1,1,101,0,0.1705061,"\int x^3 \cot (a+b x) \, dx","Int[x^3*Cot[a + b*x],x]","-\frac{3 i x^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 x \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}+\frac{x^3 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i x^4}{4}","-\frac{3 i x^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 x \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}+\frac{x^3 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i x^4}{4}",1,"(-I/4)*x^4 + (x^3*Log[1 - E^((2*I)*(a + b*x))])/b - (((3*I)/2)*x^2*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 + (3*x*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3) + (((3*I)/4)*PolyLog[4, E^((2*I)*(a + b*x))])/b^4","A",6,6,10,0.6000,1,"{3717, 2190, 2531, 6609, 2282, 6589}"
2,1,74,0,0.1400432,"\int x^2 \cot (a+b x) \, dx","Int[x^2*Cot[a + b*x],x]","-\frac{i x \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{\text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{x^2 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i x^3}{3}","-\frac{i x \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{\text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{x^2 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i x^3}{3}",1,"(-I/3)*x^3 + (x^2*Log[1 - E^((2*I)*(a + b*x))])/b - (I*x*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 + PolyLog[3, E^((2*I)*(a + b*x))]/(2*b^3)","A",5,5,10,0.5000,1,"{3717, 2190, 2531, 2282, 6589}"
3,1,53,0,0.0849125,"\int x \cot (a+b x) \, dx","Int[x*Cot[a + b*x],x]","-\frac{i \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{x \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i x^2}{2}","-\frac{i \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{x \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i x^2}{2}",1,"(-I/2)*x^2 + (x*Log[1 - E^((2*I)*(a + b*x))])/b - ((I/2)*PolyLog[2, E^((2*I)*(a + b*x))])/b^2","A",4,4,8,0.5000,1,"{3717, 2190, 2279, 2391}"
4,0,0,0,0.0159946,"\int \frac{\cot (a+b x)}{x} \, dx","Int[Cot[a + b*x]/x,x]","\int \frac{\cot (a+b x)}{x} \, dx","\text{Int}\left(\frac{\cot (a+b x)}{x},x\right)",0,"Defer[Int][Cot[a + b*x]/x, x]","A",0,0,0,0,-1,"{}"
5,0,0,0,0.0170585,"\int \frac{\cot (a+b x)}{x^2} \, dx","Int[Cot[a + b*x]/x^2,x]","\int \frac{\cot (a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\cot (a+b x)}{x^2},x\right)",0,"Defer[Int][Cot[a + b*x]/x^2, x]","A",0,0,0,0,-1,"{}"
6,1,97,0,0.1777272,"\int x^3 \cot ^2(a+b x) \, dx","Int[x^3*Cot[a + b*x]^2,x]","-\frac{3 i x \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^3}+\frac{3 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^4}+\frac{3 x^2 \log \left(1-e^{2 i (a+b x)}\right)}{b^2}-\frac{x^3 \cot (a+b x)}{b}-\frac{i x^3}{b}-\frac{x^4}{4}","-\frac{3 i x \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^3}+\frac{3 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^4}+\frac{3 x^2 \log \left(1-e^{2 i (a+b x)}\right)}{b^2}-\frac{x^3 \cot (a+b x)}{b}-\frac{i x^3}{b}-\frac{x^4}{4}",1,"((-I)*x^3)/b - x^4/4 - (x^3*Cot[a + b*x])/b + (3*x^2*Log[1 - E^((2*I)*(a + b*x))])/b^2 - ((3*I)*x*PolyLog[2, E^((2*I)*(a + b*x))])/b^3 + (3*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^4)","A",7,7,12,0.5833,1,"{3720, 3717, 2190, 2531, 2282, 6589, 30}"
7,1,74,0,0.1190137,"\int x^2 \cot ^2(a+b x) \, dx","Int[x^2*Cot[a + b*x]^2,x]","-\frac{i \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^3}+\frac{2 x \log \left(1-e^{2 i (a+b x)}\right)}{b^2}-\frac{x^2 \cot (a+b x)}{b}-\frac{i x^2}{b}-\frac{x^3}{3}","-\frac{i \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^3}+\frac{2 x \log \left(1-e^{2 i (a+b x)}\right)}{b^2}-\frac{x^2 \cot (a+b x)}{b}-\frac{i x^2}{b}-\frac{x^3}{3}",1,"((-I)*x^2)/b - x^3/3 - (x^2*Cot[a + b*x])/b + (2*x*Log[1 - E^((2*I)*(a + b*x))])/b^2 - (I*PolyLog[2, E^((2*I)*(a + b*x))])/b^3","A",6,6,12,0.5000,1,"{3720, 3717, 2190, 2279, 2391, 30}"
8,1,31,0,0.0228298,"\int x \cot ^2(a+b x) \, dx","Int[x*Cot[a + b*x]^2,x]","\frac{\log (\sin (a+b x))}{b^2}-\frac{x \cot (a+b x)}{b}-\frac{x^2}{2}","\frac{\log (\sin (a+b x))}{b^2}-\frac{x \cot (a+b x)}{b}-\frac{x^2}{2}",1,"-x^2/2 - (x*Cot[a + b*x])/b + Log[Sin[a + b*x]]/b^2","A",3,3,10,0.3000,1,"{3720, 3475, 30}"
9,0,0,0,0.029607,"\int \frac{\cot ^2(a+b x)}{x} \, dx","Int[Cot[a + b*x]^2/x,x]","\int \frac{\cot ^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\cot ^2(a+b x)}{x},x\right)",0,"Defer[Int][Cot[a + b*x]^2/x, x]","A",0,0,0,0,-1,"{}"
10,0,0,0,0.0304595,"\int \frac{\cot ^2(a+b x)}{x^2} \, dx","Int[Cot[a + b*x]^2/x^2,x]","\int \frac{\cot ^2(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\cot ^2(a+b x)}{x^2},x\right)",0,"Defer[Int][Cot[a + b*x]^2/x^2, x]","A",0,0,0,0,-1,"{}"
11,1,202,0,0.3014782,"\int x^3 \cot ^3(a+b x) \, dx","Int[x^3*Cot[a + b*x]^3,x]","\frac{3 i x^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 x \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{3 i \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}-\frac{3 x^2 \cot (a+b x)}{2 b^2}+\frac{3 x \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{x^3 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{x^3 \cot ^2(a+b x)}{2 b}-\frac{3 i x^2}{2 b^2}-\frac{x^3}{2 b}+\frac{i x^4}{4}","\frac{3 i x^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 x \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{3 i \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}-\frac{3 x^2 \cot (a+b x)}{2 b^2}+\frac{3 x \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{x^3 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{x^3 \cot ^2(a+b x)}{2 b}-\frac{3 i x^2}{2 b^2}-\frac{x^3}{2 b}+\frac{i x^4}{4}",1,"(((-3*I)/2)*x^2)/b^2 - x^3/(2*b) + (I/4)*x^4 - (3*x^2*Cot[a + b*x])/(2*b^2) - (x^3*Cot[a + b*x]^2)/(2*b) + (3*x*Log[1 - E^((2*I)*(a + b*x))])/b^3 - (x^3*Log[1 - E^((2*I)*(a + b*x))])/b - (((3*I)/2)*PolyLog[2, E^((2*I)*(a + b*x))])/b^4 + (((3*I)/2)*x^2*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (3*x*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3) - (((3*I)/4)*PolyLog[4, E^((2*I)*(a + b*x))])/b^4","A",13,10,12,0.8333,1,"{3720, 3717, 2190, 2279, 2391, 30, 2531, 6609, 2282, 6589}"
12,1,126,0,0.1861212,"\int x^2 \cot ^3(a+b x) \, dx","Int[x^2*Cot[a + b*x]^3,x]","\frac{i x \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{\text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{x \cot (a+b x)}{b^2}+\frac{\log (\sin (a+b x))}{b^3}-\frac{x^2 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{x^2 \cot ^2(a+b x)}{2 b}-\frac{x^2}{2 b}+\frac{i x^3}{3}","\frac{i x \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{\text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{x \cot (a+b x)}{b^2}+\frac{\log (\sin (a+b x))}{b^3}-\frac{x^2 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{x^2 \cot ^2(a+b x)}{2 b}-\frac{x^2}{2 b}+\frac{i x^3}{3}",1,"-x^2/(2*b) + (I/3)*x^3 - (x*Cot[a + b*x])/b^2 - (x^2*Cot[a + b*x]^2)/(2*b) - (x^2*Log[1 - E^((2*I)*(a + b*x))])/b + Log[Sin[a + b*x]]/b^3 + (I*x*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - PolyLog[3, E^((2*I)*(a + b*x))]/(2*b^3)","A",9,8,12,0.6667,1,"{3720, 3475, 30, 3717, 2190, 2531, 2282, 6589}"
13,1,91,0,0.1069746,"\int x \cot ^3(a+b x) \, dx","Int[x*Cot[a + b*x]^3,x]","\frac{i \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{\cot (a+b x)}{2 b^2}-\frac{x \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{x \cot ^2(a+b x)}{2 b}-\frac{x}{2 b}+\frac{i x^2}{2}","\frac{i \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{\cot (a+b x)}{2 b^2}-\frac{x \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{x \cot ^2(a+b x)}{2 b}-\frac{x}{2 b}+\frac{i x^2}{2}",1,"-x/(2*b) + (I/2)*x^2 - Cot[a + b*x]/(2*b^2) - (x*Cot[a + b*x]^2)/(2*b) - (x*Log[1 - E^((2*I)*(a + b*x))])/b + ((I/2)*PolyLog[2, E^((2*I)*(a + b*x))])/b^2","A",7,7,10,0.7000,1,"{3720, 3473, 8, 3717, 2190, 2279, 2391}"
14,0,0,0,0.027794,"\int \frac{\cot ^3(a+b x)}{x} \, dx","Int[Cot[a + b*x]^3/x,x]","\int \frac{\cot ^3(a+b x)}{x} \, dx","\text{Int}\left(\frac{\cot ^3(a+b x)}{x},x\right)",0,"Defer[Int][Cot[a + b*x]^3/x, x]","A",0,0,0,0,-1,"{}"
15,0,0,0,0.0298833,"\int \frac{\cot ^3(a+b x)}{x^2} \, dx","Int[Cot[a + b*x]^3/x^2,x]","\int \frac{\cot ^3(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\cot ^3(a+b x)}{x^2},x\right)",0,"Defer[Int][Cot[a + b*x]^3/x^2, x]","A",0,0,0,0,-1,"{}"
16,1,189,0,0.2000875,"\int \frac{(c+d x)^3}{a+i a \cot (e+f x)} \, dx","Int[(c + d*x)^3/(a + I*a*Cot[e + f*x]),x]","\frac{3 i d^2 (c+d x)}{4 f^3 (a+i a \cot (e+f x))}+\frac{3 d (c+d x)^2}{4 f^2 (a+i a \cot (e+f x))}-\frac{i (c+d x)^3}{2 f (a+i a \cot (e+f x))}-\frac{3 d (c+d x)^2}{8 a f^2}+\frac{i (c+d x)^3}{4 a f}+\frac{(c+d x)^4}{8 a d}-\frac{3 d^3}{8 f^4 (a+i a \cot (e+f x))}-\frac{3 i d^3 x}{8 a f^3}","\frac{3 i d^2 (c+d x)}{4 f^3 (a+i a \cot (e+f x))}+\frac{3 d (c+d x)^2}{4 f^2 (a+i a \cot (e+f x))}-\frac{i (c+d x)^3}{2 f (a+i a \cot (e+f x))}-\frac{3 d (c+d x)^2}{8 a f^2}+\frac{i (c+d x)^3}{4 a f}+\frac{(c+d x)^4}{8 a d}-\frac{3 d^3}{8 f^4 (a+i a \cot (e+f x))}-\frac{3 i d^3 x}{8 a f^3}",1,"(((-3*I)/8)*d^3*x)/(a*f^3) - (3*d*(c + d*x)^2)/(8*a*f^2) + ((I/4)*(c + d*x)^3)/(a*f) + (c + d*x)^4/(8*a*d) - (3*d^3)/(8*f^4*(a + I*a*Cot[e + f*x])) + (((3*I)/4)*d^2*(c + d*x))/(f^3*(a + I*a*Cot[e + f*x])) + (3*d*(c + d*x)^2)/(4*f^2*(a + I*a*Cot[e + f*x])) - ((I/2)*(c + d*x)^3)/(f*(a + I*a*Cot[e + f*x]))","A",5,3,23,0.1304,1,"{3723, 3479, 8}"
17,1,137,0,0.1225008,"\int \frac{(c+d x)^2}{a+i a \cot (e+f x)} \, dx","Int[(c + d*x)^2/(a + I*a*Cot[e + f*x]),x]","\frac{d (c+d x)}{2 f^2 (a+i a \cot (e+f x))}-\frac{i (c+d x)^2}{2 f (a+i a \cot (e+f x))}+\frac{i (c+d x)^2}{4 a f}+\frac{(c+d x)^3}{6 a d}+\frac{i d^2}{4 f^3 (a+i a \cot (e+f x))}-\frac{d^2 x}{4 a f^2}","\frac{d (c+d x)}{2 f^2 (a+i a \cot (e+f x))}-\frac{i (c+d x)^2}{2 f (a+i a \cot (e+f x))}+\frac{i (c+d x)^2}{4 a f}+\frac{(c+d x)^3}{6 a d}+\frac{i d^2}{4 f^3 (a+i a \cot (e+f x))}-\frac{d^2 x}{4 a f^2}",1,"-(d^2*x)/(4*a*f^2) + ((I/4)*(c + d*x)^2)/(a*f) + (c + d*x)^3/(6*a*d) + ((I/4)*d^2)/(f^3*(a + I*a*Cot[e + f*x])) + (d*(c + d*x))/(2*f^2*(a + I*a*Cot[e + f*x])) - ((I/2)*(c + d*x)^2)/(f*(a + I*a*Cot[e + f*x]))","A",4,3,23,0.1304,1,"{3723, 3479, 8}"
18,1,84,0,0.0536668,"\int \frac{c+d x}{a+i a \cot (e+f x)} \, dx","Int[(c + d*x)/(a + I*a*Cot[e + f*x]),x]","-\frac{i (c+d x)}{2 f (a+i a \cot (e+f x))}+\frac{(c+d x)^2}{4 a d}+\frac{d}{4 f^2 (a+i a \cot (e+f x))}+\frac{i d x}{4 a f}","-\frac{i (c+d x)}{2 f (a+i a \cot (e+f x))}+\frac{(c+d x)^2}{4 a d}+\frac{d}{4 f^2 (a+i a \cot (e+f x))}+\frac{i d x}{4 a f}",1,"((I/4)*d*x)/(a*f) + (c + d*x)^2/(4*a*d) + d/(4*f^2*(a + I*a*Cot[e + f*x])) - ((I/2)*(c + d*x))/(f*(a + I*a*Cot[e + f*x]))","A",3,3,21,0.1429,1,"{3723, 3479, 8}"
19,1,161,0,0.2777041,"\int \frac{1}{(c+d x) (a+i a \cot (e+f x))} \, dx","Int[1/((c + d*x)*(a + I*a*Cot[e + f*x])),x]","-\frac{i \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{2 a d}-\frac{\text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{2 a d}+\frac{\sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 a d}-\frac{i \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 a d}+\frac{\log (c+d x)}{2 a d}","-\frac{i \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{2 a d}-\frac{\text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{2 a d}+\frac{\sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 a d}-\frac{i \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 a d}+\frac{\log (c+d x)}{2 a d}",1,"-(Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/(2*a*d) + Log[c + d*x]/(2*a*d) - ((I/2)*CosIntegral[(2*c*f)/d + 2*f*x]*Sin[2*e - (2*c*f)/d])/(a*d) - ((I/2)*Cos[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(a*d) + (Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(2*a*d)","A",7,4,23,0.1739,1,"{3726, 3303, 3299, 3302}"
20,1,166,0,0.2271571,"\int \frac{1}{(c+d x)^2 (a+i a \cot (e+f x))} \, dx","Int[1/((c + d*x)^2*(a + I*a*Cot[e + f*x])),x]","\frac{f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{a d^2}-\frac{i f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{a d^2}+\frac{i f \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a d^2}+\frac{f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a d^2}-\frac{1}{d (c+d x) (a+i a \cot (e+f x))}","\frac{f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{a d^2}-\frac{i f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{a d^2}+\frac{i f \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a d^2}+\frac{f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a d^2}-\frac{1}{d (c+d x) (a+i a \cot (e+f x))}",1,"((-I)*f*Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/(a*d^2) - 1/(d*(c + d*x)*(a + I*a*Cot[e + f*x])) + (f*CosIntegral[(2*c*f)/d + 2*f*x]*Sin[2*e - (2*c*f)/d])/(a*d^2) + (f*Cos[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(a*d^2) + (I*f*Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(a*d^2)","A",7,4,23,0.1739,1,"{3724, 3303, 3299, 3302}"
21,1,227,0,0.3123563,"\int \frac{1}{(c+d x)^3 (a+i a \cot (e+f x))} \, dx","Int[1/((c + d*x)^3*(a + I*a*Cot[e + f*x])),x]","\frac{i f^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{a d^3}+\frac{f^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{a d^3}-\frac{f^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a d^3}+\frac{i f^2 \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a d^3}-\frac{i f}{d^2 (c+d x) (a+i a \cot (e+f x))}+\frac{i f}{2 a d^2 (c+d x)}-\frac{1}{2 d (c+d x)^2 (a+i a \cot (e+f x))}","\frac{i f^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{a d^3}+\frac{f^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{a d^3}-\frac{f^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a d^3}+\frac{i f^2 \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a d^3}-\frac{i f}{d^2 (c+d x) (a+i a \cot (e+f x))}+\frac{i f}{2 a d^2 (c+d x)}-\frac{1}{2 d (c+d x)^2 (a+i a \cot (e+f x))}",1,"((I/2)*f)/(a*d^2*(c + d*x)) + (f^2*Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/(a*d^3) - 1/(2*d*(c + d*x)^2*(a + I*a*Cot[e + f*x])) - (I*f)/(d^2*(c + d*x)*(a + I*a*Cot[e + f*x])) + (I*f^2*CosIntegral[(2*c*f)/d + 2*f*x]*Sin[2*e - (2*c*f)/d])/(a*d^3) + (I*f^2*Cos[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(a*d^3) - (f^2*Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(a*d^3)","A",8,5,23,0.2174,1,"{3725, 3724, 3303, 3299, 3302}"
22,1,270,0,0.2759696,"\int \frac{(c+d x)^3}{(a+i a \cot (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + I*a*Cot[e + f*x])^2,x]","-\frac{3 i d^2 (c+d x) e^{2 i e+2 i f x}}{8 a^2 f^3}+\frac{3 i d^2 (c+d x) e^{4 i e+4 i f x}}{128 a^2 f^3}-\frac{3 d (c+d x)^2 e^{2 i e+2 i f x}}{8 a^2 f^2}+\frac{3 d (c+d x)^2 e^{4 i e+4 i f x}}{64 a^2 f^2}+\frac{i (c+d x)^3 e^{2 i e+2 i f x}}{4 a^2 f}-\frac{i (c+d x)^3 e^{4 i e+4 i f x}}{16 a^2 f}+\frac{(c+d x)^4}{16 a^2 d}+\frac{3 d^3 e^{2 i e+2 i f x}}{16 a^2 f^4}-\frac{3 d^3 e^{4 i e+4 i f x}}{512 a^2 f^4}","-\frac{3 i d^2 (c+d x) e^{2 i e+2 i f x}}{8 a^2 f^3}+\frac{3 i d^2 (c+d x) e^{4 i e+4 i f x}}{128 a^2 f^3}-\frac{3 d (c+d x)^2 e^{2 i e+2 i f x}}{8 a^2 f^2}+\frac{3 d (c+d x)^2 e^{4 i e+4 i f x}}{64 a^2 f^2}+\frac{i (c+d x)^3 e^{2 i e+2 i f x}}{4 a^2 f}-\frac{i (c+d x)^3 e^{4 i e+4 i f x}}{16 a^2 f}+\frac{(c+d x)^4}{16 a^2 d}+\frac{3 d^3 e^{2 i e+2 i f x}}{16 a^2 f^4}-\frac{3 d^3 e^{4 i e+4 i f x}}{512 a^2 f^4}",1,"(3*d^3*E^((2*I)*e + (2*I)*f*x))/(16*a^2*f^4) - (3*d^3*E^((4*I)*e + (4*I)*f*x))/(512*a^2*f^4) - (((3*I)/8)*d^2*E^((2*I)*e + (2*I)*f*x)*(c + d*x))/(a^2*f^3) + (((3*I)/128)*d^2*E^((4*I)*e + (4*I)*f*x)*(c + d*x))/(a^2*f^3) - (3*d*E^((2*I)*e + (2*I)*f*x)*(c + d*x)^2)/(8*a^2*f^2) + (3*d*E^((4*I)*e + (4*I)*f*x)*(c + d*x)^2)/(64*a^2*f^2) + ((I/4)*E^((2*I)*e + (2*I)*f*x)*(c + d*x)^3)/(a^2*f) - ((I/16)*E^((4*I)*e + (4*I)*f*x)*(c + d*x)^3)/(a^2*f) + (c + d*x)^4/(16*a^2*d)","A",10,3,23,0.1304,1,"{3729, 2176, 2194}"
23,1,202,0,0.1984216,"\int \frac{(c+d x)^2}{(a+i a \cot (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + I*a*Cot[e + f*x])^2,x]","-\frac{d (c+d x) e^{2 i e+2 i f x}}{4 a^2 f^2}+\frac{d (c+d x) e^{4 i e+4 i f x}}{32 a^2 f^2}+\frac{i (c+d x)^2 e^{2 i e+2 i f x}}{4 a^2 f}-\frac{i (c+d x)^2 e^{4 i e+4 i f x}}{16 a^2 f}+\frac{(c+d x)^3}{12 a^2 d}-\frac{i d^2 e^{2 i e+2 i f x}}{8 a^2 f^3}+\frac{i d^2 e^{4 i e+4 i f x}}{128 a^2 f^3}","-\frac{d (c+d x) e^{2 i e+2 i f x}}{4 a^2 f^2}+\frac{d (c+d x) e^{4 i e+4 i f x}}{32 a^2 f^2}+\frac{i (c+d x)^2 e^{2 i e+2 i f x}}{4 a^2 f}-\frac{i (c+d x)^2 e^{4 i e+4 i f x}}{16 a^2 f}+\frac{(c+d x)^3}{12 a^2 d}-\frac{i d^2 e^{2 i e+2 i f x}}{8 a^2 f^3}+\frac{i d^2 e^{4 i e+4 i f x}}{128 a^2 f^3}",1,"((-I/8)*d^2*E^((2*I)*e + (2*I)*f*x))/(a^2*f^3) + ((I/128)*d^2*E^((4*I)*e + (4*I)*f*x))/(a^2*f^3) - (d*E^((2*I)*e + (2*I)*f*x)*(c + d*x))/(4*a^2*f^2) + (d*E^((4*I)*e + (4*I)*f*x)*(c + d*x))/(32*a^2*f^2) + ((I/4)*E^((2*I)*e + (2*I)*f*x)*(c + d*x)^2)/(a^2*f) - ((I/16)*E^((4*I)*e + (4*I)*f*x)*(c + d*x)^2)/(a^2*f) + (c + d*x)^3/(12*a^2*d)","A",8,3,23,0.1304,1,"{3729, 2176, 2194}"
24,1,151,0,0.138132,"\int \frac{c+d x}{(a+i a \cot (e+f x))^2} \, dx","Int[(c + d*x)/(a + I*a*Cot[e + f*x])^2,x]","-\frac{i (c+d x)}{4 f \left(a^2+i a^2 \cot (e+f x)\right)}+\frac{x (c+d x)}{4 a^2}+\frac{3 d}{16 f^2 \left(a^2+i a^2 \cot (e+f x)\right)}+\frac{3 i d x}{16 a^2 f}-\frac{d x^2}{8 a^2}-\frac{i (c+d x)}{4 f (a+i a \cot (e+f x))^2}+\frac{d}{16 f^2 (a+i a \cot (e+f x))^2}","-\frac{i (c+d x)}{4 f \left(a^2+i a^2 \cot (e+f x)\right)}+\frac{x (c+d x)}{4 a^2}+\frac{3 d}{16 f^2 \left(a^2+i a^2 \cot (e+f x)\right)}+\frac{3 i d x}{16 a^2 f}-\frac{d x^2}{8 a^2}-\frac{i (c+d x)}{4 f (a+i a \cot (e+f x))^2}+\frac{d}{16 f^2 (a+i a \cot (e+f x))^2}",1,"(((3*I)/16)*d*x)/(a^2*f) - (d*x^2)/(8*a^2) + (x*(c + d*x))/(4*a^2) + d/(16*f^2*(a + I*a*Cot[e + f*x])^2) - ((I/4)*(c + d*x))/(f*(a + I*a*Cot[e + f*x])^2) + (3*d)/(16*f^2*(a^2 + I*a^2*Cot[e + f*x])) - ((I/4)*(c + d*x))/(f*(a^2 + I*a^2*Cot[e + f*x]))","A",7,3,21,0.1429,1,"{3479, 8, 3730}"
25,1,305,0,0.7522179,"\int \frac{1}{(c+d x) (a+i a \cot (e+f x))^2} \, dx","Int[1/((c + d*x)*(a + I*a*Cot[e + f*x])^2),x]","-\frac{i \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{2 a^2 d}+\frac{i \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{4 a^2 d}-\frac{\text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{2 a^2 d}+\frac{\text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \cos \left(4 e-\frac{4 c f}{d}\right)}{4 a^2 d}+\frac{\sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 a^2 d}-\frac{\sin \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{4 a^2 d}-\frac{i \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 a^2 d}+\frac{i \cos \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{4 a^2 d}+\frac{\log (c+d x)}{4 a^2 d}","-\frac{i \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{2 a^2 d}+\frac{i \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{4 a^2 d}-\frac{\text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{2 a^2 d}+\frac{\text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \cos \left(4 e-\frac{4 c f}{d}\right)}{4 a^2 d}+\frac{\sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 a^2 d}-\frac{\sin \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{4 a^2 d}-\frac{i \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 a^2 d}+\frac{i \cos \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{4 a^2 d}+\frac{\log (c+d x)}{4 a^2 d}",1,"-(Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/(2*a^2*d) + (Cos[4*e - (4*c*f)/d]*CosIntegral[(4*c*f)/d + 4*f*x])/(4*a^2*d) + Log[c + d*x]/(4*a^2*d) + ((I/4)*CosIntegral[(4*c*f)/d + 4*f*x]*Sin[4*e - (4*c*f)/d])/(a^2*d) - ((I/2)*CosIntegral[(2*c*f)/d + 2*f*x]*Sin[2*e - (2*c*f)/d])/(a^2*d) - ((I/2)*Cos[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(a^2*d) + (Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(2*a^2*d) + ((I/4)*Cos[4*e - (4*c*f)/d]*SinIntegral[(4*c*f)/d + 4*f*x])/(a^2*d) - (Sin[4*e - (4*c*f)/d]*SinIntegral[(4*c*f)/d + 4*f*x])/(4*a^2*d)","A",21,5,23,0.2174,1,"{3728, 3303, 3299, 3302, 3312}"
26,1,434,0,0.6806542,"\int \frac{1}{(c+d x)^2 (a+i a \cot (e+f x))^2} \, dx","Int[1/((c + d*x)^2*(a + I*a*Cot[e + f*x])^2),x]","-\frac{f \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{a^2 d^2}+\frac{f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{i f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{a^2 d^2}+\frac{i f \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \cos \left(4 e-\frac{4 c f}{d}\right)}{a^2 d^2}+\frac{i f \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{i f \sin \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{a^2 d^2}+\frac{f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{f \cos \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{a^2 d^2}+\frac{\sin ^2(2 e+2 f x)}{4 a^2 d (c+d x)}+\frac{i \sin (2 e+2 f x)}{2 a^2 d (c+d x)}-\frac{i \sin (4 e+4 f x)}{4 a^2 d (c+d x)}-\frac{\cos ^2(2 e+2 f x)}{4 a^2 d (c+d x)}+\frac{\cos (2 e+2 f x)}{2 a^2 d (c+d x)}-\frac{1}{4 a^2 d (c+d x)}","-\frac{f \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{a^2 d^2}+\frac{f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{i f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{a^2 d^2}+\frac{i f \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \cos \left(4 e-\frac{4 c f}{d}\right)}{a^2 d^2}+\frac{i f \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{i f \sin \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{a^2 d^2}+\frac{f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{f \cos \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{a^2 d^2}+\frac{\sin ^2(2 e+2 f x)}{4 a^2 d (c+d x)}+\frac{i \sin (2 e+2 f x)}{2 a^2 d (c+d x)}-\frac{i \sin (4 e+4 f x)}{4 a^2 d (c+d x)}-\frac{\cos ^2(2 e+2 f x)}{4 a^2 d (c+d x)}+\frac{\cos (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)) + Cos[2*e + 2*f*x]/(2*a^2*d*(c + d*x)) - Cos[2*e + 2*f*x]^2/(4*a^2*d*(c + d*x)) - (I*f*Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/(a^2*d^2) + (I*f*Cos[4*e - (4*c*f)/d]*CosIntegral[(4*c*f)/d + 4*f*x])/(a^2*d^2) - (f*CosIntegral[(4*c*f)/d + 4*f*x]*Sin[4*e - (4*c*f)/d])/(a^2*d^2) + (f*CosIntegral[(2*c*f)/d + 2*f*x]*Sin[2*e - (2*c*f)/d])/(a^2*d^2) + ((I/2)*Sin[2*e + 2*f*x])/(a^2*d*(c + d*x)) + Sin[2*e + 2*f*x]^2/(4*a^2*d*(c + d*x)) - ((I/4)*Sin[4*e + 4*f*x])/(a^2*d*(c + d*x)) + (f*Cos[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(a^2*d^2) + (I*f*Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(a^2*d^2) - (f*Cos[4*e - (4*c*f)/d]*SinIntegral[(4*c*f)/d + 4*f*x])/(a^2*d^2) - (I*f*Sin[4*e - (4*c*f)/d]*SinIntegral[(4*c*f)/d + 4*f*x])/(a^2*d^2)","A",24,7,23,0.3043,1,"{3728, 3297, 3303, 3299, 3302, 3313, 12}"
27,1,396,0,0.381079,"\int \frac{(c+d x)^3}{(a+i a \cot (e+f x))^3} \, dx","Int[(c + d*x)^3/(a + I*a*Cot[e + f*x])^3,x]","-\frac{9 i d^2 (c+d x) e^{2 i e+2 i f x}}{32 a^3 f^3}+\frac{9 i d^2 (c+d x) e^{4 i e+4 i f x}}{256 a^3 f^3}-\frac{i d^2 (c+d x) e^{6 i e+6 i f x}}{288 a^3 f^3}-\frac{9 d (c+d x)^2 e^{2 i e+2 i f x}}{32 a^3 f^2}+\frac{9 d (c+d x)^2 e^{4 i e+4 i f x}}{128 a^3 f^2}-\frac{d (c+d x)^2 e^{6 i e+6 i f x}}{96 a^3 f^2}+\frac{3 i (c+d x)^3 e^{2 i e+2 i f x}}{16 a^3 f}-\frac{3 i (c+d x)^3 e^{4 i e+4 i f x}}{32 a^3 f}+\frac{i (c+d x)^3 e^{6 i e+6 i f x}}{48 a^3 f}+\frac{(c+d x)^4}{32 a^3 d}+\frac{9 d^3 e^{2 i e+2 i f x}}{64 a^3 f^4}-\frac{9 d^3 e^{4 i e+4 i f x}}{1024 a^3 f^4}+\frac{d^3 e^{6 i e+6 i f x}}{1728 a^3 f^4}","-\frac{9 i d^2 (c+d x) e^{2 i e+2 i f x}}{32 a^3 f^3}+\frac{9 i d^2 (c+d x) e^{4 i e+4 i f x}}{256 a^3 f^3}-\frac{i d^2 (c+d x) e^{6 i e+6 i f x}}{288 a^3 f^3}-\frac{9 d (c+d x)^2 e^{2 i e+2 i f x}}{32 a^3 f^2}+\frac{9 d (c+d x)^2 e^{4 i e+4 i f x}}{128 a^3 f^2}-\frac{d (c+d x)^2 e^{6 i e+6 i f x}}{96 a^3 f^2}+\frac{3 i (c+d x)^3 e^{2 i e+2 i f x}}{16 a^3 f}-\frac{3 i (c+d x)^3 e^{4 i e+4 i f x}}{32 a^3 f}+\frac{i (c+d x)^3 e^{6 i e+6 i f x}}{48 a^3 f}+\frac{(c+d x)^4}{32 a^3 d}+\frac{9 d^3 e^{2 i e+2 i f x}}{64 a^3 f^4}-\frac{9 d^3 e^{4 i e+4 i f x}}{1024 a^3 f^4}+\frac{d^3 e^{6 i e+6 i f x}}{1728 a^3 f^4}",1,"(9*d^3*E^((2*I)*e + (2*I)*f*x))/(64*a^3*f^4) - (9*d^3*E^((4*I)*e + (4*I)*f*x))/(1024*a^3*f^4) + (d^3*E^((6*I)*e + (6*I)*f*x))/(1728*a^3*f^4) - (((9*I)/32)*d^2*E^((2*I)*e + (2*I)*f*x)*(c + d*x))/(a^3*f^3) + (((9*I)/256)*d^2*E^((4*I)*e + (4*I)*f*x)*(c + d*x))/(a^3*f^3) - ((I/288)*d^2*E^((6*I)*e + (6*I)*f*x)*(c + d*x))/(a^3*f^3) - (9*d*E^((2*I)*e + (2*I)*f*x)*(c + d*x)^2)/(32*a^3*f^2) + (9*d*E^((4*I)*e + (4*I)*f*x)*(c + d*x)^2)/(128*a^3*f^2) - (d*E^((6*I)*e + (6*I)*f*x)*(c + d*x)^2)/(96*a^3*f^2) + (((3*I)/16)*E^((2*I)*e + (2*I)*f*x)*(c + d*x)^3)/(a^3*f) - (((3*I)/32)*E^((4*I)*e + (4*I)*f*x)*(c + d*x)^3)/(a^3*f) + ((I/48)*E^((6*I)*e + (6*I)*f*x)*(c + d*x)^3)/(a^3*f) + (c + d*x)^4/(32*a^3*d)","A",14,3,23,0.1304,1,"{3729, 2176, 2194}"
28,1,294,0,0.2687094,"\int \frac{(c+d x)^2}{(a+i a \cot (e+f x))^3} \, dx","Int[(c + d*x)^2/(a + I*a*Cot[e + f*x])^3,x]","-\frac{3 d (c+d x) e^{2 i e+2 i f x}}{16 a^3 f^2}+\frac{3 d (c+d x) e^{4 i e+4 i f x}}{64 a^3 f^2}-\frac{d (c+d x) e^{6 i e+6 i f x}}{144 a^3 f^2}+\frac{3 i (c+d x)^2 e^{2 i e+2 i f x}}{16 a^3 f}-\frac{3 i (c+d x)^2 e^{4 i e+4 i f x}}{32 a^3 f}+\frac{i (c+d x)^2 e^{6 i e+6 i f x}}{48 a^3 f}+\frac{(c+d x)^3}{24 a^3 d}-\frac{3 i d^2 e^{2 i e+2 i f x}}{32 a^3 f^3}+\frac{3 i d^2 e^{4 i e+4 i f x}}{256 a^3 f^3}-\frac{i d^2 e^{6 i e+6 i f x}}{864 a^3 f^3}","-\frac{3 d (c+d x) e^{2 i e+2 i f x}}{16 a^3 f^2}+\frac{3 d (c+d x) e^{4 i e+4 i f x}}{64 a^3 f^2}-\frac{d (c+d x) e^{6 i e+6 i f x}}{144 a^3 f^2}+\frac{3 i (c+d x)^2 e^{2 i e+2 i f x}}{16 a^3 f}-\frac{3 i (c+d x)^2 e^{4 i e+4 i f x}}{32 a^3 f}+\frac{i (c+d x)^2 e^{6 i e+6 i f x}}{48 a^3 f}+\frac{(c+d x)^3}{24 a^3 d}-\frac{3 i d^2 e^{2 i e+2 i f x}}{32 a^3 f^3}+\frac{3 i d^2 e^{4 i e+4 i f x}}{256 a^3 f^3}-\frac{i d^2 e^{6 i e+6 i f x}}{864 a^3 f^3}",1,"(((-3*I)/32)*d^2*E^((2*I)*e + (2*I)*f*x))/(a^3*f^3) + (((3*I)/256)*d^2*E^((4*I)*e + (4*I)*f*x))/(a^3*f^3) - ((I/864)*d^2*E^((6*I)*e + (6*I)*f*x))/(a^3*f^3) - (3*d*E^((2*I)*e + (2*I)*f*x)*(c + d*x))/(16*a^3*f^2) + (3*d*E^((4*I)*e + (4*I)*f*x)*(c + d*x))/(64*a^3*f^2) - (d*E^((6*I)*e + (6*I)*f*x)*(c + d*x))/(144*a^3*f^2) + (((3*I)/16)*E^((2*I)*e + (2*I)*f*x)*(c + d*x)^2)/(a^3*f) - (((3*I)/32)*E^((4*I)*e + (4*I)*f*x)*(c + d*x)^2)/(a^3*f) + ((I/48)*E^((6*I)*e + (6*I)*f*x)*(c + d*x)^2)/(a^3*f) + (c + d*x)^3/(24*a^3*d)","A",11,3,23,0.1304,1,"{3729, 2176, 2194}"
29,1,209,0,0.2178325,"\int \frac{c+d x}{(a+i a \cot (e+f x))^3} \, dx","Int[(c + d*x)/(a + I*a*Cot[e + f*x])^3,x]","-\frac{i (c+d x)}{8 f \left(a^3+i a^3 \cot (e+f x)\right)}+\frac{x (c+d x)}{8 a^3}+\frac{11 d}{96 f^2 \left(a^3+i a^3 \cot (e+f x)\right)}+\frac{11 i d x}{96 a^3 f}-\frac{d x^2}{16 a^3}-\frac{i (c+d x)}{8 a f (a+i a \cot (e+f x))^2}-\frac{i (c+d x)}{6 f (a+i a \cot (e+f x))^3}+\frac{5 d}{96 a f^2 (a+i a \cot (e+f x))^2}+\frac{d}{36 f^2 (a+i a \cot (e+f x))^3}","-\frac{i (c+d x)}{8 f \left(a^3+i a^3 \cot (e+f x)\right)}+\frac{x (c+d x)}{8 a^3}+\frac{11 d}{96 f^2 \left(a^3+i a^3 \cot (e+f x)\right)}+\frac{11 i d x}{96 a^3 f}-\frac{d x^2}{16 a^3}-\frac{i (c+d x)}{8 a f (a+i a \cot (e+f x))^2}-\frac{i (c+d x)}{6 f (a+i a \cot (e+f x))^3}+\frac{5 d}{96 a f^2 (a+i a \cot (e+f x))^2}+\frac{d}{36 f^2 (a+i a \cot (e+f x))^3}",1,"(((11*I)/96)*d*x)/(a^3*f) - (d*x^2)/(16*a^3) + (x*(c + d*x))/(8*a^3) + d/(36*f^2*(a + I*a*Cot[e + f*x])^3) - ((I/6)*(c + d*x))/(f*(a + I*a*Cot[e + f*x])^3) + (5*d)/(96*a*f^2*(a + I*a*Cot[e + f*x])^2) - ((I/8)*(c + d*x))/(a*f*(a + I*a*Cot[e + f*x])^2) + (11*d)/(96*f^2*(a^3 + I*a^3*Cot[e + f*x])) - ((I/8)*(c + d*x))/(f*(a^3 + I*a^3*Cot[e + f*x]))","A",11,3,21,0.1429,1,"{3479, 8, 3730}"
30,1,449,0,1.7315568,"\int \frac{1}{(c+d x) (a+i a \cot (e+f x))^3} \, dx","Int[1/((c + d*x)*(a + I*a*Cot[e + f*x])^3),x]","-\frac{3 i \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{8 a^3 d}-\frac{i \text{CosIntegral}\left(\frac{6 c f}{d}+6 f x\right) \sin \left(6 e-\frac{6 c f}{d}\right)}{8 a^3 d}+\frac{3 i \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{8 a^3 d}-\frac{3 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{8 a^3 d}+\frac{3 \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \cos \left(4 e-\frac{4 c f}{d}\right)}{8 a^3 d}-\frac{\text{CosIntegral}\left(\frac{6 c f}{d}+6 f x\right) \cos \left(6 e-\frac{6 c f}{d}\right)}{8 a^3 d}+\frac{3 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{8 a^3 d}-\frac{3 \sin \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{8 a^3 d}+\frac{\sin \left(6 e-\frac{6 c f}{d}\right) \text{Si}\left(6 x f+\frac{6 c f}{d}\right)}{8 a^3 d}-\frac{3 i \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{8 a^3 d}+\frac{3 i \cos \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{8 a^3 d}-\frac{i \cos \left(6 e-\frac{6 c f}{d}\right) \text{Si}\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 i \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{8 a^3 d}-\frac{i \text{CosIntegral}\left(\frac{6 c f}{d}+6 f x\right) \sin \left(6 e-\frac{6 c f}{d}\right)}{8 a^3 d}+\frac{3 i \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{8 a^3 d}-\frac{3 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{8 a^3 d}+\frac{3 \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \cos \left(4 e-\frac{4 c f}{d}\right)}{8 a^3 d}-\frac{\text{CosIntegral}\left(\frac{6 c f}{d}+6 f x\right) \cos \left(6 e-\frac{6 c f}{d}\right)}{8 a^3 d}+\frac{3 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{8 a^3 d}-\frac{3 \sin \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{8 a^3 d}+\frac{\sin \left(6 e-\frac{6 c f}{d}\right) \text{Si}\left(6 x f+\frac{6 c f}{d}\right)}{8 a^3 d}-\frac{3 i \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{8 a^3 d}+\frac{3 i \cos \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{8 a^3 d}-\frac{i \cos \left(6 e-\frac{6 c f}{d}\right) \text{Si}\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*Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/(8*a^3*d) + (3*Cos[4*e - (4*c*f)/d]*CosIntegral[(4*c*f)/d + 4*f*x])/(8*a^3*d) - (Cos[6*e - (6*c*f)/d]*CosIntegral[(6*c*f)/d + 6*f*x])/(8*a^3*d) + Log[c + d*x]/(8*a^3*d) - ((I/8)*CosIntegral[(6*c*f)/d + 6*f*x]*Sin[6*e - (6*c*f)/d])/(a^3*d) + (((3*I)/8)*CosIntegral[(4*c*f)/d + 4*f*x]*Sin[4*e - (4*c*f)/d])/(a^3*d) - (((3*I)/8)*CosIntegral[(2*c*f)/d + 2*f*x]*Sin[2*e - (2*c*f)/d])/(a^3*d) - (((3*I)/8)*Cos[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(a^3*d) + (3*Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(8*a^3*d) + (((3*I)/8)*Cos[4*e - (4*c*f)/d]*SinIntegral[(4*c*f)/d + 4*f*x])/(a^3*d) - (3*Sin[4*e - (4*c*f)/d]*SinIntegral[(4*c*f)/d + 4*f*x])/(8*a^3*d) - ((I/8)*Cos[6*e - (6*c*f)/d]*SinIntegral[(6*c*f)/d + 6*f*x])/(a^3*d) + (Sin[6*e - (6*c*f)/d]*SinIntegral[(6*c*f)/d + 6*f*x])/(8*a^3*d)","A",53,7,23,0.3043,1,"{3728, 3303, 3299, 3302, 3312, 4406, 4428}"
31,1,712,0,1.6433661,"\int \frac{1}{(c+d x)^2 (a+i a \cot (e+f x))^3} \, dx","Int[1/((c + d*x)^2*(a + I*a*Cot[e + f*x])^3),x]","\frac{3 f \text{CosIntegral}\left(\frac{6 c f}{d}+6 f x\right) \sin \left(6 e-\frac{6 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{2 a^3 d^2}+\frac{3 f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 i f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{4 a^3 d^2}+\frac{3 i f \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \cos \left(4 e-\frac{4 c f}{d}\right)}{2 a^3 d^2}-\frac{3 i f \text{CosIntegral}\left(\frac{6 c f}{d}+6 f x\right) \cos \left(6 e-\frac{6 c f}{d}\right)}{4 a^3 d^2}+\frac{3 i f \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 i f \sin \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{2 a^3 d^2}+\frac{3 i f \sin \left(6 e-\frac{6 c f}{d}\right) \text{Si}\left(6 x f+\frac{6 c f}{d}\right)}{4 a^3 d^2}+\frac{3 f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \cos \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{2 a^3 d^2}+\frac{3 f \cos \left(6 e-\frac{6 c f}{d}\right) \text{Si}\left(6 x f+\frac{6 c f}{d}\right)}{4 a^3 d^2}-\frac{i \sin ^3(2 e+2 f x)}{8 a^3 d (c+d x)}+\frac{3 \sin ^2(2 e+2 f x)}{8 a^3 d (c+d x)}+\frac{15 i \sin (2 e+2 f x)}{32 a^3 d (c+d x)}-\frac{3 i \sin (4 e+4 f x)}{8 a^3 d (c+d x)}+\frac{3 i \sin (6 e+6 f x)}{32 a^3 d (c+d x)}+\frac{\cos ^3(2 e+2 f x)}{8 a^3 d (c+d x)}-\frac{3 \cos ^2(2 e+2 f x)}{8 a^3 d (c+d x)}+\frac{9 \cos (2 e+2 f x)}{32 a^3 d (c+d x)}+\frac{3 \cos (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{CosIntegral}\left(\frac{6 c f}{d}+6 f x\right) \sin \left(6 e-\frac{6 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{2 a^3 d^2}+\frac{3 f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 i f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{4 a^3 d^2}+\frac{3 i f \text{CosIntegral}\left(\frac{4 c f}{d}+4 f x\right) \cos \left(4 e-\frac{4 c f}{d}\right)}{2 a^3 d^2}-\frac{3 i f \text{CosIntegral}\left(\frac{6 c f}{d}+6 f x\right) \cos \left(6 e-\frac{6 c f}{d}\right)}{4 a^3 d^2}+\frac{3 i f \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 i f \sin \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{2 a^3 d^2}+\frac{3 i f \sin \left(6 e-\frac{6 c f}{d}\right) \text{Si}\left(6 x f+\frac{6 c f}{d}\right)}{4 a^3 d^2}+\frac{3 f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \cos \left(4 e-\frac{4 c f}{d}\right) \text{Si}\left(4 x f+\frac{4 c f}{d}\right)}{2 a^3 d^2}+\frac{3 f \cos \left(6 e-\frac{6 c f}{d}\right) \text{Si}\left(6 x f+\frac{6 c f}{d}\right)}{4 a^3 d^2}-\frac{i \sin ^3(2 e+2 f x)}{8 a^3 d (c+d x)}+\frac{3 \sin ^2(2 e+2 f x)}{8 a^3 d (c+d x)}+\frac{15 i \sin (2 e+2 f x)}{32 a^3 d (c+d x)}-\frac{3 i \sin (4 e+4 f x)}{8 a^3 d (c+d x)}+\frac{3 i \sin (6 e+6 f x)}{32 a^3 d (c+d x)}+\frac{\cos ^3(2 e+2 f x)}{8 a^3 d (c+d x)}-\frac{3 \cos ^2(2 e+2 f x)}{8 a^3 d (c+d x)}+\frac{9 \cos (2 e+2 f x)}{32 a^3 d (c+d x)}+\frac{3 \cos (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*Cos[2*e + 2*f*x])/(32*a^3*d*(c + d*x)) - (3*Cos[2*e + 2*f*x]^2)/(8*a^3*d*(c + d*x)) + Cos[2*e + 2*f*x]^3/(8*a^3*d*(c + d*x)) + (3*Cos[6*e + 6*f*x])/(32*a^3*d*(c + d*x)) - (((3*I)/4)*f*Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/(a^3*d^2) + (((3*I)/2)*f*Cos[4*e - (4*c*f)/d]*CosIntegral[(4*c*f)/d + 4*f*x])/(a^3*d^2) - (((3*I)/4)*f*Cos[6*e - (6*c*f)/d]*CosIntegral[(6*c*f)/d + 6*f*x])/(a^3*d^2) + (3*f*CosIntegral[(6*c*f)/d + 6*f*x]*Sin[6*e - (6*c*f)/d])/(4*a^3*d^2) - (3*f*CosIntegral[(4*c*f)/d + 4*f*x]*Sin[4*e - (4*c*f)/d])/(2*a^3*d^2) + (3*f*CosIntegral[(2*c*f)/d + 2*f*x]*Sin[2*e - (2*c*f)/d])/(4*a^3*d^2) + (((15*I)/32)*Sin[2*e + 2*f*x])/(a^3*d*(c + d*x)) + (3*Sin[2*e + 2*f*x]^2)/(8*a^3*d*(c + d*x)) - ((I/8)*Sin[2*e + 2*f*x]^3)/(a^3*d*(c + d*x)) - (((3*I)/8)*Sin[4*e + 4*f*x])/(a^3*d*(c + d*x)) + (((3*I)/32)*Sin[6*e + 6*f*x])/(a^3*d*(c + d*x)) + (3*f*Cos[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(4*a^3*d^2) + (((3*I)/4)*f*Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(a^3*d^2) - (3*f*Cos[4*e - (4*c*f)/d]*SinIntegral[(4*c*f)/d + 4*f*x])/(2*a^3*d^2) - (((3*I)/2)*f*Sin[4*e - (4*c*f)/d]*SinIntegral[(4*c*f)/d + 4*f*x])/(a^3*d^2) + (3*f*Cos[6*e - (6*c*f)/d]*SinIntegral[(6*c*f)/d + 6*f*x])/(4*a^3*d^2) + (((3*I)/4)*f*Sin[6*e - (6*c*f)/d]*SinIntegral[(6*c*f)/d + 6*f*x])/(a^3*d^2)","A",60,9,23,0.3913,1,"{3728, 3297, 3303, 3299, 3302, 3313, 12, 4406, 4428}"
32,0,0,0,0.0509656,"\int (c+d x)^m (a+i a \cot (e+f x))^2 \, dx","Int[(c + d*x)^m*(a + I*a*Cot[e + f*x])^2,x]","\int (c+d x)^m (a+i a \cot (e+f x))^2 \, dx","\text{Int}\left((c+d x)^m (a+i a \cot (e+f x))^2,x\right)",0,"Defer[Int][(c + d*x)^m*(a + I*a*Cot[e + f*x])^2, x]","A",0,0,0,0,-1,"{}"
33,0,0,0,0.0289145,"\int (c+d x)^m (a+i a \cot (e+f x)) \, dx","Int[(c + d*x)^m*(a + I*a*Cot[e + f*x]),x]","\int (c+d x)^m (a+i a \cot (e+f x)) \, dx","\text{Int}\left((c+d x)^m (a+i a \cot (e+f x)),x\right)",0,"Defer[Int][(c + d*x)^m*(a + I*a*Cot[e + f*x]), x]","A",0,0,0,0,-1,"{}"
34,1,98,0,0.1238104,"\int \frac{(c+d x)^m}{a+i a \cot (e+f x)} \, dx","Int[(c + d*x)^m/(a + I*a*Cot[e + f*x]),x]","\frac{(c+d x)^{m+1}}{2 a d (m+1)}+\frac{i 2^{-m-2} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{a f}","\frac{(c+d x)^{m+1}}{2 a d (m+1)}+\frac{i 2^{-m-2} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{a f}",1,"(c + d*x)^(1 + m)/(2*a*d*(1 + m)) + (I*2^(-2 - m)*E^((2*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-2*I)*f*(c + d*x))/d])/(a*f*(((-I)*f*(c + d*x))/d)^m)","A",2,2,23,0.08696,1,"{3727, 2181}"
35,1,171,0,0.1847243,"\int \frac{(c+d x)^m}{(a+i a \cot (e+f x))^2} \, dx","Int[(c + d*x)^m/(a + I*a*Cot[e + f*x])^2,x]","\frac{i 2^{-m-2} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{a^2 f}-\frac{i 4^{-m-2} e^{4 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{4 i f (c+d x)}{d}\right)}{a^2 f}+\frac{(c+d x)^{m+1}}{4 a^2 d (m+1)}","\frac{i 2^{-m-2} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{a^2 f}-\frac{i 4^{-m-2} e^{4 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{4 i 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)) + (I*2^(-2 - m)*E^((2*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-2*I)*f*(c + d*x))/d])/(a^2*f*(((-I)*f*(c + d*x))/d)^m) - (I*4^(-2 - m)*E^((4*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-4*I)*f*(c + d*x))/d])/(a^2*f*(((-I)*f*(c + d*x))/d)^m)","A",4,2,23,0.08696,1,"{3729, 2181}"
36,1,251,0,0.242452,"\int \frac{(c+d x)^m}{(a+i a \cot (e+f x))^3} \, dx","Int[(c + d*x)^m/(a + I*a*Cot[e + f*x])^3,x]","\frac{3 i 2^{-m-4} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{a^3 f}-\frac{3 i 2^{-2 m-5} e^{4 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{4 i f (c+d x)}{d}\right)}{a^3 f}+\frac{i 2^{-m-4} 3^{-m-1} e^{6 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{6 i f (c+d x)}{d}\right)}{a^3 f}+\frac{(c+d x)^{m+1}}{8 a^3 d (m+1)}","\frac{3 i 2^{-m-4} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{a^3 f}-\frac{3 i 2^{-2 m-5} e^{4 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{4 i f (c+d x)}{d}\right)}{a^3 f}+\frac{i 2^{-m-4} 3^{-m-1} e^{6 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{6 i 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*I)*2^(-4 - m)*E^((2*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-2*I)*f*(c + d*x))/d])/(a^3*f*(((-I)*f*(c + d*x))/d)^m) - ((3*I)*2^(-5 - 2*m)*E^((4*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-4*I)*f*(c + d*x))/d])/(a^3*f*(((-I)*f*(c + d*x))/d)^m) + (I*2^(-4 - m)*3^(-1 - m)*E^((6*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-6*I)*f*(c + d*x))/d])/(a^3*f*(((-I)*f*(c + d*x))/d)^m)","A",5,2,23,0.08696,1,"{3729, 2181}"
37,1,147,0,0.2550467,"\int (c+d x)^3 (a+b \cot (e+f x)) \, dx","Int[(c + d*x)^3*(a + b*Cot[e + f*x]),x]","\frac{3 b d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^3}-\frac{3 i b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^2}+\frac{3 i b d^3 \text{PolyLog}\left(4,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{i b (c+d x)^4}{4 d}","\frac{3 b d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^3}-\frac{3 i b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^2}+\frac{3 i b d^3 \text{PolyLog}\left(4,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{i b (c+d x)^4}{4 d}",1,"(a*(c + d*x)^4)/(4*d) - ((I/4)*b*(c + d*x)^4)/d + (b*(c + d*x)^3*Log[1 - E^((2*I)*(e + f*x))])/f - (((3*I)/2)*b*d*(c + d*x)^2*PolyLog[2, E^((2*I)*(e + f*x))])/f^2 + (3*b*d^2*(c + d*x)*PolyLog[3, E^((2*I)*(e + f*x))])/(2*f^3) + (((3*I)/4)*b*d^3*PolyLog[4, E^((2*I)*(e + f*x))])/f^4","A",8,7,18,0.3889,1,"{3722, 3717, 2190, 2531, 6609, 2282, 6589}"
38,1,112,0,0.2095332,"\int (c+d x)^2 (a+b \cot (e+f x)) \, dx","Int[(c + d*x)^2*(a + b*Cot[e + f*x]),x]","-\frac{i b d (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^2}+\frac{b d^2 \text{PolyLog}\left(3,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{i b (c+d x)^3}{3 d}","-\frac{i b d (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^2}+\frac{b d^2 \text{PolyLog}\left(3,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{i b (c+d x)^3}{3 d}",1,"(a*(c + d*x)^3)/(3*d) - ((I/3)*b*(c + d*x)^3)/d + (b*(c + d*x)^2*Log[1 - E^((2*I)*(e + f*x))])/f - (I*b*d*(c + d*x)*PolyLog[2, E^((2*I)*(e + f*x))])/f^2 + (b*d^2*PolyLog[3, E^((2*I)*(e + f*x))])/(2*f^3)","A",7,6,18,0.3333,1,"{3722, 3717, 2190, 2531, 2282, 6589}"
39,1,83,0,0.1229307,"\int (c+d x) (a+b \cot (e+f x)) \, dx","Int[(c + d*x)*(a + b*Cot[e + f*x]),x]","-\frac{i b d \text{PolyLog}\left(2,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{i b (c+d x)^2}{2 d}","-\frac{i b d \text{PolyLog}\left(2,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{i b (c+d x)^2}{2 d}",1,"(a*(c + d*x)^2)/(2*d) - ((I/2)*b*(c + d*x)^2)/d + (b*(c + d*x)*Log[1 - E^((2*I)*(e + f*x))])/f - ((I/2)*b*d*PolyLog[2, E^((2*I)*(e + f*x))])/f^2","A",6,5,16,0.3125,1,"{3722, 3717, 2190, 2279, 2391}"
40,0,0,0,0.0291858,"\int \frac{a+b \cot (e+f x)}{c+d x} \, dx","Int[(a + b*Cot[e + f*x])/(c + d*x),x]","\int \frac{a+b \cot (e+f x)}{c+d x} \, dx","\text{Int}\left(\frac{a+b \cot (e+f x)}{c+d x},x\right)",0,"Defer[Int][(a + b*Cot[e + f*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
41,0,0,0,0.0283058,"\int \frac{a+b \cot (e+f x)}{(c+d x)^2} \, dx","Int[(a + b*Cot[e + f*x])/(c + d*x)^2,x]","\int \frac{a+b \cot (e+f x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{a+b \cot (e+f x)}{(c+d x)^2},x\right)",0,"Defer[Int][(a + b*Cot[e + f*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
42,1,295,0,0.5310473,"\int (c+d x)^3 (a+b \cot (e+f x))^2 \, dx","Int[(c + d*x)^3*(a + b*Cot[e + f*x])^2,x]","\frac{3 a b d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{f^3}-\frac{3 i a b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^2}+\frac{3 i a b d^3 \text{PolyLog}\left(4,e^{2 i (e+f x)}\right)}{2 f^4}-\frac{3 i b^2 d^2 (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^3}+\frac{3 b^2 d^3 \text{PolyLog}\left(3,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{i a b (c+d x)^4}{2 d}+\frac{3 b^2 d (c+d x)^2 \log \left(1-e^{2 i (e+f x)}\right)}{f^2}-\frac{b^2 (c+d x)^3 \cot (e+f x)}{f}-\frac{i 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 i (e+f x)}\right)}{f^3}-\frac{3 i a b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^2}+\frac{3 i a b d^3 \text{PolyLog}\left(4,e^{2 i (e+f x)}\right)}{2 f^4}-\frac{3 i b^2 d^2 (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^3}+\frac{3 b^2 d^3 \text{PolyLog}\left(3,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{i a b (c+d x)^4}{2 d}+\frac{3 b^2 d (c+d x)^2 \log \left(1-e^{2 i (e+f x)}\right)}{f^2}-\frac{b^2 (c+d x)^3 \cot (e+f x)}{f}-\frac{i b^2 (c+d x)^3}{f}-\frac{b^2 (c+d x)^4}{4 d}",1,"((-I)*b^2*(c + d*x)^3)/f + (a^2*(c + d*x)^4)/(4*d) - ((I/2)*a*b*(c + d*x)^4)/d - (b^2*(c + d*x)^4)/(4*d) - (b^2*(c + d*x)^3*Cot[e + f*x])/f + (3*b^2*d*(c + d*x)^2*Log[1 - E^((2*I)*(e + f*x))])/f^2 + (2*a*b*(c + d*x)^3*Log[1 - E^((2*I)*(e + f*x))])/f - ((3*I)*b^2*d^2*(c + d*x)*PolyLog[2, E^((2*I)*(e + f*x))])/f^3 - ((3*I)*a*b*d*(c + d*x)^2*PolyLog[2, E^((2*I)*(e + f*x))])/f^2 + (3*b^2*d^3*PolyLog[3, E^((2*I)*(e + f*x))])/(2*f^4) + (3*a*b*d^2*(c + d*x)*PolyLog[3, E^((2*I)*(e + f*x))])/f^3 + (((3*I)/2)*a*b*d^3*PolyLog[4, E^((2*I)*(e + f*x))])/f^4","A",15,9,20,0.4500,1,"{3722, 3717, 2190, 2531, 6609, 2282, 6589, 3720, 32}"
43,1,227,0,0.3833465,"\int (c+d x)^2 (a+b \cot (e+f x))^2 \, dx","Int[(c + d*x)^2*(a + b*Cot[e + f*x])^2,x]","-\frac{2 i a b d (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^2}+\frac{a b d^2 \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{f^3}-\frac{i b^2 d^2 \text{PolyLog}\left(2,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{2 i a b (c+d x)^3}{3 d}+\frac{2 b^2 d (c+d x) \log \left(1-e^{2 i (e+f x)}\right)}{f^2}-\frac{b^2 (c+d x)^2 \cot (e+f x)}{f}-\frac{i b^2 (c+d x)^2}{f}-\frac{b^2 (c+d x)^3}{3 d}","-\frac{2 i a b d (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^2}+\frac{a b d^2 \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{f^3}-\frac{i b^2 d^2 \text{PolyLog}\left(2,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{2 i a b (c+d x)^3}{3 d}+\frac{2 b^2 d (c+d x) \log \left(1-e^{2 i (e+f x)}\right)}{f^2}-\frac{b^2 (c+d x)^2 \cot (e+f x)}{f}-\frac{i b^2 (c+d x)^2}{f}-\frac{b^2 (c+d x)^3}{3 d}",1,"((-I)*b^2*(c + d*x)^2)/f + (a^2*(c + d*x)^3)/(3*d) - (((2*I)/3)*a*b*(c + d*x)^3)/d - (b^2*(c + d*x)^3)/(3*d) - (b^2*(c + d*x)^2*Cot[e + f*x])/f + (2*b^2*d*(c + d*x)*Log[1 - E^((2*I)*(e + f*x))])/f^2 + (2*a*b*(c + d*x)^2*Log[1 - E^((2*I)*(e + f*x))])/f - (I*b^2*d^2*PolyLog[2, E^((2*I)*(e + f*x))])/f^3 - ((2*I)*a*b*d*(c + d*x)*PolyLog[2, E^((2*I)*(e + f*x))])/f^2 + (a*b*d^2*PolyLog[3, E^((2*I)*(e + f*x))])/f^3","A",13,10,20,0.5000,1,"{3722, 3717, 2190, 2531, 2282, 6589, 3720, 2279, 2391, 32}"
44,1,137,0,0.1742168,"\int (c+d x) (a+b \cot (e+f x))^2 \, dx","Int[(c + d*x)*(a + b*Cot[e + f*x])^2,x]","-\frac{i a b d \text{PolyLog}\left(2,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{i a b (c+d x)^2}{d}-\frac{b^2 (c+d x) \cot (e+f x)}{f}-b^2 c x+\frac{b^2 d \log (\sin (e+f x))}{f^2}-\frac{1}{2} b^2 d x^2","-\frac{i a b d \text{PolyLog}\left(2,e^{2 i (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 i (e+f x)}\right)}{f}-\frac{i a b (c+d x)^2}{d}-\frac{b^2 (c+d x) \cot (e+f x)}{f}-b^2 c x+\frac{b^2 d \log (\sin (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) - (I*a*b*(c + d*x)^2)/d - (b^2*(c + d*x)*Cot[e + f*x])/f + (2*a*b*(c + d*x)*Log[1 - E^((2*I)*(e + f*x))])/f + (b^2*d*Log[Sin[e + f*x]])/f^2 - (I*a*b*d*PolyLog[2, E^((2*I)*(e + f*x))])/f^2","A",9,7,18,0.3889,1,"{3722, 3717, 2190, 2279, 2391, 3720, 3475}"
45,0,0,0,0.0533979,"\int \frac{(a+b \cot (e+f x))^2}{c+d x} \, dx","Int[(a + b*Cot[e + f*x])^2/(c + d*x),x]","\int \frac{(a+b \cot (e+f x))^2}{c+d x} \, dx","\text{Int}\left(\frac{(a+b \cot (e+f x))^2}{c+d x},x\right)",0,"Defer[Int][(a + b*Cot[e + f*x])^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
46,0,0,0,0.0511912,"\int \frac{(a+b \cot (e+f x))^2}{(c+d x)^2} \, dx","Int[(a + b*Cot[e + f*x])^2/(c + d*x)^2,x]","\int \frac{(a+b \cot (e+f x))^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{(a+b \cot (e+f x))^2}{(c+d x)^2},x\right)",0,"Defer[Int][(a + b*Cot[e + f*x])^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
47,1,603,0,0.9805516,"\int (c+d x)^3 (a+b \cot (e+f x))^3 \, dx","Int[(c + d*x)^3*(a + b*Cot[e + f*x])^3,x]","\frac{9 a^2 b d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^3}-\frac{9 i a^2 b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^2}+\frac{9 i a^2 b d^3 \text{PolyLog}\left(4,e^{2 i (e+f x)}\right)}{4 f^4}-\frac{9 i a b^2 d^2 (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^3}+\frac{9 a b^2 d^3 \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^4}-\frac{3 b^3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^3}+\frac{3 i b^3 d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^2}-\frac{3 i b^3 d^3 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^4}-\frac{3 i b^3 d^3 \text{PolyLog}\left(4,e^{2 i (e+f x)}\right)}{4 f^4}+\frac{3 a^2 b (c+d x)^3 \log \left(1-e^{2 i (e+f x)}\right)}{f}-\frac{3 i 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 i (e+f x)}\right)}{f^2}-\frac{3 a b^2 (c+d x)^3 \cot (e+f x)}{f}-\frac{3 i 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 i (e+f x)}\right)}{f^3}-\frac{3 b^3 d (c+d x)^2 \cot (e+f x)}{2 f^2}-\frac{b^3 (c+d x)^3 \log \left(1-e^{2 i (e+f x)}\right)}{f}-\frac{b^3 (c+d x)^3 \cot ^2(e+f x)}{2 f}-\frac{3 i b^3 d (c+d x)^2}{2 f^2}-\frac{b^3 (c+d x)^3}{2 f}+\frac{i b^3 (c+d x)^4}{4 d}","\frac{9 a^2 b d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^3}-\frac{9 i a^2 b d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^2}+\frac{9 i a^2 b d^3 \text{PolyLog}\left(4,e^{2 i (e+f x)}\right)}{4 f^4}-\frac{9 i a b^2 d^2 (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^3}+\frac{9 a b^2 d^3 \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^4}-\frac{3 b^3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^3}+\frac{3 i b^3 d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^2}-\frac{3 i b^3 d^3 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^4}-\frac{3 i b^3 d^3 \text{PolyLog}\left(4,e^{2 i (e+f x)}\right)}{4 f^4}+\frac{3 a^2 b (c+d x)^3 \log \left(1-e^{2 i (e+f x)}\right)}{f}-\frac{3 i 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 i (e+f x)}\right)}{f^2}-\frac{3 a b^2 (c+d x)^3 \cot (e+f x)}{f}-\frac{3 i 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 i (e+f x)}\right)}{f^3}-\frac{3 b^3 d (c+d x)^2 \cot (e+f x)}{2 f^2}-\frac{b^3 (c+d x)^3 \log \left(1-e^{2 i (e+f x)}\right)}{f}-\frac{b^3 (c+d x)^3 \cot ^2(e+f x)}{2 f}-\frac{3 i b^3 d (c+d x)^2}{2 f^2}-\frac{b^3 (c+d x)^3}{2 f}+\frac{i b^3 (c+d x)^4}{4 d}",1,"(((-3*I)/2)*b^3*d*(c + d*x)^2)/f^2 - ((3*I)*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*I)/4)*a^2*b*(c + d*x)^4)/d - (3*a*b^2*(c + d*x)^4)/(4*d) + ((I/4)*b^3*(c + d*x)^4)/d - (3*b^3*d*(c + d*x)^2*Cot[e + f*x])/(2*f^2) - (3*a*b^2*(c + d*x)^3*Cot[e + f*x])/f - (b^3*(c + d*x)^3*Cot[e + f*x]^2)/(2*f) + (3*b^3*d^2*(c + d*x)*Log[1 - E^((2*I)*(e + f*x))])/f^3 + (9*a*b^2*d*(c + d*x)^2*Log[1 - E^((2*I)*(e + f*x))])/f^2 + (3*a^2*b*(c + d*x)^3*Log[1 - E^((2*I)*(e + f*x))])/f - (b^3*(c + d*x)^3*Log[1 - E^((2*I)*(e + f*x))])/f - (((3*I)/2)*b^3*d^3*PolyLog[2, E^((2*I)*(e + f*x))])/f^4 - ((9*I)*a*b^2*d^2*(c + d*x)*PolyLog[2, E^((2*I)*(e + f*x))])/f^3 - (((9*I)/2)*a^2*b*d*(c + d*x)^2*PolyLog[2, E^((2*I)*(e + f*x))])/f^2 + (((3*I)/2)*b^3*d*(c + d*x)^2*PolyLog[2, E^((2*I)*(e + f*x))])/f^2 + (9*a*b^2*d^3*PolyLog[3, E^((2*I)*(e + f*x))])/(2*f^4) + (9*a^2*b*d^2*(c + d*x)*PolyLog[3, E^((2*I)*(e + f*x))])/(2*f^3) - (3*b^3*d^2*(c + d*x)*PolyLog[3, E^((2*I)*(e + f*x))])/(2*f^3) + (((9*I)/4)*a^2*b*d^3*PolyLog[4, E^((2*I)*(e + f*x))])/f^4 - (((3*I)/4)*b^3*d^3*PolyLog[4, E^((2*I)*(e + f*x))])/f^4","A",28,11,20,0.5500,1,"{3722, 3717, 2190, 2531, 6609, 2282, 6589, 3720, 32, 2279, 2391}"
48,1,433,0,0.648633,"\int (c+d x)^2 (a+b \cot (e+f x))^3 \, dx","Int[(c + d*x)^2*(a + b*Cot[e + f*x])^3,x]","-\frac{3 i a^2 b d (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^2}+\frac{3 a^2 b d^2 \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^3}-\frac{3 i a b^2 d^2 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^3}+\frac{i b^3 d (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^2}-\frac{b^3 d^2 \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^3}+\frac{3 a^2 b (c+d x)^2 \log \left(1-e^{2 i (e+f x)}\right)}{f}-\frac{i 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 i (e+f x)}\right)}{f^2}-\frac{3 a b^2 (c+d x)^2 \cot (e+f x)}{f}-\frac{3 i a b^2 (c+d x)^2}{f}-\frac{a b^2 (c+d x)^3}{d}-\frac{b^3 d (c+d x) \cot (e+f x)}{f^2}-\frac{b^3 (c+d x)^2 \log \left(1-e^{2 i (e+f x)}\right)}{f}-\frac{b^3 (c+d x)^2 \cot ^2(e+f x)}{2 f}-\frac{b^3 c d x}{f}+\frac{i b^3 (c+d x)^3}{3 d}+\frac{b^3 d^2 \log (\sin (e+f x))}{f^3}-\frac{b^3 d^2 x^2}{2 f}","-\frac{3 i a^2 b d (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^2}+\frac{3 a^2 b d^2 \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^3}-\frac{3 i a b^2 d^2 \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^3}+\frac{i b^3 d (c+d x) \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{f^2}-\frac{b^3 d^2 \text{PolyLog}\left(3,e^{2 i (e+f x)}\right)}{2 f^3}+\frac{3 a^2 b (c+d x)^2 \log \left(1-e^{2 i (e+f x)}\right)}{f}-\frac{i 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 i (e+f x)}\right)}{f^2}-\frac{3 a b^2 (c+d x)^2 \cot (e+f x)}{f}-\frac{3 i a b^2 (c+d x)^2}{f}-\frac{a b^2 (c+d x)^3}{d}-\frac{b^3 d (c+d x) \cot (e+f x)}{f^2}-\frac{b^3 (c+d x)^2 \log \left(1-e^{2 i (e+f x)}\right)}{f}-\frac{b^3 (c+d x)^2 \cot ^2(e+f x)}{2 f}-\frac{b^3 c d x}{f}+\frac{i b^3 (c+d x)^3}{3 d}+\frac{b^3 d^2 \log (\sin (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*I)*a*b^2*(c + d*x)^2)/f + (a^3*(c + d*x)^3)/(3*d) - (I*a^2*b*(c + d*x)^3)/d - (a*b^2*(c + d*x)^3)/d + ((I/3)*b^3*(c + d*x)^3)/d - (b^3*d*(c + d*x)*Cot[e + f*x])/f^2 - (3*a*b^2*(c + d*x)^2*Cot[e + f*x])/f - (b^3*(c + d*x)^2*Cot[e + f*x]^2)/(2*f) + (6*a*b^2*d*(c + d*x)*Log[1 - E^((2*I)*(e + f*x))])/f^2 + (3*a^2*b*(c + d*x)^2*Log[1 - E^((2*I)*(e + f*x))])/f - (b^3*(c + d*x)^2*Log[1 - E^((2*I)*(e + f*x))])/f + (b^3*d^2*Log[Sin[e + f*x]])/f^3 - ((3*I)*a*b^2*d^2*PolyLog[2, E^((2*I)*(e + f*x))])/f^3 - ((3*I)*a^2*b*d*(c + d*x)*PolyLog[2, E^((2*I)*(e + f*x))])/f^2 + (I*b^3*d*(c + d*x)*PolyLog[2, E^((2*I)*(e + f*x))])/f^2 + (3*a^2*b*d^2*PolyLog[3, E^((2*I)*(e + f*x))])/(2*f^3) - (b^3*d^2*PolyLog[3, E^((2*I)*(e + f*x))])/(2*f^3)","A",22,11,20,0.5500,1,"{3722, 3717, 2190, 2531, 2282, 6589, 3720, 2279, 2391, 32, 3475}"
49,1,278,0,0.3227735,"\int (c+d x) (a+b \cot (e+f x))^3 \, dx","Int[(c + d*x)*(a + b*Cot[e + f*x])^3,x]","-\frac{3 i a^2 b d \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^2}+\frac{i b^3 d \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^2}+\frac{3 a^2 b (c+d x) \log \left(1-e^{2 i (e+f x)}\right)}{f}-\frac{3 i 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) \cot (e+f x)}{f}-3 a b^2 c x+\frac{3 a b^2 d \log (\sin (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 i (e+f x)}\right)}{f}-\frac{b^3 (c+d x) \cot ^2(e+f x)}{2 f}+\frac{i b^3 (c+d x)^2}{2 d}-\frac{b^3 d \cot (e+f x)}{2 f^2}-\frac{b^3 d x}{2 f}","-\frac{3 i a^2 b d \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^2}+\frac{i b^3 d \text{PolyLog}\left(2,e^{2 i (e+f x)}\right)}{2 f^2}+\frac{3 a^2 b (c+d x) \log \left(1-e^{2 i (e+f x)}\right)}{f}-\frac{3 i 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) \cot (e+f x)}{f}-3 a b^2 c x+\frac{3 a b^2 d \log (\sin (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 i (e+f x)}\right)}{f}-\frac{b^3 (c+d x) \cot ^2(e+f x)}{2 f}+\frac{i b^3 (c+d x)^2}{2 d}-\frac{b^3 d \cot (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*I)/2)*a^2*b*(c + d*x)^2)/d + ((I/2)*b^3*(c + d*x)^2)/d - (b^3*d*Cot[e + f*x])/(2*f^2) - (3*a*b^2*(c + d*x)*Cot[e + f*x])/f - (b^3*(c + d*x)*Cot[e + f*x]^2)/(2*f) + (3*a^2*b*(c + d*x)*Log[1 - E^((2*I)*(e + f*x))])/f - (b^3*(c + d*x)*Log[1 - E^((2*I)*(e + f*x))])/f + (3*a*b^2*d*Log[Sin[e + f*x]])/f^2 - (((3*I)/2)*a^2*b*d*PolyLog[2, E^((2*I)*(e + f*x))])/f^2 + ((I/2)*b^3*d*PolyLog[2, E^((2*I)*(e + f*x))])/f^2","A",16,9,18,0.5000,1,"{3722, 3717, 2190, 2279, 2391, 3720, 3475, 3473, 8}"
50,0,0,0,0.0529378,"\int \frac{(a+b \cot (e+f x))^3}{c+d x} \, dx","Int[(a + b*Cot[e + f*x])^3/(c + d*x),x]","\int \frac{(a+b \cot (e+f x))^3}{c+d x} \, dx","\text{Int}\left(\frac{(a+b \cot (e+f x))^3}{c+d x},x\right)",0,"Defer[Int][(a + b*Cot[e + f*x])^3/(c + d*x), x]","A",0,0,0,0,-1,"{}"
51,0,0,0,0.0510741,"\int \frac{(a+b \cot (e+f x))^3}{(c+d x)^2} \, dx","Int[(a + b*Cot[e + f*x])^3/(c + d*x)^2,x]","\int \frac{(a+b \cot (e+f x))^3}{(c+d x)^2} \, dx","\text{Int}\left(\frac{(a+b \cot (e+f x))^3}{(c+d x)^2},x\right)",0,"Defer[Int][(a + b*Cot[e + f*x])^3/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
52,1,242,0,0.3411943,"\int \frac{(c+d x)^3}{a+b \cot (e+f x)} \, dx","Int[(c + d*x)^3/(a + b*Cot[e + f*x]),x]","-\frac{3 b d^2 (c+d x) \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{2 f^3 \left(a^2+b^2\right)}+\frac{3 i b d (c+d x)^2 \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{2 f^2 \left(a^2+b^2\right)}-\frac{3 i b d^3 \text{PolyLog}\left(4,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{4 f^4 \left(a^2+b^2\right)}-\frac{b (c+d x)^3 \log \left(1-\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{f \left(a^2+b^2\right)}+\frac{(c+d x)^4}{4 d (a-i b)}","-\frac{3 b d^2 (c+d x) \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{2 f^3 \left(a^2+b^2\right)}+\frac{3 i b d (c+d x)^2 \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{2 f^2 \left(a^2+b^2\right)}-\frac{3 i b d^3 \text{PolyLog}\left(4,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{4 f^4 \left(a^2+b^2\right)}-\frac{b (c+d x)^3 \log \left(1-\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{f \left(a^2+b^2\right)}+\frac{(c+d x)^4}{4 d (a-i b)}",1,"(c + d*x)^4/(4*(a - I*b)*d) - (b*(c + d*x)^3*Log[1 - ((a + I*b)*E^((2*I)*(e + f*x)))/(a - I*b)])/((a^2 + b^2)*f) + (((3*I)/2)*b*d*(c + d*x)^2*PolyLog[2, ((a + I*b)*E^((2*I)*(e + f*x)))/(a - I*b)])/((a^2 + b^2)*f^2) - (3*b*d^2*(c + d*x)*PolyLog[3, ((a + I*b)*E^((2*I)*(e + f*x)))/(a - I*b)])/(2*(a^2 + b^2)*f^3) - (((3*I)/4)*b*d^3*PolyLog[4, ((a + I*b)*E^((2*I)*(e + f*x)))/(a - I*b)])/((a^2 + b^2)*f^4)","A",6,6,20,0.3000,1,"{3731, 2190, 2531, 6609, 2282, 6589}"
53,1,181,0,0.2881923,"\int \frac{(c+d x)^2}{a+b \cot (e+f x)} \, dx","Int[(c + d*x)^2/(a + b*Cot[e + f*x]),x]","\frac{i b d (c+d x) \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{f^2 \left(a^2+b^2\right)}-\frac{b d^2 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{2 f^3 \left(a^2+b^2\right)}-\frac{b (c+d x)^2 \log \left(1-\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{f \left(a^2+b^2\right)}+\frac{(c+d x)^3}{3 d (a-i b)}","\frac{i b d (c+d x) \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{f^2 \left(a^2+b^2\right)}-\frac{b d^2 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{2 f^3 \left(a^2+b^2\right)}-\frac{b (c+d x)^2 \log \left(1-\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{f \left(a^2+b^2\right)}+\frac{(c+d x)^3}{3 d (a-i b)}",1,"(c + d*x)^3/(3*(a - I*b)*d) - (b*(c + d*x)^2*Log[1 - ((a + I*b)*E^((2*I)*(e + f*x)))/(a - I*b)])/((a^2 + b^2)*f) + (I*b*d*(c + d*x)*PolyLog[2, ((a + I*b)*E^((2*I)*(e + f*x)))/(a - I*b)])/((a^2 + b^2)*f^2) - (b*d^2*PolyLog[3, ((a + I*b)*E^((2*I)*(e + f*x)))/(a - I*b)])/(2*(a^2 + b^2)*f^3)","A",5,5,20,0.2500,1,"{3731, 2190, 2531, 2282, 6589}"
54,1,126,0,0.1623683,"\int \frac{c+d x}{a+b \cot (e+f x)} \, dx","Int[(c + d*x)/(a + b*Cot[e + f*x]),x]","\frac{i b d \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{2 f^2 \left(a^2+b^2\right)}-\frac{b (c+d x) \log \left(1-\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{f \left(a^2+b^2\right)}+\frac{(c+d x)^2}{2 d (a-i b)}","\frac{i b d \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{2 f^2 \left(a^2+b^2\right)}-\frac{b (c+d x) \log \left(1-\frac{(a+i b) e^{2 i (e+f x)}}{a-i b}\right)}{f \left(a^2+b^2\right)}+\frac{(c+d x)^2}{2 d (a-i b)}",1,"(c + d*x)^2/(2*(a - I*b)*d) - (b*(c + d*x)*Log[1 - ((a + I*b)*E^((2*I)*(e + f*x)))/(a - I*b)])/((a^2 + b^2)*f) + ((I/2)*b*d*PolyLog[2, ((a + I*b)*E^((2*I)*(e + f*x)))/(a - I*b)])/((a^2 + b^2)*f^2)","A",4,4,18,0.2222,1,"{3731, 2190, 2279, 2391}"
55,0,0,0,0.0638416,"\int \frac{1}{(c+d x) (a+b \cot (e+f x))} \, dx","Int[1/((c + d*x)*(a + b*Cot[e + f*x])),x]","\int \frac{1}{(c+d x) (a+b \cot (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \cot (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)*(a + b*Cot[e + f*x])), x]","A",0,0,0,0,-1,"{}"
56,0,0,0,0.0586164,"\int \frac{1}{(c+d x)^2 (a+b \cot (e+f x))} \, dx","Int[1/((c + d*x)^2*(a + b*Cot[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+b \cot (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \cot (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + b*Cot[e + f*x])), x]","A",0,0,0,0,-1,"{}"
57,1,839,0,1.9686912,"\int \frac{(c+d x)^3}{(a+b \cot (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + b*Cot[e + f*x])^2,x]","-\frac{b (c+d x)^4}{(a+i b)^2 (i a+b) d}+\frac{(c+d x)^4}{4 (a+i b)^2 d}-\frac{b^2 (c+d x)^4}{\left(a^2+b^2\right)^2 d}-\frac{2 b \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)^3}{(a-i b) (a+i b)^2 f}-\frac{2 i b^2 \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)^3}{\left(a^2+b^2\right)^2 f}-\frac{2 b^2 (c+d x)^3}{(a-i b) (a+i b)^2 \left(i a-(i a-b) e^{2 i e+2 i f x}+b\right) f}-\frac{2 i b^2 (c+d x)^3}{\left(a^2+b^2\right)^2 f}+\frac{3 b^2 d \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)^2}{\left(a^2+b^2\right)^2 f^2}-\frac{3 b d \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)^2}{(a+i b)^2 (i a+b) f^2}-\frac{3 b^2 d \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)^2}{\left(a^2+b^2\right)^2 f^2}-\frac{3 i b^2 d^2 \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)}{\left(a^2+b^2\right)^2 f^3}-\frac{3 b d^2 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)}{(a-i b) (a+i b)^2 f^3}-\frac{3 i b^2 d^2 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)}{\left(a^2+b^2\right)^2 f^3}+\frac{3 b^2 d^3 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{2 \left(a^2+b^2\right)^2 f^4}+\frac{3 b d^3 \text{PolyLog}\left(4,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{2 (a+i b)^2 (i a+b) f^4}+\frac{3 b^2 d^3 \text{PolyLog}\left(4,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{2 \left(a^2+b^2\right)^2 f^4}","-\frac{b (c+d x)^4}{(a+i b)^2 (i a+b) d}+\frac{(c+d x)^4}{4 (a+i b)^2 d}-\frac{b^2 (c+d x)^4}{\left(a^2+b^2\right)^2 d}-\frac{2 b \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)^3}{(a-i b) (a+i b)^2 f}-\frac{2 i b^2 \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)^3}{\left(a^2+b^2\right)^2 f}-\frac{2 b^2 (c+d x)^3}{(a-i b) (a+i b)^2 \left(i a-(i a-b) e^{2 i e+2 i f x}+b\right) f}-\frac{2 i b^2 (c+d x)^3}{\left(a^2+b^2\right)^2 f}+\frac{3 b^2 d \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)^2}{\left(a^2+b^2\right)^2 f^2}-\frac{3 b d \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)^2}{(a+i b)^2 (i a+b) f^2}-\frac{3 b^2 d \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)^2}{\left(a^2+b^2\right)^2 f^2}-\frac{3 i b^2 d^2 \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)}{\left(a^2+b^2\right)^2 f^3}-\frac{3 b d^2 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)}{(a-i b) (a+i b)^2 f^3}-\frac{3 i b^2 d^2 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right) (c+d x)}{\left(a^2+b^2\right)^2 f^3}+\frac{3 b^2 d^3 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{2 \left(a^2+b^2\right)^2 f^4}+\frac{3 b d^3 \text{PolyLog}\left(4,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{2 (a+i b)^2 (i a+b) f^4}+\frac{3 b^2 d^3 \text{PolyLog}\left(4,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{2 \left(a^2+b^2\right)^2 f^4}",1,"((-2*I)*b^2*(c + d*x)^3)/((a^2 + b^2)^2*f) - (2*b^2*(c + d*x)^3)/((a - I*b)*(a + I*b)^2*(I*a + b - (I*a - b)*E^((2*I)*e + (2*I)*f*x))*f) + (c + d*x)^4/(4*(a + I*b)^2*d) - (b*(c + d*x)^4)/((a + I*b)^2*(I*a + b)*d) - (b^2*(c + d*x)^4)/((a^2 + b^2)^2*d) + (3*b^2*d*(c + d*x)^2*Log[1 - ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a^2 + b^2)^2*f^2) - (2*b*(c + d*x)^3*Log[1 - ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a - I*b)*(a + I*b)^2*f) - ((2*I)*b^2*(c + d*x)^3*Log[1 - ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a^2 + b^2)^2*f) - ((3*I)*b^2*d^2*(c + d*x)*PolyLog[2, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a^2 + b^2)^2*f^3) - (3*b*d*(c + d*x)^2*PolyLog[2, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a + I*b)^2*(I*a + b)*f^2) - (3*b^2*d*(c + d*x)^2*PolyLog[2, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a^2 + b^2)^2*f^2) + (3*b^2*d^3*PolyLog[3, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/(2*(a^2 + b^2)^2*f^4) - (3*b*d^2*(c + d*x)*PolyLog[3, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a - I*b)*(a + I*b)^2*f^3) - ((3*I)*b^2*d^2*(c + d*x)*PolyLog[3, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a^2 + b^2)^2*f^3) + (3*b*d^3*PolyLog[4, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/(2*(a + I*b)^2*(I*a + b)*f^4) + (3*b^2*d^3*PolyLog[4, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/(2*(a^2 + b^2)^2*f^4)","A",21,9,20,0.4500,1,"{3734, 2185, 2184, 2190, 2531, 6609, 2282, 6589, 2191}"
58,1,650,0,1.4765287,"\int \frac{(c+d x)^2}{(a+b \cot (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + b*Cot[e + f*x])^2,x]","-\frac{2 b^2 d (c+d x) \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^2 \left(a^2+b^2\right)^2}-\frac{i b^2 d^2 \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^3 \left(a^2+b^2\right)^2}-\frac{i b^2 d^2 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^3 \left(a^2+b^2\right)^2}-\frac{2 b d (c+d x) \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^2 (a+i b)^2 (b+i a)}-\frac{b d^2 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^3 (a-i b) (a+i b)^2}+\frac{2 b^2 d (c+d x) \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^2 \left(a^2+b^2\right)^2}-\frac{2 i b^2 (c+d x)^2 \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f \left(a^2+b^2\right)^2}-\frac{2 i b^2 (c+d x)^2}{f \left(a^2+b^2\right)^2}-\frac{4 b^2 (c+d x)^3}{3 d \left(a^2+b^2\right)^2}-\frac{2 b^2 (c+d x)^2}{f (a-i b) (a+i b)^2 \left(-(-b+i a) e^{2 i e+2 i f x}+i a+b\right)}-\frac{2 b (c+d x)^2 \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f (a-i b) (a+i b)^2}-\frac{4 b (c+d x)^3}{3 d (a+i b)^2 (b+i a)}+\frac{(c+d x)^3}{3 d (a+i b)^2}","-\frac{2 b^2 d (c+d x) \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^2 \left(a^2+b^2\right)^2}-\frac{i b^2 d^2 \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^3 \left(a^2+b^2\right)^2}-\frac{i b^2 d^2 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^3 \left(a^2+b^2\right)^2}-\frac{2 b d (c+d x) \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^2 (a+i b)^2 (b+i a)}-\frac{b d^2 \text{PolyLog}\left(3,\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^3 (a-i b) (a+i b)^2}+\frac{2 b^2 d (c+d x) \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f^2 \left(a^2+b^2\right)^2}-\frac{2 i b^2 (c+d x)^2 \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f \left(a^2+b^2\right)^2}-\frac{2 i b^2 (c+d x)^2}{f \left(a^2+b^2\right)^2}-\frac{4 b^2 (c+d x)^3}{3 d \left(a^2+b^2\right)^2}-\frac{2 b^2 (c+d x)^2}{f (a-i b) (a+i b)^2 \left(-(-b+i a) e^{2 i e+2 i f x}+i a+b\right)}-\frac{2 b (c+d x)^2 \log \left(1-\frac{(a+i b) e^{2 i e+2 i f x}}{a-i b}\right)}{f (a-i b) (a+i b)^2}-\frac{4 b (c+d x)^3}{3 d (a+i b)^2 (b+i a)}+\frac{(c+d x)^3}{3 d (a+i b)^2}",1,"((-2*I)*b^2*(c + d*x)^2)/((a^2 + b^2)^2*f) - (2*b^2*(c + d*x)^2)/((a - I*b)*(a + I*b)^2*(I*a + b - (I*a - b)*E^((2*I)*e + (2*I)*f*x))*f) + (c + d*x)^3/(3*(a + I*b)^2*d) - (4*b*(c + d*x)^3)/(3*(a + I*b)^2*(I*a + b)*d) - (4*b^2*(c + d*x)^3)/(3*(a^2 + b^2)^2*d) + (2*b^2*d*(c + d*x)*Log[1 - ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a^2 + b^2)^2*f^2) - (2*b*(c + d*x)^2*Log[1 - ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a - I*b)*(a + I*b)^2*f) - ((2*I)*b^2*(c + d*x)^2*Log[1 - ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a^2 + b^2)^2*f) - (I*b^2*d^2*PolyLog[2, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a^2 + b^2)^2*f^3) - (2*b*d*(c + d*x)*PolyLog[2, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a + I*b)^2*(I*a + b)*f^2) - (2*b^2*d*(c + d*x)*PolyLog[2, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a^2 + b^2)^2*f^2) - (b*d^2*PolyLog[3, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a - I*b)*(a + I*b)^2*f^3) - (I*b^2*d^2*PolyLog[3, ((a + I*b)*E^((2*I)*e + (2*I)*f*x))/(a - I*b)])/((a^2 + b^2)^2*f^3)","A",18,10,20,0.5000,1,"{3734, 2185, 2184, 2190, 2531, 2282, 6589, 2191, 2279, 2391}"
59,1,213,0,0.2924669,"\int \frac{c+d x}{(a+b \cot (e+f x))^2} \, dx","Int[(c + d*x)/(a + b*Cot[e + f*x])^2,x]","\frac{i a b d \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i (e+f x)}}{a-i 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+i b) e^{2 i (e+f x)}}{a-i 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 \cot (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-i b)^2 (a+i b)}","\frac{i a b d \text{PolyLog}\left(2,\frac{(a+i b) e^{2 i (e+f x)}}{a-i 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+i b) e^{2 i (e+f x)}}{a-i 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 \cot (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-i b)^2 (a+i b)}",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 - I*b)^2*(a + I*b)*d*f^2) + (b*(c + d*x))/((a^2 + b^2)*f*(a + b*Cot[e + f*x])) + (b*(b*d - 2*a*c*f - 2*a*d*f*x)*Log[1 - ((a + I*b)*E^((2*I)*(e + f*x)))/(a - I*b)])/((a^2 + b^2)^2*f^2) + (I*a*b*d*PolyLog[2, ((a + I*b)*E^((2*I)*(e + f*x)))/(a - I*b)])/((a^2 + b^2)^2*f^2)","A",5,5,18,0.2778,1,"{3733, 3731, 2190, 2279, 2391}"
60,0,0,0,0.0594693,"\int \frac{1}{(c+d x) (a+b \cot (e+f x))^2} \, dx","Int[1/((c + d*x)*(a + b*Cot[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+b \cot (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \cot (e+f x))^2},x\right)",0,"Defer[Int][1/((c + d*x)*(a + b*Cot[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
61,0,0,0,0.0564359,"\int \frac{1}{(c+d x)^2 (a+b \cot (e+f x))^2} \, dx","Int[1/((c + d*x)^2*(a + b*Cot[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+b \cot (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \cot (e+f x))^2},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + b*Cot[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"