]/(b*n) + ArcTanh[Sqrt[Tanh[a + b*Log[c*x^n]]]]/(b*n)","A",1
198,1,44,71,0.1645915,"\int \frac{1}{x \tanh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Tanh[a + b*Log[c*x^n]]^(3/2)),x]","-\frac{2 \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};\tanh ^2\left(a+b \log \left(c x^n\right)\right)\right)}{b n \sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}}","\frac{\tanh ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}-\frac{2}{b n \sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}}-\frac{\tan ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"(-2*Hypergeometric2F1[-1/4, 1, 3/4, Tanh[a + b*Log[c*x^n]]^2])/(b*n*Sqrt[Tanh[a + b*Log[c*x^n]]])","C",1
199,1,46,72,0.2194274,"\int \frac{1}{x \tanh ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Tanh[a + b*Log[c*x^n]]^(5/2)),x]","-\frac{2 \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};\tanh ^2\left(a+b \log \left(c x^n\right)\right)\right)}{3 b n \tanh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{\tanh ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}-\frac{2}{3 b n \tanh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}+\frac{\tan ^{-1}\left(\sqrt{\tanh \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"(-2*Hypergeometric2F1[-3/4, 1, 1/4, Tanh[a + b*Log[c*x^n]]^2])/(3*b*n*Tanh[a + b*Log[c*x^n]]^(3/2))","C",1
200,1,136,135,1.3801982,"\int \frac{\tanh ^5(x)}{\sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}} \, dx","Integrate[Tanh[x]^5/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4],x]","\frac{1}{4} \left(\frac{(2 c-b) \tanh ^{-1}\left(\frac{-b-2 c \tanh ^2(x)}{2 \sqrt{c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{c^{3/2}}-\frac{2 \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}{c}+\frac{2 \tanh ^{-1}\left(\frac{2 a+(b+2 c) \tanh ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{\sqrt{a+b+c}}\right)","\frac{(b-2 c) \tanh ^{-1}\left(\frac{b+2 c \tanh ^2(x)}{2 \sqrt{c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{4 c^{3/2}}-\frac{\sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}{2 c}+\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \tanh ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{a+b+c}}",1,"(((-b + 2*c)*ArcTanh[(-b - 2*c*Tanh[x]^2)/(2*Sqrt[c]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])])/c^(3/2) + (2*ArcTanh[(2*a + b + (b + 2*c)*Tanh[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])])/Sqrt[a + b + c] - (2*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])/c)/4","A",1
201,1,105,105,0.0778334,"\int \frac{\tanh ^3(x)}{\sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}} \, dx","Integrate[Tanh[x]^3/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4],x]","\frac{1}{2} \left(\frac{\tanh ^{-1}\left(\frac{-b-2 c \tanh ^2(x)}{2 \sqrt{c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{\sqrt{c}}+\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \tanh ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{\sqrt{a+b+c}}\right)","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \tanh ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{a+b+c}}-\frac{\tanh ^{-1}\left(\frac{b+2 c \tanh ^2(x)}{2 \sqrt{c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{c}}",1,"(ArcTanh[(-b - 2*c*Tanh[x]^2)/(2*Sqrt[c]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])]/Sqrt[c] + ArcTanh[(2*a + b + (b + 2*c)*Tanh[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])]/Sqrt[a + b + c])/2","A",1
202,1,58,58,0.0328338,"\int \frac{\tanh (x)}{\sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}} \, dx","Integrate[Tanh[x]/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4],x]","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \tanh ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{a+b+c}}","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \tanh ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{a+b+c}}",1,"ArcTanh[(2*a + b + (b + 2*c)*Tanh[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])]/(2*Sqrt[a + b + c])","A",1
203,1,109,106,0.3512783,"\int \frac{\coth (x)}{\sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}} \, dx","Integrate[Coth[x]/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4],x]","-\frac{\tanh ^{-1}\left(\frac{2 a+b \tanh ^2(x)}{2 \sqrt{a} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{a}}-\frac{\tanh ^{-1}\left(\frac{-2 a-\left((b+2 c) \tanh ^2(x)\right)-b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{a+b+c}}","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \tanh ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{a+b+c}}-\frac{\tanh ^{-1}\left(\frac{2 a+b \tanh ^2(x)}{2 \sqrt{a} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{a}}",1,"-1/2*ArcTanh[(2*a + b*Tanh[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])]/Sqrt[a] - ArcTanh[(-2*a - b - (b + 2*c)*Tanh[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])]/(2*Sqrt[a + b + c])","A",1
204,1,142,183,0.6543307,"\int \frac{\coth ^3(x)}{\sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}} \, dx","Integrate[Coth[x]^3/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4],x]","-\frac{(2 a-b) \tanh ^{-1}\left(\frac{2 a+b \tanh ^2(x)}{2 \sqrt{a} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{4 a^{3/2}}+\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \tanh ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{a+b+c}}-\frac{\coth ^2(x) \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}{2 a}","\frac{b \tanh ^{-1}\left(\frac{2 a+b \tanh ^2(x)}{2 \sqrt{a} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{4 a^{3/2}}-\frac{\tanh ^{-1}\left(\frac{2 a+b \tanh ^2(x)}{2 \sqrt{a} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{a}}+\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \tanh ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{2 \sqrt{a+b+c}}-\frac{\coth ^2(x) \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}{2 a}",1,"-1/4*((2*a - b)*ArcTanh[(2*a + b*Tanh[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])])/a^(3/2) + ArcTanh[(2*a + b + (b + 2*c)*Tanh[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])]/(2*Sqrt[a + b + c]) - (Coth[x]^2*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])/(2*a)","A",1
205,1,131,132,0.3539597,"\int \tanh (x) \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)} \, dx","Integrate[Tanh[x]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4],x]","\frac{1}{4} \left(-2 \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}+\frac{(b+2 c) \tanh ^{-1}\left(\frac{-b-2 c \tanh ^2(x)}{2 \sqrt{c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{\sqrt{c}}+2 \sqrt{a+b+c} \tanh ^{-1}\left(\frac{2 a+(b+2 c) \tanh ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)\right)","-\frac{1}{2} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}-\frac{(b+2 c) \tanh ^{-1}\left(\frac{b+2 c \tanh ^2(x)}{2 \sqrt{c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)}{4 \sqrt{c}}+\frac{1}{2} \sqrt{a+b+c} \tanh ^{-1}\left(\frac{2 a+(b+2 c) \tanh ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \tanh ^2(x)+c \tanh ^4(x)}}\right)",1,"(((b + 2*c)*ArcTanh[(-b - 2*c*Tanh[x]^2)/(2*Sqrt[c]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])])/Sqrt[c] + 2*Sqrt[a + b + c]*ArcTanh[(2*a + b + (b + 2*c)*Tanh[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])] - 2*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4])/4","A",1
206,1,76,107,0.1504825,"\int e^{a+b x} \tanh ^4(a+b x) \, dx","Integrate[E^(a + b*x)*Tanh[a + b*x]^4,x]","\frac{e^{a+b x} \left(25 e^{2 (a+b x)}+24 e^{4 (a+b x)}+3 e^{6 (a+b x)}+12\right)}{3 b \left(e^{2 (a+b x)}+1\right)^3}-\frac{3 \tan ^{-1}\left(e^{a+b x}\right)}{b}","\frac{e^{a+b x}}{b}+\frac{5 e^{a+b x}}{b \left(e^{2 a+2 b x}+1\right)}-\frac{14 e^{a+b x}}{3 b \left(e^{2 a+2 b x}+1\right)^2}+\frac{8 e^{a+b x}}{3 b \left(e^{2 a+2 b x}+1\right)^3}-\frac{3 \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(E^(a + b*x)*(12 + 25*E^(2*(a + b*x)) + 24*E^(4*(a + b*x)) + 3*E^(6*(a + b*x))))/(3*b*(1 + E^(2*(a + b*x)))^3) - (3*ArcTan[E^(a + b*x)])/b","A",1
207,1,60,77,0.1190065,"\int e^{a+b x} \tanh ^3(a+b x) \, dx","Integrate[E^(a + b*x)*Tanh[a + b*x]^3,x]","\frac{e^{a+b x} \left(5 e^{2 (a+b x)}+e^{4 (a+b x)}+2\right)}{b \left(e^{2 (a+b x)}+1\right)^2}-\frac{3 \tan ^{-1}\left(e^{a+b x}\right)}{b}","\frac{e^{a+b x}}{b}+\frac{3 e^{a+b x}}{b \left(e^{2 a+2 b x}+1\right)}-\frac{2 e^{a+b x}}{b \left(e^{2 a+2 b x}+1\right)^2}-\frac{3 \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(E^(a + b*x)*(2 + 5*E^(2*(a + b*x)) + E^(4*(a + b*x))))/(b*(1 + E^(2*(a + b*x)))^2) - (3*ArcTan[E^(a + b*x)])/b","A",1
208,1,40,51,0.0970756,"\int e^{a+b x} \tanh ^2(a+b x) \, dx","Integrate[E^(a + b*x)*Tanh[a + b*x]^2,x]","\frac{e^{a+b x} \left(\frac{2}{e^{2 (a+b x)}+1}+1\right)-2 \tan ^{-1}\left(e^{a+b x}\right)}{b}","\frac{e^{a+b x}}{b}+\frac{2 e^{a+b x}}{b \left(e^{2 a+2 b x}+1\right)}-\frac{2 \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(E^(a + b*x)*(1 + 2/(1 + E^(2*(a + b*x)))) - 2*ArcTan[E^(a + b*x)])/b","A",1
209,1,22,25,0.0157256,"\int e^{a+b x} \tanh (a+b x) \, dx","Integrate[E^(a + b*x)*Tanh[a + b*x],x]","\frac{e^{a+b x}-2 \tan ^{-1}\left(e^{a+b x}\right)}{b}","\frac{e^{a+b x}}{b}-\frac{2 \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(E^(a + b*x) - 2*ArcTan[E^(a + b*x)])/b","A",1
210,1,22,25,0.0200237,"\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
211,1,179,53,1.913129,"\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
212,1,286,81,2.3705422,"\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
213,1,115,113,10.1160483,"\int e^{a+b x} \coth ^4(a+b x) \, dx","Integrate[E^(a + b*x)*Coth[a + b*x]^4,x]","\frac{-24 e^{a+b x}+50 e^{3 (a+b x)}-48 e^{5 (a+b x)}+6 e^{7 (a+b x)}+9 \left(e^{2 (a+b x)}-1\right)^3 \log \left(1-e^{a+b x}\right)-9 \left(e^{2 (a+b x)}-1\right)^3 \log \left(e^{a+b x}+1\right)}{6 b \left(e^{2 (a+b x)}-1\right)^3}","\frac{e^{a+b x}}{b}+\frac{5 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)}-\frac{14 e^{a+b x}}{3 b \left(1-e^{2 a+2 b x}\right)^2}+\frac{8 e^{a+b x}}{3 b \left(1-e^{2 a+2 b x}\right)^3}-\frac{3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(-24*E^(a + b*x) + 50*E^(3*(a + b*x)) - 48*E^(5*(a + b*x)) + 6*E^(7*(a + b*x)) + 9*(-1 + E^(2*(a + b*x)))^3*Log[1 - E^(a + b*x)] - 9*(-1 + E^(2*(a + b*x)))^3*Log[1 + E^(a + b*x)])/(6*b*(-1 + E^(2*(a + b*x)))^3)","A",1
214,1,48,113,0.047965,"\int e^x \tanh ^2(2 x) \, dx","Integrate[E^x*Tanh[2*x]^2,x]","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^4+1\&,\frac{x-\log \left(e^x-\text{$\#$1}\right)}{\text{$\#$1}^3}\&\right]+e^x+\frac{e^x}{e^{4 x}+1}","e^x+\frac{e^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,"E^x + E^x/(1 + E^(4*x)) + RootSum[1 + #1^4 & , (x - Log[E^x - #1])/#1^3 & ]/4","C",1
215,1,95,95,0.0349667,"\int e^x \tanh (2 x) \, dx","Integrate[E^x*Tanh[2*x],x]","e^x+\frac{\log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} e^x\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} e^x+1\right)}{\sqrt{2}}","e^x+\frac{\log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} e^x\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} e^x+1\right)}{\sqrt{2}}",1,"E^x + ArcTan[1 - Sqrt[2]*E^x]/Sqrt[2] - ArcTan[1 + Sqrt[2]*E^x]/Sqrt[2] + Log[1 - Sqrt[2]*E^x + E^(2*x)]/(2*Sqrt[2]) - Log[1 + Sqrt[2]*E^x + E^(2*x)]/(2*Sqrt[2])","A",1
216,1,16,16,0.012761,"\int e^x \coth (2 x) \, dx","Integrate[E^x*Coth[2*x],x]","e^x-\tan ^{-1}\left(e^x\right)-\tanh ^{-1}\left(e^x\right)","e^x-\tan ^{-1}\left(e^x\right)-\tanh ^{-1}\left(e^x\right)",1,"E^x - ArcTan[E^x] - ArcTanh[E^x]","A",1
217,1,113,35,1.6194249,"\int e^x \coth ^2(2 x) \, dx","Integrate[E^x*Coth[2*x]^2,x]","\frac{16}{585} e^{5 x} \left(e^{4 x}+1\right)^2 \, _4F_3\left(\frac{5}{4},2,2,2;1,1,\frac{17}{4};e^{4 x}\right)+\frac{1}{640} e^{-7 x} \left(5 \left(1208 e^{4 x}+102 e^{8 x}-248 e^{12 x}+e^{16 x}+729\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};e^{4 x}\right)-6769 e^{4 x}-1483 e^{8 x}+681 e^{12 x}-3645\right)","e^x+\frac{e^x}{1-e^{4 x}}-\frac{1}{2} \tan ^{-1}\left(e^x\right)-\frac{1}{2} \tanh ^{-1}\left(e^x\right)",1,"(-3645 - 6769*E^(4*x) - 1483*E^(8*x) + 681*E^(12*x) + 5*(729 + 1208*E^(4*x) + 102*E^(8*x) - 248*E^(12*x) + E^(16*x))*Hypergeometric2F1[1/4, 1, 5/4, E^(4*x)])/(640*E^(7*x)) + (16*E^(5*x)*(1 + E^(4*x))^2*HypergeometricPFQ[{5/4, 2, 2, 2}, {1, 1, 17/4}, E^(4*x)])/585","C",0
218,1,97,113,0.0837589,"\int e^x \tanh ^2(3 x) \, dx","Integrate[E^x*Tanh[3*x]^2,x]","-\frac{1}{9} \text{RootSum}\left[\text{$\#$1}^4-\text{$\#$1}^2+1\&,\frac{\text{$\#$1}^2 x-\text{$\#$1}^2 \log \left(e^x-\text{$\#$1}\right)+2 \log \left(e^x-\text{$\#$1}\right)-2 x}{2 \text{$\#$1}^3-\text{$\#$1}}\&\right]+e^x+\frac{2 e^x}{3 \left(e^{6 x}+1\right)}-\frac{2}{9} \tan ^{-1}\left(e^x\right)","e^x+\frac{2 e^x}{3 \left(e^{6 x}+1\right)}+\frac{\log \left(-\sqrt{3} e^x+e^{2 x}+1\right)}{6 \sqrt{3}}-\frac{\log \left(\sqrt{3} e^x+e^{2 x}+1\right)}{6 \sqrt{3}}-\frac{2}{9} \tan ^{-1}\left(e^x\right)+\frac{1}{9} \tan ^{-1}\left(\sqrt{3}-2 e^x\right)-\frac{1}{9} \tan ^{-1}\left(2 e^x+\sqrt{3}\right)",1,"E^x + (2*E^x)/(3*(1 + E^(6*x))) - (2*ArcTan[E^x])/9 - RootSum[1 - #1^2 + #1^4 & , (-2*x + 2*Log[E^x - #1] + x*#1^2 - Log[E^x - #1]*#1^2)/(-#1 + 2*#1^3) & ]/9","C",1
219,1,24,97,0.0130127,"\int e^x \tanh (3 x) \, dx","Integrate[E^x*Tanh[3*x],x]","e^x-2 e^x \, _2F_1\left(\frac{1}{6},1;\frac{7}{6};-e^{6 x}\right)","e^x+\frac{\log \left(-\sqrt{3} e^x+e^{2 x}+1\right)}{2 \sqrt{3}}-\frac{\log \left(\sqrt{3} e^x+e^{2 x}+1\right)}{2 \sqrt{3}}-\frac{2}{3} \tan ^{-1}\left(e^x\right)+\frac{1}{3} \tan ^{-1}\left(\sqrt{3}-2 e^x\right)-\frac{1}{3} \tan ^{-1}\left(2 e^x+\sqrt{3}\right)",1,"E^x - 2*E^x*Hypergeometric2F1[1/6, 1, 7/6, -E^(6*x)]","C",1
220,1,22,85,0.0166875,"\int e^x \coth (3 x) \, dx","Integrate[E^x*Coth[3*x],x]","e^x-2 e^x \, _2F_1\left(\frac{1}{6},1;\frac{7}{6};e^{6 x}\right)","e^x+\frac{1}{6} \log \left(-e^x+e^{2 x}+1\right)-\frac{1}{6} \log \left(e^x+e^{2 x}+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 e^x}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 e^x+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2}{3} \tanh ^{-1}\left(e^x\right)",1,"E^x - 2*E^x*Hypergeometric2F1[1/6, 1, 7/6, E^(6*x)]","C",1
221,1,113,108,1.9005871,"\int e^x \coth ^2(3 x) \, dx","Integrate[E^x*Coth[3*x]^2,x]","\frac{36 e^{7 x} \left(e^{6 x}+1\right)^2 \, _4F_3\left(\frac{7}{6},2,2,2;1,1,\frac{25}{6};e^{6 x}\right)}{1729}+\frac{e^{-11 x} \left(7 \left(3708 e^{6 x}+538 e^{12 x}-684 e^{18 x}+e^{24 x}+2197\right) \, _2F_1\left(\frac{1}{6},1;\frac{7}{6};e^{6 x}\right)-28153 e^{6 x}-5633 e^{12 x}+3109 e^{18 x}-15379\right)}{3024}","e^x+\frac{2 e^x}{3 \left(1-e^{6 x}\right)}+\frac{1}{18} \log \left(-e^x+e^{2 x}+1\right)-\frac{1}{18} \log \left(e^x+e^{2 x}+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 e^x}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 e^x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{2}{9} \tanh ^{-1}\left(e^x\right)",1,"(-15379 - 28153*E^(6*x) - 5633*E^(12*x) + 3109*E^(18*x) + 7*(2197 + 3708*E^(6*x) + 538*E^(12*x) - 684*E^(18*x) + E^(24*x))*Hypergeometric2F1[1/6, 1, 7/6, E^(6*x)])/(3024*E^(11*x)) + (36*E^(7*x)*(1 + E^(6*x))^2*HypergeometricPFQ[{7/6, 2, 2, 2}, {1, 1, 25/6}, E^(6*x)])/1729","C",0
222,1,51,382,0.0508792,"\int e^x \tanh ^2(4 x) \, dx","Integrate[E^x*Tanh[4*x]^2,x]","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8+1\&,\frac{x-\log \left(e^x-\text{$\#$1}\right)}{\text{$\#$1}^7}\&\right]+e^x+\frac{e^x}{2 \left(e^{8 x}+1\right)}","e^x+\frac{e^x}{2 \left(e^{8 x}+1\right)}+\frac{1}{32} \sqrt{2-\sqrt{2}} \log \left(-\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)-\frac{1}{32} \sqrt{2-\sqrt{2}} \log \left(\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)+\frac{1}{32} \sqrt{2+\sqrt{2}} \log \left(-\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)-\frac{1}{32} \sqrt{2+\sqrt{2}} \log \left(\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 e^x}{\sqrt{2+\sqrt{2}}}\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 e^x}{\sqrt{2-\sqrt{2}}}\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}",1,"E^x + E^x/(2*(1 + E^(8*x))) + RootSum[1 + #1^8 & , (x - Log[E^x - #1])/#1^7 & ]/16","C",1
223,1,24,366,0.013424,"\int e^x \tanh (4 x) \, dx","Integrate[E^x*Tanh[4*x],x]","e^x-2 e^x \, _2F_1\left(\frac{1}{8},1;\frac{9}{8};-e^{8 x}\right)","e^x+\frac{1}{8} \sqrt{2-\sqrt{2}} \log \left(-\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)-\frac{1}{8} \sqrt{2-\sqrt{2}} \log \left(\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)+\frac{1}{8} \sqrt{2+\sqrt{2}} \log \left(-\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)-\frac{1}{8} \sqrt{2+\sqrt{2}} \log \left(\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 e^x}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 e^x}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2 \left(2+\sqrt{2}\right)}}",1,"E^x - 2*E^x*Hypergeometric2F1[1/8, 1, 9/8, -E^(8*x)]","C",1
224,1,22,116,0.0176956,"\int e^x \coth (4 x) \, dx","Integrate[E^x*Coth[4*x],x]","e^x-2 e^x \, _2F_1\left(\frac{1}{8},1;\frac{9}{8};e^{8 x}\right)","e^x+\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{1}{2} \tan ^{-1}\left(e^x\right)+\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}}-\frac{1}{2} \tanh ^{-1}\left(e^x\right)",1,"E^x - 2*E^x*Hypergeometric2F1[1/8, 1, 9/8, E^(8*x)]","C",1
225,1,113,134,1.8793433,"\int e^x \coth ^2(4 x) \, dx","Integrate[E^x*Coth[4*x]^2,x]","\frac{64 e^{9 x} \left(e^{8 x}+1\right)^2 \, _4F_3\left(\frac{9}{8},2,2,2;1,1,\frac{33}{8};e^{8 x}\right)}{3825}+\frac{e^{-15 x} \left(9 \left(8368 e^{8 x}+1486 e^{16 x}-1456 e^{24 x}+e^{32 x}+4913\right) \, _2F_1\left(\frac{1}{8},1;\frac{9}{8};e^{8 x}\right)-80225 e^{8 x}-15127 e^{16 x}+9361 e^{24 x}-44217\right)}{9216}","e^x+\frac{e^x}{2 \left(1-e^{8 x}\right)}+\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{1}{8} \tan ^{-1}\left(e^x\right)+\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}}-\frac{1}{8} \tanh ^{-1}\left(e^x\right)",1,"(-44217 - 80225*E^(8*x) - 15127*E^(16*x) + 9361*E^(24*x) + 9*(4913 + 8368*E^(8*x) + 1486*E^(16*x) - 1456*E^(24*x) + E^(32*x))*Hypergeometric2F1[1/8, 1, 9/8, E^(8*x)])/(9216*E^(15*x)) + (64*E^(9*x)*(1 + E^(8*x))^2*HypergeometricPFQ[{9/8, 2, 2, 2}, {1, 1, 33/8}, E^(8*x)])/3825","C",0
226,1,81,107,0.0857255,"\int \frac{e^x}{a-\tanh (2 x)} \, dx","Integrate[E^x/(a - Tanh[2*x]),x]","\frac{-\sqrt[4]{1-a} (a+1)^{3/4} e^x+\tan ^{-1}\left(\frac{\sqrt[4]{1-a} e^x}{\sqrt[4]{a+1}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{1-a} e^x}{\sqrt[4]{a+1}}\right)}{(1-a)^{5/4} (a+1)^{3/4}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{1-a} e^x}{\sqrt[4]{a+1}}\right)}{(1-a) \sqrt{a+1} \sqrt[4]{1-a^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{1-a} e^x}{\sqrt[4]{a+1}}\right)}{(1-a) \sqrt{a+1} \sqrt[4]{1-a^2}}-\frac{e^x}{1-a}",1,"(-((1 - a)^(1/4)*(1 + a)^(3/4)*E^x) + ArcTan[((1 - a)^(1/4)*E^x)/(1 + a)^(1/4)] + ArcTanh[((1 - a)^(1/4)*E^x)/(1 + a)^(1/4)])/((1 - a)^(5/4)*(1 + a)^(3/4))","A",1
227,1,107,152,0.1670224,"\int \frac{e^x}{(a-\tanh (2 x))^2} \, dx","Integrate[E^x/(a - Tanh[2*x])^2,x]","\frac{(4 a+1) \text{RootSum}\left[\text{$\#$1}^4 a-\text{$\#$1}^4+a+1\&,\frac{x-\log \left(e^x-\text{$\#$1}\right)}{\text{$\#$1}^3}\&\right]+\frac{4 (a-1) e^x \left(a^2 \left(e^{4 x}+1\right)+2 a-e^{4 x}+2\right)}{a e^{4 x}+a-e^{4 x}+1}}{4 (a-1)^3 (a+1)}","-\frac{(4 a+1) \tan ^{-1}\left(\frac{\sqrt[4]{1-a} e^x}{\sqrt[4]{a+1}}\right)}{2 (1-a)^2 (a+1)^{3/2} \sqrt[4]{1-a^2}}-\frac{(4 a+1) \tanh ^{-1}\left(\frac{\sqrt[4]{1-a} e^x}{\sqrt[4]{a+1}}\right)}{2 (1-a)^2 (a+1)^{3/2} \sqrt[4]{1-a^2}}+\frac{e^x}{(1-a)^2}+\frac{e^x}{(1-a)^2 (a+1) \left((a-1) e^{4 x}+a+1\right)}",1,"((4*(-1 + a)*E^x*(2 + 2*a - E^(4*x) + a^2*(1 + E^(4*x))))/(1 + a - E^(4*x) + a*E^(4*x)) + (1 + 4*a)*RootSum[1 + a - #1^4 + a*#1^4 & , (x - Log[E^x - #1])/#1^3 & ])/(4*(-1 + a)^3*(1 + a))","C",1
228,1,205,167,4.4513384,"\int e^{c (a+b x)} \tanh ^3(d+e x) \, dx","Integrate[E^(c*(a + b*x))*Tanh[d + e*x]^3,x]","\frac{1}{2} e^{a c} \left(\frac{2 e^{2 d} \left(b^2 c^2+2 e^2\right) \left(\frac{e^{x (b c+2 e)} \, _2F_1\left(1,\frac{b c}{2 e}+1;\frac{b c}{2 e}+2;-e^{2 (d+e x)}\right)}{b c+2 e}-\frac{e^{b c x} \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;-e^{2 (d+e x)}\right)}{b c}\right)}{\left(e^{2 d}+1\right) e^2}-\frac{b c \text{sech}(d) e^{b c x} \sinh (e x) \text{sech}(d+e x)}{e^2}+\frac{e^{b c x} \text{sech}^2(d+e x)}{e}+\frac{2 \tanh (d) e^{b c x}}{b c}\right)","-\frac{6 e^{c (a+b x)} \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;-e^{2 (d+e x)}\right)}{b c}+\frac{12 e^{c (a+b x)} \, _2F_1\left(2,\frac{b c}{2 e};\frac{b c}{2 e}+1;-e^{2 (d+e x)}\right)}{b c}-\frac{8 e^{c (a+b x)} \, _2F_1\left(3,\frac{b c}{2 e};\frac{b c}{2 e}+1;-e^{2 (d+e x)}\right)}{b c}+\frac{e^{c (a+b x)}}{b c}",1,"(E^(a*c)*((2*(b^2*c^2 + 2*e^2)*E^(2*d)*((E^((b*c + 2*e)*x)*Hypergeometric2F1[1, 1 + (b*c)/(2*e), 2 + (b*c)/(2*e), -E^(2*(d + e*x))])/(b*c + 2*e) - (E^(b*c*x)*Hypergeometric2F1[1, (b*c)/(2*e), 1 + (b*c)/(2*e), -E^(2*(d + e*x))])/(b*c)))/(e^2*(1 + E^(2*d))) + (E^(b*c*x)*Sech[d + e*x]^2)/e - (b*c*E^(b*c*x)*Sech[d]*Sech[d + e*x]*Sinh[e*x])/e^2 + (2*E^(b*c*x)*Tanh[d])/(b*c)))/2","A",1
229,1,169,117,3.4829976,"\int e^{c (a+b x)} \tanh ^2(d+e x) \, dx","Integrate[E^(c*(a + b*x))*Tanh[d + e*x]^2,x]","\frac{e^{c (a+b x)} \left(2 b^2 c^2 e^{2 (d+e x)} \, _2F_1\left(1,\frac{b c}{2 e}+1;\frac{b c}{2 e}+2;-e^{2 (d+e x)}\right)-(b c+2 e) \left(2 b c e^{2 d} \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;-e^{2 (d+e x)}\right)-\left(e^{2 d}+1\right) (e-b c \text{sech}(d) \sinh (e x) \text{sech}(d+e x))\right)\right)}{b c \left(e^{2 d}+1\right) e (b c+2 e)}","-\frac{4 e^{c (a+b x)} \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;-e^{2 (d+e x)}\right)}{b c}+\frac{4 e^{c (a+b x)} \, _2F_1\left(2,\frac{b c}{2 e};\frac{b c}{2 e}+1;-e^{2 (d+e x)}\right)}{b c}+\frac{e^{c (a+b x)}}{b c}",1,"(E^(c*(a + b*x))*(2*b^2*c^2*E^(2*(d + e*x))*Hypergeometric2F1[1, 1 + (b*c)/(2*e), 2 + (b*c)/(2*e), -E^(2*(d + e*x))] - (b*c + 2*e)*(2*b*c*E^(2*d)*Hypergeometric2F1[1, (b*c)/(2*e), 1 + (b*c)/(2*e), -E^(2*(d + e*x))] - (1 + E^(2*d))*(e - b*c*Sech[d]*Sech[d + e*x]*Sinh[e*x]))))/(b*c*e*(b*c + 2*e)*(1 + E^(2*d)))","A",1
230,1,141,67,1.9580151,"\int e^{c (a+b x)} \tanh (d+e x) \, dx","Integrate[E^(c*(a + b*x))*Tanh[d + e*x],x]","\frac{e^{c (a+b x)} \left(2 b c e^{2 (d+e x)} \, _2F_1\left(1,\frac{b c}{2 e}+1;\frac{b c}{2 e}+2;-e^{2 (d+e x)}\right)-(b c+2 e) \left(2 e^{2 d} \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;-e^{2 (d+e x)}\right)-e^{2 d}+1\right)\right)}{b c \left(e^{2 d}+1\right) (b c+2 e)}","\frac{e^{c (a+b x)}}{b c}-\frac{2 e^{c (a+b x)} \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;-e^{2 (d+e x)}\right)}{b c}",1,"(E^(c*(a + b*x))*(2*b*c*E^(2*(d + e*x))*Hypergeometric2F1[1, 1 + (b*c)/(2*e), 2 + (b*c)/(2*e), -E^(2*(d + e*x))] - (b*c + 2*e)*(1 - E^(2*d) + 2*E^(2*d)*Hypergeometric2F1[1, (b*c)/(2*e), 1 + (b*c)/(2*e), -E^(2*(d + e*x))])))/(b*c*(b*c + 2*e)*(1 + E^(2*d)))","B",1
231,1,134,65,2.5394491,"\int e^{c (a+b x)} \coth (d+e x) \, dx","Integrate[E^(c*(a + b*x))*Coth[d + e*x],x]","\frac{e^{c (a+b x)} \left(2 b c e^{2 (d+e x)} \, _2F_1\left(1,\frac{b c}{2 e}+1;\frac{b c}{2 e}+2;e^{2 (d+e x)}\right)+(b c+2 e) \left(-2 e^{2 d} \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;e^{2 (d+e x)}\right)+e^{2 d}+1\right)\right)}{b c \left(e^{2 d}-1\right) (b c+2 e)}","\frac{e^{c (a+b x)}}{b c}-\frac{2 e^{c (a+b x)} \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;e^{2 (d+e x)}\right)}{b c}",1,"(E^(c*(a + b*x))*(2*b*c*E^(2*(d + e*x))*Hypergeometric2F1[1, 1 + (b*c)/(2*e), 2 + (b*c)/(2*e), E^(2*(d + e*x))] + (b*c + 2*e)*(1 + E^(2*d) - 2*E^(2*d)*Hypergeometric2F1[1, (b*c)/(2*e), 1 + (b*c)/(2*e), E^(2*(d + e*x))])))/(b*c*(b*c + 2*e)*(-1 + E^(2*d)))","B",1
232,1,145,113,3.3542692,"\int e^{c (a+b x)} \coth ^2(d+e x) \, dx","Integrate[E^(c*(a + b*x))*Coth[d + e*x]^2,x]","e^{c (a+b x)} \left(\frac{2 e^{2 d} \left(b c e^{2 e x} \, _2F_1\left(1,\frac{b c}{2 e}+1;\frac{b c}{2 e}+2;e^{2 (d+e x)}\right)-(b c+2 e) \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;e^{2 (d+e x)}\right)\right)}{\left(e^{2 d}-1\right) e (b c+2 e)}+\frac{1}{b c}+\frac{\text{csch}(d) \sinh (e x) \text{csch}(d+e x)}{e}\right)","-\frac{4 e^{c (a+b x)} \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;e^{2 (d+e x)}\right)}{b c}+\frac{4 e^{c (a+b x)} \, _2F_1\left(2,\frac{b c}{2 e};\frac{b c}{2 e}+1;e^{2 (d+e x)}\right)}{b c}+\frac{e^{c (a+b x)}}{b c}",1,"E^(c*(a + b*x))*(1/(b*c) + (2*E^(2*d)*(b*c*E^(2*e*x)*Hypergeometric2F1[1, 1 + (b*c)/(2*e), 2 + (b*c)/(2*e), E^(2*(d + e*x))] - (b*c + 2*e)*Hypergeometric2F1[1, (b*c)/(2*e), 1 + (b*c)/(2*e), E^(2*(d + e*x))]))/(e*(b*c + 2*e)*(-1 + E^(2*d))) + (Csch[d]*Csch[d + e*x]*Sinh[e*x])/e)","A",1
233,1,185,161,3.609074,"\int e^{c (a+b x)} \coth ^3(d+e x) \, dx","Integrate[E^(c*(a + b*x))*Coth[d + e*x]^3,x]","\frac{1}{2} e^{c (a+b x)} \left(\frac{2 e^{2 d} \left(b^2 c^2+2 e^2\right) \left(b c e^{2 e x} \, _2F_1\left(1,\frac{b c}{2 e}+1;\frac{b c}{2 e}+2;e^{2 (d+e x)}\right)-(b c+2 e) \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;e^{2 (d+e x)}\right)\right)}{b c \left(e^{2 d}-1\right) e^2 (b c+2 e)}+\frac{b c \text{csch}(d) \sinh (e x) \text{csch}(d+e x)}{e^2}+\frac{2 \coth (d)}{b c}-\frac{\text{csch}^2(d+e x)}{e}\right)","-\frac{6 e^{c (a+b x)} \, _2F_1\left(1,\frac{b c}{2 e};\frac{b c}{2 e}+1;e^{2 (d+e x)}\right)}{b c}+\frac{12 e^{c (a+b x)} \, _2F_1\left(2,\frac{b c}{2 e};\frac{b c}{2 e}+1;e^{2 (d+e x)}\right)}{b c}-\frac{8 e^{c (a+b x)} \, _2F_1\left(3,\frac{b c}{2 e};\frac{b c}{2 e}+1;e^{2 (d+e x)}\right)}{b c}+\frac{e^{c (a+b x)}}{b c}",1,"(E^(c*(a + b*x))*((2*Coth[d])/(b*c) - Csch[d + e*x]^2/e + (2*(b^2*c^2 + 2*e^2)*E^(2*d)*(b*c*E^(2*e*x)*Hypergeometric2F1[1, 1 + (b*c)/(2*e), 2 + (b*c)/(2*e), E^(2*(d + e*x))] - (b*c + 2*e)*Hypergeometric2F1[1, (b*c)/(2*e), 1 + (b*c)/(2*e), E^(2*(d + e*x))]))/(b*c*e^2*(b*c + 2*e)*(-1 + E^(2*d))) + (b*c*Csch[d]*Csch[d + e*x]*Sinh[e*x])/e^2))/2","A",1
234,1,133,311,0.2322781,"\int e^{c (a+b x)} \tanh ^2(a c+b c x)^{5/2} \, dx","Integrate[E^(c*(a + b*x))*(Tanh[a*c + b*c*x]^2)^(5/2),x]","\frac{\left(e^{c (a+b x)} \left(157 e^{2 c (a+b x)}+187 e^{4 c (a+b x)}+123 e^{6 c (a+b x)}+12 e^{8 c (a+b x)}+33\right)-45 \left(e^{2 c (a+b x)}+1\right)^4 \tan ^{-1}\left(e^{c (a+b x)}\right)\right) \sqrt{\tanh ^2(c (a+b x))} \coth (c (a+b x))}{12 b c \left(e^{2 c (a+b x)}+1\right)^4}","\frac{e^{c (a+b x)} \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{b c}+\frac{25 e^{c (a+b x)} \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{4 b c \left(e^{2 c (a+b x)}+1\right)}-\frac{55 e^{c (a+b x)} \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{6 b c \left(e^{2 c (a+b x)}+1\right)^2}+\frac{26 e^{c (a+b x)} \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{3 b c \left(e^{2 c (a+b x)}+1\right)^3}-\frac{4 e^{c (a+b x)} \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^4}-\frac{15 \tan ^{-1}\left(e^{c (a+b x)}\right) \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{4 b c}",1,"((E^(c*(a + b*x))*(33 + 157*E^(2*c*(a + b*x)) + 187*E^(4*c*(a + b*x)) + 123*E^(6*c*(a + b*x)) + 12*E^(8*c*(a + b*x))) - 45*(1 + E^(2*c*(a + b*x)))^4*ArcTan[E^(c*(a + b*x))])*Coth[c*(a + b*x)]*Sqrt[Tanh[c*(a + b*x)]^2])/(12*b*c*(1 + E^(2*c*(a + b*x)))^4)","A",1
235,1,104,193,0.17315,"\int e^{c (a+b x)} \tanh ^2(a c+b c x)^{3/2} \, dx","Integrate[E^(c*(a + b*x))*(Tanh[a*c + b*c*x]^2)^(3/2),x]","\frac{\left(e^{c (a+b x)} \left(5 e^{2 c (a+b x)}+e^{4 c (a+b x)}+2\right)-3 \left(e^{2 c (a+b x)}+1\right)^2 \tan ^{-1}\left(e^{c (a+b x)}\right)\right) \sqrt{\tanh ^2(c (a+b x))} \coth (c (a+b x))}{b c \left(e^{2 c (a+b x)}+1\right)^2}","\frac{e^{c (a+b x)} \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{b c}+\frac{3 e^{c (a+b x)} \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)}-\frac{2 e^{c (a+b x)} \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^2}-\frac{3 \tan ^{-1}\left(e^{c (a+b x)}\right) \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{b c}",1,"((E^(c*(a + b*x))*(2 + 5*E^(2*c*(a + b*x)) + E^(4*c*(a + b*x))) - 3*(1 + E^(2*c*(a + b*x)))^2*ArcTan[E^(c*(a + b*x))])*Coth[c*(a + b*x)]*Sqrt[Tanh[c*(a + b*x)]^2])/(b*c*(1 + E^(2*c*(a + b*x)))^2)","A",1
236,1,51,83,0.0568118,"\int e^{c (a+b x)} \sqrt{\tanh ^2(a c+b c x)} \, dx","Integrate[E^(c*(a + b*x))*Sqrt[Tanh[a*c + b*c*x]^2],x]","\frac{\left(e^{c (a+b x)}-2 \tan ^{-1}\left(e^{c (a+b x)}\right)\right) \sqrt{\tanh ^2(c (a+b x))} \coth (c (a+b x))}{b c}","\frac{e^{c (a+b x)} \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{b c}-\frac{2 \tan ^{-1}\left(e^{c (a+b x)}\right) \sqrt{\tanh ^2(a c+b c x)} \coth (a c+b c x)}{b c}",1,"((E^(c*(a + b*x)) - 2*ArcTan[E^(c*(a + b*x))])*Coth[c*(a + b*x)]*Sqrt[Tanh[c*(a + b*x)]^2])/(b*c)","A",1
237,1,51,83,0.1327329,"\int \frac{e^{c (a+b x)}}{\sqrt{\tanh ^2(a c+b c x)}} \, dx","Integrate[E^(c*(a + b*x))/Sqrt[Tanh[a*c + b*c*x]^2],x]","\frac{\left(e^{c (a+b x)}-2 \tanh ^{-1}\left(e^{c (a+b x)}\right)\right) \tanh (c (a+b x))}{b c \sqrt{\tanh ^2(c (a+b x))}}","\frac{e^{c (a+b x)} \tanh (a c+b c x)}{b c \sqrt{\tanh ^2(a c+b c x)}}-\frac{2 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x)}{b c \sqrt{\tanh ^2(a c+b c x)}}",1,"((E^(c*(a + b*x)) - 2*ArcTanh[E^(c*(a + b*x))])*Tanh[c*(a + b*x)])/(b*c*Sqrt[Tanh[c*(a + b*x)]^2])","A",1
238,1,334,197,7.7241598,"\int \frac{e^{c (a+b x)}}{\tanh ^2(a c+b c x)^{3/2}} \, dx","Integrate[E^(c*(a + b*x))/(Tanh[a*c + b*c*x]^2)^(3/2),x]","-\frac{e^{-5 c (a+b x)} \tanh ^3(c (a+b x)) \left(256 e^{8 c (a+b x)} \left(e^{2 c (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 c (a+b x)}\right)+384 e^{8 c (a+b x)} \left(5 e^{2 c (a+b x)}+7\right) \left(e^{2 c (a+b x)}+1\right)^2 \, _5F_4\left(\frac{3}{2},2,2,2,2;1,1,1,\frac{11}{2};e^{2 c (a+b x)}\right)-21 \left(507305 e^{2 c (a+b x)}+173916 e^{4 c (a+b x)}-154296 e^{6 c (a+b x)}-73885 e^{8 c (a+b x)}+4887 e^{10 c (a+b x)}+252105\right)-\frac{315 \left(-28218 e^{2 c (a+b x)}+1173 e^{4 c (a+b x)}+17748 e^{6 c (a+b x)}+4299 e^{8 c (a+b x)}-1434 e^{10 c (a+b x)}+7 e^{12 c (a+b x)}-16807\right) \tanh ^{-1}\left(\sqrt{e^{2 c (a+b x)}}\right)}{\sqrt{e^{2 c (a+b x)}}}\right)}{60480 b c \tanh ^2(c (a+b x))^{3/2}}","\frac{e^{c (a+b x)} \tanh (a c+b c x)}{b c \sqrt{\tanh ^2(a c+b c x)}}+\frac{3 e^{c (a+b x)} \tanh (a c+b c x)}{b c \left(1-e^{2 c (a+b x)}\right) \sqrt{\tanh ^2(a c+b c x)}}-\frac{2 e^{c (a+b x)} \tanh (a c+b c x)}{b c \left(1-e^{2 c (a+b x)}\right)^2 \sqrt{\tanh ^2(a c+b c x)}}-\frac{3 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x)}{b c \sqrt{\tanh ^2(a c+b c x)}}",1,"-1/60480*((-21*(252105 + 507305*E^(2*c*(a + b*x)) + 173916*E^(4*c*(a + b*x)) - 154296*E^(6*c*(a + b*x)) - 73885*E^(8*c*(a + b*x)) + 4887*E^(10*c*(a + b*x))) - (315*(-16807 - 28218*E^(2*c*(a + b*x)) + 1173*E^(4*c*(a + b*x)) + 17748*E^(6*c*(a + b*x)) + 4299*E^(8*c*(a + b*x)) - 1434*E^(10*c*(a + b*x)) + 7*E^(12*c*(a + b*x)))*ArcTanh[Sqrt[E^(2*c*(a + b*x))]])/Sqrt[E^(2*c*(a + b*x))] + 384*E^(8*c*(a + b*x))*(1 + E^(2*c*(a + b*x)))^2*(7 + 5*E^(2*c*(a + b*x)))*HypergeometricPFQ[{3/2, 2, 2, 2, 2}, {1, 1, 1, 11/2}, E^(2*c*(a + b*x))] + 256*E^(8*c*(a + b*x))*(1 + E^(2*c*(a + b*x)))^3*HypergeometricPFQ[{3/2, 2, 2, 2, 2, 2}, {1, 1, 1, 1, 11/2}, E^(2*c*(a + b*x))])*Tanh[c*(a + b*x)]^3)/(b*c*E^(5*c*(a + b*x))*(Tanh[c*(a + b*x)]^2)^(3/2))","C",0
239,1,164,319,10.6912118,"\int \frac{e^{c (a+b x)}}{\tanh ^2(a c+b c x)^{5/2}} \, dx","Integrate[E^(c*(a + b*x))/(Tanh[a*c + b*c*x]^2)^(5/2),x]","\frac{\left(66 e^{c (a+b x)}-314 e^{3 c (a+b x)}+374 e^{5 c (a+b x)}-246 e^{7 c (a+b x)}+24 e^{9 c (a+b x)}+45 \left(e^{2 c (a+b x)}-1\right)^4 \log \left(1-e^{c (a+b x)}\right)-45 \left(e^{2 c (a+b x)}-1\right)^4 \log \left(e^{c (a+b x)}+1\right)\right) \tanh (c (a+b x))}{24 b c \left(e^{2 c (a+b x)}-1\right)^4 \sqrt{\tanh ^2(c (a+b x))}}","\frac{e^{c (a+b x)} \tanh (a c+b c x)}{b c \sqrt{\tanh ^2(a c+b c x)}}+\frac{25 e^{c (a+b x)} \tanh (a c+b c x)}{4 b c \left(1-e^{2 c (a+b x)}\right) \sqrt{\tanh ^2(a c+b c x)}}-\frac{55 e^{c (a+b x)} \tanh (a c+b c x)}{6 b c \left(1-e^{2 c (a+b x)}\right)^2 \sqrt{\tanh ^2(a c+b c x)}}+\frac{26 e^{c (a+b x)} \tanh (a c+b c x)}{3 b c \left(1-e^{2 c (a+b x)}\right)^3 \sqrt{\tanh ^2(a c+b c x)}}-\frac{4 e^{c (a+b x)} \tanh (a c+b c x)}{b c \left(1-e^{2 c (a+b x)}\right)^4 \sqrt{\tanh ^2(a c+b c x)}}-\frac{15 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x)}{4 b c \sqrt{\tanh ^2(a c+b c x)}}",1,"((66*E^(c*(a + b*x)) - 314*E^(3*c*(a + b*x)) + 374*E^(5*c*(a + b*x)) - 246*E^(7*c*(a + b*x)) + 24*E^(9*c*(a + b*x)) + 45*(-1 + E^(2*c*(a + b*x)))^4*Log[1 - E^(c*(a + b*x))] - 45*(-1 + E^(2*c*(a + b*x)))^4*Log[1 + E^(c*(a + b*x))])*Tanh[c*(a + b*x)])/(24*b*c*(-1 + E^(2*c*(a + b*x)))^4*Sqrt[Tanh[c*(a + b*x)]^2])","A",1
240,1,124,157,0.2297534,"\int \sin ^3(\tanh (a+b x)) \, dx","Integrate[Sin[Tanh[a + b*x]]^3,x]","\frac{2 \sin (3) \text{Ci}(3-3 \tanh (a+b x))+2 \sin (3) \text{Ci}(3 \tanh (a+b x)+3)-6 \sin (1) \text{Ci}(1-\tanh (a+b x))-6 \sin (1) \text{Ci}(\tanh (a+b x)+1)-2 \cos (3) \text{Si}(3-3 \tanh (a+b x))+6 \cos (1) \text{Si}(1-\tanh (a+b x))+6 \cos (1) \text{Si}(\tanh (a+b x)+1)-2 \cos (3) \text{Si}(3 \tanh (a+b x)+3)}{16 b}","\frac{\sin (3) \text{Ci}(3-3 \tanh (a+b x))}{8 b}+\frac{\sin (3) \text{Ci}(3 \tanh (a+b x)+3)}{8 b}-\frac{3 \sin (1) \text{Ci}(1-\tanh (a+b x))}{8 b}-\frac{3 \sin (1) \text{Ci}(\tanh (a+b x)+1)}{8 b}-\frac{\cos (3) \text{Si}(3-3 \tanh (a+b x))}{8 b}+\frac{3 \cos (1) \text{Si}(1-\tanh (a+b x))}{8 b}+\frac{3 \cos (1) \text{Si}(\tanh (a+b x)+1)}{8 b}-\frac{\cos (3) \text{Si}(3 \tanh (a+b x)+3)}{8 b}",1,"(-6*CosIntegral[1 - Tanh[a + b*x]]*Sin[1] - 6*CosIntegral[1 + Tanh[a + b*x]]*Sin[1] + 2*CosIntegral[3 - 3*Tanh[a + b*x]]*Sin[3] + 2*CosIntegral[3 + 3*Tanh[a + b*x]]*Sin[3] - 2*Cos[3]*SinIntegral[3 - 3*Tanh[a + b*x]] + 6*Cos[1]*SinIntegral[1 - Tanh[a + b*x]] + 6*Cos[1]*SinIntegral[1 + Tanh[a + b*x]] - 2*Cos[3]*SinIntegral[3 + 3*Tanh[a + b*x]])/(16*b)","A",1
241,1,88,115,0.1527867,"\int \sin ^2(\tanh (a+b x)) \, dx","Integrate[Sin[Tanh[a + b*x]]^2,x]","\frac{\cos (2) \text{Ci}(2-2 \tanh (a+b x))-\cos (2) \text{Ci}(2 (\tanh (a+b x)+1))+\sin (2) \text{Si}(2-2 \tanh (a+b x))-\sin (2) \text{Si}(2 (\tanh (a+b x)+1))-\log (1-\tanh (a+b x))+\log (\tanh (a+b x)+1)}{4 b}","\frac{\cos (2) \text{Ci}(2-2 \tanh (a+b x))}{4 b}-\frac{\cos (2) \text{Ci}(2 \tanh (a+b x)+2)}{4 b}+\frac{\sin (2) \text{Si}(2-2 \tanh (a+b x))}{4 b}-\frac{\sin (2) \text{Si}(2 \tanh (a+b x)+2)}{4 b}-\frac{\log (1-\tanh (a+b x))}{4 b}+\frac{\log (\tanh (a+b x)+1)}{4 b}",1,"(Cos[2]*CosIntegral[2 - 2*Tanh[a + b*x]] - Cos[2]*CosIntegral[2*(1 + Tanh[a + b*x])] - Log[1 - Tanh[a + b*x]] + Log[1 + Tanh[a + b*x]] + Sin[2]*SinIntegral[2 - 2*Tanh[a + b*x]] - Sin[2]*SinIntegral[2*(1 + Tanh[a + b*x])])/(4*b)","A",1
242,1,59,77,0.1388314,"\int \sin (\tanh (a+b x)) \, dx","Integrate[Sin[Tanh[a + b*x]],x]","-\frac{\sin (1) \text{Ci}(1-\tanh (a+b x))+\sin (1) \text{Ci}(\tanh (a+b x)+1)-\cos (1) (\text{Si}(1-\tanh (a+b x))+\text{Si}(\tanh (a+b x)+1))}{2 b}","-\frac{\sin (1) \text{Ci}(1-\tanh (a+b x))}{2 b}-\frac{\sin (1) \text{Ci}(\tanh (a+b x)+1)}{2 b}+\frac{\cos (1) \text{Si}(1-\tanh (a+b x))}{2 b}+\frac{\cos (1) \text{Si}(\tanh (a+b x)+1)}{2 b}",1,"-1/2*(CosIntegral[1 - Tanh[a + b*x]]*Sin[1] + CosIntegral[1 + Tanh[a + b*x]]*Sin[1] - Cos[1]*(SinIntegral[1 - Tanh[a + b*x]] + SinIntegral[1 + Tanh[a + b*x]]))/b","A",1
243,0,0,67,3.4925476,"\int \csc (\tanh (a+b x)) \, dx","Integrate[Csc[Tanh[a + b*x]],x]","\int \csc (\tanh (a+b x)) \, dx","\frac{1}{2} \text{Int}\left(\frac{\text{sech}^2(a+b x) \csc (\tanh (a+b x))}{\tanh (a+b x)+1},x\right)-\frac{1}{2} \text{Int}\left(\frac{\text{sech}^2(a+b x) \csc (\tanh (a+b x))}{\tanh (a+b x)-1},x\right)",0,"Integrate[Csc[Tanh[a + b*x]], x]","A",-1
244,1,124,157,0.2718682,"\int \cos ^3(\tanh (a+b x)) \, dx","Integrate[Cos[Tanh[a + b*x]]^3,x]","\frac{-2 \cos (3) \text{Ci}(3-3 \tanh (a+b x))-6 \cos (1) \text{Ci}(1-\tanh (a+b x))+6 \cos (1) \text{Ci}(\tanh (a+b x)+1)+2 \cos (3) \text{Ci}(3 \tanh (a+b x)+3)-2 \sin (3) \text{Si}(3-3 \tanh (a+b x))-6 \sin (1) \text{Si}(1-\tanh (a+b x))+6 \sin (1) \text{Si}(\tanh (a+b x)+1)+2 \sin (3) \text{Si}(3 \tanh (a+b x)+3)}{16 b}","-\frac{\cos (3) \text{Ci}(3-3 \tanh (a+b x))}{8 b}-\frac{3 \cos (1) \text{Ci}(1-\tanh (a+b x))}{8 b}+\frac{3 \cos (1) \text{Ci}(\tanh (a+b x)+1)}{8 b}+\frac{\cos (3) \text{Ci}(3 \tanh (a+b x)+3)}{8 b}-\frac{\sin (3) \text{Si}(3-3 \tanh (a+b x))}{8 b}-\frac{3 \sin (1) \text{Si}(1-\tanh (a+b x))}{8 b}+\frac{3 \sin (1) \text{Si}(\tanh (a+b x)+1)}{8 b}+\frac{\sin (3) \text{Si}(3 \tanh (a+b x)+3)}{8 b}",1,"(-2*Cos[3]*CosIntegral[3 - 3*Tanh[a + b*x]] - 6*Cos[1]*CosIntegral[1 - Tanh[a + b*x]] + 6*Cos[1]*CosIntegral[1 + Tanh[a + b*x]] + 2*Cos[3]*CosIntegral[3 + 3*Tanh[a + b*x]] - 2*Sin[3]*SinIntegral[3 - 3*Tanh[a + b*x]] - 6*Sin[1]*SinIntegral[1 - Tanh[a + b*x]] + 6*Sin[1]*SinIntegral[1 + Tanh[a + b*x]] + 2*Sin[3]*SinIntegral[3 + 3*Tanh[a + b*x]])/(16*b)","A",1
245,1,88,115,0.1678724,"\int \cos ^2(\tanh (a+b x)) \, dx","Integrate[Cos[Tanh[a + b*x]]^2,x]","\frac{-\cos (2) \text{Ci}(2-2 \tanh (a+b x))+\cos (2) \text{Ci}(2 (\tanh (a+b x)+1))-\sin (2) \text{Si}(2-2 \tanh (a+b x))+\sin (2) \text{Si}(2 (\tanh (a+b x)+1))-\log (1-\tanh (a+b x))+\log (\tanh (a+b x)+1)}{4 b}","-\frac{\cos (2) \text{Ci}(2-2 \tanh (a+b x))}{4 b}+\frac{\cos (2) \text{Ci}(2 \tanh (a+b x)+2)}{4 b}-\frac{\sin (2) \text{Si}(2-2 \tanh (a+b x))}{4 b}+\frac{\sin (2) \text{Si}(2 \tanh (a+b x)+2)}{4 b}-\frac{\log (1-\tanh (a+b x))}{4 b}+\frac{\log (\tanh (a+b x)+1)}{4 b}",1,"(-(Cos[2]*CosIntegral[2 - 2*Tanh[a + b*x]]) + Cos[2]*CosIntegral[2*(1 + Tanh[a + b*x])] - Log[1 - Tanh[a + b*x]] + Log[1 + Tanh[a + b*x]] - Sin[2]*SinIntegral[2 - 2*Tanh[a + b*x]] + Sin[2]*SinIntegral[2*(1 + Tanh[a + b*x])])/(4*b)","A",1
246,1,62,77,0.1125681,"\int \cos (\tanh (a+b x)) \, dx","Integrate[Cos[Tanh[a + b*x]],x]","\frac{-\cos (1) \text{Ci}(1-\tanh (a+b x))+\cos (1) \text{Ci}(\tanh (a+b x)+1)-\sin (1) \text{Si}(1-\tanh (a+b x))+\sin (1) \text{Si}(\tanh (a+b x)+1)}{2 b}","-\frac{\cos (1) \text{Ci}(1-\tanh (a+b x))}{2 b}+\frac{\cos (1) \text{Ci}(\tanh (a+b x)+1)}{2 b}-\frac{\sin (1) \text{Si}(1-\tanh (a+b x))}{2 b}+\frac{\sin (1) \text{Si}(\tanh (a+b x)+1)}{2 b}",1,"(-(Cos[1]*CosIntegral[1 - Tanh[a + b*x]]) + Cos[1]*CosIntegral[1 + Tanh[a + b*x]] - Sin[1]*SinIntegral[1 - Tanh[a + b*x]] + Sin[1]*SinIntegral[1 + Tanh[a + b*x]])/(2*b)","A",1
247,0,0,67,5.6889062,"\int \sec (\tanh (a+b x)) \, dx","Integrate[Sec[Tanh[a + b*x]],x]","\int \sec (\tanh (a+b x)) \, dx","\frac{1}{2} \text{Int}\left(\frac{\text{sech}^2(a+b x) \sec (\tanh (a+b x))}{\tanh (a+b x)+1},x\right)-\frac{1}{2} \text{Int}\left(\frac{\text{sech}^2(a+b x) \sec (\tanh (a+b x))}{\tanh (a+b x)-1},x\right)",0,"Integrate[Sec[Tanh[a + b*x]], x]","A",-1