1,1,227,0,0.2047489,"\int (c+d x)^3 (a+a \sec (e+f x)) \, dx","Int[(c + d*x)^3*(a + a*Sec[e + f*x]),x]","-\frac{6 a d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{6 a d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{3 i a d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{3 i a d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{6 i a d^3 \text{PolyLog}\left(4,-i e^{i (e+f x)}\right)}{f^4}+\frac{6 i a d^3 \text{PolyLog}\left(4,i e^{i (e+f x)}\right)}{f^4}-\frac{2 i a (c+d x)^3 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a (c+d x)^4}{4 d}","-\frac{6 a d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{6 a d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{3 i a d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{3 i a d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{6 i a d^3 \text{PolyLog}\left(4,-i e^{i (e+f x)}\right)}{f^4}+\frac{6 i a d^3 \text{PolyLog}\left(4,i e^{i (e+f x)}\right)}{f^4}-\frac{2 i a (c+d x)^3 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a (c+d x)^4}{4 d}",1,"(a*(c + d*x)^4)/(4*d) - ((2*I)*a*(c + d*x)^3*ArcTan[E^(I*(e + f*x))])/f + ((3*I)*a*d*(c + d*x)^2*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - ((3*I)*a*d*(c + d*x)^2*PolyLog[2, I*E^(I*(e + f*x))])/f^2 - (6*a*d^2*(c + d*x)*PolyLog[3, (-I)*E^(I*(e + f*x))])/f^3 + (6*a*d^2*(c + d*x)*PolyLog[3, I*E^(I*(e + f*x))])/f^3 - ((6*I)*a*d^3*PolyLog[4, (-I)*E^(I*(e + f*x))])/f^4 + ((6*I)*a*d^3*PolyLog[4, I*E^(I*(e + f*x))])/f^4","A",11,6,18,0.3333,1,"{4190, 4181, 2531, 6609, 2282, 6589}"
2,1,157,0,0.14041,"\int (c+d x)^2 (a+a \sec (e+f x)) \, dx","Int[(c + d*x)^2*(a + a*Sec[e + f*x]),x]","\frac{2 i a d (c+d x) \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{2 i a d (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{2 a d^2 \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{2 a d^2 \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}-\frac{2 i a (c+d x)^2 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a (c+d x)^3}{3 d}","\frac{2 i a d (c+d x) \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{2 i a d (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{2 a d^2 \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{2 a d^2 \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}-\frac{2 i a (c+d x)^2 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a (c+d x)^3}{3 d}",1,"(a*(c + d*x)^3)/(3*d) - ((2*I)*a*(c + d*x)^2*ArcTan[E^(I*(e + f*x))])/f + ((2*I)*a*d*(c + d*x)*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - ((2*I)*a*d*(c + d*x)*PolyLog[2, I*E^(I*(e + f*x))])/f^2 - (2*a*d^2*PolyLog[3, (-I)*E^(I*(e + f*x))])/f^3 + (2*a*d^2*PolyLog[3, I*E^(I*(e + f*x))])/f^3","A",9,5,18,0.2778,1,"{4190, 4181, 2531, 2282, 6589}"
3,1,93,0,0.0673857,"\int (c+d x) (a+a \sec (e+f x)) \, dx","Int[(c + d*x)*(a + a*Sec[e + f*x]),x]","\frac{i a d \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{i a d \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{2 i a (c+d x) \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a (c+d x)^2}{2 d}","\frac{i a d \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{i a d \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{2 i a (c+d x) \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a (c+d x)^2}{2 d}",1,"(a*(c + d*x)^2)/(2*d) - ((2*I)*a*(c + d*x)*ArcTan[E^(I*(e + f*x))])/f + (I*a*d*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - (I*a*d*PolyLog[2, I*E^(I*(e + f*x))])/f^2","A",7,4,16,0.2500,1,"{4190, 4181, 2279, 2391}"
4,0,0,0,0.0273671,"\int \frac{a+a \sec (e+f x)}{c+d x} \, dx","Int[(a + a*Sec[e + f*x])/(c + d*x),x]","\int \frac{a+a \sec (e+f x)}{c+d x} \, dx","\text{Int}\left(\frac{a \sec (e+f x)+a}{c+d x},x\right)",0,"Defer[Int][(a + a*Sec[e + f*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
5,0,0,0,0.0263536,"\int \frac{a+a \sec (e+f x)}{(c+d x)^2} \, dx","Int[(a + a*Sec[e + f*x])/(c + d*x)^2,x]","\int \frac{a+a \sec (e+f x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{a \sec (e+f x)+a}{(c+d x)^2},x\right)",0,"Defer[Int][(a + a*Sec[e + f*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
6,1,371,0,0.443375,"\int (c+d x)^3 (a+a \sec (e+f x))^2 \, dx","Int[(c + d*x)^3*(a + a*Sec[e + f*x])^2,x]","-\frac{3 i a^2 d^2 (c+d x) \text{PolyLog}\left(2,-e^{2 i (e+f x)}\right)}{f^3}-\frac{12 a^2 d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{12 a^2 d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{6 i a^2 d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{6 i a^2 d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}+\frac{3 a^2 d^3 \text{PolyLog}\left(3,-e^{2 i (e+f x)}\right)}{2 f^4}-\frac{12 i a^2 d^3 \text{PolyLog}\left(4,-i e^{i (e+f x)}\right)}{f^4}+\frac{12 i a^2 d^3 \text{PolyLog}\left(4,i e^{i (e+f x)}\right)}{f^4}+\frac{3 a^2 d (c+d x)^2 \log \left(1+e^{2 i (e+f x)}\right)}{f^2}-\frac{4 i a^2 (c+d x)^3 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a^2 (c+d x)^3 \tan (e+f x)}{f}-\frac{i a^2 (c+d x)^3}{f}+\frac{a^2 (c+d x)^4}{4 d}","-\frac{3 i a^2 d^2 (c+d x) \text{PolyLog}\left(2,-e^{2 i (e+f x)}\right)}{f^3}-\frac{12 a^2 d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{12 a^2 d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{6 i a^2 d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{6 i a^2 d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}+\frac{3 a^2 d^3 \text{PolyLog}\left(3,-e^{2 i (e+f x)}\right)}{2 f^4}-\frac{12 i a^2 d^3 \text{PolyLog}\left(4,-i e^{i (e+f x)}\right)}{f^4}+\frac{12 i a^2 d^3 \text{PolyLog}\left(4,i e^{i (e+f x)}\right)}{f^4}+\frac{3 a^2 d (c+d x)^2 \log \left(1+e^{2 i (e+f x)}\right)}{f^2}-\frac{4 i a^2 (c+d x)^3 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a^2 (c+d x)^3 \tan (e+f x)}{f}-\frac{i a^2 (c+d x)^3}{f}+\frac{a^2 (c+d x)^4}{4 d}",1,"((-I)*a^2*(c + d*x)^3)/f + (a^2*(c + d*x)^4)/(4*d) - ((4*I)*a^2*(c + d*x)^3*ArcTan[E^(I*(e + f*x))])/f + (3*a^2*d*(c + d*x)^2*Log[1 + E^((2*I)*(e + f*x))])/f^2 + ((6*I)*a^2*d*(c + d*x)^2*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - ((6*I)*a^2*d*(c + d*x)^2*PolyLog[2, I*E^(I*(e + f*x))])/f^2 - ((3*I)*a^2*d^2*(c + d*x)*PolyLog[2, -E^((2*I)*(e + f*x))])/f^3 - (12*a^2*d^2*(c + d*x)*PolyLog[3, (-I)*E^(I*(e + f*x))])/f^3 + (12*a^2*d^2*(c + d*x)*PolyLog[3, I*E^(I*(e + f*x))])/f^3 + (3*a^2*d^3*PolyLog[3, -E^((2*I)*(e + f*x))])/(2*f^4) - ((12*I)*a^2*d^3*PolyLog[4, (-I)*E^(I*(e + f*x))])/f^4 + ((12*I)*a^2*d^3*PolyLog[4, I*E^(I*(e + f*x))])/f^4 + (a^2*(c + d*x)^3*Tan[e + f*x])/f","A",17,9,20,0.4500,1,"{4190, 4181, 2531, 6609, 2282, 6589, 4184, 3719, 2190}"
7,1,262,0,0.3130601,"\int (c+d x)^2 (a+a \sec (e+f x))^2 \, dx","Int[(c + d*x)^2*(a + a*Sec[e + f*x])^2,x]","\frac{4 i a^2 d (c+d x) \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{4 i a^2 d (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{i a^2 d^2 \text{PolyLog}\left(2,-e^{2 i (e+f x)}\right)}{f^3}-\frac{4 a^2 d^2 \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{4 a^2 d^2 \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{2 a^2 d (c+d x) \log \left(1+e^{2 i (e+f x)}\right)}{f^2}-\frac{4 i a^2 (c+d x)^2 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a^2 (c+d x)^2 \tan (e+f x)}{f}-\frac{i a^2 (c+d x)^2}{f}+\frac{a^2 (c+d x)^3}{3 d}","\frac{4 i a^2 d (c+d x) \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{4 i a^2 d (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{i a^2 d^2 \text{PolyLog}\left(2,-e^{2 i (e+f x)}\right)}{f^3}-\frac{4 a^2 d^2 \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{4 a^2 d^2 \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{2 a^2 d (c+d x) \log \left(1+e^{2 i (e+f x)}\right)}{f^2}-\frac{4 i a^2 (c+d x)^2 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a^2 (c+d x)^2 \tan (e+f x)}{f}-\frac{i a^2 (c+d x)^2}{f}+\frac{a^2 (c+d x)^3}{3 d}",1,"((-I)*a^2*(c + d*x)^2)/f + (a^2*(c + d*x)^3)/(3*d) - ((4*I)*a^2*(c + d*x)^2*ArcTan[E^(I*(e + f*x))])/f + (2*a^2*d*(c + d*x)*Log[1 + E^((2*I)*(e + f*x))])/f^2 + ((4*I)*a^2*d*(c + d*x)*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - ((4*I)*a^2*d*(c + d*x)*PolyLog[2, I*E^(I*(e + f*x))])/f^2 - (I*a^2*d^2*PolyLog[2, -E^((2*I)*(e + f*x))])/f^3 - (4*a^2*d^2*PolyLog[3, (-I)*E^(I*(e + f*x))])/f^3 + (4*a^2*d^2*PolyLog[3, I*E^(I*(e + f*x))])/f^3 + (a^2*(c + d*x)^2*Tan[e + f*x])/f","A",14,10,20,0.5000,1,"{4190, 4181, 2531, 2282, 6589, 4184, 3719, 2190, 2279, 2391}"
8,1,134,0,0.1146318,"\int (c+d x) (a+a \sec (e+f x))^2 \, dx","Int[(c + d*x)*(a + a*Sec[e + f*x])^2,x]","\frac{2 i a^2 d \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{2 i a^2 d \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{4 i a^2 (c+d x) \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a^2 (c+d x) \tan (e+f x)}{f}+\frac{a^2 (c+d x)^2}{2 d}+\frac{a^2 d \log (\cos (e+f x))}{f^2}","\frac{2 i a^2 d \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{2 i a^2 d \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{4 i a^2 (c+d x) \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{a^2 (c+d x) \tan (e+f x)}{f}+\frac{a^2 (c+d x)^2}{2 d}+\frac{a^2 d \log (\cos (e+f x))}{f^2}",1,"(a^2*(c + d*x)^2)/(2*d) - ((4*I)*a^2*(c + d*x)*ArcTan[E^(I*(e + f*x))])/f + (a^2*d*Log[Cos[e + f*x]])/f^2 + ((2*I)*a^2*d*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - ((2*I)*a^2*d*PolyLog[2, I*E^(I*(e + f*x))])/f^2 + (a^2*(c + d*x)*Tan[e + f*x])/f","A",9,6,18,0.3333,1,"{4190, 4181, 2279, 2391, 4184, 3475}"
9,0,0,0,0.0512894,"\int \frac{(a+a \sec (e+f x))^2}{c+d x} \, dx","Int[(a + a*Sec[e + f*x])^2/(c + d*x),x]","\int \frac{(a+a \sec (e+f x))^2}{c+d x} \, dx","\text{Int}\left(\frac{(a \sec (e+f x)+a)^2}{c+d x},x\right)",0,"Defer[Int][(a + a*Sec[e + f*x])^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
10,0,0,0,0.0480409,"\int \frac{(a+a \sec (e+f x))^2}{(c+d x)^2} \, dx","Int[(a + a*Sec[e + f*x])^2/(c + d*x)^2,x]","\int \frac{(a+a \sec (e+f x))^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{(a \sec (e+f x)+a)^2}{(c+d x)^2},x\right)",0,"Defer[Int][(a + a*Sec[e + f*x])^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
11,1,152,0,0.3288922,"\int \frac{(c+d x)^3}{a+a \sec (e+f x)} \, dx","Int[(c + d*x)^3/(a + a*Sec[e + f*x]),x]","\frac{12 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (e+f x)}\right)}{a f^3}-\frac{12 d^3 \text{PolyLog}\left(3,-e^{i (e+f x)}\right)}{a f^4}-\frac{6 d (c+d x)^2 \log \left(1+e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{i (c+d x)^3}{a f}+\frac{(c+d x)^4}{4 a d}","\frac{12 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (e+f x)}\right)}{a f^3}-\frac{12 d^3 \text{PolyLog}\left(3,-e^{i (e+f x)}\right)}{a f^4}-\frac{6 d (c+d x)^2 \log \left(1+e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{i (c+d x)^3}{a f}+\frac{(c+d x)^4}{4 a d}",1,"(I*(c + d*x)^3)/(a*f) + (c + d*x)^4/(4*a*d) - (6*d*(c + d*x)^2*Log[1 + E^(I*(e + f*x))])/(a*f^2) + ((12*I)*d^2*(c + d*x)*PolyLog[2, -E^(I*(e + f*x))])/(a*f^3) - (12*d^3*PolyLog[3, -E^(I*(e + f*x))])/(a*f^4) - ((c + d*x)^3*Tan[e/2 + (f*x)/2])/(a*f)","A",9,8,20,0.4000,1,"{4191, 3318, 4184, 3719, 2190, 2531, 2282, 6589}"
12,1,119,0,0.2454319,"\int \frac{(c+d x)^2}{a+a \sec (e+f x)} \, dx","Int[(c + d*x)^2/(a + a*Sec[e + f*x]),x]","\frac{4 i d^2 \text{PolyLog}\left(2,-e^{i (e+f x)}\right)}{a f^3}-\frac{4 d (c+d x) \log \left(1+e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{i (c+d x)^2}{a f}+\frac{(c+d x)^3}{3 a d}","\frac{4 i d^2 \text{PolyLog}\left(2,-e^{i (e+f x)}\right)}{a f^3}-\frac{4 d (c+d x) \log \left(1+e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{i (c+d x)^2}{a f}+\frac{(c+d x)^3}{3 a d}",1,"(I*(c + d*x)^2)/(a*f) + (c + d*x)^3/(3*a*d) - (4*d*(c + d*x)*Log[1 + E^(I*(e + f*x))])/(a*f^2) + ((4*I)*d^2*PolyLog[2, -E^(I*(e + f*x))])/(a*f^3) - ((c + d*x)^2*Tan[e/2 + (f*x)/2])/(a*f)","A",8,7,20,0.3500,1,"{4191, 3318, 4184, 3719, 2190, 2279, 2391}"
13,1,67,0,0.0971501,"\int \frac{c+d x}{a+a \sec (e+f x)} \, dx","Int[(c + d*x)/(a + a*Sec[e + f*x]),x]","-\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{(c+d x)^2}{2 a d}-\frac{2 d \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a f^2}","-\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{(c+d x)^2}{2 a d}-\frac{2 d \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a f^2}",1,"(c + d*x)^2/(2*a*d) - (2*d*Log[Cos[e/2 + (f*x)/2]])/(a*f^2) - ((c + d*x)*Tan[e/2 + (f*x)/2])/(a*f)","A",5,4,18,0.2222,1,"{4191, 3318, 4184, 3475}"
14,0,0,0,0.0577893,"\int \frac{1}{(c+d x) (a+a \sec (e+f x))} \, dx","Int[1/((c + d*x)*(a + a*Sec[e + f*x])),x]","\int \frac{1}{(c+d x) (a+a \sec (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a \sec (e+f x)+a)},x\right)",0,"Defer[Int][1/((c + d*x)*(a + a*Sec[e + f*x])), x]","A",0,0,0,0,-1,"{}"
15,0,0,0,0.0524957,"\int \frac{1}{(c+d x)^2 (a+a \sec (e+f x))} \, dx","Int[1/((c + d*x)^2*(a + a*Sec[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+a \sec (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a \sec (e+f x)+a)},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + a*Sec[e + f*x])), x]","A",0,0,0,0,-1,"{}"
16,1,288,0,0.7194614,"\int \frac{(c+d x)^3}{(a+a \sec (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + a*Sec[e + f*x])^2,x]","\frac{20 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (e+f x)}\right)}{a^2 f^3}-\frac{20 d^3 \text{PolyLog}\left(3,-e^{i (e+f x)}\right)}{a^2 f^4}+\frac{2 d^2 (c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a^2 f^3}-\frac{10 d (c+d x)^2 \log \left(1+e^{i (e+f x)}\right)}{a^2 f^2}-\frac{d (c+d x)^2 \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{2 a^2 f^2}-\frac{5 (c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}+\frac{5 i (c+d x)^3}{3 a^2 f}+\frac{(c+d x)^4}{4 a^2 d}+\frac{4 d^3 \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a^2 f^4}","\frac{20 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (e+f x)}\right)}{a^2 f^3}-\frac{20 d^3 \text{PolyLog}\left(3,-e^{i (e+f x)}\right)}{a^2 f^4}+\frac{2 d^2 (c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a^2 f^3}-\frac{10 d (c+d x)^2 \log \left(1+e^{i (e+f x)}\right)}{a^2 f^2}-\frac{d (c+d x)^2 \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{2 a^2 f^2}-\frac{5 (c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}+\frac{5 i (c+d x)^3}{3 a^2 f}+\frac{(c+d x)^4}{4 a^2 d}+\frac{4 d^3 \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a^2 f^4}",1,"(((5*I)/3)*(c + d*x)^3)/(a^2*f) + (c + d*x)^4/(4*a^2*d) - (10*d*(c + d*x)^2*Log[1 + E^(I*(e + f*x))])/(a^2*f^2) + (4*d^3*Log[Cos[e/2 + (f*x)/2]])/(a^2*f^4) + ((20*I)*d^2*(c + d*x)*PolyLog[2, -E^(I*(e + f*x))])/(a^2*f^3) - (20*d^3*PolyLog[3, -E^(I*(e + f*x))])/(a^2*f^4) - (d*(c + d*x)^2*Sec[e/2 + (f*x)/2]^2)/(2*a^2*f^2) + (2*d^2*(c + d*x)*Tan[e/2 + (f*x)/2])/(a^2*f^3) - (5*(c + d*x)^3*Tan[e/2 + (f*x)/2])/(3*a^2*f) + ((c + d*x)^3*Sec[e/2 + (f*x)/2]^2*Tan[e/2 + (f*x)/2])/(6*a^2*f)","A",19,10,20,0.5000,1,"{4191, 3318, 4186, 4184, 3475, 3719, 2190, 2531, 2282, 6589}"
17,1,229,0,0.4982579,"\int \frac{(c+d x)^2}{(a+a \sec (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + a*Sec[e + f*x])^2,x]","\frac{20 i d^2 \text{PolyLog}\left(2,-e^{i (e+f x)}\right)}{3 a^2 f^3}-\frac{20 d (c+d x) \log \left(1+e^{i (e+f x)}\right)}{3 a^2 f^2}-\frac{d (c+d x) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f^2}-\frac{5 (c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}+\frac{5 i (c+d x)^2}{3 a^2 f}+\frac{(c+d x)^3}{3 a^2 d}+\frac{2 d^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f^3}","\frac{20 i d^2 \text{PolyLog}\left(2,-e^{i (e+f x)}\right)}{3 a^2 f^3}-\frac{20 d (c+d x) \log \left(1+e^{i (e+f x)}\right)}{3 a^2 f^2}-\frac{d (c+d x) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f^2}-\frac{5 (c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}+\frac{5 i (c+d x)^2}{3 a^2 f}+\frac{(c+d x)^3}{3 a^2 d}+\frac{2 d^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f^3}",1,"(((5*I)/3)*(c + d*x)^2)/(a^2*f) + (c + d*x)^3/(3*a^2*d) - (20*d*(c + d*x)*Log[1 + E^(I*(e + f*x))])/(3*a^2*f^2) + (((20*I)/3)*d^2*PolyLog[2, -E^(I*(e + f*x))])/(a^2*f^3) - (d*(c + d*x)*Sec[e/2 + (f*x)/2]^2)/(3*a^2*f^2) + (2*d^2*Tan[e/2 + (f*x)/2])/(3*a^2*f^3) - (5*(c + d*x)^2*Tan[e/2 + (f*x)/2])/(3*a^2*f) + ((c + d*x)^2*Sec[e/2 + (f*x)/2]^2*Tan[e/2 + (f*x)/2])/(6*a^2*f)","A",17,10,20,0.5000,1,"{4191, 3318, 4186, 3767, 8, 4184, 3719, 2190, 2279, 2391}"
18,1,140,0,0.1964298,"\int \frac{c+d x}{(a+a \sec (e+f x))^2} \, dx","Int[(c + d*x)/(a + a*Sec[e + f*x])^2,x]","-\frac{5 (c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}+\frac{(c+d x)^2}{2 a^2 d}-\frac{d \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f^2}-\frac{10 d \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 a^2 f^2}","-\frac{5 (c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}+\frac{(c+d x)^2}{2 a^2 d}-\frac{d \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f^2}-\frac{10 d \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 a^2 f^2}",1,"(c + d*x)^2/(2*a^2*d) - (10*d*Log[Cos[e/2 + (f*x)/2]])/(3*a^2*f^2) - (d*Sec[e/2 + (f*x)/2]^2)/(6*a^2*f^2) - (5*(c + d*x)*Tan[e/2 + (f*x)/2])/(3*a^2*f) + ((c + d*x)*Sec[e/2 + (f*x)/2]^2*Tan[e/2 + (f*x)/2])/(6*a^2*f)","A",9,5,18,0.2778,1,"{4191, 3318, 4185, 4184, 3475}"
19,0,0,0,0.0551167,"\int \frac{1}{(c+d x) (a+a \sec (e+f x))^2} \, dx","Int[1/((c + d*x)*(a + a*Sec[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+a \sec (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a \sec (e+f x)+a)^2},x\right)",0,"Defer[Int][1/((c + d*x)*(a + a*Sec[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
20,0,0,0,0.0518937,"\int \frac{1}{(c+d x)^2 (a+a \sec (e+f x))^2} \, dx","Int[1/((c + d*x)^2*(a + a*Sec[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+a \sec (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a \sec (e+f x)+a)^2},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + a*Sec[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
21,0,0,0,0.047402,"\int (c+d x)^m (a+a \sec (e+f x))^n \, dx","Int[(c + d*x)^m*(a + a*Sec[e + f*x])^n,x]","\int (c+d x)^m (a+a \sec (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (a \sec (e+f x)+a)^n,x\right)",0,"Defer[Int][(c + d*x)^m*(a + a*Sec[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
22,0,0,0,0.0254953,"\int (c+d x)^m (a+a \sec (e+f x)) \, dx","Int[(c + d*x)^m*(a + a*Sec[e + f*x]),x]","\int (c+d x)^m (a+a \sec (e+f x)) \, dx","\text{Int}\left((c+d x)^m (a \sec (e+f x)+a),x\right)",0,"Defer[Int][(c + d*x)^m*(a + a*Sec[e + f*x]), x]","A",0,0,0,0,-1,"{}"
23,0,0,0,0.0532764,"\int \frac{(c+d x)^m}{a+a \sec (e+f x)} \, dx","Int[(c + d*x)^m/(a + a*Sec[e + f*x]),x]","\int \frac{(c+d x)^m}{a+a \sec (e+f x)} \, dx","\text{Int}\left(\frac{(c+d x)^m}{a \sec (e+f x)+a},x\right)",0,"Defer[Int][(c + d*x)^m/(a + a*Sec[e + f*x]), x]","A",0,0,0,0,-1,"{}"
24,1,227,0,0.2125372,"\int (c+d x)^3 (a+b \sec (e+f x)) \, dx","Int[(c + d*x)^3*(a + b*Sec[e + f*x]),x]","-\frac{6 b d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{6 b d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{3 i b d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{3 i b d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{6 i b d^3 \text{PolyLog}\left(4,-i e^{i (e+f x)}\right)}{f^4}+\frac{6 i b d^3 \text{PolyLog}\left(4,i e^{i (e+f x)}\right)}{f^4}+\frac{a (c+d x)^4}{4 d}-\frac{2 i b (c+d x)^3 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}","-\frac{6 b d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{6 b d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{3 i b d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{3 i b d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{6 i b d^3 \text{PolyLog}\left(4,-i e^{i (e+f x)}\right)}{f^4}+\frac{6 i b d^3 \text{PolyLog}\left(4,i e^{i (e+f x)}\right)}{f^4}+\frac{a (c+d x)^4}{4 d}-\frac{2 i b (c+d x)^3 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}",1,"(a*(c + d*x)^4)/(4*d) - ((2*I)*b*(c + d*x)^3*ArcTan[E^(I*(e + f*x))])/f + ((3*I)*b*d*(c + d*x)^2*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - ((3*I)*b*d*(c + d*x)^2*PolyLog[2, I*E^(I*(e + f*x))])/f^2 - (6*b*d^2*(c + d*x)*PolyLog[3, (-I)*E^(I*(e + f*x))])/f^3 + (6*b*d^2*(c + d*x)*PolyLog[3, I*E^(I*(e + f*x))])/f^3 - ((6*I)*b*d^3*PolyLog[4, (-I)*E^(I*(e + f*x))])/f^4 + ((6*I)*b*d^3*PolyLog[4, I*E^(I*(e + f*x))])/f^4","A",11,6,18,0.3333,1,"{4190, 4181, 2531, 6609, 2282, 6589}"
25,1,157,0,0.1405719,"\int (c+d x)^2 (a+b \sec (e+f x)) \, dx","Int[(c + d*x)^2*(a + b*Sec[e + f*x]),x]","\frac{2 i b d (c+d x) \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{2 i b d (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{2 b d^2 \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{2 b d^2 \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{a (c+d x)^3}{3 d}-\frac{2 i b (c+d x)^2 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}","\frac{2 i b d (c+d x) \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{2 i b d (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{2 b d^2 \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{2 b d^2 \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{a (c+d x)^3}{3 d}-\frac{2 i b (c+d x)^2 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}",1,"(a*(c + d*x)^3)/(3*d) - ((2*I)*b*(c + d*x)^2*ArcTan[E^(I*(e + f*x))])/f + ((2*I)*b*d*(c + d*x)*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - ((2*I)*b*d*(c + d*x)*PolyLog[2, I*E^(I*(e + f*x))])/f^2 - (2*b*d^2*PolyLog[3, (-I)*E^(I*(e + f*x))])/f^3 + (2*b*d^2*PolyLog[3, I*E^(I*(e + f*x))])/f^3","A",9,5,18,0.2778,1,"{4190, 4181, 2531, 2282, 6589}"
26,1,93,0,0.0708628,"\int (c+d x) (a+b \sec (e+f x)) \, dx","Int[(c + d*x)*(a + b*Sec[e + f*x]),x]","\frac{i b d \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{i b d \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}+\frac{a (c+d x)^2}{2 d}-\frac{2 i b (c+d x) \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}","\frac{i b d \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{i b d \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}+\frac{a (c+d x)^2}{2 d}-\frac{2 i b (c+d x) \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}",1,"(a*(c + d*x)^2)/(2*d) - ((2*I)*b*(c + d*x)*ArcTan[E^(I*(e + f*x))])/f + (I*b*d*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - (I*b*d*PolyLog[2, I*E^(I*(e + f*x))])/f^2","A",7,4,16,0.2500,1,"{4190, 4181, 2279, 2391}"
27,0,0,0,0.0278883,"\int \frac{a+b \sec (e+f x)}{c+d x} \, dx","Int[(a + b*Sec[e + f*x])/(c + d*x),x]","\int \frac{a+b \sec (e+f x)}{c+d x} \, dx","\text{Int}\left(\frac{a+b \sec (e+f x)}{c+d x},x\right)",0,"Defer[Int][(a + b*Sec[e + f*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
28,0,0,0,0.0275481,"\int \frac{a+b \sec (e+f x)}{(c+d x)^2} \, dx","Int[(a + b*Sec[e + f*x])/(c + d*x)^2,x]","\int \frac{a+b \sec (e+f x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{a+b \sec (e+f x)}{(c+d x)^2},x\right)",0,"Defer[Int][(a + b*Sec[e + f*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
29,1,364,0,0.4547568,"\int (c+d x)^3 (a+b \sec (e+f x))^2 \, dx","Int[(c + d*x)^3*(a + b*Sec[e + f*x])^2,x]","-\frac{12 a b d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{12 a b d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{6 i a b d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{6 i a b d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{12 i a b d^3 \text{PolyLog}\left(4,-i e^{i (e+f x)}\right)}{f^4}+\frac{12 i a b d^3 \text{PolyLog}\left(4,i e^{i (e+f x)}\right)}{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{4 i a b (c+d x)^3 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\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 \tan (e+f x)}{f}-\frac{i b^2 (c+d x)^3}{f}","-\frac{12 a b d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{12 a b d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{f^3}+\frac{6 i a b d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{6 i a b d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{12 i a b d^3 \text{PolyLog}\left(4,-i e^{i (e+f x)}\right)}{f^4}+\frac{12 i a b d^3 \text{PolyLog}\left(4,i e^{i (e+f x)}\right)}{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{4 i a b (c+d x)^3 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\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 \tan (e+f x)}{f}-\frac{i b^2 (c+d x)^3}{f}",1,"((-I)*b^2*(c + d*x)^3)/f + (a^2*(c + d*x)^4)/(4*d) - ((4*I)*a*b*(c + d*x)^3*ArcTan[E^(I*(e + f*x))])/f + (3*b^2*d*(c + d*x)^2*Log[1 + E^((2*I)*(e + f*x))])/f^2 + ((6*I)*a*b*d*(c + d*x)^2*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - ((6*I)*a*b*d*(c + d*x)^2*PolyLog[2, I*E^(I*(e + f*x))])/f^2 - ((3*I)*b^2*d^2*(c + d*x)*PolyLog[2, -E^((2*I)*(e + f*x))])/f^3 - (12*a*b*d^2*(c + d*x)*PolyLog[3, (-I)*E^(I*(e + f*x))])/f^3 + (12*a*b*d^2*(c + d*x)*PolyLog[3, I*E^(I*(e + f*x))])/f^3 + (3*b^2*d^3*PolyLog[3, -E^((2*I)*(e + f*x))])/(2*f^4) - ((12*I)*a*b*d^3*PolyLog[4, (-I)*E^(I*(e + f*x))])/f^4 + ((12*I)*a*b*d^3*PolyLog[4, I*E^(I*(e + f*x))])/f^4 + (b^2*(c + d*x)^3*Tan[e + f*x])/f","A",17,9,20,0.4500,1,"{4190, 4181, 2531, 6609, 2282, 6589, 4184, 3719, 2190}"
30,1,257,0,0.3076254,"\int (c+d x)^2 (a+b \sec (e+f x))^2 \, dx","Int[(c + d*x)^2*(a + b*Sec[e + f*x])^2,x]","\frac{4 i a b d (c+d x) \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{4 i a b d (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{4 a b d^2 \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{4 a b d^2 \text{PolyLog}\left(3,i e^{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{4 i a b (c+d x)^2 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\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 \tan (e+f x)}{f}-\frac{i b^2 (c+d x)^2}{f}","\frac{4 i a b d (c+d x) \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{4 i a b d (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}-\frac{4 a b d^2 \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{f^3}+\frac{4 a b d^2 \text{PolyLog}\left(3,i e^{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{4 i a b (c+d x)^2 \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\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 \tan (e+f x)}{f}-\frac{i b^2 (c+d x)^2}{f}",1,"((-I)*b^2*(c + d*x)^2)/f + (a^2*(c + d*x)^3)/(3*d) - ((4*I)*a*b*(c + d*x)^2*ArcTan[E^(I*(e + f*x))])/f + (2*b^2*d*(c + d*x)*Log[1 + E^((2*I)*(e + f*x))])/f^2 + ((4*I)*a*b*d*(c + d*x)*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - ((4*I)*a*b*d*(c + d*x)*PolyLog[2, I*E^(I*(e + f*x))])/f^2 - (I*b^2*d^2*PolyLog[2, -E^((2*I)*(e + f*x))])/f^3 - (4*a*b*d^2*PolyLog[3, (-I)*E^(I*(e + f*x))])/f^3 + (4*a*b*d^2*PolyLog[3, I*E^(I*(e + f*x))])/f^3 + (b^2*(c + d*x)^2*Tan[e + f*x])/f","A",14,10,20,0.5000,1,"{4190, 4181, 2531, 2282, 6589, 4184, 3719, 2190, 2279, 2391}"
31,1,131,0,0.1200233,"\int (c+d x) (a+b \sec (e+f x))^2 \, dx","Int[(c + d*x)*(a + b*Sec[e + f*x])^2,x]","\frac{2 i a b d \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{2 i a b d \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}+\frac{a^2 (c+d x)^2}{2 d}-\frac{4 i a b (c+d x) \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{b^2 (c+d x) \tan (e+f x)}{f}+\frac{b^2 d \log (\cos (e+f x))}{f^2}","\frac{2 i a b d \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{f^2}-\frac{2 i a b d \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{f^2}+\frac{a^2 (c+d x)^2}{2 d}-\frac{4 i a b (c+d x) \tan ^{-1}\left(e^{i (e+f x)}\right)}{f}+\frac{b^2 (c+d x) \tan (e+f x)}{f}+\frac{b^2 d \log (\cos (e+f x))}{f^2}",1,"(a^2*(c + d*x)^2)/(2*d) - ((4*I)*a*b*(c + d*x)*ArcTan[E^(I*(e + f*x))])/f + (b^2*d*Log[Cos[e + f*x]])/f^2 + ((2*I)*a*b*d*PolyLog[2, (-I)*E^(I*(e + f*x))])/f^2 - ((2*I)*a*b*d*PolyLog[2, I*E^(I*(e + f*x))])/f^2 + (b^2*(c + d*x)*Tan[e + f*x])/f","A",9,6,18,0.3333,1,"{4190, 4181, 2279, 2391, 4184, 3475}"
32,0,0,0,0.0512833,"\int \frac{(a+b \sec (e+f x))^2}{c+d x} \, dx","Int[(a + b*Sec[e + f*x])^2/(c + d*x),x]","\int \frac{(a+b \sec (e+f x))^2}{c+d x} \, dx","\text{Int}\left(\frac{(a+b \sec (e+f x))^2}{c+d x},x\right)",0,"Defer[Int][(a + b*Sec[e + f*x])^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
33,0,0,0,0.0491141,"\int \frac{(a+b \sec (e+f x))^2}{(c+d x)^2} \, dx","Int[(a + b*Sec[e + f*x])^2/(c + d*x)^2,x]","\int \frac{(a+b \sec (e+f x))^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{(a+b \sec (e+f x))^2}{(c+d x)^2},x\right)",0,"Defer[Int][(a + b*Sec[e + f*x])^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
34,1,526,0,1.0434535,"\int \frac{(c+d x)^3}{a+b \sec (e+f x)} \, dx","Int[(c + d*x)^3/(a + b*Sec[e + f*x]),x]","\frac{6 i b d^2 (c+d x) \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^3 \sqrt{b^2-a^2}}-\frac{6 i b d^2 (c+d x) \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^3 \sqrt{b^2-a^2}}+\frac{3 b d (c+d x)^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^2 \sqrt{b^2-a^2}}-\frac{3 b d (c+d x)^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^2 \sqrt{b^2-a^2}}-\frac{6 b d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^4 \sqrt{b^2-a^2}}+\frac{6 b d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^4 \sqrt{b^2-a^2}}+\frac{i b (c+d x)^3 \log \left(1+\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f \sqrt{b^2-a^2}}-\frac{i b (c+d x)^3 \log \left(1+\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f \sqrt{b^2-a^2}}+\frac{(c+d x)^4}{4 a d}","\frac{6 i b d^2 (c+d x) \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^3 \sqrt{b^2-a^2}}-\frac{6 i b d^2 (c+d x) \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^3 \sqrt{b^2-a^2}}+\frac{3 b d (c+d x)^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^2 \sqrt{b^2-a^2}}-\frac{3 b d (c+d x)^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^2 \sqrt{b^2-a^2}}-\frac{6 b d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^4 \sqrt{b^2-a^2}}+\frac{6 b d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^4 \sqrt{b^2-a^2}}+\frac{i b (c+d x)^3 \log \left(1+\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f \sqrt{b^2-a^2}}-\frac{i b (c+d x)^3 \log \left(1+\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f \sqrt{b^2-a^2}}+\frac{(c+d x)^4}{4 a d}",1,"(c + d*x)^4/(4*a*d) + (I*b*(c + d*x)^3*Log[1 + (a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*f) - (I*b*(c + d*x)^3*Log[1 + (a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*f) + (3*b*d*(c + d*x)^2*PolyLog[2, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^2) - (3*b*d*(c + d*x)^2*PolyLog[2, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^2) + ((6*I)*b*d^2*(c + d*x)*PolyLog[3, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^3) - ((6*I)*b*d^2*(c + d*x)*PolyLog[3, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^3) - (6*b*d^3*PolyLog[4, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^4) + (6*b*d^3*PolyLog[4, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^4)","A",14,8,20,0.4000,1,"{4191, 3321, 2264, 2190, 2531, 6609, 2282, 6589}"
35,1,394,0,0.8674813,"\int \frac{(c+d x)^2}{a+b \sec (e+f x)} \, dx","Int[(c + d*x)^2/(a + b*Sec[e + f*x]),x]","\frac{2 b d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^2 \sqrt{b^2-a^2}}-\frac{2 b d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^2 \sqrt{b^2-a^2}}+\frac{2 i b d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^3 \sqrt{b^2-a^2}}-\frac{2 i b d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^3 \sqrt{b^2-a^2}}+\frac{i b (c+d x)^2 \log \left(1+\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f \sqrt{b^2-a^2}}-\frac{i b (c+d x)^2 \log \left(1+\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f \sqrt{b^2-a^2}}+\frac{(c+d x)^3}{3 a d}","\frac{2 b d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^2 \sqrt{b^2-a^2}}-\frac{2 b d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^2 \sqrt{b^2-a^2}}+\frac{2 i b d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^3 \sqrt{b^2-a^2}}-\frac{2 i b d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^3 \sqrt{b^2-a^2}}+\frac{i b (c+d x)^2 \log \left(1+\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f \sqrt{b^2-a^2}}-\frac{i b (c+d x)^2 \log \left(1+\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f \sqrt{b^2-a^2}}+\frac{(c+d x)^3}{3 a d}",1,"(c + d*x)^3/(3*a*d) + (I*b*(c + d*x)^2*Log[1 + (a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*f) - (I*b*(c + d*x)^2*Log[1 + (a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*f) + (2*b*d*(c + d*x)*PolyLog[2, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^2) - (2*b*d*(c + d*x)*PolyLog[2, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^2) + ((2*I)*b*d^2*PolyLog[3, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^3) - ((2*I)*b*d^2*PolyLog[3, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^3)","A",12,7,20,0.3500,1,"{4191, 3321, 2264, 2190, 2531, 2282, 6589}"
36,1,257,0,0.4902053,"\int \frac{c+d x}{a+b \sec (e+f x)} \, dx","Int[(c + d*x)/(a + b*Sec[e + f*x]),x]","\frac{b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^2 \sqrt{b^2-a^2}}-\frac{b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^2 \sqrt{b^2-a^2}}+\frac{i b (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f \sqrt{b^2-a^2}}-\frac{i b (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f \sqrt{b^2-a^2}}+\frac{(c+d x)^2}{2 a d}","\frac{b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f^2 \sqrt{b^2-a^2}}-\frac{b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f^2 \sqrt{b^2-a^2}}+\frac{i b (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a f \sqrt{b^2-a^2}}-\frac{i b (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a f \sqrt{b^2-a^2}}+\frac{(c+d x)^2}{2 a d}",1,"(c + d*x)^2/(2*a*d) + (I*b*(c + d*x)*Log[1 + (a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*f) - (I*b*(c + d*x)*Log[1 + (a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*f) + (b*d*PolyLog[2, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^2) - (b*d*PolyLog[2, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*f^2)","A",10,6,18,0.3333,1,"{4191, 3321, 2264, 2190, 2279, 2391}"
37,0,0,0,0.0585353,"\int \frac{1}{(c+d x) (a+b \sec (e+f x))} \, dx","Int[1/((c + d*x)*(a + b*Sec[e + f*x])),x]","\int \frac{1}{(c+d x) (a+b \sec (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \sec (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)*(a + b*Sec[e + f*x])), x]","A",0,0,0,0,-1,"{}"
38,0,0,0,0.0554454,"\int \frac{1}{(c+d x)^2 (a+b \sec (e+f x))} \, dx","Int[1/((c + d*x)^2*(a + b*Sec[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+b \sec (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \sec (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + b*Sec[e + f*x])), x]","A",0,0,0,0,-1,"{}"
39,1,1523,0,2.8091554,"\int \frac{(c+d x)^3}{(a+b \sec (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + b*Sec[e + f*x])^2,x]","\frac{(c+d x)^4}{4 a^2 d}+\frac{2 i b \log \left(\frac{e^{i (e+f x)} a}{b-\sqrt{b^2-a^2}}+1\right) (c+d x)^3}{a^2 \sqrt{b^2-a^2} f}-\frac{i b^3 \log \left(\frac{e^{i (e+f x)} a}{b-\sqrt{b^2-a^2}}+1\right) (c+d x)^3}{a^2 \left(b^2-a^2\right)^{3/2} f}-\frac{2 i b \log \left(\frac{e^{i (e+f x)} a}{b+\sqrt{b^2-a^2}}+1\right) (c+d x)^3}{a^2 \sqrt{b^2-a^2} f}+\frac{i b^3 \log \left(\frac{e^{i (e+f x)} a}{b+\sqrt{b^2-a^2}}+1\right) (c+d x)^3}{a^2 \left(b^2-a^2\right)^{3/2} f}+\frac{b^2 \sin (e+f x) (c+d x)^3}{a \left(a^2-b^2\right) f (b+a \cos (e+f x))}-\frac{i b^2 (c+d x)^3}{a^2 \left(a^2-b^2\right) f}+\frac{3 b^2 d \log \left(\frac{e^{i (e+f x)} a}{b-i \sqrt{a^2-b^2}}+1\right) (c+d x)^2}{a^2 \left(a^2-b^2\right) f^2}+\frac{3 b^2 d \log \left(\frac{e^{i (e+f x)} a}{b+i \sqrt{a^2-b^2}}+1\right) (c+d x)^2}{a^2 \left(a^2-b^2\right) f^2}+\frac{6 b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) (c+d x)^2}{a^2 \sqrt{b^2-a^2} f^2}-\frac{3 b^3 d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) (c+d x)^2}{a^2 \left(b^2-a^2\right)^{3/2} f^2}-\frac{6 b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) (c+d x)^2}{a^2 \sqrt{b^2-a^2} f^2}+\frac{3 b^3 d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) (c+d x)^2}{a^2 \left(b^2-a^2\right)^{3/2} f^2}-\frac{6 i b^2 d^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-i \sqrt{a^2-b^2}}\right) (c+d x)}{a^2 \left(a^2-b^2\right) f^3}-\frac{6 i b^2 d^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+i \sqrt{a^2-b^2}}\right) (c+d x)}{a^2 \left(a^2-b^2\right) f^3}+\frac{12 i b d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) (c+d x)}{a^2 \sqrt{b^2-a^2} f^3}-\frac{6 i b^3 d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) (c+d x)}{a^2 \left(b^2-a^2\right)^{3/2} f^3}-\frac{12 i b d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) (c+d x)}{a^2 \sqrt{b^2-a^2} f^3}+\frac{6 i b^3 d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) (c+d x)}{a^2 \left(b^2-a^2\right)^{3/2} f^3}+\frac{6 b^2 d^3 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) f^4}+\frac{6 b^2 d^3 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b+i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) f^4}-\frac{12 b d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} f^4}+\frac{6 b^3 d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} f^4}+\frac{12 b d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} f^4}-\frac{6 b^3 d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} f^4}","\frac{(c+d x)^4}{4 a^2 d}+\frac{2 i b \log \left(\frac{e^{i (e+f x)} a}{b-\sqrt{b^2-a^2}}+1\right) (c+d x)^3}{a^2 \sqrt{b^2-a^2} f}-\frac{i b^3 \log \left(\frac{e^{i (e+f x)} a}{b-\sqrt{b^2-a^2}}+1\right) (c+d x)^3}{a^2 \left(b^2-a^2\right)^{3/2} f}-\frac{2 i b \log \left(\frac{e^{i (e+f x)} a}{b+\sqrt{b^2-a^2}}+1\right) (c+d x)^3}{a^2 \sqrt{b^2-a^2} f}+\frac{i b^3 \log \left(\frac{e^{i (e+f x)} a}{b+\sqrt{b^2-a^2}}+1\right) (c+d x)^3}{a^2 \left(b^2-a^2\right)^{3/2} f}+\frac{b^2 \sin (e+f x) (c+d x)^3}{a \left(a^2-b^2\right) f (b+a \cos (e+f x))}-\frac{i b^2 (c+d x)^3}{a^2 \left(a^2-b^2\right) f}+\frac{3 b^2 d \log \left(\frac{e^{i (e+f x)} a}{b-i \sqrt{a^2-b^2}}+1\right) (c+d x)^2}{a^2 \left(a^2-b^2\right) f^2}+\frac{3 b^2 d \log \left(\frac{e^{i (e+f x)} a}{b+i \sqrt{a^2-b^2}}+1\right) (c+d x)^2}{a^2 \left(a^2-b^2\right) f^2}+\frac{6 b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) (c+d x)^2}{a^2 \sqrt{b^2-a^2} f^2}-\frac{3 b^3 d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) (c+d x)^2}{a^2 \left(b^2-a^2\right)^{3/2} f^2}-\frac{6 b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) (c+d x)^2}{a^2 \sqrt{b^2-a^2} f^2}+\frac{3 b^3 d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) (c+d x)^2}{a^2 \left(b^2-a^2\right)^{3/2} f^2}-\frac{6 i b^2 d^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-i \sqrt{a^2-b^2}}\right) (c+d x)}{a^2 \left(a^2-b^2\right) f^3}-\frac{6 i b^2 d^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+i \sqrt{a^2-b^2}}\right) (c+d x)}{a^2 \left(a^2-b^2\right) f^3}+\frac{12 i b d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) (c+d x)}{a^2 \sqrt{b^2-a^2} f^3}-\frac{6 i b^3 d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) (c+d x)}{a^2 \left(b^2-a^2\right)^{3/2} f^3}-\frac{12 i b d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) (c+d x)}{a^2 \sqrt{b^2-a^2} f^3}+\frac{6 i b^3 d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) (c+d x)}{a^2 \left(b^2-a^2\right)^{3/2} f^3}+\frac{6 b^2 d^3 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) f^4}+\frac{6 b^2 d^3 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b+i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) f^4}-\frac{12 b d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} f^4}+\frac{6 b^3 d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} f^4}+\frac{12 b d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} f^4}-\frac{6 b^3 d^3 \text{PolyLog}\left(4,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} f^4}",1,"((-I)*b^2*(c + d*x)^3)/(a^2*(a^2 - b^2)*f) + (c + d*x)^4/(4*a^2*d) + (3*b^2*d*(c + d*x)^2*Log[1 + (a*E^(I*(e + f*x)))/(b - I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*f^2) + (3*b^2*d*(c + d*x)^2*Log[1 + (a*E^(I*(e + f*x)))/(b + I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*f^2) - (I*b^3*(c + d*x)^3*Log[1 + (a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*f) + ((2*I)*b*(c + d*x)^3*Log[1 + (a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*f) + (I*b^3*(c + d*x)^3*Log[1 + (a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*f) - ((2*I)*b*(c + d*x)^3*Log[1 + (a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*f) - ((6*I)*b^2*d^2*(c + d*x)*PolyLog[2, -((a*E^(I*(e + f*x)))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*f^3) - ((6*I)*b^2*d^2*(c + d*x)*PolyLog[2, -((a*E^(I*(e + f*x)))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*f^3) - (3*b^3*d*(c + d*x)^2*PolyLog[2, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^2) + (6*b*d*(c + d*x)^2*PolyLog[2, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^2) + (3*b^3*d*(c + d*x)^2*PolyLog[2, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^2) - (6*b*d*(c + d*x)^2*PolyLog[2, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^2) + (6*b^2*d^3*PolyLog[3, -((a*E^(I*(e + f*x)))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*f^4) + (6*b^2*d^3*PolyLog[3, -((a*E^(I*(e + f*x)))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*f^4) - ((6*I)*b^3*d^2*(c + d*x)*PolyLog[3, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^3) + ((12*I)*b*d^2*(c + d*x)*PolyLog[3, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^3) + ((6*I)*b^3*d^2*(c + d*x)*PolyLog[3, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^3) - ((12*I)*b*d^2*(c + d*x)*PolyLog[3, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^3) + (6*b^3*d^3*PolyLog[4, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^4) - (12*b*d^3*PolyLog[4, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^4) - (6*b^3*d^3*PolyLog[4, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^4) + (12*b*d^3*PolyLog[4, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^4) + (b^2*(c + d*x)^3*Sin[e + f*x])/(a*(a^2 - b^2)*f*(b + a*Cos[e + f*x]))","A",36,10,20,0.5000,1,"{4191, 3324, 3321, 2264, 2190, 2531, 6609, 2282, 6589, 4522}"
40,1,1117,0,2.1106293,"\int \frac{(c+d x)^2}{(a+b \sec (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + b*Sec[e + f*x])^2,x]","-\frac{i (c+d x)^2 \log \left(\frac{e^{i (e+f x)} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f}+\frac{i (c+d x)^2 \log \left(\frac{e^{i (e+f x)} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f}-\frac{2 d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f^2}+\frac{2 d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f^2}-\frac{2 i d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f^3}+\frac{2 i d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f^3}-\frac{i (c+d x)^2 b^2}{a^2 \left(a^2-b^2\right) f}+\frac{2 d (c+d x) \log \left(\frac{e^{i (e+f x)} a}{b-i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) f^2}+\frac{2 d (c+d x) \log \left(\frac{e^{i (e+f x)} a}{b+i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) f^2}-\frac{2 i d^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) f^3}-\frac{2 i d^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) f^3}+\frac{(c+d x)^2 \sin (e+f x) b^2}{a \left(a^2-b^2\right) f (b+a \cos (e+f x))}+\frac{2 i (c+d x)^2 \log \left(\frac{e^{i (e+f x)} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} f}-\frac{2 i (c+d x)^2 \log \left(\frac{e^{i (e+f x)} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} f}+\frac{4 d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} f^2}-\frac{4 d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} f^2}+\frac{4 i d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} f^3}-\frac{4 i d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} f^3}+\frac{(c+d x)^3}{3 a^2 d}","-\frac{i (c+d x)^2 \log \left(\frac{e^{i (e+f x)} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f}+\frac{i (c+d x)^2 \log \left(\frac{e^{i (e+f x)} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f}-\frac{2 d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f^2}+\frac{2 d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f^2}-\frac{2 i d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f^3}+\frac{2 i d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} f^3}-\frac{i (c+d x)^2 b^2}{a^2 \left(a^2-b^2\right) f}+\frac{2 d (c+d x) \log \left(\frac{e^{i (e+f x)} a}{b-i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) f^2}+\frac{2 d (c+d x) \log \left(\frac{e^{i (e+f x)} a}{b+i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) f^2}-\frac{2 i d^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) f^3}-\frac{2 i d^2 \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) f^3}+\frac{(c+d x)^2 \sin (e+f x) b^2}{a \left(a^2-b^2\right) f (b+a \cos (e+f x))}+\frac{2 i (c+d x)^2 \log \left(\frac{e^{i (e+f x)} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} f}-\frac{2 i (c+d x)^2 \log \left(\frac{e^{i (e+f x)} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} f}+\frac{4 d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} f^2}-\frac{4 d (c+d x) \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} f^2}+\frac{4 i d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} f^3}-\frac{4 i d^2 \text{PolyLog}\left(3,-\frac{a e^{i (e+f x)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} f^3}+\frac{(c+d x)^3}{3 a^2 d}",1,"((-I)*b^2*(c + d*x)^2)/(a^2*(a^2 - b^2)*f) + (c + d*x)^3/(3*a^2*d) + (2*b^2*d*(c + d*x)*Log[1 + (a*E^(I*(e + f*x)))/(b - I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*f^2) + (2*b^2*d*(c + d*x)*Log[1 + (a*E^(I*(e + f*x)))/(b + I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*f^2) - (I*b^3*(c + d*x)^2*Log[1 + (a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*f) + ((2*I)*b*(c + d*x)^2*Log[1 + (a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*f) + (I*b^3*(c + d*x)^2*Log[1 + (a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*f) - ((2*I)*b*(c + d*x)^2*Log[1 + (a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*f) - ((2*I)*b^2*d^2*PolyLog[2, -((a*E^(I*(e + f*x)))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*f^3) - ((2*I)*b^2*d^2*PolyLog[2, -((a*E^(I*(e + f*x)))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*f^3) - (2*b^3*d*(c + d*x)*PolyLog[2, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^2) + (4*b*d*(c + d*x)*PolyLog[2, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^2) + (2*b^3*d*(c + d*x)*PolyLog[2, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^2) - (4*b*d*(c + d*x)*PolyLog[2, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^2) - ((2*I)*b^3*d^2*PolyLog[3, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^3) + ((4*I)*b*d^2*PolyLog[3, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^3) + ((2*I)*b^3*d^2*PolyLog[3, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^3) - ((4*I)*b*d^2*PolyLog[3, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^3) + (b^2*(c + d*x)^2*Sin[e + f*x])/(a*(a^2 - b^2)*f*(b + a*Cos[e + f*x]))","A",30,11,20,0.5500,1,"{4191, 3324, 3321, 2264, 2190, 2531, 2282, 6589, 4522, 2279, 2391}"
41,1,582,0,1.0470459,"\int \frac{c+d x}{(a+b \sec (e+f x))^2} \, dx","Int[(c + d*x)/(a + b*Sec[e + f*x])^2,x]","-\frac{b^3 d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 f^2 \left(b^2-a^2\right)^{3/2}}+\frac{b^3 d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 f^2 \left(b^2-a^2\right)^{3/2}}+\frac{2 b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 f^2 \sqrt{b^2-a^2}}-\frac{2 b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 f^2 \sqrt{b^2-a^2}}-\frac{i b^3 (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 f \left(b^2-a^2\right)^{3/2}}+\frac{i b^3 (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 f \left(b^2-a^2\right)^{3/2}}+\frac{2 i b (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 f \sqrt{b^2-a^2}}-\frac{2 i b (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 f \sqrt{b^2-a^2}}+\frac{b^2 (c+d x) \sin (e+f x)}{a f \left(a^2-b^2\right) (a \cos (e+f x)+b)}+\frac{b^2 d \log (a \cos (e+f x)+b)}{a^2 f^2 \left(a^2-b^2\right)}+\frac{(c+d x)^2}{2 a^2 d}","-\frac{b^3 d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 f^2 \left(b^2-a^2\right)^{3/2}}+\frac{b^3 d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 f^2 \left(b^2-a^2\right)^{3/2}}+\frac{2 b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 f^2 \sqrt{b^2-a^2}}-\frac{2 b d \text{PolyLog}\left(2,-\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 f^2 \sqrt{b^2-a^2}}-\frac{i b^3 (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 f \left(b^2-a^2\right)^{3/2}}+\frac{i b^3 (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 f \left(b^2-a^2\right)^{3/2}}+\frac{2 i b (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 f \sqrt{b^2-a^2}}-\frac{2 i b (c+d x) \log \left(1+\frac{a e^{i (e+f x)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 f \sqrt{b^2-a^2}}+\frac{b^2 (c+d x) \sin (e+f x)}{a f \left(a^2-b^2\right) (a \cos (e+f x)+b)}+\frac{b^2 d \log (a \cos (e+f x)+b)}{a^2 f^2 \left(a^2-b^2\right)}+\frac{(c+d x)^2}{2 a^2 d}",1,"(c + d*x)^2/(2*a^2*d) - (I*b^3*(c + d*x)*Log[1 + (a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*f) + ((2*I)*b*(c + d*x)*Log[1 + (a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*f) + (I*b^3*(c + d*x)*Log[1 + (a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*f) - ((2*I)*b*(c + d*x)*Log[1 + (a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*f) + (b^2*d*Log[b + a*Cos[e + f*x]])/(a^2*(a^2 - b^2)*f^2) - (b^3*d*PolyLog[2, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^2) + (2*b*d*PolyLog[2, -((a*E^(I*(e + f*x)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^2) + (b^3*d*PolyLog[2, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*f^2) - (2*b*d*PolyLog[2, -((a*E^(I*(e + f*x)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*f^2) + (b^2*(c + d*x)*Sin[e + f*x])/(a*(a^2 - b^2)*f*(b + a*Cos[e + f*x]))","A",21,9,18,0.5000,1,"{4191, 3324, 3321, 2264, 2190, 2279, 2391, 2668, 31}"
42,0,0,0,0.0579287,"\int \frac{1}{(c+d x) (a+b \sec (e+f x))^2} \, dx","Int[1/((c + d*x)*(a + b*Sec[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+b \sec (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \sec (e+f x))^2},x\right)",0,"Defer[Int][1/((c + d*x)*(a + b*Sec[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
43,0,0,0,0.0547013,"\int \frac{1}{(c+d x)^2 (a+b \sec (e+f x))^2} \, dx","Int[1/((c + d*x)^2*(a + b*Sec[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+b \sec (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \sec (e+f x))^2},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + b*Sec[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
44,0,0,0,0.0507256,"\int (c+d x)^m (a+b \sec (e+f x))^n \, dx","Int[(c + d*x)^m*(a + b*Sec[e + f*x])^n,x]","\int (c+d x)^m (a+b \sec (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (a+b \sec (e+f x))^n,x\right)",0,"Defer[Int][(c + d*x)^m*(a + b*Sec[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
45,0,0,0,0.0259976,"\int (c+d x)^m (a+b \sec (e+f x)) \, dx","Int[(c + d*x)^m*(a + b*Sec[e + f*x]),x]","\int (c+d x)^m (a+b \sec (e+f x)) \, dx","\text{Int}\left((c+d x)^m (a+b \sec (e+f x)),x\right)",0,"Defer[Int][(c + d*x)^m*(a + b*Sec[e + f*x]), x]","A",0,0,0,0,-1,"{}"
46,0,0,0,0.0551741,"\int \frac{(c+d x)^m}{a+b \sec (e+f x)} \, dx","Int[(c + d*x)^m/(a + b*Sec[e + f*x]),x]","\int \frac{(c+d x)^m}{a+b \sec (e+f x)} \, dx","\text{Int}\left(\frac{(c+d x)^m}{a+b \sec (e+f x)},x\right)",0,"Defer[Int][(c + d*x)^m/(a + b*Sec[e + f*x]), x]","A",0,0,0,0,-1,"{}"