1,1,91,87,0.0133886,"\int x^3 \coth (a+b x) \, dx","Integrate[x^3*Coth[a + b*x],x]","\frac{3 \text{Li}_4\left(e^{2 a+2 b x}\right)}{4 b^4}-\frac{3 x \text{Li}_3\left(e^{2 a+2 b x}\right)}{2 b^3}+\frac{3 x^2 \text{Li}_2\left(e^{2 a+2 b x}\right)}{2 b^2}+\frac{x^3 \log \left(1-e^{2 a+2 b x}\right)}{b}-\frac{x^4}{4}","\frac{3 \text{Li}_4\left(e^{2 (a+b x)}\right)}{4 b^4}-\frac{3 x \text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 x^2 \text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^2}+\frac{x^3 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^4}{4}",1,"-1/4*x^4 + (x^3*Log[1 - E^(2*a + 2*b*x)])/b + (3*x^2*PolyLog[2, E^(2*a + 2*b*x)])/(2*b^2) - (3*x*PolyLog[3, E^(2*a + 2*b*x)])/(2*b^3) + (3*PolyLog[4, E^(2*a + 2*b*x)])/(4*b^4)","A",1
2,1,66,63,0.0103782,"\int x^2 \coth (a+b x) \, dx","Integrate[x^2*Coth[a + b*x],x]","-\frac{\text{Li}_3\left(e^{2 a+2 b x}\right)}{2 b^3}+\frac{x \text{Li}_2\left(e^{2 a+2 b x}\right)}{b^2}+\frac{x^2 \log \left(1-e^{2 a+2 b x}\right)}{b}-\frac{x^3}{3}","-\frac{\text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^3}+\frac{x \text{Li}_2\left(e^{2 (a+b x)}\right)}{b^2}+\frac{x^2 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^3}{3}",1,"-1/3*x^3 + (x^2*Log[1 - E^(2*a + 2*b*x)])/b + (x*PolyLog[2, E^(2*a + 2*b*x)])/b^2 - PolyLog[3, E^(2*a + 2*b*x)]/(2*b^3)","A",1
3,1,47,45,0.006935,"\int x \coth (a+b x) \, dx","Integrate[x*Coth[a + b*x],x]","\frac{\text{Li}_2\left(e^{2 a+2 b x}\right)}{2 b^2}+\frac{x \log \left(1-e^{2 a+2 b x}\right)}{b}-\frac{x^2}{2}","\frac{\text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^2}+\frac{x \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^2}{2}",1,"-1/2*x^2 + (x*Log[1 - E^(2*a + 2*b*x)])/b + PolyLog[2, E^(2*a + 2*b*x)]/(2*b^2)","A",1
4,0,0,13,13.2395349,"\int \frac{\coth (a+b x)}{x} \, dx","Integrate[Coth[a + b*x]/x,x]","\int \frac{\coth (a+b x)}{x} \, dx","\text{Int}\left(\frac{\coth (a+b x)}{x},x\right)",0,"Integrate[Coth[a + b*x]/x, x]","A",-1
5,0,0,13,19.1212234,"\int \frac{\coth (a+b x)}{x^2} \, dx","Integrate[Coth[a + b*x]/x^2,x]","\int \frac{\coth (a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\coth (a+b x)}{x^2},x\right)",0,"Integrate[Coth[a + b*x]/x^2, x]","A",-1
6,1,204,87,4.1926434,"\int x^3 \coth ^2(a+b x) \, dx","Integrate[x^3*Coth[a + b*x]^2,x]","-\frac{e^{2 a} \left(2 e^{-2 a} b^3 x^3-3 \left(1-e^{-2 a}\right) b^2 x^2 \log \left(1-e^{-a-b x}\right)-3 \left(1-e^{-2 a}\right) b^2 x^2 \log \left(e^{-a-b x}+1\right)+6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(-e^{-a-b x}\right)+\text{Li}_3\left(-e^{-a-b x}\right)\right)+6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(e^{-a-b x}\right)+\text{Li}_3\left(e^{-a-b x}\right)\right)\right)}{\left(e^{2 a}-1\right) b^4}+\frac{x^3 \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b}+\frac{x^4}{4}","-\frac{3 \text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 x \text{Li}_2\left(e^{2 (a+b x)}\right)}{b^3}+\frac{3 x^2 \log \left(1-e^{2 (a+b x)}\right)}{b^2}-\frac{x^3 \coth (a+b x)}{b}-\frac{x^3}{b}+\frac{x^4}{4}",1,"x^4/4 - (E^(2*a)*((2*b^3*x^3)/E^(2*a) - 3*b^2*(1 - E^(-2*a))*x^2*Log[1 - E^(-a - b*x)] - 3*b^2*(1 - E^(-2*a))*x^2*Log[1 + E^(-a - b*x)] + 6*(1 - E^(-2*a))*(b*x*PolyLog[2, -E^(-a - b*x)] + PolyLog[3, -E^(-a - b*x)]) + 6*(1 - E^(-2*a))*(b*x*PolyLog[2, E^(-a - b*x)] + PolyLog[3, E^(-a - b*x)])))/(b^4*(-1 + E^(2*a))) + (x^3*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b","B",1
7,1,163,65,5.4096658,"\int x^2 \coth ^2(a+b x) \, dx","Integrate[x^2*Coth[a + b*x]^2,x]","\frac{-b^2 x^2 e^{-\tanh ^{-1}(\tanh (a))} \coth (a) \sqrt{\text{sech}^2(a)}-\text{Li}_2\left(e^{-2 \left(b x+\tanh ^{-1}(\tanh (a))\right)}\right)+2 b x \log \left(1-e^{-2 \left(\tanh ^{-1}(\tanh (a))+b x\right)}\right)+2 \tanh ^{-1}(\tanh (a)) \left(\log \left(1-e^{-2 \left(\tanh ^{-1}(\tanh (a))+b x\right)}\right)-\log \left(i \sinh \left(\tanh ^{-1}(\tanh (a))+b x\right)\right)+b x\right)+i \pi  b x-i \pi  \log \left(e^{2 b x}+1\right)+i \pi  \log (\cosh (b x))}{b^3}+\frac{x^2 \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b}+\frac{x^3}{3}","\frac{\text{Li}_2\left(e^{2 (a+b x)}\right)}{b^3}+\frac{2 x \log \left(1-e^{2 (a+b x)}\right)}{b^2}-\frac{x^2 \coth (a+b x)}{b}-\frac{x^2}{b}+\frac{x^3}{3}",1,"x^3/3 + (I*b*Pi*x - I*Pi*Log[1 + E^(2*b*x)] + 2*b*x*Log[1 - E^(-2*(b*x + ArcTanh[Tanh[a]]))] + I*Pi*Log[Cosh[b*x]] + 2*ArcTanh[Tanh[a]]*(b*x + Log[1 - E^(-2*(b*x + ArcTanh[Tanh[a]]))] - Log[I*Sinh[b*x + ArcTanh[Tanh[a]]]]) - PolyLog[2, E^(-2*(b*x + ArcTanh[Tanh[a]]))] - (b^2*x^2*Coth[a]*Sqrt[Sech[a]^2])/E^ArcTanh[Tanh[a]])/b^3 + (x^2*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b","C",0
8,1,46,31,0.1643626,"\int x \coth ^2(a+b x) \, dx","Integrate[x*Coth[a + b*x]^2,x]","\frac{-2 b x \coth (a)+2 \log (\sinh (a+b x))+2 b x \text{csch}(a) \sinh (b x) \text{csch}(a+b x)+b^2 x^2}{2 b^2}","\frac{\log (\sinh (a+b x))}{b^2}-\frac{x \coth (a+b x)}{b}+\frac{x^2}{2}",1,"(b^2*x^2 - 2*b*x*Coth[a] + 2*Log[Sinh[a + b*x]] + 2*b*x*Csch[a]*Csch[a + b*x]*Sinh[b*x])/(2*b^2)","A",1
9,0,0,15,21.5321683,"\int \frac{\coth ^2(a+b x)}{x} \, dx","Integrate[Coth[a + b*x]^2/x,x]","\int \frac{\coth ^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\coth ^2(a+b x)}{x},x\right)",0,"Integrate[Coth[a + b*x]^2/x, x]","A",-1
10,0,0,15,20.4441012,"\int \frac{\coth ^2(a+b x)}{x^2} \, dx","Integrate[Coth[a + b*x]^2/x^2,x]","\int \frac{\coth ^2(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\coth ^2(a+b x)}{x^2},x\right)",0,"Integrate[Coth[a + b*x]^2/x^2, x]","A",-1
11,1,390,179,4.8863665,"\int x^3 \coth ^3(a+b x) \, dx","Integrate[x^3*Coth[a + b*x]^3,x]","\frac{1}{4} \left(\frac{6 x^2 \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b^2}-\frac{2 e^{2 a} \left(e^{-2 a} b^4 x^4-2 e^{-2 a} \left(e^{2 a}-1\right) b^3 x^3 \log \left(1-e^{-a-b x}\right)-2 e^{-2 a} \left(e^{2 a}-1\right) b^3 x^3 \log \left(e^{-a-b x}+1\right)+6 \left(1-e^{-2 a}\right) \left(b^2 x^2 \text{Li}_2\left(-e^{-a-b x}\right)+2 \left(b x \text{Li}_3\left(-e^{-a-b x}\right)+\text{Li}_4\left(-e^{-a-b x}\right)\right)\right)+6 \left(1-e^{-2 a}\right) \left(b^2 x^2 \text{Li}_2\left(e^{-a-b x}\right)+2 \left(b x \text{Li}_3\left(e^{-a-b x}\right)+\text{Li}_4\left(e^{-a-b x}\right)\right)\right)+6 e^{-2 a} b^2 x^2+6 \left(1-e^{-2 a}\right) \text{Li}_2\left(-e^{-a-b x}\right)+6 \left(1-e^{-2 a}\right) \text{Li}_2\left(e^{-a-b x}\right)-6 \left(1-e^{-2 a}\right) b x \log \left(1-e^{-a-b x}\right)-6 \left(1-e^{-2 a}\right) b x \log \left(e^{-a-b x}+1\right)\right)}{\left(e^{2 a}-1\right) b^4}-\frac{2 x^3 \text{csch}^2(a+b x)}{b}+x^4 \coth (a)\right)","\frac{3 \text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 \text{Li}_4\left(e^{2 (a+b x)}\right)}{4 b^4}-\frac{3 x \text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 x \log \left(1-e^{2 (a+b x)}\right)}{b^3}+\frac{3 x^2 \text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^2}-\frac{3 x^2 \coth (a+b x)}{2 b^2}+\frac{x^3 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^3 \coth ^2(a+b x)}{2 b}-\frac{3 x^2}{2 b^2}+\frac{x^3}{2 b}-\frac{x^4}{4}",1,"(x^4*Coth[a] - (2*x^3*Csch[a + b*x]^2)/b - (2*E^(2*a)*((6*b^2*x^2)/E^(2*a) + (b^4*x^4)/E^(2*a) - 6*b*(1 - E^(-2*a))*x*Log[1 - E^(-a - b*x)] - (2*b^3*(-1 + E^(2*a))*x^3*Log[1 - E^(-a - b*x)])/E^(2*a) - 6*b*(1 - E^(-2*a))*x*Log[1 + E^(-a - b*x)] - (2*b^3*(-1 + E^(2*a))*x^3*Log[1 + E^(-a - b*x)])/E^(2*a) + 6*(1 - E^(-2*a))*PolyLog[2, -E^(-a - b*x)] + 6*(1 - E^(-2*a))*PolyLog[2, E^(-a - b*x)] + 6*(1 - E^(-2*a))*(b^2*x^2*PolyLog[2, -E^(-a - b*x)] + 2*(b*x*PolyLog[3, -E^(-a - b*x)] + PolyLog[4, -E^(-a - b*x)])) + 6*(1 - E^(-2*a))*(b^2*x^2*PolyLog[2, E^(-a - b*x)] + 2*(b*x*PolyLog[3, E^(-a - b*x)] + PolyLog[4, E^(-a - b*x)]))))/(b^4*(-1 + E^(2*a))) + (6*x^2*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b^2)/4","B",1
12,1,295,114,3.4437285,"\int x^2 \coth ^3(a+b x) \, dx","Integrate[x^2*Coth[a + b*x]^3,x]","\frac{x \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b^2}-\frac{e^{2 a} \left(2 e^{-2 a} b^3 x^3-3 e^{-2 a} \left(e^{2 a}-1\right) b^2 x^2 \log \left(1-e^{-a-b x}\right)-3 e^{-2 a} \left(e^{2 a}-1\right) b^2 x^2 \log \left(e^{-a-b x}+1\right)+6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(-e^{-a-b x}\right)+\text{Li}_3\left(-e^{-a-b x}\right)\right)+6 \left(1-e^{-2 a}\right) \left(b x \text{Li}_2\left(e^{-a-b x}\right)+\text{Li}_3\left(e^{-a-b x}\right)\right)+6 e^{-2 a} b x+3 \left(1-e^{-2 a}\right) \left(b x-\log \left(1-e^{a+b x}\right)\right)+3 \left(1-e^{-2 a}\right) \left(b x-\log \left(e^{a+b x}+1\right)\right)\right)}{3 \left(e^{2 a}-1\right) b^3}-\frac{x^2 \text{csch}^2(a+b x)}{2 b}+\frac{1}{3} x^3 \coth (a)","-\frac{\text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^3}+\frac{\log (\sinh (a+b x))}{b^3}+\frac{x \text{Li}_2\left(e^{2 (a+b x)}\right)}{b^2}-\frac{x \coth (a+b x)}{b^2}+\frac{x^2 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^2 \coth ^2(a+b x)}{2 b}+\frac{x^2}{2 b}-\frac{x^3}{3}",1,"(x^3*Coth[a])/3 - (x^2*Csch[a + b*x]^2)/(2*b) - (E^(2*a)*((6*b*x)/E^(2*a) + (2*b^3*x^3)/E^(2*a) - (3*b^2*(-1 + E^(2*a))*x^2*Log[1 - E^(-a - b*x)])/E^(2*a) - (3*b^2*(-1 + E^(2*a))*x^2*Log[1 + E^(-a - b*x)])/E^(2*a) + 3*(1 - E^(-2*a))*(b*x - Log[1 - E^(a + b*x)]) + 3*(1 - E^(-2*a))*(b*x - Log[1 + E^(a + b*x)]) + 6*(1 - E^(-2*a))*(b*x*PolyLog[2, -E^(-a - b*x)] + PolyLog[3, -E^(-a - b*x)]) + 6*(1 - E^(-2*a))*(b*x*PolyLog[2, E^(-a - b*x)] + PolyLog[3, E^(-a - b*x)])))/(3*b^3*(-1 + E^(2*a))) + (x*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b^2","B",1
13,1,231,82,6.15105,"\int x \coth ^3(a+b x) \, dx","Integrate[x*Coth[a + b*x]^3,x]","-\frac{\text{csch}(a) \text{sech}(a) \left(b^2 x^2 e^{-\tanh ^{-1}(\tanh (a))}-\frac{i \tanh (a) \left(i \text{Li}_2\left(e^{2 i \left(i b x+i \tanh ^{-1}(\tanh (a))\right)}\right)-b x \left(-\pi +2 i \tanh ^{-1}(\tanh (a))\right)-2 \left(i \tanh ^{-1}(\tanh (a))+i b x\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}(\tanh (a))+i b x\right)}\right)+2 i \tanh ^{-1}(\tanh (a)) \log \left(i \sinh \left(\tanh ^{-1}(\tanh (a))+b x\right)\right)-\pi  \log \left(e^{2 b x}+1\right)+\pi  \log (\cosh (b x))\right)}{\sqrt{1-\tanh ^2(a)}}\right)}{2 b^2 \sqrt{\text{sech}^2(a) \left(\cosh ^2(a)-\sinh ^2(a)\right)}}+\frac{\text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{2 b^2}-\frac{x \text{csch}^2(a+b x)}{2 b}+\frac{1}{2} x^2 \coth (a)","\frac{\text{Li}_2\left(e^{2 (a+b x)}\right)}{2 b^2}-\frac{\coth (a+b x)}{2 b^2}+\frac{x \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x \coth ^2(a+b x)}{2 b}+\frac{x}{2 b}-\frac{x^2}{2}",1,"(x^2*Coth[a])/2 - (x*Csch[a + b*x]^2)/(2*b) + (Csch[a]*Csch[a + b*x]*Sinh[b*x])/(2*b^2) - (Csch[a]*Sech[a]*((b^2*x^2)/E^ArcTanh[Tanh[a]] - (I*(-(b*x*(-Pi + (2*I)*ArcTanh[Tanh[a]])) - Pi*Log[1 + E^(2*b*x)] - 2*(I*b*x + I*ArcTanh[Tanh[a]])*Log[1 - E^((2*I)*(I*b*x + I*ArcTanh[Tanh[a]]))] + Pi*Log[Cosh[b*x]] + (2*I)*ArcTanh[Tanh[a]]*Log[I*Sinh[b*x + ArcTanh[Tanh[a]]]] + I*PolyLog[2, E^((2*I)*(I*b*x + I*ArcTanh[Tanh[a]]))])*Tanh[a])/Sqrt[1 - Tanh[a]^2]))/(2*b^2*Sqrt[Sech[a]^2*(Cosh[a]^2 - Sinh[a]^2)])","C",0
14,0,0,15,16.174993,"\int \frac{\coth ^3(a+b x)}{x} \, dx","Integrate[Coth[a + b*x]^3/x,x]","\int \frac{\coth ^3(a+b x)}{x} \, dx","\text{Int}\left(\frac{\coth ^3(a+b x)}{x},x\right)",0,"Integrate[Coth[a + b*x]^3/x, x]","A",-1
15,0,0,15,12.0430423,"\int \frac{\coth ^3(a+b x)}{x^2} \, dx","Integrate[Coth[a + b*x]^3/x^2,x]","\int \frac{\coth ^3(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\coth ^3(a+b x)}{x^2},x\right)",0,"Integrate[Coth[a + b*x]^3/x^2, x]","A",-1
16,1,244,169,0.4382488,"\int \frac{(c+d x)^3}{a+a \coth (e+f x)} \, dx","Integrate[(c + d*x)^3/(a + a*Coth[e + f*x]),x]","\frac{\text{csch}(e+f x) (\sinh (f x)+\cosh (f x)) \left(2 f^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) (\sinh (e)+\cosh (e))+(\cosh (e)-\sinh (e)) \cosh (2 f x) \left(4 c^3 f^3+6 c^2 d f^2 (2 f x+1)+6 c d^2 f \left(2 f^2 x^2+2 f x+1\right)+d^3 \left(4 f^3 x^3+6 f^2 x^2+6 f x+3\right)\right)+(\sinh (e)-\cosh (e)) \sinh (2 f x) \left(4 c^3 f^3+6 c^2 d f^2 (2 f x+1)+6 c d^2 f \left(2 f^2 x^2+2 f x+1\right)+d^3 \left(4 f^3 x^3+6 f^2 x^2+6 f x+3\right)\right)\right)}{16 a f^4 (\coth (e+f x)+1)}","-\frac{3 d^2 (c+d x)}{4 f^3 (a \coth (e+f x)+a)}-\frac{3 d (c+d x)^2}{4 f^2 (a \coth (e+f x)+a)}-\frac{(c+d x)^3}{2 f (a \coth (e+f x)+a)}+\frac{3 d (c+d x)^2}{8 a f^2}+\frac{(c+d x)^3}{4 a f}+\frac{(c+d x)^4}{8 a d}-\frac{3 d^3}{8 f^4 (a \coth (e+f x)+a)}+\frac{3 d^3 x}{8 a f^3}",1,"(Csch[e + f*x]*(Cosh[f*x] + Sinh[f*x])*((4*c^3*f^3 + 6*c^2*d*f^2*(1 + 2*f*x) + 6*c*d^2*f*(1 + 2*f*x + 2*f^2*x^2) + d^3*(3 + 6*f*x + 6*f^2*x^2 + 4*f^3*x^3))*Cosh[2*f*x]*(Cosh[e] - Sinh[e]) + 2*f^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*(Cosh[e] + Sinh[e]) + (4*c^3*f^3 + 6*c^2*d*f^2*(1 + 2*f*x) + 6*c*d^2*f*(1 + 2*f*x + 2*f^2*x^2) + d^3*(3 + 6*f*x + 6*f^2*x^2 + 4*f^3*x^3))*(-Cosh[e] + Sinh[e])*Sinh[2*f*x]))/(16*a*f^4*(1 + Coth[e + f*x]))","A",1
17,1,169,122,0.281097,"\int \frac{(c+d x)^2}{a+a \coth (e+f x)} \, dx","Integrate[(c + d*x)^2/(a + a*Coth[e + f*x]),x]","\frac{\text{csch}(e+f x) (\sinh (f x)+\cosh (f x)) \left(\frac{4}{3} f^3 x \left(3 c^2+3 c d x+d^2 x^2\right) (\sinh (e)+\cosh (e))+(\cosh (e)-\sinh (e)) \cosh (2 f x) \left(2 c^2 f^2+2 c d f (2 f x+1)+d^2 \left(2 f^2 x^2+2 f x+1\right)\right)+(\sinh (e)-\cosh (e)) \sinh (2 f x) \left(2 c^2 f^2+2 c d f (2 f x+1)+d^2 \left(2 f^2 x^2+2 f x+1\right)\right)\right)}{8 a f^3 (\coth (e+f x)+1)}","-\frac{d (c+d x)}{2 f^2 (a \coth (e+f x)+a)}-\frac{(c+d x)^2}{2 f (a \coth (e+f x)+a)}+\frac{(c+d x)^2}{4 a f}+\frac{(c+d x)^3}{6 a d}-\frac{d^2}{4 f^3 (a \coth (e+f x)+a)}+\frac{d^2 x}{4 a f^2}",1,"(Csch[e + f*x]*(Cosh[f*x] + Sinh[f*x])*((2*c^2*f^2 + 2*c*d*f*(1 + 2*f*x) + d^2*(1 + 2*f*x + 2*f^2*x^2))*Cosh[2*f*x]*(Cosh[e] - Sinh[e]) + (4*f^3*x*(3*c^2 + 3*c*d*x + d^2*x^2)*(Cosh[e] + Sinh[e]))/3 + (2*c^2*f^2 + 2*c*d*f*(1 + 2*f*x) + d^2*(1 + 2*f*x + 2*f^2*x^2))*(-Cosh[e] + Sinh[e])*Sinh[2*f*x]))/(8*a*f^3*(1 + Coth[e + f*x]))","A",1
18,1,81,74,0.2891263,"\int \frac{c+d x}{a+a \coth (e+f x)} \, dx","Integrate[(c + d*x)/(a + a*Coth[e + f*x]),x]","\frac{\left(2 c f (2 f x+1)+d \left(2 f^2 x^2+2 f x+1\right)\right) \coth (e+f x)+2 c f (2 f x-1)+d \left(2 f^2 x^2-2 f x-1\right)}{8 a f^2 (\coth (e+f x)+1)}","-\frac{c+d x}{2 f (a \coth (e+f x)+a)}+\frac{(c+d x)^2}{4 a d}-\frac{d}{4 f^2 (a \coth (e+f x)+a)}+\frac{d x}{4 a f}",1,"(2*c*f*(-1 + 2*f*x) + d*(-1 - 2*f*x + 2*f^2*x^2) + (2*c*f*(1 + 2*f*x) + d*(1 + 2*f*x + 2*f^2*x^2))*Coth[e + f*x])/(8*a*f^2*(1 + Coth[e + f*x]))","A",1
19,1,122,157,0.2734208,"\int \frac{1}{(c+d x) (a+a \coth (e+f x))} \, dx","Integrate[1/((c + d*x)*(a + a*Coth[e + f*x])),x]","\frac{\text{csch}(e+f x) (\sinh (f x)+\cosh (f x)) \left(\text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \left(\sinh \left(e-\frac{2 c f}{d}\right)-\cosh \left(e-\frac{2 c f}{d}\right)\right)+\text{Shi}\left(\frac{2 f (c+d x)}{d}\right) \left(\cosh \left(e-\frac{2 c f}{d}\right)-\sinh \left(e-\frac{2 c f}{d}\right)\right)+(\sinh (e)+\cosh (e)) \log (f (c+d x))\right)}{2 a d (\coth (e+f x)+1)}","\frac{\text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{2 a d}-\frac{\text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{2 a d}-\frac{\sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{2 a d}+\frac{\cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{2 a d}+\frac{\log (c+d x)}{2 a d}",1,"(Csch[e + f*x]*(Cosh[f*x] + Sinh[f*x])*(Log[f*(c + d*x)]*(Cosh[e] + Sinh[e]) + CoshIntegral[(2*f*(c + d*x))/d]*(-Cosh[e - (2*c*f)/d] + Sinh[e - (2*c*f)/d]) + (Cosh[e - (2*c*f)/d] - Sinh[e - (2*c*f)/d])*SinhIntegral[(2*f*(c + d*x))/d]))/(2*a*d*(1 + Coth[e + f*x]))","A",1
20,1,206,159,0.8103878,"\int \frac{1}{(c+d x)^2 (a+a \coth (e+f x))} \, dx","Integrate[1/((c + d*x)^2*(a + a*Coth[e + f*x])),x]","-\frac{\text{csch}(e+f x) \left(\sinh \left(\frac{c f}{d}\right)+\cosh \left(\frac{c f}{d}\right)\right) \left(2 f (c+d x) \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \left(\sinh \left(e-\frac{f (c+d x)}{d}\right)-\cosh \left(e-\frac{f (c+d x)}{d}\right)\right)+2 f (c+d x) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right) \left(\cosh \left(e-\frac{f (c+d x)}{d}\right)-\sinh \left(e-\frac{f (c+d x)}{d}\right)\right)+d \left(\sinh \left(f \left(x-\frac{c}{d}\right)+e\right)+\sinh \left(f \left(\frac{c}{d}+x\right)+e\right)+\cosh \left(f \left(x-\frac{c}{d}\right)+e\right)-\cosh \left(f \left(\frac{c}{d}+x\right)+e\right)\right)\right)}{2 a d^2 (c+d x) (\coth (e+f x)+1)}","-\frac{f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{a d^2}+\frac{f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{a d^2}+\frac{f \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a d^2}-\frac{f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a d^2}-\frac{1}{d (c+d x) (a \coth (e+f x)+a)}",1,"-1/2*(Csch[e + f*x]*(Cosh[(c*f)/d] + Sinh[(c*f)/d])*(d*(Cosh[e + f*(-(c/d) + x)] - Cosh[e + f*(c/d + x)] + Sinh[e + f*(-(c/d) + x)] + Sinh[e + f*(c/d + x)]) + 2*f*(c + d*x)*CoshIntegral[(2*f*(c + d*x))/d]*(-Cosh[e - (f*(c + d*x))/d] + Sinh[e - (f*(c + d*x))/d]) + 2*f*(c + d*x)*(Cosh[e - (f*(c + d*x))/d] - Sinh[e - (f*(c + d*x))/d])*SinhIntegral[(2*f*(c + d*x))/d]))/(a*d^2*(c + d*x)*(1 + Coth[e + f*x]))","A",1
21,1,265,211,1.1230708,"\int \frac{1}{(c+d x)^3 (a+a \coth (e+f x))} \, dx","Integrate[1/((c + d*x)^3*(a + a*Coth[e + f*x])),x]","-\frac{\text{csch}(e+f x) \left(\sinh \left(\frac{c f}{d}\right)+\cosh \left(\frac{c f}{d}\right)\right) \left(4 f^2 (c+d x)^2 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \left(\cosh \left(e-\frac{f (c+d x)}{d}\right)-\sinh \left(e-\frac{f (c+d x)}{d}\right)\right)+4 f^2 (c+d x)^2 \text{Shi}\left(\frac{2 f (c+d x)}{d}\right) \left(\sinh \left(e-\frac{f (c+d x)}{d}\right)-\cosh \left(e-\frac{f (c+d x)}{d}\right)\right)+d \left(d \sinh \left(f \left(x-\frac{c}{d}\right)+e\right)+d \sinh \left(f \left(\frac{c}{d}+x\right)+e\right)-2 c f \sinh \left(f \left(\frac{c}{d}+x\right)+e\right)-2 d f x \sinh \left(f \left(\frac{c}{d}+x\right)+e\right)+d \cosh \left(f \left(x-\frac{c}{d}\right)+e\right)+(2 c f+2 d f x-d) \cosh \left(f \left(\frac{c}{d}+x\right)+e\right)\right)\right)}{4 a d^3 (c+d x)^2 (\coth (e+f x)+1)}","\frac{f^2 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{a d^3}-\frac{f^2 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{a d^3}-\frac{f^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a d^3}+\frac{f^2 \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a d^3}+\frac{f}{d^2 (c+d x) (a \coth (e+f x)+a)}-\frac{f}{2 a d^2 (c+d x)}-\frac{1}{2 d (c+d x)^2 (a \coth (e+f x)+a)}",1,"-1/4*(Csch[e + f*x]*(Cosh[(c*f)/d] + Sinh[(c*f)/d])*(d*(d*Cosh[e + f*(-(c/d) + x)] + (-d + 2*c*f + 2*d*f*x)*Cosh[e + f*(c/d + x)] + d*Sinh[e + f*(-(c/d) + x)] + d*Sinh[e + f*(c/d + x)] - 2*c*f*Sinh[e + f*(c/d + x)] - 2*d*f*x*Sinh[e + f*(c/d + x)]) + 4*f^2*(c + d*x)^2*CoshIntegral[(2*f*(c + d*x))/d]*(Cosh[e - (f*(c + d*x))/d] - Sinh[e - (f*(c + d*x))/d]) + 4*f^2*(c + d*x)^2*(-Cosh[e - (f*(c + d*x))/d] + Sinh[e - (f*(c + d*x))/d])*SinhIntegral[(2*f*(c + d*x))/d]))/(a*d^3*(c + d*x)^2*(1 + Coth[e + f*x]))","A",1
22,1,420,230,1.1180184,"\int \frac{(c+d x)^3}{(a+a \coth (e+f x))^2} \, dx","Integrate[(c + d*x)^3/(a + a*Coth[e + f*x])^2,x]","\frac{\text{csch}^2(e+f x) (\sinh (f x)+\cosh (f x))^2 \left(f^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) (\sinh (2 e)+\cosh (2 e))+\frac{1}{32} (\sinh (2 e)-\cosh (2 e)) \cosh (4 f x) \left(32 c^3 f^3+24 c^2 d f^2 (4 f x+1)+12 c d^2 f \left(8 f^2 x^2+4 f x+1\right)+d^3 \left(32 f^3 x^3+24 f^2 x^2+12 f x+3\right)\right)+\frac{1}{32} (\cosh (2 e)-\sinh (2 e)) \sinh (4 f x) \left(32 c^3 f^3+24 c^2 d f^2 (4 f x+1)+12 c d^2 f \left(8 f^2 x^2+4 f x+1\right)+d^3 \left(32 f^3 x^3+24 f^2 x^2+12 f x+3\right)\right)-\sinh (2 f x) \left(4 c^3 f^3+6 c^2 d f^2 (2 f x+1)+6 c d^2 f \left(2 f^2 x^2+2 f x+1\right)+d^3 \left(4 f^3 x^3+6 f^2 x^2+6 f x+3\right)\right)+\cosh (2 f x) \left(4 c^3 f^3+6 c^2 d f^2 (2 f x+1)+6 c d^2 f \left(2 f^2 x^2+2 f x+1\right)+d^3 \left(4 f^3 x^3+6 f^2 x^2+6 f x+3\right)\right)\right)}{16 a^2 f^4 (\coth (e+f x)+1)^2}","-\frac{3 d^2 (c+d x) e^{-4 e-4 f x}}{128 a^2 f^3}+\frac{3 d^2 (c+d x) e^{-2 e-2 f x}}{8 a^2 f^3}-\frac{3 d (c+d x)^2 e^{-4 e-4 f x}}{64 a^2 f^2}+\frac{3 d (c+d x)^2 e^{-2 e-2 f x}}{8 a^2 f^2}-\frac{(c+d x)^3 e^{-4 e-4 f x}}{16 a^2 f}+\frac{(c+d x)^3 e^{-2 e-2 f x}}{4 a^2 f}+\frac{(c+d x)^4}{16 a^2 d}-\frac{3 d^3 e^{-4 e-4 f x}}{512 a^2 f^4}+\frac{3 d^3 e^{-2 e-2 f x}}{16 a^2 f^4}",1,"(Csch[e + f*x]^2*(Cosh[f*x] + Sinh[f*x])^2*((4*c^3*f^3 + 6*c^2*d*f^2*(1 + 2*f*x) + 6*c*d^2*f*(1 + 2*f*x + 2*f^2*x^2) + d^3*(3 + 6*f*x + 6*f^2*x^2 + 4*f^3*x^3))*Cosh[2*f*x] + ((32*c^3*f^3 + 24*c^2*d*f^2*(1 + 4*f*x) + 12*c*d^2*f*(1 + 4*f*x + 8*f^2*x^2) + d^3*(3 + 12*f*x + 24*f^2*x^2 + 32*f^3*x^3))*Cosh[4*f*x]*(-Cosh[2*e] + Sinh[2*e]))/32 + f^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*(Cosh[2*e] + Sinh[2*e]) - (4*c^3*f^3 + 6*c^2*d*f^2*(1 + 2*f*x) + 6*c*d^2*f*(1 + 2*f*x + 2*f^2*x^2) + d^3*(3 + 6*f*x + 6*f^2*x^2 + 4*f^3*x^3))*Sinh[2*f*x] + ((32*c^3*f^3 + 24*c^2*d*f^2*(1 + 4*f*x) + 12*c*d^2*f*(1 + 4*f*x + 8*f^2*x^2) + d^3*(3 + 12*f*x + 24*f^2*x^2 + 32*f^3*x^3))*(Cosh[2*e] - Sinh[2*e])*Sinh[4*f*x])/32))/(16*a^2*f^4*(1 + Coth[e + f*x])^2)","A",1
23,1,207,170,1.0437324,"\int \frac{(c+d x)^2}{(a+a \coth (e+f x))^2} \, dx","Integrate[(c + d*x)^2/(a + a*Coth[e + f*x])^2,x]","\frac{\text{csch}^2(e+f x) \left(\left(24 c^2 f^2 (4 f x+1)+12 c d f \left(8 f^2 x^2+4 f x+1\right)+d^2 \left(32 f^3 x^3+24 f^2 x^2+12 f x+3\right)\right) \sinh (2 (e+f x))+\left(24 c^2 f^2 (4 f x-1)+12 c d f \left(8 f^2 x^2-4 f x-1\right)+d^2 \left(32 f^3 x^3-24 f^2 x^2-12 f x-3\right)\right) \cosh (2 (e+f x))+48 \left(2 c^2 f^2+2 c d f (2 f x+1)+d^2 \left(2 f^2 x^2+2 f x+1\right)\right)\right)}{384 a^2 f^3 (\coth (e+f x)+1)^2}","-\frac{d (c+d x) e^{-4 e-4 f x}}{32 a^2 f^2}+\frac{d (c+d x) e^{-2 e-2 f x}}{4 a^2 f^2}-\frac{(c+d x)^2 e^{-4 e-4 f x}}{16 a^2 f}+\frac{(c+d x)^2 e^{-2 e-2 f x}}{4 a^2 f}+\frac{(c+d x)^3}{12 a^2 d}-\frac{d^2 e^{-4 e-4 f x}}{128 a^2 f^3}+\frac{d^2 e^{-2 e-2 f x}}{8 a^2 f^3}",1,"(Csch[e + f*x]^2*(48*(2*c^2*f^2 + 2*c*d*f*(1 + 2*f*x) + d^2*(1 + 2*f*x + 2*f^2*x^2)) + (24*c^2*f^2*(-1 + 4*f*x) + 12*c*d*f*(-1 - 4*f*x + 8*f^2*x^2) + d^2*(-3 - 12*f*x - 24*f^2*x^2 + 32*f^3*x^3))*Cosh[2*(e + f*x)] + (24*c^2*f^2*(1 + 4*f*x) + 12*c*d*f*(1 + 4*f*x + 8*f^2*x^2) + d^2*(3 + 12*f*x + 24*f^2*x^2 + 32*f^3*x^3))*Sinh[2*(e + f*x)]))/(384*a^2*f^3*(1 + Coth[e + f*x])^2)","A",1
24,1,114,133,0.5552436,"\int \frac{c+d x}{(a+a \coth (e+f x))^2} \, dx","Integrate[(c + d*x)/(a + a*Coth[e + f*x])^2,x]","\frac{\text{csch}^2(e+f x) \left(\left(4 c f (4 f x+1)+d \left(8 f^2 x^2+4 f x+1\right)\right) \sinh (2 (e+f x))+\left(4 c f (4 f x-1)+d \left(8 f^2 x^2-4 f x-1\right)\right) \cosh (2 (e+f x))+8 (2 c f+2 d f x+d)\right)}{64 a^2 f^2 (\coth (e+f x)+1)^2}","-\frac{c+d x}{4 f \left(a^2 \coth (e+f x)+a^2\right)}+\frac{x (c+d x)}{4 a^2}-\frac{3 d}{16 f^2 \left(a^2 \coth (e+f x)+a^2\right)}+\frac{3 d x}{16 a^2 f}-\frac{d x^2}{8 a^2}-\frac{c+d x}{4 f (a \coth (e+f x)+a)^2}-\frac{d}{16 f^2 (a \coth (e+f x)+a)^2}",1,"(Csch[e + f*x]^2*(8*(d + 2*c*f + 2*d*f*x) + (4*c*f*(-1 + 4*f*x) + d*(-1 - 4*f*x + 8*f^2*x^2))*Cosh[2*(e + f*x)] + (4*c*f*(1 + 4*f*x) + d*(1 + 4*f*x + 8*f^2*x^2))*Sinh[2*(e + f*x)]))/(64*a^2*f^2*(1 + Coth[e + f*x])^2)","A",1
25,1,199,297,0.4666938,"\int \frac{1}{(c+d x) (a+a \coth (e+f x))^2} \, dx","Integrate[1/((c + d*x)*(a + a*Coth[e + f*x])^2),x]","\frac{\left(\cosh \left(2 e-\frac{2 c f}{d}\right)-\sinh \left(2 e-\frac{2 c f}{d}\right)\right) \left(\text{Chi}\left(\frac{4 f (c+d x)}{d}\right) \left(\cosh \left(2 e-\frac{2 c f}{d}\right)-\sinh \left(2 e-\frac{2 c f}{d}\right)\right)-2 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right)+\sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{4 f (c+d x)}{d}\right)-\cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{4 f (c+d x)}{d}\right)+\sinh \left(2 e-\frac{2 c f}{d}\right) \log (f (c+d x))+\cosh \left(2 e-\frac{2 c f}{d}\right) \log (f (c+d x))+2 \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)\right)}{4 a^2 d}","\frac{\text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{2 a^2 d}-\frac{\text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \sinh \left(4 e-\frac{4 c f}{d}\right)}{4 a^2 d}-\frac{\text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{2 a^2 d}+\frac{\text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \cosh \left(4 e-\frac{4 c f}{d}\right)}{4 a^2 d}-\frac{\sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{2 a^2 d}+\frac{\sinh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{4 a^2 d}+\frac{\cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{2 a^2 d}-\frac{\cosh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{4 a^2 d}+\frac{\log (c+d x)}{4 a^2 d}",1,"((Cosh[2*e - (2*c*f)/d] - Sinh[2*e - (2*c*f)/d])*(-2*CoshIntegral[(2*f*(c + d*x))/d] + Cosh[2*e - (2*c*f)/d]*Log[f*(c + d*x)] + CoshIntegral[(4*f*(c + d*x))/d]*(Cosh[2*e - (2*c*f)/d] - Sinh[2*e - (2*c*f)/d]) + Log[f*(c + d*x)]*Sinh[2*e - (2*c*f)/d] + 2*SinhIntegral[(2*f*(c + d*x))/d] - Cosh[2*e - (2*c*f)/d]*SinhIntegral[(4*f*(c + d*x))/d] + Sinh[2*e - (2*c*f)/d]*SinhIntegral[(4*f*(c + d*x))/d]))/(4*a^2*d)","A",1
26,1,442,420,1.4819387,"\int \frac{1}{(c+d x)^2 (a+a \coth (e+f x))^2} \, dx","Integrate[1/((c + d*x)^2*(a + a*Coth[e + f*x])^2),x]","\frac{\left(\sinh \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)-\cosh \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)\right) \left(4 f (c+d x) \text{Chi}\left(\frac{4 f (c+d x)}{d}\right) \left(\cosh \left(2 e-\frac{2 f (c+d x)}{d}\right)-\sinh \left(2 e-\frac{2 f (c+d x)}{d}\right)\right)-4 f (c+d x) (\sinh (2 f x)+\cosh (2 f x)) \text{Chi}\left(\frac{2 f (c+d x)}{d}\right)+4 c f \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \sinh \left(2 e-\frac{2 f (c+d x)}{d}\right)+4 d f x \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \sinh \left(2 e-\frac{2 f (c+d x)}{d}\right)-4 c f \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 f (c+d x)}{d}\right)-4 d f x \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 f (c+d x)}{d}\right)+d \sinh \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)-d \sinh \left(2 \left(f \left(\frac{c}{d}+x\right)+e\right)\right)+d \cosh \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)+d \cosh \left(2 \left(f \left(\frac{c}{d}+x\right)+e\right)\right)+4 c f \sinh (2 f x) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+4 d f x \sinh (2 f x) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+4 c f \cosh (2 f x) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+4 d f x \cosh (2 f x) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+2 d \sinh \left(\frac{2 c f}{d}\right)-2 d \cosh \left(\frac{2 c f}{d}\right)\right)}{4 a^2 d^2 (c+d x)}","\frac{f \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \sinh \left(4 e-\frac{4 c f}{d}\right)}{a^2 d^2}-\frac{f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{a^2 d^2}+\frac{f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{f \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \cosh \left(4 e-\frac{4 c f}{d}\right)}{a^2 d^2}+\frac{f \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{f \sinh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{a^2 d^2}-\frac{f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a^2 d^2}+\frac{f \cosh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{a^2 d^2}-\frac{\sinh ^2(2 e+2 f x)}{4 a^2 d (c+d x)}-\frac{\sinh (2 e+2 f x)}{2 a^2 d (c+d x)}+\frac{\sinh (4 e+4 f x)}{4 a^2 d (c+d x)}-\frac{\cosh ^2(2 e+2 f x)}{4 a^2 d (c+d x)}+\frac{\cosh (2 e+2 f x)}{2 a^2 d (c+d x)}-\frac{1}{4 a^2 d (c+d x)}",1,"((-Cosh[2*(e + f*(-(c/d) + x))] + Sinh[2*(e + f*(-(c/d) + x))])*(-2*d*Cosh[(2*c*f)/d] + d*Cosh[2*(e + f*(-(c/d) + x))] + d*Cosh[2*(e + f*(c/d + x))] + 2*d*Sinh[(2*c*f)/d] - 4*f*(c + d*x)*CoshIntegral[(2*f*(c + d*x))/d]*(Cosh[2*f*x] + Sinh[2*f*x]) + d*Sinh[2*(e + f*(-(c/d) + x))] - d*Sinh[2*(e + f*(c/d + x))] + 4*f*(c + d*x)*CoshIntegral[(4*f*(c + d*x))/d]*(Cosh[2*e - (2*f*(c + d*x))/d] - Sinh[2*e - (2*f*(c + d*x))/d]) + 4*c*f*Cosh[2*f*x]*SinhIntegral[(2*f*(c + d*x))/d] + 4*d*f*x*Cosh[2*f*x]*SinhIntegral[(2*f*(c + d*x))/d] + 4*c*f*Sinh[2*f*x]*SinhIntegral[(2*f*(c + d*x))/d] + 4*d*f*x*Sinh[2*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 4*c*f*Cosh[2*e - (2*f*(c + d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] - 4*d*f*x*Cosh[2*e - (2*f*(c + d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] + 4*c*f*Sinh[2*e - (2*f*(c + d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] + 4*d*f*x*Sinh[2*e - (2*f*(c + d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d]))/(4*a^2*d^2*(c + d*x))","A",1
27,1,615,336,2.4764665,"\int \frac{(c+d x)^3}{(a+a \coth (e+f x))^3} \, dx","Integrate[(c + d*x)^3/(a + a*Coth[e + f*x])^3,x]","\frac{\text{csch}^3(e+f x) \left(3456 c^3 f^4 x \sinh (3 (e+f x))+7776 c^3 f^3 \sinh (e+f x)-576 c^3 f^3 \sinh (3 (e+f x))+5184 c^2 d f^4 x^2 \sinh (3 (e+f x))+23328 c^2 d f^3 x \sinh (e+f x)-1728 c^2 d f^3 x \sinh (3 (e+f x))+9720 c^2 d f^2 \sinh (e+f x)-288 c^2 d f^2 \sinh (3 (e+f x))+81 \left(32 c^3 f^3+24 c^2 d f^2 (4 f x+3)+12 c d^2 f \left(8 f^2 x^2+12 f x+7\right)+d^3 \left(32 f^3 x^3+72 f^2 x^2+84 f x+45\right)\right) \cosh (e+f x)+16 \left(36 c^3 f^3 (6 f x+1)+18 c^2 d f^2 \left(18 f^2 x^2+6 f x+1\right)+6 c d^2 f \left(36 f^3 x^3+18 f^2 x^2+6 f x+1\right)+d^3 \left(54 f^4 x^4+36 f^3 x^3+18 f^2 x^2+6 f x+1\right)\right) \cosh (3 (e+f x))+3456 c d^2 f^4 x^3 \sinh (3 (e+f x))+23328 c d^2 f^3 x^2 \sinh (e+f x)-1728 c d^2 f^3 x^2 \sinh (3 (e+f x))+19440 c d^2 f^2 x \sinh (e+f x)-576 c d^2 f^2 x \sinh (3 (e+f x))+8748 c d^2 f \sinh (e+f x)-96 c d^2 f \sinh (3 (e+f x))+864 d^3 f^4 x^4 \sinh (3 (e+f x))+7776 d^3 f^3 x^3 \sinh (e+f x)-576 d^3 f^3 x^3 \sinh (3 (e+f x))+9720 d^3 f^2 x^2 \sinh (e+f x)-288 d^3 f^2 x^2 \sinh (3 (e+f x))+8748 d^3 f x \sinh (e+f x)-96 d^3 f x \sinh (3 (e+f x))+4131 d^3 \sinh (e+f x)-16 d^3 \sinh (3 (e+f x))\right)}{27648 a^3 f^4 (\coth (e+f x)+1)^3}","\frac{d^2 (c+d x) e^{-6 e-6 f x}}{288 a^3 f^3}-\frac{9 d^2 (c+d x) e^{-4 e-4 f x}}{256 a^3 f^3}+\frac{9 d^2 (c+d x) e^{-2 e-2 f x}}{32 a^3 f^3}+\frac{d (c+d x)^2 e^{-6 e-6 f x}}{96 a^3 f^2}-\frac{9 d (c+d x)^2 e^{-4 e-4 f x}}{128 a^3 f^2}+\frac{9 d (c+d x)^2 e^{-2 e-2 f x}}{32 a^3 f^2}+\frac{(c+d x)^3 e^{-6 e-6 f x}}{48 a^3 f}-\frac{3 (c+d x)^3 e^{-4 e-4 f x}}{32 a^3 f}+\frac{3 (c+d x)^3 e^{-2 e-2 f x}}{16 a^3 f}+\frac{(c+d x)^4}{32 a^3 d}+\frac{d^3 e^{-6 e-6 f x}}{1728 a^3 f^4}-\frac{9 d^3 e^{-4 e-4 f x}}{1024 a^3 f^4}+\frac{9 d^3 e^{-2 e-2 f x}}{64 a^3 f^4}",1,"(Csch[e + f*x]^3*(81*(32*c^3*f^3 + 24*c^2*d*f^2*(3 + 4*f*x) + 12*c*d^2*f*(7 + 12*f*x + 8*f^2*x^2) + d^3*(45 + 84*f*x + 72*f^2*x^2 + 32*f^3*x^3))*Cosh[e + f*x] + 16*(36*c^3*f^3*(1 + 6*f*x) + 18*c^2*d*f^2*(1 + 6*f*x + 18*f^2*x^2) + 6*c*d^2*f*(1 + 6*f*x + 18*f^2*x^2 + 36*f^3*x^3) + d^3*(1 + 6*f*x + 18*f^2*x^2 + 36*f^3*x^3 + 54*f^4*x^4))*Cosh[3*(e + f*x)] + 4131*d^3*Sinh[e + f*x] + 8748*c*d^2*f*Sinh[e + f*x] + 9720*c^2*d*f^2*Sinh[e + f*x] + 7776*c^3*f^3*Sinh[e + f*x] + 8748*d^3*f*x*Sinh[e + f*x] + 19440*c*d^2*f^2*x*Sinh[e + f*x] + 23328*c^2*d*f^3*x*Sinh[e + f*x] + 9720*d^3*f^2*x^2*Sinh[e + f*x] + 23328*c*d^2*f^3*x^2*Sinh[e + f*x] + 7776*d^3*f^3*x^3*Sinh[e + f*x] - 16*d^3*Sinh[3*(e + f*x)] - 96*c*d^2*f*Sinh[3*(e + f*x)] - 288*c^2*d*f^2*Sinh[3*(e + f*x)] - 576*c^3*f^3*Sinh[3*(e + f*x)] - 96*d^3*f*x*Sinh[3*(e + f*x)] - 576*c*d^2*f^2*x*Sinh[3*(e + f*x)] - 1728*c^2*d*f^3*x*Sinh[3*(e + f*x)] + 3456*c^3*f^4*x*Sinh[3*(e + f*x)] - 288*d^3*f^2*x^2*Sinh[3*(e + f*x)] - 1728*c*d^2*f^3*x^2*Sinh[3*(e + f*x)] + 5184*c^2*d*f^4*x^2*Sinh[3*(e + f*x)] - 576*d^3*f^3*x^3*Sinh[3*(e + f*x)] + 3456*c*d^2*f^4*x^3*Sinh[3*(e + f*x)] + 864*d^3*f^4*x^4*Sinh[3*(e + f*x)]))/(27648*a^3*f^4*(1 + Coth[e + f*x])^3)","A",1
28,1,371,246,1.4985807,"\int \frac{(c+d x)^2}{(a+a \coth (e+f x))^3} \, dx","Integrate[(c + d*x)^2/(a + a*Coth[e + f*x])^3,x]","\frac{\text{csch}^3(e+f x) \left(81 \left(8 c^2 f^2+4 c d f (4 f x+3)+d^2 \left(8 f^2 x^2+12 f x+7\right)\right) \cosh (e+f x)+8 \left(18 c^2 f^2 (6 f x+1)+6 c d f \left(18 f^2 x^2+6 f x+1\right)+d^2 \left(36 f^3 x^3+18 f^2 x^2+6 f x+1\right)\right) \cosh (3 (e+f x))+864 c^2 f^3 x \sinh (3 (e+f x))+1944 c^2 f^2 \sinh (e+f x)-144 c^2 f^2 \sinh (3 (e+f x))+864 c d f^3 x^2 \sinh (3 (e+f x))+3888 c d f^2 x \sinh (e+f x)-288 c d f^2 x \sinh (3 (e+f x))+1620 c d f \sinh (e+f x)-48 c d f \sinh (3 (e+f x))+288 d^2 f^3 x^3 \sinh (3 (e+f x))+1944 d^2 f^2 x^2 \sinh (e+f x)-144 d^2 f^2 x^2 \sinh (3 (e+f x))+1620 d^2 f x \sinh (e+f x)-48 d^2 f x \sinh (3 (e+f x))+729 d^2 \sinh (e+f x)-8 d^2 \sinh (3 (e+f x))\right)}{6912 a^3 f^3 (\coth (e+f x)+1)^3}","\frac{d (c+d x) e^{-6 e-6 f x}}{144 a^3 f^2}-\frac{3 d (c+d x) e^{-4 e-4 f x}}{64 a^3 f^2}+\frac{3 d (c+d x) e^{-2 e-2 f x}}{16 a^3 f^2}+\frac{(c+d x)^2 e^{-6 e-6 f x}}{48 a^3 f}-\frac{3 (c+d x)^2 e^{-4 e-4 f x}}{32 a^3 f}+\frac{3 (c+d x)^2 e^{-2 e-2 f x}}{16 a^3 f}+\frac{(c+d x)^3}{24 a^3 d}+\frac{d^2 e^{-6 e-6 f x}}{864 a^3 f^3}-\frac{3 d^2 e^{-4 e-4 f x}}{256 a^3 f^3}+\frac{3 d^2 e^{-2 e-2 f x}}{32 a^3 f^3}",1,"(Csch[e + f*x]^3*(81*(8*c^2*f^2 + 4*c*d*f*(3 + 4*f*x) + d^2*(7 + 12*f*x + 8*f^2*x^2))*Cosh[e + f*x] + 8*(18*c^2*f^2*(1 + 6*f*x) + 6*c*d*f*(1 + 6*f*x + 18*f^2*x^2) + d^2*(1 + 6*f*x + 18*f^2*x^2 + 36*f^3*x^3))*Cosh[3*(e + f*x)] + 729*d^2*Sinh[e + f*x] + 1620*c*d*f*Sinh[e + f*x] + 1944*c^2*f^2*Sinh[e + f*x] + 1620*d^2*f*x*Sinh[e + f*x] + 3888*c*d*f^2*x*Sinh[e + f*x] + 1944*d^2*f^2*x^2*Sinh[e + f*x] - 8*d^2*Sinh[3*(e + f*x)] - 48*c*d*f*Sinh[3*(e + f*x)] - 144*c^2*f^2*Sinh[3*(e + f*x)] - 48*d^2*f*x*Sinh[3*(e + f*x)] - 288*c*d*f^2*x*Sinh[3*(e + f*x)] + 864*c^2*f^3*x*Sinh[3*(e + f*x)] - 144*d^2*f^2*x^2*Sinh[3*(e + f*x)] + 864*c*d*f^3*x^2*Sinh[3*(e + f*x)] + 288*d^2*f^3*x^3*Sinh[3*(e + f*x)]))/(6912*a^3*f^3*(1 + Coth[e + f*x])^3)","A",1
29,1,185,183,0.7693082,"\int \frac{c+d x}{(a+a \coth (e+f x))^3} \, dx","Integrate[(c + d*x)/(a + a*Coth[e + f*x])^3,x]","\frac{\text{csch}^3(e+f x) \left(4 \left(6 c f (6 f x+1)+d \left(18 f^2 x^2+6 f x+1\right)\right) \cosh (3 (e+f x))+27 (4 c f+d (4 f x+3)) \cosh (e+f x)+144 c f^2 x \sinh (3 (e+f x))+324 c f \sinh (e+f x)-24 c f \sinh (3 (e+f x))+72 d f^2 x^2 \sinh (3 (e+f x))+324 d f x \sinh (e+f x)-24 d f x \sinh (3 (e+f x))+135 d \sinh (e+f x)-4 d \sinh (3 (e+f x))\right)}{1152 a^3 f^2 (\coth (e+f x)+1)^3}","-\frac{c+d x}{8 f \left(a^3 \coth (e+f x)+a^3\right)}+\frac{x (c+d x)}{8 a^3}-\frac{11 d}{96 f^2 \left(a^3 \coth (e+f x)+a^3\right)}+\frac{11 d x}{96 a^3 f}-\frac{d x^2}{16 a^3}-\frac{c+d x}{8 a f (a \coth (e+f x)+a)^2}-\frac{c+d x}{6 f (a \coth (e+f x)+a)^3}-\frac{5 d}{96 a f^2 (a \coth (e+f x)+a)^2}-\frac{d}{36 f^2 (a \coth (e+f x)+a)^3}",1,"(Csch[e + f*x]^3*(27*(4*c*f + d*(3 + 4*f*x))*Cosh[e + f*x] + 4*(6*c*f*(1 + 6*f*x) + d*(1 + 6*f*x + 18*f^2*x^2))*Cosh[3*(e + f*x)] + 135*d*Sinh[e + f*x] + 324*c*f*Sinh[e + f*x] + 324*d*f*x*Sinh[e + f*x] - 4*d*Sinh[3*(e + f*x)] - 24*c*f*Sinh[3*(e + f*x)] - 24*d*f*x*Sinh[3*(e + f*x)] + 144*c*f^2*x*Sinh[3*(e + f*x)] + 72*d*f^2*x^2*Sinh[3*(e + f*x)]))/(1152*a^3*f^2*(1 + Coth[e + f*x])^3)","A",1
30,1,312,437,0.7053709,"\int \frac{1}{(c+d x) (a+a \coth (e+f x))^3} \, dx","Integrate[1/((c + d*x)*(a + a*Coth[e + f*x])^3),x]","\frac{\text{csch}^3(e+f x) (\sinh (f x)+\cosh (f x))^3 \left(\left(\sinh \left(e-\frac{4 c f}{d}\right)-\cosh \left(e-\frac{4 c f}{d}\right)\right) \left(-\text{Chi}\left(\frac{6 f (c+d x)}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)+\text{Chi}\left(\frac{6 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)+3 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \left(\sinh \left(2 e-\frac{2 c f}{d}\right)+\cosh \left(2 e-\frac{2 c f}{d}\right)\right)-3 \text{Chi}\left(\frac{4 f (c+d x)}{d}\right)-3 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+\sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{6 f (c+d x)}{d}\right)-3 \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-\cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{6 f (c+d x)}{d}\right)+3 \text{Shi}\left(\frac{4 f (c+d x)}{d}\right)\right)+\sinh (3 e) \log (f (c+d x))+\cosh (3 e) \log (f (c+d x))\right)}{8 a^3 d (\coth (e+f x)+1)^3}","\frac{3 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{8 a^3 d}+\frac{\text{Chi}\left(6 x f+\frac{6 c f}{d}\right) \sinh \left(6 e-\frac{6 c f}{d}\right)}{8 a^3 d}-\frac{3 \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \sinh \left(4 e-\frac{4 c f}{d}\right)}{8 a^3 d}-\frac{3 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{8 a^3 d}+\frac{3 \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \cosh \left(4 e-\frac{4 c f}{d}\right)}{8 a^3 d}-\frac{\text{Chi}\left(6 x f+\frac{6 c f}{d}\right) \cosh \left(6 e-\frac{6 c f}{d}\right)}{8 a^3 d}-\frac{3 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{8 a^3 d}+\frac{3 \sinh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{8 a^3 d}-\frac{\sinh \left(6 e-\frac{6 c f}{d}\right) \text{Shi}\left(6 x f+\frac{6 c f}{d}\right)}{8 a^3 d}+\frac{3 \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{8 a^3 d}-\frac{3 \cosh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{8 a^3 d}+\frac{\cosh \left(6 e-\frac{6 c f}{d}\right) \text{Shi}\left(6 x f+\frac{6 c f}{d}\right)}{8 a^3 d}+\frac{\log (c+d x)}{8 a^3 d}",1,"(Csch[e + f*x]^3*(Cosh[f*x] + Sinh[f*x])^3*(Cosh[3*e]*Log[f*(c + d*x)] + Log[f*(c + d*x)]*Sinh[3*e] + (-Cosh[e - (4*c*f)/d] + Sinh[e - (4*c*f)/d])*(-3*CoshIntegral[(4*f*(c + d*x))/d] + Cosh[2*e - (2*c*f)/d]*CoshIntegral[(6*f*(c + d*x))/d] - CoshIntegral[(6*f*(c + d*x))/d]*Sinh[2*e - (2*c*f)/d] + 3*CoshIntegral[(2*f*(c + d*x))/d]*(Cosh[2*e - (2*c*f)/d] + Sinh[2*e - (2*c*f)/d]) - 3*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] - 3*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] + 3*SinhIntegral[(4*f*(c + d*x))/d] - Cosh[2*e - (2*c*f)/d]*SinhIntegral[(6*f*(c + d*x))/d] + Sinh[2*e - (2*c*f)/d]*SinhIntegral[(6*f*(c + d*x))/d])))/(8*a^3*d*(1 + Coth[e + f*x])^3)","A",1
31,1,796,692,3.1171357,"\int \frac{1}{(c+d x)^2 (a+a \coth (e+f x))^3} \, dx","Integrate[1/((c + d*x)^2*(a + a*Coth[e + f*x])^3),x]","\frac{\text{csch}^3(e+f x) \left(\cosh \left(\frac{3 c f}{d}\right)+\sinh \left(\frac{3 c f}{d}\right)\right) \left(3 d \cosh \left(e+f \left(x-\frac{3 c}{d}\right)\right)-d \cosh \left(3 \left(e+f \left(x-\frac{c}{d}\right)\right)\right)+d \cosh \left(3 \left(e+f \left(\frac{c}{d}+x\right)\right)\right)-3 d \cosh \left(e+f \left(\frac{3 c}{d}+x\right)\right)+6 c f \cosh \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Chi}\left(\frac{6 f (c+d x)}{d}\right)+6 d f x \cosh \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Chi}\left(\frac{6 f (c+d x)}{d}\right)+6 f (c+d x) \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \left(\cosh \left(e-\frac{c f}{d}+3 f x\right)+\sinh \left(e-\frac{c f}{d}+3 f x\right)\right)+3 d \sinh \left(e+f \left(x-\frac{3 c}{d}\right)\right)-d \sinh \left(3 \left(e+f \left(x-\frac{c}{d}\right)\right)\right)-d \sinh \left(3 \left(e+f \left(\frac{c}{d}+x\right)\right)\right)+3 d \sinh \left(e+f \left(\frac{3 c}{d}+x\right)\right)-6 c f \text{Chi}\left(\frac{6 f (c+d x)}{d}\right) \sinh \left(3 e-\frac{3 f (c+d x)}{d}\right)-6 d f x \text{Chi}\left(\frac{6 f (c+d x)}{d}\right) \sinh \left(3 e-\frac{3 f (c+d x)}{d}\right)+12 f (c+d x) \text{Chi}\left(\frac{4 f (c+d x)}{d}\right) \left(\sinh \left(e-\frac{f (c+3 d x)}{d}\right)-\cosh \left(e-\frac{f (c+3 d x)}{d}\right)\right)-6 c f \cosh \left(e-\frac{c f}{d}+3 f x\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-6 d f x \cosh \left(e-\frac{c f}{d}+3 f x\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-6 c f \sinh \left(e-\frac{c f}{d}+3 f x\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-6 d f x \sinh \left(e-\frac{c f}{d}+3 f x\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+12 c f \cosh \left(e-\frac{f (c+3 d x)}{d}\right) \text{Shi}\left(\frac{4 f (c+d x)}{d}\right)+12 d f x \cosh \left(e-\frac{f (c+3 d x)}{d}\right) \text{Shi}\left(\frac{4 f (c+d x)}{d}\right)-12 c f \sinh \left(e-\frac{f (c+3 d x)}{d}\right) \text{Shi}\left(\frac{4 f (c+d x)}{d}\right)-12 d f x \sinh \left(e-\frac{f (c+3 d x)}{d}\right) \text{Shi}\left(\frac{4 f (c+d x)}{d}\right)-6 c f \cosh \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Shi}\left(\frac{6 f (c+d x)}{d}\right)-6 d f x \cosh \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Shi}\left(\frac{6 f (c+d x)}{d}\right)+6 c f \sinh \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Shi}\left(\frac{6 f (c+d x)}{d}\right)+6 d f x \sinh \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Shi}\left(\frac{6 f (c+d x)}{d}\right)\right)}{8 a^3 d^2 (c+d x) (\coth (e+f x)+1)^3}","-\frac{3 f \text{Chi}\left(6 x f+\frac{6 c f}{d}\right) \sinh \left(6 e-\frac{6 c f}{d}\right)}{4 a^3 d^2}+\frac{3 f \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \sinh \left(4 e-\frac{4 c f}{d}\right)}{2 a^3 d^2}-\frac{3 f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{4 a^3 d^2}+\frac{3 f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \cosh \left(4 e-\frac{4 c f}{d}\right)}{2 a^3 d^2}+\frac{3 f \text{Chi}\left(6 x f+\frac{6 c f}{d}\right) \cosh \left(6 e-\frac{6 c f}{d}\right)}{4 a^3 d^2}+\frac{3 f \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \sinh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{2 a^3 d^2}+\frac{3 f \sinh \left(6 e-\frac{6 c f}{d}\right) \text{Shi}\left(6 x f+\frac{6 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{4 a^3 d^2}+\frac{3 f \cosh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{2 a^3 d^2}-\frac{3 f \cosh \left(6 e-\frac{6 c f}{d}\right) \text{Shi}\left(6 x f+\frac{6 c f}{d}\right)}{4 a^3 d^2}-\frac{\sinh ^3(2 e+2 f x)}{8 a^3 d (c+d x)}-\frac{3 \sinh ^2(2 e+2 f x)}{8 a^3 d (c+d x)}-\frac{15 \sinh (2 e+2 f x)}{32 a^3 d (c+d x)}+\frac{3 \sinh (4 e+4 f x)}{8 a^3 d (c+d x)}-\frac{3 \sinh (6 e+6 f x)}{32 a^3 d (c+d x)}+\frac{\cosh ^3(2 e+2 f x)}{8 a^3 d (c+d x)}-\frac{3 \cosh ^2(2 e+2 f x)}{8 a^3 d (c+d x)}+\frac{9 \cosh (2 e+2 f x)}{32 a^3 d (c+d x)}+\frac{3 \cosh (6 e+6 f x)}{32 a^3 d (c+d x)}-\frac{1}{8 a^3 d (c+d x)}",1,"(Csch[e + f*x]^3*(Cosh[(3*c*f)/d] + Sinh[(3*c*f)/d])*(3*d*Cosh[e + f*((-3*c)/d + x)] - d*Cosh[3*(e + f*(-(c/d) + x))] + d*Cosh[3*(e + f*(c/d + x))] - 3*d*Cosh[e + f*((3*c)/d + x)] + 6*c*f*Cosh[3*e - (3*f*(c + d*x))/d]*CoshIntegral[(6*f*(c + d*x))/d] + 6*d*f*x*Cosh[3*e - (3*f*(c + d*x))/d]*CoshIntegral[(6*f*(c + d*x))/d] + 6*f*(c + d*x)*CoshIntegral[(2*f*(c + d*x))/d]*(Cosh[e - (c*f)/d + 3*f*x] + Sinh[e - (c*f)/d + 3*f*x]) + 3*d*Sinh[e + f*((-3*c)/d + x)] - d*Sinh[3*(e + f*(-(c/d) + x))] - d*Sinh[3*(e + f*(c/d + x))] + 3*d*Sinh[e + f*((3*c)/d + x)] - 6*c*f*CoshIntegral[(6*f*(c + d*x))/d]*Sinh[3*e - (3*f*(c + d*x))/d] - 6*d*f*x*CoshIntegral[(6*f*(c + d*x))/d]*Sinh[3*e - (3*f*(c + d*x))/d] + 12*f*(c + d*x)*CoshIntegral[(4*f*(c + d*x))/d]*(-Cosh[e - (f*(c + 3*d*x))/d] + Sinh[e - (f*(c + 3*d*x))/d]) - 6*c*f*Cosh[e - (c*f)/d + 3*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 6*d*f*x*Cosh[e - (c*f)/d + 3*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 6*c*f*Sinh[e - (c*f)/d + 3*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 6*d*f*x*Sinh[e - (c*f)/d + 3*f*x]*SinhIntegral[(2*f*(c + d*x))/d] + 12*c*f*Cosh[e - (f*(c + 3*d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] + 12*d*f*x*Cosh[e - (f*(c + 3*d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] - 12*c*f*Sinh[e - (f*(c + 3*d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] - 12*d*f*x*Sinh[e - (f*(c + 3*d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] - 6*c*f*Cosh[3*e - (3*f*(c + d*x))/d]*SinhIntegral[(6*f*(c + d*x))/d] - 6*d*f*x*Cosh[3*e - (3*f*(c + d*x))/d]*SinhIntegral[(6*f*(c + d*x))/d] + 6*c*f*Sinh[3*e - (3*f*(c + d*x))/d]*SinhIntegral[(6*f*(c + d*x))/d] + 6*d*f*x*Sinh[3*e - (3*f*(c + d*x))/d]*SinhIntegral[(6*f*(c + d*x))/d]))/(8*a^3*d^2*(c + d*x)*(1 + Coth[e + f*x])^3)","A",0
32,0,0,23,36.1077571,"\int (c+d x)^m (a+a \coth (e+f x))^2 \, dx","Integrate[(c + d*x)^m*(a + a*Coth[e + f*x])^2,x]","\int (c+d x)^m (a+a \coth (e+f x))^2 \, dx","\text{Int}\left((c+d x)^m (a \coth (e+f x)+a)^2,x\right)",0,"Integrate[(c + d*x)^m*(a + a*Coth[e + f*x])^2, x]","A",-1
33,0,0,21,14.5841175,"\int (c+d x)^m (a+a \coth (e+f x)) \, dx","Integrate[(c + d*x)^m*(a + a*Coth[e + f*x]),x]","\int (c+d x)^m (a+a \coth (e+f x)) \, dx","\text{Int}\left((c+d x)^m (a \coth (e+f x)+a),x\right)",0,"Integrate[(c + d*x)^m*(a + a*Coth[e + f*x]), x]","A",-1
34,1,186,88,1.1984189,"\int \frac{(c+d x)^m}{a+a \coth (e+f x)} \, dx","Integrate[(c + d*x)^m/(a + a*Coth[e + f*x]),x]","\frac{2^{-m-2} (c+d x)^m \text{csch}(e+f x) \left(-\frac{f (c+d x)}{d}\right)^m \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^{-m} \left(\sinh \left(f \left(\frac{c}{d}+x\right)\right)+\cosh \left(f \left(\frac{c}{d}+x\right)\right)\right) \left(f 2^{m+1} (c+d x) \left(f \left(\frac{c}{d}+x\right)\right)^m \left(\sinh \left(e-\frac{c f}{d}\right)+\cosh \left(e-\frac{c f}{d}\right)\right)+d (m+1) \left(\cosh \left(e-\frac{c f}{d}\right)-\sinh \left(e-\frac{c f}{d}\right)\right) \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)\right)}{a d f (m+1) (\coth (e+f x)+1)}","\frac{2^{-m-2} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{a f}+\frac{(c+d x)^{m+1}}{2 a d (m+1)}",1,"(2^(-2 - m)*(c + d*x)^m*(-((f*(c + d*x))/d))^m*Csch[e + f*x]*(d*(1 + m)*Gamma[1 + m, (2*f*(c + d*x))/d]*(Cosh[e - (c*f)/d] - Sinh[e - (c*f)/d]) + 2^(1 + m)*f*(f*(c/d + x))^m*(c + d*x)*(Cosh[e - (c*f)/d] + Sinh[e - (c*f)/d]))*(Cosh[f*(c/d + x)] + Sinh[f*(c/d + x)]))/(a*d*f*(1 + m)*(-((f^2*(c + d*x)^2)/d^2))^m*(1 + Coth[e + f*x]))","B",1
35,1,194,152,8.5754375,"\int \frac{(c+d x)^m}{(a+a \coth (e+f x))^2} \, dx","Integrate[(c + d*x)^m/(a + a*Coth[e + f*x])^2,x]","\frac{4^{-m-2} (c+d x)^m \text{csch}^2(e+f x) (\sinh (2 f x)+\cosh (2 f x)) \left(-\frac{f (c+d x)}{d}\right)^m \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^{-m} \left(d 4^{m+1} (\sinh (e)+\cosh (e))^2 \left(\frac{f (c+d x)}{d}\right)^{m+1}-d (m+1) e^{\frac{4 c f}{d}} (\cosh (2 e)-\sinh (2 e)) \Gamma \left(m+1,\frac{4 f (c+d x)}{d}\right)+d 2^{m+2} (m+1) e^{\frac{2 c f}{d}} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)\right)}{a^2 d f (m+1) (\coth (e+f x)+1)^2}","\frac{2^{-m-2} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{a^2 f}-\frac{4^{-m-2} e^{\frac{4 c f}{d}-4 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{4 f (c+d x)}{d}\right)}{a^2 f}+\frac{(c+d x)^{m+1}}{4 a^2 d (m+1)}",1,"(4^(-2 - m)*(c + d*x)^m*(-((f*(c + d*x))/d))^m*Csch[e + f*x]^2*(2^(2 + m)*d*E^((2*c*f)/d)*(1 + m)*Gamma[1 + m, (2*f*(c + d*x))/d] + 4^(1 + m)*d*((f*(c + d*x))/d)^(1 + m)*(Cosh[e] + Sinh[e])^2 - d*E^((4*c*f)/d)*(1 + m)*Gamma[1 + m, (4*f*(c + d*x))/d]*(Cosh[2*e] - Sinh[2*e]))*(Cosh[2*f*x] + Sinh[2*f*x]))/(a^2*d*f*(1 + m)*(-((f^2*(c + d*x)^2)/d^2))^m*(1 + Coth[e + f*x])^2)","A",1
36,-1,0,223,180.0015437,"\int \frac{(c+d x)^m}{(a+a \coth (e+f x))^3} \, dx","Integrate[(c + d*x)^m/(a + a*Coth[e + f*x])^3,x]","\text{\$Aborted}","\frac{3\ 2^{-m-4} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{a^3 f}-\frac{3\ 2^{-2 m-5} e^{\frac{4 c f}{d}-4 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{4 f (c+d x)}{d}\right)}{a^3 f}+\frac{2^{-m-4} 3^{-m-1} e^{\frac{6 c f}{d}-6 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{6 f (c+d x)}{d}\right)}{a^3 f}+\frac{(c+d x)^{m+1}}{8 a^3 d (m+1)}",1,"$Aborted","F",-1
37,1,249,133,0.3894349,"\int (c+d x)^3 (a+b \coth (e+f x)) \, dx","Integrate[(c + d*x)^3*(a + b*Coth[e + f*x]),x]","\frac{1}{4} \left(4 a c^3 x+6 a c^2 d x^2+4 a c d^2 x^3+a d^3 x^4+\frac{4 b c^3 \log (\tanh (e+f x))}{f}+\frac{4 b c^3 \log (\cosh (e+f x))}{f}+\frac{12 b c^2 d x \log \left(1-e^{2 (e+f x)}\right)}{f}-6 b c^2 d x^2-\frac{6 b d^2 (c+d x) \text{Li}_3\left(e^{2 (e+f x)}\right)}{f^3}+\frac{12 b c d^2 x^2 \log \left(1-e^{2 (e+f x)}\right)}{f}-4 b c d^2 x^3+\frac{6 b d (c+d x)^2 \text{Li}_2\left(e^{2 (e+f x)}\right)}{f^2}+\frac{3 b d^3 \text{Li}_4\left(e^{2 (e+f x)}\right)}{f^4}+\frac{4 b d^3 x^3 \log \left(1-e^{2 (e+f x)}\right)}{f}-b d^3 x^4\right)","\frac{a (c+d x)^4}{4 d}-\frac{3 b d^2 (c+d x) \text{Li}_3\left(e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 b d (c+d x)^2 \text{Li}_2\left(e^{2 (e+f x)}\right)}{2 f^2}+\frac{b (c+d x)^3 \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{b (c+d x)^4}{4 d}+\frac{3 b d^3 \text{Li}_4\left(e^{2 (e+f x)}\right)}{4 f^4}",1,"(4*a*c^3*x + 6*a*c^2*d*x^2 - 6*b*c^2*d*x^2 + 4*a*c*d^2*x^3 - 4*b*c*d^2*x^3 + a*d^3*x^4 - b*d^3*x^4 + (12*b*c^2*d*x*Log[1 - E^(2*(e + f*x))])/f + (12*b*c*d^2*x^2*Log[1 - E^(2*(e + f*x))])/f + (4*b*d^3*x^3*Log[1 - E^(2*(e + f*x))])/f + (4*b*c^3*Log[Cosh[e + f*x]])/f + (4*b*c^3*Log[Tanh[e + f*x]])/f + (6*b*d*(c + d*x)^2*PolyLog[2, E^(2*(e + f*x))])/f^2 - (6*b*d^2*(c + d*x)*PolyLog[3, E^(2*(e + f*x))])/f^3 + (3*b*d^3*PolyLog[4, E^(2*(e + f*x))])/f^4)/4","A",1
38,1,149,101,0.2369793,"\int (c+d x)^2 (a+b \coth (e+f x)) \, dx","Integrate[(c + d*x)^2*(a + b*Coth[e + f*x]),x]","\frac{2 f^2 \left(3 a c^2 f x+3 a c d f x^2+a d^2 f x^3+3 b c^2 \log (\tanh (e+f x))+3 b c^2 \log (\cosh (e+f x))+3 b d x (2 c+d x) \log \left(1-e^{2 (e+f x)}\right)-3 b c d f x^2-b d^2 f x^3\right)+6 b d f (c+d x) \text{Li}_2\left(e^{2 (e+f x)}\right)-3 b d^2 \text{Li}_3\left(e^{2 (e+f x)}\right)}{6 f^3}","\frac{a (c+d x)^3}{3 d}+\frac{b d (c+d x) \text{Li}_2\left(e^{2 (e+f x)}\right)}{f^2}+\frac{b (c+d x)^2 \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{b (c+d x)^3}{3 d}-\frac{b d^2 \text{Li}_3\left(e^{2 (e+f x)}\right)}{2 f^3}",1,"(2*f^2*(3*a*c^2*f*x + 3*a*c*d*f*x^2 - 3*b*c*d*f*x^2 + a*d^2*f*x^3 - b*d^2*f*x^3 + 3*b*d*x*(2*c + d*x)*Log[1 - E^(2*(e + f*x))] + 3*b*c^2*Log[Cosh[e + f*x]] + 3*b*c^2*Log[Tanh[e + f*x]]) + 6*b*d*f*(c + d*x)*PolyLog[2, E^(2*(e + f*x))] - 3*b*d^2*PolyLog[3, E^(2*(e + f*x))])/(6*f^3)","A",1
39,1,87,75,0.0558786,"\int (c+d x) (a+b \coth (e+f x)) \, dx","Integrate[(c + d*x)*(a + b*Coth[e + f*x]),x]","a c x+\frac{1}{2} a d x^2+\frac{b c (\log (\tanh (e+f x))+\log (\cosh (e+f x)))}{f}+\frac{b d \text{Li}_2\left(e^{2 e+2 f x}\right)}{2 f^2}+\frac{b d x \log \left(1-e^{2 e+2 f x}\right)}{f}-\frac{1}{2} b d x^2","\frac{a (c+d x)^2}{2 d}+\frac{b (c+d x) \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{b (c+d x)^2}{2 d}+\frac{b d \text{Li}_2\left(e^{2 (e+f x)}\right)}{2 f^2}",1,"a*c*x + (a*d*x^2)/2 - (b*d*x^2)/2 + (b*d*x*Log[1 - E^(2*e + 2*f*x)])/f + (b*c*(Log[Cosh[e + f*x]] + Log[Tanh[e + f*x]]))/f + (b*d*PolyLog[2, E^(2*e + 2*f*x)])/(2*f^2)","A",1
40,0,0,21,5.3174803,"\int \frac{a+b \coth (e+f x)}{c+d x} \, dx","Integrate[(a + b*Coth[e + f*x])/(c + d*x),x]","\int \frac{a+b \coth (e+f x)}{c+d x} \, dx","\text{Int}\left(\frac{a+b \coth (e+f x)}{c+d x},x\right)",0,"Integrate[(a + b*Coth[e + f*x])/(c + d*x), x]","A",-1
41,0,0,21,21.3733184,"\int \frac{a+b \coth (e+f x)}{(c+d x)^2} \, dx","Integrate[(a + b*Coth[e + f*x])/(c + d*x)^2,x]","\int \frac{a+b \coth (e+f x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{a+b \coth (e+f x)}{(c+d x)^2},x\right)",0,"Integrate[(a + b*Coth[e + f*x])/(c + d*x)^2, x]","A",-1
42,1,1138,271,13.6430937,"\int (c+d x)^3 (a+b \coth (e+f x))^2 \, dx","Integrate[(c + d*x)^3*(a + b*Coth[e + f*x])^2,x]","\frac{\text{csch}(e) \text{csch}(e+f x) \left(-a^2 d^3 f \cosh (f x) x^4-b^2 d^3 f \cosh (f x) x^4+a^2 d^3 f \cosh (2 e+f x) x^4+b^2 d^3 f \cosh (2 e+f x) x^4+2 a b d^3 f \sinh (f x) x^4+2 a b d^3 f \sinh (2 e+f x) x^4-4 a^2 c d^2 f \cosh (f x) x^3-4 b^2 c d^2 f \cosh (f x) x^3+4 a^2 c d^2 f \cosh (2 e+f x) x^3+4 b^2 c d^2 f \cosh (2 e+f x) x^3+8 b^2 d^3 \sinh (f x) x^3+8 a b c d^2 f \sinh (f x) x^3+8 a b c d^2 f \sinh (2 e+f x) x^3-6 a^2 c^2 d f \cosh (f x) x^2-6 b^2 c^2 d f \cosh (f x) x^2+6 a^2 c^2 d f \cosh (2 e+f x) x^2+6 b^2 c^2 d f \cosh (2 e+f x) x^2+24 b^2 c d^2 \sinh (f x) x^2+12 a b c^2 d f \sinh (f x) x^2+12 a b c^2 d f \sinh (2 e+f x) x^2-4 a^2 c^3 f \cosh (f x) x-4 b^2 c^3 f \cosh (f x) x+4 a^2 c^3 f \cosh (2 e+f x) x+4 b^2 c^3 f \cosh (2 e+f x) x+24 b^2 c^2 d \sinh (f x) x+8 a b c^3 f \sinh (f x) x+8 a b c^3 f \sinh (2 e+f x) x+8 b^2 c^3 \sinh (f x)\right)}{8 f}-\frac{b \left(-4 a f^3 x^3 \log (\cosh (e+f x)-\sinh (e+f x)+1) d^4-4 a f^3 x^3 \log (-\cosh (e+f x)+\sinh (e+f x)+1) d^4+12 a \left(f^2 \text{Li}_2(\cosh (e+f x)-\sinh (e+f x)) x^2+2 (f x \text{Li}_3(\cosh (e+f x)-\sinh (e+f x))+\text{Li}_4(\cosh (e+f x)-\sinh (e+f x)))\right) d^4+12 a \left(f^2 \text{Li}_2(\sinh (e+f x)-\cosh (e+f x)) x^2+2 (f x \text{Li}_3(\sinh (e+f x)-\cosh (e+f x))+\text{Li}_4(\sinh (e+f x)-\cosh (e+f x)))\right) d^4-6 f^2 (b d+2 a c f) x^2 \log (\cosh (e+f x)-\sinh (e+f x)+1) d^3-6 f^2 (b d+2 a c f) x^2 \log (-\cosh (e+f x)+\sinh (e+f x)+1) d^3+12 (b d+2 a c f) (f x \text{Li}_2(\cosh (e+f x)-\sinh (e+f x))+\text{Li}_3(\cosh (e+f x)-\sinh (e+f x))) d^3+12 (b d+2 a c f) (f x \text{Li}_2(\sinh (e+f x)-\cosh (e+f x))+\text{Li}_3(\sinh (e+f x)-\cosh (e+f x))) d^3-12 c f^2 (b d+a c f) x \log (\cosh (e+f x)-\sinh (e+f x)+1) d^2-12 c f^2 (b d+a c f) x \log (-\cosh (e+f x)+\sinh (e+f x)+1) d^2+12 c f (b d+a c f) \text{Li}_2(\cosh (e+f x)-\sinh (e+f x)) d^2+12 c f (b d+a c f) \text{Li}_2(\sinh (e+f x)-\cosh (e+f x)) d^2+2 b f^3 (c+d x)^3 (\coth (e)-1) d+2 c^2 f^2 (3 b d+2 a c f) (f x-\log (-\cosh (e+f x)-\sinh (e+f x)+1)) d+2 c^2 f^2 (3 b d+2 a c f) (f x-\log (\cosh (e+f x)+\sinh (e+f x)+1)) d+a f^4 (c+d x)^4 (\coth (e)-1)\right)}{2 d f^4}","\frac{a^2 (c+d x)^4}{4 d}-\frac{3 a b d^2 (c+d x) \text{Li}_3\left(e^{2 (e+f x)}\right)}{f^3}+\frac{3 a b d (c+d x)^2 \text{Li}_2\left(e^{2 (e+f x)}\right)}{f^2}+\frac{2 a b (c+d x)^3 \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{a b (c+d x)^4}{2 d}+\frac{3 a b d^3 \text{Li}_4\left(e^{2 (e+f x)}\right)}{2 f^4}+\frac{3 b^2 d^2 (c+d x) \text{Li}_2\left(e^{2 (e+f x)}\right)}{f^3}+\frac{3 b^2 d (c+d x)^2 \log \left(1-e^{2 (e+f x)}\right)}{f^2}-\frac{b^2 (c+d x)^3 \coth (e+f x)}{f}-\frac{b^2 (c+d x)^3}{f}+\frac{b^2 (c+d x)^4}{4 d}-\frac{3 b^2 d^3 \text{Li}_3\left(e^{2 (e+f x)}\right)}{2 f^4}",1,"-1/2*(b*(2*b*d*f^3*(c + d*x)^3*(-1 + Coth[e]) + a*f^4*(c + d*x)^4*(-1 + Coth[e]) + 2*c^2*d*f^2*(3*b*d + 2*a*c*f)*(f*x - Log[1 - Cosh[e + f*x] - Sinh[e + f*x]]) - 12*c*d^2*f^2*(b*d + a*c*f)*x*Log[1 + Cosh[e + f*x] - Sinh[e + f*x]] - 6*d^3*f^2*(b*d + 2*a*c*f)*x^2*Log[1 + Cosh[e + f*x] - Sinh[e + f*x]] - 4*a*d^4*f^3*x^3*Log[1 + Cosh[e + f*x] - Sinh[e + f*x]] - 12*c*d^2*f^2*(b*d + a*c*f)*x*Log[1 - Cosh[e + f*x] + Sinh[e + f*x]] - 6*d^3*f^2*(b*d + 2*a*c*f)*x^2*Log[1 - Cosh[e + f*x] + Sinh[e + f*x]] - 4*a*d^4*f^3*x^3*Log[1 - Cosh[e + f*x] + Sinh[e + f*x]] + 2*c^2*d*f^2*(3*b*d + 2*a*c*f)*(f*x - Log[1 + Cosh[e + f*x] + Sinh[e + f*x]]) + 12*c*d^2*f*(b*d + a*c*f)*PolyLog[2, Cosh[e + f*x] - Sinh[e + f*x]] + 12*c*d^2*f*(b*d + a*c*f)*PolyLog[2, -Cosh[e + f*x] + Sinh[e + f*x]] + 12*d^3*(b*d + 2*a*c*f)*(f*x*PolyLog[2, Cosh[e + f*x] - Sinh[e + f*x]] + PolyLog[3, Cosh[e + f*x] - Sinh[e + f*x]]) + 12*d^3*(b*d + 2*a*c*f)*(f*x*PolyLog[2, -Cosh[e + f*x] + Sinh[e + f*x]] + PolyLog[3, -Cosh[e + f*x] + Sinh[e + f*x]]) + 12*a*d^4*(f^2*x^2*PolyLog[2, Cosh[e + f*x] - Sinh[e + f*x]] + 2*(f*x*PolyLog[3, Cosh[e + f*x] - Sinh[e + f*x]] + PolyLog[4, Cosh[e + f*x] - Sinh[e + f*x]])) + 12*a*d^4*(f^2*x^2*PolyLog[2, -Cosh[e + f*x] + Sinh[e + f*x]] + 2*(f*x*PolyLog[3, -Cosh[e + f*x] + Sinh[e + f*x]] + PolyLog[4, -Cosh[e + f*x] + Sinh[e + f*x]]))))/(d*f^4) + (Csch[e]*Csch[e + f*x]*(-4*a^2*c^3*f*x*Cosh[f*x] - 4*b^2*c^3*f*x*Cosh[f*x] - 6*a^2*c^2*d*f*x^2*Cosh[f*x] - 6*b^2*c^2*d*f*x^2*Cosh[f*x] - 4*a^2*c*d^2*f*x^3*Cosh[f*x] - 4*b^2*c*d^2*f*x^3*Cosh[f*x] - a^2*d^3*f*x^4*Cosh[f*x] - b^2*d^3*f*x^4*Cosh[f*x] + 4*a^2*c^3*f*x*Cosh[2*e + f*x] + 4*b^2*c^3*f*x*Cosh[2*e + f*x] + 6*a^2*c^2*d*f*x^2*Cosh[2*e + f*x] + 6*b^2*c^2*d*f*x^2*Cosh[2*e + f*x] + 4*a^2*c*d^2*f*x^3*Cosh[2*e + f*x] + 4*b^2*c*d^2*f*x^3*Cosh[2*e + f*x] + a^2*d^3*f*x^4*Cosh[2*e + f*x] + b^2*d^3*f*x^4*Cosh[2*e + f*x] + 8*b^2*c^3*Sinh[f*x] + 24*b^2*c^2*d*x*Sinh[f*x] + 8*a*b*c^3*f*x*Sinh[f*x] + 24*b^2*c*d^2*x^2*Sinh[f*x] + 12*a*b*c^2*d*f*x^2*Sinh[f*x] + 8*b^2*d^3*x^3*Sinh[f*x] + 8*a*b*c*d^2*f*x^3*Sinh[f*x] + 2*a*b*d^3*f*x^4*Sinh[f*x] + 8*a*b*c^3*f*x*Sinh[2*e + f*x] + 12*a*b*c^2*d*f*x^2*Sinh[2*e + f*x] + 8*a*b*c*d^2*f*x^3*Sinh[2*e + f*x] + 2*a*b*d^3*f*x^4*Sinh[2*e + f*x]))/(8*f)","B",1
43,1,478,209,10.3340383,"\int (c+d x)^2 (a+b \coth (e+f x))^2 \, dx","Integrate[(c + d*x)^2*(a + b*Coth[e + f*x])^2,x]","\frac{1}{3} x \text{csch}(e) \left(3 c^2+3 c d x+d^2 x^2\right) \left(a^2 \sinh (e)+2 a b \cosh (e)+b^2 \sinh (e)\right)+\frac{2}{3} b \left(-\frac{3 d \text{Li}_2\left(-e^{-e-f x}\right) (2 a c f+b d)}{f^3}-\frac{3 d \text{Li}_2\left(e^{-e-f x}\right) (2 a c f+b d)}{f^3}+\frac{3 d x \log \left(1-e^{-e-f x}\right) (2 a c f+b d)}{f^2}+\frac{3 d x \log \left(e^{-e-f x}+1\right) (2 a c f+b d)}{f^2}-\frac{3 c \left(f x-\log \left(1-e^{e+f x}\right)\right) (a c f+b d)}{f^2}-\frac{3 c \left(f x-\log \left(e^{e+f x}+1\right)\right) (a c f+b d)}{f^2}-\frac{3 d x^2 (2 a c f+b d)}{\left(e^{2 e}-1\right) f}-\frac{6 c x (a c f+b d)}{\left(e^{2 e}-1\right) f}-\frac{6 a d^2 \left(f x \text{Li}_2\left(-e^{-e-f x}\right)+\text{Li}_3\left(-e^{-e-f x}\right)\right)}{f^3}-\frac{6 a d^2 \left(f x \text{Li}_2\left(e^{-e-f x}\right)+\text{Li}_3\left(e^{-e-f x}\right)\right)}{f^3}+\frac{3 a d^2 x^2 \log \left(1-e^{-e-f x}\right)}{f}+\frac{3 a d^2 x^2 \log \left(e^{-e-f x}+1\right)}{f}-\frac{2 a d^2 x^3}{e^{2 e}-1}\right)+\frac{\text{csch}(e) \text{csch}(e+f x) \left(b^2 c^2 \sinh (f x)+2 b^2 c d x \sinh (f x)+b^2 d^2 x^2 \sinh (f x)\right)}{f}","\frac{a^2 (c+d x)^3}{3 d}+\frac{2 a b d (c+d x) \text{Li}_2\left(e^{2 (e+f x)}\right)}{f^2}+\frac{2 a b (c+d x)^2 \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{2 a b (c+d x)^3}{3 d}-\frac{a b d^2 \text{Li}_3\left(e^{2 (e+f x)}\right)}{f^3}+\frac{2 b^2 d (c+d x) \log \left(1-e^{2 (e+f x)}\right)}{f^2}-\frac{b^2 (c+d x)^2 \coth (e+f x)}{f}-\frac{b^2 (c+d x)^2}{f}+\frac{b^2 (c+d x)^3}{3 d}+\frac{b^2 d^2 \text{Li}_2\left(e^{2 (e+f x)}\right)}{f^3}",1,"(2*b*((-6*c*(b*d + a*c*f)*x)/((-1 + E^(2*e))*f) - (3*d*(b*d + 2*a*c*f)*x^2)/((-1 + E^(2*e))*f) - (2*a*d^2*x^3)/(-1 + E^(2*e)) + (3*d*(b*d + 2*a*c*f)*x*Log[1 - E^(-e - f*x)])/f^2 + (3*a*d^2*x^2*Log[1 - E^(-e - f*x)])/f + (3*d*(b*d + 2*a*c*f)*x*Log[1 + E^(-e - f*x)])/f^2 + (3*a*d^2*x^2*Log[1 + E^(-e - f*x)])/f - (3*c*(b*d + a*c*f)*(f*x - Log[1 - E^(e + f*x)]))/f^2 - (3*c*(b*d + a*c*f)*(f*x - Log[1 + E^(e + f*x)]))/f^2 - (3*d*(b*d + 2*a*c*f)*PolyLog[2, -E^(-e - f*x)])/f^3 - (3*d*(b*d + 2*a*c*f)*PolyLog[2, E^(-e - f*x)])/f^3 - (6*a*d^2*(f*x*PolyLog[2, -E^(-e - f*x)] + PolyLog[3, -E^(-e - f*x)]))/f^3 - (6*a*d^2*(f*x*PolyLog[2, E^(-e - f*x)] + PolyLog[3, E^(-e - f*x)]))/f^3))/3 + (x*(3*c^2 + 3*c*d*x + d^2*x^2)*Csch[e]*(2*a*b*Cosh[e] + a^2*Sinh[e] + b^2*Sinh[e]))/3 + (Csch[e]*Csch[e + f*x]*(b^2*c^2*Sinh[f*x] + 2*b^2*c*d*x*Sinh[f*x] + b^2*d^2*x^2*Sinh[f*x]))/f","B",1
44,1,192,127,1.9818732,"\int (c+d x) (a+b \coth (e+f x))^2 \, dx","Integrate[(c + d*x)*(a + b*Coth[e + f*x])^2,x]","\frac{\sinh (e+f x) (a+b \coth (e+f x))^2 \left(\sinh (e+f x) \left(-\left((e+f x) \left(a^2 (-2 c f+d e-d f x)-2 a b d (e+f x)+b^2 (-2 c f+d e-d f x)\right)\right)+2 b \log (\sinh (e+f x)) (2 a c f-2 a d e+b d)+4 a b d (e+f x) \log \left(1-e^{-2 (e+f x)}\right)\right)-2 a b d \text{Li}_2\left(e^{-2 (e+f x)}\right) \sinh (e+f x)-2 b^2 f (c+d x) \cosh (e+f x)\right)}{2 f^2 (a \sinh (e+f x)+b \cosh (e+f x))^2}","\frac{a^2 (c+d x)^2}{2 d}+\frac{2 a b (c+d x) \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{a b (c+d x)^2}{d}+\frac{a b d \text{Li}_2\left(e^{2 (e+f x)}\right)}{f^2}-\frac{b^2 (c+d x) \coth (e+f x)}{f}+b^2 c x+\frac{b^2 d \log (\sinh (e+f x))}{f^2}+\frac{1}{2} b^2 d x^2",1,"((a + b*Coth[e + f*x])^2*Sinh[e + f*x]*(-2*b^2*f*(c + d*x)*Cosh[e + f*x] + (-((e + f*x)*(-2*a*b*d*(e + f*x) + a^2*(d*e - 2*c*f - d*f*x) + b^2*(d*e - 2*c*f - d*f*x))) + 4*a*b*d*(e + f*x)*Log[1 - E^(-2*(e + f*x))] + 2*b*(b*d - 2*a*d*e + 2*a*c*f)*Log[Sinh[e + f*x]])*Sinh[e + f*x] - 2*a*b*d*PolyLog[2, E^(-2*(e + f*x))]*Sinh[e + f*x]))/(2*f^2*(b*Cosh[e + f*x] + a*Sinh[e + f*x])^2)","A",1
45,0,0,23,45.4871772,"\int \frac{(a+b \coth (e+f x))^2}{c+d x} \, dx","Integrate[(a + b*Coth[e + f*x])^2/(c + d*x),x]","\int \frac{(a+b \coth (e+f x))^2}{c+d x} \, dx","\text{Int}\left(\frac{(a+b \coth (e+f x))^2}{c+d x},x\right)",0,"Integrate[(a + b*Coth[e + f*x])^2/(c + d*x), x]","A",-1
46,0,0,23,32.085773,"\int \frac{(a+b \coth (e+f x))^2}{(c+d x)^2} \, dx","Integrate[(a + b*Coth[e + f*x])^2/(c + d*x)^2,x]","\int \frac{(a+b \coth (e+f x))^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{(a+b \coth (e+f x))^2}{(c+d x)^2},x\right)",0,"Integrate[(a + b*Coth[e + f*x])^2/(c + d*x)^2, x]","A",-1
47,1,2043,556,14.5201035,"\int (c+d x)^3 (a+b \coth (e+f x))^3 \, dx","Integrate[(c + d*x)^3*(a + b*Coth[e + f*x])^3,x]","\text{Result too large to show}","\frac{a^3 (c+d x)^4}{4 d}-\frac{9 a^2 b d^2 (c+d x) \text{Li}_3\left(e^{2 (e+f x)}\right)}{2 f^3}+\frac{9 a^2 b d (c+d x)^2 \text{Li}_2\left(e^{2 (e+f x)}\right)}{2 f^2}+\frac{3 a^2 b (c+d x)^3 \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{3 a^2 b (c+d x)^4}{4 d}+\frac{9 a^2 b d^3 \text{Li}_4\left(e^{2 (e+f x)}\right)}{4 f^4}+\frac{9 a b^2 d^2 (c+d x) \text{Li}_2\left(e^{2 (e+f x)}\right)}{f^3}+\frac{9 a b^2 d (c+d x)^2 \log \left(1-e^{2 (e+f x)}\right)}{f^2}-\frac{3 a b^2 (c+d x)^3 \coth (e+f x)}{f}-\frac{3 a b^2 (c+d x)^3}{f}+\frac{3 a b^2 (c+d x)^4}{4 d}-\frac{9 a b^2 d^3 \text{Li}_3\left(e^{2 (e+f x)}\right)}{2 f^4}-\frac{3 b^3 d^2 (c+d x) \text{Li}_3\left(e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 b^3 d^2 (c+d x) \log \left(1-e^{2 (e+f x)}\right)}{f^3}+\frac{3 b^3 d (c+d x)^2 \text{Li}_2\left(e^{2 (e+f x)}\right)}{2 f^2}-\frac{3 b^3 d (c+d x)^2 \coth (e+f x)}{2 f^2}+\frac{b^3 (c+d x)^3 \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{b^3 (c+d x)^3 \coth ^2(e+f x)}{2 f}-\frac{3 b^3 d (c+d x)^2}{2 f^2}+\frac{b^3 (c+d x)^3}{2 f}-\frac{b^3 (c+d x)^4}{4 d}+\frac{3 b^3 d^3 \text{Li}_2\left(e^{2 (e+f x)}\right)}{2 f^4}+\frac{3 b^3 d^3 \text{Li}_4\left(e^{2 (e+f x)}\right)}{4 f^4}",1,"((-(b^3*c^3) - 3*b^3*c^2*d*x - 3*b^3*c*d^2*x^2 - b^3*d^3*x^3)*Csch[e + f*x]^2)/(2*f) - (b*E^(2*e)*(24*b^2*c*d^2*x + 72*a*b*c^2*d*f*x + 24*a^2*c^3*f^2*x + 8*b^2*c^3*f^2*x + 12*b^2*d^3*x^2 + 72*a*b*c*d^2*f*x^2 + 36*a^2*c^2*d*f^2*x^2 + 12*b^2*c^2*d*f^2*x^2 + 24*a*b*d^3*f*x^3 + 24*a^2*c*d^2*f^2*x^3 + 8*b^2*c*d^2*f^2*x^3 + 6*a^2*d^3*f^2*x^4 + 2*b^2*d^3*f^2*x^4 - 36*a*b*c^2*d*Log[1 - E^(2*(e + f*x))] + (36*a*b*c^2*d*Log[1 - E^(2*(e + f*x))])/E^(2*e) - (12*b^2*c*d^2*Log[1 - E^(2*(e + f*x))])/f + (12*b^2*c*d^2*Log[1 - E^(2*(e + f*x))])/(E^(2*e)*f) - 12*a^2*c^3*f*Log[1 - E^(2*(e + f*x))] - 4*b^2*c^3*f*Log[1 - E^(2*(e + f*x))] + (12*a^2*c^3*f*Log[1 - E^(2*(e + f*x))])/E^(2*e) + (4*b^2*c^3*f*Log[1 - E^(2*(e + f*x))])/E^(2*e) - 72*a*b*c*d^2*x*Log[1 - E^(2*(e + f*x))] + (72*a*b*c*d^2*x*Log[1 - E^(2*(e + f*x))])/E^(2*e) - (12*b^2*d^3*x*Log[1 - E^(2*(e + f*x))])/f + (12*b^2*d^3*x*Log[1 - E^(2*(e + f*x))])/(E^(2*e)*f) - 36*a^2*c^2*d*f*x*Log[1 - E^(2*(e + f*x))] - 12*b^2*c^2*d*f*x*Log[1 - E^(2*(e + f*x))] + (36*a^2*c^2*d*f*x*Log[1 - E^(2*(e + f*x))])/E^(2*e) + (12*b^2*c^2*d*f*x*Log[1 - E^(2*(e + f*x))])/E^(2*e) - 36*a*b*d^3*x^2*Log[1 - E^(2*(e + f*x))] + (36*a*b*d^3*x^2*Log[1 - E^(2*(e + f*x))])/E^(2*e) - 36*a^2*c*d^2*f*x^2*Log[1 - E^(2*(e + f*x))] - 12*b^2*c*d^2*f*x^2*Log[1 - E^(2*(e + f*x))] + (36*a^2*c*d^2*f*x^2*Log[1 - E^(2*(e + f*x))])/E^(2*e) + (12*b^2*c*d^2*f*x^2*Log[1 - E^(2*(e + f*x))])/E^(2*e) - 12*a^2*d^3*f*x^3*Log[1 - E^(2*(e + f*x))] - 4*b^2*d^3*f*x^3*Log[1 - E^(2*(e + f*x))] + (12*a^2*d^3*f*x^3*Log[1 - E^(2*(e + f*x))])/E^(2*e) + (4*b^2*d^3*f*x^3*Log[1 - E^(2*(e + f*x))])/E^(2*e) - (6*d*(-1 + E^(2*e))*(6*a*b*d*f*(c + d*x) + 3*a^2*f^2*(c + d*x)^2 + b^2*(d^2 + c^2*f^2 + 2*c*d*f^2*x + d^2*f^2*x^2))*PolyLog[2, E^(2*(e + f*x))])/(E^(2*e)*f^2) + (6*d^2*(-1 + E^(2*e))*(3*a*b*d + 3*a^2*f*(c + d*x) + b^2*f*(c + d*x))*PolyLog[3, E^(2*(e + f*x))])/(E^(2*e)*f^2) - (9*a^2*d^3*PolyLog[4, E^(2*(e + f*x))])/f^2 - (3*b^2*d^3*PolyLog[4, E^(2*(e + f*x))])/f^2 + (9*a^2*d^3*PolyLog[4, E^(2*(e + f*x))])/(E^(2*e)*f^2) + (3*b^2*d^3*PolyLog[4, E^(2*(e + f*x))])/(E^(2*e)*f^2)))/(4*(-1 + E^(2*e))*f^2) + (3*x^2*(-(a^3*c^2*d) + 3*a^2*b*c^2*d - 3*a*b^2*c^2*d + b^3*c^2*d + a^3*c^2*d*Cosh[2*e] + 3*a^2*b*c^2*d*Cosh[2*e] + 3*a*b^2*c^2*d*Cosh[2*e] + b^3*c^2*d*Cosh[2*e] + a^3*c^2*d*Sinh[2*e] + 3*a^2*b*c^2*d*Sinh[2*e] + 3*a*b^2*c^2*d*Sinh[2*e] + b^3*c^2*d*Sinh[2*e]))/(2*(-1 + Cosh[2*e] + Sinh[2*e])) + (x^3*(-(a^3*c*d^2) + 3*a^2*b*c*d^2 - 3*a*b^2*c*d^2 + b^3*c*d^2 + a^3*c*d^2*Cosh[2*e] + 3*a^2*b*c*d^2*Cosh[2*e] + 3*a*b^2*c*d^2*Cosh[2*e] + b^3*c*d^2*Cosh[2*e] + a^3*c*d^2*Sinh[2*e] + 3*a^2*b*c*d^2*Sinh[2*e] + 3*a*b^2*c*d^2*Sinh[2*e] + b^3*c*d^2*Sinh[2*e]))/(-1 + Cosh[2*e] + Sinh[2*e]) + (x^4*(-(a^3*d^3) + 3*a^2*b*d^3 - 3*a*b^2*d^3 + b^3*d^3 + a^3*d^3*Cosh[2*e] + 3*a^2*b*d^3*Cosh[2*e] + 3*a*b^2*d^3*Cosh[2*e] + b^3*d^3*Cosh[2*e] + a^3*d^3*Sinh[2*e] + 3*a^2*b*d^3*Sinh[2*e] + 3*a*b^2*d^3*Sinh[2*e] + b^3*d^3*Sinh[2*e]))/(4*(-1 + Cosh[2*e] + Sinh[2*e])) + x*(a^3*c^3 + 3*a*b^2*c^3 + (3*a^2*b*c^3)/(-1 + Cosh[2*e] + Sinh[2*e]) + (3*a^2*b*c^3*Cosh[2*e] + 3*a^2*b*c^3*Sinh[2*e])/(-1 + Cosh[2*e] + Sinh[2*e]) + (2*b^3*c^3*Cosh[2*e] + 2*b^3*c^3*Sinh[2*e])/((-1 + Cosh[2*e] + Sinh[2*e])*(1 + Cosh[2*e] + Cosh[4*e] + Sinh[2*e] + Sinh[4*e])) + (2*b^3*c^3*Cosh[4*e] + 2*b^3*c^3*Sinh[4*e])/((-1 + Cosh[2*e] + Sinh[2*e])*(1 + Cosh[2*e] + Cosh[4*e] + Sinh[2*e] + Sinh[4*e])) + (b^3*c^3)/(-1 + Cosh[6*e] + Sinh[6*e]) + (b^3*c^3*Cosh[6*e] + b^3*c^3*Sinh[6*e])/(-1 + Cosh[6*e] + Sinh[6*e])) + (3*Csch[e]*Csch[e + f*x]*(b^3*c^2*d*Sinh[f*x] + 2*a*b^2*c^3*f*Sinh[f*x] + 2*b^3*c*d^2*x*Sinh[f*x] + 6*a*b^2*c^2*d*f*x*Sinh[f*x] + b^3*d^3*x^2*Sinh[f*x] + 6*a*b^2*c*d^2*f*x^2*Sinh[f*x] + 2*a*b^2*d^3*f*x^3*Sinh[f*x]))/(2*f^2)","B",1
48,1,2029,401,13.3869482,"\int (c+d x)^2 (a+b \coth (e+f x))^3 \, dx","Integrate[(c + d*x)^2*(a + b*Coth[e + f*x])^3,x]","\text{Result too large to show}","\frac{a^3 (c+d x)^3}{3 d}+\frac{3 a^2 b d (c+d x) \text{Li}_2\left(e^{2 (e+f x)}\right)}{f^2}+\frac{3 a^2 b (c+d x)^2 \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{a^2 b (c+d x)^3}{d}-\frac{3 a^2 b d^2 \text{Li}_3\left(e^{2 (e+f x)}\right)}{2 f^3}+\frac{6 a b^2 d (c+d x) \log \left(1-e^{2 (e+f x)}\right)}{f^2}-\frac{3 a b^2 (c+d x)^2 \coth (e+f x)}{f}-\frac{3 a b^2 (c+d x)^2}{f}+\frac{a b^2 (c+d x)^3}{d}+\frac{3 a b^2 d^2 \text{Li}_2\left(e^{2 (e+f x)}\right)}{f^3}+\frac{b^3 d (c+d x) \text{Li}_2\left(e^{2 (e+f x)}\right)}{f^2}-\frac{b^3 d (c+d x) \coth (e+f x)}{f^2}+\frac{b^3 (c+d x)^2 \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{b^3 (c+d x)^2 \coth ^2(e+f x)}{2 f}+\frac{b^3 c d x}{f}-\frac{b^3 (c+d x)^3}{3 d}-\frac{b^3 d^2 \text{Li}_3\left(e^{2 (e+f x)}\right)}{2 f^3}+\frac{b^3 d^2 \log (\sinh (e+f x))}{f^3}+\frac{b^3 d^2 x^2}{2 f}",1,"-1/2*(a^2*b*d^2*E^e*Csch[e]*((2*f^3*x^3)/E^(2*e) - 3*(1 - E^(-2*e))*f^2*x^2*Log[1 - E^(-e - f*x)] - 3*(1 - E^(-2*e))*f^2*x^2*Log[1 + E^(-e - f*x)] + 6*(1 - E^(-2*e))*(f*x*PolyLog[2, -E^(-e - f*x)] + PolyLog[3, -E^(-e - f*x)]) + 6*(1 - E^(-2*e))*(f*x*PolyLog[2, E^(-e - f*x)] + PolyLog[3, E^(-e - f*x)])))/f^3 - (b^3*d^2*E^e*Csch[e]*((2*f^3*x^3)/E^(2*e) - 3*(1 - E^(-2*e))*f^2*x^2*Log[1 - E^(-e - f*x)] - 3*(1 - E^(-2*e))*f^2*x^2*Log[1 + E^(-e - f*x)] + 6*(1 - E^(-2*e))*(f*x*PolyLog[2, -E^(-e - f*x)] + PolyLog[3, -E^(-e - f*x)]) + 6*(1 - E^(-2*e))*(f*x*PolyLog[2, E^(-e - f*x)] + PolyLog[3, E^(-e - f*x)])))/(6*f^3) - (b^3*d^2*Csch[e]*(-(f*x*Cosh[e]) + Log[Cosh[f*x]*Sinh[e] + Cosh[e]*Sinh[f*x]]*Sinh[e]))/(f^3*(-Cosh[e]^2 + Sinh[e]^2)) - (6*a*b^2*c*d*Csch[e]*(-(f*x*Cosh[e]) + Log[Cosh[f*x]*Sinh[e] + Cosh[e]*Sinh[f*x]]*Sinh[e]))/(f^2*(-Cosh[e]^2 + Sinh[e]^2)) - (3*a^2*b*c^2*Csch[e]*(-(f*x*Cosh[e]) + Log[Cosh[f*x]*Sinh[e] + Cosh[e]*Sinh[f*x]]*Sinh[e]))/(f*(-Cosh[e]^2 + Sinh[e]^2)) - (b^3*c^2*Csch[e]*(-(f*x*Cosh[e]) + Log[Cosh[f*x]*Sinh[e] + Cosh[e]*Sinh[f*x]]*Sinh[e]))/(f*(-Cosh[e]^2 + Sinh[e]^2)) + (Csch[e]*Csch[e + f*x]^2*(-6*b^3*c*d*Cosh[e] - 18*a*b^2*c^2*f*Cosh[e] - 6*b^3*d^2*x*Cosh[e] - 36*a*b^2*c*d*f*x*Cosh[e] - 18*a^2*b*c^2*f^2*x*Cosh[e] - 6*b^3*c^2*f^2*x*Cosh[e] - 18*a*b^2*d^2*f*x^2*Cosh[e] - 18*a^2*b*c*d*f^2*x^2*Cosh[e] - 6*b^3*c*d*f^2*x^2*Cosh[e] - 6*a^2*b*d^2*f^2*x^3*Cosh[e] - 2*b^3*d^2*f^2*x^3*Cosh[e] + 6*b^3*c*d*Cosh[e + 2*f*x] + 18*a*b^2*c^2*f*Cosh[e + 2*f*x] + 6*b^3*d^2*x*Cosh[e + 2*f*x] + 36*a*b^2*c*d*f*x*Cosh[e + 2*f*x] + 9*a^2*b*c^2*f^2*x*Cosh[e + 2*f*x] + 3*b^3*c^2*f^2*x*Cosh[e + 2*f*x] + 18*a*b^2*d^2*f*x^2*Cosh[e + 2*f*x] + 9*a^2*b*c*d*f^2*x^2*Cosh[e + 2*f*x] + 3*b^3*c*d*f^2*x^2*Cosh[e + 2*f*x] + 3*a^2*b*d^2*f^2*x^3*Cosh[e + 2*f*x] + b^3*d^2*f^2*x^3*Cosh[e + 2*f*x] + 9*a^2*b*c^2*f^2*x*Cosh[3*e + 2*f*x] + 3*b^3*c^2*f^2*x*Cosh[3*e + 2*f*x] + 9*a^2*b*c*d*f^2*x^2*Cosh[3*e + 2*f*x] + 3*b^3*c*d*f^2*x^2*Cosh[3*e + 2*f*x] + 3*a^2*b*d^2*f^2*x^3*Cosh[3*e + 2*f*x] + b^3*d^2*f^2*x^3*Cosh[3*e + 2*f*x] - 6*b^3*c^2*f*Sinh[e] - 12*b^3*c*d*f*x*Sinh[e] - 6*a^3*c^2*f^2*x*Sinh[e] - 18*a*b^2*c^2*f^2*x*Sinh[e] - 6*b^3*d^2*f*x^2*Sinh[e] - 6*a^3*c*d*f^2*x^2*Sinh[e] - 18*a*b^2*c*d*f^2*x^2*Sinh[e] - 2*a^3*d^2*f^2*x^3*Sinh[e] - 6*a*b^2*d^2*f^2*x^3*Sinh[e] - 3*a^3*c^2*f^2*x*Sinh[e + 2*f*x] - 9*a*b^2*c^2*f^2*x*Sinh[e + 2*f*x] - 3*a^3*c*d*f^2*x^2*Sinh[e + 2*f*x] - 9*a*b^2*c*d*f^2*x^2*Sinh[e + 2*f*x] - a^3*d^2*f^2*x^3*Sinh[e + 2*f*x] - 3*a*b^2*d^2*f^2*x^3*Sinh[e + 2*f*x] + 3*a^3*c^2*f^2*x*Sinh[3*e + 2*f*x] + 9*a*b^2*c^2*f^2*x*Sinh[3*e + 2*f*x] + 3*a^3*c*d*f^2*x^2*Sinh[3*e + 2*f*x] + 9*a*b^2*c*d*f^2*x^2*Sinh[3*e + 2*f*x] + a^3*d^2*f^2*x^3*Sinh[3*e + 2*f*x] + 3*a*b^2*d^2*f^2*x^3*Sinh[3*e + 2*f*x]))/(12*f^2) - (3*a*b^2*d^2*Csch[e]*Sech[e]*((f^2*x^2)/E^ArcTanh[Tanh[e]] - (I*(-(f*x*(-Pi + (2*I)*ArcTanh[Tanh[e]])) - Pi*Log[1 + E^(2*f*x)] - 2*(I*f*x + I*ArcTanh[Tanh[e]])*Log[1 - E^((2*I)*(I*f*x + I*ArcTanh[Tanh[e]]))] + Pi*Log[Cosh[f*x]] + (2*I)*ArcTanh[Tanh[e]]*Log[I*Sinh[f*x + ArcTanh[Tanh[e]]]] + I*PolyLog[2, E^((2*I)*(I*f*x + I*ArcTanh[Tanh[e]]))])*Tanh[e])/Sqrt[1 - Tanh[e]^2]))/(f^3*Sqrt[Sech[e]^2*(Cosh[e]^2 - Sinh[e]^2)]) - (3*a^2*b*c*d*Csch[e]*Sech[e]*((f^2*x^2)/E^ArcTanh[Tanh[e]] - (I*(-(f*x*(-Pi + (2*I)*ArcTanh[Tanh[e]])) - Pi*Log[1 + E^(2*f*x)] - 2*(I*f*x + I*ArcTanh[Tanh[e]])*Log[1 - E^((2*I)*(I*f*x + I*ArcTanh[Tanh[e]]))] + Pi*Log[Cosh[f*x]] + (2*I)*ArcTanh[Tanh[e]]*Log[I*Sinh[f*x + ArcTanh[Tanh[e]]]] + I*PolyLog[2, E^((2*I)*(I*f*x + I*ArcTanh[Tanh[e]]))])*Tanh[e])/Sqrt[1 - Tanh[e]^2]))/(f^2*Sqrt[Sech[e]^2*(Cosh[e]^2 - Sinh[e]^2)]) - (b^3*c*d*Csch[e]*Sech[e]*((f^2*x^2)/E^ArcTanh[Tanh[e]] - (I*(-(f*x*(-Pi + (2*I)*ArcTanh[Tanh[e]])) - Pi*Log[1 + E^(2*f*x)] - 2*(I*f*x + I*ArcTanh[Tanh[e]])*Log[1 - E^((2*I)*(I*f*x + I*ArcTanh[Tanh[e]]))] + Pi*Log[Cosh[f*x]] + (2*I)*ArcTanh[Tanh[e]]*Log[I*Sinh[f*x + ArcTanh[Tanh[e]]]] + I*PolyLog[2, E^((2*I)*(I*f*x + I*ArcTanh[Tanh[e]]))])*Tanh[e])/Sqrt[1 - Tanh[e]^2]))/(f^2*Sqrt[Sech[e]^2*(Cosh[e]^2 - Sinh[e]^2)])","C",0
49,1,266,261,3.7677377,"\int (c+d x) (a+b \coth (e+f x))^3 \, dx","Integrate[(c + d*x)*(a + b*Coth[e + f*x])^3,x]","\frac{\sinh (e+f x) (a+b \coth (e+f x))^3 \left(-b d \left(3 a^2+b^2\right) \text{Li}_2\left(e^{-2 (e+f x)}\right) \sinh ^2(e+f x)+\sinh ^2(e+f x) \left(-2 b \log (\sinh (e+f x)) \left(3 a^2 (d e-c f)-3 a b d+b^2 (d e-c f)\right)+2 b d \left(3 a^2+b^2\right) (e+f x) \log \left(1-e^{-2 (e+f x)}\right)-\left((e+f x) \left(a^3 (d (e-f x)-2 c f)-3 a^2 b d (e+f x)+3 a b^2 (d (e-f x)-2 c f)-b^3 d (e+f x)\right)\right)\right)-\frac{1}{2} b^2 (\sinh (2 (e+f x)) (6 a f (c+d x)+b d)+2 b f (c+d x))\right)}{2 f^2 (a \sinh (e+f x)+b \cosh (e+f x))^3}","\frac{a^3 (c+d x)^2}{2 d}+\frac{3 a^2 b (c+d x) \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{3 a^2 b (c+d x)^2}{2 d}+\frac{3 a^2 b d \text{Li}_2\left(e^{2 (e+f x)}\right)}{2 f^2}-\frac{3 a b^2 (c+d x) \coth (e+f x)}{f}+3 a b^2 c x+\frac{3 a b^2 d \log (\sinh (e+f x))}{f^2}+\frac{3}{2} a b^2 d x^2+\frac{b^3 (c+d x) \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{b^3 (c+d x) \coth ^2(e+f x)}{2 f}-\frac{b^3 (c+d x)^2}{2 d}+\frac{b^3 d \text{Li}_2\left(e^{2 (e+f x)}\right)}{2 f^2}-\frac{b^3 d \coth (e+f x)}{2 f^2}+\frac{b^3 d x}{2 f}",1,"((a + b*Coth[e + f*x])^3*Sinh[e + f*x]*((-((e + f*x)*(-3*a^2*b*d*(e + f*x) - b^3*d*(e + f*x) + a^3*(-2*c*f + d*(e - f*x)) + 3*a*b^2*(-2*c*f + d*(e - f*x)))) + 2*b*(3*a^2 + b^2)*d*(e + f*x)*Log[1 - E^(-2*(e + f*x))] - 2*b*(-3*a*b*d + 3*a^2*(d*e - c*f) + b^2*(d*e - c*f))*Log[Sinh[e + f*x]])*Sinh[e + f*x]^2 - b*(3*a^2 + b^2)*d*PolyLog[2, E^(-2*(e + f*x))]*Sinh[e + f*x]^2 - (b^2*(2*b*f*(c + d*x) + (b*d + 6*a*f*(c + d*x))*Sinh[2*(e + f*x)]))/2))/(2*f^2*(b*Cosh[e + f*x] + a*Sinh[e + f*x])^3)","A",1
50,0,0,23,65.8380682,"\int \frac{(a+b \coth (e+f x))^3}{c+d x} \, dx","Integrate[(a + b*Coth[e + f*x])^3/(c + d*x),x]","\int \frac{(a+b \coth (e+f x))^3}{c+d x} \, dx","\text{Int}\left(\frac{(a+b \coth (e+f x))^3}{c+d x},x\right)",0,"Integrate[(a + b*Coth[e + f*x])^3/(c + d*x), x]","A",-1
51,0,0,23,60.8365079,"\int \frac{(a+b \coth (e+f x))^3}{(c+d x)^2} \, dx","Integrate[(a + b*Coth[e + f*x])^3/(c + d*x)^2,x]","\int \frac{(a+b \coth (e+f x))^3}{(c+d x)^2} \, dx","\text{Int}\left(\frac{(a+b \coth (e+f x))^3}{(c+d x)^2},x\right)",0,"Integrate[(a + b*Coth[e + f*x])^3/(c + d*x)^2, x]","A",-1
52,1,239,210,3.3543631,"\int \frac{(c+d x)^3}{a+b \coth (e+f x)} \, dx","Integrate[(c + d*x)^3/(a + b*Coth[e + f*x]),x]","\frac{x \sinh (e) \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)}{4 (a \sinh (e)+b \cosh (e))}+\frac{b \left(\frac{3 d \left(2 f^2 (c+d x)^2 \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)+d \left(2 f (c+d x) \text{Li}_3\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)+d \text{Li}_4\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)\right)\right)}{f^4 (a-b)}-\frac{4 (c+d x)^3 \log \left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}+1\right)}{f (a-b)}+\frac{2 (c+d x)^4}{d \left(a \left(e^{2 e}-1\right)+b \left(e^{2 e}+1\right)\right)}\right)}{4 (a+b)}","\frac{3 b d^2 (c+d x) \text{Li}_3\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^3 \left(a^2-b^2\right)}+\frac{3 b d (c+d x)^2 \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^2 \left(a^2-b^2\right)}-\frac{b (c+d x)^3 \log \left(1-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f \left(a^2-b^2\right)}+\frac{3 b d^3 \text{Li}_4\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{4 f^4 \left(a^2-b^2\right)}+\frac{(c+d x)^4}{4 d (a+b)}",1,"(b*((2*(c + d*x)^4)/(d*(a*(-1 + E^(2*e)) + b*(1 + E^(2*e)))) - (4*(c + d*x)^3*Log[1 + (-a + b)/((a + b)*E^(2*(e + f*x)))])/((a - b)*f) + (3*d*(2*f^2*(c + d*x)^2*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))] + d*(2*f*(c + d*x)*PolyLog[3, (a - b)/((a + b)*E^(2*(e + f*x)))] + d*PolyLog[4, (a - b)/((a + b)*E^(2*(e + f*x)))])))/((a - b)*f^4)))/(4*(a + b)) + (x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Sinh[e])/(4*(b*Cosh[e] + a*Sinh[e]))","A",1
53,1,191,156,3.6937897,"\int \frac{(c+d x)^2}{a+b \coth (e+f x)} \, dx","Integrate[(c + d*x)^2/(a + b*Coth[e + f*x]),x]","\frac{x \sinh (e) \left(3 c^2+3 c d x+d^2 x^2\right)}{3 (a \sinh (e)+b \cosh (e))}+\frac{b \left(\frac{3 d \left(2 f (c+d x) \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)+d \text{Li}_3\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)\right)}{f^3 (a-b)}-\frac{6 (c+d x)^2 \log \left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}+1\right)}{f (a-b)}+\frac{4 (c+d x)^3}{d \left(a \left(e^{2 e}-1\right)+b \left(e^{2 e}+1\right)\right)}\right)}{6 (a+b)}","\frac{b d (c+d x) \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f^2 \left(a^2-b^2\right)}-\frac{b (c+d x)^2 \log \left(1-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f \left(a^2-b^2\right)}+\frac{b d^2 \text{Li}_3\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^3 \left(a^2-b^2\right)}+\frac{(c+d x)^3}{3 d (a+b)}",1,"(b*((4*(c + d*x)^3)/(d*(a*(-1 + E^(2*e)) + b*(1 + E^(2*e)))) - (6*(c + d*x)^2*Log[1 + (-a + b)/((a + b)*E^(2*(e + f*x)))])/((a - b)*f) + (3*d*(2*f*(c + d*x)*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))] + d*PolyLog[3, (a - b)/((a + b)*E^(2*(e + f*x)))]))/((a - b)*f^3)))/(6*(a + b)) + (x*(3*c^2 + 3*c*d*x + d^2*x^2)*Sinh[e])/(3*(b*Cosh[e] + a*Sinh[e]))","A",1
54,1,144,108,3.1806204,"\int \frac{c+d x}{a+b \coth (e+f x)} \, dx","Integrate[(c + d*x)/(a + b*Coth[e + f*x]),x]","\frac{b \left(-\frac{2 (c+d x) \log \left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}+1\right)}{f (a-b)}+\frac{2 (c+d x)^2}{d \left(a \left(e^{2 e}-1\right)+b \left(e^{2 e}+1\right)\right)}+\frac{d \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f^2 (a-b)}\right)}{2 (a+b)}+\frac{x \sinh (e) (2 c+d x)}{2 (a \sinh (e)+b \cosh (e))}","-\frac{b (c+d x) \log \left(1-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f \left(a^2-b^2\right)}+\frac{b d \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^2 \left(a^2-b^2\right)}+\frac{(c+d x)^2}{2 d (a+b)}",1,"(b*((2*(c + d*x)^2)/(d*(a*(-1 + E^(2*e)) + b*(1 + E^(2*e)))) - (2*(c + d*x)*Log[1 + (-a + b)/((a + b)*E^(2*(e + f*x)))])/((a - b)*f) + (d*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))])/((a - b)*f^2)))/(2*(a + b)) + (x*(2*c + d*x)*Sinh[e])/(2*(b*Cosh[e] + a*Sinh[e]))","A",1
55,0,0,23,15.0946465,"\int \frac{1}{(c+d x) (a+b \coth (e+f x))} \, dx","Integrate[1/((c + d*x)*(a + b*Coth[e + f*x])),x]","\int \frac{1}{(c+d x) (a+b \coth (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \coth (e+f x))},x\right)",0,"Integrate[1/((c + d*x)*(a + b*Coth[e + f*x])), x]","A",-1
56,0,0,23,23.938598,"\int \frac{1}{(c+d x)^2 (a+b \coth (e+f x))} \, dx","Integrate[1/((c + d*x)^2*(a + b*Coth[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+b \coth (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \coth (e+f x))},x\right)",0,"Integrate[1/((c + d*x)^2*(a + b*Coth[e + f*x])), x]","A",-1
57,1,1022,638,12.7100478,"\int \frac{(c+d x)^3}{(a+b \coth (e+f x))^2} \, dx","Integrate[(c + d*x)^3/(a + b*Coth[e + f*x])^2,x]","\frac{b \left(-4 a \left(a \left(-1+e^{2 e}\right)+b \left(1+e^{2 e}\right)\right) f^3 x^3 \log \left(\frac{e^{-2 (e+f x)} (b-a)}{a+b}+1\right) d^4+3 a \left(a \left(-1+e^{2 e}\right)+b \left(1+e^{2 e}\right)\right) \left(2 f^2 \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right) x^2+2 f \text{Li}_3\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right) x+\text{Li}_4\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)\right) d^4+6 \left(a \left(-1+e^{2 e}\right)+b \left(1+e^{2 e}\right)\right) f^2 (b d-2 a c f) x^2 \log \left(\frac{e^{-2 (e+f x)} (b-a)}{a+b}+1\right) d^3-3 \left(a \left(-1+e^{2 e}\right)+b \left(1+e^{2 e}\right)\right) (b d-2 a c f) \left(2 f x \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)+\text{Li}_3\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)\right) d^3-12 c \left(a \left(-1+e^{2 e}\right)+b \left(1+e^{2 e}\right)\right) f^2 (a c f-b d) x \log \left(\frac{e^{-2 (e+f x)} (b-a)}{a+b}+1\right) d^2+6 c \left(a \left(-1+e^{2 e}\right)+b \left(1+e^{2 e}\right)\right) f (a c f-b d) \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right) d^2-4 (a-b) b f^3 (c+d x)^3 d+2 c^2 \left(a \left(-1+e^{2 e}\right)+b \left(1+e^{2 e}\right)\right) f^2 (2 a c f-3 b d) \left(2 f x-\log \left(a-(a+b) e^{2 (e+f x)}-b\right)\right) d+2 a (a-b) f^4 (c+d x)^4\right)}{2 (a-b)^2 (a+b)^2 d \left(a \left(-1+e^{2 e}\right)+b \left(1+e^{2 e}\right)\right) f^4}+\frac{-a^2 d^3 f \cosh (f x) x^4-b^2 d^3 f \cosh (f x) x^4+a^2 d^3 f \cosh (2 e+f x) x^4-b^2 d^3 f \cosh (2 e+f x) x^4-2 a b d^3 f \sinh (f x) x^4-4 a^2 c d^2 f \cosh (f x) x^3-4 b^2 c d^2 f \cosh (f x) x^3+4 a^2 c d^2 f \cosh (2 e+f x) x^3-4 b^2 c d^2 f \cosh (2 e+f x) x^3+8 b^2 d^3 \sinh (f x) x^3-8 a b c d^2 f \sinh (f x) x^3-6 a^2 c^2 d f \cosh (f x) x^2-6 b^2 c^2 d f \cosh (f x) x^2+6 a^2 c^2 d f \cosh (2 e+f x) x^2-6 b^2 c^2 d f \cosh (2 e+f x) x^2+24 b^2 c d^2 \sinh (f x) x^2-12 a b c^2 d f \sinh (f x) x^2-4 a^2 c^3 f \cosh (f x) x-4 b^2 c^3 f \cosh (f x) x+4 a^2 c^3 f \cosh (2 e+f x) x-4 b^2 c^3 f \cosh (2 e+f x) x+24 b^2 c^2 d \sinh (f x) x-8 a b c^3 f \sinh (f x) x+8 b^2 c^3 \sinh (f x)}{8 (a-b) (a+b) f (b \cosh (e)+a \sinh (e)) (b \cosh (e+f x)+a \sinh (e+f x))}","\frac{3 b^2 d^2 (c+d x) \text{Li}_2\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 \left(a^2-b^2\right)^2}-\frac{3 b^2 d^2 (c+d x) \text{Li}_3\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 \left(a^2-b^2\right)^2}+\frac{3 b^2 d (c+d x)^2 \text{Li}_2\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{3 b^2 d (c+d x)^2 \log \left(1-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{2 b^2 (c+d x)^3 \log \left(1-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f \left(a^2-b^2\right)^2}-\frac{2 b^2 (c+d x)^3}{f \left(a^2-b^2\right)^2}-\frac{3 b^2 d^3 \text{Li}_3\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{2 f^4 \left(a^2-b^2\right)^2}+\frac{3 b^2 d^3 \text{Li}_4\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{2 f^4 \left(a^2-b^2\right)^2}+\frac{2 b^2 (c+d x)^3}{f (a-b) (a+b)^2 \left(-(a+b) e^{2 e+2 f x}+a-b\right)}+\frac{3 b d^2 (c+d x) \text{Li}_3\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 (a-b)^2 (a+b)}-\frac{3 b d (c+d x)^2 \text{Li}_2\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 (a-b)^2 (a+b)}-\frac{2 b (c+d x)^3 \log \left(1-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f (a-b)^2 (a+b)}+\frac{(c+d x)^4}{4 d (a-b)^2}-\frac{3 b d^3 \text{Li}_4\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{2 f^4 (a-b)^2 (a+b)}",1,"(b*(-4*(a - b)*b*d*f^3*(c + d*x)^3 + 2*a*(a - b)*f^4*(c + d*x)^4 - 12*c*d^2*(a*(-1 + E^(2*e)) + b*(1 + E^(2*e)))*f^2*(-(b*d) + a*c*f)*x*Log[1 + (-a + b)/((a + b)*E^(2*(e + f*x)))] + 6*d^3*(a*(-1 + E^(2*e)) + b*(1 + E^(2*e)))*f^2*(b*d - 2*a*c*f)*x^2*Log[1 + (-a + b)/((a + b)*E^(2*(e + f*x)))] - 4*a*d^4*(a*(-1 + E^(2*e)) + b*(1 + E^(2*e)))*f^3*x^3*Log[1 + (-a + b)/((a + b)*E^(2*(e + f*x)))] + 2*c^2*d*(a*(-1 + E^(2*e)) + b*(1 + E^(2*e)))*f^2*(-3*b*d + 2*a*c*f)*(2*f*x - Log[a - b - (a + b)*E^(2*(e + f*x))]) + 6*c*d^2*(a*(-1 + E^(2*e)) + b*(1 + E^(2*e)))*f*(-(b*d) + a*c*f)*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))] - 3*d^3*(a*(-1 + E^(2*e)) + b*(1 + E^(2*e)))*(b*d - 2*a*c*f)*(2*f*x*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))] + PolyLog[3, (a - b)/((a + b)*E^(2*(e + f*x)))]) + 3*a*d^4*(a*(-1 + E^(2*e)) + b*(1 + E^(2*e)))*(2*f^2*x^2*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))] + 2*f*x*PolyLog[3, (a - b)/((a + b)*E^(2*(e + f*x)))] + PolyLog[4, (a - b)/((a + b)*E^(2*(e + f*x)))])))/(2*(a - b)^2*(a + b)^2*d*(a*(-1 + E^(2*e)) + b*(1 + E^(2*e)))*f^4) + (-4*a^2*c^3*f*x*Cosh[f*x] - 4*b^2*c^3*f*x*Cosh[f*x] - 6*a^2*c^2*d*f*x^2*Cosh[f*x] - 6*b^2*c^2*d*f*x^2*Cosh[f*x] - 4*a^2*c*d^2*f*x^3*Cosh[f*x] - 4*b^2*c*d^2*f*x^3*Cosh[f*x] - a^2*d^3*f*x^4*Cosh[f*x] - b^2*d^3*f*x^4*Cosh[f*x] + 4*a^2*c^3*f*x*Cosh[2*e + f*x] - 4*b^2*c^3*f*x*Cosh[2*e + f*x] + 6*a^2*c^2*d*f*x^2*Cosh[2*e + f*x] - 6*b^2*c^2*d*f*x^2*Cosh[2*e + f*x] + 4*a^2*c*d^2*f*x^3*Cosh[2*e + f*x] - 4*b^2*c*d^2*f*x^3*Cosh[2*e + f*x] + a^2*d^3*f*x^4*Cosh[2*e + f*x] - b^2*d^3*f*x^4*Cosh[2*e + f*x] + 8*b^2*c^3*Sinh[f*x] + 24*b^2*c^2*d*x*Sinh[f*x] - 8*a*b*c^3*f*x*Sinh[f*x] + 24*b^2*c*d^2*x^2*Sinh[f*x] - 12*a*b*c^2*d*f*x^2*Sinh[f*x] + 8*b^2*d^3*x^3*Sinh[f*x] - 8*a*b*c*d^2*f*x^3*Sinh[f*x] - 2*a*b*d^3*f*x^4*Sinh[f*x])/(8*(a - b)*(a + b)*f*(b*Cosh[e] + a*Sinh[e])*(b*Cosh[e + f*x] + a*Sinh[e + f*x]))","A",1
58,1,509,475,8.7058865,"\int \frac{(c+d x)^2}{(a+b \coth (e+f x))^2} \, dx","Integrate[(c + d*x)^2/(a + b*Coth[e + f*x])^2,x]","\frac{-\frac{f^2 (a-b) (a+b) \left(-f x \left(a^2-b^2\right) \left(3 c^2+3 c d x+d^2 x^2\right) \cosh (2 e+f x)+f x \left(a^2+b^2\right) \left(3 c^2+3 c d x+d^2 x^2\right) \cosh (f x)+2 b \sinh (f x) \left(a f x \left(3 c^2+3 c d x+d^2 x^2\right)-3 b (c+d x)^2\right)\right)}{(a \sinh (e)+b \cosh (e)) (a \sinh (e+f x)+b \cosh (e+f x))}+\frac{12 b d f^2 x^2 (a-b) (2 a c f-b d)}{a \left(e^{2 e}-1\right)+b \left(e^{2 e}+1\right)}+\frac{24 b c f^2 x (a-b) (a c f-b d)}{a \left(e^{2 e}-1\right)+b \left(e^{2 e}+1\right)}-6 b d (b d-2 a c f) \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)+12 b d f x (b d-2 a c f) \log \left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}+1\right)+12 b c f (a c f-b d) \left(2 f x-\log \left(-(a+b) e^{2 (e+f x)}+a-b\right)\right)+\frac{8 a b d^2 f^3 x^3 (a-b)}{a \left(e^{2 e}-1\right)+b \left(e^{2 e}+1\right)}-12 a b d^2 f^2 x^2 \log \left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}+1\right)+6 a b d^2 \left(2 f x \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)+\text{Li}_3\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)\right)}{6 f^3 (a-b)^2 (a+b)^2}","\frac{2 b^2 d (c+d x) \text{Li}_2\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{2 b^2 d (c+d x) \log \left(1-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{2 b^2 (c+d x)^2 \log \left(1-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f \left(a^2-b^2\right)^2}-\frac{2 b^2 (c+d x)^2}{f \left(a^2-b^2\right)^2}+\frac{b^2 d^2 \text{Li}_2\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 \left(a^2-b^2\right)^2}-\frac{b^2 d^2 \text{Li}_3\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 \left(a^2-b^2\right)^2}+\frac{2 b^2 (c+d x)^2}{f (a-b) (a+b)^2 \left(-(a+b) e^{2 e+2 f x}+a-b\right)}-\frac{2 b d (c+d x) \text{Li}_2\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 (a-b)^2 (a+b)}-\frac{2 b (c+d x)^2 \log \left(1-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f (a-b)^2 (a+b)}+\frac{(c+d x)^3}{3 d (a-b)^2}+\frac{b d^2 \text{Li}_3\left(\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 (a-b)^2 (a+b)}",1,"((24*(a - b)*b*c*f^2*(-(b*d) + a*c*f)*x)/(a*(-1 + E^(2*e)) + b*(1 + E^(2*e))) + (12*(a - b)*b*d*f^2*(-(b*d) + 2*a*c*f)*x^2)/(a*(-1 + E^(2*e)) + b*(1 + E^(2*e))) + (8*a*(a - b)*b*d^2*f^3*x^3)/(a*(-1 + E^(2*e)) + b*(1 + E^(2*e))) + 12*b*d*f*(b*d - 2*a*c*f)*x*Log[1 + (-a + b)/((a + b)*E^(2*(e + f*x)))] - 12*a*b*d^2*f^2*x^2*Log[1 + (-a + b)/((a + b)*E^(2*(e + f*x)))] + 12*b*c*f*(-(b*d) + a*c*f)*(2*f*x - Log[a - b - (a + b)*E^(2*(e + f*x))]) - 6*b*d*(b*d - 2*a*c*f)*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))] + 6*a*b*d^2*(2*f*x*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))] + PolyLog[3, (a - b)/((a + b)*E^(2*(e + f*x)))]) - ((a - b)*(a + b)*f^2*((a^2 + b^2)*f*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Cosh[f*x] - (a^2 - b^2)*f*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Cosh[2*e + f*x] + 2*b*(-3*b*(c + d*x)^2 + a*f*x*(3*c^2 + 3*c*d*x + d^2*x^2))*Sinh[f*x]))/((b*Cosh[e] + a*Sinh[e])*(b*Cosh[e + f*x] + a*Sinh[e + f*x])))/(6*(a - b)^2*(a + b)^2*f^3)","A",1
59,1,477,196,6.234313,"\int \frac{c+d x}{(a+b \coth (e+f x))^2} \, dx","Integrate[(c + d*x)/(a + b*Coth[e + f*x])^2,x]","\frac{\text{csch}^2(e+f x) (a \sinh (e+f x)+b \cosh (e+f x)) \left(2 b f \left(b^2-a^2\right) (c+d x) \sinh (e+f x)-\left(a^2-b^2\right) (e+f x) (d (e-f x)-2 c f) (a \sinh (e+f x)+b \cosh (e+f x))-2 a d (a \sinh (e+f x)+b \cosh (e+f x)) \left(a \sqrt{1-\frac{b^2}{a^2}} e^{-\tanh ^{-1}\left(\frac{b}{a}\right)} (e+f x)^2+b \text{Li}_2\left(e^{-2 \left(e+f x+\tanh ^{-1}\left(\frac{b}{a}\right)\right)}\right)-i b \left(\pi -2 i \tanh ^{-1}\left(\frac{b}{a}\right)\right) (e+f x)-2 b \left(\tanh ^{-1}\left(\frac{b}{a}\right)+e+f x\right) \log \left(1-e^{-2 \left(\tanh ^{-1}\left(\frac{b}{a}\right)+e+f x\right)}\right)+2 b \tanh ^{-1}\left(\frac{b}{a}\right) \log \left(i \sinh \left(\tanh ^{-1}\left(\frac{b}{a}\right)+e+f x\right)\right)+i \pi  b \log \left(e^{2 (e+f x)}+1\right)-i \pi  b \log (\cosh (e+f x))\right)-4 a c f (a \sinh (e+f x)+b \cosh (e+f x)) (a (e+f x)-b \log (a \sinh (e+f x)+b \cosh (e+f x)))+2 b d (a \sinh (e+f x)+b \cosh (e+f x)) (a (e+f x)-b \log (a \sinh (e+f x)+b \cosh (e+f x)))+4 a d e (a \sinh (e+f x)+b \cosh (e+f x)) (a (e+f x)-b \log (a \sinh (e+f x)+b \cosh (e+f x)))\right)}{2 f^2 (b-a) (a+b) \left(a^2-b^2\right) (a+b \coth (e+f x))^2}","\frac{b (-2 a c f-2 a d f x+b d) \log \left(1-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{b (c+d x)}{f \left(a^2-b^2\right) (a+b \coth (e+f x))}-\frac{(c+d x)^2}{2 d \left(a^2-b^2\right)}+\frac{a b d \text{Li}_2\left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{(-2 a c f-2 a d f x+b d)^2}{4 a d f^2 (a-b) (a+b)^2}",1,"(Csch[e + f*x]^2*(b*Cosh[e + f*x] + a*Sinh[e + f*x])*(2*b*(-a^2 + b^2)*f*(c + d*x)*Sinh[e + f*x] - (a^2 - b^2)*(e + f*x)*(-2*c*f + d*(e - f*x))*(b*Cosh[e + f*x] + a*Sinh[e + f*x]) + 2*b*d*(a*(e + f*x) - b*Log[b*Cosh[e + f*x] + a*Sinh[e + f*x]])*(b*Cosh[e + f*x] + a*Sinh[e + f*x]) + 4*a*d*e*(a*(e + f*x) - b*Log[b*Cosh[e + f*x] + a*Sinh[e + f*x]])*(b*Cosh[e + f*x] + a*Sinh[e + f*x]) - 4*a*c*f*(a*(e + f*x) - b*Log[b*Cosh[e + f*x] + a*Sinh[e + f*x]])*(b*Cosh[e + f*x] + a*Sinh[e + f*x]) - 2*a*d*((a*Sqrt[1 - b^2/a^2]*(e + f*x)^2)/E^ArcTanh[b/a] - I*b*(e + f*x)*(Pi - (2*I)*ArcTanh[b/a]) + I*b*Pi*Log[1 + E^(2*(e + f*x))] - 2*b*(e + f*x + ArcTanh[b/a])*Log[1 - E^(-2*(e + f*x + ArcTanh[b/a]))] - I*b*Pi*Log[Cosh[e + f*x]] + 2*b*ArcTanh[b/a]*Log[I*Sinh[e + f*x + ArcTanh[b/a]]] + b*PolyLog[2, E^(-2*(e + f*x + ArcTanh[b/a]))])*(b*Cosh[e + f*x] + a*Sinh[e + f*x])))/(2*(-a + b)*(a + b)*(a^2 - b^2)*f^2*(a + b*Coth[e + f*x])^2)","C",0
60,0,0,23,155.0097255,"\int \frac{1}{(c+d x) (a+b \coth (e+f x))^2} \, dx","Integrate[1/((c + d*x)*(a + b*Coth[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+b \coth (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \coth (e+f x))^2},x\right)",0,"Integrate[1/((c + d*x)*(a + b*Coth[e + f*x])^2), x]","A",-1
61,0,0,23,125.762448,"\int \frac{1}{(c+d x)^2 (a+b \coth (e+f x))^2} \, dx","Integrate[1/((c + d*x)^2*(a + b*Coth[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+b \coth (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \coth (e+f x))^2},x\right)",0,"Integrate[1/((c + d*x)^2*(a + b*Coth[e + f*x])^2), x]","A",-1