1,1,87,0,0.1587729,"\int x^3 \coth (a+b x) \, dx","Int[x^3*Coth[a + b*x],x]","\frac{3 x^2 \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{2 b^2}-\frac{3 x \text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 \text{PolyLog}\left(4,e^{2 (a+b x)}\right)}{4 b^4}+\frac{x^3 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^4}{4}","\frac{3 x^2 \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{2 b^2}-\frac{3 x \text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 \text{PolyLog}\left(4,e^{2 (a+b x)}\right)}{4 b^4}+\frac{x^3 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^4}{4}",1,"-x^4/4 + (x^3*Log[1 - E^(2*(a + b*x))])/b + (3*x^2*PolyLog[2, E^(2*(a + b*x))])/(2*b^2) - (3*x*PolyLog[3, E^(2*(a + b*x))])/(2*b^3) + (3*PolyLog[4, E^(2*(a + b*x))])/(4*b^4)","A",6,6,10,0.6000,1,"{3716, 2190, 2531, 6609, 2282, 6589}"
2,1,63,0,0.1345402,"\int x^2 \coth (a+b x) \, dx","Int[x^2*Coth[a + b*x],x]","\frac{x \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{b^2}-\frac{\text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^3}+\frac{x^2 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^3}{3}","\frac{x \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{b^2}-\frac{\text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^3}+\frac{x^2 \log \left(1-e^{2 (a+b x)}\right)}{b}-\frac{x^3}{3}",1,"-x^3/3 + (x^2*Log[1 - E^(2*(a + b*x))])/b + (x*PolyLog[2, E^(2*(a + b*x))])/b^2 - PolyLog[3, E^(2*(a + b*x))]/(2*b^3)","A",5,5,10,0.5000,1,"{3716, 2190, 2531, 2282, 6589}"
3,1,45,0,0.0847552,"\int x \coth (a+b x) \, dx","Int[x*Coth[a + b*x],x]","\frac{\text{PolyLog}\left(2,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}","\frac{\text{PolyLog}\left(2,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,"-x^2/2 + (x*Log[1 - E^(2*(a + b*x))])/b + PolyLog[2, E^(2*(a + b*x))]/(2*b^2)","A",4,4,8,0.5000,1,"{3716, 2190, 2279, 2391}"
4,0,0,0,0.0164414,"\int \frac{\coth (a+b x)}{x} \, dx","Int[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,"Defer[Int][Coth[a + b*x]/x, x]","A",0,0,0,0,-1,"{}"
5,0,0,0,0.016917,"\int \frac{\coth (a+b x)}{x^2} \, dx","Int[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,"Defer[Int][Coth[a + b*x]/x^2, x]","A",0,0,0,0,-1,"{}"
6,1,87,0,0.1776012,"\int x^3 \coth ^2(a+b x) \, dx","Int[x^3*Coth[a + b*x]^2,x]","\frac{3 x \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{b^3}-\frac{3 \text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^4}+\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}","\frac{3 x \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{b^3}-\frac{3 \text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^4}+\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^3/b) + x^4/4 - (x^3*Coth[a + b*x])/b + (3*x^2*Log[1 - E^(2*(a + b*x))])/b^2 + (3*x*PolyLog[2, E^(2*(a + b*x))])/b^3 - (3*PolyLog[3, E^(2*(a + b*x))])/(2*b^4)","A",7,7,12,0.5833,1,"{3720, 3716, 2190, 2531, 2282, 6589, 30}"
7,1,65,0,0.119435,"\int x^2 \coth ^2(a+b x) \, dx","Int[x^2*Coth[a + b*x]^2,x]","\frac{\text{PolyLog}\left(2,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}","\frac{\text{PolyLog}\left(2,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^2/b) + x^3/3 - (x^2*Coth[a + b*x])/b + (2*x*Log[1 - E^(2*(a + b*x))])/b^2 + PolyLog[2, E^(2*(a + b*x))]/b^3","A",6,6,12,0.5000,1,"{3720, 3716, 2190, 2279, 2391, 30}"
8,1,31,0,0.0267439,"\int x \coth ^2(a+b x) \, dx","Int[x*Coth[a + b*x]^2,x]","\frac{\log (\sinh (a+b x))}{b^2}-\frac{x \coth (a+b x)}{b}+\frac{x^2}{2}","\frac{\log (\sinh (a+b x))}{b^2}-\frac{x \coth (a+b x)}{b}+\frac{x^2}{2}",1,"x^2/2 - (x*Coth[a + b*x])/b + Log[Sinh[a + b*x]]/b^2","A",3,3,10,0.3000,1,"{3720, 3475, 30}"
9,0,0,0,0.0279736,"\int \frac{\coth ^2(a+b x)}{x} \, dx","Int[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,"Defer[Int][Coth[a + b*x]^2/x, x]","A",0,0,0,0,-1,"{}"
10,0,0,0,0.0289372,"\int \frac{\coth ^2(a+b x)}{x^2} \, dx","Int[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,"Defer[Int][Coth[a + b*x]^2/x^2, x]","A",0,0,0,0,-1,"{}"
11,1,179,0,0.3297019,"\int x^3 \coth ^3(a+b x) \, dx","Int[x^3*Coth[a + b*x]^3,x]","\frac{3 x^2 \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{2 b^2}-\frac{3 x \text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 \text{PolyLog}\left(4,e^{2 (a+b x)}\right)}{4 b^4}-\frac{3 x^2 \coth (a+b x)}{2 b^2}+\frac{3 x \log \left(1-e^{2 (a+b x)}\right)}{b^3}+\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}","\frac{3 x^2 \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{2 b^2}-\frac{3 x \text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^3}+\frac{3 \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 \text{PolyLog}\left(4,e^{2 (a+b x)}\right)}{4 b^4}-\frac{3 x^2 \coth (a+b x)}{2 b^2}+\frac{3 x \log \left(1-e^{2 (a+b x)}\right)}{b^3}+\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,"(-3*x^2)/(2*b^2) + x^3/(2*b) - x^4/4 - (3*x^2*Coth[a + b*x])/(2*b^2) - (x^3*Coth[a + b*x]^2)/(2*b) + (3*x*Log[1 - E^(2*(a + b*x))])/b^3 + (x^3*Log[1 - E^(2*(a + b*x))])/b + (3*PolyLog[2, E^(2*(a + b*x))])/(2*b^4) + (3*x^2*PolyLog[2, E^(2*(a + b*x))])/(2*b^2) - (3*x*PolyLog[3, E^(2*(a + b*x))])/(2*b^3) + (3*PolyLog[4, E^(2*(a + b*x))])/(4*b^4)","A",13,10,12,0.8333,1,"{3720, 3716, 2190, 2279, 2391, 30, 2531, 6609, 2282, 6589}"
12,1,114,0,0.2070704,"\int x^2 \coth ^3(a+b x) \, dx","Int[x^2*Coth[a + b*x]^3,x]","\frac{x \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{b^2}-\frac{\text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^3}-\frac{x \coth (a+b x)}{b^2}+\frac{\log (\sinh (a+b x))}{b^3}+\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}","\frac{x \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{b^2}-\frac{\text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^3}-\frac{x \coth (a+b x)}{b^2}+\frac{\log (\sinh (a+b x))}{b^3}+\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^2/(2*b) - x^3/3 - (x*Coth[a + b*x])/b^2 - (x^2*Coth[a + b*x]^2)/(2*b) + (x^2*Log[1 - E^(2*(a + b*x))])/b + Log[Sinh[a + b*x]]/b^3 + (x*PolyLog[2, E^(2*(a + b*x))])/b^2 - PolyLog[3, E^(2*(a + b*x))]/(2*b^3)","A",9,8,12,0.6667,1,"{3720, 3475, 30, 3716, 2190, 2531, 2282, 6589}"
13,1,82,0,0.1216049,"\int x \coth ^3(a+b x) \, dx","Int[x*Coth[a + b*x]^3,x]","\frac{\text{PolyLog}\left(2,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}","\frac{\text{PolyLog}\left(2,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*b) - x^2/2 - Coth[a + b*x]/(2*b^2) - (x*Coth[a + b*x]^2)/(2*b) + (x*Log[1 - E^(2*(a + b*x))])/b + PolyLog[2, E^(2*(a + b*x))]/(2*b^2)","A",7,7,10,0.7000,1,"{3720, 3473, 8, 3716, 2190, 2279, 2391}"
14,0,0,0,0.0283809,"\int \frac{\coth ^3(a+b x)}{x} \, dx","Int[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,"Defer[Int][Coth[a + b*x]^3/x, x]","A",0,0,0,0,-1,"{}"
15,0,0,0,0.0286649,"\int \frac{\coth ^3(a+b x)}{x^2} \, dx","Int[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,"Defer[Int][Coth[a + b*x]^3/x^2, x]","A",0,0,0,0,-1,"{}"
16,1,169,0,0.1854846,"\int \frac{(c+d x)^3}{a+a \coth (e+f x)} \, dx","Int[(c + d*x)^3/(a + a*Coth[e + f*x]),x]","-\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}","-\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,"(3*d^3*x)/(8*a*f^3) + (3*d*(c + d*x)^2)/(8*a*f^2) + (c + d*x)^3/(4*a*f) + (c + d*x)^4/(8*a*d) - (3*d^3)/(8*f^4*(a + a*Coth[e + f*x])) - (3*d^2*(c + d*x))/(4*f^3*(a + a*Coth[e + f*x])) - (3*d*(c + d*x)^2)/(4*f^2*(a + a*Coth[e + f*x])) - (c + d*x)^3/(2*f*(a + a*Coth[e + f*x]))","A",5,3,20,0.1500,1,"{3723, 3479, 8}"
17,1,122,0,0.1174479,"\int \frac{(c+d x)^2}{a+a \coth (e+f x)} \, dx","Int[(c + d*x)^2/(a + a*Coth[e + f*x]),x]","-\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}","-\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,"(d^2*x)/(4*a*f^2) + (c + d*x)^2/(4*a*f) + (c + d*x)^3/(6*a*d) - d^2/(4*f^3*(a + a*Coth[e + f*x])) - (d*(c + d*x))/(2*f^2*(a + a*Coth[e + f*x])) - (c + d*x)^2/(2*f*(a + a*Coth[e + f*x]))","A",4,3,20,0.1500,1,"{3723, 3479, 8}"
18,1,74,0,0.051007,"\int \frac{c+d x}{a+a \coth (e+f x)} \, dx","Int[(c + d*x)/(a + a*Coth[e + f*x]),x]","-\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}","-\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,"(d*x)/(4*a*f) + (c + d*x)^2/(4*a*d) - d/(4*f^2*(a + a*Coth[e + f*x])) - (c + d*x)/(2*f*(a + a*Coth[e + f*x]))","A",3,3,18,0.1667,1,"{3723, 3479, 8}"
19,1,157,0,0.2510865,"\int \frac{1}{(c+d x) (a+a \coth (e+f x))} \, dx","Int[1/((c + d*x)*(a + a*Coth[e + f*x])),x]","\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}","\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,"-(Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*c*f)/d + 2*f*x])/(2*a*d) + Log[c + d*x]/(2*a*d) + (CoshIntegral[(2*c*f)/d + 2*f*x]*Sinh[2*e - (2*c*f)/d])/(2*a*d) + (Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(2*a*d) - (Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(2*a*d)","A",7,4,20,0.2000,1,"{3726, 3303, 3298, 3301}"
20,1,159,0,0.2130133,"\int \frac{1}{(c+d x)^2 (a+a \coth (e+f x))} \, dx","Int[1/((c + d*x)^2*(a + a*Coth[e + f*x])),x]","-\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)}","-\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,"(f*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*c*f)/d + 2*f*x])/(a*d^2) - 1/(d*(c + d*x)*(a + a*Coth[e + f*x])) - (f*CoshIntegral[(2*c*f)/d + 2*f*x]*Sinh[2*e - (2*c*f)/d])/(a*d^2) - (f*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(a*d^2) + (f*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(a*d^2)","A",7,4,20,0.2000,1,"{3724, 3303, 3298, 3301}"
21,1,211,0,0.3008017,"\int \frac{1}{(c+d x)^3 (a+a \coth (e+f x))} \, dx","Int[1/((c + d*x)^3*(a + a*Coth[e + f*x])),x]","\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)}","\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,"-f/(2*a*d^2*(c + d*x)) - (f^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*c*f)/d + 2*f*x])/(a*d^3) - 1/(2*d*(c + d*x)^2*(a + a*Coth[e + f*x])) + f/(d^2*(c + d*x)*(a + a*Coth[e + f*x])) + (f^2*CoshIntegral[(2*c*f)/d + 2*f*x]*Sinh[2*e - (2*c*f)/d])/(a*d^3) + (f^2*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(a*d^3) - (f^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(a*d^3)","A",8,5,20,0.2500,1,"{3725, 3724, 3303, 3298, 3301}"
22,1,230,0,0.2681803,"\int \frac{(c+d x)^3}{(a+a \coth (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + a*Coth[e + f*x])^2,x]","-\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}","-\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,"(-3*d^3*E^(-4*e - 4*f*x))/(512*a^2*f^4) + (3*d^3*E^(-2*e - 2*f*x))/(16*a^2*f^4) - (3*d^2*E^(-4*e - 4*f*x)*(c + d*x))/(128*a^2*f^3) + (3*d^2*E^(-2*e - 2*f*x)*(c + d*x))/(8*a^2*f^3) - (3*d*E^(-4*e - 4*f*x)*(c + d*x)^2)/(64*a^2*f^2) + (3*d*E^(-2*e - 2*f*x)*(c + d*x)^2)/(8*a^2*f^2) - (E^(-4*e - 4*f*x)*(c + d*x)^3)/(16*a^2*f) + (E^(-2*e - 2*f*x)*(c + d*x)^3)/(4*a^2*f) + (c + d*x)^4/(16*a^2*d)","A",10,3,20,0.1500,1,"{3729, 2176, 2194}"
23,1,170,0,0.1919683,"\int \frac{(c+d x)^2}{(a+a \coth (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + a*Coth[e + f*x])^2,x]","-\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}","-\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,"-(d^2*E^(-4*e - 4*f*x))/(128*a^2*f^3) + (d^2*E^(-2*e - 2*f*x))/(8*a^2*f^3) - (d*E^(-4*e - 4*f*x)*(c + d*x))/(32*a^2*f^2) + (d*E^(-2*e - 2*f*x)*(c + d*x))/(4*a^2*f^2) - (E^(-4*e - 4*f*x)*(c + d*x)^2)/(16*a^2*f) + (E^(-2*e - 2*f*x)*(c + d*x)^2)/(4*a^2*f) + (c + d*x)^3/(12*a^2*d)","A",8,3,20,0.1500,1,"{3729, 2176, 2194}"
24,1,133,0,0.1294564,"\int \frac{c+d x}{(a+a \coth (e+f x))^2} \, dx","Int[(c + d*x)/(a + a*Coth[e + f*x])^2,x]","-\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}","-\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,"(3*d*x)/(16*a^2*f) - (d*x^2)/(8*a^2) + (x*(c + d*x))/(4*a^2) - d/(16*f^2*(a + a*Coth[e + f*x])^2) - (c + d*x)/(4*f*(a + a*Coth[e + f*x])^2) - (3*d)/(16*f^2*(a^2 + a^2*Coth[e + f*x])) - (c + d*x)/(4*f*(a^2 + a^2*Coth[e + f*x]))","A",7,3,18,0.1667,1,"{3479, 8, 3730}"
25,1,297,0,0.7035878,"\int \frac{1}{(c+d x) (a+a \coth (e+f x))^2} \, dx","Int[1/((c + d*x)*(a + a*Coth[e + f*x])^2),x]","\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}","\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]*CoshIntegral[(2*c*f)/d + 2*f*x])/(2*a^2*d) + (Cosh[4*e - (4*c*f)/d]*CoshIntegral[(4*c*f)/d + 4*f*x])/(4*a^2*d) + Log[c + d*x]/(4*a^2*d) - (CoshIntegral[(4*c*f)/d + 4*f*x]*Sinh[4*e - (4*c*f)/d])/(4*a^2*d) + (CoshIntegral[(2*c*f)/d + 2*f*x]*Sinh[2*e - (2*c*f)/d])/(2*a^2*d) + (Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(2*a^2*d) - (Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(2*a^2*d) - (Cosh[4*e - (4*c*f)/d]*SinhIntegral[(4*c*f)/d + 4*f*x])/(4*a^2*d) + (Sinh[4*e - (4*c*f)/d]*SinhIntegral[(4*c*f)/d + 4*f*x])/(4*a^2*d)","A",21,5,20,0.2500,1,"{3728, 3303, 3298, 3301, 3312}"
26,1,420,0,0.7326558,"\int \frac{1}{(c+d x)^2 (a+a \coth (e+f x))^2} \, dx","Int[1/((c + d*x)^2*(a + a*Coth[e + f*x])^2),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)}","\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,"-1/(4*a^2*d*(c + d*x)) + Cosh[2*e + 2*f*x]/(2*a^2*d*(c + d*x)) - Cosh[2*e + 2*f*x]^2/(4*a^2*d*(c + d*x)) + (f*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*c*f)/d + 2*f*x])/(a^2*d^2) - (f*Cosh[4*e - (4*c*f)/d]*CoshIntegral[(4*c*f)/d + 4*f*x])/(a^2*d^2) + (f*CoshIntegral[(4*c*f)/d + 4*f*x]*Sinh[4*e - (4*c*f)/d])/(a^2*d^2) - (f*CoshIntegral[(2*c*f)/d + 2*f*x]*Sinh[2*e - (2*c*f)/d])/(a^2*d^2) - Sinh[2*e + 2*f*x]/(2*a^2*d*(c + d*x)) - Sinh[2*e + 2*f*x]^2/(4*a^2*d*(c + d*x)) + Sinh[4*e + 4*f*x]/(4*a^2*d*(c + d*x)) - (f*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(a^2*d^2) + (f*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(a^2*d^2) + (f*Cosh[4*e - (4*c*f)/d]*SinhIntegral[(4*c*f)/d + 4*f*x])/(a^2*d^2) - (f*Sinh[4*e - (4*c*f)/d]*SinhIntegral[(4*c*f)/d + 4*f*x])/(a^2*d^2)","A",24,7,20,0.3500,1,"{3728, 3297, 3303, 3298, 3301, 3313, 12}"
27,1,336,0,0.3698958,"\int \frac{(c+d x)^3}{(a+a \coth (e+f x))^3} \, dx","Int[(c + d*x)^3/(a + a*Coth[e + f*x])^3,x]","\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}","\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,"(d^3*E^(-6*e - 6*f*x))/(1728*a^3*f^4) - (9*d^3*E^(-4*e - 4*f*x))/(1024*a^3*f^4) + (9*d^3*E^(-2*e - 2*f*x))/(64*a^3*f^4) + (d^2*E^(-6*e - 6*f*x)*(c + d*x))/(288*a^3*f^3) - (9*d^2*E^(-4*e - 4*f*x)*(c + d*x))/(256*a^3*f^3) + (9*d^2*E^(-2*e - 2*f*x)*(c + d*x))/(32*a^3*f^3) + (d*E^(-6*e - 6*f*x)*(c + d*x)^2)/(96*a^3*f^2) - (9*d*E^(-4*e - 4*f*x)*(c + d*x)^2)/(128*a^3*f^2) + (9*d*E^(-2*e - 2*f*x)*(c + d*x)^2)/(32*a^3*f^2) + (E^(-6*e - 6*f*x)*(c + d*x)^3)/(48*a^3*f) - (3*E^(-4*e - 4*f*x)*(c + d*x)^3)/(32*a^3*f) + (3*E^(-2*e - 2*f*x)*(c + d*x)^3)/(16*a^3*f) + (c + d*x)^4/(32*a^3*d)","A",14,3,20,0.1500,1,"{3729, 2176, 2194}"
28,1,246,0,0.2575888,"\int \frac{(c+d x)^2}{(a+a \coth (e+f x))^3} \, dx","Int[(c + d*x)^2/(a + a*Coth[e + f*x])^3,x]","\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}","\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,"(d^2*E^(-6*e - 6*f*x))/(864*a^3*f^3) - (3*d^2*E^(-4*e - 4*f*x))/(256*a^3*f^3) + (3*d^2*E^(-2*e - 2*f*x))/(32*a^3*f^3) + (d*E^(-6*e - 6*f*x)*(c + d*x))/(144*a^3*f^2) - (3*d*E^(-4*e - 4*f*x)*(c + d*x))/(64*a^3*f^2) + (3*d*E^(-2*e - 2*f*x)*(c + d*x))/(16*a^3*f^2) + (E^(-6*e - 6*f*x)*(c + d*x)^2)/(48*a^3*f) - (3*E^(-4*e - 4*f*x)*(c + d*x)^2)/(32*a^3*f) + (3*E^(-2*e - 2*f*x)*(c + d*x)^2)/(16*a^3*f) + (c + d*x)^3/(24*a^3*d)","A",11,3,20,0.1500,1,"{3729, 2176, 2194}"
29,1,183,0,0.2051717,"\int \frac{c+d x}{(a+a \coth (e+f x))^3} \, dx","Int[(c + d*x)/(a + a*Coth[e + f*x])^3,x]","-\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}","-\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,"(11*d*x)/(96*a^3*f) - (d*x^2)/(16*a^3) + (x*(c + d*x))/(8*a^3) - d/(36*f^2*(a + a*Coth[e + f*x])^3) - (c + d*x)/(6*f*(a + a*Coth[e + f*x])^3) - (5*d)/(96*a*f^2*(a + a*Coth[e + f*x])^2) - (c + d*x)/(8*a*f*(a + a*Coth[e + f*x])^2) - (11*d)/(96*f^2*(a^3 + a^3*Coth[e + f*x])) - (c + d*x)/(8*f*(a^3 + a^3*Coth[e + f*x]))","A",11,3,18,0.1667,1,"{3479, 8, 3730}"
30,1,437,0,1.7645452,"\int \frac{1}{(c+d x) (a+a \coth (e+f x))^3} \, dx","Int[1/((c + d*x)*(a + a*Coth[e + f*x])^3),x]","\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}","\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,"(-3*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*c*f)/d + 2*f*x])/(8*a^3*d) + (3*Cosh[4*e - (4*c*f)/d]*CoshIntegral[(4*c*f)/d + 4*f*x])/(8*a^3*d) - (Cosh[6*e - (6*c*f)/d]*CoshIntegral[(6*c*f)/d + 6*f*x])/(8*a^3*d) + Log[c + d*x]/(8*a^3*d) + (CoshIntegral[(6*c*f)/d + 6*f*x]*Sinh[6*e - (6*c*f)/d])/(8*a^3*d) - (3*CoshIntegral[(4*c*f)/d + 4*f*x]*Sinh[4*e - (4*c*f)/d])/(8*a^3*d) + (3*CoshIntegral[(2*c*f)/d + 2*f*x]*Sinh[2*e - (2*c*f)/d])/(8*a^3*d) + (3*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(8*a^3*d) - (3*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(8*a^3*d) - (3*Cosh[4*e - (4*c*f)/d]*SinhIntegral[(4*c*f)/d + 4*f*x])/(8*a^3*d) + (3*Sinh[4*e - (4*c*f)/d]*SinhIntegral[(4*c*f)/d + 4*f*x])/(8*a^3*d) + (Cosh[6*e - (6*c*f)/d]*SinhIntegral[(6*c*f)/d + 6*f*x])/(8*a^3*d) - (Sinh[6*e - (6*c*f)/d]*SinhIntegral[(6*c*f)/d + 6*f*x])/(8*a^3*d)","A",53,7,20,0.3500,1,"{3728, 3303, 3298, 3301, 3312, 5448, 5470}"
31,1,692,0,1.7619457,"\int \frac{1}{(c+d x)^2 (a+a \coth (e+f x))^3} \, dx","Int[1/((c + d*x)^2*(a + a*Coth[e + f*x])^3),x]","-\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)}","-\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,"-1/(8*a^3*d*(c + d*x)) + (9*Cosh[2*e + 2*f*x])/(32*a^3*d*(c + d*x)) - (3*Cosh[2*e + 2*f*x]^2)/(8*a^3*d*(c + d*x)) + Cosh[2*e + 2*f*x]^3/(8*a^3*d*(c + d*x)) + (3*Cosh[6*e + 6*f*x])/(32*a^3*d*(c + d*x)) + (3*f*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*c*f)/d + 2*f*x])/(4*a^3*d^2) - (3*f*Cosh[4*e - (4*c*f)/d]*CoshIntegral[(4*c*f)/d + 4*f*x])/(2*a^3*d^2) + (3*f*Cosh[6*e - (6*c*f)/d]*CoshIntegral[(6*c*f)/d + 6*f*x])/(4*a^3*d^2) - (3*f*CoshIntegral[(6*c*f)/d + 6*f*x]*Sinh[6*e - (6*c*f)/d])/(4*a^3*d^2) + (3*f*CoshIntegral[(4*c*f)/d + 4*f*x]*Sinh[4*e - (4*c*f)/d])/(2*a^3*d^2) - (3*f*CoshIntegral[(2*c*f)/d + 2*f*x]*Sinh[2*e - (2*c*f)/d])/(4*a^3*d^2) - (15*Sinh[2*e + 2*f*x])/(32*a^3*d*(c + d*x)) - (3*Sinh[2*e + 2*f*x]^2)/(8*a^3*d*(c + d*x)) - Sinh[2*e + 2*f*x]^3/(8*a^3*d*(c + d*x)) + (3*Sinh[4*e + 4*f*x])/(8*a^3*d*(c + d*x)) - (3*Sinh[6*e + 6*f*x])/(32*a^3*d*(c + d*x)) - (3*f*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(4*a^3*d^2) + (3*f*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(4*a^3*d^2) + (3*f*Cosh[4*e - (4*c*f)/d]*SinhIntegral[(4*c*f)/d + 4*f*x])/(2*a^3*d^2) - (3*f*Sinh[4*e - (4*c*f)/d]*SinhIntegral[(4*c*f)/d + 4*f*x])/(2*a^3*d^2) - (3*f*Cosh[6*e - (6*c*f)/d]*SinhIntegral[(6*c*f)/d + 6*f*x])/(4*a^3*d^2) + (3*f*Sinh[6*e - (6*c*f)/d]*SinhIntegral[(6*c*f)/d + 6*f*x])/(4*a^3*d^2)","A",60,9,20,0.4500,1,"{3728, 3297, 3303, 3298, 3301, 3313, 12, 5448, 5470}"
32,0,0,0,0.0495698,"\int (c+d x)^m (a+a \coth (e+f x))^2 \, dx","Int[(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,"Defer[Int][(c + d*x)^m*(a + a*Coth[e + f*x])^2, x]","A",0,0,0,0,-1,"{}"
33,0,0,0,0.0268701,"\int (c+d x)^m (a+a \coth (e+f x)) \, dx","Int[(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,"Defer[Int][(c + d*x)^m*(a + a*Coth[e + f*x]), x]","A",0,0,0,0,-1,"{}"
34,1,88,0,0.116941,"\int \frac{(c+d x)^m}{a+a \coth (e+f x)} \, dx","Int[(c + d*x)^m/(a + a*Coth[e + f*x]),x]","\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} \text{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)}","\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} \text{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,"(c + d*x)^(1 + m)/(2*a*d*(1 + m)) + (2^(-2 - m)*E^(-2*e + (2*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (2*f*(c + d*x))/d])/(a*f*((f*(c + d*x))/d)^m)","A",2,2,20,0.1000,1,"{3727, 2181}"
35,1,152,0,0.1724267,"\int \frac{(c+d x)^m}{(a+a \coth (e+f x))^2} \, dx","Int[(c + d*x)^m/(a + a*Coth[e + f*x])^2,x]","\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} \text{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} \text{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)}","\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} \text{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} \text{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,"(c + d*x)^(1 + m)/(4*a^2*d*(1 + m)) + (2^(-2 - m)*E^(-2*e + (2*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (2*f*(c + d*x))/d])/(a^2*f*((f*(c + d*x))/d)^m) - (4^(-2 - m)*E^(-4*e + (4*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (4*f*(c + d*x))/d])/(a^2*f*((f*(c + d*x))/d)^m)","A",4,2,20,0.1000,1,"{3729, 2181}"
36,1,223,0,0.2331177,"\int \frac{(c+d x)^m}{(a+a \coth (e+f x))^3} \, dx","Int[(c + d*x)^m/(a + a*Coth[e + f*x])^3,x]","\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} \text{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} \text{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} \text{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)}","\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} \text{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} \text{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} \text{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,"(c + d*x)^(1 + m)/(8*a^3*d*(1 + m)) + (3*2^(-4 - m)*E^(-2*e + (2*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (2*f*(c + d*x))/d])/(a^3*f*((f*(c + d*x))/d)^m) - (3*2^(-5 - 2*m)*E^(-4*e + (4*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (4*f*(c + d*x))/d])/(a^3*f*((f*(c + d*x))/d)^m) + (2^(-4 - m)*3^(-1 - m)*E^(-6*e + (6*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (6*f*(c + d*x))/d])/(a^3*f*((f*(c + d*x))/d)^m)","A",5,2,20,0.1000,1,"{3729, 2181}"
37,1,133,0,0.259571,"\int (c+d x)^3 (a+b \coth (e+f x)) \, dx","Int[(c + d*x)^3*(a + b*Coth[e + f*x]),x]","-\frac{3 b d^2 (c+d x) \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^2}+\frac{3 b d^3 \text{PolyLog}\left(4,e^{2 (e+f x)}\right)}{4 f^4}+\frac{a (c+d x)^4}{4 d}+\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^2 (c+d x) \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^2}+\frac{3 b d^3 \text{PolyLog}\left(4,e^{2 (e+f x)}\right)}{4 f^4}+\frac{a (c+d x)^4}{4 d}+\frac{b (c+d x)^3 \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{b (c+d x)^4}{4 d}",1,"(a*(c + d*x)^4)/(4*d) - (b*(c + d*x)^4)/(4*d) + (b*(c + d*x)^3*Log[1 - E^(2*(e + f*x))])/f + (3*b*d*(c + d*x)^2*PolyLog[2, E^(2*(e + f*x))])/(2*f^2) - (3*b*d^2*(c + d*x)*PolyLog[3, E^(2*(e + f*x))])/(2*f^3) + (3*b*d^3*PolyLog[4, E^(2*(e + f*x))])/(4*f^4)","A",8,7,18,0.3889,1,"{3722, 3716, 2190, 2531, 6609, 2282, 6589}"
38,1,101,0,0.2166688,"\int (c+d x)^2 (a+b \coth (e+f x)) \, dx","Int[(c + d*x)^2*(a + b*Coth[e + f*x]),x]","\frac{b d (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^2}-\frac{b d^2 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\frac{a (c+d x)^3}{3 d}+\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 (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^2}-\frac{b d^2 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\frac{a (c+d x)^3}{3 d}+\frac{b (c+d x)^2 \log \left(1-e^{2 (e+f x)}\right)}{f}-\frac{b (c+d x)^3}{3 d}",1,"(a*(c + d*x)^3)/(3*d) - (b*(c + d*x)^3)/(3*d) + (b*(c + d*x)^2*Log[1 - E^(2*(e + f*x))])/f + (b*d*(c + d*x)*PolyLog[2, E^(2*(e + f*x))])/f^2 - (b*d^2*PolyLog[3, E^(2*(e + f*x))])/(2*f^3)","A",7,6,18,0.3333,1,"{3722, 3716, 2190, 2531, 2282, 6589}"
39,1,75,0,0.1263184,"\int (c+d x) (a+b \coth (e+f x)) \, dx","Int[(c + d*x)*(a + b*Coth[e + f*x]),x]","\frac{b d \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^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{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^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}",1,"(a*(c + d*x)^2)/(2*d) - (b*(c + d*x)^2)/(2*d) + (b*(c + d*x)*Log[1 - E^(2*(e + f*x))])/f + (b*d*PolyLog[2, E^(2*(e + f*x))])/(2*f^2)","A",6,5,16,0.3125,1,"{3722, 3716, 2190, 2279, 2391}"
40,0,0,0,0.0293813,"\int \frac{a+b \coth (e+f x)}{c+d x} \, dx","Int[(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,"Defer[Int][(a + b*Coth[e + f*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
41,0,0,0,0.0288114,"\int \frac{a+b \coth (e+f x)}{(c+d x)^2} \, dx","Int[(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,"Defer[Int][(a + b*Coth[e + f*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
42,1,271,0,0.5463934,"\int (c+d x)^3 (a+b \coth (e+f x))^2 \, dx","Int[(c + d*x)^3*(a + b*Coth[e + f*x])^2,x]","-\frac{3 a b d^2 (c+d x) \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{f^3}+\frac{3 a b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^2}+\frac{3 a b d^3 \text{PolyLog}\left(4,e^{2 (e+f x)}\right)}{2 f^4}+\frac{3 b^2 d^2 (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^3}-\frac{3 b^2 d^3 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^4}+\frac{a^2 (c+d x)^4}{4 d}+\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 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 a b d^2 (c+d x) \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{f^3}+\frac{3 a b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^2}+\frac{3 a b d^3 \text{PolyLog}\left(4,e^{2 (e+f x)}\right)}{2 f^4}+\frac{3 b^2 d^2 (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^3}-\frac{3 b^2 d^3 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^4}+\frac{a^2 (c+d x)^4}{4 d}+\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 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}",1,"-((b^2*(c + d*x)^3)/f) + (a^2*(c + d*x)^4)/(4*d) - (a*b*(c + d*x)^4)/(2*d) + (b^2*(c + d*x)^4)/(4*d) - (b^2*(c + d*x)^3*Coth[e + f*x])/f + (3*b^2*d*(c + d*x)^2*Log[1 - E^(2*(e + f*x))])/f^2 + (2*a*b*(c + d*x)^3*Log[1 - E^(2*(e + f*x))])/f + (3*b^2*d^2*(c + d*x)*PolyLog[2, E^(2*(e + f*x))])/f^3 + (3*a*b*d*(c + d*x)^2*PolyLog[2, E^(2*(e + f*x))])/f^2 - (3*b^2*d^3*PolyLog[3, E^(2*(e + f*x))])/(2*f^4) - (3*a*b*d^2*(c + d*x)*PolyLog[3, E^(2*(e + f*x))])/f^3 + (3*a*b*d^3*PolyLog[4, E^(2*(e + f*x))])/(2*f^4)","A",15,9,20,0.4500,1,"{3722, 3716, 2190, 2531, 6609, 2282, 6589, 3720, 32}"
43,1,209,0,0.404291,"\int (c+d x)^2 (a+b \coth (e+f x))^2 \, dx","Int[(c + d*x)^2*(a + b*Coth[e + f*x])^2,x]","\frac{2 a b d (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^2}-\frac{a b d^2 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{f^3}+\frac{b^2 d^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^3}+\frac{a^2 (c+d x)^3}{3 d}+\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{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{2 a b d (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^2}-\frac{a b d^2 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{f^3}+\frac{b^2 d^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^3}+\frac{a^2 (c+d x)^3}{3 d}+\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{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}",1,"-((b^2*(c + d*x)^2)/f) + (a^2*(c + d*x)^3)/(3*d) - (2*a*b*(c + d*x)^3)/(3*d) + (b^2*(c + d*x)^3)/(3*d) - (b^2*(c + d*x)^2*Coth[e + f*x])/f + (2*b^2*d*(c + d*x)*Log[1 - E^(2*(e + f*x))])/f^2 + (2*a*b*(c + d*x)^2*Log[1 - E^(2*(e + f*x))])/f + (b^2*d^2*PolyLog[2, E^(2*(e + f*x))])/f^3 + (2*a*b*d*(c + d*x)*PolyLog[2, E^(2*(e + f*x))])/f^2 - (a*b*d^2*PolyLog[3, E^(2*(e + f*x))])/f^3","A",13,10,20,0.5000,1,"{3722, 3716, 2190, 2531, 2282, 6589, 3720, 2279, 2391, 32}"
44,1,127,0,0.1843767,"\int (c+d x) (a+b \coth (e+f x))^2 \, dx","Int[(c + d*x)*(a + b*Coth[e + f*x])^2,x]","\frac{a b d \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^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{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","\frac{a b d \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^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{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,"b^2*c*x + (b^2*d*x^2)/2 + (a^2*(c + d*x)^2)/(2*d) - (a*b*(c + d*x)^2)/d - (b^2*(c + d*x)*Coth[e + f*x])/f + (2*a*b*(c + d*x)*Log[1 - E^(2*(e + f*x))])/f + (b^2*d*Log[Sinh[e + f*x]])/f^2 + (a*b*d*PolyLog[2, E^(2*(e + f*x))])/f^2","A",9,7,18,0.3889,1,"{3722, 3716, 2190, 2279, 2391, 3720, 3475}"
45,0,0,0,0.0552581,"\int \frac{(a+b \coth (e+f x))^2}{c+d x} \, dx","Int[(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,"Defer[Int][(a + b*Coth[e + f*x])^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
46,0,0,0,0.0525684,"\int \frac{(a+b \coth (e+f x))^2}{(c+d x)^2} \, dx","Int[(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,"Defer[Int][(a + b*Coth[e + f*x])^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
47,1,556,0,1.049088,"\int (c+d x)^3 (a+b \coth (e+f x))^3 \, dx","Int[(c + d*x)^3*(a + b*Coth[e + f*x])^3,x]","-\frac{9 a^2 b d^2 (c+d x) \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\frac{9 a^2 b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^2}+\frac{9 a^2 b d^3 \text{PolyLog}\left(4,e^{2 (e+f x)}\right)}{4 f^4}+\frac{9 a b^2 d^2 (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^3}-\frac{9 a b^2 d^3 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^4}-\frac{3 b^3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 b^3 d (c+d x)^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^2}+\frac{3 b^3 d^3 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^4}+\frac{3 b^3 d^3 \text{PolyLog}\left(4,e^{2 (e+f x)}\right)}{4 f^4}+\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{a^3 (c+d x)^4}{4 d}+\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{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 \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{9 a^2 b d^2 (c+d x) \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\frac{9 a^2 b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^2}+\frac{9 a^2 b d^3 \text{PolyLog}\left(4,e^{2 (e+f x)}\right)}{4 f^4}+\frac{9 a b^2 d^2 (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^3}-\frac{9 a b^2 d^3 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^4}-\frac{3 b^3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 b^3 d (c+d x)^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^2}+\frac{3 b^3 d^3 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^4}+\frac{3 b^3 d^3 \text{PolyLog}\left(4,e^{2 (e+f x)}\right)}{4 f^4}+\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{a^3 (c+d x)^4}{4 d}+\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{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 \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}",1,"(-3*b^3*d*(c + d*x)^2)/(2*f^2) - (3*a*b^2*(c + d*x)^3)/f + (b^3*(c + d*x)^3)/(2*f) + (a^3*(c + d*x)^4)/(4*d) - (3*a^2*b*(c + d*x)^4)/(4*d) + (3*a*b^2*(c + d*x)^4)/(4*d) - (b^3*(c + d*x)^4)/(4*d) - (3*b^3*d*(c + d*x)^2*Coth[e + f*x])/(2*f^2) - (3*a*b^2*(c + d*x)^3*Coth[e + f*x])/f - (b^3*(c + d*x)^3*Coth[e + f*x]^2)/(2*f) + (3*b^3*d^2*(c + d*x)*Log[1 - E^(2*(e + f*x))])/f^3 + (9*a*b^2*d*(c + d*x)^2*Log[1 - E^(2*(e + f*x))])/f^2 + (3*a^2*b*(c + d*x)^3*Log[1 - E^(2*(e + f*x))])/f + (b^3*(c + d*x)^3*Log[1 - E^(2*(e + f*x))])/f + (3*b^3*d^3*PolyLog[2, E^(2*(e + f*x))])/(2*f^4) + (9*a*b^2*d^2*(c + d*x)*PolyLog[2, E^(2*(e + f*x))])/f^3 + (9*a^2*b*d*(c + d*x)^2*PolyLog[2, E^(2*(e + f*x))])/(2*f^2) + (3*b^3*d*(c + d*x)^2*PolyLog[2, E^(2*(e + f*x))])/(2*f^2) - (9*a*b^2*d^3*PolyLog[3, E^(2*(e + f*x))])/(2*f^4) - (9*a^2*b*d^2*(c + d*x)*PolyLog[3, E^(2*(e + f*x))])/(2*f^3) - (3*b^3*d^2*(c + d*x)*PolyLog[3, E^(2*(e + f*x))])/(2*f^3) + (9*a^2*b*d^3*PolyLog[4, E^(2*(e + f*x))])/(4*f^4) + (3*b^3*d^3*PolyLog[4, E^(2*(e + f*x))])/(4*f^4)","A",28,11,20,0.5500,1,"{3722, 3716, 2190, 2531, 6609, 2282, 6589, 3720, 32, 2279, 2391}"
48,1,401,0,0.6978708,"\int (c+d x)^2 (a+b \coth (e+f x))^3 \, dx","Int[(c + d*x)^2*(a + b*Coth[e + f*x])^3,x]","\frac{3 a^2 b d (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^2}-\frac{3 a^2 b d^2 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 a b^2 d^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^3}+\frac{b^3 d (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^2}-\frac{b^3 d^2 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\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{a^3 (c+d x)^3}{3 d}+\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{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 \log (\sinh (e+f x))}{f^3}+\frac{b^3 d^2 x^2}{2 f}","\frac{3 a^2 b d (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^2}-\frac{3 a^2 b d^2 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 a b^2 d^2 \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^3}+\frac{b^3 d (c+d x) \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{f^2}-\frac{b^3 d^2 \text{PolyLog}\left(3,e^{2 (e+f x)}\right)}{2 f^3}+\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{a^3 (c+d x)^3}{3 d}+\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{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 \log (\sinh (e+f x))}{f^3}+\frac{b^3 d^2 x^2}{2 f}",1,"(b^3*c*d*x)/f + (b^3*d^2*x^2)/(2*f) - (3*a*b^2*(c + d*x)^2)/f + (a^3*(c + d*x)^3)/(3*d) - (a^2*b*(c + d*x)^3)/d + (a*b^2*(c + d*x)^3)/d - (b^3*(c + d*x)^3)/(3*d) - (b^3*d*(c + d*x)*Coth[e + f*x])/f^2 - (3*a*b^2*(c + d*x)^2*Coth[e + f*x])/f - (b^3*(c + d*x)^2*Coth[e + f*x]^2)/(2*f) + (6*a*b^2*d*(c + d*x)*Log[1 - E^(2*(e + f*x))])/f^2 + (3*a^2*b*(c + d*x)^2*Log[1 - E^(2*(e + f*x))])/f + (b^3*(c + d*x)^2*Log[1 - E^(2*(e + f*x))])/f + (b^3*d^2*Log[Sinh[e + f*x]])/f^3 + (3*a*b^2*d^2*PolyLog[2, E^(2*(e + f*x))])/f^3 + (3*a^2*b*d*(c + d*x)*PolyLog[2, E^(2*(e + f*x))])/f^2 + (b^3*d*(c + d*x)*PolyLog[2, E^(2*(e + f*x))])/f^2 - (3*a^2*b*d^2*PolyLog[3, E^(2*(e + f*x))])/(2*f^3) - (b^3*d^2*PolyLog[3, E^(2*(e + f*x))])/(2*f^3)","A",22,11,20,0.5500,1,"{3722, 3716, 2190, 2531, 2282, 6589, 3720, 2279, 2391, 32, 3475}"
49,1,261,0,0.3500417,"\int (c+d x) (a+b \coth (e+f x))^3 \, dx","Int[(c + d*x)*(a + b*Coth[e + f*x])^3,x]","\frac{3 a^2 b d \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^2}+\frac{b^3 d \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^2}+\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{a^3 (c+d x)^2}{2 d}-\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 \coth (e+f x)}{2 f^2}+\frac{b^3 d x}{2 f}","\frac{3 a^2 b d \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^2}+\frac{b^3 d \text{PolyLog}\left(2,e^{2 (e+f x)}\right)}{2 f^2}+\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{a^3 (c+d x)^2}{2 d}-\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 \coth (e+f x)}{2 f^2}+\frac{b^3 d x}{2 f}",1,"3*a*b^2*c*x + (b^3*d*x)/(2*f) + (3*a*b^2*d*x^2)/2 + (a^3*(c + d*x)^2)/(2*d) - (3*a^2*b*(c + d*x)^2)/(2*d) - (b^3*(c + d*x)^2)/(2*d) - (b^3*d*Coth[e + f*x])/(2*f^2) - (3*a*b^2*(c + d*x)*Coth[e + f*x])/f - (b^3*(c + d*x)*Coth[e + f*x]^2)/(2*f) + (3*a^2*b*(c + d*x)*Log[1 - E^(2*(e + f*x))])/f + (b^3*(c + d*x)*Log[1 - E^(2*(e + f*x))])/f + (3*a*b^2*d*Log[Sinh[e + f*x]])/f^2 + (3*a^2*b*d*PolyLog[2, E^(2*(e + f*x))])/(2*f^2) + (b^3*d*PolyLog[2, E^(2*(e + f*x))])/(2*f^2)","A",16,9,18,0.5000,1,"{3722, 3716, 2190, 2279, 2391, 3720, 3475, 3473, 8}"
50,0,0,0,0.054938,"\int \frac{(a+b \coth (e+f x))^3}{c+d x} \, dx","Int[(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,"Defer[Int][(a + b*Coth[e + f*x])^3/(c + d*x), x]","A",0,0,0,0,-1,"{}"
51,0,0,0,0.0529811,"\int \frac{(a+b \coth (e+f x))^3}{(c+d x)^2} \, dx","Int[(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,"Defer[Int][(a + b*Coth[e + f*x])^3/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
52,1,210,0,0.3448833,"\int \frac{(c+d x)^3}{a+b \coth (e+f x)} \, dx","Int[(c + d*x)^3/(a + b*Coth[e + f*x]),x]","\frac{3 b d^2 (c+d x) \text{PolyLog}\left(3,\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{PolyLog}\left(2,\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^2 \left(a^2-b^2\right)}+\frac{3 b d^3 \text{PolyLog}\left(4,\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{4 f^4 \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{(c+d x)^4}{4 d (a+b)}","\frac{3 b d^2 (c+d x) \text{PolyLog}\left(3,\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{PolyLog}\left(2,\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^2 \left(a^2-b^2\right)}+\frac{3 b d^3 \text{PolyLog}\left(4,\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{4 f^4 \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{(c+d x)^4}{4 d (a+b)}",1,"(c + d*x)^4/(4*(a + b)*d) - (b*(c + d*x)^3*Log[1 - (a - b)/((a + b)*E^(2*(e + f*x)))])/((a^2 - b^2)*f) + (3*b*d*(c + d*x)^2*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))])/(2*(a^2 - b^2)*f^2) + (3*b*d^2*(c + d*x)*PolyLog[3, (a - b)/((a + b)*E^(2*(e + f*x)))])/(2*(a^2 - b^2)*f^3) + (3*b*d^3*PolyLog[4, (a - b)/((a + b)*E^(2*(e + f*x)))])/(4*(a^2 - b^2)*f^4)","A",6,6,20,0.3000,1,"{3731, 2190, 2531, 6609, 2282, 6589}"
53,1,156,0,0.2843523,"\int \frac{(c+d x)^2}{a+b \coth (e+f x)} \, dx","Int[(c + d*x)^2/(a + b*Coth[e + f*x]),x]","\frac{b d (c+d x) \text{PolyLog}\left(2,\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f^2 \left(a^2-b^2\right)}+\frac{b d^2 \text{PolyLog}\left(3,\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^3 \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{(c+d x)^3}{3 d (a+b)}","\frac{b d (c+d x) \text{PolyLog}\left(2,\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f^2 \left(a^2-b^2\right)}+\frac{b d^2 \text{PolyLog}\left(3,\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^3 \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{(c+d x)^3}{3 d (a+b)}",1,"(c + d*x)^3/(3*(a + b)*d) - (b*(c + d*x)^2*Log[1 - (a - b)/((a + b)*E^(2*(e + f*x)))])/((a^2 - b^2)*f) + (b*d*(c + d*x)*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))])/((a^2 - b^2)*f^2) + (b*d^2*PolyLog[3, (a - b)/((a + b)*E^(2*(e + f*x)))])/(2*(a^2 - b^2)*f^3)","A",5,5,20,0.2500,1,"{3731, 2190, 2531, 2282, 6589}"
54,1,108,0,0.1629618,"\int \frac{c+d x}{a+b \coth (e+f x)} \, dx","Int[(c + d*x)/(a + b*Coth[e + f*x]),x]","\frac{b d \text{PolyLog}\left(2,\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) \log \left(1-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f \left(a^2-b^2\right)}+\frac{(c+d x)^2}{2 d (a+b)}","\frac{b d \text{PolyLog}\left(2,\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) \log \left(1-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f \left(a^2-b^2\right)}+\frac{(c+d x)^2}{2 d (a+b)}",1,"(c + d*x)^2/(2*(a + b)*d) - (b*(c + d*x)*Log[1 - (a - b)/((a + b)*E^(2*(e + f*x)))])/((a^2 - b^2)*f) + (b*d*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))])/(2*(a^2 - b^2)*f^2)","A",4,4,18,0.2222,1,"{3731, 2190, 2279, 2391}"
55,0,0,0,0.0627868,"\int \frac{1}{(c+d x) (a+b \coth (e+f x))} \, dx","Int[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,"Defer[Int][1/((c + d*x)*(a + b*Coth[e + f*x])), x]","A",0,0,0,0,-1,"{}"
56,0,0,0,0.0599392,"\int \frac{1}{(c+d x)^2 (a+b \coth (e+f x))} \, dx","Int[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,"Defer[Int][1/((c + d*x)^2*(a + b*Coth[e + f*x])), x]","A",0,0,0,0,-1,"{}"
57,1,638,0,2.2736531,"\int \frac{(c+d x)^3}{(a+b \coth (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + b*Coth[e + f*x])^2,x]","\frac{3 b^2 d^2 (c+d x) \text{PolyLog}\left(2,\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{PolyLog}\left(3,\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{PolyLog}\left(2,\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^3 \text{PolyLog}\left(3,\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{PolyLog}\left(4,\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 d^2 (c+d x) \text{PolyLog}\left(3,\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{PolyLog}\left(2,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 (a-b)^2 (a+b)}-\frac{3 b d^3 \text{PolyLog}\left(4,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{2 f^4 (a-b)^2 (a+b)}+\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{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{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^2 d^2 (c+d x) \text{PolyLog}\left(2,\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{PolyLog}\left(3,\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{PolyLog}\left(2,\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^3 \text{PolyLog}\left(3,\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{PolyLog}\left(4,\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 d^2 (c+d x) \text{PolyLog}\left(3,\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{PolyLog}\left(2,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 (a-b)^2 (a+b)}-\frac{3 b d^3 \text{PolyLog}\left(4,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{2 f^4 (a-b)^2 (a+b)}+\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{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{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}",1,"(-2*b^2*(c + d*x)^3)/((a^2 - b^2)^2*f) + (2*b^2*(c + d*x)^3)/((a - b)*(a + b)^2*(a - b - (a + b)*E^(2*e + 2*f*x))*f) + (c + d*x)^4/(4*(a - b)^2*d) + (3*b^2*d*(c + d*x)^2*Log[1 - ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a^2 - b^2)^2*f^2) - (2*b*(c + d*x)^3*Log[1 - ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a - b)^2*(a + b)*f) + (2*b^2*(c + d*x)^3*Log[1 - ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a^2 - b^2)^2*f) + (3*b^2*d^2*(c + d*x)*PolyLog[2, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a^2 - b^2)^2*f^3) - (3*b*d*(c + d*x)^2*PolyLog[2, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a - b)^2*(a + b)*f^2) + (3*b^2*d*(c + d*x)^2*PolyLog[2, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a^2 - b^2)^2*f^2) - (3*b^2*d^3*PolyLog[3, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/(2*(a^2 - b^2)^2*f^4) + (3*b*d^2*(c + d*x)*PolyLog[3, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a - b)^2*(a + b)*f^3) - (3*b^2*d^2*(c + d*x)*PolyLog[3, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a^2 - b^2)^2*f^3) - (3*b*d^3*PolyLog[4, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/(2*(a - b)^2*(a + b)*f^4) + (3*b^2*d^3*PolyLog[4, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/(2*(a^2 - b^2)^2*f^4)","A",28,10,20,0.5000,1,"{3734, 2254, 2185, 2184, 2190, 2531, 6609, 2282, 6589, 2191}"
58,1,475,0,1.7144497,"\int \frac{(c+d x)^2}{(a+b \coth (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + b*Coth[e + f*x])^2,x]","\frac{2 b^2 d (c+d x) \text{PolyLog}\left(2,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{b^2 d^2 \text{PolyLog}\left(2,\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{PolyLog}\left(3,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 \left(a^2-b^2\right)^2}-\frac{2 b d (c+d x) \text{PolyLog}\left(2,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 (a-b)^2 (a+b)}+\frac{b d^2 \text{PolyLog}\left(3,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 (a-b)^2 (a+b)}+\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{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 (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{2 b^2 d (c+d x) \text{PolyLog}\left(2,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{b^2 d^2 \text{PolyLog}\left(2,\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{PolyLog}\left(3,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 \left(a^2-b^2\right)^2}-\frac{2 b d (c+d x) \text{PolyLog}\left(2,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 (a-b)^2 (a+b)}+\frac{b d^2 \text{PolyLog}\left(3,\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 (a-b)^2 (a+b)}+\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{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 (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}",1,"(-2*b^2*(c + d*x)^2)/((a^2 - b^2)^2*f) + (2*b^2*(c + d*x)^2)/((a - b)*(a + b)^2*(a - b - (a + b)*E^(2*e + 2*f*x))*f) + (c + d*x)^3/(3*(a - b)^2*d) + (2*b^2*d*(c + d*x)*Log[1 - ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a^2 - b^2)^2*f^2) - (2*b*(c + d*x)^2*Log[1 - ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a - b)^2*(a + b)*f) + (2*b^2*(c + d*x)^2*Log[1 - ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a^2 - b^2)^2*f) + (b^2*d^2*PolyLog[2, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a^2 - b^2)^2*f^3) - (2*b*d*(c + d*x)*PolyLog[2, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a - b)^2*(a + b)*f^2) + (2*b^2*d*(c + d*x)*PolyLog[2, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a^2 - b^2)^2*f^2) + (b*d^2*PolyLog[3, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a - b)^2*(a + b)*f^3) - (b^2*d^2*PolyLog[3, ((a + b)*E^(2*e + 2*f*x))/(a - b)])/((a^2 - b^2)^2*f^3)","A",24,11,20,0.5500,1,"{3734, 2254, 2185, 2184, 2190, 2531, 2282, 6589, 2191, 2279, 2391}"
59,1,196,0,0.2957845,"\int \frac{c+d x}{(a+b \coth (e+f x))^2} \, dx","Int[(c + d*x)/(a + b*Coth[e + f*x])^2,x]","\frac{a b d \text{PolyLog}\left(2,\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f^2 \left(a^2-b^2\right)^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{(-2 a c f-2 a d f x+b d)^2}{4 a d f^2 (a-b) (a+b)^2}","\frac{a b d \text{PolyLog}\left(2,\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f^2 \left(a^2-b^2\right)^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{(-2 a c f-2 a d f x+b d)^2}{4 a d f^2 (a-b) (a+b)^2}",1,"-(c + d*x)^2/(2*(a^2 - b^2)*d) + (b*d - 2*a*c*f - 2*a*d*f*x)^2/(4*a*(a - b)*(a + b)^2*d*f^2) + (b*(c + d*x))/((a^2 - b^2)*f*(a + b*Coth[e + f*x])) + (b*(b*d - 2*a*c*f - 2*a*d*f*x)*Log[1 - (a - b)/((a + b)*E^(2*(e + f*x)))])/((a^2 - b^2)^2*f^2) + (a*b*d*PolyLog[2, (a - b)/((a + b)*E^(2*(e + f*x)))])/((a^2 - b^2)^2*f^2)","A",5,5,18,0.2778,1,"{3733, 3731, 2190, 2279, 2391}"
60,0,0,0,0.0619273,"\int \frac{1}{(c+d x) (a+b \coth (e+f x))^2} \, dx","Int[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,"Defer[Int][1/((c + d*x)*(a + b*Coth[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
61,0,0,0,0.0586905,"\int \frac{1}{(c+d x)^2 (a+b \coth (e+f x))^2} \, dx","Int[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,"Defer[Int][1/((c + d*x)^2*(a + b*Coth[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"