1,1,83,97,0.2376414,"\int (b \coth (c+d x))^{7/2} \, dx","Integrate[(b*Coth[c + d*x])^(7/2),x]","\frac{b^3 \sqrt{b \coth (c+d x)} \left(-2 \coth ^{\frac{5}{2}}(c+d x)-10 \sqrt{\coth (c+d x)}+5 \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)+5 \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)\right)}{5 d \sqrt{\coth (c+d x)}}","\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}+\frac{b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b^3 \sqrt{b \coth (c+d x)}}{d}-\frac{2 b (b \coth (c+d x))^{5/2}}{5 d}",1,"(b^3*Sqrt[b*Coth[c + d*x]]*(5*ArcTan[Sqrt[Coth[c + d*x]]] + 5*ArcTanh[Sqrt[Coth[c + d*x]]] - 10*Sqrt[Coth[c + d*x]] - 2*Coth[c + d*x]^(5/2)))/(5*d*Sqrt[Coth[c + d*x]])","A",1
2,1,68,78,0.2216062,"\int (b \coth (c+d x))^{5/2} \, dx","Integrate[(b*Coth[c + d*x])^(5/2),x]","-\frac{(b \coth (c+d x))^{5/2} \left(2 \coth ^{\frac{3}{2}}(c+d x)+3 \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)-3 \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)\right)}{3 d \coth ^{\frac{5}{2}}(c+d x)}","-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}+\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b (b \coth (c+d x))^{3/2}}{3 d}",1,"-1/3*((b*Coth[c + d*x])^(5/2)*(3*ArcTan[Sqrt[Coth[c + d*x]]] - 3*ArcTanh[Sqrt[Coth[c + d*x]]] + 2*Coth[c + d*x]^(3/2)))/(d*Coth[c + d*x]^(5/2))","A",1
3,1,61,75,0.0930839,"\int (b \coth (c+d x))^{3/2} \, dx","Integrate[(b*Coth[c + d*x])^(3/2),x]","\frac{(b \coth (c+d x))^{3/2} \left(-2 \sqrt{\coth (c+d x)}+\tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)+\tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)\right)}{d \coth ^{\frac{3}{2}}(c+d x)}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}+\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b \sqrt{b \coth (c+d x)}}{d}",1,"((ArcTan[Sqrt[Coth[c + d*x]]] + ArcTanh[Sqrt[Coth[c + d*x]]] - 2*Sqrt[Coth[c + d*x]])*(b*Coth[c + d*x])^(3/2))/(d*Coth[c + d*x]^(3/2))","A",1
4,1,51,58,0.0414363,"\int \sqrt{b \coth (c+d x)} \, dx","Integrate[Sqrt[b*Coth[c + d*x]],x]","\frac{\sqrt{b \coth (c+d x)} \left(\tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)-\tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)\right)}{d \sqrt{\coth (c+d x)}}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}",1,"((-ArcTan[Sqrt[Coth[c + d*x]]] + ArcTanh[Sqrt[Coth[c + d*x]]])*Sqrt[b*Coth[c + d*x]])/(d*Sqrt[Coth[c + d*x]])","A",1
5,1,49,57,0.0349069,"\int \frac{1}{\sqrt{b \coth (c+d x)}} \, dx","Integrate[1/Sqrt[b*Coth[c + d*x]],x]","\frac{\sqrt{\coth (c+d x)} \left(\tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)+\tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)\right)}{d \sqrt{b \coth (c+d x)}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}",1,"((ArcTan[Sqrt[Coth[c + d*x]]] + ArcTanh[Sqrt[Coth[c + d*x]]])*Sqrt[Coth[c + d*x]])/(d*Sqrt[b*Coth[c + d*x]])","A",1
6,1,36,78,0.0770191,"\int \frac{1}{(b \coth (c+d x))^{3/2}} \, dx","Integrate[(b*Coth[c + d*x])^(-3/2),x]","-\frac{2 \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};\coth ^2(c+d x)\right)}{b d \sqrt{b \coth (c+d x)}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2}{b d \sqrt{b \coth (c+d x)}}",1,"(-2*Hypergeometric2F1[-1/4, 1, 3/4, Coth[c + d*x]^2])/(b*d*Sqrt[b*Coth[c + d*x]])","C",1
7,1,38,79,0.0715292,"\int \frac{1}{(b \coth (c+d x))^{5/2}} \, dx","Integrate[(b*Coth[c + d*x])^(-5/2),x]","-\frac{2 \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};\coth ^2(c+d x)\right)}{3 b d (b \coth (c+d x))^{3/2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}-\frac{2}{3 b d (b \coth (c+d x))^{3/2}}",1,"(-2*Hypergeometric2F1[-3/4, 1, 1/4, Coth[c + d*x]^2])/(3*b*d*(b*Coth[c + d*x])^(3/2))","C",1
8,1,38,100,0.1000343,"\int \frac{1}{(b \coth (c+d x))^{7/2}} \, dx","Integrate[(b*Coth[c + d*x])^(-7/2),x]","-\frac{2 \, _2F_1\left(-\frac{5}{4},1;-\frac{1}{4};\coth ^2(c+d x)\right)}{5 b d (b \coth (c+d x))^{5/2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{7/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{7/2} d}-\frac{2}{b^3 d \sqrt{b \coth (c+d x)}}-\frac{2}{5 b d (b \coth (c+d x))^{5/2}}",1,"(-2*Hypergeometric2F1[-5/4, 1, -1/4, Coth[c + d*x]^2])/(5*b*d*(b*Coth[c + d*x])^(5/2))","C",1
9,1,36,236,0.026738,"\int (b \coth (c+d x))^{4/3} \, dx","Integrate[(b*Coth[c + d*x])^(4/3),x]","\frac{3 b \sqrt[3]{b \coth (c+d x)} \left(\, _2F_1\left(\frac{1}{6},1;\frac{7}{6};\coth ^2(c+d x)\right)-1\right)}{d}","-\frac{b^{4/3} \log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}+\frac{b^{4/3} \log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}-\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 d}+\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 d}+\frac{b^{4/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{d}-\frac{3 b \sqrt[3]{b \coth (c+d x)}}{d}",1,"(3*b*(b*Coth[c + d*x])^(1/3)*(-1 + Hypergeometric2F1[1/6, 1, 7/6, Coth[c + d*x]^2]))/d","C",1
10,1,149,218,0.1861255,"\int (b \coth (c+d x))^{2/3} \, dx","Integrate[(b*Coth[c + d*x])^(2/3),x]","\frac{(b \coth (c+d x))^{2/3} \left(-\log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)+\log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)+4 \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}","-\frac{b^{2/3} \log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}+\frac{b^{2/3} \log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}+\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 d}-\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 d}+\frac{b^{2/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{d}",1,"((b*Coth[c + d*x])^(2/3)*(2*Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]] + 4*ArcTanh[Coth[c + d*x]^(1/3)] - Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)] + Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)]))/(4*d*Coth[c + d*x]^(2/3))","A",1
11,1,38,132,0.0428553,"\int \sqrt[3]{b \coth (c+d x)} \, dx","Integrate[(b*Coth[c + d*x])^(1/3),x]","\frac{3 (b \coth (c+d x))^{4/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\coth ^2(c+d x)\right)}{4 b d}","-\frac{\sqrt[3]{b} \log \left(b^{2/3}-(b \coth (c+d x))^{2/3}\right)}{2 d}+\frac{\sqrt[3]{b} \log \left(b^{2/3} (b \coth (c+d x))^{2/3}+b^{4/3}+(b \coth (c+d x))^{4/3}\right)}{4 d}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{b^{2/3}+2 (b \coth (c+d x))^{2/3}}{\sqrt{3} b^{2/3}}\right)}{2 d}",1,"(3*(b*Coth[c + d*x])^(4/3)*Hypergeometric2F1[2/3, 1, 5/3, Coth[c + d*x]^2])/(4*b*d)","C",1
12,1,98,132,0.1263301,"\int \frac{1}{\sqrt[3]{b \coth (c+d x)}} \, dx","Integrate[(b*Coth[c + d*x])^(-1/3),x]","\frac{\sqrt[3]{\coth (c+d x)} \left(-2 \log \left(1-\coth ^{\frac{2}{3}}(c+d x)\right)+\log \left(\coth ^{\frac{4}{3}}(c+d x)+\coth ^{\frac{2}{3}}(c+d x)+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \coth ^{\frac{2}{3}}(c+d x)+1}{\sqrt{3}}\right)\right)}{4 d \sqrt[3]{b \coth (c+d x)}}","-\frac{\log \left(b^{2/3}-(b \coth (c+d x))^{2/3}\right)}{2 \sqrt[3]{b} d}+\frac{\log \left(b^{2/3} (b \coth (c+d x))^{2/3}+b^{4/3}+(b \coth (c+d x))^{4/3}\right)}{4 \sqrt[3]{b} d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{b^{2/3}+2 (b \coth (c+d x))^{2/3}}{\sqrt{3} b^{2/3}}\right)}{2 \sqrt[3]{b} d}",1,"(Coth[c + d*x]^(1/3)*(2*Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(2/3))/Sqrt[3]] - 2*Log[1 - Coth[c + d*x]^(2/3)] + Log[1 + Coth[c + d*x]^(2/3) + Coth[c + d*x]^(4/3)]))/(4*d*(b*Coth[c + d*x])^(1/3))","A",1
13,1,36,218,0.0305369,"\int \frac{1}{(b \coth (c+d x))^{2/3}} \, dx","Integrate[(b*Coth[c + d*x])^(-2/3),x]","\frac{3 \sqrt[3]{b \coth (c+d x)} \, _2F_1\left(\frac{1}{6},1;\frac{7}{6};\coth ^2(c+d x)\right)}{b d}","-\frac{\log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{2/3} d}+\frac{\log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{2/3} d}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 b^{2/3} d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 b^{2/3} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{b^{2/3} d}",1,"(3*(b*Coth[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1, 7/6, Coth[c + d*x]^2])/(b*d)","C",1
14,1,36,238,0.0611845,"\int \frac{1}{(b \coth (c+d x))^{4/3}} \, dx","Integrate[(b*Coth[c + d*x])^(-4/3),x]","-\frac{3 \, _2F_1\left(-\frac{1}{6},1;\frac{5}{6};\coth ^2(c+d x)\right)}{b d \sqrt[3]{b \coth (c+d x)}}","-\frac{\log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{4/3} d}+\frac{\log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{4/3} d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 b^{4/3} d}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 b^{4/3} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{b^{4/3} d}-\frac{3}{b d \sqrt[3]{b \coth (c+d x)}}",1,"(-3*Hypergeometric2F1[-1/6, 1, 5/6, Coth[c + d*x]^2])/(b*d*(b*Coth[c + d*x])^(1/3))","C",1
15,1,45,43,0.0675245,"\int \coth ^n(a+b x) \, dx","Integrate[Coth[a + b*x]^n,x]","\frac{\coth ^{n+1}(a+b x) \, _2F_1\left(1,\frac{n+1}{2};\frac{n+1}{2}+1;\coth ^2(a+b x)\right)}{b (n+1)}","\frac{\coth ^{n+1}(a+b x) \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\coth ^2(a+b x)\right)}{b (n+1)}",1,"(Coth[a + b*x]^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, 1 + (1 + n)/2, Coth[a + b*x]^2])/(b*(1 + n))","A",1
16,1,51,48,0.0417769,"\int (b \coth (c+d x))^n \, dx","Integrate[(b*Coth[c + d*x])^n,x]","\frac{\coth (c+d x) (b \coth (c+d x))^n \, _2F_1\left(1,\frac{n+1}{2};\frac{n+1}{2}+1;\coth ^2(c+d x)\right)}{d (n+1)}","\frac{(b \coth (c+d x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\coth ^2(c+d x)\right)}{b d (n+1)}",1,"(Coth[c + d*x]*(b*Coth[c + d*x])^n*Hypergeometric2F1[1, (1 + n)/2, 1 + (1 + n)/2, Coth[c + d*x]^2])/(d*(1 + n))","A",1
17,1,47,57,0.0513478,"\int \left(b \coth ^2(c+d x)\right)^n \, dx","Integrate[(b*Coth[c + d*x]^2)^n,x]","\frac{\coth (c+d x) \left(b \coth ^2(c+d x)\right)^n \, _2F_1\left(1,n+\frac{1}{2};n+\frac{3}{2};\coth ^2(c+d x)\right)}{2 d n+d}","\frac{\coth (c+d x) \left(b \coth ^2(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (2 n+1);\frac{1}{2} (2 n+3);\coth ^2(c+d x)\right)}{d (2 n+1)}",1,"(Coth[c + d*x]*(b*Coth[c + d*x]^2)^n*Hypergeometric2F1[1, 1/2 + n, 3/2 + n, Coth[c + d*x]^2])/(d + 2*d*n)","A",1
18,1,56,61,0.1285984,"\int \left(b \coth ^2(c+d x)\right)^{3/2} \, dx","Integrate[(b*Coth[c + d*x]^2)^(3/2),x]","-\frac{\tanh ^3(c+d x) \left(b \coth ^2(c+d x)\right)^{3/2} \left(\coth ^2(c+d x)-2 \log (\tanh (c+d x))-2 \log (\cosh (c+d x))\right)}{2 d}","\frac{b \tanh (c+d x) \sqrt{b \coth ^2(c+d x)} \log (\sinh (c+d x))}{d}-\frac{b \coth (c+d x) \sqrt{b \coth ^2(c+d x)}}{2 d}",1,"-1/2*((b*Coth[c + d*x]^2)^(3/2)*(Coth[c + d*x]^2 - 2*Log[Cosh[c + d*x]] - 2*Log[Tanh[c + d*x]])*Tanh[c + d*x]^3)/d","A",1
19,1,39,31,0.04741,"\int \sqrt{b \coth ^2(c+d x)} \, dx","Integrate[Sqrt[b*Coth[c + d*x]^2],x]","\frac{\tanh (c+d x) \sqrt{b \coth ^2(c+d x)} (\log (\tanh (c+d x))+\log (\cosh (c+d x)))}{d}","\frac{\tanh (c+d x) \sqrt{b \coth ^2(c+d x)} \log (\sinh (c+d x))}{d}",1,"(Sqrt[b*Coth[c + d*x]^2]*(Log[Cosh[c + d*x]] + Log[Tanh[c + d*x]])*Tanh[c + d*x])/d","A",1
20,1,31,31,0.0630182,"\int \frac{1}{\sqrt{b \coth ^2(c+d x)}} \, dx","Integrate[1/Sqrt[b*Coth[c + d*x]^2],x]","\frac{\coth (c+d x) \log (\cosh (c+d x))}{d \sqrt{b \coth ^2(c+d x)}}","\frac{\coth (c+d x) \log (\cosh (c+d x))}{d \sqrt{b \coth ^2(c+d x)}}",1,"(Coth[c + d*x]*Log[Cosh[c + d*x]])/(d*Sqrt[b*Coth[c + d*x]^2])","A",1
21,1,48,65,0.1503135,"\int \frac{1}{\left(b \coth ^2(c+d x)\right)^{3/2}} \, dx","Integrate[(b*Coth[c + d*x]^2)^(-3/2),x]","\frac{2 \coth (c+d x) \log (\cosh (c+d x))-\tanh (c+d x)}{2 b d \sqrt{b \coth ^2(c+d x)}}","\frac{\coth (c+d x) \log (\cosh (c+d x))}{b d \sqrt{b \coth ^2(c+d x)}}-\frac{\tanh (c+d x)}{2 b d \sqrt{b \coth ^2(c+d x)}}",1,"(2*Coth[c + d*x]*Log[Cosh[c + d*x]] - Tanh[c + d*x])/(2*b*d*Sqrt[b*Coth[c + d*x]^2])","A",1
22,1,166,297,0.3521088,"\int \left(b \coth ^2(c+d x)\right)^{4/3} \, dx","Integrate[(b*Coth[c + d*x]^2)^(4/3),x]","-\frac{\left(b \coth ^2(c+d x)\right)^{4/3} \left(12 \coth ^{\frac{5}{3}}(c+d x)-20 \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)-5 \left(-\log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)+\log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)\right)\right)}{20 d \coth ^{\frac{8}{3}}(c+d x)}","-\frac{3 b \coth (c+d x) \sqrt[3]{b \coth ^2(c+d x)}}{5 d}-\frac{b \sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt{3} b \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}-\frac{\sqrt{3} b \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^2(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{2}{3}}(c+d x)}",1,"-1/20*((b*Coth[c + d*x]^2)^(4/3)*(-20*ArcTanh[Coth[c + d*x]^(1/3)] + 12*Coth[c + d*x]^(5/3) - 5*(2*Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]] - Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)] + Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])))/(d*Coth[c + d*x]^(8/3))","A",1
23,1,43,289,0.0406152,"\int \left(b \coth ^2(c+d x)\right)^{2/3} \, dx","Integrate[(b*Coth[c + d*x]^2)^(2/3),x]","\frac{3 \tanh (c+d x) \left(b \coth ^2(c+d x)\right)^{2/3} \left(\, _2F_1\left(\frac{1}{6},1;\frac{7}{6};\coth ^2(c+d x)\right)-1\right)}{d}","-\frac{3 \tanh (c+d x) \left(b \coth ^2(c+d x)\right)^{2/3}}{d}-\frac{\left(b \coth ^2(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\left(b \coth ^2(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}-\frac{\sqrt{3} \left(b \coth ^2(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt{3} \left(b \coth ^2(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\left(b \coth ^2(c+d x)\right)^{2/3} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{4}{3}}(c+d x)}",1,"(3*(b*Coth[c + d*x]^2)^(2/3)*(-1 + Hypergeometric2F1[1/6, 1, 7/6, Coth[c + d*x]^2])*Tanh[c + d*x])/d","C",1
24,1,151,264,0.1092916,"\int \sqrt[3]{b \coth ^2(c+d x)} \, dx","Integrate[(b*Coth[c + d*x]^2)^(1/3),x]","\frac{\sqrt[3]{b \coth ^2(c+d x)} \left(-\log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)+\log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)+4 \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}","-\frac{\sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt{3} \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}-\frac{\sqrt{3} \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^2(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{2}{3}}(c+d x)}",1,"((b*Coth[c + d*x]^2)^(1/3)*(2*Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]] + 4*ArcTanh[Coth[c + d*x]^(1/3)] - Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)] + Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)]))/(4*d*Coth[c + d*x]^(2/3))","A",1
25,1,41,264,0.055805,"\int \frac{1}{\sqrt[3]{b \coth ^2(c+d x)}} \, dx","Integrate[(b*Coth[c + d*x]^2)^(-1/3),x]","\frac{3 \coth (c+d x) \, _2F_1\left(\frac{1}{6},1;\frac{7}{6};\coth ^2(c+d x)\right)}{d \sqrt[3]{b \coth ^2(c+d x)}}","-\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^2(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \sqrt[3]{b \coth ^2(c+d x)}}",1,"(3*Coth[c + d*x]*Hypergeometric2F1[1/6, 1, 7/6, Coth[c + d*x]^2])/(d*(b*Coth[c + d*x]^2)^(1/3))","C",1
26,1,41,289,0.0661344,"\int \frac{1}{\left(b \coth ^2(c+d x)\right)^{2/3}} \, dx","Integrate[(b*Coth[c + d*x]^2)^(-2/3),x]","-\frac{3 \coth (c+d x) \, _2F_1\left(-\frac{1}{6},1;\frac{5}{6};\coth ^2(c+d x)\right)}{d \left(b \coth ^2(c+d x)\right)^{2/3}}","-\frac{3 \coth (c+d x)}{d \left(b \coth ^2(c+d x)\right)^{2/3}}-\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^2(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^2(c+d x)\right)^{2/3}}+\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \left(b \coth ^2(c+d x)\right)^{2/3}}-\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \left(b \coth ^2(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \left(b \coth ^2(c+d x)\right)^{2/3}}",1,"(-3*Coth[c + d*x]*Hypergeometric2F1[-1/6, 1, 5/6, Coth[c + d*x]^2])/(d*(b*Coth[c + d*x]^2)^(2/3))","C",1
27,1,43,309,0.1569804,"\int \frac{1}{\left(b \coth ^2(c+d x)\right)^{4/3}} \, dx","Integrate[(b*Coth[c + d*x]^2)^(-4/3),x]","-\frac{3 \coth (c+d x) \, _2F_1\left(-\frac{5}{6},1;\frac{1}{6};\coth ^2(c+d x)\right)}{5 d \left(b \coth ^2(c+d x)\right)^{4/3}}","-\frac{3 \tanh (c+d x)}{5 b d \sqrt[3]{b \coth ^2(c+d x)}}-\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^2(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{b d \sqrt[3]{b \coth ^2(c+d x)}}",1,"(-3*Coth[c + d*x]*Hypergeometric2F1[-5/6, 1, 1/6, Coth[c + d*x]^2])/(5*d*(b*Coth[c + d*x]^2)^(4/3))","C",1
28,1,53,55,0.0423281,"\int \left(b \coth ^3(c+d x)\right)^n \, dx","Integrate[(b*Coth[c + d*x]^3)^n,x]","\frac{\coth (c+d x) \left(b \coth ^3(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (3 n+1);\frac{3 (n+1)}{2};\coth ^2(c+d x)\right)}{3 d n+d}","\frac{\coth (c+d x) \left(b \coth ^3(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (3 n+1);\frac{3 (n+1)}{2};\coth ^2(c+d x)\right)}{d (3 n+1)}",1,"(Coth[c + d*x]*(b*Coth[c + d*x]^3)^n*Hypergeometric2F1[1, (1 + 3*n)/2, (3*(1 + n))/2, Coth[c + d*x]^2])/(d + 3*d*n)","A",1
29,1,82,134,0.5306175,"\int \left(b \coth ^3(c+d x)\right)^{3/2} \, dx","Integrate[(b*Coth[c + d*x]^3)^(3/2),x]","-\frac{\left(b \coth ^3(c+d x)\right)^{3/2} \left(6 \coth ^{\frac{7}{2}}(c+d x)+14 \coth ^{\frac{3}{2}}(c+d x)+21 \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)-21 \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)\right)}{21 d \coth ^{\frac{9}{2}}(c+d x)}","-\frac{2 b \sqrt{b \coth ^3(c+d x)}}{3 d}-\frac{2 b \coth ^2(c+d x) \sqrt{b \coth ^3(c+d x)}}{7 d}-\frac{b \sqrt{b \coth ^3(c+d x)} \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}+\frac{b \sqrt{b \coth ^3(c+d x)} \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}",1,"-1/21*((b*Coth[c + d*x]^3)^(3/2)*(21*ArcTan[Sqrt[Coth[c + d*x]]] - 21*ArcTanh[Sqrt[Coth[c + d*x]]] + 14*Coth[c + d*x]^(3/2) + 6*Coth[c + d*x]^(7/2)))/(d*Coth[c + d*x]^(9/2))","A",1
30,1,63,104,0.103354,"\int \sqrt{b \coth ^3(c+d x)} \, dx","Integrate[Sqrt[b*Coth[c + d*x]^3],x]","\frac{\sqrt{b \coth ^3(c+d x)} \left(-2 \sqrt{\coth (c+d x)}+\tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)+\tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)\right)}{d \coth ^{\frac{3}{2}}(c+d x)}","-\frac{2 \tanh (c+d x) \sqrt{b \coth ^3(c+d x)}}{d}+\frac{\sqrt{b \coth ^3(c+d x)} \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}+\frac{\sqrt{b \coth ^3(c+d x)} \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}",1,"((ArcTan[Sqrt[Coth[c + d*x]]] + ArcTanh[Sqrt[Coth[c + d*x]]] - 2*Sqrt[Coth[c + d*x]])*Sqrt[b*Coth[c + d*x]^3])/(d*Coth[c + d*x]^(3/2))","A",1
31,1,41,105,0.0324374,"\int \frac{1}{\sqrt{b \coth ^3(c+d x)}} \, dx","Integrate[1/Sqrt[b*Coth[c + d*x]^3],x]","-\frac{2 \coth (c+d x) \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};\coth ^2(c+d x)\right)}{d \sqrt{b \coth ^3(c+d x)}}","-\frac{2 \coth (c+d x)}{d \sqrt{b \coth ^3(c+d x)}}-\frac{\coth ^{\frac{3}{2}}(c+d x) \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \sqrt{b \coth ^3(c+d x)}}+\frac{\coth ^{\frac{3}{2}}(c+d x) \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \sqrt{b \coth ^3(c+d x)}}",1,"(-2*Coth[c + d*x]*Hypergeometric2F1[-1/4, 1, 3/4, Coth[c + d*x]^2])/(d*Sqrt[b*Coth[c + d*x]^3])","C",1
32,1,43,141,0.0688939,"\int \frac{1}{\left(b \coth ^3(c+d x)\right)^{3/2}} \, dx","Integrate[(b*Coth[c + d*x]^3)^(-3/2),x]","-\frac{2 \coth (c+d x) \, _2F_1\left(-\frac{7}{4},1;-\frac{3}{4};\coth ^2(c+d x)\right)}{7 d \left(b \coth ^3(c+d x)\right)^{3/2}}","-\frac{2}{3 b d \sqrt{b \coth ^3(c+d x)}}-\frac{2 \tanh ^2(c+d x)}{7 b d \sqrt{b \coth ^3(c+d x)}}+\frac{\coth ^{\frac{3}{2}}(c+d x) \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{b d \sqrt{b \coth ^3(c+d x)}}+\frac{\coth ^{\frac{3}{2}}(c+d x) \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{b d \sqrt{b \coth ^3(c+d x)}}",1,"(-2*Coth[c + d*x]*Hypergeometric2F1[-7/4, 1, -3/4, Coth[c + d*x]^2])/(7*d*(b*Coth[c + d*x]^3)^(3/2))","C",1
33,1,43,74,0.0654624,"\int \left(b \coth ^3(c+d x)\right)^{4/3} \, dx","Integrate[(b*Coth[c + d*x]^3)^(4/3),x]","-\frac{\tanh (c+d x) \left(b \coth ^3(c+d x)\right)^{4/3} \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\tanh ^2(c+d x)\right)}{3 d}","-\frac{b \sqrt[3]{b \coth ^3(c+d x)}}{d}-\frac{b \coth ^2(c+d x) \sqrt[3]{b \coth ^3(c+d x)}}{3 d}+b x \tanh (c+d x) \sqrt[3]{b \coth ^3(c+d x)}",1,"-1/3*((b*Coth[c + d*x]^3)^(4/3)*Hypergeometric2F1[-3/2, 1, -1/2, Tanh[c + d*x]^2]*Tanh[c + d*x])/d","C",1
34,1,41,50,0.0333901,"\int \left(b \coth ^3(c+d x)\right)^{2/3} \, dx","Integrate[(b*Coth[c + d*x]^3)^(2/3),x]","-\frac{\tanh (c+d x) \left(b \coth ^3(c+d x)\right)^{2/3} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\tanh ^2(c+d x)\right)}{d}","x \tanh ^2(c+d x) \left(b \coth ^3(c+d x)\right)^{2/3}-\frac{\tanh (c+d x) \left(b \coth ^3(c+d x)\right)^{2/3}}{d}",1,"-(((b*Coth[c + d*x]^3)^(2/3)*Hypergeometric2F1[-1/2, 1, 1/2, Tanh[c + d*x]^2]*Tanh[c + d*x])/d)","C",1
35,1,39,31,0.0285178,"\int \sqrt[3]{b \coth ^3(c+d x)} \, dx","Integrate[(b*Coth[c + d*x]^3)^(1/3),x]","\frac{\tanh (c+d x) \sqrt[3]{b \coth ^3(c+d x)} (\log (\tanh (c+d x))+\log (\cosh (c+d x)))}{d}","\frac{\tanh (c+d x) \sqrt[3]{b \coth ^3(c+d x)} \log (\sinh (c+d x))}{d}",1,"((b*Coth[c + d*x]^3)^(1/3)*(Log[Cosh[c + d*x]] + Log[Tanh[c + d*x]])*Tanh[c + d*x])/d","A",1
36,1,31,31,0.0307828,"\int \frac{1}{\sqrt[3]{b \coth ^3(c+d x)}} \, dx","Integrate[(b*Coth[c + d*x]^3)^(-1/3),x]","\frac{\coth (c+d x) \log (\cosh (c+d x))}{d \sqrt[3]{b \coth ^3(c+d x)}}","\frac{\coth (c+d x) \log (\cosh (c+d x))}{d \sqrt[3]{b \coth ^3(c+d x)}}",1,"(Coth[c + d*x]*Log[Cosh[c + d*x]])/(d*(b*Coth[c + d*x]^3)^(1/3))","A",1
37,1,40,50,0.0637271,"\int \frac{1}{\left(b \coth ^3(c+d x)\right)^{2/3}} \, dx","Integrate[(b*Coth[c + d*x]^3)^(-2/3),x]","\frac{\coth (c+d x) \left(\tanh ^{-1}(\tanh (c+d x)) \coth (c+d x)-1\right)}{d \left(b \coth ^3(c+d x)\right)^{2/3}}","\frac{x \coth ^2(c+d x)}{\left(b \coth ^3(c+d x)\right)^{2/3}}-\frac{\coth (c+d x)}{d \left(b \coth ^3(c+d x)\right)^{2/3}}",1,"(Coth[c + d*x]*(-1 + ArcTanh[Tanh[c + d*x]]*Coth[c + d*x]))/(d*(b*Coth[c + d*x]^3)^(2/3))","A",1
38,1,51,80,0.0963132,"\int \frac{1}{\left(b \coth ^3(c+d x)\right)^{4/3}} \, dx","Integrate[(b*Coth[c + d*x]^3)^(-4/3),x]","\frac{-\tanh ^2(c+d x)+3 \tanh ^{-1}(\tanh (c+d x)) \coth (c+d x)-3}{3 b d \sqrt[3]{b \coth ^3(c+d x)}}","\frac{x \coth (c+d x)}{b \sqrt[3]{b \coth ^3(c+d x)}}-\frac{1}{b d \sqrt[3]{b \coth ^3(c+d x)}}-\frac{\tanh ^2(c+d x)}{3 b d \sqrt[3]{b \coth ^3(c+d x)}}",1,"(-3 + 3*ArcTanh[Tanh[c + d*x]]*Coth[c + d*x] - Tanh[c + d*x]^2)/(3*b*d*(b*Coth[c + d*x]^3)^(1/3))","A",1
39,1,51,57,0.0447925,"\int \left(b \coth ^4(c+d x)\right)^n \, dx","Integrate[(b*Coth[c + d*x]^4)^n,x]","\frac{\coth (c+d x) \left(b \coth ^4(c+d x)\right)^n \, _2F_1\left(1,2 n+\frac{1}{2};2 n+\frac{3}{2};\coth ^2(c+d x)\right)}{4 d n+d}","\frac{\coth (c+d x) \left(b \coth ^4(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (4 n+1);\frac{1}{2} (4 n+3);\coth ^2(c+d x)\right)}{d (4 n+1)}",1,"(Coth[c + d*x]*(b*Coth[c + d*x]^4)^n*Hypergeometric2F1[1, 1/2 + 2*n, 3/2 + 2*n, Coth[c + d*x]^2])/(d + 4*d*n)","A",1
40,1,43,110,0.0672495,"\int \left(b \coth ^4(c+d x)\right)^{3/2} \, dx","Integrate[(b*Coth[c + d*x]^4)^(3/2),x]","-\frac{\tanh (c+d x) \left(b \coth ^4(c+d x)\right)^{3/2} \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\tanh ^2(c+d x)\right)}{5 d}","-\frac{b \coth (c+d x) \sqrt{b \coth ^4(c+d x)}}{3 d}-\frac{b \coth ^3(c+d x) \sqrt{b \coth ^4(c+d x)}}{5 d}+b x \tanh ^2(c+d x) \sqrt{b \coth ^4(c+d x)}-\frac{b \tanh (c+d x) \sqrt{b \coth ^4(c+d x)}}{d}",1,"-1/5*((b*Coth[c + d*x]^4)^(3/2)*Hypergeometric2F1[-5/2, 1, -3/2, Tanh[c + d*x]^2]*Tanh[c + d*x])/d","C",1
41,1,41,50,0.0347213,"\int \sqrt{b \coth ^4(c+d x)} \, dx","Integrate[Sqrt[b*Coth[c + d*x]^4],x]","-\frac{\tanh (c+d x) \sqrt{b \coth ^4(c+d x)} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\tanh ^2(c+d x)\right)}{d}","x \tanh ^2(c+d x) \sqrt{b \coth ^4(c+d x)}-\frac{\tanh (c+d x) \sqrt{b \coth ^4(c+d x)}}{d}",1,"-((Sqrt[b*Coth[c + d*x]^4]*Hypergeometric2F1[-1/2, 1, 1/2, Tanh[c + d*x]^2]*Tanh[c + d*x])/d)","C",1
42,1,40,50,0.0713731,"\int \frac{1}{\sqrt{b \coth ^4(c+d x)}} \, dx","Integrate[1/Sqrt[b*Coth[c + d*x]^4],x]","\frac{\coth (c+d x) \left(\tanh ^{-1}(\tanh (c+d x)) \coth (c+d x)-1\right)}{d \sqrt{b \coth ^4(c+d x)}}","\frac{x \coth ^2(c+d x)}{\sqrt{b \coth ^4(c+d x)}}-\frac{\coth (c+d x)}{d \sqrt{b \coth ^4(c+d x)}}",1,"(Coth[c + d*x]*(-1 + ArcTanh[Tanh[c + d*x]]*Coth[c + d*x]))/(d*Sqrt[b*Coth[c + d*x]^4])","A",1
43,1,68,118,0.2580526,"\int \frac{1}{\left(b \coth ^4(c+d x)\right)^{3/2}} \, dx","Integrate[(b*Coth[c + d*x]^4)^(-3/2),x]","\frac{-3 \tanh ^3(c+d x)-5 \tanh (c+d x)-15 \coth (c+d x)+15 \tanh ^{-1}(\tanh (c+d x)) \coth ^2(c+d x)}{15 b d \sqrt{b \coth ^4(c+d x)}}","-\frac{\coth (c+d x)}{b d \sqrt{b \coth ^4(c+d x)}}+\frac{x \coth ^2(c+d x)}{b \sqrt{b \coth ^4(c+d x)}}-\frac{\tanh ^3(c+d x)}{5 b d \sqrt{b \coth ^4(c+d x)}}-\frac{\tanh (c+d x)}{3 b d \sqrt{b \coth ^4(c+d x)}}",1,"(-15*Coth[c + d*x] + 15*ArcTanh[Tanh[c + d*x]]*Coth[c + d*x]^2 - 5*Tanh[c + d*x] - 3*Tanh[c + d*x]^3)/(15*b*d*Sqrt[b*Coth[c + d*x]^4])","A",1
44,1,68,353,0.1434772,"\int \left(b \coth ^4(c+d x)\right)^{4/3} \, dx","Integrate[(b*Coth[c + d*x]^4)^(4/3),x]","-\frac{3 b \tanh (c+d x) \sqrt[3]{b \coth ^4(c+d x)} \left(-91 \, _2F_1\left(\frac{1}{6},1;\frac{7}{6};\coth ^2(c+d x)\right)+7 \coth ^4(c+d x)+13 \coth ^2(c+d x)+91\right)}{91 d}","-\frac{3 b \coth (c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{7 d}-\frac{3 b \coth ^3(c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{13 d}-\frac{3 b \tanh (c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{d}-\frac{b \sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}-\frac{\sqrt{3} b \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt{3} b \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^4(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{4}{3}}(c+d x)}",1,"(-3*b*(b*Coth[c + d*x]^4)^(1/3)*(91 + 13*Coth[c + d*x]^2 + 7*Coth[c + d*x]^4 - 91*Hypergeometric2F1[1/6, 1, 7/6, Coth[c + d*x]^2])*Tanh[c + d*x])/(91*d)","C",1
45,1,166,291,0.4163574,"\int \left(b \coth ^4(c+d x)\right)^{2/3} \, dx","Integrate[(b*Coth[c + d*x]^4)^(2/3),x]","\frac{\left(b \coth ^4(c+d x)\right)^{2/3} \left(-12 \coth ^{\frac{5}{3}}(c+d x)+20 \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)+5 \left(-\log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)+\log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)\right)\right)}{20 d \coth ^{\frac{8}{3}}(c+d x)}","-\frac{3 \tanh (c+d x) \left(b \coth ^4(c+d x)\right)^{2/3}}{5 d}-\frac{\left(b \coth ^4(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{8}{3}}(c+d x)}+\frac{\left(b \coth ^4(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{8}{3}}(c+d x)}+\frac{\sqrt{3} \left(b \coth ^4(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{8}{3}}(c+d x)}-\frac{\sqrt{3} \left(b \coth ^4(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{8}{3}}(c+d x)}+\frac{\left(b \coth ^4(c+d x)\right)^{2/3} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{8}{3}}(c+d x)}",1,"((b*Coth[c + d*x]^4)^(2/3)*(20*ArcTanh[Coth[c + d*x]^(1/3)] - 12*Coth[c + d*x]^(5/3) + 5*(2*Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]] - Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)] + Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])))/(20*d*Coth[c + d*x]^(8/3))","A",1
46,1,43,289,0.0283831,"\int \sqrt[3]{b \coth ^4(c+d x)} \, dx","Integrate[(b*Coth[c + d*x]^4)^(1/3),x]","\frac{3 \tanh (c+d x) \sqrt[3]{b \coth ^4(c+d x)} \left(\, _2F_1\left(\frac{1}{6},1;\frac{7}{6};\coth ^2(c+d x)\right)-1\right)}{d}","-\frac{3 \tanh (c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{d}-\frac{\sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}-\frac{\sqrt{3} \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt{3} \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^4(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{4}{3}}(c+d x)}",1,"(3*(b*Coth[c + d*x]^4)^(1/3)*(-1 + Hypergeometric2F1[1/6, 1, 7/6, Coth[c + d*x]^2])*Tanh[c + d*x])/d","C",1
47,1,41,289,0.0532694,"\int \frac{1}{\sqrt[3]{b \coth ^4(c+d x)}} \, dx","Integrate[(b*Coth[c + d*x]^4)^(-1/3),x]","-\frac{3 \coth (c+d x) \, _2F_1\left(-\frac{1}{6},1;\frac{5}{6};\coth ^2(c+d x)\right)}{d \sqrt[3]{b \coth ^4(c+d x)}}","-\frac{3 \coth (c+d x)}{d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \sqrt[3]{b \coth ^4(c+d x)}}",1,"(-3*Coth[c + d*x]*Hypergeometric2F1[-1/6, 1, 5/6, Coth[c + d*x]^2])/(d*(b*Coth[c + d*x]^4)^(1/3))","C",1
48,1,43,291,0.0545547,"\int \frac{1}{\left(b \coth ^4(c+d x)\right)^{2/3}} \, dx","Integrate[(b*Coth[c + d*x]^4)^(-2/3),x]","-\frac{3 \coth (c+d x) \, _2F_1\left(-\frac{5}{6},1;\frac{1}{6};\coth ^2(c+d x)\right)}{5 d \left(b \coth ^4(c+d x)\right)^{2/3}}","-\frac{3 \coth (c+d x)}{5 d \left(b \coth ^4(c+d x)\right)^{2/3}}-\frac{\coth ^{\frac{8}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^4(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{8}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^4(c+d x)\right)^{2/3}}-\frac{\sqrt{3} \coth ^{\frac{8}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \left(b \coth ^4(c+d x)\right)^{2/3}}+\frac{\sqrt{3} \coth ^{\frac{8}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \left(b \coth ^4(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{8}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \left(b \coth ^4(c+d x)\right)^{2/3}}",1,"(-3*Coth[c + d*x]*Hypergeometric2F1[-5/6, 1, 1/6, Coth[c + d*x]^2])/(5*d*(b*Coth[c + d*x]^4)^(2/3))","C",1
49,1,43,369,0.0443772,"\int \frac{1}{\left(b \coth ^4(c+d x)\right)^{4/3}} \, dx","Integrate[(b*Coth[c + d*x]^4)^(-4/3),x]","-\frac{3 \coth (c+d x) \, _2F_1\left(-\frac{13}{6},1;-\frac{7}{6};\coth ^2(c+d x)\right)}{13 d \left(b \coth ^4(c+d x)\right)^{4/3}}","-\frac{3 \coth (c+d x)}{b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{3 \tanh ^3(c+d x)}{13 b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{3 \tanh (c+d x)}{7 b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{b d \sqrt[3]{b \coth ^4(c+d x)}}",1,"(-3*Coth[c + d*x]*Hypergeometric2F1[-13/6, 1, -7/6, Coth[c + d*x]^2])/(13*d*(b*Coth[c + d*x]^4)^(4/3))","C",1
50,1,55,57,0.0517541,"\int \left(b \coth ^m(c+d x)\right)^n \, dx","Integrate[(b*Coth[c + d*x]^m)^n,x]","\frac{\coth (c+d x) \left(b \coth ^m(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (m n+1);\frac{1}{2} (m n+3);\coth ^2(c+d x)\right)}{d m n+d}","\frac{\coth (c+d x) \left(b \coth ^m(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (m n+1);\frac{1}{2} (m n+3);\coth ^2(c+d x)\right)}{d (m n+1)}",1,"(Coth[c + d*x]*(b*Coth[c + d*x]^m)^n*Hypergeometric2F1[1, (1 + m*n)/2, (3 + m*n)/2, Coth[c + d*x]^2])/(d + d*m*n)","A",1
51,1,58,63,0.0770979,"\int \left(b \coth ^m(c+d x)\right)^{3/2} \, dx","Integrate[(b*Coth[c + d*x]^m)^(3/2),x]","\frac{2 \coth (c+d x) \left(b \coth ^m(c+d x)\right)^{3/2} \, _2F_1\left(1,\frac{1}{4} (3 m+2);\frac{3 (m+2)}{4};\coth ^2(c+d x)\right)}{d (3 m+2)}","\frac{2 b \coth ^{m+1}(c+d x) \sqrt{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{1}{4} (3 m+2);\frac{3 (m+2)}{4};\coth ^2(c+d x)\right)}{d (3 m+2)}",1,"(2*Coth[c + d*x]*(b*Coth[c + d*x]^m)^(3/2)*Hypergeometric2F1[1, (2 + 3*m)/4, (3*(2 + m))/4, Coth[c + d*x]^2])/(d*(2 + 3*m))","A",1
52,1,54,54,0.0405367,"\int \sqrt{b \coth ^m(c+d x)} \, dx","Integrate[Sqrt[b*Coth[c + d*x]^m],x]","\frac{2 \coth (c+d x) \sqrt{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{m+2}{4};\frac{m+6}{4};\coth ^2(c+d x)\right)}{d (m+2)}","\frac{2 \coth (c+d x) \sqrt{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{m+2}{4};\frac{m+6}{4};\coth ^2(c+d x)\right)}{d (m+2)}",1,"(2*Coth[c + d*x]*Sqrt[b*Coth[c + d*x]^m]*Hypergeometric2F1[1, (2 + m)/4, (6 + m)/4, Coth[c + d*x]^2])/(d*(2 + m))","A",1
53,1,58,60,0.0486794,"\int \frac{1}{\sqrt{b \coth ^m(c+d x)}} \, dx","Integrate[1/Sqrt[b*Coth[c + d*x]^m],x]","-\frac{2 \coth (c+d x) \, _2F_1\left(1,\frac{2-m}{4};\frac{6-m}{4};\coth ^2(c+d x)\right)}{d (m-2) \sqrt{b \coth ^m(c+d x)}}","\frac{2 \coth (c+d x) \, _2F_1\left(1,\frac{2-m}{4};\frac{6-m}{4};\coth ^2(c+d x)\right)}{d (2-m) \sqrt{b \coth ^m(c+d x)}}",1,"(-2*Coth[c + d*x]*Hypergeometric2F1[1, (2 - m)/4, (6 - m)/4, Coth[c + d*x]^2])/(d*(-2 + m)*Sqrt[b*Coth[c + d*x]^m])","A",1
54,1,58,69,0.0691706,"\int \frac{1}{\left(b \coth ^m(c+d x)\right)^{3/2}} \, dx","Integrate[(b*Coth[c + d*x]^m)^(-3/2),x]","-\frac{2 \coth (c+d x) \, _2F_1\left(1,\frac{1}{4} (2-3 m);-\frac{3}{4} (m-2);\coth ^2(c+d x)\right)}{d (3 m-2) \left(b \coth ^m(c+d x)\right)^{3/2}}","\frac{2 \coth ^{1-m}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2-3 m);\frac{3 (2-m)}{4};\coth ^2(c+d x)\right)}{b d (2-3 m) \sqrt{b \coth ^m(c+d x)}}",1,"(-2*Coth[c + d*x]*Hypergeometric2F1[1, (2 - 3*m)/4, (-3*(-2 + m))/4, Coth[c + d*x]^2])/(d*(-2 + 3*m)*(b*Coth[c + d*x]^m)^(3/2))","A",1
55,1,60,65,0.0728238,"\int \left(b \coth ^m(c+d x)\right)^{4/3} \, dx","Integrate[(b*Coth[c + d*x]^m)^(4/3),x]","\frac{3 \coth (c+d x) \left(b \coth ^m(c+d x)\right)^{4/3} \, _2F_1\left(1,\frac{1}{6} (4 m+3);\frac{1}{6} (4 m+9);\coth ^2(c+d x)\right)}{d (4 m+3)}","\frac{3 b \coth ^{m+1}(c+d x) \sqrt[3]{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{1}{6} (4 m+3);\frac{1}{6} (4 m+9);\coth ^2(c+d x)\right)}{d (4 m+3)}",1,"(3*Coth[c + d*x]*(b*Coth[c + d*x]^m)^(4/3)*Hypergeometric2F1[1, (3 + 4*m)/6, (9 + 4*m)/6, Coth[c + d*x]^2])/(d*(3 + 4*m))","A",1
56,1,60,60,0.0444836,"\int \left(b \coth ^m(c+d x)\right)^{2/3} \, dx","Integrate[(b*Coth[c + d*x]^m)^(2/3),x]","\frac{3 \coth (c+d x) \left(b \coth ^m(c+d x)\right)^{2/3} \, _2F_1\left(1,\frac{1}{6} (2 m+3);\frac{1}{6} (2 m+9);\coth ^2(c+d x)\right)}{d (2 m+3)}","\frac{3 \coth (c+d x) \left(b \coth ^m(c+d x)\right)^{2/3} \, _2F_1\left(1,\frac{1}{6} (2 m+3);\frac{1}{6} (2 m+9);\coth ^2(c+d x)\right)}{d (2 m+3)}",1,"(3*Coth[c + d*x]*(b*Coth[c + d*x]^m)^(2/3)*Hypergeometric2F1[1, (3 + 2*m)/6, (9 + 2*m)/6, Coth[c + d*x]^2])/(d*(3 + 2*m))","A",1
57,1,54,54,0.0411951,"\int \sqrt[3]{b \coth ^m(c+d x)} \, dx","Integrate[(b*Coth[c + d*x]^m)^(1/3),x]","\frac{3 \coth (c+d x) \sqrt[3]{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{m+3}{6};\frac{m+9}{6};\coth ^2(c+d x)\right)}{d (m+3)}","\frac{3 \coth (c+d x) \sqrt[3]{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{m+3}{6};\frac{m+9}{6};\coth ^2(c+d x)\right)}{d (m+3)}",1,"(3*Coth[c + d*x]*(b*Coth[c + d*x]^m)^(1/3)*Hypergeometric2F1[1, (3 + m)/6, (9 + m)/6, Coth[c + d*x]^2])/(d*(3 + m))","A",1
58,1,58,60,0.0408291,"\int \frac{1}{\sqrt[3]{b \coth ^m(c+d x)}} \, dx","Integrate[(b*Coth[c + d*x]^m)^(-1/3),x]","-\frac{3 \coth (c+d x) \, _2F_1\left(1,\frac{3-m}{6};\frac{9-m}{6};\coth ^2(c+d x)\right)}{d (m-3) \sqrt[3]{b \coth ^m(c+d x)}}","\frac{3 \coth (c+d x) \, _2F_1\left(1,\frac{3-m}{6};\frac{9-m}{6};\coth ^2(c+d x)\right)}{d (3-m) \sqrt[3]{b \coth ^m(c+d x)}}",1,"(-3*Coth[c + d*x]*Hypergeometric2F1[1, (3 - m)/6, (9 - m)/6, Coth[c + d*x]^2])/(d*(-3 + m)*(b*Coth[c + d*x]^m)^(1/3))","A",1
59,1,60,60,0.0419962,"\int \frac{1}{\left(b \coth ^m(c+d x)\right)^{2/3}} \, dx","Integrate[(b*Coth[c + d*x]^m)^(-2/3),x]","-\frac{3 \coth (c+d x) \, _2F_1\left(1,\frac{1}{6} (3-2 m);\frac{1}{6} (9-2 m);\coth ^2(c+d x)\right)}{d (2 m-3) \left(b \coth ^m(c+d x)\right)^{2/3}}","\frac{3 \coth (c+d x) \, _2F_1\left(1,\frac{1}{6} (3-2 m);\frac{1}{6} (9-2 m);\coth ^2(c+d x)\right)}{d (3-2 m) \left(b \coth ^m(c+d x)\right)^{2/3}}",1,"(-3*Coth[c + d*x]*Hypergeometric2F1[1, (3 - 2*m)/6, (9 - 2*m)/6, Coth[c + d*x]^2])/(d*(-3 + 2*m)*(b*Coth[c + d*x]^m)^(2/3))","A",1
60,1,60,69,0.0696185,"\int \frac{1}{\left(b \coth ^m(c+d x)\right)^{4/3}} \, dx","Integrate[(b*Coth[c + d*x]^m)^(-4/3),x]","-\frac{3 \coth (c+d x) \, _2F_1\left(1,\frac{1}{6} (3-4 m);\frac{1}{6} (9-4 m);\coth ^2(c+d x)\right)}{d (4 m-3) \left(b \coth ^m(c+d x)\right)^{4/3}}","\frac{3 \coth ^{1-m}(c+d x) \, _2F_1\left(1,\frac{1}{6} (3-4 m);\frac{1}{6} (9-4 m);\coth ^2(c+d x)\right)}{b d (3-4 m) \sqrt[3]{b \coth ^m(c+d x)}}",1,"(-3*Coth[c + d*x]*Hypergeometric2F1[1, (3 - 4*m)/6, (9 - 4*m)/6, Coth[c + d*x]^2])/(d*(-3 + 4*m)*(b*Coth[c + d*x]^m)^(4/3))","A",1
61,1,94,41,0.2492415,"\int (1+\coth (x))^5 \, dx","Integrate[(1 + Coth[x])^5,x]","\frac{\sinh (x) (\coth (x)+1)^5 \left(-20 \sinh (x) \cosh ^3(x) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\tanh ^2(x)\right)-120 \sinh ^3(x) \cosh (x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\tanh ^2(x)\right)-3 \cosh ^4(x)-66 \sinh ^2(x) \cosh ^2(x)+12 \sinh ^4(x) (x+16 \log (\tanh (x))+16 \log (\cosh (x)))\right)}{12 (\sinh (x)+\cosh (x))^5}","16 x-\frac{1}{4} (\coth (x)+1)^4-\frac{2}{3} (\coth (x)+1)^3-2 (\coth (x)+1)^2-8 \coth (x)+16 \log (\sinh (x))",1,"((1 + Coth[x])^5*Sinh[x]*(-3*Cosh[x]^4 - 20*Cosh[x]^3*Hypergeometric2F1[-3/2, 1, -1/2, Tanh[x]^2]*Sinh[x] - 66*Cosh[x]^2*Sinh[x]^2 - 120*Cosh[x]*Hypergeometric2F1[-1/2, 1, 1/2, Tanh[x]^2]*Sinh[x]^3 + 12*(x + 16*Log[Cosh[x]] + 16*Log[Tanh[x]])*Sinh[x]^4))/(12*(Cosh[x] + Sinh[x])^5)","C",1
62,1,84,31,0.1871702,"\int (1+\coth (x))^4 \, dx","Integrate[(1 + Coth[x])^4,x]","\frac{\sinh (x) (\coth (x)+1)^4 \left(3 \sinh (x) \left(-6 \sinh (x) \cosh (x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\tanh ^2(x)\right)-2 \cosh ^2(x)+\sinh ^2(x) (x+8 \log (\tanh (x))+8 \log (\cosh (x)))\right)-\cosh ^3(x) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\tanh ^2(x)\right)\right)}{3 (\sinh (x)+\cosh (x))^4}","8 x-\frac{1}{3} (\coth (x)+1)^3-(\coth (x)+1)^2-4 \coth (x)+8 \log (\sinh (x))",1,"((1 + Coth[x])^4*Sinh[x]*(-(Cosh[x]^3*Hypergeometric2F1[-3/2, 1, -1/2, Tanh[x]^2]) + 3*Sinh[x]*(-2*Cosh[x]^2 - 6*Cosh[x]*Hypergeometric2F1[-1/2, 1, 1/2, Tanh[x]^2]*Sinh[x] + (x + 8*Log[Cosh[x]] + 8*Log[Tanh[x]])*Sinh[x]^2)))/(3*(Cosh[x] + Sinh[x])^4)","C",1
63,1,61,23,0.1552493,"\int (1+\coth (x))^3 \, dx","Integrate[(1 + Coth[x])^3,x]","\frac{1}{4} \text{csch}^2(x) \left(-6 \sinh (2 x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\tanh ^2(x)\right)-2 x-8 \log (\tanh (x))-8 \log (\cosh (x))+\cosh (2 x) (2 x+8 \log (\tanh (x))+8 \log (\cosh (x))-1)-1\right)","4 x-\frac{1}{2} (\coth (x)+1)^2-2 \coth (x)+4 \log (\sinh (x))",1,"(Csch[x]^2*(-1 - 2*x - 8*Log[Cosh[x]] - 8*Log[Tanh[x]] + Cosh[2*x]*(-1 + 2*x + 8*Log[Cosh[x]] + 8*Log[Tanh[x]]) - 6*Hypergeometric2F1[-1/2, 1, 1/2, Tanh[x]^2]*Sinh[2*x]))/4","C",1
64,1,13,13,0.0047363,"\int (1+\coth (x))^2 \, dx","Integrate[(1 + Coth[x])^2,x]","2 x-\coth (x)+2 \log (\sinh (x))","2 x-\coth (x)+2 \log (\sinh (x))",1,"2*x - Coth[x] + 2*Log[Sinh[x]]","A",1
65,1,18,16,0.0307567,"\int \frac{1}{1+\coth (x)} \, dx","Integrate[(1 + Coth[x])^(-1),x]","\frac{1}{4} (2 x-\sinh (2 x)+\cosh (2 x))","\frac{x}{2}-\frac{1}{2 (\coth (x)+1)}",1,"(2*x + Cosh[2*x] - Sinh[2*x])/4","A",1
66,1,30,26,0.0608419,"\int \frac{1}{(1+\coth (x))^2} \, dx","Integrate[(1 + Coth[x])^(-2),x]","\frac{1}{16} (4 x-4 \sinh (2 x)+\sinh (4 x)+4 \cosh (2 x)-\cosh (4 x))","\frac{x}{4}-\frac{1}{4 (\coth (x)+1)}-\frac{1}{4 (\coth (x)+1)^2}",1,"(4*x + 4*Cosh[2*x] - Cosh[4*x] - 4*Sinh[2*x] + Sinh[4*x])/16","A",1
67,1,44,36,0.0924401,"\int \frac{1}{(1+\coth (x))^3} \, dx","Integrate[(1 + Coth[x])^(-3),x]","\frac{1}{96} (12 x-18 \sinh (2 x)+9 \sinh (4 x)-2 \sinh (6 x)+18 \cosh (2 x)-9 \cosh (4 x)+2 \cosh (6 x))","\frac{x}{8}-\frac{1}{8 (\coth (x)+1)}-\frac{1}{8 (\coth (x)+1)^2}-\frac{1}{6 (\coth (x)+1)^3}",1,"(12*x + 18*Cosh[2*x] - 9*Cosh[4*x] + 2*Cosh[6*x] - 18*Sinh[2*x] + 9*Sinh[4*x] - 2*Sinh[6*x])/96","A",1
68,1,53,46,0.1272715,"\int \frac{1}{(1+\coth (x))^4} \, dx","Integrate[(1 + Coth[x])^(-4),x]","\frac{1}{384} (\cosh (4 x)-\sinh (4 x)) (32 \sinh (2 x)+24 x \sinh (4 x)+3 \sinh (4 x)+64 \cosh (2 x)+3 (8 x-1) \cosh (4 x)-36)","\frac{x}{16}-\frac{1}{16 (\coth (x)+1)}-\frac{1}{16 (\coth (x)+1)^2}-\frac{1}{12 (\coth (x)+1)^3}-\frac{1}{8 (\coth (x)+1)^4}",1,"((Cosh[4*x] - Sinh[4*x])*(-36 + 64*Cosh[2*x] + 3*(-1 + 8*x)*Cosh[4*x] + 32*Sinh[2*x] + 3*Sinh[4*x] + 24*x*Sinh[4*x]))/384","A",1
69,1,62,56,0.144672,"\int \frac{1}{(1+\coth (x))^5} \, dx","Integrate[(1 + Coth[x])^(-5),x]","\frac{(\cosh (5 x)-\sinh (5 x)) (-500 \sinh (x)+375 \sinh (3 x)+120 x \sinh (5 x)-12 \sinh (5 x)-100 \cosh (x)+225 \cosh (3 x)+120 x \cosh (5 x)+12 \cosh (5 x))}{3840}","\frac{x}{32}-\frac{1}{32 (\coth (x)+1)}-\frac{1}{32 (\coth (x)+1)^2}-\frac{1}{24 (\coth (x)+1)^3}-\frac{1}{16 (\coth (x)+1)^4}-\frac{1}{10 (\coth (x)+1)^5}",1,"((Cosh[5*x] - Sinh[5*x])*(-100*Cosh[x] + 225*Cosh[3*x] + 12*Cosh[5*x] + 120*x*Cosh[5*x] - 500*Sinh[x] + 375*Sinh[3*x] - 12*Sinh[5*x] + 120*x*Sinh[5*x]))/3840","A",1
70,1,101,57,0.2699093,"\int (1+\coth (x))^{7/2} \, dx","Integrate[(1 + Coth[x])^(7/2),x]","-\frac{2 (\coth (x)+1)^{7/2} \left((8 \sinh (2 x)+3) \sinh (x) \sqrt{i (\coth (x)+1)}+4 \sinh ^3(x) \left(19 \sqrt{i (\coth (x)+1)}-(15-15 i) \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)\right)\right)}{15 \sqrt{i (\coth (x)+1)} (\sinh (x)+\cosh (x))^3}","-\frac{2}{5} (\coth (x)+1)^{5/2}-\frac{4}{3} (\coth (x)+1)^{3/2}-8 \sqrt{\coth (x)+1}+8 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)",1,"(-2*(1 + Coth[x])^(7/2)*(4*((-15 + 15*I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]] + 19*Sqrt[I*(1 + Coth[x])])*Sinh[x]^3 + Sqrt[I*(1 + Coth[x])]*Sinh[x]*(3 + 8*Sinh[2*x])))/(15*Sqrt[I*(1 + Coth[x])]*(Cosh[x] + Sinh[x])^3)","C",1
71,1,92,45,0.1589932,"\int (1+\coth (x))^{5/2} \, dx","Integrate[(1 + Coth[x])^(5/2),x]","-\frac{2 \sinh (x) (\coth (x)+1)^{5/2} \left(\cosh (x) \sqrt{i (\coth (x)+1)}+\sinh (x) \left(7 \sqrt{i (\coth (x)+1)}-(6-6 i) \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)\right)\right)}{3 \sqrt{i (\coth (x)+1)} (\sinh (x)+\cosh (x))^2}","-\frac{2}{3} (\coth (x)+1)^{3/2}-4 \sqrt{\coth (x)+1}+4 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)",1,"(-2*(1 + Coth[x])^(5/2)*Sinh[x]*(Cosh[x]*Sqrt[I*(1 + Coth[x])] + ((-6 + 6*I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]] + 7*Sqrt[I*(1 + Coth[x])])*Sinh[x]))/(3*Sqrt[I*(1 + Coth[x])]*(Cosh[x] + Sinh[x])^2)","C",1
72,1,69,33,0.1104157,"\int (1+\coth (x))^{3/2} \, dx","Integrate[(1 + Coth[x])^(3/2),x]","-\frac{2 \sinh (x) (\coth (x)+1)^{3/2} \left(\sqrt{i (\coth (x)+1)}-(1-i) \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)\right)}{\sqrt{i (\coth (x)+1)} (\sinh (x)+\cosh (x))}","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)-2 \sqrt{\coth (x)+1}",1,"(-2*(1 + Coth[x])^(3/2)*((-1 + I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]] + Sqrt[I*(1 + Coth[x])])*Sinh[x])/(Sqrt[I*(1 + Coth[x])]*(Cosh[x] + Sinh[x]))","C",1
73,1,45,21,0.0771114,"\int \sqrt{1+\coth (x)} \, dx","Integrate[Sqrt[1 + Coth[x]],x]","\frac{(1+i) (\coth (x)+1)^{3/2} \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)}{(i (\coth (x)+1))^{3/2}}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)",1,"((1 + I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]]*(1 + Coth[x])^(3/2))/(I*(1 + Coth[x]))^(3/2)","C",1
74,1,51,32,0.3053082,"\int \frac{1}{\sqrt{1+\coth (x)}} \, dx","Integrate[1/Sqrt[1 + Coth[x]],x]","\frac{-2+(-1-i) \sqrt{i (\coth (x)+1)} \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)}{2 \sqrt{\coth (x)+1}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{1}{\sqrt{\coth (x)+1}}",1,"(-2 - (1 + I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]]*Sqrt[I*(1 + Coth[x])])/(2*Sqrt[1 + Coth[x]])","C",1
75,1,86,49,0.3241484,"\int \frac{1}{(1+\coth (x))^{3/2}} \, dx","Integrate[(1 + Coth[x])^(-3/2),x]","\left(\frac{1}{4}+\frac{i}{4}\right) \sqrt{\coth (x)+1} \left(\left(\frac{1}{6}-\frac{i}{6}\right) (-5 \sinh (2 x)+\sinh (4 x)+5 \cosh (2 x)-\cosh (4 x)-4)-\frac{i \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)}{\sqrt{i (\coth (x)+1)}}\right)","-\frac{1}{2 \sqrt{\coth (x)+1}}-\frac{1}{3 (\coth (x)+1)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"(1/4 + I/4)*Sqrt[1 + Coth[x]]*(((-I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]])/Sqrt[I*(1 + Coth[x])] + (1/6 - I/6)*(-4 + 5*Cosh[2*x] - Cosh[4*x] - 5*Sinh[2*x] + Sinh[4*x]))","C",1
76,1,94,61,0.7971378,"\int \frac{1}{(1+\coth (x))^{5/2}} \, dx","Integrate[(1 + Coth[x])^(-5/2),x]","-\frac{1}{60} \sqrt{\coth (x)+1} (\cosh (3 x)-\sinh (3 x)) (-24 \sinh (x)+13 \sinh (3 x)-10 \cosh (x)+10 \cosh (3 x))+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (\coth (x)+1)^{3/2} \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)}{(i (\coth (x)+1))^{3/2}}","-\frac{1}{4 \sqrt{\coth (x)+1}}-\frac{1}{6 (\coth (x)+1)^{3/2}}-\frac{1}{5 (\coth (x)+1)^{5/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{4 \sqrt{2}}",1,"((1/8 + I/8)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]]*(1 + Coth[x])^(3/2))/(I*(1 + Coth[x]))^(3/2) - (Sqrt[1 + Coth[x]]*(Cosh[3*x] - Sinh[3*x])*(-10*Cosh[x] + 10*Cosh[3*x] - 24*Sinh[x] + 13*Sinh[3*x]))/60","C",1
77,1,141,142,0.818085,"\int (a+b \coth (c+d x))^5 \, dx","Integrate[(a + b*Coth[c + d*x])^5,x]","-\frac{60 a b^2 \left(2 a^2+b^2\right) \coth (c+d x)+6 b^3 \left(10 a^2+b^2\right) \coth ^2(c+d x)-12 b \left(5 a^4+10 a^2 b^2+b^4\right) \log (\tanh (c+d x))+20 a b^4 \coth ^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 \coth ^4(c+d x)}{12 d}","-\frac{b \left(3 a^2+b^2\right) (a+b \coth (c+d x))^2}{2 d}-\frac{4 a b^2 \left(a^2+b^2\right) \coth (c+d x)}{d}+\frac{b \left(5 a^4+10 a^2 b^2+b^4\right) \log (\sinh (c+d x))}{d}+a x \left(a^4+10 a^2 b^2+5 b^4\right)-\frac{b (a+b \coth (c+d x))^4}{4 d}-\frac{2 a b (a+b \coth (c+d x))^3}{3 d}",1,"-1/12*(60*a*b^2*(2*a^2 + b^2)*Coth[c + d*x] + 6*b^3*(10*a^2 + b^2)*Coth[c + d*x]^2 + 20*a*b^4*Coth[c + d*x]^3 + 3*b^5*Coth[c + d*x]^4 + 6*(a + b)^5*Log[1 - Tanh[c + d*x]] - 12*b*(5*a^4 + 10*a^2*b^2 + b^4)*Log[Tanh[c + d*x]] - 6*(a - b)^5*Log[1 + Tanh[c + d*x]])/d","A",1
78,1,109,101,0.9226589,"\int (a+b \coth (c+d x))^4 \, dx","Integrate[(a + b*Coth[c + d*x])^4,x]","-\frac{6 b^2 \left(6 a^2+b^2\right) \coth (c+d x)-24 a b \left(a^2+b^2\right) \log (\tanh (c+d x))+12 a b^3 \coth ^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 \coth ^3(c+d x)}{6 d}","-\frac{b^2 \left(3 a^2+b^2\right) \coth (c+d x)}{d}+\frac{4 a b \left(a^2+b^2\right) \log (\sinh (c+d x))}{d}+x \left(a^4+6 a^2 b^2+b^4\right)-\frac{b (a+b \coth (c+d x))^3}{3 d}-\frac{a b (a+b \coth (c+d x))^2}{d}",1,"-1/6*(6*b^2*(6*a^2 + b^2)*Coth[c + d*x] + 12*a*b^3*Coth[c + d*x]^2 + 2*b^4*Coth[c + d*x]^3 + 3*(a + b)^4*Log[1 - Tanh[c + d*x]] - 24*a*b*(a^2 + b^2)*Log[Tanh[c + d*x]] - 3*(a - b)^4*Log[1 + Tanh[c + d*x]])/d","A",1
79,1,86,69,0.4155597,"\int (a+b \coth (c+d x))^3 \, dx","Integrate[(a + b*Coth[c + d*x])^3,x]","-\frac{-2 b \left(3 a^2+b^2\right) \log (\tanh (c+d x))+6 a b^2 \coth (c+d x)+(a-b)^3 (-\log (\tanh (c+d x)+1))+(a+b)^3 \log (1-\tanh (c+d x))+b^3 \coth ^2(c+d x)}{2 d}","\frac{b \left(3 a^2+b^2\right) \log (\sinh (c+d x))}{d}+a x \left(a^2+3 b^2\right)-\frac{2 a b^2 \coth (c+d x)}{d}-\frac{b (a+b \coth (c+d x))^2}{2 d}",1,"-1/2*(6*a*b^2*Coth[c + d*x] + b^3*Coth[c + d*x]^2 + (a + b)^3*Log[1 - Tanh[c + d*x]] - 2*b*(3*a^2 + b^2)*Log[Tanh[c + d*x]] - (a - b)^3*Log[1 + Tanh[c + d*x]])/d","A",1
80,1,65,38,0.1315173,"\int (a+b \coth (c+d x))^2 \, dx","Integrate[(a + b*Coth[c + d*x])^2,x]","\frac{(a-b)^2 \log (\tanh (c+d x)+1)-(a+b)^2 \log (1-\tanh (c+d x))+4 a b \log (\tanh (c+d x))-2 b^2 \coth (c+d x)}{2 d}","x \left(a^2+b^2\right)+\frac{2 a b \log (\sinh (c+d x))}{d}-\frac{b^2 \coth (c+d x)}{d}",1,"(-2*b^2*Coth[c + d*x] - (a + b)^2*Log[1 - Tanh[c + d*x]] + 4*a*b*Log[Tanh[c + d*x]] + (a - b)^2*Log[1 + Tanh[c + d*x]])/(2*d)","A",1
81,1,64,50,0.0825042,"\int \frac{1}{a+b \coth (c+d x)} \, dx","Integrate[(a + b*Coth[c + d*x])^(-1),x]","\frac{(b-a) \log (1-\coth (c+d x))+(a+b) \log (\coth (c+d x)+1)-2 b \log (a+b \coth (c+d x))}{2 d (a-b) (a+b)}","\frac{a x}{a^2-b^2}-\frac{b \log (a \sinh (c+d x)+b \cosh (c+d x))}{d \left(a^2-b^2\right)}",1,"((-a + b)*Log[1 - Coth[c + d*x]] + (a + b)*Log[1 + Coth[c + d*x]] - 2*b*Log[a + b*Coth[c + d*x]])/(2*(a - b)*(a + b)*d)","A",1
82,1,100,85,1.55893,"\int \frac{1}{(a+b \coth (c+d x))^2} \, dx","Integrate[(a + b*Coth[c + d*x])^(-2),x]","\frac{\frac{2 b \left(\frac{b^3-a^2 b}{a \tanh (c+d x)+b}-2 a^2 \log (a \tanh (c+d x)+b)\right)}{a \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 \coth (c+d x))}-\frac{2 a b \log (a \sinh (c+d x)+b \cosh (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^2*Log[b + a*Tanh[c + d*x]] + (-(a^2*b) + b^3)/(b + a*Tanh[c + d*x])))/(a*(a^2 - b^2)^2))/(2*d)","A",1
83,1,134,129,3.621362,"\int \frac{1}{(a+b \coth (c+d x))^3} \, dx","Integrate[(a + b*Coth[c + d*x])^(-3),x]","-\frac{\frac{b \left(2 \left(3 a^2+b^2\right) \log (a \tanh (c+d x)+b)+\frac{b \left(b^2-a^2\right) \left(\left(2 a b^2-6 a^3\right) \tanh (c+d x)-5 a^2 b+b^3\right)}{a^2 (a \tanh (c+d x)+b)^2}\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 \coth (c+d x))}+\frac{b}{2 d \left(a^2-b^2\right) (a+b \coth (c+d x))^2}-\frac{b \left(3 a^2+b^2\right) \log (a \sinh (c+d x)+b \cosh (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,"-1/2*(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[b + a*Tanh[c + d*x]] + (b*(-a^2 + b^2)*(-5*a^2*b + b^3 + (-6*a^3 + 2*a*b^2)*Tanh[c + d*x]))/(a^2*(b + a*Tanh[c + d*x])^2)))/(a^2 - b^2)^3)/d","A",1
84,1,214,169,6.2208849,"\int \frac{1}{(a+b \coth (c+d x))^4} \, dx","Integrate[(a + b*Coth[c + d*x])^(-4),x]","-\frac{4 a b \left(a^2+b^2\right) \log (a \tanh (c+d x)+b)}{d \left(a^2-b^2\right)^4}-\frac{b^4}{3 a^3 d \left(a^2-b^2\right) (a \tanh (c+d x)+b)^3}+\frac{b^3 \left(2 a^2-b^2\right)}{a^3 d \left(a^2-b^2\right)^2 (a \tanh (c+d x)+b)^2}-\frac{b^2 \left(6 a^4-3 a^2 b^2+b^4\right)}{a^3 d \left(a^2-b^2\right)^3 (a \tanh (c+d x)+b)}-\frac{\log (1-\tanh (c+d x))}{2 d (a+b)^4}+\frac{\log (\tanh (c+d x)+1)}{2 d (a-b)^4}","\frac{b \left(3 a^2+b^2\right)}{d \left(a^2-b^2\right)^3 (a+b \coth (c+d x))}+\frac{a b}{d \left(a^2-b^2\right)^2 (a+b \coth (c+d x))^2}+\frac{b}{3 d \left(a^2-b^2\right) (a+b \coth (c+d x))^3}-\frac{4 a b \left(a^2+b^2\right) \log (a \sinh (c+d x)+b \cosh (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,"-1/2*Log[1 - Tanh[c + d*x]]/((a + b)^4*d) + Log[1 + Tanh[c + d*x]]/(2*(a - b)^4*d) - (4*a*b*(a^2 + b^2)*Log[b + a*Tanh[c + d*x]])/((a^2 - b^2)^4*d) - b^4/(3*a^3*(a^2 - b^2)*d*(b + a*Tanh[c + d*x])^3) + (b^3*(2*a^2 - b^2))/(a^3*(a^2 - b^2)^2*d*(b + a*Tanh[c + d*x])^2) - (b^2*(6*a^4 - 3*a^2*b^2 + b^4))/(a^3*(a^2 - b^2)^3*d*(b + a*Tanh[c + d*x]))","A",1
85,1,53,31,0.0427572,"\int \frac{1}{4+6 \coth (c+d x)} \, dx","Integrate[(4 + 6*Coth[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 (2 \tanh (c+d x)+3)}{10 d}","\frac{3 \log (2 \sinh (c+d x)+3 \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[3 + 2*Tanh[c + d*x]])/(10*d)","A",1
86,1,53,31,0.0400883,"\int \frac{1}{4-6 \coth (c+d x)} \, dx","Integrate[(4 - 6*Coth[c + d*x])^(-1),x]","-\frac{3 \log (3-2 \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 (3 \cosh (c+d x)-2 \sinh (c+d x))}{10 d}-\frac{x}{5}",1,"(-3*Log[3 - 2*Tanh[c + d*x]])/(10*d) + Log[1 - Tanh[c + d*x]]/(4*d) + Log[1 + Tanh[c + d*x]]/(20*d)","A",1
87,1,128,74,3.2849565,"\int \sqrt{a+b \coth (c+d x)} \, dx","Integrate[Sqrt[a + b*Coth[c + d*x]],x]","\frac{\sqrt{a+b \coth (c+d x)} \left(\sqrt{i (a+b)} \tanh ^{-1}\left(\frac{\sqrt{i (a+b \coth (c+d x))}}{\sqrt{i (a+b)}}\right)-\sqrt{i (a-b)} \tanh ^{-1}\left(\frac{\sqrt{i (a+b \coth (c+d x))}}{\sqrt{i (a-b)}}\right)\right)}{d \sqrt{i (a+b \coth (c+d x))}}","\frac{\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a+b}}\right)}{d}-\frac{\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a-b}}\right)}{d}",1,"((-(Sqrt[I*(a - b)]*ArcTanh[Sqrt[I*(a + b*Coth[c + d*x])]/Sqrt[I*(a - b)]]) + Sqrt[I*(a + b)]*ArcTanh[Sqrt[I*(a + b*Coth[c + d*x])]/Sqrt[I*(a + b)]])*Sqrt[a + b*Coth[c + d*x]])/(d*Sqrt[I*(a + b*Coth[c + d*x])])","C",1
88,1,73,74,0.15391,"\int \frac{1}{\sqrt{a+b \coth (c+d x)}} \, dx","Integrate[1/Sqrt[a + b*Coth[c + d*x]],x]","-\frac{\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}}{d}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a+b}}\right)}{d \sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a-b}}\right)}{d \sqrt{a-b}}",1,"-((ArcTanh[Sqrt[a + b*Coth[c + d*x]]/Sqrt[a - b]]/Sqrt[a - b] - ArcTanh[Sqrt[a + b*Coth[c + d*x]]/Sqrt[a + b]]/Sqrt[a + b])/d)","A",1
89,1,42,60,0.1114227,"\int \frac{\sinh ^4(x)}{1+\coth (x)} \, dx","Integrate[Sinh[x]^4/(1 + Coth[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-\coth (x))}-\frac{3}{16 (\coth (x)+1)}+\frac{1}{32 (1-\coth (x))^2}-\frac{3}{32 (\coth (x)+1)^2}-\frac{1}{24 (\coth (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
90,1,36,29,0.0806481,"\int \frac{\sinh ^3(x)}{1+\coth (x)} \, dx","Integrate[Sinh[x]^3/(1 + Coth[x]),x]","\frac{\text{csch}(x) (-40 \sinh (2 x)+4 \sinh (4 x)-20 \cosh (2 x)+\cosh (4 x)-45)}{120 (\coth (x)+1)}","\frac{4 \cosh ^3(x)}{15}-\frac{4 \cosh (x)}{5}-\frac{\sinh ^3(x)}{5 (\coth (x)+1)}",1,"(Csch[x]*(-45 - 20*Cosh[2*x] + Cosh[4*x] - 40*Sinh[2*x] + 4*Sinh[4*x]))/(120*(1 + Coth[x]))","A",1
91,1,30,38,0.0544063,"\int \frac{\sinh ^2(x)}{1+\coth (x)} \, dx","Integrate[Sinh[x]^2/(1 + Coth[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-\coth (x))}+\frac{1}{4 (\coth (x)+1)}+\frac{1}{8 (\coth (x)+1)^2}",1,"(-12*x - 4*Cosh[2*x] + Cosh[4*x] + 8*Sinh[2*x] - Sinh[4*x])/32","A",1
92,1,21,19,0.0506415,"\int \frac{\sinh (x)}{1+\coth (x)} \, dx","Integrate[Sinh[x]/(1 + Coth[x]),x]","\frac{1}{12} \left(4 \sinh ^3(x)+9 \cosh (x)-\cosh (3 x)\right)","\frac{2 \cosh (x)}{3}-\frac{\sinh (x)}{3 (\coth (x)+1)}",1,"(9*Cosh[x] - Cosh[3*x] + 4*Sinh[x]^3)/12","A",1
93,1,7,10,0.0036441,"\int \frac{\text{csch}(x)}{1+\coth (x)} \, dx","Integrate[Csch[x]/(1 + Coth[x]),x]","\sinh (x)-\cosh (x)","-\frac{\text{csch}(x)}{\coth (x)+1}",1,"-Cosh[x] + Sinh[x]","A",1
94,1,7,7,0.0031277,"\int \frac{\text{csch}^2(x)}{1+\coth (x)} \, dx","Integrate[Csch[x]^2/(1 + Coth[x]),x]","\log (\sinh (x))-x","-\log (\coth (x)+1)",1,"-x + Log[Sinh[x]]","A",1
95,1,14,8,0.0382939,"\int \frac{\text{csch}^3(x)}{1+\coth (x)} \, dx","Integrate[Csch[x]^3/(1 + Coth[x]),x]","-\text{csch}(x)-\log \left(\tanh \left(\frac{x}{2}\right)\right)","\tanh ^{-1}(\cosh (x))-\text{csch}(x)",1,"-Csch[x] - Log[Tanh[x/2]]","A",1
96,1,11,11,0.0256165,"\int \frac{\text{csch}^4(x)}{1+\coth (x)} \, dx","Integrate[Csch[x]^4/(1 + Coth[x]),x]","\coth (x)-\frac{\text{csch}^2(x)}{2}","\coth (x)-\frac{\coth ^2(x)}{2}",1,"Coth[x] - Csch[x]^2/2","A",1
97,1,156,155,0.2939421,"\int \frac{\sinh ^4(x)}{a+b \coth (x)} \, dx","Integrate[Sinh[x]^4/(a + b*Coth[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 \sinh (x)+b \cosh (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-\coth (x))}{16 (a+b)^3}+\frac{\left(3 a^2-9 a b+8 b^2\right) \log (\coth (x)+1)}{16 (a-b)^3}-\frac{\sinh ^4(x) (b-a \coth (x))}{4 \left(a^2-b^2\right)}-\frac{b^5 \log (a+b \coth (x))}{\left(a^2-b^2\right)^3}-\frac{\sinh ^2(x) \left(4 b^3-a b^2 \left(7-\frac{3 a^2}{b^2}\right) \coth (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[b*Cosh[x] + a*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
98,1,171,134,0.8261618,"\int \frac{\sinh ^3(x)}{a+b \coth (x)} \, dx","Integrate[Sinh[x]^3/(a + b*Coth[x]),x]","\frac{3 b \sqrt{b-a} \left(a^3+a^2 b-5 a b^2-5 b^3\right) \sinh (x)-3 a \sqrt{b-a} \left(3 a^3+3 a^2 b-7 a b^2-7 b^3\right) \cosh (x)+24 b^4 \sqrt{a+b} \tan ^{-1}\left(\frac{a+b \tanh \left(\frac{x}{2}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)+b (b-a)^{3/2} (a+b)^2 \sinh (3 x)-a (b-a)^{3/2} (a+b)^2 \cosh (3 x)}{12 (b-a)^{5/2} (a+b)^3}","-\frac{b \sinh ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a \cosh ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a b^2 \cosh (x)}{\left(a^2-b^2\right)^2}-\frac{a \cosh (x)}{a^2-b^2}-\frac{b^4 \tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}-\frac{b^3 \sinh (x)}{\left(a^2-b^2\right)^2}",1,"(24*b^4*Sqrt[a + b]*ArcTan[(a + b*Tanh[x/2])/(Sqrt[-a + b]*Sqrt[a + b])] - 3*a*Sqrt[-a + b]*(3*a^3 + 3*a^2*b - 7*a*b^2 - 7*b^3)*Cosh[x] - a*(-a + b)^(3/2)*(a + b)^2*Cosh[3*x] + 3*b*Sqrt[-a + b]*(a^3 + a^2*b - 5*a*b^2 - 5*b^3)*Sinh[x] + b*(-a + b)^(3/2)*(a + b)^2*Sinh[3*x])/(12*(-a + b)^(5/2)*(a + b)^3)","A",1
99,1,75,92,0.1703863,"\int \frac{\sinh ^2(x)}{a+b \coth (x)} \, dx","Integrate[Sinh[x]^2/(a + b*Coth[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 \sinh (x)+b \cosh (x))+6 a b^2 x}{4 (a-b)^2 (a+b)^2}","-\frac{\sinh ^2(x) (b-a \coth (x))}{2 \left(a^2-b^2\right)}-\frac{b^3 \log (a+b \coth (x))}{\left(a^2-b^2\right)^2}+\frac{(a+2 b) \log (1-\coth (x))}{4 (a+b)^2}-\frac{(a-2 b) \log (\coth (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[b*Cosh[x] + a*Sinh[x]] + a*(a^2 - b^2)*Sinh[2*x])/(4*(a - b)^2*(a + b)^2)","A",1
100,1,80,73,0.464377,"\int \frac{\sinh (x)}{a+b \coth (x)} \, dx","Integrate[Sinh[x]/(a + b*Coth[x]),x]","\frac{a \cosh (x)}{a^2-b^2}+b \left(\frac{\sinh (x)}{b^2-a^2}-\frac{2 b \tan ^{-1}\left(\frac{a+b \tanh \left(\frac{x}{2}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)}{(b-a)^{3/2} (a+b)^{3/2}}\right)","-\frac{b \sinh (x)}{a^2-b^2}+\frac{a \cosh (x)}{a^2-b^2}-\frac{b^2 \tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}",1,"(a*Cosh[x])/(a^2 - b^2) + b*((-2*b*ArcTan[(a + b*Tanh[x/2])/(Sqrt[-a + b]*Sqrt[a + b])])/((-a + b)^(3/2)*(a + b)^(3/2)) + Sinh[x]/(-a^2 + b^2))","A",1
101,1,46,38,0.035933,"\int \frac{\text{csch}(x)}{a+b \coth (x)} \, dx","Integrate[Csch[x]/(a + b*Coth[x]),x]","\frac{2 \tan ^{-1}\left(\frac{a+b \tanh \left(\frac{x}{2}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)}{\sqrt{b-a} \sqrt{a+b}}","-\frac{\tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}",1,"(2*ArcTan[(a + b*Tanh[x/2])/(Sqrt[-a + b]*Sqrt[a + b])])/(Sqrt[-a + b]*Sqrt[a + b])","A",1
102,1,20,12,0.0631318,"\int \frac{\text{csch}^2(x)}{a+b \coth (x)} \, dx","Integrate[Csch[x]^2/(a + b*Coth[x]),x]","\frac{\log (\sinh (x))-\log (a \sinh (x)+b \cosh (x))}{b}","-\frac{\log (a+b \coth (x))}{b}",1,"(Log[Sinh[x]] - Log[b*Cosh[x] + a*Sinh[x]])/b","A",1
103,1,65,57,0.1149098,"\int \frac{\text{csch}^3(x)}{a+b \coth (x)} \, dx","Integrate[Csch[x]^3/(a + b*Coth[x]),x]","-\frac{2 \sqrt{b-a} \sqrt{a+b} \tan ^{-1}\left(\frac{a+b \tanh \left(\frac{x}{2}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)+a \log \left(\tanh \left(\frac{x}{2}\right)\right)+b \text{csch}(x)}{b^2}","-\frac{\sqrt{a^2-b^2} \tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{b^2}+\frac{a \tanh ^{-1}(\cosh (x))}{b^2}-\frac{\text{csch}(x)}{b}",1,"-((2*Sqrt[-a + b]*Sqrt[a + b]*ArcTan[(a + b*Tanh[x/2])/(Sqrt[-a + b]*Sqrt[a + b])] + b*Csch[x] + a*Log[Tanh[x/2]])/b^2)","A",1
104,1,50,40,0.1679259,"\int \frac{\text{csch}^4(x)}{a+b \coth (x)} \, dx","Integrate[Csch[x]^4/(a + b*Coth[x]),x]","\frac{2 \left(a^2-b^2\right) (\log (\sinh (x))-\log (a \sinh (x)+b \cosh (x)))+2 a b \coth (x)-b^2 \text{csch}^2(x)}{2 b^3}","-\frac{\left(a^2-b^2\right) \log (a+b \coth (x))}{b^3}+\frac{a \coth (x)}{b^2}-\frac{\coth ^2(x)}{2 b}",1,"(2*a*b*Coth[x] - b^2*Csch[x]^2 + 2*(a^2 - b^2)*(Log[Sinh[x]] - Log[b*Cosh[x] + a*Sinh[x]]))/(2*b^3)","A",1
105,1,42,60,0.0907522,"\int \frac{\cosh ^4(x)}{1+\coth (x)} \, dx","Integrate[Cosh[x]^4/(1 + Coth[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-\coth (x))}-\frac{3}{16 (\coth (x)+1)}+\frac{1}{32 (1-\coth (x))^2}+\frac{5}{32 (\coth (x)+1)^2}-\frac{1}{24 (\coth (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
106,1,34,25,0.0582197,"\int \frac{\cosh ^3(x)}{1+\coth (x)} \, dx","Integrate[Cosh[x]^3/(1 + Coth[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{\sinh ^3(x)}{3}+\frac{\cosh ^5(x)}{5}",1,"((Cosh[x] - Sinh[x])*(20*Cosh[2*x] + 4*Cosh[4*x] + 10*Sinh[2*x] + Sinh[4*x]))/120","A",1
107,1,24,38,0.0498059,"\int \frac{\cosh ^2(x)}{1+\coth (x)} \, dx","Integrate[Cosh[x]^2/(1 + Coth[x]),x]","\frac{1}{32} (4 x-\sinh (4 x)+4 \cosh (2 x)+\cosh (4 x))","\frac{x}{8}-\frac{1}{8 (1-\coth (x))}-\frac{1}{4 (\coth (x)+1)}+\frac{1}{8 (\coth (x)+1)^2}",1,"(4*x + 4*Cosh[2*x] + Cosh[4*x] - Sinh[4*x])/32","A",1
108,1,19,17,0.0176181,"\int \frac{\cosh (x)}{1+\coth (x)} \, dx","Integrate[Cosh[x]/(1 + Coth[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
109,1,16,10,0.0244138,"\int \frac{\text{sech}(x)}{1+\coth (x)} \, dx","Integrate[Sech[x]/(1 + Coth[x]),x]","-\sinh (x)+\cosh (x)+2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)","-\sinh (x)+\cosh (x)+\tan ^{-1}(\sinh (x))",1,"2*ArcTan[Tanh[x/2]] + Cosh[x] - Sinh[x]","A",1
110,1,9,15,0.031744,"\int \frac{\text{sech}^2(x)}{1+\coth (x)} \, dx","Integrate[Sech[x]^2/(1 + Coth[x]),x]","-x+\tanh (x)+\log (\cosh (x))","\tanh (x)-\log (\tanh (x))-\log (\coth (x)+1)",1,"-x + Log[Cosh[x]] + Tanh[x]","A",1
111,1,20,20,0.040143,"\int \frac{\text{sech}^3(x)}{1+\coth (x)} \, dx","Integrate[Sech[x]^3/(1 + Coth[x]),x]","\frac{1}{2} (\tanh (x)-2) \text{sech}(x)-\tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)","-\text{sech}(x)-\frac{1}{2} \tan ^{-1}(\sinh (x))+\frac{1}{2} \tanh (x) \text{sech}(x)",1,"-ArcTan[Tanh[x/2]] + (Sech[x]*(-2 + Tanh[x]))/2","A",1
112,1,17,17,0.0522826,"\int \frac{\text{sech}^4(x)}{1+\coth (x)} \, dx","Integrate[Sech[x]^4/(1 + Coth[x]),x]","\frac{1}{6} \left(-2 \tanh ^3(x)-3 \text{sech}^2(x)\right)","\frac{\tanh ^2(x)}{2}-\frac{\tanh ^3(x)}{3}",1,"(-3*Sech[x]^2 - 2*Tanh[x]^3)/6","A",1
113,1,160,21,5.2711546,"\int \sqrt{1+\coth (x)} \text{sech}^2(x) \, dx","Integrate[Sqrt[1 + Coth[x]]*Sech[x]^2,x]","\frac{1}{2} \sqrt{\coth (x)+1} \left(2 \tanh (x)+\frac{(1-i) \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)}{\sqrt{i (\coth (x)+1)}}+\frac{\sinh \left(\frac{x}{2}\right) \left(4 \tanh ^{-1}\left(\sqrt{\tanh \left(\frac{x}{2}\right)}\right)+\sqrt{2} \left(\log \left(\tanh \left(\frac{x}{2}\right)-\sqrt{2} \sqrt{\tanh \left(\frac{x}{2}\right)}+1\right)-\log \left(\tanh \left(\frac{x}{2}\right)+\sqrt{2} \sqrt{\tanh \left(\frac{x}{2}\right)}+1\right)\right)\right) \left(\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)}{\sqrt{\tanh \left(\frac{x}{2}\right)}}\right)","\tanh ^{-1}\left(\sqrt{\coth (x)+1}\right)+\tanh (x) \sqrt{\coth (x)+1}",1,"(Sqrt[1 + Coth[x]]*(((1 - I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]])/Sqrt[I*(1 + Coth[x])] + ((4*ArcTanh[Sqrt[Tanh[x/2]]] + Sqrt[2]*(Log[1 - Sqrt[2]*Sqrt[Tanh[x/2]] + Tanh[x/2]] - Log[1 + Sqrt[2]*Sqrt[Tanh[x/2]] + Tanh[x/2]]))*Sinh[x/2]*(-Cosh[x/2] + Sinh[x/2]))/Sqrt[Tanh[x/2]] + 2*Tanh[x]))/2","C",1
114,1,144,147,0.5701188,"\int \frac{\cosh ^4(x)}{a+b \coth (x)} \, dx","Integrate[Cosh[x]^4/(a + b*Coth[x]),x]","\frac{12 a^5 x+a^5 \sinh (4 x)-32 a^4 b \log (a \sinh (x)+b \cosh (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{\sinh ^4(x) (b-a \coth (x))}{4 \left(a^2-b^2\right)}-\frac{\sinh ^2(x) \left(4 b \left(2 a^2-b^2\right)-a \left(5 a^2-b^2\right) \coth (x)\right)}{8 \left(a^2-b^2\right)^2}-\frac{a^4 b \log (a+b \coth (x))}{\left(a^2-b^2\right)^3}-\frac{a (3 a+b) \log (1-\coth (x))}{16 (a+b)^3}+\frac{a (3 a-b) \log (\coth (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[b*Cosh[x] + a*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
115,1,167,135,1.4833775,"\int \frac{\cosh ^3(x)}{a+b \coth (x)} \, dx","Integrate[Cosh[x]^3/(a + b*Coth[x]),x]","\frac{1}{12} \left(\frac{a^3 \sinh (3 x)}{(a-b)^2 (a+b)^2}-\frac{24 a^3 b \tan ^{-1}\left(\frac{a+b \tanh \left(\frac{x}{2}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)}{(b-a)^{5/2} (a+b)^{5/2}}+\frac{3 a \left(3 a^2+b^2\right) \sinh (x)}{(a-b)^2 (a+b)^2}+\frac{3 b \left(b^2-5 a^2\right) \cosh (x)}{(a-b)^2 (a+b)^2}-\frac{a b^2 \sinh (3 x)}{(a-b)^2 (a+b)^2}+\frac{b \cosh (3 x)}{(b-a) (a+b)}\right)","\frac{a \sinh ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a \sinh (x)}{a^2-b^2}+\frac{a b^2 \sinh (x)}{\left(a^2-b^2\right)^2}-\frac{b \cosh ^3(x)}{3 \left(a^2-b^2\right)}-\frac{a^2 b \cosh (x)}{\left(a^2-b^2\right)^2}+\frac{a^3 b \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}",1,"((-24*a^3*b*ArcTan[(a + b*Tanh[x/2])/(Sqrt[-a + b]*Sqrt[a + b])])/((-a + b)^(5/2)*(a + b)^(5/2)) + (3*b*(-5*a^2 + b^2)*Cosh[x])/((a - b)^2*(a + b)^2) + (b*Cosh[3*x])/((-a + b)*(a + b)) + (3*a*(3*a^2 + b^2)*Sinh[x])/((a - b)^2*(a + b)^2) + (a^3*Sinh[3*x])/((a - b)^2*(a + b)^2) - (a*b^2*Sinh[3*x])/((a - b)^2*(a + b)^2))/12","A",1
116,1,73,85,0.2583033,"\int \frac{\cosh ^2(x)}{a+b \coth (x)} \, dx","Integrate[Cosh[x]^2/(a + b*Coth[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 \sinh (x)+b \cosh (x))\right)}{4 (a-b)^2 (a+b)^2}","-\frac{a^2 b \log (a+b \coth (x))}{\left(a^2-b^2\right)^2}-\frac{\sinh ^2(x) (b-a \coth (x))}{2 \left(a^2-b^2\right)}-\frac{a \log (1-\coth (x))}{4 (a+b)^2}+\frac{a \log (\coth (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[b*Cosh[x] + a*Sinh[x]] + (a^2 - b^2)*Sinh[2*x]))/(4*(a - b)^2*(a + b)^2)","A",1
117,1,79,72,0.3079886,"\int \frac{\cosh (x)}{a+b \coth (x)} \, dx","Integrate[Cosh[x]/(a + b*Coth[x]),x]","\frac{a \sinh (x)}{a^2-b^2}+\frac{b \cosh (x)}{b^2-a^2}+\frac{2 a b \tan ^{-1}\left(\frac{a+b \tanh \left(\frac{x}{2}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)}{(b-a)^{3/2} (a+b)^{3/2}}","\frac{a \sinh (x)}{a^2-b^2}-\frac{b \cosh (x)}{a^2-b^2}+\frac{a b \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}",1,"(2*a*b*ArcTan[(a + b*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
118,1,60,50,0.1229983,"\int \frac{\text{sech}(x)}{a+b \coth (x)} \, dx","Integrate[Sech[x]/(a + b*Coth[x]),x]","\frac{2 \left(\tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-\frac{b \tan ^{-1}\left(\frac{a+b \tanh \left(\frac{x}{2}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)}{a}","\frac{b \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{a \sqrt{a^2-b^2}}+\frac{\tan ^{-1}(\sinh (x))}{a}",1,"(2*(ArcTan[Tanh[x/2]] - (b*ArcTan[(a + b*Tanh[x/2])/(Sqrt[-a + b]*Sqrt[a + b])])/(Sqrt[-a + b]*Sqrt[a + b])))/a","A",1
119,1,27,29,0.0970311,"\int \frac{\text{sech}^2(x)}{a+b \coth (x)} \, dx","Integrate[Sech[x]^2/(a + b*Coth[x]),x]","\frac{-b \log (a \sinh (x)+b \cosh (x))+a \tanh (x)+b \log (\cosh (x))}{a^2}","-\frac{b \log (\tanh (x))}{a^2}-\frac{b \log (a+b \coth (x))}{a^2}+\frac{\tanh (x)}{a}",1,"(b*Log[Cosh[x]] - b*Log[b*Cosh[x] + a*Sinh[x]] + a*Tanh[x])/a^2","A",1
120,1,85,83,0.1995043,"\int \frac{\text{sech}^3(x)}{a+b \coth (x)} \, dx","Integrate[Sech[x]^3/(a + b*Coth[x]),x]","\frac{2 \left(a^2-2 b^2\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+4 b \sqrt{b-a} \sqrt{a+b} \tan ^{-1}\left(\frac{a+b \tanh \left(\frac{x}{2}\right)}{\sqrt{b-a} \sqrt{a+b}}\right)+a \text{sech}(x) (a \tanh (x)-2 b)}{2 a^3}","-\frac{b^2 \tan ^{-1}(\sinh (x))}{a^3}-\frac{b \text{sech}(x)}{a^2}+\frac{b \sqrt{a^2-b^2} \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{a^3}+\frac{\tan ^{-1}(\sinh (x))}{2 a}+\frac{\tanh (x) \text{sech}(x)}{2 a}",1,"(2*(a^2 - 2*b^2)*ArcTan[Tanh[x/2]] + 4*b*Sqrt[-a + b]*Sqrt[a + b]*ArcTan[(a + b*Tanh[x/2])/(Sqrt[-a + b]*Sqrt[a + b])] + a*Sech[x]*(-2*b + a*Tanh[x]))/(2*a^3)","A",1
121,1,68,79,0.308562,"\int \frac{\text{sech}^4(x)}{a+b \coth (x)} \, dx","Integrate[Sech[x]^4/(a + b*Coth[x]),x]","\frac{\left(4 a^3-6 a b^2\right) \tanh (x)-6 b \left(b^2-a^2\right) (\log (\cosh (x))-\log (a \sinh (x)+b \cosh (x)))+a^2 \text{sech}^2(x) (2 a \tanh (x)-3 b)}{6 a^4}","\frac{b \tanh ^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 \coth (x))}{a^4}+\frac{\left(a^2-b^2\right) \tanh (x)}{a^3}-\frac{\tanh ^3(x)}{3 a}",1,"(-6*b*(-a^2 + b^2)*(Log[Cosh[x]] - Log[b*Cosh[x] + a*Sinh[x]]) + (4*a^3 - 6*a*b^2)*Tanh[x] + a^2*Sech[x]^2*(-3*b + 2*a*Tanh[x]))/(6*a^4)","A",1
122,1,38,31,0.0526922,"\int \frac{\text{sech}(x)}{i+2 \coth (x)} \, dx","Integrate[Sech[x]/(I + 2*Coth[x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{1-2 i \tanh \left(\frac{x}{2}\right)}{\sqrt{5}}\right)}{\sqrt{5}}-2 i \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)","-i \tan ^{-1}(\sinh (x))-\frac{2 \tanh ^{-1}\left(\frac{\cosh (x)-2 i \sinh (x)}{\sqrt{5}}\right)}{\sqrt{5}}",1,"(-2*I)*ArcTan[Tanh[x/2]] - (4*ArcTanh[(1 - (2*I)*Tanh[x/2])/Sqrt[5]])/Sqrt[5]","A",1
123,1,40,43,0.1013278,"\int \frac{\tanh ^4(x)}{1+\coth (x)} \, dx","Integrate[Tanh[x]^4/(1 + Coth[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{5 \tanh ^3(x)}{6}+\tanh ^2(x)-\frac{5 \tanh (x)}{2}-2 \log (\cosh (x))+\frac{\tanh ^3(x)}{2 (\coth (x)+1)}",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
124,1,33,37,0.056414,"\int \frac{\tanh ^3(x)}{1+\coth (x)} \, dx","Integrate[Tanh[x]^3/(1 + Coth[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}-\tanh ^2(x)+\frac{3 \tanh (x)}{2}+2 \log (\cosh (x))+\frac{\tanh ^2(x)}{2 (\coth (x)+1)}",1,"(-6*x - Cosh[2*x] + 8*Log[Cosh[x]] + 2*Sech[x]^2 + Sinh[2*x] + 4*Tanh[x])/4","A",1
125,1,27,29,0.0494658,"\int \frac{\tanh ^2(x)}{1+\coth (x)} \, dx","Integrate[Tanh[x]^2/(1 + Coth[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{3 \tanh (x)}{2}-\log (\cosh (x))+\frac{\tanh (x)}{2 (\coth (x)+1)}",1,"(6*x + Cosh[2*x] - 4*Log[Cosh[x]] - Sinh[2*x] - 4*Tanh[x])/4","A",1
126,1,23,19,0.0290763,"\int \frac{\tanh (x)}{1+\coth (x)} \, dx","Integrate[Tanh[x]/(1 + Coth[x]),x]","\frac{1}{4} (-2 x+\sinh (2 x)-\cosh (2 x)+4 \log (\cosh (x)))","-\frac{x}{2}+\frac{1}{2 (\coth (x)+1)}+\log (\cosh (x))",1,"(-2*x - Cosh[2*x] + 4*Log[Cosh[x]] + Sinh[2*x])/4","A",1
127,1,18,16,0.0268523,"\int \frac{1}{1+\coth (x)} \, dx","Integrate[(1 + Coth[x])^(-1),x]","\frac{1}{4} (2 x-\sinh (2 x)+\cosh (2 x))","\frac{x}{2}-\frac{1}{2 (\coth (x)+1)}",1,"(2*x + Cosh[2*x] - Sinh[2*x])/4","A",1
128,1,18,16,0.0165793,"\int \frac{\coth (x)}{1+\coth (x)} \, dx","Integrate[Coth[x]/(1 + Coth[x]),x]","\frac{1}{4} (2 x+\sinh (2 x)-\cosh (2 x))","\frac{x}{2}+\frac{1}{2 (\coth (x)+1)}",1,"(2*x - Cosh[2*x] + Sinh[2*x])/4","A",1
129,1,23,19,0.0283501,"\int \frac{\coth ^2(x)}{1+\coth (x)} \, dx","Integrate[Coth[x]^2/(1 + Coth[x]),x]","\frac{1}{4} (-2 x-\sinh (2 x)+\cosh (2 x)+4 \log (\sinh (x)))","-\frac{x}{2}-\frac{1}{2 (\coth (x)+1)}+\log (\sinh (x))",1,"(-2*x + Cosh[2*x] + 4*Log[Sinh[x]] - Sinh[2*x])/4","A",1
130,1,27,31,0.0428883,"\int \frac{\coth ^3(x)}{1+\coth (x)} \, dx","Integrate[Coth[x]^3/(1 + Coth[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{\coth ^2(x)}{2 (\coth (x)+1)}-\frac{3 \coth (x)}{2}-\log (\sinh (x))",1,"(6*x - Cosh[2*x] - 4*Coth[x] - 4*Log[Sinh[x]] + Sinh[2*x])/4","A",1
131,1,33,37,0.060335,"\int \frac{\coth ^4(x)}{1+\coth (x)} \, dx","Integrate[Coth[x]^4/(1 + Coth[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}+\frac{\coth ^3(x)}{2 (\coth (x)+1)}-\coth ^2(x)+\frac{3 \coth (x)}{2}+2 \log (\sinh (x))",1,"(-6*x + Cosh[2*x] + 4*Coth[x] - 2*Csch[x]^2 + 8*Log[Sinh[x]] - Sinh[2*x])/4","A",1
132,1,90,45,0.1393737,"\int \coth (x) (1+\coth (x))^{3/2} \, dx","Integrate[Coth[x]*(1 + Coth[x])^(3/2),x]","-\frac{2 (\coth (x)+1)^{3/2} \left(\cosh (x) \sqrt{i (\coth (x)+1)}+4 \sinh (x) \sqrt{i (\coth (x)+1)}-(3-3 i) \sinh (x) \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)\right)}{3 \sqrt{i (\coth (x)+1)} (\sinh (x)+\cosh (x))}","-\frac{2}{3} (\coth (x)+1)^{3/2}-2 \sqrt{\coth (x)+1}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)",1,"(-2*(1 + Coth[x])^(3/2)*(Cosh[x]*Sqrt[I*(1 + Coth[x])] - (3 - 3*I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]]*Sinh[x] + 4*Sqrt[I*(1 + Coth[x])]*Sinh[x]))/(3*Sqrt[I*(1 + Coth[x])]*(Cosh[x] + Sinh[x]))","C",1
133,1,53,32,0.1223461,"\int \coth (x) \sqrt{1+\coth (x)} \, dx","Integrate[Coth[x]*Sqrt[1 + Coth[x]],x]","(1+i) \sqrt{\coth (x)+1} \left(-\frac{i \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)}{\sqrt{i (\coth (x)+1)}}-(1-i)\right)","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)-2 \sqrt{\coth (x)+1}",1,"(1 + I)*Sqrt[1 + Coth[x]]*((-1 + I) - (I*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]])/Sqrt[I*(1 + Coth[x])])","C",1
134,1,97,30,0.1991066,"\int \frac{\coth (x)}{\sqrt{1+\coth (x)}} \, dx","Integrate[Coth[x]/Sqrt[1 + Coth[x]],x]","\frac{\text{csch}(x) \left(\frac{1}{2} \sinh (2 x)-\frac{1}{2} \cosh (2 x)+\frac{1}{2}\right) (\sinh (x)+\cosh (x))}{\sqrt{\coth (x)+1}}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \text{csch}(x) (\sinh (x)+\cosh (x)) \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i \coth (x)+i}\right)}{\sqrt{i \coth (x)+i} \sqrt{\coth (x)+1}}","\frac{1}{\sqrt{\coth (x)+1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"((1/2 - I/2)*ArcTan[(1/2 + I/2)*Sqrt[I + I*Coth[x]]]*Csch[x]*(Cosh[x] + Sinh[x]))/(Sqrt[I + I*Coth[x]]*Sqrt[1 + Coth[x]]) + (Csch[x]*(Cosh[x] + Sinh[x])*(1/2 - Cosh[2*x]/2 + Sinh[2*x]/2))/Sqrt[1 + Coth[x]]","C",1
135,1,84,49,0.3478676,"\int \frac{\coth (x)}{(1+\coth (x))^{3/2}} \, dx","Integrate[Coth[x]/(1 + Coth[x])^(3/2),x]","\left(\frac{1}{4}+\frac{i}{4}\right) \sqrt{\coth (x)+1} \left(\left(\frac{1}{6}-\frac{i}{6}\right) (-\sinh (2 x)-\sinh (4 x)+\cosh (2 x)+\cosh (4 x)-2)-\frac{i \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)}{\sqrt{i (\coth (x)+1)}}\right)","-\frac{1}{2 \sqrt{\coth (x)+1}}+\frac{1}{3 (\coth (x)+1)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"(1/4 + I/4)*Sqrt[1 + Coth[x]]*(((-I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]])/Sqrt[I*(1 + Coth[x])] + (1/6 - I/6)*(-2 + Cosh[2*x] + Cosh[4*x] - Sinh[2*x] - Sinh[4*x]))","C",1
136,1,70,45,0.2629769,"\int \coth ^2(x) (1+\coth (x))^{3/2} \, dx","Integrate[Coth[x]^2*(1 + Coth[x])^(3/2),x]","-\frac{2 \left(2 \coth ^2(x)+\text{csch}^2(x)+(5+5 i) \sqrt{i (\coth (x)+1)} \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)+\coth (x) \left(\text{csch}^2(x)+9\right)+7\right)}{5 \sqrt{\coth (x)+1}}","-\frac{2}{5} (\coth (x)+1)^{5/2}-2 \sqrt{\coth (x)+1}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)",1,"(-2*(7 + 2*Coth[x]^2 + (5 + 5*I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]]*Sqrt[I*(1 + Coth[x])] + Csch[x]^2 + Coth[x]*(9 + Csch[x]^2)))/(5*Sqrt[1 + Coth[x]])","C",1
137,1,61,34,0.1796893,"\int \coth ^2(x) \sqrt{1+\coth (x)} \, dx","Integrate[Coth[x]^2*Sqrt[1 + Coth[x]],x]","\frac{-2 \coth ^2(x)-4 \coth (x)-(3+3 i) \sqrt{i (\coth (x)+1)} \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)-2}{3 \sqrt{\coth (x)+1}}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)-\frac{2}{3} (\coth (x)+1)^{3/2}",1,"(-2 - 4*Coth[x] - 2*Coth[x]^2 - (3 + 3*I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]]*Sqrt[I*(1 + Coth[x])])/(3*Sqrt[1 + Coth[x]])","C",1
138,1,81,42,0.3740737,"\int \frac{\coth ^2(x)}{\sqrt{1+\coth (x)}} \, dx","Integrate[Coth[x]^2/Sqrt[1 + Coth[x]],x]","\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \text{csch}(x) (\sinh (x)+\cosh (x)) \left(\left(\frac{1}{2}-\frac{i}{2}\right) (-\sinh (2 x)+\cosh (2 x)-5)-\frac{i \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)}{\sqrt{i (\coth (x)+1)}}\right)}{\sqrt{\coth (x)+1}}","-2 \sqrt{\coth (x)+1}-\frac{1}{\sqrt{\coth (x)+1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"((1/2 + I/2)*Csch[x]*(Cosh[x] + Sinh[x])*(((-I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]])/Sqrt[I*(1 + Coth[x])] + (1/2 - I/2)*(-5 + Cosh[2*x] - Sinh[2*x])))/Sqrt[1 + Coth[x]]","C",1
139,1,86,49,0.3672018,"\int \frac{\coth ^2(x)}{(1+\coth (x))^{3/2}} \, dx","Integrate[Coth[x]^2/(1 + Coth[x])^(3/2),x]","\left(\frac{1}{4}+\frac{i}{4}\right) \sqrt{\coth (x)+1} \left(-\left(\frac{1}{6}-\frac{i}{6}\right) (-7 \sinh (2 x)-\sinh (4 x)+7 \cosh (2 x)+\cosh (4 x)-8)-\frac{i \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i (\coth (x)+1)}\right)}{\sqrt{i (\coth (x)+1)}}\right)","\frac{3}{2 \sqrt{\coth (x)+1}}-\frac{1}{3 (\coth (x)+1)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"(1/4 + I/4)*Sqrt[1 + Coth[x]]*(((-I)*ArcTan[(1/2 + I/2)*Sqrt[I*(1 + Coth[x])]])/Sqrt[I*(1 + Coth[x])] - (1/6 - I/6)*(-8 + 7*Cosh[2*x] + Cosh[4*x] - 7*Sinh[2*x] - Sinh[4*x]))","C",1
140,1,105,97,0.3578525,"\int \frac{\tanh ^4(x)}{a+b \coth (x)} \, dx","Integrate[Tanh[x]^4/(a + b*Coth[x]),x]","\frac{6 a^5 x+6 \left(b^5-a^4 b\right) \log (\cosh (x))+a^2 \left(a^2-b^2\right) \text{sech}^2(x) (2 a \tanh (x)-3 b)+\left(-8 a^5+2 a^3 b^2+6 a b^4\right) \tanh (x)-6 b^5 \log (a \sinh (x)+b \cosh (x))}{6 a^4 (a-b) (a+b)}","\frac{a x}{a^2-b^2}+\frac{b \tanh ^2(x)}{2 a^2}-\frac{b \left(a^2+b^2\right) \log (\cosh (x))}{a^4}-\frac{b^5 \log (a \sinh (x)+b \cosh (x))}{a^4 \left(a^2-b^2\right)}-\frac{\left(a^2+b^2\right) \tanh (x)}{a^3}-\frac{\tanh ^3(x)}{3 a}",1,"(6*a^5*x + 6*(-(a^4*b) + b^5)*Log[Cosh[x]] - 6*b^5*Log[b*Cosh[x] + a*Sinh[x]] + (-8*a^5 + 2*a^3*b^2 + 6*a*b^4)*Tanh[x] + a^2*(a^2 - b^2)*Sech[x]^2*(-3*b + 2*a*Tanh[x]))/(6*a^4*(a - b)*(a + b))","A",1
141,1,88,76,0.32613,"\int \frac{\tanh ^3(x)}{a+b \coth (x)} \, dx","Integrate[Tanh[x]^3/(a + b*Coth[x]),x]","\frac{a^2 \left(a^2-b^2\right) \text{sech}^2(x)+2 \left(\left(a^4-b^4\right) \log (\cosh (x))-a^3 b x+a b \left(a^2-b^2\right) \tanh (x)+b^4 \log (a \sinh (x)+b \cosh (x))\right)}{2 a^3 (a-b) (a+b)}","-\frac{b x}{a^2-b^2}+\frac{b \tanh (x)}{a^2}+\frac{\left(a^2+b^2\right) \log (\cosh (x))}{a^3}+\frac{b^4 \log (a \sinh (x)+b \cosh (x))}{a^3 \left(a^2-b^2\right)}-\frac{\tanh ^2(x)}{2 a}",1,"(a^2*(a^2 - b^2)*Sech[x]^2 + 2*(-(a^3*b*x) + (a^4 - b^4)*Log[Cosh[x]] + b^4*Log[b*Cosh[x] + a*Sinh[x]] + a*b*(a^2 - b^2)*Tanh[x]))/(2*a^3*(a - b)*(a + b))","A",1
142,1,64,60,0.1447507,"\int \frac{\tanh ^2(x)}{a+b \coth (x)} \, dx","Integrate[Tanh[x]^2/(a + b*Coth[x]),x]","\frac{\left(a b^2-a^3\right) \tanh (x)+a^3 x+\left(b^3-a^2 b\right) \log (\cosh (x))-b^3 \log (a \sinh (x)+b \cosh (x))}{a^4-a^2 b^2}","\frac{a x}{a^2-b^2}-\frac{b^3 \log (a \sinh (x)+b \cosh (x))}{a^2 \left(a^2-b^2\right)}-\frac{b \log (\cosh (x))}{a^2}-\frac{\tanh (x)}{a}",1,"(a^3*x + (-(a^2*b) + b^3)*Log[Cosh[x]] - b^3*Log[b*Cosh[x] + a*Sinh[x]] + (-a^3 + a*b^2)*Tanh[x])/(a^4 - a^2*b^2)","A",1
143,1,46,51,0.0941904,"\int \frac{\tanh (x)}{a+b \coth (x)} \, dx","Integrate[Tanh[x]/(a + b*Coth[x]),x]","\frac{\left(a^2-b^2\right) \log (\cosh (x))+b (b \log (a \sinh (x)+b \cosh (x))-a x)}{a^3-a b^2}","-\frac{b x}{a^2-b^2}+\frac{b^2 \log (a \sinh (x)+b \cosh (x))}{a \left(a^2-b^2\right)}+\frac{\log (\cosh (x))}{a}",1,"((a^2 - b^2)*Log[Cosh[x]] + b*(-(a*x) + b*Log[b*Cosh[x] + a*Sinh[x]]))/(a^3 - a*b^2)","A",1
144,1,29,39,0.0620908,"\int \frac{1}{a+b \coth (x)} \, dx","Integrate[(a + b*Coth[x])^(-1),x]","\frac{a x-b \log (a \sinh (x)+b \cosh (x))}{a^2-b^2}","\frac{a x}{a^2-b^2}-\frac{b \log (a \sinh (x)+b \cosh (x))}{a^2-b^2}",1,"(a*x - b*Log[b*Cosh[x] + a*Sinh[x]])/(a^2 - b^2)","A",1
145,1,29,39,0.0594213,"\int \frac{\coth (x)}{a+b \coth (x)} \, dx","Integrate[Coth[x]/(a + b*Coth[x]),x]","\frac{a \log (a \sinh (x)+b \cosh (x))-b x}{a^2-b^2}","\frac{a \log (a \sinh (x)+b \cosh (x))}{a^2-b^2}-\frac{b x}{a^2-b^2}",1,"(-(b*x) + a*Log[b*Cosh[x] + a*Sinh[x]])/(a^2 - b^2)","A",1
146,1,49,63,0.0874897,"\int \frac{\coth ^2(x)}{a+b \coth (x)} \, dx","Integrate[Coth[x]^2/(a + b*Coth[x]),x]","\frac{-a^2 \log (a \sinh (x)+b \cosh (x))+a^2 \log (\sinh (x))+a b x-b^2 \log (\sinh (x))}{a^2 b-b^3}","-\frac{a^2 \log (a \sinh (x)+b \cosh (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 (\sinh (x))}{b}",1,"(a*b*x + a^2*Log[Sinh[x]] - b^2*Log[Sinh[x]] - a^2*Log[b*Cosh[x] + a*Sinh[x]])/(a^2*b - b^3)","A",1
147,1,64,64,0.13709,"\int \frac{\coth ^3(x)}{a+b \coth (x)} \, dx","Integrate[Coth[x]^3/(a + b*Coth[x]),x]","\frac{a^3 (-\log (a \sinh (x)+b \cosh (x)))+b \left(a^2-b^2\right) \coth (x)+a \left(a^2-b^2\right) \log (\sinh (x))+b^3 x}{b^2 (b-a) (a+b)}","-\frac{b x}{a^2-b^2}+\frac{a \log (\sinh (x))}{a^2-b^2}+\frac{a^3 \log (a+b \coth (x))}{b^2 \left(a^2-b^2\right)}-\frac{\coth (x)}{b}",1,"(b^3*x + b*(a^2 - b^2)*Coth[x] + a*(a^2 - b^2)*Log[Sinh[x]] - a^3*Log[b*Cosh[x] + a*Sinh[x]])/(b^2*(-a + b)*(a + b))","A",1
148,1,88,76,0.2292432,"\int \frac{\coth ^4(x)}{a+b \coth (x)} \, dx","Integrate[Coth[x]^4/(a + b*Coth[x]),x]","\frac{2 \left(a^4-b^4\right) \log (\sinh (x))-2 a^4 \log (a \sinh (x)+b \cosh (x))+2 a b \left(a^2-b^2\right) \coth (x)+\left(b^4-a^2 b^2\right) \text{csch}^2(x)+2 a b^3 x}{2 b^3 (a-b) (a+b)}","\frac{a x}{a^2-b^2}-\frac{b \log (\sinh (x))}{a^2-b^2}-\frac{a^4 \log (a+b \coth (x))}{b^3 \left(a^2-b^2\right)}+\frac{a \coth (x)}{b^2}-\frac{\coth ^2(x)}{2 b}",1,"(2*a*b^3*x + 2*a*b*(a^2 - b^2)*Coth[x] + (-(a^2*b^2) + b^4)*Csch[x]^2 + 2*(a^4 - b^4)*Log[Sinh[x]] - 2*a^4*Log[b*Cosh[x] + a*Sinh[x]])/(2*(a - b)*b^3*(a + b))","A",1
149,1,108,94,0.3224189,"\int \frac{\coth ^5(x)}{a+b \coth (x)} \, dx","Integrate[Coth[x]^5/(a + b*Coth[x]),x]","\frac{-6 a^5 \log (a \sinh (x)+b \cosh (x))+6 a \left(a^4-b^4\right) \log (\sinh (x))-3 a b^2 \left(a^2-b^2\right) \text{csch}^2(x)+2 b \left(a^2-b^2\right) \coth (x) \left(3 a^2+b^2 \text{csch}^2(x)+4 b^2\right)+6 b^5 x}{6 b^4 (b-a) (a+b)}","-\frac{b x}{a^2-b^2}+\frac{a \log (\sinh (x))}{a^2-b^2}-\frac{\left(a^2+b^2\right) \coth (x)}{b^3}+\frac{a^5 \log (a+b \coth (x))}{b^4 \left(a^2-b^2\right)}+\frac{a \coth ^2(x)}{2 b^2}-\frac{\coth ^3(x)}{3 b}",1,"(6*b^5*x - 3*a*b^2*(a^2 - b^2)*Csch[x]^2 + 2*b*(a^2 - b^2)*Coth[x]*(3*a^2 + 4*b^2 + b^2*Csch[x]^2) + 6*a*(a^4 - b^4)*Log[Sinh[x]] - 6*a^5*Log[b*Cosh[x] + a*Sinh[x]])/(6*b^4*(-a + b)*(a + b))","A",1
150,1,49,54,0.1783872,"\int \frac{x \text{csch}^2(x)}{(a+b \coth (x))^2} \, dx","Integrate[(x*Csch[x]^2)/(a + b*Coth[x])^2,x]","\frac{a x-b \log (a \sinh (x)+b \cosh (x))}{b^3-a^2 b}+\frac{x \sinh (x)}{a b \sinh (x)+b^2 \cosh (x)}","-\frac{a x}{b \left(a^2-b^2\right)}+\frac{\log (a \sinh (x)+b \cosh (x))}{a^2-b^2}+\frac{x}{b (a+b \coth (x))}",1,"(a*x - b*Log[b*Cosh[x] + a*Sinh[x]])/(-(a^2*b) + b^3) + (x*Sinh[x])/(b^2*Cosh[x] + a*b*Sinh[x])","A",1
151,1,64,30,0.0312778,"\int x^3 \coth (a+2 \log (x)) \, dx","Integrate[x^3*Coth[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{1}{2} e^{-2 a} \log \left(1-e^{2 a} x^4\right)+\frac{x^4}{4}",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
152,1,64,45,0.2416548,"\int x^2 \coth (a+2 \log (x)) \, dx","Integrate[x^2*Coth[a + 2*Log[x]],x]","\frac{1}{6} \left(3 (\sinh (2 a)-\cosh (2 a)) \text{RootSum}\left[\text{$\#$1}^4 \sinh (a)+\text{$\#$1}^4 \cosh (a)+\sinh (a)-\cosh (a)\&,\frac{\log (x)-\log (x-\text{$\#$1})}{\text{$\#$1}}\&\right]+2 x^3\right)","e^{-3 a/2} \tan ^{-1}\left(e^{a/2} x\right)-e^{-3 a/2} \tanh ^{-1}\left(e^{a/2} x\right)+\frac{x^3}{3}",1,"(2*x^3 + 3*RootSum[-Cosh[a] + Sinh[a] + Cosh[a]*#1^4 + Sinh[a]*#1^4 & , (Log[x] - Log[x - #1])/#1 & ]*(-Cosh[2*a] + Sinh[2*a]))/6","C",1
153,1,26,23,0.1876476,"\int x \coth (a+2 \log (x)) \, dx","Integrate[x*Coth[a + 2*Log[x]],x]","(\sinh (a)-\cosh (a)) \tanh ^{-1}\left(x^2 (\sinh (a)+\cosh (a))\right)+\frac{x^2}{2}","\frac{x^2}{2}-e^{-a} \tanh ^{-1}\left(e^a x^2\right)",1,"x^2/2 + ArcTanh[x^2*(Cosh[a] + Sinh[a])]*(-Cosh[a] + Sinh[a])","A",1
154,1,58,40,0.1867581,"\int \coth (a+2 \log (x)) \, dx","Integrate[Coth[a + 2*Log[x]],x]","\frac{1}{2} (\sinh (2 a)-\cosh (2 a)) \text{RootSum}\left[\text{$\#$1}^4 \sinh (a)+\text{$\#$1}^4 \cosh (a)+\sinh (a)-\cosh (a)\&,\frac{\log (x)-\log (x-\text{$\#$1})}{\text{$\#$1}^3}\&\right]+x","-e^{-a/2} \tan ^{-1}\left(e^{a/2} x\right)-e^{-a/2} \tanh ^{-1}\left(e^{a/2} x\right)+x",1,"x + (RootSum[-Cosh[a] + Sinh[a] + Cosh[a]*#1^4 + Sinh[a]*#1^4 & , (Log[x] - Log[x - #1])/#1^3 & ]*(-Cosh[2*a] + Sinh[2*a]))/2","C",1
155,1,21,12,0.0301255,"\int \frac{\coth (a+2 \log (x))}{x} \, dx","Integrate[Coth[a + 2*Log[x]]/x,x]","\frac{1}{2} (\log (\tanh (a+2 \log (x)))+\log (\cosh (a+2 \log (x))))","\frac{1}{2} \log (\sinh (a+2 \log (x)))",1,"(Log[Cosh[a + 2*Log[x]]] + Log[Tanh[a + 2*Log[x]]])/2","A",1
156,1,62,41,0.1724234,"\int \frac{\coth (a+2 \log (x))}{x^2} \, dx","Integrate[Coth[a + 2*Log[x]]/x^2,x]","\frac{x (\sinh (a)+\cosh (a))^2 \text{RootSum}\left[-\text{$\#$1}^4 \sinh (a)+\text{$\#$1}^4 \cosh (a)-\sinh (a)-\cosh (a)\&,\frac{\log \left(\frac{1}{x}-\text{$\#$1}\right)+\log (x)}{\text{$\#$1}^3}\&\right]+2}{2 x}","e^{a/2} \tan ^{-1}\left(e^{a/2} x\right)-e^{a/2} \tanh ^{-1}\left(e^{a/2} x\right)+\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
157,1,27,21,0.1628819,"\int \frac{\coth (a+2 \log (x))}{x^3} \, dx","Integrate[Coth[a + 2*Log[x]]/x^3,x]","\frac{1}{2 x^2}-(\sinh (a)+\cosh (a)) \tanh ^{-1}\left(\frac{\cosh (a)-\sinh (a)}{x^2}\right)","\frac{1}{2 x^2}-e^a \tanh ^{-1}\left(e^a x^2\right)",1,"1/(2*x^2) - ArcTanh[(Cosh[a] - Sinh[a])/x^2]*(Cosh[a] + Sinh[a])","A",1
158,1,86,47,0.1104012,"\int x^3 \coth ^2(a+2 \log (x)) \, dx","Integrate[x^3*Coth[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}}{1-e^{2 a} x^4}+e^{-2 a} \log \left(1-e^{2 a} x^4\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
159,1,154,68,2.9451732,"\int x^2 \coth ^2(a+2 \log (x)) \, dx","Integrate[x^2*Coth[a + 2*Log[x]]^2,x]","\frac{16 e^{2 a} x^7 \left(e^{2 a} x^4+1\right)^2 \, _4F_3\left(\frac{7}{4},2,2,2;1,1,\frac{19}{4};e^{2 a} x^4\right)}{1155}+\frac{e^{-4 a} \left(7 \left(27 e^{8 a} x^{16}-632 e^{6 a} x^{12}-398 e^{4 a} x^8+1976 e^{2 a} x^4+1331\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};e^{2 a} x^4\right)+1481 e^{6 a} x^{12}-4787 e^{4 a} x^8-17825 e^{2 a} x^4-9317\right)}{2688 x^5}","\frac{x^3}{1-e^{2 a} x^4}+\frac{3}{2} e^{-3 a/2} \tan ^{-1}\left(e^{a/2} x\right)-\frac{3}{2} e^{-3 a/2} \tanh ^{-1}\left(e^{a/2} x\right)+\frac{x^3}{3}",1,"(-9317 - 17825*E^(2*a)*x^4 - 4787*E^(4*a)*x^8 + 1481*E^(6*a)*x^12 + 7*(1331 + 1976*E^(2*a)*x^4 - 398*E^(4*a)*x^8 - 632*E^(6*a)*x^12 + 27*E^(8*a)*x^16)*Hypergeometric2F1[3/4, 1, 7/4, E^(2*a)*x^4])/(2688*E^(4*a)*x^5) + (16*E^(2*a)*x^7*(1 + E^(2*a)*x^4)^2*HypergeometricPFQ[{7/4, 2, 2, 2}, {1, 1, 19/4}, E^(2*a)*x^4])/1155","C",0
160,1,163,41,3.065067,"\int x \coth ^2(a+2 \log (x)) \, dx","Integrate[x*Coth[a + 2*Log[x]]^2,x]","\frac{2}{105} e^{2 a} x^6 \left(e^{2 a} x^4+1\right)^2 \, _4F_3\left(\frac{3}{2},2,2,2;1,1,\frac{9}{2};e^{2 a} x^4\right)+\frac{e^{-4 a} \left(61 e^{6 a} x^{12}-181 e^{4 a} x^8-713 e^{2 a} x^4+\frac{3 \left(e^{8 a} x^{16}-52 e^{6 a} x^{12}-14 e^{4 a} x^8+196 e^{2 a} x^4+125\right) \tanh ^{-1}\left(\sqrt{e^{2 a} x^4}\right)}{\sqrt{e^{2 a} x^4}}-375\right)}{96 x^6}","-e^{-a} \tanh ^{-1}\left(e^a x^2\right)+\frac{x^2}{1-e^{2 a} x^4}+\frac{x^2}{2}",1,"(-375 - 713*E^(2*a)*x^4 - 181*E^(4*a)*x^8 + 61*E^(6*a)*x^12 + (3*(125 + 196*E^(2*a)*x^4 - 14*E^(4*a)*x^8 - 52*E^(6*a)*x^12 + E^(8*a)*x^16)*ArcTanh[Sqrt[E^(2*a)*x^4]])/Sqrt[E^(2*a)*x^4])/(96*E^(4*a)*x^6) + (2*E^(2*a)*x^6*(1 + E^(2*a)*x^4)^2*HypergeometricPFQ[{3/2, 2, 2, 2}, {1, 1, 9/2}, E^(2*a)*x^4])/105","C",0
161,1,153,60,2.2387935,"\int \coth ^2(a+2 \log (x)) \, dx","Integrate[Coth[a + 2*Log[x]]^2,x]","\frac{16}{585} e^{2 a} x^5 \left(e^{2 a} x^4+1\right)^2 \, _4F_3\left(\frac{5}{4},2,2,2;1,1,\frac{17}{4};e^{2 a} x^4\right)+\frac{e^{-4 a} \left(5 \left(e^{8 a} x^{16}-248 e^{6 a} x^{12}+102 e^{4 a} x^8+1208 e^{2 a} x^4+729\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};e^{2 a} x^4\right)+681 e^{6 a} x^{12}-1483 e^{4 a} x^8-6769 e^{2 a} x^4-3645\right)}{640 x^7}","\frac{x}{1-e^{2 a} x^4}-\frac{1}{2} e^{-a/2} \tan ^{-1}\left(e^{a/2} x\right)-\frac{1}{2} e^{-a/2} \tanh ^{-1}\left(e^{a/2} x\right)+x",1,"(-3645 - 6769*E^(2*a)*x^4 - 1483*E^(4*a)*x^8 + 681*E^(6*a)*x^12 + 5*(729 + 1208*E^(2*a)*x^4 + 102*E^(4*a)*x^8 - 248*E^(6*a)*x^12 + E^(8*a)*x^16)*Hypergeometric2F1[1/4, 1, 5/4, E^(2*a)*x^4])/(640*E^(4*a)*x^7) + (16*E^(2*a)*x^5*(1 + E^(2*a)*x^4)^2*HypergeometricPFQ[{5/4, 2, 2, 2}, {1, 1, 17/4}, E^(2*a)*x^4])/585","C",0
162,1,28,14,0.0538413,"\int \frac{\coth ^2(a+2 \log (x))}{x} \, dx","Integrate[Coth[a + 2*Log[x]]^2/x,x]","-\frac{1}{2} \coth (a+2 \log (x)) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\tanh ^2(a+2 \log (x))\right)","\log (x)-\frac{1}{2} \coth (a+2 \log (x))",1,"-1/2*(Coth[a + 2*Log[x]]*Hypergeometric2F1[-1/2, 1, 1/2, Tanh[a + 2*Log[x]]^2])","C",1
163,1,153,86,2.8506876,"\int \frac{\coth ^2(a+2 \log (x))}{x^2} \, dx","Integrate[Coth[a + 2*Log[x]]^2/x^2,x]","\frac{16}{231} e^{2 a} x^3 \left(e^{2 a} x^4+1\right)^2 \, _4F_3\left(\frac{3}{4},2,2,2;1,1,\frac{15}{4};e^{2 a} x^4\right)+\frac{e^{-2 a} \left(\left(-e^{8 a} x^{16}-56 e^{6 a} x^{12}+362 e^{4 a} x^8+632 e^{2 a} x^4+343\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};e^{2 a} x^4\right)+3 e^{6 a} x^{12}-241 e^{4 a} x^8-1163 e^{2 a} x^4-343\right)}{384 x^5}","-\frac{1}{x \left(1-e^{2 a} x^4\right)}+\frac{2 e^{2 a} x^3}{1-e^{2 a} x^4}-\frac{1}{2} e^{a/2} \tan ^{-1}\left(e^{a/2} x\right)+\frac{1}{2} e^{a/2} \tanh ^{-1}\left(e^{a/2} x\right)",1,"(-343 - 1163*E^(2*a)*x^4 - 241*E^(4*a)*x^8 + 3*E^(6*a)*x^12 + (343 + 632*E^(2*a)*x^4 + 362*E^(4*a)*x^8 - 56*E^(6*a)*x^12 - E^(8*a)*x^16)*Hypergeometric2F1[3/4, 1, 7/4, E^(2*a)*x^4])/(384*E^(2*a)*x^5) + (16*E^(2*a)*x^3*(1 + E^(2*a)*x^4)^2*HypergeometricPFQ[{3/4, 2, 2, 2}, {1, 1, 15/4}, E^(2*a)*x^4])/231","C",0
164,1,155,60,3.2502653,"\int \frac{\coth ^2(a+2 \log (x))}{x^3} \, dx","Integrate[Coth[a + 2*Log[x]]^2/x^3,x]","\frac{64 \left(e^{3 a} x^6+e^a x^2\right)^2 \, _4F_3\left(\frac{1}{2},2,2,2;1,1,\frac{7}{2};e^{2 a} x^4\right)+15 \left(e^{4 a} x^8-17 e^{2 a} x^4-\frac{27 e^{-2 a}}{x^4}-77\right)-\frac{15 \left(e^{8 a} x^{16}+4 e^{6 a} x^{12}-54 e^{4 a} x^8-52 e^{2 a} x^4-27\right) \tanh ^{-1}\left(\sqrt{e^{2 a} x^4}\right)}{\left(e^{2 a} x^4\right)^{3/2}}}{480 x^2}","e^a \tanh ^{-1}\left(e^a x^2\right)+\frac{3 e^{2 a} x^2}{2 \left(1-e^{2 a} x^4\right)}-\frac{1}{2 x^2 \left(1-e^{2 a} x^4\right)}",1,"(15*(-77 - 27/(E^(2*a)*x^4) - 17*E^(2*a)*x^4 + E^(4*a)*x^8) - (15*(-27 - 52*E^(2*a)*x^4 - 54*E^(4*a)*x^8 + 4*E^(6*a)*x^12 + E^(8*a)*x^16)*ArcTanh[Sqrt[E^(2*a)*x^4]])/(E^(2*a)*x^4)^(3/2) + 64*(E^a*x^2 + E^(3*a)*x^6)^2*HypergeometricPFQ[{1/2, 2, 2, 2}, {1, 1, 7/2}, E^(2*a)*x^4])/(480*x^2)","C",0
165,1,46,59,0.1022074,"\int (e x)^m \coth (a+2 \log (x)) \, dx","Integrate[(e*x)^m*Coth[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
166,1,77,79,0.1766912,"\int (e x)^m \coth ^2(a+2 \log (x)) \, dx","Integrate[(e*x)^m*Coth[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(1-e^{2 a} x^4\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
167,1,108,177,0.2329794,"\int (e x)^m \coth ^3(a+2 \log (x)) \, dx","Integrate[(e*x)^m*Coth[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{\left(e^{2 a} x^4+1\right)^2 (e x)^{m+1}}{4 e \left(1-e^{2 a} x^4\right)^2}-\frac{e^{-2 a} \left(e^{2 a} (3-m)-e^{4 a} (m+5) x^4\right) (e x)^{m+1}}{8 e \left(1-e^{2 a} x^4\right)}+\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
168,1,259,79,2.0583523,"\int \coth ^p(a+b \log (x)) \, dx","Integrate[Coth[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};p,1-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+1,-p;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(-e^{2 a} x^{2 b}-1\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), p, 1 - 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), 1 + p, -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
169,1,126,99,3.2304583,"\int (e x)^m \coth ^p(a+b \log (x)) \, dx","Integrate[(e*x)^m*Coth[a + b*Log[x]]^p,x]","\frac{x (e x)^m \left(1-e^{2 a} x^{2 b}\right)^p \left(e^{2 a} x^{2 b}+1\right)^{-p} \left(\frac{e^{2 a} x^{2 b}+1}{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(-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)}{e (m+1)}",1,"(x*(e*x)^m*(1 - E^(2*a)*x^(2*b))^p*((1 + E^(2*a)*x^(2*b))/(-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
170,1,83,52,0.4316275,"\int \coth ^p\left(a+\frac{\log (x)}{2}\right) \, dx","Integrate[Coth[a + Log[x]/2]^p,x]","-\frac{e^{-2 a} 2^p \left(e^{2 a} x+1\right)^{1-p} \left(\frac{e^{2 a} x+1}{e^{2 a} x-1}\right)^{p-1} \, _2F_1\left(1-p,-p;2-p;\frac{1}{2}-\frac{1}{2} e^{2 a} x\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(e^{2 a} x+1\right)\right)}{p+1}",1,"-((2^p*(1 + E^(2*a)*x)^(1 - p)*((1 + E^(2*a)*x)/(-1 + E^(2*a)*x))^(-1 + p)*Hypergeometric2F1[1 - p, -p, 2 - p, 1/2 - (E^(2*a)*x)/2])/(E^(2*a)*(-1 + p)))","A",0
171,1,125,108,0.5595314,"\int \coth ^p\left(a+\frac{\log (x)}{4}\right) \, dx","Integrate[Coth[a + Log[x]/4]^p,x]","\frac{e^{-4 a} \left(e^{2 a} \sqrt{x}+1\right)^{1-p} \left(\frac{e^{2 a} \sqrt{x}+1}{e^{2 a} \sqrt{x}-1}\right)^{p-1} \left((p-1) \left(e^{2 a} \sqrt{x}+1\right)^{p+1}-2^{p+1} p \, _2F_1\left(1-p,-p;2-p;\frac{1}{2}-\frac{1}{2} e^{2 a} \sqrt{x}\right)\right)}{p-1}","e^{-4 a} \left(-e^{2 a} \sqrt{x}-1\right)^{p+1} \left(1-e^{2 a} \sqrt{x}\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(e^{2 a} \sqrt{x}+1\right)\right)}{p+1}",1,"((1 + E^(2*a)*Sqrt[x])^(1 - p)*((1 + E^(2*a)*Sqrt[x])/(-1 + E^(2*a)*Sqrt[x]))^(-1 + p)*((-1 + p)*(1 + E^(2*a)*Sqrt[x])^(1 + p) - 2^(1 + p)*p*Hypergeometric2F1[1 - p, -p, 2 - p, 1/2 - (E^(2*a)*Sqrt[x])/2]))/(E^(4*a)*(-1 + p))","A",0
172,1,142,162,0.5993838,"\int \coth ^p\left(a+\frac{\log (x)}{6}\right) \, dx","Integrate[Coth[a + Log[x]/6]^p,x]","\frac{e^{-6 a} \left(e^{2 a} \sqrt[3]{x}+1\right)^{1-p} \left(\frac{e^{2 a} \sqrt[3]{x}+1}{e^{2 a} \sqrt[3]{x}-1}\right)^{p-1} \left((p-1) \left(e^{2 a} \sqrt[3]{x}+1\right)^{p+1} \left(e^{2 a} \sqrt[3]{x}+p\right)-2^p \left(2 p^2+1\right) \, _2F_1\left(1-p,-p;2-p;\frac{1}{2}-\frac{1}{2} e^{2 a} \sqrt[3]{x}\right)\right)}{p-1}","-\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(e^{2 a} \sqrt[3]{x}+1\right)\right)}{p+1}+e^{-6 a} p \left(-e^{2 a} \sqrt[3]{x}-1\right)^{p+1} \left(1-e^{2 a} \sqrt[3]{x}\right)^{1-p}+e^{-4 a} \sqrt[3]{x} \left(-e^{2 a} \sqrt[3]{x}-1\right)^{p+1} \left(1-e^{2 a} \sqrt[3]{x}\right)^{1-p}",1,"((1 + E^(2*a)*x^(1/3))^(1 - p)*((1 + E^(2*a)*x^(1/3))/(-1 + E^(2*a)*x^(1/3)))^(-1 + p)*((-1 + p)*(1 + E^(2*a)*x^(1/3))^(1 + p)*(p + E^(2*a)*x^(1/3)) - 2^p*(1 + 2*p^2)*Hypergeometric2F1[1 - p, -p, 2 - p, 1/2 - (E^(2*a)*x^(1/3))/2]))/(E^(6*a)*(-1 + p))","A",0
173,1,223,194,0.9471252,"\int \coth ^p\left(a+\frac{\log (x)}{8}\right) \, dx","Integrate[Coth[a + Log[x]/8]^p,x]","\frac{e^{-8 a} \left(e^{2 a} \sqrt[4]{x}+1\right)^{1-p} \left(\frac{e^{2 a} \sqrt[4]{x}+1}{e^{2 a} \sqrt[4]{x}-1}\right)^{p-1} \left(-2^{p+3} p \, _2F_1\left(-p-2,1-p;2-p;\frac{1}{2}-\frac{1}{2} e^{2 a} \sqrt[4]{x}\right)+2^{p+2} (2 p-1) \, _2F_1\left(-p-1,1-p;2-p;\frac{1}{2}-\frac{1}{2} e^{2 a} \sqrt[4]{x}\right)+(p-1) \left(e^{4 a} \sqrt{x} \left(e^{2 a} \sqrt[4]{x}+1\right)^{p+1}-2^{p+1} \, _2F_1\left(1-p,-p;2-p;\frac{1}{2}-\frac{1}{2} e^{2 a} \sqrt[4]{x}\right)\right)\right)}{p-1}","-\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(e^{2 a} \sqrt[4]{x}+1\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(1-e^{2 a} \sqrt[4]{x}\right)^{1-p}+e^{-4 a} \sqrt{x} \left(-e^{2 a} \sqrt[4]{x}-1\right)^{p+1} \left(1-e^{2 a} \sqrt[4]{x}\right)^{1-p}",1,"((1 + E^(2*a)*x^(1/4))^(1 - p)*((1 + E^(2*a)*x^(1/4))/(-1 + E^(2*a)*x^(1/4)))^(-1 + p)*(-(2^(3 + p)*p*Hypergeometric2F1[-2 - p, 1 - p, 2 - p, 1/2 - (E^(2*a)*x^(1/4))/2]) + 2^(2 + p)*(-1 + 2*p)*Hypergeometric2F1[-1 - p, 1 - p, 2 - p, 1/2 - (E^(2*a)*x^(1/4))/2] + (-1 + p)*(E^(4*a)*(1 + E^(2*a)*x^(1/4))^(1 + p)*Sqrt[x] - 2^(1 + p)*Hypergeometric2F1[1 - p, -p, 2 - p, 1/2 - (E^(2*a)*x^(1/4))/2])))/(E^(8*a)*(-1 + p))","A",0
174,1,171,61,1.7571946,"\int \coth ^p(a+\log (x)) \, dx","Integrate[Coth[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)}{2 e^{2 a} p x^2 \left(F_1\left(\frac{3}{2};p,1-p;\frac{5}{2};e^{2 a} x^2,-e^{2 a} x^2\right)+F_1\left(\frac{3}{2};p+1,-p;\frac{5}{2};e^{2 a} x^2,-e^{2 a} x^2\right)\right)+3 F_1\left(\frac{1}{2};p,-p;\frac{3}{2};e^{2 a} x^2,-e^{2 a} x^2\right)}","x \left(-e^{2 a} x^2-1\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, p, 1 - p, 5/2, E^(2*a)*x^2, -(E^(2*a)*x^2)] + AppellF1[3/2, 1 + p, -p, 5/2, E^(2*a)*x^2, -(E^(2*a)*x^2)]))","B",0
175,1,171,61,1.949062,"\int \coth ^p(a+2 \log (x)) \, dx","Integrate[Coth[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)}{4 e^{2 a} p x^4 \left(F_1\left(\frac{5}{4};p,1-p;\frac{9}{4};e^{2 a} x^4,-e^{2 a} x^4\right)+F_1\left(\frac{5}{4};p+1,-p;\frac{9}{4};e^{2 a} x^4,-e^{2 a} x^4\right)\right)+5 F_1\left(\frac{1}{4};p,-p;\frac{5}{4};e^{2 a} x^4,-e^{2 a} x^4\right)}","x \left(-e^{2 a} x^4-1\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, p, 1 - p, 9/4, E^(2*a)*x^4, -(E^(2*a)*x^4)] + AppellF1[5/4, 1 + p, -p, 9/4, E^(2*a)*x^4, -(E^(2*a)*x^4)]))","B",0
176,1,171,61,2.0090558,"\int \coth ^p(a+3 \log (x)) \, dx","Integrate[Coth[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)}{6 e^{2 a} p x^6 \left(F_1\left(\frac{7}{6};p,1-p;\frac{13}{6};e^{2 a} x^6,-e^{2 a} x^6\right)+F_1\left(\frac{7}{6};p+1,-p;\frac{13}{6};e^{2 a} x^6,-e^{2 a} x^6\right)\right)+7 F_1\left(\frac{1}{6};p,-p;\frac{7}{6};e^{2 a} x^6,-e^{2 a} x^6\right)}","x \left(-e^{2 a} x^6-1\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, p, 1 - p, 13/6, E^(2*a)*x^6, -(E^(2*a)*x^6)] + AppellF1[7/6, 1 + p, -p, 13/6, E^(2*a)*x^6, -(E^(2*a)*x^6)]))","B",0
177,1,198,58,7.1635994,"\int x^3 \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^3*Coth[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) \left(\, _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)+\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)-\coth \left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)+\sinh (b d n \log (x)) \text{csch}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \text{csch}\left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\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)*(Coth[d*(a + b*Log[c*x^n])] - Coth[d*(a - b*n*Log[x] + b*Log[c*x^n])] + Hypergeometric2F1[1, 2/(b*d*n), 1 + 2/(b*d*n), E^(2*d*(a + b*Log[c*x^n]))] + Csch[d*(a + b*Log[c*x^n])]*Csch[d*(a - b*n*Log[x] + b*Log[c*x^n])]*Sinh[b*d*n*Log[x]])))/(8 + 4*b*d*n))","B",0
178,1,207,62,4.9993925,"\int x^2 \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^2*Coth[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) \left(\, _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)+\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)-\coth \left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)+\sinh (b d n \log (x)) \text{csch}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \text{csch}\left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\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)*(Coth[d*(a + b*Log[c*x^n])] - Coth[d*(a - b*n*Log[x] + b*Log[c*x^n])] + Hypergeometric2F1[1, 3/(2*b*d*n), 1 + 3/(2*b*d*n), E^(2*d*(a + b*Log[c*x^n]))] + Csch[d*(a + b*Log[c*x^n])]*Csch[d*(a - b*n*Log[x] + b*Log[c*x^n])]*Sinh[b*d*n*Log[x]])))/(9 + 6*b*d*n))","B",0
179,1,193,54,6.9862697,"\int x \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x*Coth[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) \left(\, _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)+\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)-\coth \left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)+\sinh (b d n \log (x)) \text{csch}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \text{csch}\left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\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)*(Coth[d*(a + b*Log[c*x^n])] - Coth[d*(a - b*n*Log[x] + b*Log[c*x^n])] + Hypergeometric2F1[1, 1/(b*d*n), 1 + 1/(b*d*n), E^(2*d*(a + b*Log[c*x^n]))] + Csch[d*(a + b*Log[c*x^n])]*Csch[d*(a - b*n*Log[x] + b*Log[c*x^n])]*Sinh[b*d*n*Log[x]])))/(2 + 2*b*d*n))","B",0
180,1,198,52,8.3625166,"\int \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[Coth[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 \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)+\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)-\coth \left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)+\sinh (b d n \log (x)) \text{csch}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \text{csch}\left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\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*(Coth[d*(a + b*Log[c*x^n])] - Coth[d*(a - b*n*Log[x] + b*Log[c*x^n])] + Hypergeometric2F1[1, 1/(2*b*d*n), 1 + 1/(2*b*d*n), E^(2*d*(a + b*Log[c*x^n]))] + Csch[d*(a + b*Log[c*x^n])]*Csch[d*(a - b*n*Log[x] + b*Log[c*x^n])]*Sinh[b*d*n*Log[x]])","B",0
181,1,40,25,0.0661294,"\int \frac{\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Integrate[Coth[d*(a + b*Log[c*x^n])]/x,x]","\frac{\log \left(\tanh \left(a d+b d \log \left(c x^n\right)\right)\right)+\log \left(\cosh \left(d \left(a+b \log \left(c x^n\right)\right)\right)\right)}{b d n}","\frac{\log \left(\sinh \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])]] + Log[Tanh[a*d + b*d*Log[c*x^n]]])/(b*d*n)","A",1
182,1,197,58,3.7929194,"\int \frac{\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Integrate[Coth[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)+\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)-\coth \left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)+\sinh (b d n \log (x)) \text{csch}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \text{csch}\left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\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,"(Coth[d*(a + b*Log[c*x^n])] - Coth[d*(a - b*n*Log[x] + b*Log[c*x^n])] - (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]))] + Csch[d*(a + b*Log[c*x^n])]*Csch[d*(a - b*n*Log[x] + b*Log[c*x^n])]*Sinh[b*d*n*Log[x]])/x","B",0
183,1,191,55,3.7628142,"\int \frac{\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Integrate[Coth[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)+\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)-\coth \left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)+\sinh (b d n \log (x)) \text{csch}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \text{csch}\left(d \left(a+b \log \left(c x^n\right)-b n \log (x)\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,"(Coth[d*(a + b*Log[c*x^n])] - Coth[d*(a - b*n*Log[x] + b*Log[c*x^n])] - (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]))] + Csch[d*(a + b*Log[c*x^n])]*Csch[d*(a - b*n*Log[x] + b*Log[c*x^n])]*Sinh[b*d*n*Log[x]])/(2*x^2)","B",0
184,1,155,132,6.724388,"\int x^3 \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^3*Coth[d*(a + b*Log[c*x^n])]^2,x]","\frac{x^4 \left((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 \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)+b d n\right)-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)\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(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}{b d n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\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*Coth[d*(a + b*Log[c*x^n])] - 4*Hypergeometric2F1[1, 2/(b*d*n), 1 + 2/(b*d*n), E^(2*d*(a + b*Log[c*x^n]))])))/(4*b*d*n*(2 + b*d*n))","A",1
185,1,165,136,4.6227491,"\int x^2 \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^2*Coth[d*(a + b*Log[c*x^n])]^2,x]","\frac{x^3 \left((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 \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)+b d n\right)-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)\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(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}{b d n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\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*Coth[d*(a + b*Log[c*x^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*b*d*n*(3 + 2*b*d*n))","A",1
186,1,151,130,6.6251896,"\int x \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x*Coth[d*(a + b*Log[c*x^n])]^2,x]","\frac{x^2 \left((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 \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)+b d n\right)-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)\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(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}{b d n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\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*Coth[d*(a + b*Log[c*x^n])] - 2*Hypergeometric2F1[1, 1/(b*d*n), 1 + 1/(b*d*n), E^(2*d*(a + b*Log[c*x^n]))])))/(2*b*d*n*(1 + b*d*n))","A",1
187,1,160,126,7.8794383,"\int \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[Coth[d*(a + b*Log[c*x^n])]^2,x]","\frac{x \left((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)-\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)+b d n\right)-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)\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(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}{b d n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\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 - Coth[d*(a + b*Log[c*x^n])] - Hypergeometric2F1[1, 1/(2*b*d*n), 1 + 1/(2*b*d*n), E^(2*d*(a + b*Log[c*x^n]))])))/(b*d*n*(1 + 2*b*d*n))","A",1
188,1,49,28,0.1073871,"\int \frac{\coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Integrate[Coth[d*(a + b*Log[c*x^n])]^2/x,x]","-\frac{\coth \left(a d+b d \log \left(c x^n\right)\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\tanh ^2\left(a d+b \log \left(c x^n\right) d\right)\right)}{b d n}","\log (x)-\frac{\coth \left(a d+b d \log \left(c x^n\right)\right)}{b d n}",1,"-((Coth[a*d + b*d*Log[c*x^n]]*Hypergeometric2F1[-1/2, 1, 1/2, Tanh[a*d + b*d*Log[c*x^n]]^2])/(b*d*n))","C",1
189,1,158,134,3.6299579,"\int \frac{\coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Integrate[Coth[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)+\coth \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{e^{2 a d} \left(c x^n\right)^{2 b d}+1}{b d n x \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\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 + Coth[d*(a + b*Log[c*x^n])] + Hypergeometric2F1[1, -1/2*1/(b*d*n), 1 - 1/(2*b*d*n), E^(2*d*(a + b*Log[c*x^n]))]))/(b*d*n*(-1 + 2*b*d*n)*x)","A",1
190,1,156,135,3.5933086,"\int \frac{\coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Integrate[Coth[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 \coth \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{e^{2 a d} \left(c x^n\right)^{2 b d}+1}{b d n x^2 \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}+\frac{2-b d n}{2 b d n x^2}",1,"(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*Coth[d*(a + b*Log[c*x^n])] + 2*Hypergeometric2F1[1, -(1/(b*d*n)), 1 - 1/(b*d*n), E^(2*d*(a + b*Log[c*x^n]))]))/(2*b*d*n*(-1 + b*d*n)*x^2)","A",1
191,1,52,43,0.2168128,"\int \frac{\coth ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Coth[a + b*Log[c*x^n]]^3/x,x]","-\frac{-2 \log \left(\tanh \left(a+b \log \left(c x^n\right)\right)\right)-2 \log \left(\cosh \left(a+b \log \left(c x^n\right)\right)\right)+\coth ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}","\frac{\log \left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\coth ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"-1/2*(Coth[a + b*Log[c*x^n]]^2 - 2*Log[Cosh[a + b*Log[c*x^n]]] - 2*Log[Tanh[a + b*Log[c*x^n]]])/(b*n)","A",1
192,1,44,45,0.1181782,"\int \frac{\coth ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Coth[a + b*Log[c*x^n]]^4/x,x]","-\frac{\coth ^3\left(a+b \log \left(c x^n\right)\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\tanh ^2\left(a+b \log \left(c x^n\right)\right)\right)}{3 b n}","-\frac{\coth ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\coth \left(a+b \log \left(c x^n\right)\right)}{b n}+\log (x)",1,"-1/3*(Coth[a + b*Log[c*x^n]]^3*Hypergeometric2F1[-3/2, 1, -1/2, Tanh[a + b*Log[c*x^n]]^2])/(b*n)","C",1
193,1,67,66,0.2887098,"\int \frac{\coth ^5\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Coth[a + b*Log[c*x^n]]^5/x,x]","-\frac{-4 \log \left(\tanh \left(a+b \log \left(c x^n\right)\right)\right)-4 \log \left(\cosh \left(a+b \log \left(c x^n\right)\right)\right)+\coth ^4\left(a+b \log \left(c x^n\right)\right)+2 \coth ^2\left(a+b \log \left(c x^n\right)\right)}{4 b n}","\frac{\log \left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\coth ^4\left(a+b \log \left(c x^n\right)\right)}{4 b n}-\frac{\coth ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"-1/4*(2*Coth[a + b*Log[c*x^n]]^2 + Coth[a + b*Log[c*x^n]]^4 - 4*Log[Cosh[a + b*Log[c*x^n]]] - 4*Log[Tanh[a + b*Log[c*x^n]]])/(b*n)","A",1
194,1,158,87,13.476622,"\int (e x)^m \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Coth[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
195,1,312,168,14.8813706,"\int (e x)^m \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Coth[d*(a + b*Log[c*x^n])]^2,x]","(e x)^m \left(\frac{x}{m+1}-\frac{x^{-2 m} \exp \left(-\frac{(2 m+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left((m+1) x^{2 b d n+2 m+1} \exp \left(\frac{(2 b d n+2 m+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\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) e^{\frac{(2 m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}} \, _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)+(2 b d n+m+1) e^{\frac{(2 m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}} \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)\right)}{b d n (2 b d n+m+1)}\right)","-\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(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}{b d e n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}+\frac{(e x)^{m+1} (b d n+m+1)}{b d e (m+1) n}",1,"(e*x)^m*(x/(1 + m) - (E^(((1 + 2*m)*(a + b*Log[c*x^n]))/(b*n))*(1 + m + 2*b*d*n)*Coth[d*(a + b*Log[c*x^n])] + E^(((1 + 2*m)*(a + b*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^(((1 + 2*m + 2*b*d*n)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m)*x^(1 + 2*m + 2*b*d*n)*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]))])/(b*d*E^(((1 + 2*m)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*n*(1 + m + 2*b*d*n)*x^(2*m)))","A",1
196,1,600,306,16.8280749,"\int (e x)^m \coth ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Coth[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{csch}\left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)\right) \left(\frac{\sinh \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) \coth \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)}+\frac{x^{m+1} \sinh (b d n \log (x)) \text{csch}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{m+1}\right)}{2 b^2 d^2 n^2}+\frac{(m+1) x (e x)^m \sinh (b d n \log (x)) \text{csch}\left(d \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)\right) \text{csch}\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 \coth \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{csch}^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^{4 a d} (2 b d n+m+1) \left(c x^n\right)^{2 b d}}{n}+\frac{e^{2 a d} (-2 b d n+m+1)}{n}\right)}{2 b^2 d^2 e n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}-\frac{(e x)^{m+1} \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)^2}{2 b d e n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\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*Coth[d*(a + b*(-(n*Log[x]) + Log[c*x^n]))])/(1 + m) - (x*(e*x)^m*Csch[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*Csch[d*(a + b*(-(n*Log[x]) + Log[c*x^n]))]*Csch[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*Csch[d*(a + b*(-(n*Log[x]) + Log[c*x^n]))]*((x^(1 + m)*Csch[d*(a + b*Log[c*x^n])]*Sinh[b*d*n*Log[x]])/(1 + m) + ((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)*Coth[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)*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]))])*Sinh[d*(a + b*(-(n*Log[x]) + 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)","A",0
197,1,387,115,3.9726291,"\int \coth ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[Coth[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};p,1-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+1,-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+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(-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{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), 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))] + 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))] + (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
198,1,174,135,5.4202685,"\int (e x)^m \coth ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Coth[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(e^{2 a d} \left(c x^n\right)^{2 b d}+1\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 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(-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)}{e (m+1)}",1,"(x*(e*x)^m*(1 - E^(2*a*d)*(c*x^n)^(2*b*d))^p*((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 + 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
199,1,64,73,0.2871835,"\int \frac{\coth ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Coth[a + b*Log[c*x^n]]^(5/2)/x,x]","-\frac{2 \coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)+3 \tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)-3 \tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{3 b n}","-\frac{2 \coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"-1/3*(3*ArcTan[Sqrt[Coth[a + b*Log[c*x^n]]]] - 3*ArcTanh[Sqrt[Coth[a + b*Log[c*x^n]]]] + 2*Coth[a + b*Log[c*x^n]]^(3/2))/(b*n)","A",1
200,1,57,70,0.1493674,"\int \frac{\coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Coth[a + b*Log[c*x^n]]^(3/2)/x,x]","\frac{-2 \sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}+\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)+\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","-\frac{2 \sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}}{b n}+\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"(ArcTan[Sqrt[Coth[a + b*Log[c*x^n]]]] + ArcTanh[Sqrt[Coth[a + b*Log[c*x^n]]]] - 2*Sqrt[Coth[a + b*Log[c*x^n]]])/(b*n)","A",1
201,1,48,48,0.0785031,"\int \frac{\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Integrate[Sqrt[Coth[a + b*Log[c*x^n]]]/x,x]","\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}-\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}-\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"-(ArcTan[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n)) + ArcTanh[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n)","A",1
202,1,47,47,0.115131,"\int \frac{1}{x \sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}} \, dx","Integrate[1/(x*Sqrt[Coth[a + b*Log[c*x^n]]]),x]","\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"ArcTan[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n) + ArcTanh[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n)","A",1
203,1,44,71,0.1522156,"\int \frac{1}{x \coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Coth[a + b*Log[c*x^n]]^(3/2)),x]","-\frac{2 \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};\coth ^2\left(a+b \log \left(c x^n\right)\right)\right)}{b n \sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}}","-\frac{2}{b n \sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}}-\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"(-2*Hypergeometric2F1[-1/4, 1, 3/4, Coth[a + b*Log[c*x^n]]^2])/(b*n*Sqrt[Coth[a + b*Log[c*x^n]]])","C",1
204,1,46,72,0.2060148,"\int \frac{1}{x \coth ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Coth[a + b*Log[c*x^n]]^(5/2)),x]","-\frac{2 \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};\coth ^2\left(a+b \log \left(c x^n\right)\right)\right)}{3 b n \coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","-\frac{2}{3 b n \coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}+\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"(-2*Hypergeometric2F1[-3/4, 1, 1/4, Coth[a + b*Log[c*x^n]]^2])/(3*b*n*Coth[a + b*Log[c*x^n]]^(3/2))","C",1
205,1,266,135,9.0758645,"\int \frac{\coth ^5(x)}{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}} \, dx","Integrate[Coth[x]^5/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","\frac{\frac{2 \text{csch}^2(x) \sqrt{\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c} \left(2 c^{3/2} \tanh ^{-1}\left(\frac{\cosh (2 x) (a+b+c)-a+c}{2 \sqrt{a+b+c} \sqrt{\sinh ^4(x) (a+b+c)+(b+2 c) \sinh ^2(x)+c}}\right)+(b-2 c) \sqrt{a+b+c} \tanh ^{-1}\left(\frac{(b+2 c) \sinh ^2(x)+2 c}{2 \sqrt{c} \sqrt{\sinh ^4(x) (a+b+c)+(b+2 c) \sinh ^2(x)+c}}\right)\right)}{\sqrt{a+b+c}}-\sqrt{2} \sqrt{c} \text{csch}^4(x) (\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c)}{8 c^{3/2} \sqrt{\text{csch}^4(x) (\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c)}}","\frac{(b-2 c) \tanh ^{-1}\left(\frac{b+2 c \coth ^2(x)}{2 \sqrt{c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{4 c^{3/2}}-\frac{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}{2 c}+\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}",1,"((2*(2*c^(3/2)*ArcTanh[(-a + c + (a + b + c)*Cosh[2*x])/(2*Sqrt[a + b + c]*Sqrt[c + (b + 2*c)*Sinh[x]^2 + (a + b + c)*Sinh[x]^4])] + (b - 2*c)*Sqrt[a + b + c]*ArcTanh[(2*c + (b + 2*c)*Sinh[x]^2)/(2*Sqrt[c]*Sqrt[c + (b + 2*c)*Sinh[x]^2 + (a + b + c)*Sinh[x]^4])])*Sqrt[3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x]]*Csch[x]^2)/Sqrt[a + b + c] - Sqrt[2]*Sqrt[c]*(3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x])*Csch[x]^4)/(8*c^(3/2)*Sqrt[(3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x])*Csch[x]^4])","A",1
206,1,199,105,26.6016282,"\int \frac{\coth ^3(x)}{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}} \, dx","Integrate[Coth[x]^3/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","\frac{\text{csch}^2(x) \sqrt{\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c} \left(\frac{\tanh ^{-1}\left(\frac{\cosh (2 x) (a+b+c)-a+c}{2 \sqrt{a+b+c} \sqrt{\sinh ^4(x) (a+b+c)+(b+2 c) \sinh ^2(x)+c}}\right)}{\sqrt{a+b+c}}-\frac{\tanh ^{-1}\left(\frac{(b+2 c) \sinh ^2(x)+2 c}{2 \sqrt{c} \sqrt{\sinh ^4(x) (a+b+c)+(b+2 c) \sinh ^2(x)+c}}\right)}{\sqrt{c}}\right)}{2 \sqrt{\text{csch}^4(x) (\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c)}}","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}-\frac{\tanh ^{-1}\left(\frac{b+2 c \coth ^2(x)}{2 \sqrt{c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{c}}",1,"((ArcTanh[(-a + c + (a + b + c)*Cosh[2*x])/(2*Sqrt[a + b + c]*Sqrt[c + (b + 2*c)*Sinh[x]^2 + (a + b + c)*Sinh[x]^4])]/Sqrt[a + b + c] - ArcTanh[(2*c + (b + 2*c)*Sinh[x]^2)/(2*Sqrt[c]*Sqrt[c + (b + 2*c)*Sinh[x]^2 + (a + b + c)*Sinh[x]^4])]/Sqrt[c])*Sqrt[3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x]]*Csch[x]^2)/(2*Sqrt[(3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x])*Csch[x]^4])","A",1
207,1,141,58,18.6007657,"\int \frac{\coth (x)}{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}} \, dx","Integrate[Coth[x]/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","\frac{\text{csch}^2(x) \sqrt{\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c} \tanh ^{-1}\left(\frac{\cosh (2 x) (a+b+c)-a+c}{2 \sqrt{a+b+c} \sqrt{\sinh ^4(x) (a+b+c)+(b+2 c) \sinh ^2(x)+c}}\right)}{2 \sqrt{a+b+c} \sqrt{\text{csch}^4(x) (\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c)}}","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}",1,"(ArcTanh[(-a + c + (a + b + c)*Cosh[2*x])/(2*Sqrt[a + b + c]*Sqrt[c + (b + 2*c)*Sinh[x]^2 + (a + b + c)*Sinh[x]^4])]*Sqrt[3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x]]*Csch[x]^2)/(2*Sqrt[a + b + c]*Sqrt[(3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x])*Csch[x]^4])","B",1
208,1,203,106,7.7367975,"\int \frac{\tanh (x)}{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}} \, dx","Integrate[Tanh[x]/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","-\frac{\text{csch}^2(x) \sqrt{\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c} \left(-\frac{\tanh ^{-1}\left(\frac{2 a-(2 a+b) \cosh ^2(x)}{2 \sqrt{a} \sqrt{\cosh ^4(x) (a+b+c)-(2 a+b) \cosh ^2(x)+a}}\right)}{\sqrt{a}}-\frac{\tanh ^{-1}\left(\frac{\cosh (2 x) (a+b+c)-a+c}{2 \sqrt{a+b+c} \sqrt{\cosh ^4(x) (a+b+c)-(2 a+b) \cosh ^2(x)+a}}\right)}{\sqrt{a+b+c}}\right)}{2 \sqrt{\text{csch}^4(x) (\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c)}}","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}-\frac{\tanh ^{-1}\left(\frac{2 a+b \coth ^2(x)}{2 \sqrt{a} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a}}",1,"-1/2*((-(ArcTanh[(2*a - (2*a + b)*Cosh[x]^2)/(2*Sqrt[a]*Sqrt[a - (2*a + b)*Cosh[x]^2 + (a + b + c)*Cosh[x]^4])]/Sqrt[a]) - ArcTanh[(-a + c + (a + b + c)*Cosh[2*x])/(2*Sqrt[a + b + c]*Sqrt[a - (2*a + b)*Cosh[x]^2 + (a + b + c)*Cosh[x]^4])]/Sqrt[a + b + c])*Sqrt[3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x]]*Csch[x]^2)/Sqrt[(3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x])*Csch[x]^4]","A",1
209,1,278,183,11.0789569,"\int \frac{\tanh ^3(x)}{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}} \, dx","Integrate[Tanh[x]^3/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","\frac{\text{csch}^2(x) \sqrt{\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c} \left(2 a^{3/2} \tanh ^{-1}\left(\frac{\cosh (2 x) (a+b+c)-a+c}{2 \sqrt{a+b+c} \sqrt{\cosh ^4(x) (a+b+c)-(2 a+b) \cosh ^2(x)+a}}\right)+(2 a-b) \sqrt{a+b+c} \tanh ^{-1}\left(\frac{2 a-(2 a+b) \cosh ^2(x)}{2 \sqrt{a} \sqrt{\cosh ^4(x) (a+b+c)-(2 a+b) \cosh ^2(x)+a}}\right)\right)}{4 a^{3/2} \sqrt{a+b+c} \sqrt{\text{csch}^4(x) (\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c)}}-\frac{\tanh ^2(x) \sqrt{\text{csch}^4(x) (\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c)}}{4 \sqrt{2} a}","\frac{b \tanh ^{-1}\left(\frac{2 a+b \coth ^2(x)}{2 \sqrt{a} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{4 a^{3/2}}-\frac{\tanh ^{-1}\left(\frac{2 a+b \coth ^2(x)}{2 \sqrt{a} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a}}+\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}-\frac{\tanh ^2(x) \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}{2 a}",1,"(((2*a - b)*Sqrt[a + b + c]*ArcTanh[(2*a - (2*a + b)*Cosh[x]^2)/(2*Sqrt[a]*Sqrt[a - (2*a + b)*Cosh[x]^2 + (a + b + c)*Cosh[x]^4])] + 2*a^(3/2)*ArcTanh[(-a + c + (a + b + c)*Cosh[2*x])/(2*Sqrt[a + b + c]*Sqrt[a - (2*a + b)*Cosh[x]^2 + (a + b + c)*Cosh[x]^4])])*Sqrt[3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x]]*Csch[x]^2)/(4*a^(3/2)*Sqrt[a + b + c]*Sqrt[(3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x])*Csch[x]^4]) - (Sqrt[(3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x])*Csch[x]^4]*Tanh[x]^2)/(4*Sqrt[2]*a)","A",1
210,1,304,132,8.4189383,"\int \coth (x) \sqrt{a+b \coth ^2(x)+c \coth ^4(x)} \, dx","Integrate[Coth[x]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","\frac{\text{csch}^2(x) \left(4 \sqrt{c} (a+b+c) \sqrt{\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c} \tanh ^{-1}\left(\frac{\cosh (2 x) (a+b+c)-a+c}{2 \sqrt{a+b+c} \sqrt{\sinh ^4(x) (a+b+c)+(b+2 c) \sinh ^2(x)+c}}\right)+\sqrt{a+b+c} \left(-\sqrt{2} \sqrt{c} \text{csch}^2(x) (\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c)-2 (b+2 c) \sqrt{\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c} \tanh ^{-1}\left(\frac{(b+2 c) \sinh ^2(x)+2 c}{2 \sqrt{c} \sqrt{\sinh ^4(x) (a+b+c)+(b+2 c) \sinh ^2(x)+c}}\right)\right)\right)}{8 \sqrt{c} \sqrt{a+b+c} \sqrt{\text{csch}^4(x) (\cosh (4 x) (a+b+c)-4 (a-c) \cosh (2 x)+3 a-b+3 c)}}","-\frac{1}{2} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}-\frac{(b+2 c) \tanh ^{-1}\left(\frac{b+2 c \coth ^2(x)}{2 \sqrt{c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{4 \sqrt{c}}+\frac{1}{2} \sqrt{a+b+c} \tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)",1,"(Csch[x]^2*(4*Sqrt[c]*(a + b + c)*ArcTanh[(-a + c + (a + b + c)*Cosh[2*x])/(2*Sqrt[a + b + c]*Sqrt[c + (b + 2*c)*Sinh[x]^2 + (a + b + c)*Sinh[x]^4])]*Sqrt[3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x]] + Sqrt[a + b + c]*(-2*(b + 2*c)*ArcTanh[(2*c + (b + 2*c)*Sinh[x]^2)/(2*Sqrt[c]*Sqrt[c + (b + 2*c)*Sinh[x]^2 + (a + b + c)*Sinh[x]^4])]*Sqrt[3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x]] - Sqrt[2]*Sqrt[c]*(3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x])*Csch[x]^2)))/(8*Sqrt[c]*Sqrt[a + b + c]*Sqrt[(3*a - b + 3*c - 4*(a - c)*Cosh[2*x] + (a + b + c)*Cosh[4*x])*Csch[x]^4])","B",1
211,1,164,319,10.2759861,"\int e^{c (a+b x)} \coth ^2(a c+b c x)^{5/2} \, dx","Integrate[E^(c*(a + b*x))*(Coth[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)) \sqrt{\coth ^2(c (a+b x))}}{24 b c \left(e^{2 c (a+b x)}-1\right)^4}","-\frac{15 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{4 b c}+\frac{e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}+\frac{25 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{4 b c \left(1-e^{2 c (a+b x)}\right)}-\frac{55 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{6 b c \left(1-e^{2 c (a+b x)}\right)^2}+\frac{26 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{3 b c \left(1-e^{2 c (a+b x)}\right)^3}-\frac{4 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)^4}",1,"(Sqrt[Coth[c*(a + b*x)]^2]*(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)","A",1
212,1,334,197,3.8181983,"\int e^{c (a+b x)} \coth ^2(a c+b c x)^{3/2} \, dx","Integrate[E^(c*(a + b*x))*(Coth[a*c + b*c*x]^2)^(3/2),x]","-\frac{e^{-5 c (a+b x)} \tanh ^3(c (a+b x)) \coth ^2(c (a+b x))^{3/2} \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}","-\frac{3 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}+\frac{e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}+\frac{3 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)}-\frac{2 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)^2}",1,"-1/60480*((Coth[c*(a + b*x)]^2)^(3/2)*(-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)))","C",0
213,1,51,83,0.0620125,"\int e^{c (a+b x)} \sqrt{\coth ^2(a c+b c x)} \, dx","Integrate[E^(c*(a + b*x))*Sqrt[Coth[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)) \sqrt{\coth ^2(c (a+b x))}}{b c}","\frac{e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}-\frac{2 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}",1,"((E^(c*(a + b*x)) - 2*ArcTanh[E^(c*(a + b*x))])*Sqrt[Coth[c*(a + b*x)]^2]*Tanh[c*(a + b*x)])/(b*c)","A",1
214,1,51,83,0.1263757,"\int \frac{e^{c (a+b x)}}{\sqrt{\coth ^2(a c+b c x)}} \, dx","Integrate[E^(c*(a + b*x))/Sqrt[Coth[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) \coth (c (a+b x))}{b c \sqrt{\coth ^2(c (a+b x))}}","\frac{e^{c (a+b x)} \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}-\frac{2 \tan ^{-1}\left(e^{c (a+b x)}\right) \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}",1,"((E^(c*(a + b*x)) - 2*ArcTan[E^(c*(a + b*x))])*Coth[c*(a + b*x)])/(b*c*Sqrt[Coth[c*(a + b*x)]^2])","A",1
215,1,104,193,0.305523,"\int \frac{e^{c (a+b x)}}{\coth ^2(a c+b c x)^{3/2}} \, dx","Integrate[E^(c*(a + b*x))/(Coth[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) \coth (c (a+b x))}{b c \left(e^{2 c (a+b x)}+1\right)^2 \sqrt{\coth ^2(c (a+b x))}}","\frac{e^{c (a+b x)} \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}+\frac{3 e^{c (a+b x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right) \sqrt{\coth ^2(a c+b c x)}}-\frac{2 e^{c (a+b x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^2 \sqrt{\coth ^2(a c+b c x)}}-\frac{3 \tan ^{-1}\left(e^{c (a+b x)}\right) \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}",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)])/(b*c*(1 + E^(2*c*(a + b*x)))^2*Sqrt[Coth[c*(a + b*x)]^2])","A",1
216,1,133,311,0.481565,"\int \frac{e^{c (a+b x)}}{\coth ^2(a c+b c x)^{5/2}} \, dx","Integrate[E^(c*(a + b*x))/(Coth[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) \coth (c (a+b x))}{12 b c \left(e^{2 c (a+b x)}+1\right)^4 \sqrt{\coth ^2(c (a+b x))}}","\frac{e^{c (a+b x)} \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}+\frac{25 e^{c (a+b x)} \coth (a c+b c x)}{4 b c \left(e^{2 c (a+b x)}+1\right) \sqrt{\coth ^2(a c+b c x)}}-\frac{55 e^{c (a+b x)} \coth (a c+b c x)}{6 b c \left(e^{2 c (a+b x)}+1\right)^2 \sqrt{\coth ^2(a c+b c x)}}+\frac{26 e^{c (a+b x)} \coth (a c+b c x)}{3 b c \left(e^{2 c (a+b x)}+1\right)^3 \sqrt{\coth ^2(a c+b c x)}}-\frac{4 e^{c (a+b x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^4 \sqrt{\coth ^2(a c+b c x)}}-\frac{15 \tan ^{-1}\left(e^{c (a+b x)}\right) \coth (a c+b c x)}{4 b c \sqrt{\coth ^2(a c+b c x)}}",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)])/(12*b*c*(1 + E^(2*c*(a + b*x)))^4*Sqrt[Coth[c*(a + b*x)]^2])","A",1
217,1,124,157,0.2628097,"\int \sin ^3(\coth (a+b x)) \, dx","Integrate[Sin[Coth[a + b*x]]^3,x]","\frac{2 \sin (3) \text{Ci}(3-3 \coth (a+b x))+2 \sin (3) \text{Ci}(3 \coth (a+b x)+3)-6 \sin (1) \text{Ci}(1-\coth (a+b x))-6 \sin (1) \text{Ci}(\coth (a+b x)+1)-2 \cos (3) \text{Si}(3-3 \coth (a+b x))+6 \cos (1) \text{Si}(1-\coth (a+b x))+6 \cos (1) \text{Si}(\coth (a+b x)+1)-2 \cos (3) \text{Si}(3 \coth (a+b x)+3)}{16 b}","\frac{\sin (3) \text{Ci}(3-3 \coth (a+b x))}{8 b}+\frac{\sin (3) \text{Ci}(3 \coth (a+b x)+3)}{8 b}-\frac{3 \sin (1) \text{Ci}(1-\coth (a+b x))}{8 b}-\frac{3 \sin (1) \text{Ci}(\coth (a+b x)+1)}{8 b}-\frac{\cos (3) \text{Si}(3-3 \coth (a+b x))}{8 b}+\frac{3 \cos (1) \text{Si}(1-\coth (a+b x))}{8 b}+\frac{3 \cos (1) \text{Si}(\coth (a+b x)+1)}{8 b}-\frac{\cos (3) \text{Si}(3 \coth (a+b x)+3)}{8 b}",1,"(-6*CosIntegral[1 - Coth[a + b*x]]*Sin[1] - 6*CosIntegral[1 + Coth[a + b*x]]*Sin[1] + 2*CosIntegral[3 - 3*Coth[a + b*x]]*Sin[3] + 2*CosIntegral[3 + 3*Coth[a + b*x]]*Sin[3] - 2*Cos[3]*SinIntegral[3 - 3*Coth[a + b*x]] + 6*Cos[1]*SinIntegral[1 - Coth[a + b*x]] + 6*Cos[1]*SinIntegral[1 + Coth[a + b*x]] - 2*Cos[3]*SinIntegral[3 + 3*Coth[a + b*x]])/(16*b)","A",1
218,1,88,115,0.1744986,"\int \sin ^2(\coth (a+b x)) \, dx","Integrate[Sin[Coth[a + b*x]]^2,x]","\frac{\cos (2) \text{Ci}(2-2 \coth (a+b x))-\cos (2) \text{Ci}(2 (\coth (a+b x)+1))+\sin (2) \text{Si}(2-2 \coth (a+b x))-\sin (2) \text{Si}(2 (\coth (a+b x)+1))-\log (1-\coth (a+b x))+\log (\coth (a+b x)+1)}{4 b}","\frac{\cos (2) \text{Ci}(2-2 \coth (a+b x))}{4 b}-\frac{\cos (2) \text{Ci}(2 \coth (a+b x)+2)}{4 b}+\frac{\sin (2) \text{Si}(2-2 \coth (a+b x))}{4 b}-\frac{\sin (2) \text{Si}(2 \coth (a+b x)+2)}{4 b}-\frac{\log (1-\coth (a+b x))}{4 b}+\frac{\log (\coth (a+b x)+1)}{4 b}",1,"(Cos[2]*CosIntegral[2 - 2*Coth[a + b*x]] - Cos[2]*CosIntegral[2*(1 + Coth[a + b*x])] - Log[1 - Coth[a + b*x]] + Log[1 + Coth[a + b*x]] + Sin[2]*SinIntegral[2 - 2*Coth[a + b*x]] - Sin[2]*SinIntegral[2*(1 + Coth[a + b*x])])/(4*b)","A",1
219,1,59,77,0.1373919,"\int \sin (\coth (a+b x)) \, dx","Integrate[Sin[Coth[a + b*x]],x]","-\frac{\sin (1) \text{Ci}(1-\coth (a+b x))+\sin (1) \text{Ci}(\coth (a+b x)+1)-\cos (1) (\text{Si}(1-\coth (a+b x))+\text{Si}(\coth (a+b x)+1))}{2 b}","-\frac{\sin (1) \text{Ci}(1-\coth (a+b x))}{2 b}-\frac{\sin (1) \text{Ci}(\coth (a+b x)+1)}{2 b}+\frac{\cos (1) \text{Si}(1-\coth (a+b x))}{2 b}+\frac{\cos (1) \text{Si}(\coth (a+b x)+1)}{2 b}",1,"-1/2*(CosIntegral[1 - Coth[a + b*x]]*Sin[1] + CosIntegral[1 + Coth[a + b*x]]*Sin[1] - Cos[1]*(SinIntegral[1 - Coth[a + b*x]] + SinIntegral[1 + Coth[a + b*x]]))/b","A",1
220,0,0,67,3.5457267,"\int \csc (\coth (a+b x)) \, dx","Integrate[Csc[Coth[a + b*x]],x]","\int \csc (\coth (a+b x)) \, dx","\frac{1}{2} \text{Int}\left(\frac{\text{csch}^2(a+b x) \csc (\coth (a+b x))}{\coth (a+b x)-1},x\right)-\frac{1}{2} \text{Int}\left(\frac{\text{csch}^2(a+b x) \csc (\coth (a+b x))}{\coth (a+b x)+1},x\right)",0,"Integrate[Csc[Coth[a + b*x]], x]","A",-1
221,1,124,157,0.2605663,"\int \cos ^3(\coth (a+b x)) \, dx","Integrate[Cos[Coth[a + b*x]]^3,x]","\frac{-2 \cos (3) \text{Ci}(3-3 \coth (a+b x))-6 \cos (1) \text{Ci}(1-\coth (a+b x))+6 \cos (1) \text{Ci}(\coth (a+b x)+1)+2 \cos (3) \text{Ci}(3 \coth (a+b x)+3)-2 \sin (3) \text{Si}(3-3 \coth (a+b x))-6 \sin (1) \text{Si}(1-\coth (a+b x))+6 \sin (1) \text{Si}(\coth (a+b x)+1)+2 \sin (3) \text{Si}(3 \coth (a+b x)+3)}{16 b}","-\frac{\cos (3) \text{Ci}(3-3 \coth (a+b x))}{8 b}-\frac{3 \cos (1) \text{Ci}(1-\coth (a+b x))}{8 b}+\frac{3 \cos (1) \text{Ci}(\coth (a+b x)+1)}{8 b}+\frac{\cos (3) \text{Ci}(3 \coth (a+b x)+3)}{8 b}-\frac{\sin (3) \text{Si}(3-3 \coth (a+b x))}{8 b}-\frac{3 \sin (1) \text{Si}(1-\coth (a+b x))}{8 b}+\frac{3 \sin (1) \text{Si}(\coth (a+b x)+1)}{8 b}+\frac{\sin (3) \text{Si}(3 \coth (a+b x)+3)}{8 b}",1,"(-2*Cos[3]*CosIntegral[3 - 3*Coth[a + b*x]] - 6*Cos[1]*CosIntegral[1 - Coth[a + b*x]] + 6*Cos[1]*CosIntegral[1 + Coth[a + b*x]] + 2*Cos[3]*CosIntegral[3 + 3*Coth[a + b*x]] - 2*Sin[3]*SinIntegral[3 - 3*Coth[a + b*x]] - 6*Sin[1]*SinIntegral[1 - Coth[a + b*x]] + 6*Sin[1]*SinIntegral[1 + Coth[a + b*x]] + 2*Sin[3]*SinIntegral[3 + 3*Coth[a + b*x]])/(16*b)","A",1
222,1,88,115,0.1800533,"\int \cos ^2(\coth (a+b x)) \, dx","Integrate[Cos[Coth[a + b*x]]^2,x]","\frac{-\cos (2) \text{Ci}(2-2 \coth (a+b x))+\cos (2) \text{Ci}(2 (\coth (a+b x)+1))-\sin (2) \text{Si}(2-2 \coth (a+b x))+\sin (2) \text{Si}(2 (\coth (a+b x)+1))-\log (1-\coth (a+b x))+\log (\coth (a+b x)+1)}{4 b}","-\frac{\cos (2) \text{Ci}(2-2 \coth (a+b x))}{4 b}+\frac{\cos (2) \text{Ci}(2 \coth (a+b x)+2)}{4 b}-\frac{\sin (2) \text{Si}(2-2 \coth (a+b x))}{4 b}+\frac{\sin (2) \text{Si}(2 \coth (a+b x)+2)}{4 b}-\frac{\log (1-\coth (a+b x))}{4 b}+\frac{\log (\coth (a+b x)+1)}{4 b}",1,"(-(Cos[2]*CosIntegral[2 - 2*Coth[a + b*x]]) + Cos[2]*CosIntegral[2*(1 + Coth[a + b*x])] - Log[1 - Coth[a + b*x]] + Log[1 + Coth[a + b*x]] - Sin[2]*SinIntegral[2 - 2*Coth[a + b*x]] + Sin[2]*SinIntegral[2*(1 + Coth[a + b*x])])/(4*b)","A",1
223,1,62,77,0.1141696,"\int \cos (\coth (a+b x)) \, dx","Integrate[Cos[Coth[a + b*x]],x]","-\frac{\cos (1) \text{Ci}(1-\coth (a+b x))-\cos (1) \text{Ci}(\coth (a+b x)+1)+\sin (1) \text{Si}(1-\coth (a+b x))-\sin (1) \text{Si}(\coth (a+b x)+1)}{2 b}","-\frac{\cos (1) \text{Ci}(1-\coth (a+b x))}{2 b}+\frac{\cos (1) \text{Ci}(\coth (a+b x)+1)}{2 b}-\frac{\sin (1) \text{Si}(1-\coth (a+b x))}{2 b}+\frac{\sin (1) \text{Si}(\coth (a+b x)+1)}{2 b}",1,"-1/2*(Cos[1]*CosIntegral[1 - Coth[a + b*x]] - Cos[1]*CosIntegral[1 + Coth[a + b*x]] + Sin[1]*SinIntegral[1 - Coth[a + b*x]] - Sin[1]*SinIntegral[1 + Coth[a + b*x]])/b","A",1
224,0,0,67,6.6308611,"\int \sec (\coth (a+b x)) \, dx","Integrate[Sec[Coth[a + b*x]],x]","\int \sec (\coth (a+b x)) \, dx","\frac{1}{2} \text{Int}\left(\frac{\text{csch}^2(a+b x) \sec (\coth (a+b x))}{\coth (a+b x)-1},x\right)-\frac{1}{2} \text{Int}\left(\frac{\text{csch}^2(a+b x) \sec (\coth (a+b x))}{\coth (a+b x)+1},x\right)",0,"Integrate[Sec[Coth[a + b*x]], x]","A",-1