1,1,38,12,0.0155286,"\int \text{csch}(a+b x) \, dx","Integrate[Csch[a + b*x],x]","\frac{\log \left(\sinh \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}-\frac{\log \left(\cosh \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}","-\frac{\tanh ^{-1}(\cosh (a+b x))}{b}",1,"-(Log[Cosh[a/2 + (b*x)/2]]/b) + Log[Sinh[a/2 + (b*x)/2]]/b","B",1
2,1,11,11,0.0111965,"\int \text{csch}^2(a+b x) \, dx","Integrate[Csch[a + b*x]^2,x]","-\frac{\coth (a+b x)}{b}","-\frac{\coth (a+b x)}{b}",1,"-(Coth[a + b*x]/b)","A",1
3,1,57,34,0.0133884,"\int \text{csch}^3(a+b x) \, dx","Integrate[Csch[a + b*x]^3,x]","-\frac{\text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{\text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{\log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b}","\frac{\tanh ^{-1}(\cosh (a+b x))}{2 b}-\frac{\coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-1/8*Csch[(a + b*x)/2]^2/b - Log[Tanh[(a + b*x)/2]]/(2*b) - Sech[(a + b*x)/2]^2/(8*b)","A",1
4,1,35,26,0.013252,"\int \text{csch}^4(a+b x) \, dx","Integrate[Csch[a + b*x]^4,x]","\frac{2 \coth (a+b x)}{3 b}-\frac{\coth (a+b x) \text{csch}^2(a+b x)}{3 b}","\frac{\coth (a+b x)}{b}-\frac{\coth ^3(a+b x)}{3 b}",1,"(2*Coth[a + b*x])/(3*b) - (Coth[a + b*x]*Csch[a + b*x]^2)/(3*b)","A",1
5,1,95,55,0.0164552,"\int \text{csch}^5(a+b x) \, dx","Integrate[Csch[a + b*x]^5,x]","-\frac{\text{csch}^4\left(\frac{1}{2} (a+b x)\right)}{64 b}+\frac{3 \text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{32 b}+\frac{\text{sech}^4\left(\frac{1}{2} (a+b x)\right)}{64 b}+\frac{3 \text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{32 b}+\frac{3 \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{8 b}","-\frac{3 \tanh ^{-1}(\cosh (a+b x))}{8 b}-\frac{\coth (a+b x) \text{csch}^3(a+b x)}{4 b}+\frac{3 \coth (a+b x) \text{csch}(a+b x)}{8 b}",1,"(3*Csch[(a + b*x)/2]^2)/(32*b) - Csch[(a + b*x)/2]^4/(64*b) + (3*Log[Tanh[(a + b*x)/2]])/(8*b) + (3*Sech[(a + b*x)/2]^2)/(32*b) + Sech[(a + b*x)/2]^4/(64*b)","A",1
6,1,56,42,0.0173505,"\int \text{csch}^6(a+b x) \, dx","Integrate[Csch[a + b*x]^6,x]","-\frac{8 \coth (a+b x)}{15 b}-\frac{\coth (a+b x) \text{csch}^4(a+b x)}{5 b}+\frac{4 \coth (a+b x) \text{csch}^2(a+b x)}{15 b}","-\frac{\coth ^5(a+b x)}{5 b}+\frac{2 \coth ^3(a+b x)}{3 b}-\frac{\coth (a+b x)}{b}",1,"(-8*Coth[a + b*x])/(15*b) + (4*Coth[a + b*x]*Csch[a + b*x]^2)/(15*b) - (Coth[a + b*x]*Csch[a + b*x]^4)/(5*b)","A",1
7,1,61,80,0.1262312,"\int \text{csch}^{\frac{5}{2}}(a+b x) \, dx","Integrate[Csch[a + b*x]^(5/2),x]","-\frac{2 \sqrt{\text{csch}(a+b x)} \left(\coth (a+b x)+i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)\right)}{3 b}","-\frac{2 \cosh (a+b x) \text{csch}^{\frac{3}{2}}(a+b x)}{3 b}+\frac{2 i \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{3 b}",1,"(-2*Sqrt[Csch[a + b*x]]*(Coth[a + b*x] + I*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]]))/(3*b)","A",1
8,1,57,76,0.2215169,"\int \text{csch}^{\frac{3}{2}}(a+b x) \, dx","Integrate[Csch[a + b*x]^(3/2),x]","-\frac{2 \sqrt{\text{csch}(a+b x)} \left(\cosh (a+b x)-\sqrt{i \sinh (a+b x)} E\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)\right)}{b}","-\frac{2 \cosh (a+b x) \sqrt{\text{csch}(a+b x)}}{b}-\frac{2 i E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{b \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)}}",1,"(-2*Sqrt[Csch[a + b*x]]*(Cosh[a + b*x] - EllipticE[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]]))/b","A",1
9,1,48,54,0.1933964,"\int \sqrt{\text{csch}(a+b x)} \, dx","Integrate[Sqrt[Csch[a + b*x]],x]","\frac{2 (i \sinh (a+b x))^{3/2} \text{csch}^{\frac{3}{2}}(a+b x) F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)}{b}","-\frac{2 i \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{b}",1,"(2*Csch[a + b*x]^(3/2)*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*(I*Sinh[a + b*x])^(3/2))/b","A",1
10,1,50,54,0.037185,"\int \frac{1}{\sqrt{\text{csch}(a+b x)}} \, dx","Integrate[1/Sqrt[Csch[a + b*x]],x]","\frac{2 \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)} E\left(\left.\frac{1}{2} \left(\frac{\pi }{2}-i (a+b x)\right)\right|2\right)}{b}","-\frac{2 i E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{b \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)}}",1,"(2*Sqrt[Csch[a + b*x]]*EllipticE[(Pi/2 - I*(a + b*x))/2, 2]*Sqrt[I*Sinh[a + b*x]])/b","A",1
11,1,63,80,0.0677832,"\int \frac{1}{\text{csch}^{\frac{3}{2}}(a+b x)} \, dx","Integrate[Csch[a + b*x]^(-3/2),x]","\frac{\sqrt{\text{csch}(a+b x)} \left(\sinh (2 (a+b x))-2 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)\right)}{3 b}","\frac{2 \cosh (a+b x)}{3 b \sqrt{\text{csch}(a+b x)}}+\frac{2 i \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{3 b}",1,"(Sqrt[Csch[a + b*x]]*((-2*I)*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]] + Sinh[2*(a + b*x)]))/(3*b)","A",1
12,1,67,80,0.1299965,"\int \frac{1}{\text{csch}^{\frac{5}{2}}(a+b x)} \, dx","Integrate[Csch[a + b*x]^(-5/2),x]","\frac{2 \left(\cosh (a+b x)-3 \sqrt{i \sinh (a+b x)} \text{csch}^2(a+b x) E\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)\right)}{5 b \text{csch}^{\frac{3}{2}}(a+b x)}","\frac{2 \cosh (a+b x)}{5 b \text{csch}^{\frac{3}{2}}(a+b x)}+\frac{6 i E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{5 b \sqrt{i \sinh (a+b x)} \sqrt{\text{csch}(a+b x)}}",1,"(2*(Cosh[a + b*x] - 3*Csch[a + b*x]^2*EllipticE[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]]))/(5*b*Csch[a + b*x]^(3/2))","A",1
13,1,79,116,0.1601507,"\int (b \text{csch}(c+d x))^{7/2} \, dx","Integrate[(b*Csch[c + d*x])^(7/2),x]","-\frac{2 b^3 \sqrt{b \text{csch}(c+d x)} \left(-3 \cosh (c+d x)+\coth (c+d x) \text{csch}(c+d x)+3 \sqrt{i \sinh (c+d x)} E\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)\right)}{5 d}","\frac{6 i b^4 E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{5 d \sqrt{i \sinh (c+d x)} \sqrt{b \text{csch}(c+d x)}}+\frac{6 b^3 \cosh (c+d x) \sqrt{b \text{csch}(c+d x)}}{5 d}-\frac{2 b \cosh (c+d x) (b \text{csch}(c+d x))^{5/2}}{5 d}",1,"(-2*b^3*Sqrt[b*Csch[c + d*x]]*(-3*Cosh[c + d*x] + Coth[c + d*x]*Csch[c + d*x] + 3*EllipticE[((-2*I)*c + Pi - (2*I)*d*x)/4, 2]*Sqrt[I*Sinh[c + d*x]]))/(5*d)","A",1
14,1,66,88,0.111606,"\int (b \text{csch}(c+d x))^{5/2} \, dx","Integrate[(b*Csch[c + d*x])^(5/2),x]","-\frac{2 b^2 \sqrt{b \text{csch}(c+d x)} \left(\coth (c+d x)+i \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)\right)}{3 d}","-\frac{2 b \cosh (c+d x) (b \text{csch}(c+d x))^{3/2}}{3 d}+\frac{2 i b^2 \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \text{csch}(c+d x)}}{3 d}",1,"(-2*b^2*Sqrt[b*Csch[c + d*x]]*(Coth[c + d*x] + I*EllipticF[((-2*I)*c + Pi - (2*I)*d*x)/4, 2]*Sqrt[I*Sinh[c + d*x]]))/(3*d)","A",1
15,1,60,84,0.0612716,"\int (b \text{csch}(c+d x))^{3/2} \, dx","Integrate[(b*Csch[c + d*x])^(3/2),x]","-\frac{2 b \sqrt{b \text{csch}(c+d x)} \left(\cosh (c+d x)-\sqrt{i \sinh (c+d x)} E\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)\right)}{d}","-\frac{2 b \cosh (c+d x) \sqrt{b \text{csch}(c+d x)}}{d}-\frac{2 i b^2 E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{d \sqrt{i \sinh (c+d x)} \sqrt{b \text{csch}(c+d x)}}",1,"(-2*b*Sqrt[b*Csch[c + d*x]]*(Cosh[c + d*x] - EllipticE[((-2*I)*c + Pi - (2*I)*d*x)/4, 2]*Sqrt[I*Sinh[c + d*x]]))/d","A",1
16,1,54,56,0.0363406,"\int \sqrt{b \text{csch}(c+d x)} \, dx","Integrate[Sqrt[b*Csch[c + d*x]],x]","\frac{2 i \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{2} \left(\frac{\pi }{2}-i (c+d x)\right)\right|2\right) \sqrt{b \text{csch}(c+d x)}}{d}","-\frac{2 i \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \text{csch}(c+d x)}}{d}",1,"((2*I)*Sqrt[b*Csch[c + d*x]]*EllipticF[(Pi/2 - I*(c + d*x))/2, 2]*Sqrt[I*Sinh[c + d*x]])/d","A",1
17,1,52,56,0.0459181,"\int \frac{1}{\sqrt{b \text{csch}(c+d x)}} \, dx","Integrate[1/Sqrt[b*Csch[c + d*x]],x]","\frac{2 i E\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)}{d \sqrt{i \sinh (c+d x)} \sqrt{b \text{csch}(c+d x)}}","-\frac{2 i E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{d \sqrt{i \sinh (c+d x)} \sqrt{b \text{csch}(c+d x)}}",1,"((2*I)*EllipticE[((-2*I)*c + Pi - (2*I)*d*x)/4, 2])/(d*Sqrt[b*Csch[c + d*x]]*Sqrt[I*Sinh[c + d*x]])","A",1
18,1,73,90,0.0906929,"\int \frac{1}{(b \text{csch}(c+d x))^{3/2}} \, dx","Integrate[(b*Csch[c + d*x])^(-3/2),x]","\frac{\text{csch}^2(c+d x) \left(\sinh (2 (c+d x))-2 i \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)\right)}{3 d (b \text{csch}(c+d x))^{3/2}}","\frac{2 \cosh (c+d x)}{3 b d \sqrt{b \text{csch}(c+d x)}}+\frac{2 i \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \text{csch}(c+d x)}}{3 b^2 d}",1,"(Csch[c + d*x]^2*((-2*I)*EllipticF[((-2*I)*c + Pi - (2*I)*d*x)/4, 2]*Sqrt[I*Sinh[c + d*x]] + Sinh[2*(c + d*x)]))/(3*d*(b*Csch[c + d*x])^(3/2))","A",1
19,1,68,90,0.1361515,"\int \frac{1}{(b \text{csch}(c+d x))^{5/2}} \, dx","Integrate[(b*Csch[c + d*x])^(-5/2),x]","\frac{\sinh (2 (c+d x))-\frac{6 i E\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)}{\sqrt{i \sinh (c+d x)}}}{5 b^2 d \sqrt{b \text{csch}(c+d x)}}","\frac{2 \cosh (c+d x)}{5 b d (b \text{csch}(c+d x))^{3/2}}+\frac{6 i E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{5 b^2 d \sqrt{i \sinh (c+d x)} \sqrt{b \text{csch}(c+d x)}}",1,"(((-6*I)*EllipticE[((-2*I)*c + Pi - (2*I)*d*x)/4, 2])/Sqrt[I*Sinh[c + d*x]] + Sinh[2*(c + d*x)])/(5*b^2*d*Sqrt[b*Csch[c + d*x]])","A",1
20,1,80,118,0.1623303,"\int \frac{1}{(b \text{csch}(c+d x))^{7/2}} \, dx","Integrate[(b*Csch[c + d*x])^(-7/2),x]","\frac{\sqrt{b \text{csch}(c+d x)} \left(-26 \sinh (2 (c+d x))+3 \sinh (4 (c+d x))+40 i \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)\right)}{84 b^4 d}","-\frac{10 i \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \text{csch}(c+d x)}}{21 b^4 d}-\frac{10 \cosh (c+d x)}{21 b^3 d \sqrt{b \text{csch}(c+d x)}}+\frac{2 \cosh (c+d x)}{7 b d (b \text{csch}(c+d x))^{5/2}}",1,"(Sqrt[b*Csch[c + d*x]]*((40*I)*EllipticF[((-2*I)*c + Pi - (2*I)*d*x)/4, 2]*Sqrt[I*Sinh[c + d*x]] - 26*Sinh[2*(c + d*x)] + 3*Sinh[4*(c + d*x)]))/(84*b^4*d)","A",1
21,1,67,74,0.1041496,"\int (b \text{csch}(c+d x))^n \, dx","Integrate[(b*Csch[c + d*x])^n,x]","-\frac{\sinh (c+d x) \cosh (c+d x) \left(-\sinh ^2(c+d x)\right)^{\frac{n-1}{2}} (b \text{csch}(c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{3}{2};\cosh ^2(c+d x)\right)}{d}","\frac{b \cosh (c+d x) (b \text{csch}(c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};-\sinh ^2(c+d x)\right)}{d (1-n) \sqrt{\cosh ^2(c+d x)}}",1,"-((Cosh[c + d*x]*(b*Csch[c + d*x])^n*Hypergeometric2F1[1/2, (1 + n)/2, 3/2, Cosh[c + d*x]^2]*Sinh[c + d*x]*(-Sinh[c + d*x]^2)^((-1 + n)/2))/d)","A",1
22,1,41,40,0.1241729,"\int \left(-\text{csch}^2(x)\right)^{5/2} \, dx","Integrate[(-Csch[x]^2)^(5/2),x]","\frac{1}{64} \sinh (x) \left(-\text{csch}^2(x)\right)^{5/2} \left(6 \left(\cosh (3 x)+4 \sinh ^4(x) \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)-22 \cosh (x)\right)","\frac{3}{8} \sin ^{-1}(\coth (x))+\frac{1}{4} \coth (x) \left(-\text{csch}^2(x)\right)^{3/2}+\frac{3}{8} \coth (x) \sqrt{-\text{csch}^2(x)}",1,"((-Csch[x]^2)^(5/2)*Sinh[x]*(-22*Cosh[x] + 6*(Cosh[3*x] + 4*Log[Tanh[x/2]]*Sinh[x]^4)))/64","A",1
23,1,41,24,0.0631089,"\int \left(-\text{csch}^2(x)\right)^{3/2} \, dx","Integrate[(-Csch[x]^2)^(3/2),x]","\frac{1}{4} \text{csch}\left(\frac{x}{2}\right) \sqrt{-\text{csch}^2(x)} \text{sech}\left(\frac{x}{2}\right) \left(\cosh (x)+\sinh ^2(x) \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)","\frac{1}{2} \sin ^{-1}(\coth (x))+\frac{1}{2} \coth (x) \sqrt{-\text{csch}^2(x)}",1,"(Csch[x/2]*Sqrt[-Csch[x]^2]*Sech[x/2]*(Cosh[x] + Log[Tanh[x/2]]*Sinh[x]^2))/4","A",1
24,1,20,3,0.005063,"\int \sqrt{-\text{csch}^2(x)} \, dx","Integrate[Sqrt[-Csch[x]^2],x]","\sinh (x) \sqrt{-\text{csch}^2(x)} \log \left(\tanh \left(\frac{x}{2}\right)\right)","\sin ^{-1}(\coth (x))",1,"Sqrt[-Csch[x]^2]*Log[Tanh[x/2]]*Sinh[x]","B",1
25,1,13,13,0.0052967,"\int \frac{1}{\sqrt{-\text{csch}^2(x)}} \, dx","Integrate[1/Sqrt[-Csch[x]^2],x]","\frac{\coth (x)}{\sqrt{-\text{csch}^2(x)}}","\frac{\coth (x)}{\sqrt{-\text{csch}^2(x)}}",1,"Coth[x]/Sqrt[-Csch[x]^2]","A",1
26,1,27,33,0.0147069,"\int \frac{1}{\left(-\text{csch}^2(x)\right)^{3/2}} \, dx","Integrate[(-Csch[x]^2)^(-3/2),x]","\frac{9 \coth (x)-\cosh (3 x) \text{csch}(x)}{12 \sqrt{-\text{csch}^2(x)}}","\frac{2 \coth (x)}{3 \sqrt{-\text{csch}^2(x)}}+\frac{\coth (x)}{3 \left(-\text{csch}^2(x)\right)^{3/2}}",1,"(9*Coth[x] - Cosh[3*x]*Csch[x])/(12*Sqrt[-Csch[x]^2])","A",1
27,1,33,49,0.025344,"\int \frac{1}{\left(-\text{csch}^2(x)\right)^{5/2}} \, dx","Integrate[(-Csch[x]^2)^(-5/2),x]","\frac{(150 \cosh (x)-25 \cosh (3 x)+3 \cosh (5 x)) \text{csch}(x)}{240 \sqrt{-\text{csch}^2(x)}}","\frac{8 \coth (x)}{15 \sqrt{-\text{csch}^2(x)}}+\frac{4 \coth (x)}{15 \left(-\text{csch}^2(x)\right)^{3/2}}+\frac{\coth (x)}{5 \left(-\text{csch}^2(x)\right)^{5/2}}",1,"((150*Cosh[x] - 25*Cosh[3*x] + 3*Cosh[5*x])*Csch[x])/(240*Sqrt[-Csch[x]^2])","A",1
28,1,39,65,0.0365229,"\int \frac{1}{\left(-\text{csch}^2(x)\right)^{7/2}} \, dx","Integrate[(-Csch[x]^2)^(-7/2),x]","\frac{(1225 \cosh (x)-245 \cosh (3 x)+49 \cosh (5 x)-5 \cosh (7 x)) \text{csch}(x)}{2240 \sqrt{-\text{csch}^2(x)}}","\frac{16 \coth (x)}{35 \sqrt{-\text{csch}^2(x)}}+\frac{8 \coth (x)}{35 \left(-\text{csch}^2(x)\right)^{3/2}}+\frac{6 \coth (x)}{35 \left(-\text{csch}^2(x)\right)^{5/2}}+\frac{\coth (x)}{7 \left(-\text{csch}^2(x)\right)^{7/2}}",1,"((1225*Cosh[x] - 245*Cosh[3*x] + 49*Cosh[5*x] - 5*Cosh[7*x])*Csch[x])/(2240*Sqrt[-Csch[x]^2])","A",1
29,1,41,65,0.100278,"\int \left(a \text{csch}^2(x)\right)^{5/2} \, dx","Integrate[(a*Csch[x]^2)^(5/2),x]","\frac{1}{64} \sinh (x) \left(a \text{csch}^2(x)\right)^{5/2} \left(6 \left(\cosh (3 x)+4 \sinh ^4(x) \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)-22 \cosh (x)\right)","-\frac{3}{8} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (x)}{\sqrt{a \text{csch}^2(x)}}\right)+\frac{3}{8} a^2 \coth (x) \sqrt{a \text{csch}^2(x)}-\frac{1}{4} a \coth (x) \left(a \text{csch}^2(x)\right)^{3/2}",1,"((a*Csch[x]^2)^(5/2)*Sinh[x]*(-22*Cosh[x] + 6*(Cosh[3*x] + 4*Log[Tanh[x/2]]*Sinh[x]^4)))/64","A",1
30,1,30,46,0.0682831,"\int \left(a \text{csch}^2(x)\right)^{3/2} \, dx","Integrate[(a*Csch[x]^2)^(3/2),x]","-\frac{1}{2} a \sinh (x) \sqrt{a \text{csch}^2(x)} \left(\log \left(\tanh \left(\frac{x}{2}\right)\right)+\coth (x) \text{csch}(x)\right)","\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (x)}{\sqrt{a \text{csch}^2(x)}}\right)-\frac{1}{2} a \coth (x) \sqrt{a \text{csch}^2(x)}",1,"-1/2*(a*Sqrt[a*Csch[x]^2]*(Coth[x]*Csch[x] + Log[Tanh[x/2]])*Sinh[x])","A",1
31,1,20,26,0.0054837,"\int \sqrt{a \text{csch}^2(x)} \, dx","Integrate[Sqrt[a*Csch[x]^2],x]","\sinh (x) \sqrt{a \text{csch}^2(x)} \log \left(\tanh \left(\frac{x}{2}\right)\right)","-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (x)}{\sqrt{a \text{csch}^2(x)}}\right)",1,"Sqrt[a*Csch[x]^2]*Log[Tanh[x/2]]*Sinh[x]","A",1
32,1,13,13,0.0056005,"\int \frac{1}{\sqrt{a \text{csch}^2(x)}} \, dx","Integrate[1/Sqrt[a*Csch[x]^2],x]","\frac{\coth (x)}{\sqrt{a \text{csch}^2(x)}}","\frac{\coth (x)}{\sqrt{a \text{csch}^2(x)}}",1,"Coth[x]/Sqrt[a*Csch[x]^2]","A",1
33,1,27,36,0.0227728,"\int \frac{1}{\left(a \text{csch}^2(x)\right)^{3/2}} \, dx","Integrate[(a*Csch[x]^2)^(-3/2),x]","\frac{(\cosh (3 x)-9 \cosh (x)) \text{csch}^3(x)}{12 \left(a \text{csch}^2(x)\right)^{3/2}}","\frac{\coth (x)}{3 \left(a \text{csch}^2(x)\right)^{3/2}}-\frac{2 \coth (x)}{3 a \sqrt{a \text{csch}^2(x)}}",1,"((-9*Cosh[x] + Cosh[3*x])*Csch[x]^3)/(12*(a*Csch[x]^2)^(3/2))","A",1
34,1,36,55,0.0283605,"\int \frac{1}{\left(a \text{csch}^2(x)\right)^{5/2}} \, dx","Integrate[(a*Csch[x]^2)^(-5/2),x]","\frac{\sinh (x) (150 \cosh (x)-25 \cosh (3 x)+3 \cosh (5 x)) \sqrt{a \text{csch}^2(x)}}{240 a^3}","\frac{8 \coth (x)}{15 a^2 \sqrt{a \text{csch}^2(x)}}-\frac{4 \coth (x)}{15 a \left(a \text{csch}^2(x)\right)^{3/2}}+\frac{\coth (x)}{5 \left(a \text{csch}^2(x)\right)^{5/2}}",1,"((150*Cosh[x] - 25*Cosh[3*x] + 3*Cosh[5*x])*Sqrt[a*Csch[x]^2]*Sinh[x])/(240*a^3)","A",1
35,1,42,74,0.0563582,"\int \frac{1}{\left(a \text{csch}^2(x)\right)^{7/2}} \, dx","Integrate[(a*Csch[x]^2)^(-7/2),x]","\frac{\sinh (x) (-1225 \cosh (x)+245 \cosh (3 x)-49 \cosh (5 x)+5 \cosh (7 x)) \sqrt{a \text{csch}^2(x)}}{2240 a^4}","-\frac{16 \coth (x)}{35 a^3 \sqrt{a \text{csch}^2(x)}}+\frac{8 \coth (x)}{35 a^2 \left(a \text{csch}^2(x)\right)^{3/2}}-\frac{6 \coth (x)}{35 a \left(a \text{csch}^2(x)\right)^{5/2}}+\frac{\coth (x)}{7 \left(a \text{csch}^2(x)\right)^{7/2}}",1,"((-1225*Cosh[x] + 245*Cosh[3*x] - 49*Cosh[5*x] + 5*Cosh[7*x])*Sqrt[a*Csch[x]^2]*Sinh[x])/(2240*a^4)","A",1
36,1,68,135,0.1767001,"\int \left(a \text{csch}^3(x)\right)^{5/2} \, dx","Integrate[(a*Csch[x]^3)^(5/2),x]","-\frac{2}{585} a^2 \sinh (x) \sqrt{a \text{csch}^3(x)} \left(-231 \cosh (x)+\coth (x) \text{csch}(x) \left(45 \text{csch}^4(x)-55 \text{csch}^2(x)+77\right)+231 \sqrt{i \sinh (x)} E\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)\right)","-\frac{154}{585} a^2 \coth (x) \sqrt{a \text{csch}^3(x)}-\frac{2}{13} a^2 \coth (x) \text{csch}^4(x) \sqrt{a \text{csch}^3(x)}+\frac{22}{117} a^2 \coth (x) \text{csch}^2(x) \sqrt{a \text{csch}^3(x)}+\frac{154}{195} a^2 \sinh (x) \cosh (x) \sqrt{a \text{csch}^3(x)}-\frac{154 i a^2 \sinh ^2(x) E\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right) \sqrt{a \text{csch}^3(x)}}{195 \sqrt{i \sinh (x)}}",1,"(-2*a^2*Sqrt[a*Csch[x]^3]*(-231*Cosh[x] + Coth[x]*Csch[x]*(77 - 55*Csch[x]^2 + 45*Csch[x]^4) + 231*EllipticE[(Pi - (2*I)*x)/4, 2]*Sqrt[I*Sinh[x]])*Sinh[x])/585","A",1
37,1,56,81,0.1205253,"\int \left(a \text{csch}^3(x)\right)^{3/2} \, dx","Integrate[(a*Csch[x]^3)^(3/2),x]","-\frac{2}{21} a \sinh (x) \sqrt{a \text{csch}^3(x)} \left(\coth (x) \left(3 \text{csch}^2(x)-5\right)-5 i \sqrt{i \sinh (x)} F\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)\right)","\frac{10}{21} a \cosh (x) \sqrt{a \text{csch}^3(x)}-\frac{2}{7} a \coth (x) \text{csch}(x) \sqrt{a \text{csch}^3(x)}+\frac{10}{21} i a \sqrt{i \sinh (x)} \sinh (x) F\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right) \sqrt{a \text{csch}^3(x)}",1,"(-2*a*Sqrt[a*Csch[x]^3]*(Coth[x]*(-5 + 3*Csch[x]^2) - (5*I)*EllipticF[(Pi - (2*I)*x)/4, 2]*Sqrt[I*Sinh[x]])*Sinh[x])/21","A",1
38,1,42,56,0.0305314,"\int \sqrt{a \text{csch}^3(x)} \, dx","Integrate[Sqrt[a*Csch[x]^3],x]","-2 \sinh (x) \sqrt{a \text{csch}^3(x)} \left(\cosh (x)-\sqrt{i \sinh (x)} E\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)\right)","-2 \sinh (x) \cosh (x) \sqrt{a \text{csch}^3(x)}-2 i (i \sinh (x))^{3/2} E\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right) \sqrt{a \text{csch}^3(x)}",1,"-2*Sqrt[a*Csch[x]^3]*(Cosh[x] - EllipticE[(Pi - (2*I)*x)/4, 2]*Sqrt[I*Sinh[x]])*Sinh[x]","A",1
39,1,43,62,0.0767284,"\int \frac{1}{\sqrt{a \text{csch}^3(x)}} \, dx","Integrate[1/Sqrt[a*Csch[x]^3],x]","\frac{2 \left(\coth (x)+\frac{\text{csch}(x) F\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)}{\sqrt{i \sinh (x)}}\right)}{3 \sqrt{a \text{csch}^3(x)}}","\frac{2 \coth (x)}{3 \sqrt{a \text{csch}^3(x)}}-\frac{2 i \sqrt{i \sinh (x)} \text{csch}^2(x) F\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right)}{3 \sqrt{a \text{csch}^3(x)}}",1,"(2*(Coth[x] + (Csch[x]*EllipticF[(Pi - (2*I)*x)/4, 2])/Sqrt[I*Sinh[x]]))/(3*Sqrt[a*Csch[x]^3])","A",1
40,1,57,89,0.0775703,"\int \frac{1}{\left(a \text{csch}^3(x)\right)^{3/2}} \, dx","Integrate[(a*Csch[x]^3)^(-3/2),x]","\frac{-33 \cosh (x)+5 \cosh (3 x)+84 \sqrt{i \sinh (x)} \text{csch}^2(x) E\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)}{90 a \sqrt{a \text{csch}^3(x)}}","-\frac{14 \cosh (x)}{45 a \sqrt{a \text{csch}^3(x)}}+\frac{2 \sinh ^2(x) \cosh (x)}{9 a \sqrt{a \text{csch}^3(x)}}+\frac{14 i \text{csch}(x) E\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right)}{15 a \sqrt{i \sinh (x)} \sqrt{a \text{csch}^3(x)}}",1,"(-33*Cosh[x] + 5*Cosh[3*x] + 84*Csch[x]^2*EllipticE[(Pi - (2*I)*x)/4, 2]*Sqrt[I*Sinh[x]])/(90*a*Sqrt[a*Csch[x]^3])","A",1
41,1,71,135,0.1279049,"\int \frac{1}{\left(a \text{csch}^3(x)\right)^{5/2}} \, dx","Integrate[(a*Csch[x]^3)^(-5/2),x]","\frac{\sinh (x) \sqrt{a \text{csch}^3(x)} \left(-19122 \sinh (2 x)+4406 \sinh (4 x)-826 \sinh (6 x)+77 \sinh (8 x)+24960 i \sqrt{i \sinh (x)} F\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)\right)}{73920 a^3}","-\frac{26 \coth (x)}{77 a^2 \sqrt{a \text{csch}^3(x)}}+\frac{2 \sinh ^5(x) \cosh (x)}{15 a^2 \sqrt{a \text{csch}^3(x)}}-\frac{26 \sinh ^3(x) \cosh (x)}{165 a^2 \sqrt{a \text{csch}^3(x)}}+\frac{78 \sinh (x) \cosh (x)}{385 a^2 \sqrt{a \text{csch}^3(x)}}+\frac{26 i \sqrt{i \sinh (x)} \text{csch}^2(x) F\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right)}{77 a^2 \sqrt{a \text{csch}^3(x)}}",1,"(Sqrt[a*Csch[x]^3]*Sinh[x]*((24960*I)*EllipticF[(Pi - (2*I)*x)/4, 2]*Sqrt[I*Sinh[x]] - 19122*Sinh[2*x] + 4406*Sinh[4*x] - 826*Sinh[6*x] + 77*Sinh[8*x]))/(73920*a^3)","A",1
42,1,59,164,0.0515013,"\int \left(a \text{csch}^4(x)\right)^{7/2} \, dx","Integrate[(a*Csch[x]^4)^(7/2),x]","-\frac{a^3 \sinh (x) \cosh (x) \left(231 \text{csch}^{12}(x)-252 \text{csch}^{10}(x)+280 \text{csch}^8(x)-320 \text{csch}^6(x)+384 \text{csch}^4(x)-512 \text{csch}^2(x)+1024\right) \sqrt{a \text{csch}^4(x)}}{3003}","-\frac{1}{13} a^3 \cosh ^2(x) \coth ^{11}(x) \sqrt{a \text{csch}^4(x)}+\frac{6}{11} a^3 \cosh ^2(x) \coth ^9(x) \sqrt{a \text{csch}^4(x)}-\frac{5}{3} a^3 \cosh ^2(x) \coth ^7(x) \sqrt{a \text{csch}^4(x)}+\frac{20}{7} a^3 \cosh ^2(x) \coth ^5(x) \sqrt{a \text{csch}^4(x)}-3 a^3 \cosh ^2(x) \coth ^3(x) \sqrt{a \text{csch}^4(x)}+2 a^3 \cosh ^2(x) \coth (x) \sqrt{a \text{csch}^4(x)}-a^3 \sinh (x) \cosh (x) \sqrt{a \text{csch}^4(x)}",1,"-1/3003*(a^3*Cosh[x]*Sqrt[a*Csch[x]^4]*(1024 - 512*Csch[x]^2 + 384*Csch[x]^4 - 320*Csch[x]^6 + 280*Csch[x]^8 - 252*Csch[x]^10 + 231*Csch[x]^12)*Sinh[x])","A",1
43,1,47,118,0.0316631,"\int \left(a \text{csch}^4(x)\right)^{5/2} \, dx","Integrate[(a*Csch[x]^4)^(5/2),x]","-\frac{1}{315} a^2 \sinh (x) \cosh (x) \left(35 \text{csch}^8(x)-40 \text{csch}^6(x)+48 \text{csch}^4(x)-64 \text{csch}^2(x)+128\right) \sqrt{a \text{csch}^4(x)}","-\frac{1}{9} a^2 \cosh ^2(x) \coth ^7(x) \sqrt{a \text{csch}^4(x)}+\frac{4}{7} a^2 \cosh ^2(x) \coth ^5(x) \sqrt{a \text{csch}^4(x)}-\frac{6}{5} a^2 \cosh ^2(x) \coth ^3(x) \sqrt{a \text{csch}^4(x)}+\frac{4}{3} a^2 \cosh ^2(x) \coth (x) \sqrt{a \text{csch}^4(x)}-a^2 \sinh (x) \cosh (x) \sqrt{a \text{csch}^4(x)}",1,"-1/315*(a^2*Cosh[x]*Sqrt[a*Csch[x]^4]*(128 - 64*Csch[x]^2 + 48*Csch[x]^4 - 40*Csch[x]^6 + 35*Csch[x]^8)*Sinh[x])","A",1
44,1,33,62,0.0190846,"\int \left(a \text{csch}^4(x)\right)^{3/2} \, dx","Integrate[(a*Csch[x]^4)^(3/2),x]","-\frac{1}{15} a \sinh (x) \cosh (x) \left(3 \text{csch}^4(x)-4 \text{csch}^2(x)+8\right) \sqrt{a \text{csch}^4(x)}","-\frac{1}{5} a \cosh ^2(x) \coth ^3(x) \sqrt{a \text{csch}^4(x)}+\frac{2}{3} a \cosh ^2(x) \coth (x) \sqrt{a \text{csch}^4(x)}-a \sinh (x) \cosh (x) \sqrt{a \text{csch}^4(x)}",1,"-1/15*(a*Cosh[x]*Sqrt[a*Csch[x]^4]*(8 - 4*Csch[x]^2 + 3*Csch[x]^4)*Sinh[x])","A",1
45,1,16,16,0.0060106,"\int \sqrt{a \text{csch}^4(x)} \, dx","Integrate[Sqrt[a*Csch[x]^4],x]","\sinh (x) (-\cosh (x)) \sqrt{a \text{csch}^4(x)}","\sinh (x) (-\cosh (x)) \sqrt{a \text{csch}^4(x)}",1,"-(Cosh[x]*Sqrt[a*Csch[x]^4]*Sinh[x])","A",1
46,1,24,36,0.0253977,"\int \frac{1}{\sqrt{a \text{csch}^4(x)}} \, dx","Integrate[1/Sqrt[a*Csch[x]^4],x]","\frac{\coth (x)-x \text{csch}^2(x)}{2 \sqrt{a \text{csch}^4(x)}}","\frac{\coth (x)}{2 \sqrt{a \text{csch}^4(x)}}-\frac{x \text{csch}^2(x)}{2 \sqrt{a \text{csch}^4(x)}}",1,"(Coth[x] - x*Csch[x]^2)/(2*Sqrt[a*Csch[x]^4])","A",1
47,1,38,86,0.039768,"\int \frac{1}{\left(a \text{csch}^4(x)\right)^{3/2}} \, dx","Integrate[(a*Csch[x]^4)^(-3/2),x]","\frac{(-60 x+45 \sinh (2 x)-9 \sinh (4 x)+\sinh (6 x)) \text{csch}^6(x)}{192 \left(a \text{csch}^4(x)\right)^{3/2}}","-\frac{5 x \text{csch}^2(x)}{16 a \sqrt{a \text{csch}^4(x)}}+\frac{5 \coth (x)}{16 a \sqrt{a \text{csch}^4(x)}}+\frac{\sinh ^3(x) \cosh (x)}{6 a \sqrt{a \text{csch}^4(x)}}-\frac{5 \sinh (x) \cosh (x)}{24 a \sqrt{a \text{csch}^4(x)}}",1,"(Csch[x]^6*(-60*x + 45*Sinh[2*x] - 9*Sinh[4*x] + Sinh[6*x]))/(192*(a*Csch[x]^4)^(3/2))","A",1
48,1,55,132,0.1158614,"\int \frac{1}{\left(a \text{csch}^4(x)\right)^{5/2}} \, dx","Integrate[(a*Csch[x]^4)^(-5/2),x]","\frac{\sinh ^2(x) (-2520 x+2100 \sinh (2 x)-600 \sinh (4 x)+150 \sinh (6 x)-25 \sinh (8 x)+2 \sinh (10 x)) \sqrt{a \text{csch}^4(x)}}{10240 a^3}","-\frac{63 x \text{csch}^2(x)}{256 a^2 \sqrt{a \text{csch}^4(x)}}+\frac{63 \coth (x)}{256 a^2 \sqrt{a \text{csch}^4(x)}}+\frac{\sinh ^7(x) \cosh (x)}{10 a^2 \sqrt{a \text{csch}^4(x)}}-\frac{9 \sinh ^5(x) \cosh (x)}{80 a^2 \sqrt{a \text{csch}^4(x)}}+\frac{21 \sinh ^3(x) \cosh (x)}{160 a^2 \sqrt{a \text{csch}^4(x)}}-\frac{21 \sinh (x) \cosh (x)}{128 a^2 \sqrt{a \text{csch}^4(x)}}",1,"(Sqrt[a*Csch[x]^4]*Sinh[x]^2*(-2520*x + 2100*Sinh[2*x] - 600*Sinh[4*x] + 150*Sinh[6*x] - 25*Sinh[8*x] + 2*Sinh[10*x]))/(10240*a^3)","A",1
49,1,54,32,0.1221643,"\int \frac{1}{a+i a \text{csch}(a+b x)} \, dx","Integrate[(a + I*a*Csch[a + b*x])^(-1),x]","-\frac{2 \sinh \left(\frac{1}{2} (a+b x)\right)}{a b \left(\cosh \left(\frac{1}{2} (a+b x)\right)-i \sinh \left(\frac{1}{2} (a+b x)\right)\right)}+\frac{x}{a}+\frac{1}{b}","\frac{x}{a}-\frac{\coth (a+b x)}{b (a+i a \text{csch}(a+b x))}",1,"b^(-1) + x/a - (2*Sinh[(a + b*x)/2])/(a*b*(Cosh[(a + b*x)/2] - I*Sinh[(a + b*x)/2]))","A",1
50,1,54,32,0.1078725,"\int \frac{1}{a-i a \text{csch}(a+b x)} \, dx","Integrate[(a - I*a*Csch[a + b*x])^(-1),x]","-\frac{2 \sinh \left(\frac{1}{2} (a+b x)\right)}{a b \left(\cosh \left(\frac{1}{2} (a+b x)\right)+i \sinh \left(\frac{1}{2} (a+b x)\right)\right)}+\frac{x}{a}+\frac{1}{b}","\frac{x}{a}-\frac{\coth (a+b x)}{b (a-i a \text{csch}(a+b x))}",1,"b^(-1) + x/a - (2*Sinh[(a + b*x)/2])/(a*b*(Cosh[(a + b*x)/2] + I*Sinh[(a + b*x)/2]))","A",1
51,1,136,107,1.4812644,"\int (a+i a \text{csch}(c+d x))^{5/2} \, dx","Integrate[(a + I*a*Csch[c + d*x])^(5/2),x]","\frac{2 a^2 \sqrt{a+i a \text{csch}(c+d x)} \left(\coth (c+d x)+\frac{14 \sinh \left(\frac{1}{2} (c+d x)\right)}{\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)}+\frac{3 (-1)^{3/4} \coth (c+d x) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\text{csch}(c+d x)+i}\right)}{(\text{csch}(c+d x)-i) \sqrt{\text{csch}(c+d x)+i}}-7 i\right)}{3 d}","\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+i a \text{csch}(c+d x)}}\right)}{d}+\frac{14 a^3 \coth (c+d x)}{3 d \sqrt{a+i a \text{csch}(c+d x)}}+\frac{2 a^2 \coth (c+d x) \sqrt{a+i a \text{csch}(c+d x)}}{3 d}",1,"(2*a^2*Sqrt[a + I*a*Csch[c + d*x]]*(-7*I + Coth[c + d*x] + (3*(-1)^(3/4)*ArcTanh[(-1)^(3/4)*Sqrt[I + Csch[c + d*x]]]*Coth[c + d*x])/((-I + Csch[c + d*x])*Sqrt[I + Csch[c + d*x]]) + (14*Sinh[(c + d*x)/2])/(Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2])))/(3*d)","A",1
52,1,100,72,1.2474243,"\int (a+i a \text{csch}(c+d x))^{3/2} \, dx","Integrate[(a + I*a*Csch[c + d*x])^(3/2),x]","-\frac{2 i a \coth (c+d x) \sqrt{a+i a \text{csch}(c+d x)} \left(\sqrt{\text{csch}(c+d x)+i}-\sqrt[4]{-1} \tanh ^{-1}\left((-1)^{3/4} \sqrt{\text{csch}(c+d x)+i}\right)\right)}{d (\text{csch}(c+d x)-i) \sqrt{\text{csch}(c+d x)+i}}","\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+i a \text{csch}(c+d x)}}\right)}{d}+\frac{2 a^2 \coth (c+d x)}{d \sqrt{a+i a \text{csch}(c+d x)}}",1,"((-2*I)*a*Coth[c + d*x]*Sqrt[a + I*a*Csch[c + d*x]]*(-((-1)^(1/4)*ArcTanh[(-1)^(3/4)*Sqrt[I + Csch[c + d*x]]]) + Sqrt[I + Csch[c + d*x]]))/(d*(-I + Csch[c + d*x])*Sqrt[I + Csch[c + d*x]])","A",1
53,1,80,40,0.9349172,"\int \sqrt{a+i a \text{csch}(c+d x)} \, dx","Integrate[Sqrt[a + I*a*Csch[c + d*x]],x]","\frac{2 (-1)^{3/4} \coth (c+d x) \sqrt{a+i a \text{csch}(c+d x)} \tanh ^{-1}\left((-1)^{3/4} \sqrt{\text{csch}(c+d x)+i}\right)}{d (\text{csch}(c+d x)-i) \sqrt{\text{csch}(c+d x)+i}}","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+i a \text{csch}(c+d x)}}\right)}{d}",1,"(2*(-1)^(3/4)*ArcTanh[(-1)^(3/4)*Sqrt[I + Csch[c + d*x]]]*Coth[c + d*x]*Sqrt[a + I*a*Csch[c + d*x]])/(d*(-I + Csch[c + d*x])*Sqrt[I + Csch[c + d*x]])","A",1
54,1,118,91,1.1198339,"\int \frac{1}{\sqrt{a+i a \text{csch}(c+d x)}} \, dx","Integrate[1/Sqrt[a + I*a*Csch[c + d*x]],x]","\frac{\sqrt{a} \coth (c+d x) \left(2 \tan ^{-1}\left(\frac{\sqrt{i a (\text{csch}(c+d x)+i)}}{\sqrt{a}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{i a (\text{csch}(c+d x)+i)}}{\sqrt{2} \sqrt{a}}\right)\right)}{d \sqrt{i a (\text{csch}(c+d x)+i)} \sqrt{a+i a \text{csch}(c+d x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+i a \text{csch}(c+d x)}}\right)}{\sqrt{a} d}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{2} \sqrt{a+i a \text{csch}(c+d x)}}\right)}{\sqrt{a} d}",1,"(Sqrt[a]*(2*ArcTan[Sqrt[I*a*(I + Csch[c + d*x])]/Sqrt[a]] - Sqrt[2]*ArcTan[Sqrt[I*a*(I + Csch[c + d*x])]/(Sqrt[2]*Sqrt[a])])*Coth[c + d*x])/(d*Sqrt[I*a*(I + Csch[c + d*x])]*Sqrt[a + I*a*Csch[c + d*x]])","A",1
55,1,327,123,2.4504418,"\int \frac{1}{(a+i a \text{csch}(c+d x))^{3/2}} \, dx","Integrate[(a + I*a*Csch[c + d*x])^(-3/2),x]","\frac{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left(-8 \sqrt{i a (\text{csch}(c+d x)+i)} \tan ^{-1}\left(\frac{\sqrt{i a (\text{csch}(c+d x)+i)}}{\sqrt{a}}\right)+i \text{csch}(c+d x) \left(-8 \sqrt{i a (\text{csch}(c+d x)+i)} \tan ^{-1}\left(\frac{\sqrt{i a (\text{csch}(c+d x)+i)}}{\sqrt{a}}\right)+5 \sqrt{2} \sqrt{i a (\text{csch}(c+d x)+i)} \tan ^{-1}\left(\frac{\sqrt{i a (\text{csch}(c+d x)+i)}}{\sqrt{2} \sqrt{a}}\right)+2 \sqrt{a}\right)+5 \sqrt{2} \sqrt{i a (\text{csch}(c+d x)+i)} \tan ^{-1}\left(\frac{\sqrt{i a (\text{csch}(c+d x)+i)}}{\sqrt{2} \sqrt{a}}\right)-2 \sqrt{a}\right)}{4 a^{3/2} d (\text{csch}(c+d x)+i) \sqrt{a+i a \text{csch}(c+d x)} \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+i a \text{csch}(c+d x)}}\right)}{a^{3/2} d}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{2} \sqrt{a+i a \text{csch}(c+d x)}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{\coth (c+d x)}{2 d (a+i a \text{csch}(c+d x))^{3/2}}",1,"((-2*Sqrt[a] - 8*ArcTan[Sqrt[I*a*(I + Csch[c + d*x])]/Sqrt[a]]*Sqrt[I*a*(I + Csch[c + d*x])] + 5*Sqrt[2]*ArcTan[Sqrt[I*a*(I + Csch[c + d*x])]/(Sqrt[2]*Sqrt[a])]*Sqrt[I*a*(I + Csch[c + d*x])] + I*Csch[c + d*x]*(2*Sqrt[a] - 8*ArcTan[Sqrt[I*a*(I + Csch[c + d*x])]/Sqrt[a]]*Sqrt[I*a*(I + Csch[c + d*x])] + 5*Sqrt[2]*ArcTan[Sqrt[I*a*(I + Csch[c + d*x])]/(Sqrt[2]*Sqrt[a])]*Sqrt[I*a*(I + Csch[c + d*x])]))*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]))/(4*a^(3/2)*d*(I + Csch[c + d*x])*Sqrt[a + I*a*Csch[c + d*x]]*(Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2]))","B",1
56,1,80,40,1.0086807,"\int \sqrt{a-i a \text{csch}(c+d x)} \, dx","Integrate[Sqrt[a - I*a*Csch[c + d*x]],x]","-\frac{2 (-1)^{3/4} \coth (c+d x) \sqrt{a-i a \text{csch}(c+d x)} \tan ^{-1}\left((-1)^{3/4} \sqrt{\text{csch}(c+d x)-i}\right)}{d \sqrt{\text{csch}(c+d x)-i} (\text{csch}(c+d x)+i)}","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a-i a \text{csch}(c+d x)}}\right)}{d}",1,"(-2*(-1)^(3/4)*ArcTan[(-1)^(3/4)*Sqrt[-I + Csch[c + d*x]]]*Coth[c + d*x]*Sqrt[a - I*a*Csch[c + d*x]])/(d*Sqrt[-I + Csch[c + d*x]]*(I + Csch[c + d*x]))","A",1
57,1,117,91,1.0978567,"\int \frac{1}{\sqrt{a-i a \text{csch}(c+d x)}} \, dx","Integrate[1/Sqrt[a - I*a*Csch[c + d*x]],x]","\frac{\sqrt{a} \coth (c+d x) \left(2 \tan ^{-1}\left(\frac{\sqrt{-i a (\text{csch}(c+d x)-i)}}{\sqrt{a}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{-i a (\text{csch}(c+d x)-i)}}{\sqrt{2} \sqrt{a}}\right)\right)}{d \sqrt{a (-1-i \text{csch}(c+d x))} \sqrt{a-i a \text{csch}(c+d x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a-i a \text{csch}(c+d x)}}\right)}{\sqrt{a} d}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{2} \sqrt{a-i a \text{csch}(c+d x)}}\right)}{\sqrt{a} d}",1,"(Sqrt[a]*(2*ArcTan[Sqrt[(-I)*a*(-I + Csch[c + d*x])]/Sqrt[a]] - Sqrt[2]*ArcTan[Sqrt[(-I)*a*(-I + Csch[c + d*x])]/(Sqrt[2]*Sqrt[a])])*Coth[c + d*x])/(d*Sqrt[a*(-1 - I*Csch[c + d*x])]*Sqrt[a - I*a*Csch[c + d*x]])","A",1
58,1,46,23,0.7360854,"\int \sqrt{3+3 i \text{csch}(x)} \, dx","Integrate[Sqrt[3 + (3*I)*Csch[x]],x]","\frac{2 \sqrt{3} \coth (x) \tan ^{-1}\left(\sqrt{-1+i \text{csch}(x)}\right)}{\sqrt{-1+i \text{csch}(x)} \sqrt{1+i \text{csch}(x)}}","2 \sqrt{3} \tanh ^{-1}\left(\frac{\coth (x)}{\sqrt{1+i \text{csch}(x)}}\right)",1,"(2*Sqrt[3]*ArcTan[Sqrt[-1 + I*Csch[x]]]*Coth[x])/(Sqrt[-1 + I*Csch[x]]*Sqrt[1 + I*Csch[x]])","A",1
59,1,46,23,0.7157381,"\int \sqrt{3-3 i \text{csch}(x)} \, dx","Integrate[Sqrt[3 - (3*I)*Csch[x]],x]","\frac{2 \sqrt{3} \coth (x) \tan ^{-1}\left(\sqrt{-1-i \text{csch}(x)}\right)}{\sqrt{-1-i \text{csch}(x)} \sqrt{1-i \text{csch}(x)}}","2 \sqrt{3} \tanh ^{-1}\left(\frac{\coth (x)}{\sqrt{1-i \text{csch}(x)}}\right)",1,"(2*Sqrt[3]*ArcTan[Sqrt[-1 - I*Csch[x]]]*Coth[x])/(Sqrt[-1 - I*Csch[x]]*Sqrt[1 - I*Csch[x]])","A",1
60,1,46,23,0.6893092,"\int \sqrt{-3+3 i \text{csch}(x)} \, dx","Integrate[Sqrt[-3 + (3*I)*Csch[x]],x]","-\frac{2 \sqrt{3} \coth (x) \tanh ^{-1}\left(\sqrt{1+i \text{csch}(x)}\right)}{\sqrt{-1+i \text{csch}(x)} \sqrt{1+i \text{csch}(x)}}","-2 \sqrt{3} \tan ^{-1}\left(\frac{\coth (x)}{\sqrt{-1+i \text{csch}(x)}}\right)",1,"(-2*Sqrt[3]*ArcTanh[Sqrt[1 + I*Csch[x]]]*Coth[x])/(Sqrt[-1 + I*Csch[x]]*Sqrt[1 + I*Csch[x]])","A",1
61,1,46,23,0.6853137,"\int \sqrt{-3-3 i \text{csch}(x)} \, dx","Integrate[Sqrt[-3 - (3*I)*Csch[x]],x]","-\frac{2 \sqrt{3} \coth (x) \tanh ^{-1}\left(\sqrt{1-i \text{csch}(x)}\right)}{\sqrt{-1-i \text{csch}(x)} \sqrt{1-i \text{csch}(x)}}","-2 \sqrt{3} \tan ^{-1}\left(\frac{\coth (x)}{\sqrt{-1-i \text{csch}(x)}}\right)",1,"(-2*Sqrt[3]*ArcTanh[Sqrt[1 - I*Csch[x]]]*Coth[x])/(Sqrt[-1 - I*Csch[x]]*Sqrt[1 - I*Csch[x]])","A",1
62,1,63,58,0.1503937,"\int \frac{\sinh ^4(x)}{i+\text{csch}(x)} \, dx","Integrate[Sinh[x]^4/(I + Csch[x]),x]","\frac{1}{96} \left(-180 i x+48 i \sinh (2 x)-3 i \sinh (4 x)-168 \cosh (x)+8 \cosh (3 x)+\frac{192 \sinh \left(\frac{x}{2}\right)}{\sinh \left(\frac{x}{2}\right)-i \cosh \left(\frac{x}{2}\right)}\right)","-\frac{15 i x}{8}+\frac{4 \cosh ^3(x)}{3}-4 \cosh (x)-\frac{5}{4} i \sinh ^3(x) \cosh (x)+\frac{15}{8} i \sinh (x) \cosh (x)-\frac{\sinh ^3(x) \cosh (x)}{\text{csch}(x)+i}",1,"((-180*I)*x - 168*Cosh[x] + 8*Cosh[3*x] + (192*Sinh[x/2])/((-I)*Cosh[x/2] + Sinh[x/2]) + (48*I)*Sinh[2*x] - (3*I)*Sinh[4*x])/96","A",1
63,1,56,46,0.1346114,"\int \frac{\sinh ^3(x)}{i+\text{csch}(x)} \, dx","Integrate[Sinh[x]^3/(I + Csch[x]),x]","\frac{1}{12} \left(21 i \cosh (x)-i \cosh (3 x)+3 \left(-6 x+\sinh (2 x)+\frac{8 \sinh \left(\frac{x}{2}\right)}{\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)}\right)\right)","-\frac{3 x}{2}-\frac{4}{3} i \cosh ^3(x)+4 i \cosh (x)+\frac{3}{2} \sinh (x) \cosh (x)-\frac{\sinh ^2(x) \cosh (x)}{\text{csch}(x)+i}",1,"((21*I)*Cosh[x] - I*Cosh[3*x] + 3*(-6*x + (8*Sinh[x/2])/(Cosh[x/2] + I*Sinh[x/2]) + Sinh[2*x]))/12","A",1
64,1,46,36,0.1268439,"\int \frac{\sinh ^2(x)}{i+\text{csch}(x)} \, dx","Integrate[Sinh[x]^2/(I + Csch[x]),x]","\cosh (x)+\frac{1}{4} i \left(6 x-\sinh (2 x)-\frac{8 \sinh \left(\frac{x}{2}\right)}{\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)}\right)","\frac{3 i x}{2}+2 \cosh (x)-\frac{3}{2} i \sinh (x) \cosh (x)-\frac{\sinh (x) \cosh (x)}{\text{csch}(x)+i}",1,"Cosh[x] + (I/4)*(6*x - (8*Sinh[x/2])/(Cosh[x/2] + I*Sinh[x/2]) - Sinh[2*x])","A",1
65,1,35,20,0.0525668,"\int \frac{\sinh (x)}{i+\text{csch}(x)} \, dx","Integrate[Sinh[x]/(I + Csch[x]),x]","x-i \cosh (x)-\frac{2 \sinh \left(\frac{x}{2}\right)}{\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)}","x-2 i \cosh (x)-\frac{\cosh (x)}{\text{csch}(x)+i}",1,"x - I*Cosh[x] - (2*Sinh[x/2])/(Cosh[x/2] + I*Sinh[x/2])","A",1
66,1,27,14,0.0187781,"\int \frac{\text{csch}(x)}{i+\text{csch}(x)} \, dx","Integrate[Csch[x]/(I + Csch[x]),x]","\frac{2 \sinh \left(\frac{x}{2}\right)}{\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)}","\frac{i \coth (x)}{\text{csch}(x)+i}",1,"(2*Sinh[x/2])/(Cosh[x/2] + I*Sinh[x/2])","A",1
67,1,37,17,0.0348166,"\int \frac{\text{csch}^2(x)}{i+\text{csch}(x)} \, dx","Integrate[Csch[x]^2/(I + Csch[x]),x]","\log \left(\tanh \left(\frac{x}{2}\right)\right)-\frac{2 i \sinh \left(\frac{x}{2}\right)}{\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)}","-\tanh ^{-1}(\cosh (x))+\frac{\coth (x)}{\text{csch}(x)+i}",1,"Log[Tanh[x/2]] - ((2*I)*Sinh[x/2])/(Cosh[x/2] + I*Sinh[x/2])","B",1
68,1,70,26,0.1145643,"\int \frac{\text{csch}^3(x)}{i+\text{csch}(x)} \, dx","Integrate[Csch[x]^3/(I + Csch[x]),x]","-\frac{1}{2} \tanh \left(\frac{x}{2}\right)-\frac{1}{2} \coth \left(\frac{x}{2}\right)-i \log \left(\sinh \left(\frac{x}{2}\right)\right)+i \log \left(\cosh \left(\frac{x}{2}\right)\right)-\frac{2 \sinh \left(\frac{x}{2}\right)}{\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)}","-\coth (x)+i \tanh ^{-1}(\cosh (x))-\frac{i \coth (x)}{\text{csch}(x)+i}",1,"-1/2*Coth[x/2] + I*Log[Cosh[x/2]] - I*Log[Sinh[x/2]] - (2*Sinh[x/2])/(Cosh[x/2] + I*Sinh[x/2]) - Tanh[x/2]/2","B",1
69,1,81,37,0.3277725,"\int \frac{\text{csch}^4(x)}{i+\text{csch}(x)} \, dx","Integrate[Csch[x]^4/(I + Csch[x]),x]","\frac{1}{8} \left(4 i \tanh \left(\frac{x}{2}\right)+4 i \coth \left(\frac{x}{2}\right)-\text{csch}^2\left(\frac{x}{2}\right)-\text{sech}^2\left(\frac{x}{2}\right)-12 \log \left(\tanh \left(\frac{x}{2}\right)\right)+\frac{16 \sinh \left(\frac{x}{2}\right)}{\sinh \left(\frac{x}{2}\right)-i \cosh \left(\frac{x}{2}\right)}\right)","2 i \coth (x)+\frac{3}{2} \tanh ^{-1}(\cosh (x))+\frac{\coth (x) \text{csch}^2(x)}{\text{csch}(x)+i}-\frac{3}{2} \coth (x) \text{csch}(x)",1,"((4*I)*Coth[x/2] - Csch[x/2]^2 - 12*Log[Tanh[x/2]] - Sech[x/2]^2 + (16*Sinh[x/2])/((-I)*Cosh[x/2] + Sinh[x/2]) + (4*I)*Tanh[x/2])/8","B",1
70,1,508,109,6.2442387,"\int (a+b \text{csch}(c+d x))^4 \, dx","Integrate[(a + b*Csch[c + d*x])^4,x]","\frac{a^4 (c+d x) \sinh ^4(c+d x) (a+b \text{csch}(c+d x))^4}{d (a \sinh (c+d x)+b)^4}+\frac{2 a b \left(2 a^2-b^2\right) \sinh ^4(c+d x) \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) (a+b \text{csch}(c+d x))^4}{d (a \sinh (c+d x)+b)^4}+\frac{\sinh ^4(c+d x) \text{csch}\left(\frac{1}{2} (c+d x)\right) \left(b^4 \cosh \left(\frac{1}{2} (c+d x)\right)-9 a^2 b^2 \cosh \left(\frac{1}{2} (c+d x)\right)\right) (a+b \text{csch}(c+d x))^4}{3 d (a \sinh (c+d x)+b)^4}+\frac{\sinh ^4(c+d x) \text{sech}\left(\frac{1}{2} (c+d x)\right) \left(b^4 \sinh \left(\frac{1}{2} (c+d x)\right)-9 a^2 b^2 \sinh \left(\frac{1}{2} (c+d x)\right)\right) (a+b \text{csch}(c+d x))^4}{3 d (a \sinh (c+d x)+b)^4}-\frac{b^4 \sinh ^4(c+d x) \coth \left(\frac{1}{2} (c+d x)\right) \text{csch}^2\left(\frac{1}{2} (c+d x)\right) (a+b \text{csch}(c+d x))^4}{24 d (a \sinh (c+d x)+b)^4}+\frac{b^4 \sinh ^4(c+d x) \tanh \left(\frac{1}{2} (c+d x)\right) \text{sech}^2\left(\frac{1}{2} (c+d x)\right) (a+b \text{csch}(c+d x))^4}{24 d (a \sinh (c+d x)+b)^4}-\frac{a b^3 \sinh ^4(c+d x) \text{csch}^2\left(\frac{1}{2} (c+d x)\right) (a+b \text{csch}(c+d x))^4}{2 d (a \sinh (c+d x)+b)^4}-\frac{a b^3 \sinh ^4(c+d x) \text{sech}^2\left(\frac{1}{2} (c+d x)\right) (a+b \text{csch}(c+d x))^4}{2 d (a \sinh (c+d x)+b)^4}","a^4 x-\frac{b^2 \left(17 a^2-2 b^2\right) \coth (c+d x)}{3 d}-\frac{2 a b \left(2 a^2-b^2\right) \tanh ^{-1}(\cosh (c+d x))}{d}-\frac{4 a b^3 \coth (c+d x) \text{csch}(c+d x)}{3 d}-\frac{b^2 \coth (c+d x) (a+b \text{csch}(c+d x))^2}{3 d}",1,"(a^4*(c + d*x)*(a + b*Csch[c + d*x])^4*Sinh[c + d*x]^4)/(d*(b + a*Sinh[c + d*x])^4) + ((-9*a^2*b^2*Cosh[(c + d*x)/2] + b^4*Cosh[(c + d*x)/2])*Csch[(c + d*x)/2]*(a + b*Csch[c + d*x])^4*Sinh[c + d*x]^4)/(3*d*(b + a*Sinh[c + d*x])^4) - (a*b^3*Csch[(c + d*x)/2]^2*(a + b*Csch[c + d*x])^4*Sinh[c + d*x]^4)/(2*d*(b + a*Sinh[c + d*x])^4) - (b^4*Coth[(c + d*x)/2]*Csch[(c + d*x)/2]^2*(a + b*Csch[c + d*x])^4*Sinh[c + d*x]^4)/(24*d*(b + a*Sinh[c + d*x])^4) + (2*a*b*(2*a^2 - b^2)*(a + b*Csch[c + d*x])^4*Log[Tanh[(c + d*x)/2]]*Sinh[c + d*x]^4)/(d*(b + a*Sinh[c + d*x])^4) - (a*b^3*(a + b*Csch[c + d*x])^4*Sech[(c + d*x)/2]^2*Sinh[c + d*x]^4)/(2*d*(b + a*Sinh[c + d*x])^4) + ((a + b*Csch[c + d*x])^4*Sech[(c + d*x)/2]*(-9*a^2*b^2*Sinh[(c + d*x)/2] + b^4*Sinh[(c + d*x)/2])*Sinh[c + d*x]^4)/(3*d*(b + a*Sinh[c + d*x])^4) + (b^4*(a + b*Csch[c + d*x])^4*Sech[(c + d*x)/2]^2*Sinh[c + d*x]^4*Tanh[(c + d*x)/2])/(24*d*(b + a*Sinh[c + d*x])^4)","B",1
71,1,118,75,0.8718208,"\int (a+b \text{csch}(c+d x))^3 \, dx","Integrate[(a + b*Csch[c + d*x])^3,x]","-\frac{-8 a^3 c-8 a^3 d x-24 a^2 b \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+12 a b^2 \tanh \left(\frac{1}{2} (c+d x)\right)+12 a b^2 \coth \left(\frac{1}{2} (c+d x)\right)+b^3 \text{csch}^2\left(\frac{1}{2} (c+d x)\right)+b^3 \text{sech}^2\left(\frac{1}{2} (c+d x)\right)+4 b^3 \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{8 d}","a^3 x-\frac{b \left(6 a^2-b^2\right) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{5 a b^2 \coth (c+d x)}{2 d}-\frac{b^2 \coth (c+d x) (a+b \text{csch}(c+d x))}{2 d}",1,"-1/8*(-8*a^3*c - 8*a^3*d*x + 12*a*b^2*Coth[(c + d*x)/2] + b^3*Csch[(c + d*x)/2]^2 - 24*a^2*b*Log[Tanh[(c + d*x)/2]] + 4*b^3*Log[Tanh[(c + d*x)/2]] + b^3*Sech[(c + d*x)/2]^2 + 12*a*b^2*Tanh[(c + d*x)/2])/d","A",1
72,1,61,34,0.2215231,"\int (a+b \text{csch}(c+d x))^2 \, dx","Integrate[(a + b*Csch[c + d*x])^2,x]","-\frac{-2 a \left(a c+a d x+2 b \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)\right)+b^2 \tanh \left(\frac{1}{2} (c+d x)\right)+b^2 \coth \left(\frac{1}{2} (c+d x)\right)}{2 d}","a^2 x-\frac{2 a b \tanh ^{-1}(\cosh (c+d x))}{d}-\frac{b^2 \coth (c+d x)}{d}",1,"-1/2*(b^2*Coth[(c + d*x)/2] - 2*a*(a*c + a*d*x + 2*b*Log[Tanh[(c + d*x)/2]]) + b^2*Tanh[(c + d*x)/2])/d","A",1
73,1,43,17,0.0111346,"\int (a+b \text{csch}(c+d x)) \, dx","Integrate[a + b*Csch[c + d*x],x]","a x+\frac{b \log \left(\sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{d}-\frac{b \log \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{d}","a x-\frac{b \tanh ^{-1}(\cosh (c+d x))}{d}",1,"a*x - (b*Log[Cosh[c/2 + (d*x)/2]])/d + (b*Log[Sinh[c/2 + (d*x)/2]])/d","B",1
74,1,64,54,0.1091251,"\int \frac{1}{a+b \text{csch}(c+d x)} \, dx","Integrate[(a + b*Csch[c + d*x])^(-1),x]","\frac{-\frac{2 b \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{d \sqrt{-a^2-b^2}}+\frac{c}{d}+x}{a}","\frac{2 b \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a d \sqrt{a^2+b^2}}+\frac{x}{a}",1,"(c/d + x - (2*b*ArcTan[(a - b*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d))/a","A",1
75,1,142,101,0.3937245,"\int \frac{1}{(a+b \text{csch}(c+d x))^2} \, dx","Integrate[(a + b*Csch[c + d*x])^(-2),x]","\frac{\text{csch}(c+d x) (a \sinh (c+d x)+b) \left(-\frac{a b^2 \coth (c+d x)}{a^2+b^2}+\frac{2 b \left(2 a^2+b^2\right) (a+b \text{csch}(c+d x)) \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}+(c+d x) (a+b \text{csch}(c+d x))\right)}{a^2 d (a+b \text{csch}(c+d x))^2}","\frac{2 b \left(2 a^2+b^2\right) \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a^2 d \left(a^2+b^2\right)^{3/2}}-\frac{b^2 \coth (c+d x)}{a d \left(a^2+b^2\right) (a+b \text{csch}(c+d x))}+\frac{x}{a^2}",1,"(Csch[c + d*x]*(-((a*b^2*Coth[c + d*x])/(a^2 + b^2)) + (c + d*x)*(a + b*Csch[c + d*x]) + (2*b*(2*a^2 + b^2)*ArcTan[(a - b*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]]*(a + b*Csch[c + d*x]))/(-a^2 - b^2)^(3/2))*(b + a*Sinh[c + d*x]))/(a^2*d*(a + b*Csch[c + d*x])^2)","A",1
76,1,213,163,0.930414,"\int \frac{1}{(a+b \text{csch}(c+d x))^3} \, dx","Integrate[(a + b*Csch[c + d*x])^(-3),x]","\frac{\text{csch}^2(c+d x) (a \sinh (c+d x)+b) \left(-\frac{3 a b^2 \left(2 a^2+b^2\right) \coth (c+d x) (a \sinh (c+d x)+b)}{\left(a^2+b^2\right)^2}+\frac{a b^3 \coth (c+d x)}{a^2+b^2}-\frac{2 b \left(6 a^4+5 a^2 b^2+2 b^4\right) \text{csch}(c+d x) (a \sinh (c+d x)+b)^2 \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{5/2}}+2 (c+d x) \text{csch}(c+d x) (a \sinh (c+d x)+b)^2\right)}{2 a^3 d (a+b \text{csch}(c+d x))^3}","\frac{x}{a^3}-\frac{b^2 \left(5 a^2+2 b^2\right) \coth (c+d x)}{2 a^2 d \left(a^2+b^2\right)^2 (a+b \text{csch}(c+d x))}-\frac{b^2 \coth (c+d x)}{2 a d \left(a^2+b^2\right) (a+b \text{csch}(c+d x))^2}+\frac{b \left(6 a^4+5 a^2 b^2+2 b^4\right) \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a^3 d \left(a^2+b^2\right)^{5/2}}",1,"(Csch[c + d*x]^2*(b + a*Sinh[c + d*x])*((a*b^3*Coth[c + d*x])/(a^2 + b^2) - (3*a*b^2*(2*a^2 + b^2)*Coth[c + d*x]*(b + a*Sinh[c + d*x]))/(a^2 + b^2)^2 + 2*(c + d*x)*Csch[c + d*x]*(b + a*Sinh[c + d*x])^2 - (2*b*(6*a^4 + 5*a^2*b^2 + 2*b^4)*ArcTan[(a - b*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]]*Csch[c + d*x]*(b + a*Sinh[c + d*x])^2)/(-a^2 - b^2)^(5/2)))/(2*a^3*d*(a + b*Csch[c + d*x])^3)","A",1
77,1,104,107,0.4299707,"\int \frac{\sinh ^3(x)}{a+b \text{csch}(x)} \, dx","Integrate[Sinh[x]^3/(a + b*Csch[x]),x]","\frac{\left(12 a b^2-9 a^3\right) \cosh (x)+a^3 \cosh (3 x)+3 b \left(\frac{8 b^3 \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+2 a^2 x-a^2 \sinh (2 x)-4 b^2 x\right)}{12 a^4}","-\frac{b \sinh (x) \cosh (x)}{2 a^2}+\frac{b x \left(a^2-2 b^2\right)}{2 a^4}-\frac{2 b^4 \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^4 \sqrt{a^2+b^2}}-\frac{\left(2 a^2-3 b^2\right) \cosh (x)}{3 a^3}+\frac{\sinh ^2(x) \cosh (x)}{3 a}",1,"((-9*a^3 + 12*a*b^2)*Cosh[x] + a^3*Cosh[3*x] + 3*b*(2*a^2*x - 4*b^2*x + (8*b^3*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - a^2*Sinh[2*x]))/(12*a^4)","A",1
78,1,82,80,0.132298,"\int \frac{\sinh ^2(x)}{a+b \text{csch}(x)} \, dx","Integrate[Sinh[x]^2/(a + b*Csch[x]),x]","\frac{-\frac{8 b^3 \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-2 a^2 x+a^2 \sinh (2 x)-4 a b \cosh (x)+4 b^2 x}{4 a^3}","-\frac{b \cosh (x)}{a^2}-\frac{x \left(a^2-2 b^2\right)}{2 a^3}+\frac{2 b^3 \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^3 \sqrt{a^2+b^2}}+\frac{\sinh (x) \cosh (x)}{2 a}",1,"(-2*a^2*x + 4*b^2*x - (8*b^3*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Cosh[x] + a^2*Sinh[2*x])/(4*a^3)","A",1
79,1,61,57,0.1060894,"\int \frac{\sinh (x)}{a+b \text{csch}(x)} \, dx","Integrate[Sinh[x]/(a + b*Csch[x]),x]","\frac{b \left(\frac{2 b \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-x\right)+a \cosh (x)}{a^2}","-\frac{2 b^2 \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^2 \sqrt{a^2+b^2}}-\frac{b x}{a^2}+\frac{\cosh (x)}{a}",1,"(b*(-x + (2*b*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2]) + a*Cosh[x])/a^2","A",1
80,1,45,37,0.0255748,"\int \frac{\text{csch}(x)}{a+b \text{csch}(x)} \, dx","Integrate[Csch[x]/(a + b*Csch[x]),x]","\frac{2 \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}","-\frac{2 \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}",1,"(2*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2]","A",1
81,1,58,50,0.0509289,"\int \frac{\text{csch}^2(x)}{a+b \text{csch}(x)} \, dx","Integrate[Csch[x]^2/(a + b*Csch[x]),x]","\frac{\log \left(\tanh \left(\frac{x}{2}\right)\right)-\frac{2 a \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}}{b}","\frac{2 a \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b \sqrt{a^2+b^2}}-\frac{\tanh ^{-1}(\cosh (x))}{b}",1,"((-2*a*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + Log[Tanh[x/2]])/b","A",1
82,1,71,59,0.2894902,"\int \frac{\text{csch}^3(x)}{a+b \text{csch}(x)} \, dx","Integrate[Csch[x]^3/(a + b*Csch[x]),x]","\frac{\frac{4 a^2 \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-2 a \log \left(\tanh \left(\frac{x}{2}\right)\right)-2 b \coth (x)}{2 b^2}","-\frac{2 a^2 \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^2 \sqrt{a^2+b^2}}+\frac{a \tanh ^{-1}(\cosh (x))}{b^2}-\frac{\coth (x)}{b}",1,"((4*a^2*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 2*b*Coth[x] - 2*a*Log[Tanh[x/2]])/(2*b^2)","A",1
83,1,124,83,0.4811123,"\int \frac{\text{csch}^4(x)}{a+b \text{csch}(x)} \, dx","Integrate[Csch[x]^4/(a + b*Csch[x]),x]","-\frac{-8 a^2 \log \left(\tanh \left(\frac{x}{2}\right)\right)+\frac{16 a^3 \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-4 a b \tanh \left(\frac{x}{2}\right)-4 a b \coth \left(\frac{x}{2}\right)+b^2 \text{csch}^2\left(\frac{x}{2}\right)+b^2 \text{sech}^2\left(\frac{x}{2}\right)+4 b^2 \log \left(\tanh \left(\frac{x}{2}\right)\right)}{8 b^3}","-\frac{\left(2 a^2-b^2\right) \tanh ^{-1}(\cosh (x))}{2 b^3}+\frac{2 a^3 \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^3 \sqrt{a^2+b^2}}+\frac{a \coth (x)}{b^2}-\frac{\coth (x) \text{csch}(x)}{2 b}",1,"-1/8*((16*a^3*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Coth[x/2] + b^2*Csch[x/2]^2 - 8*a^2*Log[Tanh[x/2]] + 4*b^2*Log[Tanh[x/2]] + b^2*Sech[x/2]^2 - 4*a*b*Tanh[x/2])/b^3","A",1
84,1,32,38,0.0340562,"\int \frac{\cosh ^4(x)}{i+\text{csch}(x)} \, dx","Integrate[Cosh[x]^4/(I + Csch[x]),x]","\frac{i x}{8}-\frac{1}{32} i \sinh (4 x)+\frac{\cosh (x)}{4}+\frac{1}{12} \cosh (3 x)","\frac{i x}{8}+\frac{\cosh ^3(x)}{3}-\frac{1}{4} i \sinh (x) \cosh ^3(x)+\frac{1}{8} i \sinh (x) \cosh (x)",1,"(I/8)*x + Cosh[x]/4 + Cosh[3*x]/12 - (I/32)*Sinh[4*x]","A",1
85,1,19,19,0.0102314,"\int \frac{\cosh ^3(x)}{i+\text{csch}(x)} \, dx","Integrate[Cosh[x]^3/(I + Csch[x]),x]","\frac{\sinh ^2(x)}{2}-\frac{1}{3} i \sinh ^3(x)","\frac{\sinh ^2(x)}{2}-\frac{1}{3} i \sinh ^3(x)",1,"Sinh[x]^2/2 - (I/3)*Sinh[x]^3","A",1
86,1,20,20,0.0306241,"\int \frac{\cosh ^2(x)}{i+\text{csch}(x)} \, dx","Integrate[Cosh[x]^2/(I + Csch[x]),x]","\frac{i x}{2}-\frac{1}{4} i \sinh (2 x)+\cosh (x)","\frac{i x}{2}+\cosh (x)-\frac{1}{2} i \sinh (x) \cosh (x)",1,"(I/2)*x + Cosh[x] - (I/4)*Sinh[2*x]","A",1
87,1,16,16,0.0099825,"\int \frac{\cosh (x)}{i+\text{csch}(x)} \, dx","Integrate[Cosh[x]/(I + Csch[x]),x]","\log (-\sinh (x)+i)-i \sinh (x)","\log (-\sinh (x)+i)-i \sinh (x)",1,"Log[I - Sinh[x]] - I*Sinh[x]","A",1
88,1,20,28,0.0294443,"\int \frac{\text{sech}(x)}{i+\text{csch}(x)} \, dx","Integrate[Sech[x]/(I + Csch[x]),x]","-\frac{1}{2} i \left(\tan ^{-1}(\sinh (x))+\frac{1}{-\sinh (x)+i}\right)","-\frac{1}{2} \text{sech}^2(x)-\frac{1}{2} i \tan ^{-1}(\sinh (x))+\frac{1}{2} i \tanh (x) \text{sech}(x)",1,"(-1/2*I)*(ArcTan[Sinh[x]] + (I - Sinh[x])^(-1))","A",1
89,1,64,19,0.0561211,"\int \frac{\text{sech}^2(x)}{i+\text{csch}(x)} \, dx","Integrate[Sech[x]^2/(I + Csch[x]),x]","\frac{-2 i \sinh (x)+\cosh (x)+\cosh (2 x)+i \sinh (x) \cosh (x)-3}{6 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right) \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^3}","-\frac{1}{3} \text{sech}^3(x)-\frac{1}{3} i \tanh ^3(x)",1,"(-3 + Cosh[x] + Cosh[2*x] - (2*I)*Sinh[x] + I*Cosh[x]*Sinh[x])/(6*(Cosh[x/2] - I*Sinh[x/2])*(Cosh[x/2] + I*Sinh[x/2])^3)","B",1
90,1,32,40,0.0623396,"\int \frac{\text{sech}^3(x)}{i+\text{csch}(x)} \, dx","Integrate[Sech[x]^3/(I + Csch[x]),x]","\frac{1}{8} \left(-\frac{i}{\sinh (x)+i}+\frac{1}{(\sinh (x)-i)^2}-i \tan ^{-1}(\sinh (x))\right)","-\frac{1}{4} \text{sech}^4(x)-\frac{1}{8} i \tan ^{-1}(\sinh (x))+\frac{1}{4} i \tanh (x) \text{sech}^3(x)-\frac{1}{8} i \tanh (x) \text{sech}(x)",1,"((-I)*ArcTan[Sinh[x]] + (-I + Sinh[x])^(-2) - I/(I + Sinh[x]))/8","A",1
91,1,96,29,0.1107593,"\int \frac{\text{sech}^4(x)}{i+\text{csch}(x)} \, dx","Integrate[Sech[x]^4/(I + Csch[x]),x]","\frac{-96 i \sinh (x)+18 i \sinh (2 x)-32 i \sinh (3 x)+9 i \sinh (4 x)+54 \cosh (x)+32 \cosh (2 x)+18 \cosh (3 x)+16 \cosh (4 x)-240}{960 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^3 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^5}","\frac{1}{5} i \tanh ^5(x)-\frac{1}{3} i \tanh ^3(x)-\frac{1}{5} \text{sech}^5(x)",1,"(-240 + 54*Cosh[x] + 32*Cosh[2*x] + 18*Cosh[3*x] + 16*Cosh[4*x] - (96*I)*Sinh[x] + (18*I)*Sinh[2*x] - (32*I)*Sinh[3*x] + (9*I)*Sinh[4*x])/(960*(Cosh[x/2] - I*Sinh[x/2])^3*(Cosh[x/2] + I*Sinh[x/2])^5)","B",1
92,1,97,102,0.287018,"\int \frac{\cosh ^5(x)}{a+b \text{csch}(x)} \, dx","Integrate[Cosh[x]^5/(a + b*Csch[x]),x]","\frac{12 a^5 \sinh ^5(x)-15 a^4 b \sinh ^4(x)-30 a^2 b \left(2 a^2+b^2\right) \sinh ^2(x)+60 a \left(a^2+b^2\right)^2 \sinh (x)-60 b \left(a^2+b^2\right)^2 \log (a \sinh (x)+b)+20 a^3 \left(2 a^2+b^2\right) \sinh ^3(x)}{60 a^6}","-\frac{b \sinh ^4(x)}{4 a^2}-\frac{b \left(a^2+b^2\right)^2 \log (a \sinh (x)+b)}{a^6}+\frac{\left(a^2+b^2\right)^2 \sinh (x)}{a^5}-\frac{b \left(2 a^2+b^2\right) \sinh ^2(x)}{2 a^4}+\frac{\left(2 a^2+b^2\right) \sinh ^3(x)}{3 a^3}+\frac{\sinh ^5(x)}{5 a}",1,"(-60*b*(a^2 + b^2)^2*Log[b + a*Sinh[x]] + 60*a*(a^2 + b^2)^2*Sinh[x] - 30*a^2*b*(2*a^2 + b^2)*Sinh[x]^2 + 20*a^3*(2*a^2 + b^2)*Sinh[x]^3 - 15*a^4*b*Sinh[x]^4 + 12*a^5*Sinh[x]^5)/(60*a^6)","A",1
93,1,180,125,1.2065472,"\int \frac{\cosh ^4(x)}{a+b \text{csch}(x)} \, dx","Integrate[Cosh[x]^4/(a + b*Csch[x]),x]","\frac{-8 a^3 b \cosh (3 x)-24 a b \left(5 a^2+4 b^2\right) \cosh (x)+3 \left(12 a^4 x+a^4 \sinh (4 x)+48 a^2 b^2 x+8 a^2 \left(a^2+b^2\right) \sinh (2 x)+64 a^2 b \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)+64 b^3 \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)+32 b^4 x\right)}{96 a^5}","-\frac{\cosh ^3(x) (4 b-3 a \sinh (x))}{12 a^2}+\frac{2 b \left(a^2+b^2\right)^{3/2} \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^5}-\frac{\cosh (x) \left(8 b \left(a^2+b^2\right)-a \left(3 a^2+4 b^2\right) \sinh (x)\right)}{8 a^4}+\frac{x \left(3 a^4+12 a^2 b^2+8 b^4\right)}{8 a^5}",1,"(-24*a*b*(5*a^2 + 4*b^2)*Cosh[x] - 8*a^3*b*Cosh[3*x] + 3*(12*a^4*x + 48*a^2*b^2*x + 32*b^4*x + 64*a^2*b*Sqrt[-a^2 - b^2]*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]] + 64*b^3*Sqrt[-a^2 - b^2]*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]] + 8*a^2*(a^2 + b^2)*Sinh[2*x] + a^4*Sinh[4*x]))/(96*a^5)","A",1
94,1,56,57,0.1108395,"\int \frac{\cosh ^3(x)}{a+b \text{csch}(x)} \, dx","Integrate[Cosh[x]^3/(a + b*Csch[x]),x]","\frac{2 a^3 \sinh ^3(x)+6 a \left(a^2+b^2\right) \sinh (x)-6 b \left(a^2+b^2\right) \log (a \sinh (x)+b)-3 a^2 b \sinh ^2(x)}{6 a^4}","-\frac{b \sinh ^2(x)}{2 a^2}-\frac{b \left(a^2+b^2\right) \log (a \sinh (x)+b)}{a^4}+\frac{\left(a^2+b^2\right) \sinh (x)}{a^3}+\frac{\sinh ^3(x)}{3 a}",1,"(-6*b*(a^2 + b^2)*Log[b + a*Sinh[x]] + 6*a*(a^2 + b^2)*Sinh[x] - 3*a^2*b*Sinh[x]^2 + 2*a^3*Sinh[x]^3)/(6*a^4)","A",1
95,1,80,77,0.2225951,"\int \frac{\cosh ^2(x)}{a+b \text{csch}(x)} \, dx","Integrate[Cosh[x]^2/(a + b*Csch[x]),x]","\frac{8 b \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)+2 a^2 x+a^2 \sinh (2 x)-4 a b \cosh (x)+4 b^2 x}{4 a^3}","-\frac{\cosh (x) (2 b-a \sinh (x))}{2 a^2}+\frac{x \left(a^2+2 b^2\right)}{2 a^3}+\frac{2 b \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^3}",1,"(2*a^2*x + 4*b^2*x + 8*b*Sqrt[-a^2 - b^2]*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]] - 4*a*b*Cosh[x] + a^2*Sinh[2*x])/(4*a^3)","A",1
96,1,19,20,0.0131799,"\int \frac{\cosh (x)}{a+b \text{csch}(x)} \, dx","Integrate[Cosh[x]/(a + b*Csch[x]),x]","\frac{a \sinh (x)-b \log (a \sinh (x)+b)}{a^2}","\frac{\sinh (x)}{a}-\frac{b \log (a \sinh (x)+b)}{a^2}",1,"(-(b*Log[b + a*Sinh[x]]) + a*Sinh[x])/a^2","A",1
97,1,36,64,0.0589489,"\int \frac{\text{sech}(x)}{a+b \text{csch}(x)} \, dx","Integrate[Sech[x]/(a + b*Csch[x]),x]","\frac{-b \log (a \sinh (x)+b)+2 a \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+b \log (\cosh (x))}{a^2+b^2}","-\frac{b \log (a \sinh (x)+b)}{a^2+b^2}+\frac{\log (-\sinh (x)+i)}{2 (b+i a)}-\frac{\log (\sinh (x)+i)}{2 (-b+i a)}",1,"(2*a*ArcTan[Tanh[x/2]] + b*Log[Cosh[x]] - b*Log[b + a*Sinh[x]])/(a^2 + b^2)","A",1
98,1,67,60,0.1844431,"\int \frac{\text{sech}^2(x)}{a+b \text{csch}(x)} \, dx","Integrate[Sech[x]^2/(a + b*Csch[x]),x]","\frac{a \left(\tanh (x)-\frac{2 b \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}\right)-b \text{sech}(x)}{a^2+b^2}","\frac{2 a b \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{3/2}}-\frac{\text{sech}(x) (b-a \sinh (x))}{a^2+b^2}",1,"(-(b*Sech[x]) + a*((-2*b*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + Tanh[x]))/(a^2 + b^2)","A",1
99,1,78,95,0.1559614,"\int \frac{\text{sech}^3(x)}{a+b \text{csch}(x)} \, dx","Integrate[Sech[x]^3/(a + b*Csch[x]),x]","\frac{-b \left(a^2+b^2\right) \text{sech}^2(x)+a \left(a^2+b^2\right) \tanh (x) \text{sech}(x)+2 a \left(\left(a^2-b^2\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+a b (\log (\cosh (x))-\log (a \sinh (x)+b))\right)}{2 \left(a^2+b^2\right)^2}","-\frac{a^2 b \log (a \sinh (x)+b)}{\left(a^2+b^2\right)^2}-\frac{\text{sech}^2(x) (b-a \sinh (x))}{2 \left(a^2+b^2\right)}-\frac{i a \log (-\sinh (x)+i)}{4 (a-i b)^2}+\frac{i a \log (\sinh (x)+i)}{4 (a+i b)^2}",1,"(2*a*((a^2 - b^2)*ArcTan[Tanh[x/2]] + a*b*(Log[Cosh[x]] - Log[b + a*Sinh[x]])) - b*(a^2 + b^2)*Sech[x]^2 + a*(a^2 + b^2)*Sech[x]*Tanh[x])/(2*(a^2 + b^2)^2)","A",1
100,1,114,104,0.6294411,"\int \frac{\text{sech}^4(x)}{a+b \text{csch}(x)} \, dx","Integrate[Sech[x]^4/(a + b*Csch[x]),x]","-\frac{\left(a b^2-2 a^3\right) \tanh (x)+b \left(a^2+b^2\right) \text{sech}^3(x)-a \left(a^2+b^2\right) \tanh (x) \text{sech}^2(x)+3 a^2 b \text{sech}(x)+\frac{6 a^3 b \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}}{3 \left(a^2+b^2\right)^2}","-\frac{\text{sech}^3(x) (b-a \sinh (x))}{3 \left(a^2+b^2\right)}-\frac{\text{sech}(x) \left(3 a^2 b-a \left(2 a^2-b^2\right) \sinh (x)\right)}{3 \left(a^2+b^2\right)^2}+\frac{2 a^3 b \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{5/2}}",1,"-1/3*((6*a^3*b*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + 3*a^2*b*Sech[x] + b*(a^2 + b^2)*Sech[x]^3 + (-2*a^3 + a*b^2)*Tanh[x] - a*(a^2 + b^2)*Sech[x]^2*Tanh[x])/(a^2 + b^2)^2","A",1
101,1,138,149,0.283939,"\int \frac{\text{sech}^5(x)}{a+b \text{csch}(x)} \, dx","Integrate[Sech[x]^5/(a + b*Csch[x]),x]","\frac{8 a^4 b (\log (\cosh (x))-\log (a \sinh (x)+b))-2 b \left(a^2+b^2\right)^2 \text{sech}^4(x)-4 a^2 b \left(a^2+b^2\right) \text{sech}^2(x)+2 a \left(a^2+b^2\right)^2 \tanh (x) \text{sech}^3(x)+2 a \left(3 a^4-6 a^2 b^2-b^4\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+a \left(3 a^4+2 a^2 b^2-b^4\right) \tanh (x) \text{sech}(x)}{8 \left(a^2+b^2\right)^3}","-\frac{\text{sech}^4(x) (b-a \sinh (x))}{4 \left(a^2+b^2\right)}-\frac{\text{sech}^2(x) \left(4 a^2 b-a \left(3 a^2-b^2\right) \sinh (x)\right)}{8 \left(a^2+b^2\right)^2}-\frac{a^4 b \log (a \sinh (x)+b)}{\left(a^2+b^2\right)^3}-\frac{a (b+3 i a) \log (-\sinh (x)+i)}{16 (a-i b)^3}+\frac{a (3 a+i b) \log (\sinh (x)+i)}{16 (-b+i a)^3}",1,"(2*a*(3*a^4 - 6*a^2*b^2 - b^4)*ArcTan[Tanh[x/2]] + 8*a^4*b*(Log[Cosh[x]] - Log[b + a*Sinh[x]]) - 4*a^2*b*(a^2 + b^2)*Sech[x]^2 - 2*b*(a^2 + b^2)^2*Sech[x]^4 + a*(3*a^4 + 2*a^2*b^2 - b^4)*Sech[x]*Tanh[x] + 2*a*(a^2 + b^2)^2*Sech[x]^3*Tanh[x])/(8*(a^2 + b^2)^3)","A",1
102,1,75,109,0.203433,"\int \frac{\tanh ^5(x)}{i+\text{csch}(x)} \, dx","Integrate[Tanh[x]^5/(I + Csch[x]),x]","\frac{1}{96} \left(-\frac{2 \left(33 \sinh ^4(x)+39 i \sinh ^3(x)+79 \sinh ^2(x)+29 i \sinh (x)+44\right)}{(\sinh (x)-i)^3 (\sinh (x)+i)^2}-63 i \log (-\sinh (x)+i)-33 i \log (\sinh (x)+i)\right)","-\frac{i}{4 (1-i \sinh (x))}-\frac{15 i}{16 (1+i \sinh (x))}+\frac{i}{32 (1-i \sinh (x))^2}+\frac{9 i}{32 (1+i \sinh (x))^2}-\frac{i}{24 (1+i \sinh (x))^3}-\frac{21}{32} i \log (-\sinh (x)+i)-\frac{11}{32} i \log (\sinh (x)+i)",1,"((-63*I)*Log[I - Sinh[x]] - (33*I)*Log[I + Sinh[x]] - (2*(44 + (29*I)*Sinh[x] + 79*Sinh[x]^2 + (39*I)*Sinh[x]^3 + 33*Sinh[x]^4))/((-I + Sinh[x])^3*(I + Sinh[x])^2))/96","A",1
103,1,126,52,0.1354473,"\int \frac{\tanh ^4(x)}{i+\text{csch}(x)} \, dx","Integrate[Tanh[x]^4/(I + Csch[x]),x]","\frac{64 i \sinh (x)+240 x \sinh (2 x)+178 i \sinh (2 x)+128 i \sinh (3 x)+120 x \sinh (4 x)+89 i \sinh (4 x)+6 (89-120 i x) \cosh (x)-128 \cosh (2 x)-240 i x \cosh (3 x)+178 \cosh (3 x)-184 \cosh (4 x)-200}{960 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^3 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^5}","-i x+\frac{1}{5} \tanh ^5(x) (-\text{csch}(x)+i)+\frac{1}{15} \tanh ^3(x) (-4 \text{csch}(x)+5 i)+\frac{1}{15} \tanh (x) (-8 \text{csch}(x)+15 i)",1,"(-200 + 6*(89 - (120*I)*x)*Cosh[x] - 128*Cosh[2*x] + 178*Cosh[3*x] - (240*I)*x*Cosh[3*x] - 184*Cosh[4*x] + (64*I)*Sinh[x] + (178*I)*Sinh[2*x] + 240*x*Sinh[2*x] + (128*I)*Sinh[3*x] + (89*I)*Sinh[4*x] + 120*x*Sinh[4*x])/(960*(Cosh[x/2] - I*Sinh[x/2])^3*(Cosh[x/2] + I*Sinh[x/2])^5)","B",1
104,1,61,77,0.1235946,"\int \frac{\tanh ^3(x)}{i+\text{csch}(x)} \, dx","Integrate[Tanh[x]^3/(I + Csch[x]),x]","\frac{1}{16} \left(-\frac{2 \left(5 \sinh ^2(x)+3 i \sinh (x)+6\right)}{(\sinh (x)-i)^2 (\sinh (x)+i)}-11 i \log (-\sinh (x)+i)-5 i \log (\sinh (x)+i)\right)","-\frac{i}{8 (1-i \sinh (x))}-\frac{3 i}{4 (1+i \sinh (x))}+\frac{i}{8 (1+i \sinh (x))^2}-\frac{11}{16} i \log (-\sinh (x)+i)-\frac{5}{16} i \log (\sinh (x)+i)",1,"((-11*I)*Log[I - Sinh[x]] - (5*I)*Log[I + Sinh[x]] - (2*(6 + (3*I)*Sinh[x] + 5*Sinh[x]^2))/((-I + Sinh[x])^2*(I + Sinh[x])))/16","A",1
105,1,71,36,0.086776,"\int \frac{\tanh ^2(x)}{i+\text{csch}(x)} \, dx","Integrate[Tanh[x]^2/(I + Csch[x]),x]","\frac{2 i \sinh (x)-4 \cosh (2 x)+(6 x+5 i) (\sinh (x)-i) \cosh (x)}{6 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right) \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^3}","-i x+\frac{1}{3} \tanh ^3(x) (-\text{csch}(x)+i)+\frac{1}{3} \tanh (x) (-2 \text{csch}(x)+3 i)",1,"(-4*Cosh[2*x] + (2*I)*Sinh[x] + (5*I + 6*x)*Cosh[x]*(-I + Sinh[x]))/(6*(Cosh[x/2] - I*Sinh[x/2])*(Cosh[x/2] + I*Sinh[x/2])^3)","A",1
106,1,39,45,0.0399068,"\int \frac{\tanh (x)}{i+\text{csch}(x)} \, dx","Integrate[Tanh[x]/(I + Csch[x]),x]","\frac{1}{4} \left(-\frac{2}{\sinh (x)-i}-3 i \log (-\sinh (x)+i)-i \log (\sinh (x)+i)\right)","-\frac{i}{2 (1+i \sinh (x))}-\frac{3}{4} i \log (-\sinh (x)+i)-\frac{1}{4} i \log (\sinh (x)+i)",1,"((-3*I)*Log[I - Sinh[x]] - I*Log[I + Sinh[x]] - 2/(-I + Sinh[x]))/4","A",1
107,1,13,13,0.0083531,"\int \frac{\coth (x)}{i+\text{csch}(x)} \, dx","Integrate[Coth[x]/(I + Csch[x]),x]","-i \log (-\sinh (x)+i)","-i \log (-\sinh (x)+i)",1,"(-I)*Log[I - Sinh[x]]","A",1
108,1,13,11,0.0357693,"\int \frac{\coth ^2(x)}{i+\text{csch}(x)} \, dx","Integrate[Coth[x]^2/(I + Csch[x]),x]","\log \left(\tanh \left(\frac{x}{2}\right)\right)-i x","-\tanh ^{-1}(\cosh (x))-i x",1,"(-I)*x + Log[Tanh[x/2]]","A",1
109,1,12,12,0.0111434,"\int \frac{\coth ^3(x)}{i+\text{csch}(x)} \, dx","Integrate[Coth[x]^3/(I + Csch[x]),x]","-\text{csch}(x)-i \log (\sinh (x))","-\text{csch}(x)-i \log (\sinh (x))",1,"-Csch[x] - I*Log[Sinh[x]]","A",1
110,1,65,27,0.0368323,"\int \frac{\coth ^4(x)}{i+\text{csch}(x)} \, dx","Integrate[Coth[x]^4/(I + Csch[x]),x]","-i x+\frac{1}{2} i \tanh \left(\frac{x}{2}\right)+\frac{1}{2} i \coth \left(\frac{x}{2}\right)-\frac{1}{8} \text{csch}^2\left(\frac{x}{2}\right)-\frac{1}{8} \text{sech}^2\left(\frac{x}{2}\right)+\frac{1}{2} \log \left(\tanh \left(\frac{x}{2}\right)\right)","-i x-\frac{1}{2} \tanh ^{-1}(\cosh (x))+\frac{1}{2} \coth (x) (-\text{csch}(x)+2 i)",1,"(-I)*x + (I/2)*Coth[x/2] - Csch[x/2]^2/8 + Log[Tanh[x/2]]/2 - Sech[x/2]^2/8 + (I/2)*Tanh[x/2]","B",1
111,1,30,30,0.0151625,"\int \frac{\coth ^5(x)}{i+\text{csch}(x)} \, dx","Integrate[Coth[x]^5/(I + Csch[x]),x]","-\frac{1}{3} \text{csch}^3(x)+\frac{1}{2} i \text{csch}^2(x)-\text{csch}(x)-i \log (\sinh (x))","-\frac{1}{3} \text{csch}^3(x)+\frac{1}{2} i \text{csch}^2(x)-\text{csch}(x)-i \log (\sinh (x))",1,"-Csch[x] + (I/2)*Csch[x]^2 - Csch[x]^3/3 - I*Log[Sinh[x]]","A",1
112,1,129,43,0.0424086,"\int \frac{\coth ^6(x)}{i+\text{csch}(x)} \, dx","Integrate[Coth[x]^6/(I + Csch[x]),x]","-i x+\frac{2}{3} i \tanh \left(\frac{x}{2}\right)+\frac{2}{3} i \coth \left(\frac{x}{2}\right)-\frac{1}{64} \text{csch}^4\left(\frac{x}{2}\right)-\frac{5}{32} \text{csch}^2\left(\frac{x}{2}\right)+\frac{1}{64} \text{sech}^4\left(\frac{x}{2}\right)-\frac{5}{32} \text{sech}^2\left(\frac{x}{2}\right)+\frac{3}{8} \log \left(\tanh \left(\frac{x}{2}\right)\right)+\frac{1}{24} i \coth \left(\frac{x}{2}\right) \text{csch}^2\left(\frac{x}{2}\right)-\frac{1}{24} i \tanh \left(\frac{x}{2}\right) \text{sech}^2\left(\frac{x}{2}\right)","-i x-\frac{3}{8} \tanh ^{-1}(\cosh (x))+\frac{1}{12} \coth ^3(x) (-3 \text{csch}(x)+4 i)+\frac{1}{8} \coth (x) (-3 \text{csch}(x)+8 i)",1,"(-I)*x + ((2*I)/3)*Coth[x/2] - (5*Csch[x/2]^2)/32 + (I/24)*Coth[x/2]*Csch[x/2]^2 - Csch[x/2]^4/64 + (3*Log[Tanh[x/2]])/8 - (5*Sech[x/2]^2)/32 + Sech[x/2]^4/64 + ((2*I)/3)*Tanh[x/2] - (I/24)*Sech[x/2]^2*Tanh[x/2]","B",1
113,1,253,194,0.5063645,"\int \frac{\tanh ^5(x)}{a+b \text{csch}(x)} \, dx","Integrate[Tanh[x]^5/(a + b*Csch[x]),x]","\frac{-2 a^2 \left(a^2+b^2\right)^2 \text{sech}^4(x)-2 a b \left(a^2+b^2\right)^2 \tanh (x) \text{sech}^3(x)+4 a^2 \left(2 a^4+5 a^2 b^2+3 b^4\right) \text{sech}^2(x)+a b \left(5 a^4+14 a^2 b^2+9 b^4\right) \tan ^{-1}(\sinh (x))+a b \left(5 a^4+14 a^2 b^2+9 b^4\right) \tanh (x) \text{sech}(x)+4 a \left(a^5+i a^4 b+3 a^3 b^2+3 i a^2 b^3+3 a b^4+3 i b^5\right) \log (-\sinh (x)+i)+4 a \left(a^5-i a^4 b+3 a^3 b^2-3 i a^2 b^3+3 a b^4-3 i b^5\right) \log (\sinh (x)+i)+8 b^6 \log (a \sinh (x)+b)}{8 a \left(a^2+b^2\right)^3}","-\frac{3 b \tan ^{-1}(\sinh (x))}{8 \left(a^2+b^2\right)}-\frac{\tanh ^4(x) (a-b \text{csch}(x))}{4 \left(a^2+b^2\right)}+\frac{3 b \tanh (x) \text{sech}(x)}{8 \left(a^2+b^2\right)}+\frac{b^6 \log (a+b \text{csch}(x))}{a \left(a^2+b^2\right)^3}-\frac{b^5 \tan ^{-1}(\sinh (x))}{\left(a^2+b^2\right)^3}-\frac{b^3 \tan ^{-1}(\sinh (x))}{2 \left(a^2+b^2\right)^2}-\frac{\tanh ^2(x) \left(a \left(a^2+2 b^2\right)-b^3 \text{csch}(x)\right)}{2 \left(a^2+b^2\right)^2}-\frac{a \left(a^4+3 a^2 b^2+3 b^4\right) \log (\tanh (x))}{\left(a^2+b^2\right)^3}+\frac{\log (\sinh (x))}{a}",1,"(a*b*(5*a^4 + 14*a^2*b^2 + 9*b^4)*ArcTan[Sinh[x]] + 4*a*(a^5 + I*a^4*b + 3*a^3*b^2 + (3*I)*a^2*b^3 + 3*a*b^4 + (3*I)*b^5)*Log[I - Sinh[x]] + 4*a*(a^5 - I*a^4*b + 3*a^3*b^2 - (3*I)*a^2*b^3 + 3*a*b^4 - (3*I)*b^5)*Log[I + Sinh[x]] + 8*b^6*Log[b + a*Sinh[x]] + 4*a^2*(2*a^4 + 5*a^2*b^2 + 3*b^4)*Sech[x]^2 - 2*a^2*(a^2 + b^2)^2*Sech[x]^4 + a*b*(5*a^4 + 14*a^2*b^2 + 9*b^4)*Sech[x]*Tanh[x] - 2*a*b*(a^2 + b^2)^2*Sech[x]^3*Tanh[x])/(8*a*(a^2 + b^2)^3)","C",1
114,1,141,183,0.743668,"\int \frac{\tanh ^4(x)}{a+b \text{csch}(x)} \, dx","Integrate[Tanh[x]^4/(a + b*Csch[x]),x]","\frac{1}{3} \left(-\frac{a \left(4 a^2+7 b^2\right) \tanh (x)}{\left(a^2+b^2\right)^2}-\frac{b \text{sech}^3(x)}{a^2+b^2}+\frac{3 b \left(a^2+2 b^2\right) \text{sech}(x)}{\left(a^2+b^2\right)^2}+\frac{a \tanh (x) \text{sech}^2(x)}{a^2+b^2}+\frac{3 \left(x-\frac{2 b^5 \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{5/2}}\right)}{a}\right)","\frac{a b^2 x}{\left(a^2+b^2\right)^2}+\frac{a x}{a^2+b^2}-\frac{a \tanh ^3(x)}{3 \left(a^2+b^2\right)}-\frac{a b^2 \tanh (x)}{\left(a^2+b^2\right)^2}-\frac{a \tanh (x)}{a^2+b^2}-\frac{b \text{sech}^3(x)}{3 \left(a^2+b^2\right)}+\frac{b \text{sech}(x)}{a^2+b^2}+\frac{2 b^5 \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a \left(a^2+b^2\right)^{5/2}}+\frac{b^4 x}{a \left(a^2+b^2\right)^2}+\frac{b^3 \text{sech}(x)}{\left(a^2+b^2\right)^2}",1,"((3*(x - (2*b^5*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(5/2)))/a + (3*b*(a^2 + 2*b^2)*Sech[x])/(a^2 + b^2)^2 - (b*Sech[x]^3)/(a^2 + b^2) - (a*(4*a^2 + 7*b^2)*Tanh[x])/(a^2 + b^2)^2 + (a*Sech[x]^2*Tanh[x])/(a^2 + b^2))/3","A",1
115,1,191,113,0.2009182,"\int \frac{\tanh ^3(x)}{a+b \text{csch}(x)} \, dx","Integrate[Tanh[x]^3/(a + b*Csch[x]),x]","\frac{a^4 \log (-\sinh (x)+i)+a^4 \log (\sinh (x)+i)+i a^3 b \log (-\sinh (x)+i)-i a^3 b \log (\sinh (x)+i)+a^2 \left(a^2+b^2\right) \text{sech}^2(x)+2 a^2 b^2 \log (-\sinh (x)+i)+2 a^2 b^2 \log (\sinh (x)+i)+a b \left(a^2+b^2\right) \tan ^{-1}(\sinh (x))+a b \left(a^2+b^2\right) \tanh (x) \text{sech}(x)+2 b^4 \log (a \sinh (x)+b)+2 i a b^3 \log (-\sinh (x)+i)-2 i a b^3 \log (\sinh (x)+i)}{2 a \left(a^2+b^2\right)^2}","-\frac{a \left(a^2+2 b^2\right) \log (\tanh (x))}{\left(a^2+b^2\right)^2}-\frac{b \tan ^{-1}(\sinh (x))}{2 \left(a^2+b^2\right)}-\frac{\tanh ^2(x) (a-b \text{csch}(x))}{2 \left(a^2+b^2\right)}+\frac{b^4 \log (a+b \text{csch}(x))}{a \left(a^2+b^2\right)^2}-\frac{b^3 \tan ^{-1}(\sinh (x))}{\left(a^2+b^2\right)^2}+\frac{\log (\sinh (x))}{a}",1,"(a*b*(a^2 + b^2)*ArcTan[Sinh[x]] + a^4*Log[I - Sinh[x]] + I*a^3*b*Log[I - Sinh[x]] + 2*a^2*b^2*Log[I - Sinh[x]] + (2*I)*a*b^3*Log[I - Sinh[x]] + a^4*Log[I + Sinh[x]] - I*a^3*b*Log[I + Sinh[x]] + 2*a^2*b^2*Log[I + Sinh[x]] - (2*I)*a*b^3*Log[I + Sinh[x]] + 2*b^4*Log[b + a*Sinh[x]] + a^2*(a^2 + b^2)*Sech[x]^2 + a*b*(a^2 + b^2)*Sech[x]*Tanh[x])/(2*a*(a^2 + b^2)^2)","C",1
116,1,82,100,0.3321045,"\int \frac{\tanh ^2(x)}{a+b \text{csch}(x)} \, dx","Integrate[Tanh[x]^2/(a + b*Csch[x]),x]","-\frac{a \tanh (x)}{a^2+b^2}+\frac{b \text{sech}(x)}{a^2+b^2}+\frac{\frac{2 b^3 \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}+x}{a}","\frac{b^2 x}{a \left(a^2+b^2\right)}+\frac{a x}{a^2+b^2}-\frac{a \tanh (x)}{a^2+b^2}+\frac{b \text{sech}(x)}{a^2+b^2}+\frac{2 b^3 \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a \left(a^2+b^2\right)^{3/2}}",1,"(x + (2*b^3*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2))/a + (b*Sech[x])/(a^2 + b^2) - (a*Tanh[x])/(a^2 + b^2)","A",1
117,1,63,61,0.0616316,"\int \frac{\tanh (x)}{a+b \text{csch}(x)} \, dx","Integrate[Tanh[x]/(a + b*Csch[x]),x]","\frac{2 b^2 \log (a \sinh (x)+b)+a (a+i b) \log (-\sinh (x)+i)+a (a-i b) \log (\sinh (x)+i)}{2 a \left(a^2+b^2\right)}","-\frac{a \log (\tanh (x))}{a^2+b^2}-\frac{b \tan ^{-1}(\sinh (x))}{a^2+b^2}+\frac{b^2 \log (a+b \text{csch}(x))}{a \left(a^2+b^2\right)}+\frac{\log (\sinh (x))}{a}",1,"(a*(a + I*b)*Log[I - Sinh[x]] + a*(a - I*b)*Log[I + Sinh[x]] + 2*b^2*Log[b + a*Sinh[x]])/(2*a*(a^2 + b^2))","C",1
118,1,11,19,0.008194,"\int \frac{\coth (x)}{a+b \text{csch}(x)} \, dx","Integrate[Coth[x]/(a + b*Csch[x]),x]","\frac{\log (a \sinh (x)+b)}{a}","\frac{\log (a+b \text{csch}(x))}{a}+\frac{\log (\sinh (x))}{a}",1,"Log[b + a*Sinh[x]]/a","A",1
119,1,65,57,0.0847168,"\int \frac{\coth ^2(x)}{a+b \text{csch}(x)} \, dx","Integrate[Coth[x]^2/(a + b*Csch[x]),x]","\frac{2 \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)+a \log \left(\tanh \left(\frac{x}{2}\right)\right)+b x}{a b}","\frac{2 \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a b}+\frac{x}{a}-\frac{\tanh ^{-1}(\cosh (x))}{b}",1,"(b*x + 2*Sqrt[-a^2 - b^2]*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]] + a*Log[Tanh[x/2]])/(a*b)","A",1
120,1,37,32,0.0525767,"\int \frac{\coth ^3(x)}{a+b \text{csch}(x)} \, dx","Integrate[Coth[x]^3/(a + b*Csch[x]),x]","\frac{\left(a^2+b^2\right) \log (a \sinh (x)+b)+a^2 (-\log (\sinh (x)))-a b \text{csch}(x)}{a b^2}","\left(\frac{a}{b^2}+\frac{1}{a}\right) \log (a+b \text{csch}(x))+\frac{\log (\sinh (x))}{a}-\frac{\text{csch}(x)}{b}",1,"(-(a*b*Csch[x]) - a^2*Log[Sinh[x]] + (a^2 + b^2)*Log[b + a*Sinh[x]])/(a*b^2)","A",1
121,1,151,88,0.5883706,"\int \frac{\coth ^4(x)}{a+b \text{csch}(x)} \, dx","Integrate[Coth[x]^4/(a + b*Csch[x]),x]","\frac{\text{csch}(x) (a \sinh (x)+b) \left(4 a \left(2 a^2+3 b^2\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)-16 \left(-a^2-b^2\right)^{3/2} \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)+4 a^2 b \tanh \left(\frac{x}{2}\right)+4 a^2 b \coth \left(\frac{x}{2}\right)-a b^2 \text{csch}^2\left(\frac{x}{2}\right)-a b^2 \text{sech}^2\left(\frac{x}{2}\right)+8 b^3 x\right)}{8 a b^3 (a+b \text{csch}(x))}","\frac{2 \left(a^2+b^2\right)^{3/2} \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a b^3}-\frac{\left(2 a^2+3 b^2\right) \tanh ^{-1}(\cosh (x))}{2 b^3}+\frac{a \coth (x)}{b^2}+\frac{x}{a}-\frac{\coth (x) \text{csch}(x)}{2 b}",1,"(Csch[x]*(b + a*Sinh[x])*(8*b^3*x - 16*(-a^2 - b^2)^(3/2)*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]] + 4*a^2*b*Coth[x/2] - a*b^2*Csch[x/2]^2 + 4*a*(2*a^2 + 3*b^2)*Log[Tanh[x/2]] - a*b^2*Sech[x/2]^2 + 4*a^2*b*Tanh[x/2]))/(8*a*b^3*(a + b*Csch[x]))","A",1
122,1,83,70,0.1350733,"\int \frac{\coth ^5(x)}{a+b \text{csch}(x)} \, dx","Integrate[Coth[x]^5/(a + b*Csch[x]),x]","\frac{3 a^2 b^2 \text{csch}^2(x)-6 a b \left(a^2+2 b^2\right) \text{csch}(x)-6 a^2 \left(a^2+2 b^2\right) \log (\sinh (x))+6 \left(a^2+b^2\right)^2 \log (a \sinh (x)+b)-2 a b^3 \text{csch}^3(x)}{6 a b^4}","\frac{\left(a^2+b^2\right)^2 \log (a+b \text{csch}(x))}{a b^4}-\frac{\left(a^2+2 b^2\right) \text{csch}(x)}{b^3}+\frac{a \text{csch}^2(x)}{2 b^2}+\frac{\log (\sinh (x))}{a}-\frac{\text{csch}^3(x)}{3 b}",1,"(-6*a*b*(a^2 + 2*b^2)*Csch[x] + 3*a^2*b^2*Csch[x]^2 - 2*a*b^3*Csch[x]^3 - 6*a^2*(a^2 + 2*b^2)*Log[Sinh[x]] + 6*(a^2 + b^2)^2*Log[b + a*Sinh[x]])/(6*a*b^4)","A",1
123,1,269,183,1.5793451,"\int \frac{\coth ^6(x)}{a+b \text{csch}(x)} \, dx","Integrate[Coth[x]^6/(a + b*Csch[x]),x]","\frac{\text{csch}(x) (a \sinh (x)+b) \left(4 a^2 b^3 \sinh (x) \text{csch}^4\left(\frac{x}{2}\right)-64 a^2 b^3 \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)+32 a^2 b \left(3 a^2+7 b^2\right) \tanh \left(\frac{x}{2}\right)+32 a^2 b \left(3 a^2+7 b^2\right) \coth \left(\frac{x}{2}\right)-6 a b^2 \left(4 a^2+9 b^2\right) \text{csch}^2\left(\frac{x}{2}\right)-6 a b^2 \left(4 a^2+9 b^2\right) \text{sech}^2\left(\frac{x}{2}\right)+384 \left(-a^2-b^2\right)^{5/2} \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)+24 a \left(8 a^4+20 a^2 b^2+15 b^4\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)-3 a b^4 \text{csch}^4\left(\frac{x}{2}\right)+3 a b^4 \text{sech}^4\left(\frac{x}{2}\right)+192 b^5 x\right)}{192 a b^5 (a+b \text{csch}(x))}","\frac{2 \left(a^2+b^2\right)^{5/2} \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a b^5}+\frac{a \left(a^2+3 b^2\right) \coth (x)}{b^4}+\frac{\left(a^2+3 b^2\right) \tanh ^{-1}(\cosh (x))}{2 b^3}-\frac{\left(a^2+3 b^2\right) \coth (x) \text{csch}(x)}{2 b^3}-\frac{\left(a^4+3 a^2 b^2+3 b^4\right) \tanh ^{-1}(\cosh (x))}{b^5}+\frac{a \coth ^3(x)}{3 b^2}-\frac{a \coth (x)}{b^2}+\frac{x}{a}-\frac{3 \tanh ^{-1}(\cosh (x))}{8 b}-\frac{\coth (x) \text{csch}^3(x)}{4 b}+\frac{3 \coth (x) \text{csch}(x)}{8 b}",1,"(Csch[x]*(b + a*Sinh[x])*(192*b^5*x + 384*(-a^2 - b^2)^(5/2)*ArcTan[(a - b*Tanh[x/2])/Sqrt[-a^2 - b^2]] + 32*a^2*b*(3*a^2 + 7*b^2)*Coth[x/2] - 6*a*b^2*(4*a^2 + 9*b^2)*Csch[x/2]^2 - 3*a*b^4*Csch[x/2]^4 + 24*a*(8*a^4 + 20*a^2*b^2 + 15*b^4)*Log[Tanh[x/2]] - 6*a*b^2*(4*a^2 + 9*b^2)*Sech[x/2]^2 + 3*a*b^4*Sech[x/2]^4 - 64*a^2*b^3*Csch[x]^3*Sinh[x/2]^4 + 4*a^2*b^3*Csch[x/2]^4*Sinh[x] + 32*a^2*b*(3*a^2 + 7*b^2)*Tanh[x/2]))/(192*a*b^5*(a + b*Csch[x]))","A",1
124,1,130,119,0.2589604,"\int \frac{\coth ^7(x)}{a+b \text{csch}(x)} \, dx","Integrate[Coth[x]^7/(a + b*Csch[x]),x]","\frac{30 a b^2 \left(a^2+3 b^2\right) \text{csch}^2(x)+\frac{60 \left(a^2+b^2\right)^3 \log (a \sinh (x)+b)}{a}-20 b^3 \left(a^2+3 b^2\right) \text{csch}^3(x)-60 b \left(a^4+3 a^2 b^2+3 b^4\right) \text{csch}(x)-60 a \left(a^4+3 a^2 b^2+3 b^4\right) \log (\sinh (x))+15 a b^4 \text{csch}^4(x)-12 b^5 \text{csch}^5(x)}{60 b^6}","\frac{\left(a^2+b^2\right)^3 \log (a+b \text{csch}(x))}{a b^6}+\frac{a \left(a^2+3 b^2\right) \text{csch}^2(x)}{2 b^4}-\frac{\left(a^2+3 b^2\right) \text{csch}^3(x)}{3 b^3}-\frac{\left(a^4+3 a^2 b^2+3 b^4\right) \text{csch}(x)}{b^5}+\frac{a \text{csch}^4(x)}{4 b^2}+\frac{\log (\sinh (x))}{a}-\frac{\text{csch}^5(x)}{5 b}",1,"(-60*b*(a^4 + 3*a^2*b^2 + 3*b^4)*Csch[x] + 30*a*b^2*(a^2 + 3*b^2)*Csch[x]^2 - 20*b^3*(a^2 + 3*b^2)*Csch[x]^3 + 15*a*b^4*Csch[x]^4 - 12*b^5*Csch[x]^5 - 60*a*(a^4 + 3*a^2*b^2 + 3*b^4)*Log[Sinh[x]] + (60*(a^2 + b^2)^3*Log[b + a*Sinh[x]])/a)/(60*b^6)","A",1
125,1,84,199,0.0819269,"\int e^{c (a+b x)} \text{csch}^2(a c+b c x)^{7/2} \, dx","Integrate[E^(c*(a + b*x))*(Csch[a*c + b*c*x]^2)^(7/2),x]","-\frac{16 \left(6 e^{2 c (a+b x)}-15 e^{4 c (a+b x)}+20 e^{6 c (a+b x)}-1\right) \sinh (c (a+b x)) \sqrt{\text{csch}^2(c (a+b x))}}{15 b c \left(e^{2 c (a+b x)}-1\right)^6}","\frac{64 \sinh (a c+b c x) \sqrt{\text{csch}^2(a c+b c x)}}{3 b c \left(1-e^{2 c (a+b x)}\right)^3}-\frac{48 \sinh (a c+b c x) \sqrt{\text{csch}^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)^4}+\frac{192 \sinh (a c+b c x) \sqrt{\text{csch}^2(a c+b c x)}}{5 b c \left(1-e^{2 c (a+b x)}\right)^5}-\frac{32 \sinh (a c+b c x) \sqrt{\text{csch}^2(a c+b c x)}}{3 b c \left(1-e^{2 c (a+b x)}\right)^6}",1,"(-16*(-1 + 6*E^(2*c*(a + b*x)) - 15*E^(4*c*(a + b*x)) + 20*E^(6*c*(a + b*x)))*Sqrt[Csch[c*(a + b*x)]^2]*Sinh[c*(a + b*x)])/(15*b*c*(-1 + E^(2*c*(a + b*x)))^6)","A",1
126,1,72,147,0.0665427,"\int e^{c (a+b x)} \text{csch}^2(a c+b c x)^{5/2} \, dx","Integrate[E^(c*(a + b*x))*(Csch[a*c + b*c*x]^2)^(5/2),x]","-\frac{4 \left(-4 e^{2 c (a+b x)}+6 e^{4 c (a+b x)}+1\right) \sinh (c (a+b x)) \sqrt{\text{csch}^2(c (a+b x))}}{3 b c \left(e^{2 c (a+b x)}-1\right)^4}","-\frac{8 \sinh (a c+b c x) \sqrt{\text{csch}^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)^2}+\frac{32 \sinh (a c+b c x) \sqrt{\text{csch}^2(a c+b c x)}}{3 b c \left(1-e^{2 c (a+b x)}\right)^3}-\frac{4 \sinh (a c+b c x) \sqrt{\text{csch}^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)^4}",1,"(-4*(1 - 4*E^(2*c*(a + b*x)) + 6*E^(4*c*(a + b*x)))*Sqrt[Csch[c*(a + b*x)]^2]*Sinh[c*(a + b*x)])/(3*b*c*(-1 + E^(2*c*(a + b*x)))^4)","A",1
127,1,56,58,0.0446607,"\int e^{c (a+b x)} \text{csch}^2(a c+b c x)^{3/2} \, dx","Integrate[E^(c*(a + b*x))*(Csch[a*c + b*c*x]^2)^(3/2),x]","-\frac{2 e^{4 c (a+b x)} \sinh ^3(c (a+b x)) \text{csch}^2(c (a+b x))^{3/2}}{b c \left(e^{2 c (a+b x)}-1\right)^2}","-\frac{2 e^{4 c (a+b x)} \sinh (a c+b c x) \sqrt{\text{csch}^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)^2}",1,"(-2*E^(4*c*(a + b*x))*(Csch[c*(a + b*x)]^2)^(3/2)*Sinh[c*(a + b*x)]^3)/(b*c*(-1 + E^(2*c*(a + b*x)))^2)","A",1
128,1,44,46,0.0372527,"\int e^{c (a+b x)} \sqrt{\text{csch}^2(a c+b c x)} \, dx","Integrate[E^(c*(a + b*x))*Sqrt[Csch[a*c + b*c*x]^2],x]","\frac{\log \left(1-e^{2 c (a+b x)}\right) \sinh (c (a+b x)) \sqrt{\text{csch}^2(c (a+b x))}}{b c}","\frac{\log \left(1-e^{2 c (a+b x)}\right) \sinh (a c+b c x) \sqrt{\text{csch}^2(a c+b c x)}}{b c}",1,"(Sqrt[Csch[c*(a + b*x)]^2]*Log[1 - E^(2*c*(a + b*x))]*Sinh[c*(a + b*x)])/(b*c)","A",1
129,1,48,74,0.0514919,"\int \frac{e^{c (a+b x)}}{\sqrt{\text{csch}^2(a c+b c x)}} \, dx","Integrate[E^(c*(a + b*x))/Sqrt[Csch[a*c + b*c*x]^2],x]","\frac{\left(e^{2 c (a+b x)}-2 b c x\right) \text{csch}(c (a+b x))}{4 b c \sqrt{\text{csch}^2(c (a+b x))}}","\frac{e^{2 c (a+b x)} \text{csch}(a c+b c x)}{4 b c \sqrt{\text{csch}^2(a c+b c x)}}-\frac{x \text{csch}(a c+b c x)}{2 \sqrt{\text{csch}^2(a c+b c x)}}",1,"((E^(2*c*(a + b*x)) - 2*b*c*x)*Csch[c*(a + b*x)])/(4*b*c*Sqrt[Csch[c*(a + b*x)]^2])","A",1
130,1,76,162,0.0655198,"\int \frac{e^{c (a+b x)}}{\text{csch}^2(a c+b c x)^{3/2}} \, dx","Integrate[E^(c*(a + b*x))/(Csch[a*c + b*c*x]^2)^(3/2),x]","\frac{\left(e^{-2 c (a+b x)}-3 e^{2 c (a+b x)}+\frac{1}{2} e^{4 c (a+b x)}+6 b c x\right) \text{csch}^3(c (a+b x))}{16 b c \text{csch}^2(c (a+b x))^{3/2}}","\frac{e^{-2 c (a+b x)} \text{csch}(a c+b c x)}{16 b c \sqrt{\text{csch}^2(a c+b c x)}}-\frac{3 e^{2 c (a+b x)} \text{csch}(a c+b c x)}{16 b c \sqrt{\text{csch}^2(a c+b c x)}}+\frac{e^{4 c (a+b x)} \text{csch}(a c+b c x)}{32 b c \sqrt{\text{csch}^2(a c+b c x)}}+\frac{3 x \text{csch}(a c+b c x)}{8 \sqrt{\text{csch}^2(a c+b c x)}}",1,"((E^(-2*c*(a + b*x)) - 3*E^(2*c*(a + b*x)) + E^(4*c*(a + b*x))/2 + 6*b*c*x)*Csch[c*(a + b*x)]^3)/(16*b*c*(Csch[c*(a + b*x)]^2)^(3/2))","A",1
131,1,106,250,0.1037954,"\int \frac{e^{c (a+b x)}}{\text{csch}^2(a c+b c x)^{5/2}} \, dx","Integrate[E^(c*(a + b*x))/(Csch[a*c + b*c*x]^2)^(5/2),x]","\frac{\left(\frac{1}{2} e^{-4 c (a+b x)}-5 e^{-2 c (a+b x)}+10 e^{2 c (a+b x)}-\frac{5}{2} e^{4 c (a+b x)}+\frac{1}{3} e^{6 c (a+b x)}-20 b c x\right) \text{csch}^5(c (a+b x))}{64 b c \text{csch}^2(c (a+b x))^{5/2}}","\frac{e^{-4 c (a+b x)} \text{csch}(a c+b c x)}{128 b c \sqrt{\text{csch}^2(a c+b c x)}}-\frac{5 e^{-2 c (a+b x)} \text{csch}(a c+b c x)}{64 b c \sqrt{\text{csch}^2(a c+b c x)}}+\frac{5 e^{2 c (a+b x)} \text{csch}(a c+b c x)}{32 b c \sqrt{\text{csch}^2(a c+b c x)}}-\frac{5 e^{4 c (a+b x)} \text{csch}(a c+b c x)}{128 b c \sqrt{\text{csch}^2(a c+b c x)}}+\frac{e^{6 c (a+b x)} \text{csch}(a c+b c x)}{192 b c \sqrt{\text{csch}^2(a c+b c x)}}-\frac{5 x \text{csch}(a c+b c x)}{16 \sqrt{\text{csch}^2(a c+b c x)}}",1,"((1/(2*E^(4*c*(a + b*x))) - 5/E^(2*c*(a + b*x)) + 10*E^(2*c*(a + b*x)) - (5*E^(4*c*(a + b*x)))/2 + E^(6*c*(a + b*x))/3 - 20*b*c*x)*Csch[c*(a + b*x)]^5)/(64*b*c*(Csch[c*(a + b*x)]^2)^(5/2))","A",1
132,1,80,81,0.1786897,"\int \frac{x^5}{\sqrt{\text{csch}(2 \log (c x))}} \, dx","Integrate[x^5/Sqrt[Csch[2*Log[c*x]]],x]","\frac{x^2 \left(\, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};c^4 x^4\right)-\left(1-c^4 x^4\right)^{3/2}\right)}{7 c^4 \sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}}}","-\frac{2 x^2}{21 c^4 \sqrt{\text{csch}(2 \log (c x))}}+\frac{2 F\left(\left.\csc ^{-1}(c x)\right|-1\right)}{21 c^7 x \sqrt{1-\frac{1}{c^4 x^4}} \sqrt{\text{csch}(2 \log (c x))}}+\frac{x^6}{7 \sqrt{\text{csch}(2 \log (c x))}}",1,"(x^2*(-(1 - c^4*x^4)^(3/2) + Hypergeometric2F1[-1/2, 1/4, 5/4, c^4*x^4]))/(7*c^4*Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)])","C",1
133,1,44,30,0.049824,"\int \frac{x^4}{\sqrt{\text{csch}(2 \log (c x))}} \, dx","Integrate[x^4/Sqrt[Csch[2*Log[c*x]]],x]","\frac{\left(c^4 x^4-1\right)^2 \sqrt{\frac{c^2 x^2}{2 c^4 x^4-2}}}{6 c^6 x}","\frac{x^5 \left(c^4-\frac{1}{x^4}\right)}{6 c^4 \sqrt{\text{csch}(2 \log (c x))}}",1,"((-1 + c^4*x^4)^2*Sqrt[(c^2*x^2)/(-2 + 2*c^4*x^4)])/(6*c^6*x)","A",1
134,1,60,119,0.1162101,"\int \frac{x^3}{\sqrt{\text{csch}(2 \log (c x))}} \, dx","Integrate[x^3/Sqrt[Csch[2*Log[c*x]]],x]","\frac{x^4 \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};c^4 x^4\right)}{3 \sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}}}","-\frac{2}{5 c^4 \sqrt{\text{csch}(2 \log (c x))}}+\frac{2 F\left(\left.\csc ^{-1}(c x)\right|-1\right)}{5 c^5 x \sqrt{1-\frac{1}{c^4 x^4}} \sqrt{\text{csch}(2 \log (c x))}}-\frac{2 E\left(\left.\csc ^{-1}(c x)\right|-1\right)}{5 c^5 x \sqrt{1-\frac{1}{c^4 x^4}} \sqrt{\text{csch}(2 \log (c x))}}+\frac{x^4}{5 \sqrt{\text{csch}(2 \log (c x))}}",1,"(x^4*Hypergeometric2F1[-1/2, 3/4, 7/4, c^4*x^4])/(3*Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)])","C",1
135,1,74,69,0.1435894,"\int \frac{x^2}{\sqrt{\text{csch}(2 \log (c x))}} \, dx","Integrate[x^2/Sqrt[Csch[2*Log[c*x]]],x]","\frac{x \left(\sin ^{-1}\left(c^2 x^2\right)+c^2 x^2 \sqrt{1-c^4 x^4}\right)}{4 c^2 \sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}}}","\frac{x^3}{4 \sqrt{\text{csch}(2 \log (c x))}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{c^4 x^4}}\right)}{4 c^4 x \sqrt{1-\frac{1}{c^4 x^4}} \sqrt{\text{csch}(2 \log (c x))}}",1,"(x*(c^2*x^2*Sqrt[1 - c^4*x^4] + ArcSin[c^2*x^2]))/(4*c^2*Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)])","A",1
136,1,57,60,0.1087721,"\int \frac{x}{\sqrt{\text{csch}(2 \log (c x))}} \, dx","Integrate[x/Sqrt[Csch[2*Log[c*x]]],x]","\frac{x^2 \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};c^4 x^4\right)}{\sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}}}","\frac{2 F\left(\left.\csc ^{-1}(c x)\right|-1\right)}{3 c^3 x \sqrt{1-\frac{1}{c^4 x^4}} \sqrt{\text{csch}(2 \log (c x))}}+\frac{x^2}{3 \sqrt{\text{csch}(2 \log (c x))}}",1,"(x^2*Hypergeometric2F1[-1/2, 1/4, 5/4, c^4*x^4])/(Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)])","C",1
137,1,77,60,0.0899586,"\int \frac{1}{\sqrt{\text{csch}(2 \log (c x))}} \, dx","Integrate[1/Sqrt[Csch[2*Log[c*x]]],x]","\frac{x \left(2 \sqrt{c^4 x^4-1}-2 \tan ^{-1}\left(\sqrt{c^4 x^4-1}\right)\right)}{4 \sqrt{2} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}} \sqrt{c^4 x^4-1}}","\frac{\csc ^{-1}\left(c^2 x^2\right)}{2 c^2 x \sqrt{1-\frac{1}{c^4 x^4}} \sqrt{\text{csch}(2 \log (c x))}}+\frac{x}{2 \sqrt{\text{csch}(2 \log (c x))}}",1,"(x*(2*Sqrt[-1 + c^4*x^4] - 2*ArcTan[Sqrt[-1 + c^4*x^4]]))/(4*Sqrt[2]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)]*Sqrt[-1 + c^4*x^4])","A",1
138,1,43,46,0.0748479,"\int \frac{\sqrt{\text{csch}(2 \log (c x))}}{x} \, dx","Integrate[Sqrt[Csch[2*Log[c*x]]]/x,x]","(i \sinh (2 \log (c x)))^{3/2} \text{csch}^{\frac{3}{2}}(2 \log (c x)) F\left(\left.\frac{\pi }{4}-i \log (c x)\right|2\right)","i \sqrt{i \sinh (2 \log (c x))} \sqrt{\text{csch}(2 \log (c x))} F\left(\left.\frac{\pi }{4}-i \log (c x)\right|2\right)",1,"Csch[2*Log[c*x]]^(3/2)*EllipticF[Pi/4 - I*Log[c*x], 2]*(I*Sinh[2*Log[c*x]])^(3/2)","A",1
139,1,54,41,0.1182107,"\int \frac{\sqrt{\text{csch}(2 \log (c x))}}{x^2} \, dx","Integrate[Sqrt[Csch[2*Log[c*x]]]/x^2,x]","\frac{\sqrt{c^4 x^4-1} \sqrt{\frac{c^2 x^2}{2 c^4 x^4-2}} \tan ^{-1}\left(\sqrt{c^4 x^4-1}\right)}{x}","-\frac{1}{2} c^2 x \sqrt{1-\frac{1}{c^4 x^4}} \csc ^{-1}\left(c^2 x^2\right) \sqrt{\text{csch}(2 \log (c x))}",1,"(Sqrt[-1 + c^4*x^4]*Sqrt[(c^2*x^2)/(-2 + 2*c^4*x^4)]*ArcTan[Sqrt[-1 + c^4*x^4]])/x","A",1
140,1,58,74,0.0960204,"\int \frac{\sqrt{\text{csch}(2 \log (c x))}}{x^3} \, dx","Integrate[Sqrt[Csch[2*Log[c*x]]]/x^3,x]","-\frac{\sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};c^4 x^4\right)}{x^2}","c^3 x \sqrt{1-\frac{1}{c^4 x^4}} F\left(\left.\csc ^{-1}(c x)\right|-1\right) \sqrt{\text{csch}(2 \log (c x))}-c^3 x \sqrt{1-\frac{1}{c^4 x^4}} E\left(\left.\csc ^{-1}(c x)\right|-1\right) \sqrt{\text{csch}(2 \log (c x))}",1,"-((Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)]*Hypergeometric2F1[-1/4, 1/2, 3/4, c^4*x^4])/x^2)","C",1
141,1,33,25,0.0398133,"\int \frac{\sqrt{\text{csch}(2 \log (c x))}}{x^4} \, dx","Integrate[Sqrt[Csch[2*Log[c*x]]]/x^4,x]","\frac{c^2}{2 x \sqrt{\frac{c^2 x^2}{2 c^4 x^4-2}}}","\frac{1}{2} x \left(c^4-\frac{1}{x^4}\right) \sqrt{\text{csch}(2 \log (c x))}",1,"c^2/(2*x*Sqrt[(c^2*x^2)/(-2 + 2*c^4*x^4)])","A",1
142,1,60,64,0.0993764,"\int \frac{\sqrt{\text{csch}(2 \log (c x))}}{x^5} \, dx","Integrate[Sqrt[Csch[2*Log[c*x]]]/x^5,x]","-\frac{\sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};c^4 x^4\right)}{3 x^4}","\frac{1}{3} \left(c^4-\frac{1}{x^4}\right) \sqrt{\text{csch}(2 \log (c x))}-\frac{1}{3} c^5 x \sqrt{1-\frac{1}{c^4 x^4}} F\left(\left.\csc ^{-1}(c x)\right|-1\right) \sqrt{\text{csch}(2 \log (c x))}",1,"-1/3*(Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)]*Hypergeometric2F1[-3/4, 1/2, 1/4, c^4*x^4])/x^4","C",1
143,1,95,128,0.2078918,"\int \frac{x^8}{\text{csch}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^8/Csch[2*Log[c*x]]^(3/2),x]","\frac{c^3 x^3 \sqrt{1-c^4 x^4} \left(8 c^8 x^8-14 c^4 x^4+3\right)-3 c x \sin ^{-1}\left(c^2 x^2\right)}{192 c^9 \sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}}}","\frac{x}{32 c^4 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))}-\frac{x^5}{16 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{c^4 x^4}}\right)}{32 c^{12} x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^9}{12 \text{csch}^{\frac{3}{2}}(2 \log (c x))}",1,"(c^3*x^3*Sqrt[1 - c^4*x^4]*(3 - 14*c^4*x^4 + 8*c^8*x^8) - 3*c*x*ArcSin[c^2*x^2])/(192*c^9*Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)])","A",1
144,1,80,118,0.1759937,"\int \frac{x^7}{\text{csch}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^7/Csch[2*Log[c*x]]^(3/2),x]","\frac{x^2 \left(\left(1-c^4 x^4\right)^{5/2}-\, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};c^4 x^4\right)\right)}{22 c^6 \sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}}}","-\frac{6 x^4}{77 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{4}{77 c^4 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))}-\frac{4 F\left(\left.\csc ^{-1}(c x)\right|-1\right)}{77 c^{11} x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^8}{11 \text{csch}^{\frac{3}{2}}(2 \log (c x))}",1,"(x^2*((1 - c^4*x^4)^(5/2) - Hypergeometric2F1[-3/2, 1/4, 5/4, c^4*x^4]))/(22*c^6*Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)])","C",1
145,1,44,30,0.0515742,"\int \frac{x^6}{\text{csch}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^6/Csch[2*Log[c*x]]^(3/2),x]","\frac{\left(c^4 x^4-1\right)^3 \sqrt{\frac{c^2 x^2}{2 c^4 x^4-2}}}{20 c^8 x}","\frac{x^7 \left(c^4-\frac{1}{x^4}\right)}{10 c^4 \text{csch}^{\frac{3}{2}}(2 \log (c x))}",1,"((-1 + c^4*x^4)^3*Sqrt[(c^2*x^2)/(-2 + 2*c^4*x^4)])/(20*c^8*x)","A",1
146,1,63,162,0.1271634,"\int \frac{x^5}{\text{csch}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^5/Csch[2*Log[c*x]]^(3/2),x]","-\frac{x^4 \, _2F_1\left(-\frac{3}{2},\frac{3}{4};\frac{7}{4};c^4 x^4\right)}{6 c^2 \sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}}}","-\frac{2 x^2}{15 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{4}{15 c^4 x^2 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))}-\frac{4 F\left(\left.\csc ^{-1}(c x)\right|-1\right)}{15 c^9 x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{4 E\left(\left.\csc ^{-1}(c x)\right|-1\right)}{15 c^9 x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^6}{9 \text{csch}^{\frac{3}{2}}(2 \log (c x))}",1,"-1/6*(x^4*Hypergeometric2F1[-3/2, 3/4, 7/4, c^4*x^4])/(c^2*Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)])","C",1
147,1,87,96,0.1844387,"\int \frac{x^4}{\text{csch}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^4/Csch[2*Log[c*x]]^(3/2),x]","\frac{c^3 x^3 \sqrt{1-c^4 x^4} \left(2 c^4 x^4-5\right)-3 c x \sin ^{-1}\left(c^2 x^2\right)}{32 c^5 \sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}}}","-\frac{3 x}{16 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^4 x^4}}\right)}{16 c^8 x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^5}{8 \text{csch}^{\frac{3}{2}}(2 \log (c x))}",1,"(c^3*x^3*Sqrt[1 - c^4*x^4]*(-5 + 2*c^4*x^4) - 3*c*x*ArcSin[c^2*x^2])/(32*c^5*Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)])","A",1
148,1,65,86,0.1276644,"\int \frac{x^3}{\text{csch}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^3/Csch[2*Log[c*x]]^(3/2),x]","\frac{\sqrt{1-c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}} \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};c^4 x^4\right)}{2 \sqrt{2} c^4}","-\frac{2}{7 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))}-\frac{4 F\left(\left.\csc ^{-1}(c x)\right|-1\right)}{7 c^7 x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^4}{7 \text{csch}^{\frac{3}{2}}(2 \log (c x))}",1,"(Sqrt[1 - c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)]*Hypergeometric2F1[-3/2, 1/4, 5/4, c^4*x^4])/(2*Sqrt[2]*c^4)","C",1
149,1,88,91,0.1620672,"\int \frac{x^2}{\text{csch}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^2/Csch[2*Log[c*x]]^(3/2),x]","\frac{x \left(\sqrt{c^4 x^4-1} \left(c^4 x^4-4\right)+3 \tan ^{-1}\left(\sqrt{c^4 x^4-1}\right)\right)}{12 \sqrt{2} c^2 \sqrt{\frac{c^2 x^2}{c^4 x^4-1}} \sqrt{c^4 x^4-1}}","-\frac{1}{2 x \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))}-\frac{\csc ^{-1}\left(c^2 x^2\right)}{2 c^6 x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^3}{6 \text{csch}^{\frac{3}{2}}(2 \log (c x))}",1,"(x*((-4 + c^4*x^4)*Sqrt[-1 + c^4*x^4] + 3*ArcTan[Sqrt[-1 + c^4*x^4]]))/(12*Sqrt[2]*c^2*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)]*Sqrt[-1 + c^4*x^4])","A",1
150,1,60,130,0.1146791,"\int \frac{x}{\text{csch}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x/Csch[2*Log[c*x]]^(3/2),x]","\frac{\, _2F_1\left(-\frac{3}{2},-\frac{1}{4};\frac{3}{4};c^4 x^4\right)}{2 c^2 \sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}}}","-\frac{6}{5 x^2 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{12 F\left(\left.\csc ^{-1}(c x)\right|-1\right)}{5 c^5 x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} \text{csch}^{\frac{3}{2}}(2 \log (c x))}-\frac{12 E\left(\left.\csc ^{-1}(c x)\right|-1\right)}{5 c^5 x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^2}{5 \text{csch}^{\frac{3}{2}}(2 \log (c x))}",1,"Hypergeometric2F1[-3/2, -1/4, 3/4, c^4*x^4]/(2*c^2*Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)])","C",1
151,1,63,96,0.0959941,"\int \frac{1}{\text{csch}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[Csch[2*Log[c*x]]^(-3/2),x]","\frac{\, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};c^4 x^4\right)}{4 c^2 x \sqrt{2-2 c^4 x^4} \sqrt{\frac{c^2 x^2}{c^4 x^4-1}}}","\frac{3}{4 x^3 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))}-\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^4 x^4}}\right)}{4 c^4 x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} \text{csch}^{\frac{3}{2}}(2 \log (c x))}+\frac{x}{4 \text{csch}^{\frac{3}{2}}(2 \log (c x))}",1,"Hypergeometric2F1[-3/2, -1/2, 1/2, c^4*x^4]/(4*c^2*x*Sqrt[2 - 2*c^4*x^4]*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)])","C",1
152,1,54,67,0.0982774,"\int \frac{\text{csch}^{\frac{3}{2}}(2 \log (c x))}{x} \, dx","Integrate[Csch[2*Log[c*x]]^(3/2)/x,x]","\sqrt{\text{csch}(2 \log (c x))} \left(-\cosh (2 \log (c x))+\sqrt{i \sinh (2 \log (c x))} E\left(\left.\frac{\pi }{4}-i \log (c x)\right|2\right)\right)","-\cosh (2 \log (c x)) \sqrt{\text{csch}(2 \log (c x))}+\frac{i E\left(\left.\frac{\pi }{4}-i \log (c x)\right|2\right)}{\sqrt{i \sinh (2 \log (c x))} \sqrt{\text{csch}(2 \log (c x))}}",1,"Sqrt[Csch[2*Log[c*x]]]*(-Cosh[2*Log[c*x]] + EllipticE[Pi/4 - I*Log[c*x], 2]*Sqrt[I*Sinh[2*Log[c*x]]])","A",1
153,1,33,27,0.0348575,"\int \frac{\text{csch}^{\frac{3}{2}}(2 \log (c x))}{x^2} \, dx","Integrate[Csch[2*Log[c*x]]^(3/2)/x^2,x]","-\sqrt{2} c^2 x \sqrt{\frac{c^2 x^2}{c^4 x^4-1}}","-\frac{1}{2} x^3 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))",1,"-(Sqrt[2]*c^2*x*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)])","A",1
154,1,66,69,0.1083341,"\int \frac{\text{csch}^{\frac{3}{2}}(2 \log (c x))}{x^3} \, dx","Integrate[Csch[2*Log[c*x]]^(3/2)/x^3,x]","-\sqrt{2} c^2 \sqrt{\frac{c^2 x^2}{c^4 x^4-1}} \left(\sqrt{1-c^4 x^4} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};c^4 x^4\right)+1\right)","\frac{1}{2} c^5 x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} F\left(\left.\csc ^{-1}(c x)\right|-1\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))-\frac{1}{2} x^2 \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))",1,"-(Sqrt[2]*c^2*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)]*(1 + Sqrt[1 - c^4*x^4]*Hypergeometric2F1[1/4, 1/2, 5/4, c^4*x^4]))","C",1
155,1,53,69,0.10685,"\int \frac{\text{csch}^{\frac{3}{2}}(2 \log (c x))}{x^4} \, dx","Integrate[Csch[2*Log[c*x]]^(3/2)/x^4,x]","-\frac{\sqrt{2} c^2 \sqrt{\frac{c^2 x^2}{c^4 x^4-1}} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};1-c^4 x^4\right)}{x}","\frac{1}{2} c^6 x^3 \left(1-\frac{1}{c^4 x^4}\right)^{3/2} \csc ^{-1}\left(c^2 x^2\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))-\frac{1}{2} x \left(c^4-\frac{1}{x^4}\right) \text{csch}^{\frac{3}{2}}(2 \log (c x))",1,"-((Sqrt[2]*c^2*Sqrt[(c^2*x^2)/(-1 + c^4*x^4)]*Hypergeometric2F1[-1/2, 1, 1/2, 1 - c^4*x^4])/x)","C",1
156,1,62,62,1.2014954,"\int \text{csch}\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Csch[a + b*Log[c*x^n]],x]","-\frac{2 e^a x \left(c x^n\right)^b \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{1}{b n}\right);\frac{1}{2} \left(3+\frac{1}{b n}\right);e^{2 \left(a+b \log \left(c x^n\right)\right)}\right)}{b n+1}","-\frac{2 e^a x \left(c x^n\right)^b \, _2F_1\left(1,\frac{b+\frac{1}{n}}{2 b};\frac{1}{2} \left(3+\frac{1}{b n}\right);e^{2 a} \left(c x^n\right)^{2 b}\right)}{b n+1}",1,"(-2*E^a*x*(c*x^n)^b*Hypergeometric2F1[1, (1 + 1/(b*n))/2, (3 + 1/(b*n))/2, E^(2*(a + b*Log[c*x^n]))])/(1 + b*n)","A",1
157,1,126,68,4.3201455,"\int \text{csch}^2\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Csch[a + b*Log[c*x^n]]^2,x]","\frac{x \left(-\frac{e^{2 a} \left(c x^n\right)^{2 b} \, _2F_1\left(1,1+\frac{1}{2 b n};2+\frac{1}{2 b n};e^{2 \left(a+b \log \left(c x^n\right)\right)}\right)}{2 b n+1}-\, _2F_1\left(1,\frac{1}{2 b n};1+\frac{1}{2 b n};e^{2 \left(a+b \log \left(c x^n\right)\right)}\right)-\coth \left(a+b \log \left(c x^n\right)\right)\right)}{b n}","\frac{4 e^{2 a} x \left(c x^n\right)^{2 b} \, _2F_1\left(2,\frac{1}{2} \left(2+\frac{1}{b n}\right);\frac{1}{2} \left(4+\frac{1}{b n}\right);e^{2 a} \left(c x^n\right)^{2 b}\right)}{2 b n+1}",1,"(x*(-Coth[a + b*Log[c*x^n]] - (E^(2*a)*(c*x^n)^(2*b)*Hypergeometric2F1[1, 1 + 1/(2*b*n), 2 + 1/(2*b*n), E^(2*(a + b*Log[c*x^n]))])/(1 + 2*b*n) - Hypergeometric2F1[1, 1/(2*b*n), 1 + 1/(2*b*n), E^(2*(a + b*Log[c*x^n]))]))/(b*n)","A",0
158,1,101,69,5.0969463,"\int \text{csch}^3\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Csch[a + b*Log[c*x^n]]^3,x]","\frac{8 e^a x (b n-1) \left(c x^n\right)^b \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{1}{b n}\right);\frac{1}{2} \left(3+\frac{1}{b n}\right);e^{2 \left(a+b \log \left(c x^n\right)\right)}\right)-4 x \left(b n \coth \left(a+b \log \left(c x^n\right)\right)+1\right) \text{csch}\left(a+b \log \left(c x^n\right)\right)}{8 b^2 n^2}","-\frac{8 e^{3 a} x \left(c x^n\right)^{3 b} \, _2F_1\left(3,\frac{3 b+\frac{1}{n}}{2 b};\frac{1}{2} \left(5+\frac{1}{b n}\right);e^{2 a} \left(c x^n\right)^{2 b}\right)}{3 b n+1}",1,"(-4*x*(1 + b*n*Coth[a + b*Log[c*x^n]])*Csch[a + b*Log[c*x^n]] + 8*E^a*(-1 + b*n)*x*(c*x^n)^b*Hypergeometric2F1[1, (1 + 1/(b*n))/2, (3 + 1/(b*n))/2, E^(2*(a + b*Log[c*x^n]))])/(8*b^2*n^2)","A",0
159,1,200,68,9.0236246,"\int \text{csch}^4\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Csch[a + b*Log[c*x^n]]^4,x]","\frac{x \left(4 \left(4 b^2 n^2-1\right) \, _2F_1\left(1,\frac{1}{2 b n};1+\frac{1}{2 b n};e^{2 \left(a+b \log \left(c x^n\right)\right)}\right)+\text{csch}^3\left(a+b \log \left(c x^n\right)\right) \left(\left(1-12 b^2 n^2\right) \cosh \left(a+b \log \left(c x^n\right)\right)+\left(4 b^2 n^2-1\right) \cosh \left(3 \left(a+b \log \left(c x^n\right)\right)\right)-4 b n \sinh \left(a+b \log \left(c x^n\right)\right)\right)+4 e^{2 a} (2 b n-1) \left(c x^n\right)^{2 b} \, _2F_1\left(1,1+\frac{1}{2 b n};2+\frac{1}{2 b n};e^{2 \left(a+b \log \left(c x^n\right)\right)}\right)\right)}{24 b^3 n^3}","\frac{16 e^{4 a} x \left(c x^n\right)^{4 b} \, _2F_1\left(4,\frac{1}{2} \left(4+\frac{1}{b n}\right);\frac{1}{2} \left(6+\frac{1}{b n}\right);e^{2 a} \left(c x^n\right)^{2 b}\right)}{4 b n+1}",1,"(x*(4*E^(2*a)*(-1 + 2*b*n)*(c*x^n)^(2*b)*Hypergeometric2F1[1, 1 + 1/(2*b*n), 2 + 1/(2*b*n), E^(2*(a + b*Log[c*x^n]))] + 4*(-1 + 4*b^2*n^2)*Hypergeometric2F1[1, 1/(2*b*n), 1 + 1/(2*b*n), E^(2*(a + b*Log[c*x^n]))] + Csch[a + b*Log[c*x^n]]^3*((1 - 12*b^2*n^2)*Cosh[a + b*Log[c*x^n]] + (-1 + 4*b^2*n^2)*Cosh[3*(a + b*Log[c*x^n])] - 4*b*n*Sinh[a + b*Log[c*x^n]])))/(24*b^3*n^3)","B",0
160,1,30,42,0.4243952,"\int \left(-\left(\left(1-b^2 n^2\right) \text{csch}\left(a+b \log \left(c x^n\right)\right)\right)+2 b^2 n^2 \text{csch}^3\left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[-((1 - b^2*n^2)*Csch[a + b*Log[c*x^n]]) + 2*b^2*n^2*Csch[a + b*Log[c*x^n]]^3,x]","-x \left(b n \coth \left(a+b \log \left(c x^n\right)\right)+1\right) \text{csch}\left(a+b \log \left(c x^n\right)\right)","-x \text{csch}\left(a+b \log \left(c x^n\right)\right)-b n x \coth \left(a+b \log \left(c x^n\right)\right) \text{csch}\left(a+b \log \left(c x^n\right)\right)",1,"-(x*(1 + b*n*Coth[a + b*Log[c*x^n]])*Csch[a + b*Log[c*x^n]])","A",1
161,1,62,26,0.1274768,"\int \text{csch}^3\left(a+2 \log \left(c \sqrt{x}\right)\right) \, dx","Integrate[Csch[a + 2*Log[c*Sqrt[x]]]^3,x]","\frac{2 (\cosh (a)-\sinh (a)) \left(\sinh ^2(a)+\cosh ^2(a)-2 \sinh (a) \cosh (a)-2 c^4 x^2\right)}{c^2 \left(\sinh (a) \left(c^4 x^2+1\right)+\cosh (a) \left(c^4 x^2-1\right)\right)^2}","-\frac{2 e^{-a} c^6}{\left(c^4-\frac{e^{-2 a}}{x^2}\right)^2}",1,"(2*(Cosh[a] - Sinh[a])*(-2*c^4*x^2 + Cosh[a]^2 - 2*Cosh[a]*Sinh[a] + Sinh[a]^2))/(c^2*((-1 + c^4*x^2)*Cosh[a] + (1 + c^4*x^2)*Sinh[a])^2)","B",1
162,1,65,26,0.1118043,"\int \text{csch}^3\left(a+2 \log \left(\frac{c}{\sqrt{x}}\right)\right) \, dx","Integrate[Csch[a + 2*Log[c/Sqrt[x]]]^3,x]","-\frac{2 c^6 (\sinh (2 a)+\cosh (2 a)) \left(\sinh (a) \left(c^4+2 x^2\right)+\cosh (a) \left(c^4-2 x^2\right)\right)}{\left(\cosh (a) \left(x^2-c^4\right)-\sinh (a) \left(c^4+x^2\right)\right)^2}","\frac{2 e^{-3 a} c^2}{\left(e^{-2 a}-\frac{c^4}{x^2}\right)^2}",1,"(-2*c^6*((c^4 - 2*x^2)*Cosh[a] + (c^4 + 2*x^2)*Sinh[a])*(Cosh[2*a] + Sinh[2*a]))/((-c^4 + x^2)*Cosh[a] - (c^4 + x^2)*Sinh[a])^2","B",1
163,1,115,90,6.7560377,"\int \text{csch}^p\left(a+\frac{\log \left(c x^n\right)}{n (-2+p)}\right) \, dx","Integrate[Csch[a + Log[c*x^n]/(n*(-2 + p))]^p,x]","\frac{2^{p-1} (p-2) x \left(\frac{e^a \left(c x^n\right)^{\frac{1}{n (p-2)}}}{e^{2 a} \left(c x^n\right)^{\frac{2}{n (p-2)}}-1}\right)^p \left(e^{2 a} \left(c x^n\right)^{\frac{2}{n (p-2)}} \left(\left(1-e^{-2 a} \left(c x^n\right)^{-\frac{2}{n (p-2)}}\right)^p-1\right)+1\right)}{p-1}","-\frac{e^{2 a} (2-p) x \left(c x^n\right)^{-\frac{2}{n (2-p)}} \left(1-e^{-2 a} \left(c x^n\right)^{\frac{2}{n (2-p)}}\right) \text{csch}^p\left(a-\frac{\log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}",1,"(2^(-1 + p)*(-2 + p)*x*((E^a*(c*x^n)^(1/(n*(-2 + p))))/(-1 + E^(2*a)*(c*x^n)^(2/(n*(-2 + p)))))^p*(1 + E^(2*a)*(c*x^n)^(2/(n*(-2 + p)))*(-1 + (1 - 1/(E^(2*a)*(c*x^n)^(2/(n*(-2 + p)))))^p)))/(-1 + p)","A",0
164,1,64,66,0.9184665,"\int \text{csch}^p\left(a-\frac{\log \left(c x^n\right)}{n (-2+p)}\right) \, dx","Integrate[Csch[a - Log[c*x^n]/(n*(-2 + p))]^p,x]","\frac{e^{-2 a} (p-2) x \left(e^{2 a}-\left(c x^n\right)^{\frac{2}{n (p-2)}}\right) \text{csch}^p\left(a+\frac{\log \left(c x^n\right)}{2 n-n p}\right)}{2 (p-1)}","\frac{(2-p) x \left(1-e^{-2 a} \left(c x^n\right)^{-\frac{2}{n (2-p)}}\right) \text{csch}^p\left(a+\frac{\log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}",1,"((-2 + p)*x*(E^(2*a) - (c*x^n)^(2/(n*(-2 + p))))*Csch[a + Log[c*x^n]/(2*n - n*p)]^p)/(2*E^(2*a)*(-1 + p))","A",1
165,1,54,20,0.0623212,"\int \frac{\text{csch}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Csch[a + b*Log[c*x^n]]/x,x]","\frac{\log \left(\sinh \left(\frac{a}{2}+\frac{1}{2} b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\log \left(\cosh \left(\frac{a}{2}+\frac{1}{2} b \log \left(c x^n\right)\right)\right)}{b n}","-\frac{\tanh ^{-1}\left(\cosh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}",1,"-(Log[Cosh[a/2 + (b*Log[c*x^n])/2]]/(b*n)) + Log[Sinh[a/2 + (b*Log[c*x^n])/2]]/(b*n)","B",1
166,1,19,19,0.0724742,"\int \frac{\text{csch}^2\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Csch[a + b*Log[c*x^n]]^2/x,x]","-\frac{\coth \left(a+b \log \left(c x^n\right)\right)}{b n}","-\frac{\coth \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"-(Coth[a + b*Log[c*x^n]]/(b*n))","A",1
167,1,81,55,0.0625075,"\int \frac{\text{csch}^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Csch[a + b*Log[c*x^n]]^3/x,x]","-\frac{\log \left(\tanh \left(\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right)\right)}{2 b n}-\frac{\text{sech}^2\left(\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right)}{8 b n}-\frac{\text{csch}^2\left(\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right)}{8 b n}","\frac{\tanh ^{-1}\left(\cosh \left(a+b \log \left(c x^n\right)\right)\right)}{2 b n}-\frac{\coth \left(a+b \log \left(c x^n\right)\right) \text{csch}\left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"-1/8*Csch[(a + b*Log[c*x^n])/2]^2/(b*n) - Log[Tanh[(a + b*Log[c*x^n])/2]]/(2*b*n) - Sech[(a + b*Log[c*x^n])/2]^2/(8*b*n)","A",1
168,1,56,42,0.0683713,"\int \frac{\text{csch}^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Csch[a + b*Log[c*x^n]]^4/x,x]","\frac{2 \coth \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) \text{csch}^2\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}-\frac{\coth ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}",1,"(2*Coth[a + b*Log[c*x^n]])/(3*b*n) - (Coth[a + b*Log[c*x^n]]*Csch[a + b*Log[c*x^n]]^2)/(3*b*n)","A",1
169,1,135,89,0.0631956,"\int \frac{\text{csch}^5\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Csch[a + b*Log[c*x^n]]^5/x,x]","\frac{3 \log \left(\tanh \left(\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right)\right)}{8 b n}+\frac{\text{sech}^4\left(\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right)}{64 b n}+\frac{3 \text{sech}^2\left(\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right)}{32 b n}-\frac{\text{csch}^4\left(\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right)}{64 b n}+\frac{3 \text{csch}^2\left(\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right)}{32 b n}","-\frac{3 \tanh ^{-1}\left(\cosh \left(a+b \log \left(c x^n\right)\right)\right)}{8 b n}-\frac{\coth \left(a+b \log \left(c x^n\right)\right) \text{csch}^3\left(a+b \log \left(c x^n\right)\right)}{4 b n}+\frac{3 \coth \left(a+b \log \left(c x^n\right)\right) \text{csch}\left(a+b \log \left(c x^n\right)\right)}{8 b n}",1,"(3*Csch[(a + b*Log[c*x^n])/2]^2)/(32*b*n) - Csch[(a + b*Log[c*x^n])/2]^4/(64*b*n) + (3*Log[Tanh[(a + b*Log[c*x^n])/2]])/(8*b*n) + (3*Sech[(a + b*Log[c*x^n])/2]^2)/(32*b*n) + Sech[(a + b*Log[c*x^n])/2]^4/(64*b*n)","A",1
170,1,84,111,0.2234974,"\int \frac{\text{csch}^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Csch[a + b*Log[c*x^n]]^(5/2)/x,x]","-\frac{2 \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)} \left(\coth \left(a+b \log \left(c x^n\right)\right)+i \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{4} \left(-2 i a-2 i b \log \left(c x^n\right)+\pi \right)\right|2\right)\right)}{3 b n}","-\frac{2 \cosh \left(a+b \log \left(c x^n\right)\right) \text{csch}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{2 i \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n}",1,"(-2*Sqrt[Csch[a + b*Log[c*x^n]]]*(Coth[a + b*Log[c*x^n]] + I*EllipticF[((-2*I)*a + Pi - (2*I)*b*Log[c*x^n])/4, 2]*Sqrt[I*Sinh[a + b*Log[c*x^n]]]))/(3*b*n)","A",1
171,1,80,107,0.1154653,"\int \frac{\text{csch}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Csch[a + b*Log[c*x^n]]^(3/2)/x,x]","-\frac{2 \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)} \left(\cosh \left(a+b \log \left(c x^n\right)\right)-\sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{4} \left(-2 i a-2 i b \log \left(c x^n\right)+\pi \right)\right|2\right)\right)}{b n}","-\frac{2 \cosh \left(a+b \log \left(c x^n\right)\right) \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)}}{b n}-\frac{2 i E\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)}}",1,"(-2*Sqrt[Csch[a + b*Log[c*x^n]]]*(Cosh[a + b*Log[c*x^n]] - EllipticE[((-2*I)*a + Pi - (2*I)*b*Log[c*x^n])/4, 2]*Sqrt[I*Sinh[a + b*Log[c*x^n]]]))/(b*n)","A",1
172,1,66,72,0.0971913,"\int \frac{\sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Integrate[Sqrt[Csch[a + b*Log[c*x^n]]]/x,x]","\frac{2 \left(i \sinh \left(a+b \log \left(c x^n\right)\right)\right)^{3/2} \text{csch}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) F\left(\left.\frac{1}{4} \left(-2 i a-2 i b \log \left(c x^n\right)+\pi \right)\right|2\right)}{b n}","-\frac{2 i \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}",1,"(2*Csch[a + b*Log[c*x^n]]^(3/2)*EllipticF[((-2*I)*a + Pi - (2*I)*b*Log[c*x^n])/4, 2]*(I*Sinh[a + b*Log[c*x^n]])^(3/2))/(b*n)","A",1
173,1,68,72,0.0816882,"\int \frac{1}{x \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)}} \, dx","Integrate[1/(x*Sqrt[Csch[a + b*Log[c*x^n]]]),x]","\frac{2 \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(\frac{\pi }{2}-i \left(a+b \log \left(c x^n\right)\right)\right)\right|2\right)}{b n}","-\frac{2 i E\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)}}",1,"(2*Sqrt[Csch[a + b*Log[c*x^n]]]*EllipticE[(Pi/2 - I*(a + b*Log[c*x^n]))/2, 2]*Sqrt[I*Sinh[a + b*Log[c*x^n]]])/(b*n)","A",1
174,1,86,111,0.1351083,"\int \frac{1}{x \text{csch}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Csch[a + b*Log[c*x^n]]^(3/2)),x]","\frac{\sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)} \left(\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-2 i \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{4} \left(-2 i a-2 i b \log \left(c x^n\right)+\pi \right)\right|2\right)\right)}{3 b n}","\frac{2 \cosh \left(a+b \log \left(c x^n\right)\right)}{3 b n \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)}}+\frac{2 i \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n}",1,"(Sqrt[Csch[a + b*Log[c*x^n]]]*((-2*I)*EllipticF[((-2*I)*a + Pi - (2*I)*b*Log[c*x^n])/4, 2]*Sqrt[I*Sinh[a + b*Log[c*x^n]]] + Sinh[2*(a + b*Log[c*x^n])]))/(3*b*n)","A",1
175,1,95,111,0.1895005,"\int \frac{1}{x \text{csch}^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Csch[a + b*Log[c*x^n]]^(5/2)),x]","\frac{2 \left(\cosh \left(a+b \log \left(c x^n\right)\right)-3 \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} \text{csch}^2\left(a+b \log \left(c x^n\right)\right) E\left(\left.\frac{1}{4} \left(-2 i a-2 i b \log \left(c x^n\right)+\pi \right)\right|2\right)\right)}{5 b n \text{csch}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 \cosh \left(a+b \log \left(c x^n\right)\right)}{5 b n \text{csch}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}+\frac{6 i E\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{5 b n \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} \sqrt{\text{csch}\left(a+b \log \left(c x^n\right)\right)}}",1,"(2*(Cosh[a + b*Log[c*x^n]] - 3*Csch[a + b*Log[c*x^n]]^2*EllipticE[((-2*I)*a + Pi - (2*I)*b*Log[c*x^n])/4, 2]*Sqrt[I*Sinh[a + b*Log[c*x^n]]]))/(5*b*n*Csch[a + b*Log[c*x^n]]^(3/2))","A",1