1,1,106,106,0.04318,"\int x^3 \tan (a+b x) \, dx","Integrate[x^3*Tan[a + b*x],x]","-\frac{3 i \text{Li}_4\left(-e^{2 i (a+b x)}\right)}{4 b^4}-\frac{3 x \text{Li}_3\left(-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i x^2 \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{x^3 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{i x^4}{4}","-\frac{3 i \text{Li}_4\left(-e^{2 i (a+b x)}\right)}{4 b^4}-\frac{3 x \text{Li}_3\left(-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i x^2 \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{2 b^2}-\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",1
2,1,77,77,0.0097526,"\int x^2 \tan (a+b x) \, dx","Integrate[x^2*Tan[a + b*x],x]","-\frac{\text{Li}_3\left(-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{i x \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{b^2}-\frac{x^2 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{i x^3}{3}","-\frac{\text{Li}_3\left(-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{i x \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{b^2}-\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",1
3,1,54,54,0.0061531,"\int x \tan (a+b x) \, dx","Integrate[x*Tan[a + b*x],x]","\frac{i \text{Li}_2\left(-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{Li}_2\left(-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",1
4,0,0,13,2.1273164,"\int \frac{\tan (a+b x)}{x} \, dx","Integrate[Tan[a + b*x]/x,x]","\int \frac{\tan (a+b x)}{x} \, dx","\text{Int}\left(\frac{\tan (a+b x)}{x},x\right)",0,"Integrate[Tan[a + b*x]/x, x]","A",-1
5,0,0,13,3.012798,"\int \frac{\tan (a+b x)}{x^2} \, dx","Integrate[Tan[a + b*x]/x^2,x]","\int \frac{\tan (a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\tan (a+b x)}{x^2},x\right)",0,"Integrate[Tan[a + b*x]/x^2, x]","A",-1
6,1,115,98,0.7891902,"\int x^3 \tan ^2(a+b x) \, dx","Integrate[x^3*Tan[a + b*x]^2,x]","\frac{2 b^2 x^2 \left(\frac{2 i b x}{1+e^{2 i a}}+3 \log \left(1+e^{-2 i (a+b x)}\right)\right)+6 i b x \text{Li}_2\left(-e^{-2 i (a+b x)}\right)+3 \text{Li}_3\left(-e^{-2 i (a+b x)}\right)}{2 b^4}+\frac{x^3 \sec (a) \sin (b x) \sec (a+b x)}{b}-\frac{x^4}{4}","\frac{3 \text{Li}_3\left(-e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i x \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{b^3}+\frac{3 x^2 \log \left(1+e^{2 i (a+b x)}\right)}{b^2}+\frac{x^3 \tan (a+b x)}{b}-\frac{i x^3}{b}-\frac{x^4}{4}",1,"-1/4*x^4 + (2*b^2*x^2*(((2*I)*b*x)/(1 + E^((2*I)*a)) + 3*Log[1 + E^((-2*I)*(a + b*x))]) + (6*I)*b*x*PolyLog[2, -E^((-2*I)*(a + b*x))] + 3*PolyLog[3, -E^((-2*I)*(a + b*x))])/(2*b^4) + (x^3*Sec[a]*Sec[a + b*x]*Sin[b*x])/b","A",1
7,1,189,73,6.1853891,"\int x^2 \tan ^2(a+b x) \, dx","Integrate[x^2*Tan[a + b*x]^2,x]","\frac{\csc (a) \sec (a) \left(b^2 x^2 e^{-i \tan ^{-1}(\cot (a))}-\frac{\cot (a) \left(i \text{Li}_2\left(e^{2 i \left(b x-\tan ^{-1}(\cot (a))\right)}\right)+i b x \left(-2 \tan ^{-1}(\cot (a))-\pi \right)-2 \left(b x-\tan ^{-1}(\cot (a))\right) \log \left(1-e^{2 i \left(b x-\tan ^{-1}(\cot (a))\right)}\right)-2 \tan ^{-1}(\cot (a)) \log \left(\sin \left(b x-\tan ^{-1}(\cot (a))\right)\right)-\pi  \log \left(1+e^{-2 i b x}\right)+\pi  \log (\cos (b x))\right)}{\sqrt{\cot ^2(a)+1}}\right)}{b^3 \sqrt{\csc ^2(a) \left(\sin ^2(a)+\cos ^2(a)\right)}}+\frac{x^2 \sec (a) \sin (b x) \sec (a+b x)}{b}-\frac{x^3}{3}","-\frac{i \text{Li}_2\left(-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 \tan (a+b x)}{b}-\frac{i x^2}{b}-\frac{x^3}{3}",1,"-1/3*x^3 + (Csc[a]*((b^2*x^2)/E^(I*ArcTan[Cot[a]]) - (Cot[a]*(I*b*x*(-Pi - 2*ArcTan[Cot[a]]) - Pi*Log[1 + E^((-2*I)*b*x)] - 2*(b*x - ArcTan[Cot[a]])*Log[1 - E^((2*I)*(b*x - ArcTan[Cot[a]]))] + Pi*Log[Cos[b*x]] - 2*ArcTan[Cot[a]]*Log[Sin[b*x - ArcTan[Cot[a]]]] + I*PolyLog[2, E^((2*I)*(b*x - ArcTan[Cot[a]]))]))/Sqrt[1 + Cot[a]^2])*Sec[a])/(b^3*Sqrt[Csc[a]^2*(Cos[a]^2 + Sin[a]^2)]) + (x^2*Sec[a]*Sec[a + b*x]*Sin[b*x])/b","B",0
8,1,43,30,0.1822563,"\int x \tan ^2(a+b x) \, dx","Integrate[x*Tan[a + b*x]^2,x]","\frac{\log (\cos (a+b x))}{b^2}+\frac{x \tan (a)}{b}+\frac{x \sec (a) \sin (b x) \sec (a+b x)}{b}-\frac{x^2}{2}","\frac{\log (\cos (a+b x))}{b^2}+\frac{x \tan (a+b x)}{b}-\frac{x^2}{2}",1,"-1/2*x^2 + Log[Cos[a + b*x]]/b^2 + (x*Sec[a]*Sec[a + b*x]*Sin[b*x])/b + (x*Tan[a])/b","A",1
9,0,0,15,2.7620117,"\int \frac{\tan ^2(a+b x)}{x} \, dx","Integrate[Tan[a + b*x]^2/x,x]","\int \frac{\tan ^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\tan ^2(a+b x)}{x},x\right)",0,"Integrate[Tan[a + b*x]^2/x, x]","A",-1
10,0,0,15,2.9780825,"\int \frac{\tan ^2(a+b x)}{x^2} \, dx","Integrate[Tan[a + b*x]^2/x^2,x]","\int \frac{\tan ^2(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\tan ^2(a+b x)}{x^2},x\right)",0,"Integrate[Tan[a + b*x]^2/x^2, x]","A",-1
11,1,359,205,6.6720889,"\int x^3 \tan ^3(a+b x) \, dx","Integrate[x^3*Tan[a + b*x]^3,x]","-\frac{3 x^2 \sec (a) \sin (b x) \sec (a+b x)}{2 b^2}-\frac{3 \csc (a) \sec (a) \left(b^2 x^2 e^{-i \tan ^{-1}(\cot (a))}-\frac{\cot (a) \left(i \text{Li}_2\left(e^{2 i \left(b x-\tan ^{-1}(\cot (a))\right)}\right)+i b x \left(-2 \tan ^{-1}(\cot (a))-\pi \right)-2 \left(b x-\tan ^{-1}(\cot (a))\right) \log \left(1-e^{2 i \left(b x-\tan ^{-1}(\cot (a))\right)}\right)-2 \tan ^{-1}(\cot (a)) \log \left(\sin \left(b x-\tan ^{-1}(\cot (a))\right)\right)-\pi  \log \left(1+e^{-2 i b x}\right)+\pi  \log (\cos (b x))\right)}{\sqrt{\cot ^2(a)+1}}\right)}{2 b^4 \sqrt{\csc ^2(a) \left(\sin ^2(a)+\cos ^2(a)\right)}}+\frac{1}{8} i e^{i a} \sec (a) \left(\frac{3 e^{-2 i a} \left(1+e^{2 i a}\right) \left(2 b^2 x^2 \text{Li}_2\left(-e^{-2 i (a+b x)}\right)-2 i b x \text{Li}_3\left(-e^{-2 i (a+b x)}\right)-\text{Li}_4\left(-e^{-2 i (a+b x)}\right)\right)}{b^4}-\frac{4 i \left(1+e^{-2 i a}\right) x^3 \log \left(1+e^{-2 i (a+b x)}\right)}{b}+2 e^{-2 i a} x^4\right)+\frac{x^3 \sec ^2(a+b x)}{2 b}-\frac{1}{4} x^4 \tan (a)","\frac{3 i \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{2 b^4}+\frac{3 i \text{Li}_4\left(-e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 x \text{Li}_3\left(-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{3 x \log \left(1+e^{2 i (a+b x)}\right)}{b^3}-\frac{3 i x^2 \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 x^2 \tan (a+b x)}{2 b^2}+\frac{x^3 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{x^3 \tan ^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,"(I/8)*E^(I*a)*((2*x^4)/E^((2*I)*a) - ((4*I)*(1 + E^((-2*I)*a))*x^3*Log[1 + E^((-2*I)*(a + b*x))])/b + (3*(1 + E^((2*I)*a))*(2*b^2*x^2*PolyLog[2, -E^((-2*I)*(a + b*x))] - (2*I)*b*x*PolyLog[3, -E^((-2*I)*(a + b*x))] - PolyLog[4, -E^((-2*I)*(a + b*x))]))/(b^4*E^((2*I)*a)))*Sec[a] + (x^3*Sec[a + b*x]^2)/(2*b) - (3*Csc[a]*((b^2*x^2)/E^(I*ArcTan[Cot[a]]) - (Cot[a]*(I*b*x*(-Pi - 2*ArcTan[Cot[a]]) - Pi*Log[1 + E^((-2*I)*b*x)] - 2*(b*x - ArcTan[Cot[a]])*Log[1 - E^((2*I)*(b*x - ArcTan[Cot[a]]))] + Pi*Log[Cos[b*x]] - 2*ArcTan[Cot[a]]*Log[Sin[b*x - ArcTan[Cot[a]]]] + I*PolyLog[2, E^((2*I)*(b*x - ArcTan[Cot[a]]))]))/Sqrt[1 + Cot[a]^2])*Sec[a])/(2*b^4*Sqrt[Csc[a]^2*(Cos[a]^2 + Sin[a]^2)]) - (3*x^2*Sec[a]*Sec[a + b*x]*Sin[b*x])/(2*b^2) - (x^4*Tan[a])/4","A",0
12,1,172,128,3.1434849,"\int x^2 \tan ^3(a+b x) \, dx","Integrate[x^2*Tan[a + b*x]^3,x]","\frac{-4 b^3 x^3 \tan (a)+e^{-i a} \sec (a) \left(2 b^2 x^2 \left(3 \left(1+e^{2 i a}\right) \log \left(1+e^{-2 i (a+b x)}\right)+2 i b x\right)+6 i \left(1+e^{2 i a}\right) b x \text{Li}_2\left(-e^{-2 i (a+b x)}\right)+3 \left(1+e^{2 i a}\right) \text{Li}_3\left(-e^{-2 i (a+b x)}\right)\right)+6 b^2 x^2 \sec ^2(a+b x)-12 b x \sec (a) \sin (b x) \sec (a+b x)-12 (b x \tan (a)+\log (\cos (a+b x)))}{12 b^3}","\frac{\text{Li}_3\left(-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{\log (\cos (a+b x))}{b^3}-\frac{i x \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{b^2}-\frac{x \tan (a+b x)}{b^2}+\frac{x^2 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{x^2 \tan ^2(a+b x)}{2 b}+\frac{x^2}{2 b}-\frac{i x^3}{3}",1,"(((2*b^2*x^2*((2*I)*b*x + 3*(1 + E^((2*I)*a))*Log[1 + E^((-2*I)*(a + b*x))]) + (6*I)*b*(1 + E^((2*I)*a))*x*PolyLog[2, -E^((-2*I)*(a + b*x))] + 3*(1 + E^((2*I)*a))*PolyLog[3, -E^((-2*I)*(a + b*x))])*Sec[a])/E^(I*a) + 6*b^2*x^2*Sec[a + b*x]^2 - 12*b*x*Sec[a]*Sec[a + b*x]*Sin[b*x] - 4*b^3*x^3*Tan[a] - 12*(Log[Cos[a + b*x]] + b*x*Tan[a]))/(12*b^3)","A",1
13,1,210,90,6.1488356,"\int x \tan ^3(a+b x) \, dx","Integrate[x*Tan[a + b*x]^3,x]","\frac{\csc (a) \sec (a) \left(b^2 x^2 e^{-i \tan ^{-1}(\cot (a))}-\frac{\cot (a) \left(i \text{Li}_2\left(e^{2 i \left(b x-\tan ^{-1}(\cot (a))\right)}\right)+i b x \left(-2 \tan ^{-1}(\cot (a))-\pi \right)-2 \left(b x-\tan ^{-1}(\cot (a))\right) \log \left(1-e^{2 i \left(b x-\tan ^{-1}(\cot (a))\right)}\right)-2 \tan ^{-1}(\cot (a)) \log \left(\sin \left(b x-\tan ^{-1}(\cot (a))\right)\right)-\pi  \log \left(1+e^{-2 i b x}\right)+\pi  \log (\cos (b x))\right)}{\sqrt{\cot ^2(a)+1}}\right)}{2 b^2 \sqrt{\csc ^2(a) \left(\sin ^2(a)+\cos ^2(a)\right)}}-\frac{\sec (a) \sin (b x) \sec (a+b x)}{2 b^2}+\frac{x \sec ^2(a+b x)}{2 b}-\frac{1}{2} x^2 \tan (a)","-\frac{i \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{\tan (a+b x)}{2 b^2}+\frac{x \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{x \tan ^2(a+b x)}{2 b}+\frac{x}{2 b}-\frac{i x^2}{2}",1,"(x*Sec[a + b*x]^2)/(2*b) + (Csc[a]*((b^2*x^2)/E^(I*ArcTan[Cot[a]]) - (Cot[a]*(I*b*x*(-Pi - 2*ArcTan[Cot[a]]) - Pi*Log[1 + E^((-2*I)*b*x)] - 2*(b*x - ArcTan[Cot[a]])*Log[1 - E^((2*I)*(b*x - ArcTan[Cot[a]]))] + Pi*Log[Cos[b*x]] - 2*ArcTan[Cot[a]]*Log[Sin[b*x - ArcTan[Cot[a]]]] + I*PolyLog[2, E^((2*I)*(b*x - ArcTan[Cot[a]]))]))/Sqrt[1 + Cot[a]^2])*Sec[a])/(2*b^2*Sqrt[Csc[a]^2*(Cos[a]^2 + Sin[a]^2)]) - (Sec[a]*Sec[a + b*x]*Sin[b*x])/(2*b^2) - (x^2*Tan[a])/2","B",0
14,0,0,15,5.1213918,"\int \frac{\tan ^3(a+b x)}{x} \, dx","Integrate[Tan[a + b*x]^3/x,x]","\int \frac{\tan ^3(a+b x)}{x} \, dx","\text{Int}\left(\frac{\tan ^3(a+b x)}{x},x\right)",0,"Integrate[Tan[a + b*x]^3/x, x]","A",-1
15,0,0,15,3.4218463,"\int \frac{\tan ^3(a+b x)}{x^2} \, dx","Integrate[Tan[a + b*x]^3/x^2,x]","\int \frac{\tan ^3(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\tan ^3(a+b x)}{x^2},x\right)",0,"Integrate[Tan[a + b*x]^3/x^2, x]","A",-1
16,1,18,18,0.9647657,"\int \left(\frac{x^2}{\tan ^{\frac{3}{2}}(a+b x)}-\frac{4 x}{b \sqrt{\tan (a+b x)}}+x^2 \sqrt{\tan (a+b x)}\right) \, dx","Integrate[x^2/Tan[a + b*x]^(3/2) - (4*x)/(b*Sqrt[Tan[a + b*x]]) + x^2*Sqrt[Tan[a + b*x]],x]","-\frac{2 x^2}{b \sqrt{\tan (a+b x)}}","-\frac{2 x^2}{b \sqrt{\tan (a+b x)}}",1,"(-2*x^2)/(b*Sqrt[Tan[a + b*x]])","A",1
17,1,17,17,0.603293,"\int \left(\frac{x^2}{\sqrt{\tan \left(a+b x^2\right)}}+\frac{\sqrt{\tan \left(a+b x^2\right)}}{b}+x^2 \tan ^{\frac{3}{2}}\left(a+b x^2\right)\right) \, dx","Integrate[x^2/Sqrt[Tan[a + b*x^2]] + Sqrt[Tan[a + b*x^2]]/b + x^2*Tan[a + b*x^2]^(3/2),x]","\frac{x \sqrt{\tan \left(a+b x^2\right)}}{b}","\frac{x \sqrt{\tan \left(a+b x^2\right)}}{b}",1,"(x*Sqrt[Tan[a + b*x^2]])/b","A",1
18,1,278,189,0.705394,"\int \frac{(c+d x)^3}{a+i a \tan (e+f x)} \, dx","Integrate[(c + d*x)^3/(a + I*a*Tan[e + f*x]),x]","\frac{\sec (e+f x) (\cos (f x)+i \sin (f x)) \left(2 f^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) (\cos (e)+i \sin (e))+(\cos (e)-i \sin (e)) \cos (2 f x) \left(4 i c^3 f^3+6 c^2 d f^2 (1+2 i f x)+6 c d^2 f \left(2 i f^2 x^2+2 f x-i\right)+d^3 \left(4 i f^3 x^3+6 f^2 x^2-6 i f x-3\right)\right)+(\cos (e)-i \sin (e)) \sin (2 f x) \left(4 c^3 f^3+6 c^2 d f^2 (2 f x-i)+6 c d^2 f \left(2 f^2 x^2-2 i f x-1\right)+d^3 \left(4 f^3 x^3-6 i f^2 x^2-6 f x+3 i\right)\right)\right)}{16 f^4 (a+i a \tan (e+f x))}","-\frac{3 i d^2 (c+d x)}{4 f^3 (a+i a \tan (e+f x))}+\frac{3 d (c+d x)^2}{4 f^2 (a+i a \tan (e+f x))}+\frac{i (c+d x)^3}{2 f (a+i a \tan (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 \tan (e+f x))}+\frac{3 i d^3 x}{8 a f^3}",1,"(Sec[e + f*x]*(Cos[f*x] + I*Sin[f*x])*(((4*I)*c^3*f^3 + 6*c^2*d*f^2*(1 + (2*I)*f*x) + 6*c*d^2*f*(-I + 2*f*x + (2*I)*f^2*x^2) + d^3*(-3 - (6*I)*f*x + 6*f^2*x^2 + (4*I)*f^3*x^3))*Cos[2*f*x]*(Cos[e] - I*Sin[e]) + 2*f^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*(Cos[e] + I*Sin[e]) + (4*c^3*f^3 + 6*c^2*d*f^2*(-I + 2*f*x) + 6*c*d^2*f*(-1 - (2*I)*f*x + 2*f^2*x^2) + d^3*(3*I - 6*f*x - (6*I)*f^2*x^2 + 4*f^3*x^3))*(Cos[e] - I*Sin[e])*Sin[2*f*x]))/(16*f^4*(a + I*a*Tan[e + f*x]))","A",1
19,1,178,137,0.4029283,"\int \frac{(c+d x)^2}{a+i a \tan (e+f x)} \, dx","Integrate[(c + d*x)^2/(a + I*a*Tan[e + f*x]),x]","\frac{\sec (e+f x) (\cos (f x)+i \sin (f x)) \left(\frac{4}{3} f^3 x \left(3 c^2+3 c d x+d^2 x^2\right) (\cos (e)+i \sin (e))+(\cos (e)-i \sin (e)) \cos (2 f x) ((1+i) c f+(1+i) d f x+d) ((1+i) c f+d ((1+i) f x-i))-i (\cos (e)-i \sin (e)) \sin (2 f x) ((1+i) c f+(1+i) d f x+d) ((1+i) c f+d ((1+i) f x-i))\right)}{8 f^3 (a+i a \tan (e+f x))}","\frac{d (c+d x)}{2 f^2 (a+i a \tan (e+f x))}+\frac{i (c+d x)^2}{2 f (a+i a \tan (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 \tan (e+f x))}-\frac{d^2 x}{4 a f^2}",1,"(Sec[e + f*x]*(Cos[f*x] + I*Sin[f*x])*((d + (1 + I)*c*f + (1 + I)*d*f*x)*((1 + I)*c*f + d*(-I + (1 + I)*f*x))*Cos[2*f*x]*(Cos[e] - I*Sin[e]) + (4*f^3*x*(3*c^2 + 3*c*d*x + d^2*x^2)*(Cos[e] + I*Sin[e]))/3 - I*(d + (1 + I)*c*f + (1 + I)*d*f*x)*((1 + I)*c*f + d*(-I + (1 + I)*f*x))*(Cos[e] - I*Sin[e])*Sin[2*f*x]))/(8*f^3*(a + I*a*Tan[e + f*x]))","A",1
20,1,96,84,0.4367672,"\int \frac{c+d x}{a+i a \tan (e+f x)} \, dx","Integrate[(c + d*x)/(a + I*a*Tan[e + f*x]),x]","\frac{\left(2 c f (2 f x-i)+d \left(2 f^2 x^2-2 i f x-1\right)\right) \tan (e+f x)-i \left(2 c f (2 f x+i)+d \left(2 f^2 x^2+2 i f x+1\right)\right)}{8 a f^2 (\tan (e+f x)-i)}","\frac{i (c+d x)}{2 f (a+i a \tan (e+f x))}+\frac{(c+d x)^2}{4 a d}+\frac{d}{4 f^2 (a+i a \tan (e+f x))}-\frac{i d x}{4 a f}",1,"((-I)*(2*c*f*(I + 2*f*x) + d*(1 + (2*I)*f*x + 2*f^2*x^2)) + (2*c*f*(-I + 2*f*x) + d*(-1 - (2*I)*f*x + 2*f^2*x^2))*Tan[e + f*x])/(8*a*f^2*(-I + Tan[e + f*x]))","A",1
21,1,166,161,0.3545254,"\int \frac{1}{(c+d x) (a+i a \tan (e+f x))} \, dx","Integrate[1/((c + d*x)*(a + I*a*Tan[e + f*x])),x]","\frac{\sec (e+f x) \left(\sin \left(f \left(\frac{c}{d}+x\right)\right)-i \cos \left(f \left(\frac{c}{d}+x\right)\right)\right) \left(\text{Ci}\left(\frac{2 f (c+d x)}{d}\right) \left(\cos \left(e-\frac{c f}{d}\right)-i \sin \left(e-\frac{c f}{d}\right)\right)+\text{Si}\left(\frac{2 f (c+d x)}{d}\right) \left(-\sin \left(e-\frac{c f}{d}\right)-i \cos \left(e-\frac{c f}{d}\right)\right)+\log (f (c+d x)) \left(\cos \left(e-\frac{c f}{d}\right)+i \sin \left(e-\frac{c f}{d}\right)\right)\right)}{2 a d (\tan (e+f x)-i)}","-\frac{i \text{Ci}\left(2 x f+\frac{2 c f}{d}\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{2 a d}+\frac{\text{Ci}\left(2 x f+\frac{2 c f}{d}\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,"(Sec[e + f*x]*((-I)*Cos[f*(c/d + x)] + Sin[f*(c/d + x)])*(CosIntegral[(2*f*(c + d*x))/d]*(Cos[e - (c*f)/d] - I*Sin[e - (c*f)/d]) + Log[f*(c + d*x)]*(Cos[e - (c*f)/d] + I*Sin[e - (c*f)/d]) + ((-I)*Cos[e - (c*f)/d] - Sin[e - (c*f)/d])*SinIntegral[(2*f*(c + d*x))/d]))/(2*a*d*(-I + Tan[e + f*x]))","A",0
22,1,224,168,0.8532037,"\int \frac{1}{(c+d x)^2 (a+i a \tan (e+f x))} \, dx","Integrate[1/((c + d*x)^2*(a + I*a*Tan[e + f*x])),x]","\frac{\sec (e+f x) \left(\cos \left(\frac{c f}{d}\right)+i \sin \left(\frac{c f}{d}\right)\right) \left(-2 f (c+d x) \text{Ci}\left(\frac{2 f (c+d x)}{d}\right) \left(\cos \left(e-\frac{f (c+d x)}{d}\right)-i \sin \left(e-\frac{f (c+d x)}{d}\right)\right)+2 f (c+d x) \text{Si}\left(\frac{2 f (c+d x)}{d}\right) \left(\sin \left(e-\frac{f (c+d x)}{d}\right)+i \cos \left(e-\frac{f (c+d x)}{d}\right)\right)+d \left(-\sin \left(f \left(x-\frac{c}{d}\right)+e\right)+\sin \left(f \left(\frac{c}{d}+x\right)+e\right)+i \cos \left(f \left(x-\frac{c}{d}\right)+e\right)+i \cos \left(f \left(\frac{c}{d}+x\right)+e\right)\right)\right)}{2 a d^2 (c+d x) (\tan (e+f x)-i)}","-\frac{f \text{Ci}\left(2 x f+\frac{2 c f}{d}\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{a d^2}-\frac{i f \text{Ci}\left(2 x f+\frac{2 c f}{d}\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 \tan (e+f x))}",1,"(Sec[e + f*x]*(Cos[(c*f)/d] + I*Sin[(c*f)/d])*(d*(I*Cos[e + f*(-(c/d) + x)] + I*Cos[e + f*(c/d + x)] - Sin[e + f*(-(c/d) + x)] + Sin[e + f*(c/d + x)]) - 2*f*(c + d*x)*CosIntegral[(2*f*(c + d*x))/d]*(Cos[e - (f*(c + d*x))/d] - I*Sin[e - (f*(c + d*x))/d]) + 2*f*(c + d*x)*(I*Cos[e - (f*(c + d*x))/d] + Sin[e - (f*(c + d*x))/d])*SinIntegral[(2*f*(c + d*x))/d]))/(2*a*d^2*(c + d*x)*(-I + Tan[e + f*x]))","A",1
23,1,285,227,1.2006445,"\int \frac{1}{(c+d x)^3 (a+i a \tan (e+f x))} \, dx","Integrate[1/((c + d*x)^3*(a + I*a*Tan[e + f*x])),x]","\frac{\sec (e+f x) \left(\cos \left(\frac{c f}{d}\right)+i \sin \left(\frac{c f}{d}\right)\right) \left(4 f^2 (c+d x)^2 \text{Ci}\left(\frac{2 f (c+d x)}{d}\right) \left(\sin \left(e-\frac{f (c+d x)}{d}\right)+i \cos \left(e-\frac{f (c+d x)}{d}\right)\right)+4 f^2 (c+d x)^2 \text{Si}\left(\frac{2 f (c+d x)}{d}\right) \left(\cos \left(e-\frac{f (c+d x)}{d}\right)-i \sin \left(e-\frac{f (c+d x)}{d}\right)\right)+d \left(-d \sin \left(f \left(x-\frac{c}{d}\right)+e\right)+d \sin \left(f \left(\frac{c}{d}+x\right)+e\right)-2 i c f \sin \left(f \left(\frac{c}{d}+x\right)+e\right)-2 i d f x \sin \left(f \left(\frac{c}{d}+x\right)+e\right)+i d \cos \left(f \left(x-\frac{c}{d}\right)+e\right)+(2 c f+2 d f x+i d) \cos \left(f \left(\frac{c}{d}+x\right)+e\right)\right)\right)}{4 a d^3 (c+d x)^2 (\tan (e+f x)-i)}","\frac{i f^2 \text{Ci}\left(2 x f+\frac{2 c f}{d}\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{a d^3}-\frac{f^2 \text{Ci}\left(2 x f+\frac{2 c f}{d}\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 \tan (e+f x))}-\frac{i f}{2 a d^2 (c+d x)}-\frac{1}{2 d (c+d x)^2 (a+i a \tan (e+f x))}",1,"(Sec[e + f*x]*(Cos[(c*f)/d] + I*Sin[(c*f)/d])*(d*(I*d*Cos[e + f*(-(c/d) + x)] + (I*d + 2*c*f + 2*d*f*x)*Cos[e + f*(c/d + x)] - d*Sin[e + f*(-(c/d) + x)] + d*Sin[e + f*(c/d + x)] - (2*I)*c*f*Sin[e + f*(c/d + x)] - (2*I)*d*f*x*Sin[e + f*(c/d + x)]) + 4*f^2*(c + d*x)^2*CosIntegral[(2*f*(c + d*x))/d]*(I*Cos[e - (f*(c + d*x))/d] + Sin[e - (f*(c + d*x))/d]) + 4*f^2*(c + d*x)^2*(Cos[e - (f*(c + d*x))/d] - I*Sin[e - (f*(c + d*x))/d])*SinIntegral[(2*f*(c + d*x))/d]))/(4*a*d^3*(c + d*x)^2*(-I + Tan[e + f*x]))","A",1
24,1,473,270,1.3801214,"\int \frac{(c+d x)^3}{(a+i a \tan (e+f x))^2} \, dx","Integrate[(c + d*x)^3/(a + I*a*Tan[e + f*x])^2,x]","\frac{\sec ^2(e+f x) (\cos (f x)+i \sin (f x))^2 \left(f^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) (\cos (2 e)+i \sin (2 e))+\frac{1}{32} (\cos (2 e)-i \sin (2 e)) \cos (4 f x) \left(32 i c^3 f^3+24 c^2 d f^2 (1+4 i f x)+12 c d^2 f \left(8 i f^2 x^2+4 f x-i\right)+d^3 \left(32 i f^3 x^3+24 f^2 x^2-12 i f x-3\right)\right)+\frac{1}{32} (\cos (2 e)-i \sin (2 e)) \sin (4 f x) \left(32 c^3 f^3+24 c^2 d f^2 (4 f x-i)+12 c d^2 f \left(8 f^2 x^2-4 i f x-1\right)+d^3 \left(32 f^3 x^3-24 i f^2 x^2-12 f x+3 i\right)\right)+\sin (2 f x) \left(4 c^3 f^3+6 c^2 d f^2 (2 f x-i)+6 c d^2 f \left(2 f^2 x^2-2 i f x-1\right)+d^3 \left(4 f^3 x^3-6 i f^2 x^2-6 f x+3 i\right)\right)+\cos (2 f x) \left(4 i c^3 f^3+6 c^2 d f^2 (1+2 i f x)+6 c d^2 f \left(2 i f^2 x^2+2 f x-i\right)+d^3 \left(4 i f^3 x^3+6 f^2 x^2-6 i f x-3\right)\right)\right)}{16 f^4 (a+i a \tan (e+f x))^2}","-\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,"(Sec[e + f*x]^2*(Cos[f*x] + I*Sin[f*x])^2*(((4*I)*c^3*f^3 + 6*c^2*d*f^2*(1 + (2*I)*f*x) + 6*c*d^2*f*(-I + 2*f*x + (2*I)*f^2*x^2) + d^3*(-3 - (6*I)*f*x + 6*f^2*x^2 + (4*I)*f^3*x^3))*Cos[2*f*x] + (((32*I)*c^3*f^3 + 24*c^2*d*f^2*(1 + (4*I)*f*x) + 12*c*d^2*f*(-I + 4*f*x + (8*I)*f^2*x^2) + d^3*(-3 - (12*I)*f*x + 24*f^2*x^2 + (32*I)*f^3*x^3))*Cos[4*f*x]*(Cos[2*e] - I*Sin[2*e]))/32 + f^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*(Cos[2*e] + I*Sin[2*e]) + (4*c^3*f^3 + 6*c^2*d*f^2*(-I + 2*f*x) + 6*c*d^2*f*(-1 - (2*I)*f*x + 2*f^2*x^2) + d^3*(3*I - 6*f*x - (6*I)*f^2*x^2 + 4*f^3*x^3))*Sin[2*f*x] + ((32*c^3*f^3 + 24*c^2*d*f^2*(-I + 4*f*x) + 12*c*d^2*f*(-1 - (4*I)*f*x + 8*f^2*x^2) + d^3*(3*I - 12*f*x - (24*I)*f^2*x^2 + 32*f^3*x^3))*(Cos[2*e] - I*Sin[2*e])*Sin[4*f*x])/32))/(16*f^4*(a + I*a*Tan[e + f*x])^2)","A",1
25,1,282,202,0.8879462,"\int \frac{(c+d x)^2}{(a+i a \tan (e+f x))^2} \, dx","Integrate[(c + d*x)^2/(a + I*a*Tan[e + f*x])^2,x]","\frac{\sec ^2(e+f x) (\cos (f x)+i \sin (f x))^2 \left(\frac{2}{3} f^3 x \left(3 c^2+3 c d x+d^2 x^2\right) (\cos (2 e)+i \sin (2 e))+\frac{1}{16} (\cos (2 e)-i \sin (2 e)) \cos (4 f x) ((2+2 i) c f+(2+2 i) d f x+d) ((2+2 i) c f+d ((2+2 i) f x-i))-\frac{1}{16} i (\cos (2 e)-i \sin (2 e)) \sin (4 f x) ((2+2 i) c f+(2+2 i) d f x+d) ((2+2 i) c f+d ((2+2 i) f x-i))-i \sin (2 f x) ((1+i) c f+(1+i) d f x+d) ((1+i) c f+d ((1+i) f x-i))+\cos (2 f x) ((1+i) c f+(1+i) d f x+d) ((1+i) c f+d ((1+i) f x-i))\right)}{8 f^3 (a+i a \tan (e+f x))^2}","\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,"(Sec[e + f*x]^2*(Cos[f*x] + I*Sin[f*x])^2*((d + (1 + I)*c*f + (1 + I)*d*f*x)*((1 + I)*c*f + d*(-I + (1 + I)*f*x))*Cos[2*f*x] + ((d + (2 + 2*I)*c*f + (2 + 2*I)*d*f*x)*((2 + 2*I)*c*f + d*(-I + (2 + 2*I)*f*x))*Cos[4*f*x]*(Cos[2*e] - I*Sin[2*e]))/16 + (2*f^3*x*(3*c^2 + 3*c*d*x + d^2*x^2)*(Cos[2*e] + I*Sin[2*e]))/3 - I*(d + (1 + I)*c*f + (1 + I)*d*f*x)*((1 + I)*c*f + d*(-I + (1 + I)*f*x))*Sin[2*f*x] - (I/16)*(d + (2 + 2*I)*c*f + (2 + 2*I)*d*f*x)*((2 + 2*I)*c*f + d*(-I + (2 + 2*I)*f*x))*(Cos[2*e] - I*Sin[2*e])*Sin[4*f*x]))/(8*f^3*(a + I*a*Tan[e + f*x])^2)","A",1
26,1,130,151,0.5941841,"\int \frac{c+d x}{(a+i a \tan (e+f x))^2} \, dx","Integrate[(c + d*x)/(a + I*a*Tan[e + f*x])^2,x]","-\frac{\sec ^2(e+f x) \left(\left(4 c f (1+4 i f x)+d \left(8 i f^2 x^2+4 f x-i\right)\right) \sin (2 (e+f x))+\left(4 c f (4 f x+i)+d \left(8 f^2 x^2+4 i f x+1\right)\right) \cos (2 (e+f x))+8 (2 i c f+2 i d f x+d)\right)}{64 a^2 f^2 (\tan (e+f x)-i)^2}","\frac{i (c+d x)}{4 f \left(a^2+i a^2 \tan (e+f x)\right)}+\frac{x (c+d x)}{4 a^2}+\frac{3 d}{16 f^2 \left(a^2+i a^2 \tan (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 \tan (e+f x))^2}+\frac{d}{16 f^2 (a+i a \tan (e+f x))^2}",1,"-1/64*(Sec[e + f*x]^2*(8*(d + (2*I)*c*f + (2*I)*d*f*x) + (4*c*f*(I + 4*f*x) + d*(1 + (4*I)*f*x + 8*f^2*x^2))*Cos[2*(e + f*x)] + (4*c*f*(1 + (4*I)*f*x) + d*(-I + 4*f*x + (8*I)*f^2*x^2))*Sin[2*(e + f*x)]))/(a^2*f^2*(-I + Tan[e + f*x])^2)","A",1
27,1,211,305,0.5234144,"\int \frac{1}{(c+d x) (a+i a \tan (e+f x))^2} \, dx","Integrate[1/((c + d*x)*(a + I*a*Tan[e + f*x])^2),x]","\frac{\left(\cos \left(2 e-\frac{2 c f}{d}\right)-i \sin \left(2 e-\frac{2 c f}{d}\right)\right) \left(\text{Ci}\left(\frac{4 f (c+d x)}{d}\right) \left(\cos \left(2 e-\frac{2 c f}{d}\right)-i \sin \left(2 e-\frac{2 c f}{d}\right)\right)+2 \text{Ci}\left(\frac{2 f (c+d x)}{d}\right)-\sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(\frac{4 f (c+d x)}{d}\right)-i \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(\frac{4 f (c+d x)}{d}\right)+i \sin \left(2 e-\frac{2 c f}{d}\right) \log (f (c+d x))+\cos \left(2 e-\frac{2 c f}{d}\right) \log (f (c+d x))-2 i \text{Si}\left(\frac{2 f (c+d x)}{d}\right)\right)}{4 a^2 d}","-\frac{i \text{Ci}\left(2 x f+\frac{2 c f}{d}\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{2 a^2 d}-\frac{i \text{Ci}\left(4 x f+\frac{4 c f}{d}\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{4 a^2 d}+\frac{\text{Ci}\left(2 x f+\frac{2 c f}{d}\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{2 a^2 d}+\frac{\text{Ci}\left(4 x f+\frac{4 c f}{d}\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] - I*Sin[2*e - (2*c*f)/d])*(2*CosIntegral[(2*f*(c + d*x))/d] + Cos[2*e - (2*c*f)/d]*Log[f*(c + d*x)] + CosIntegral[(4*f*(c + d*x))/d]*(Cos[2*e - (2*c*f)/d] - I*Sin[2*e - (2*c*f)/d]) + I*Log[f*(c + d*x)]*Sin[2*e - (2*c*f)/d] - (2*I)*SinIntegral[(2*f*(c + d*x))/d] - I*Cos[2*e - (2*c*f)/d]*SinIntegral[(4*f*(c + d*x))/d] - Sin[2*e - (2*c*f)/d]*SinIntegral[(4*f*(c + d*x))/d]))/(4*a^2*d)","A",0
28,1,467,436,1.6097614,"\int \frac{1}{(c+d x)^2 (a+i a \tan (e+f x))^2} \, dx","Integrate[1/((c + d*x)^2*(a + I*a*Tan[e + f*x])^2),x]","-\frac{\left(\cos \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)-i \sin \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)\right) \left(4 f (c+d x) \text{Ci}\left(\frac{4 f (c+d x)}{d}\right) \left(\sin \left(2 e-\frac{2 f (c+d x)}{d}\right)+i \cos \left(2 e-\frac{2 f (c+d x)}{d}\right)\right)+4 i f (c+d x) (\cos (2 f x)+i \sin (2 f x)) \text{Ci}\left(\frac{2 f (c+d x)}{d}\right)-4 i c f \text{Si}\left(\frac{4 f (c+d x)}{d}\right) \sin \left(2 e-\frac{2 f (c+d x)}{d}\right)-4 i d f x \text{Si}\left(\frac{4 f (c+d x)}{d}\right) \sin \left(2 e-\frac{2 f (c+d x)}{d}\right)+4 c f \text{Si}\left(\frac{4 f (c+d x)}{d}\right) \cos \left(2 e-\frac{2 f (c+d x)}{d}\right)+4 d f x \text{Si}\left(\frac{4 f (c+d x)}{d}\right) \cos \left(2 e-\frac{2 f (c+d x)}{d}\right)+i d \sin \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)-i d \sin \left(2 \left(f \left(\frac{c}{d}+x\right)+e\right)\right)+d \cos \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)+d \cos \left(2 \left(f \left(\frac{c}{d}+x\right)+e\right)\right)+4 i c f \sin (2 f x) \text{Si}\left(\frac{2 f (c+d x)}{d}\right)+4 i d f x \sin (2 f x) \text{Si}\left(\frac{2 f (c+d x)}{d}\right)+4 c f \cos (2 f x) \text{Si}\left(\frac{2 f (c+d x)}{d}\right)+4 d f x \cos (2 f x) \text{Si}\left(\frac{2 f (c+d x)}{d}\right)-2 i d \sin \left(\frac{2 c f}{d}\right)+2 d \cos \left(\frac{2 c f}{d}\right)\right)}{4 a^2 d^2 (c+d x)}","-\frac{f \text{Ci}\left(4 x f+\frac{4 c f}{d}\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{a^2 d^2}-\frac{f \text{Ci}\left(2 x f+\frac{2 c f}{d}\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{i f \text{Ci}\left(2 x f+\frac{2 c f}{d}\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{i f \text{Ci}\left(4 x f+\frac{4 c f}{d}\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*((Cos[2*(e + f*(-(c/d) + x))] - I*Sin[2*(e + f*(-(c/d) + x))])*(2*d*Cos[(2*c*f)/d] + d*Cos[2*(e + f*(-(c/d) + x))] + d*Cos[2*(e + f*(c/d + x))] - (2*I)*d*Sin[(2*c*f)/d] + (4*I)*f*(c + d*x)*CosIntegral[(2*f*(c + d*x))/d]*(Cos[2*f*x] + I*Sin[2*f*x]) + I*d*Sin[2*(e + f*(-(c/d) + x))] - I*d*Sin[2*(e + f*(c/d + x))] + 4*f*(c + d*x)*CosIntegral[(4*f*(c + d*x))/d]*(I*Cos[2*e - (2*f*(c + d*x))/d] + Sin[2*e - (2*f*(c + d*x))/d]) + 4*c*f*Cos[2*f*x]*SinIntegral[(2*f*(c + d*x))/d] + 4*d*f*x*Cos[2*f*x]*SinIntegral[(2*f*(c + d*x))/d] + (4*I)*c*f*Sin[2*f*x]*SinIntegral[(2*f*(c + d*x))/d] + (4*I)*d*f*x*Sin[2*f*x]*SinIntegral[(2*f*(c + d*x))/d] + 4*c*f*Cos[2*e - (2*f*(c + d*x))/d]*SinIntegral[(4*f*(c + d*x))/d] + 4*d*f*x*Cos[2*e - (2*f*(c + d*x))/d]*SinIntegral[(4*f*(c + d*x))/d] - (4*I)*c*f*Sin[2*e - (2*f*(c + d*x))/d]*SinIntegral[(4*f*(c + d*x))/d] - (4*I)*d*f*x*Sin[2*e - (2*f*(c + d*x))/d]*SinIntegral[(4*f*(c + d*x))/d]))/(a^2*d^2*(c + d*x))","A",0
29,1,667,396,2.739489,"\int \frac{(c+d x)^3}{(a+i a \tan (e+f x))^3} \, dx","Integrate[(c + d*x)^3/(a + I*a*Tan[e + f*x])^3,x]","\frac{i \sec ^3(e+f x) \left(3456 i c^3 f^4 x \sin (3 (e+f x))-2592 c^3 f^3 \sin (e+f x)+576 c^3 f^3 \sin (3 (e+f x))+5184 i c^2 d f^4 x^2 \sin (3 (e+f x))-7776 c^2 d f^3 x \sin (e+f x)+1728 c^2 d f^3 x \sin (3 (e+f x))+5832 i c^2 d f^2 \sin (e+f x)-288 i c^2 d f^2 \sin (3 (e+f x))+243 \left(32 i c^3 f^3+8 c^2 d f^2 (5+12 i f x)+4 c d^2 f \left(24 i f^2 x^2+20 f x-9 i\right)+d^3 \left(32 i f^3 x^3+40 f^2 x^2-36 i f x-17\right)\right) \cos (e+f x)+16 \left(36 c^3 f^3 (6 f x+i)+18 c^2 d f^2 \left(18 f^2 x^2+6 i f x+1\right)+6 c d^2 f \left(36 f^3 x^3+18 i f^2 x^2+6 f x-i\right)+d^3 \left(54 f^4 x^4+36 i f^3 x^3+18 f^2 x^2-6 i f x-1\right)\right) \cos (3 (e+f x))+3456 i c d^2 f^4 x^3 \sin (3 (e+f x))-7776 c d^2 f^3 x^2 \sin (e+f x)+1728 c d^2 f^3 x^2 \sin (3 (e+f x))+11664 i c d^2 f^2 x \sin (e+f x)-576 i c d^2 f^2 x \sin (3 (e+f x))+6804 c d^2 f \sin (e+f x)-96 c d^2 f \sin (3 (e+f x))+864 i d^3 f^4 x^4 \sin (3 (e+f x))-2592 d^3 f^3 x^3 \sin (e+f x)+576 d^3 f^3 x^3 \sin (3 (e+f x))+5832 i d^3 f^2 x^2 \sin (e+f x)-288 i d^3 f^2 x^2 \sin (3 (e+f x))+6804 d^3 f x \sin (e+f x)-96 d^3 f x \sin (3 (e+f x))-3645 i d^3 \sin (e+f x)+16 i d^3 \sin (3 (e+f x))\right)}{27648 a^3 f^4 (\tan (e+f x)-i)^3}","-\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,"((I/27648)*Sec[e + f*x]^3*(243*((32*I)*c^3*f^3 + 8*c^2*d*f^2*(5 + (12*I)*f*x) + 4*c*d^2*f*(-9*I + 20*f*x + (24*I)*f^2*x^2) + d^3*(-17 - (36*I)*f*x + 40*f^2*x^2 + (32*I)*f^3*x^3))*Cos[e + f*x] + 16*(36*c^3*f^3*(I + 6*f*x) + 18*c^2*d*f^2*(1 + (6*I)*f*x + 18*f^2*x^2) + 6*c*d^2*f*(-I + 6*f*x + (18*I)*f^2*x^2 + 36*f^3*x^3) + d^3*(-1 - (6*I)*f*x + 18*f^2*x^2 + (36*I)*f^3*x^3 + 54*f^4*x^4))*Cos[3*(e + f*x)] - (3645*I)*d^3*Sin[e + f*x] + 6804*c*d^2*f*Sin[e + f*x] + (5832*I)*c^2*d*f^2*Sin[e + f*x] - 2592*c^3*f^3*Sin[e + f*x] + 6804*d^3*f*x*Sin[e + f*x] + (11664*I)*c*d^2*f^2*x*Sin[e + f*x] - 7776*c^2*d*f^3*x*Sin[e + f*x] + (5832*I)*d^3*f^2*x^2*Sin[e + f*x] - 7776*c*d^2*f^3*x^2*Sin[e + f*x] - 2592*d^3*f^3*x^3*Sin[e + f*x] + (16*I)*d^3*Sin[3*(e + f*x)] - 96*c*d^2*f*Sin[3*(e + f*x)] - (288*I)*c^2*d*f^2*Sin[3*(e + f*x)] + 576*c^3*f^3*Sin[3*(e + f*x)] - 96*d^3*f*x*Sin[3*(e + f*x)] - (576*I)*c*d^2*f^2*x*Sin[3*(e + f*x)] + 1728*c^2*d*f^3*x*Sin[3*(e + f*x)] + (3456*I)*c^3*f^4*x*Sin[3*(e + f*x)] - (288*I)*d^3*f^2*x^2*Sin[3*(e + f*x)] + 1728*c*d^2*f^3*x^2*Sin[3*(e + f*x)] + (5184*I)*c^2*d*f^4*x^2*Sin[3*(e + f*x)] + 576*d^3*f^3*x^3*Sin[3*(e + f*x)] + (3456*I)*c*d^2*f^4*x^3*Sin[3*(e + f*x)] + (864*I)*d^3*f^4*x^4*Sin[3*(e + f*x)]))/(a^3*f^4*(-I + Tan[e + f*x])^3)","A",1
30,1,405,294,1.8052073,"\int \frac{(c+d x)^2}{(a+i a \tan (e+f x))^3} \, dx","Integrate[(c + d*x)^2/(a + I*a*Tan[e + f*x])^3,x]","\frac{i \sec ^3(e+f x) \left(81 \left(24 i c^2 f^2+4 c d f (5+12 i f x)+d^2 \left(24 i f^2 x^2+20 f x-9 i\right)\right) \cos (e+f x)+8 \left(18 c^2 f^2 (6 f x+i)+6 c d f \left(18 f^2 x^2+6 i f x+1\right)+d^2 \left(36 f^3 x^3+18 i f^2 x^2+6 f x-i\right)\right) \cos (3 (e+f x))+864 i c^2 f^3 x \sin (3 (e+f x))-648 c^2 f^2 \sin (e+f x)+144 c^2 f^2 \sin (3 (e+f x))+864 i c d f^3 x^2 \sin (3 (e+f x))-1296 c d f^2 x \sin (e+f x)+288 c d f^2 x \sin (3 (e+f x))+972 i c d f \sin (e+f x)-48 i c d f \sin (3 (e+f x))+288 i d^2 f^3 x^3 \sin (3 (e+f x))-648 d^2 f^2 x^2 \sin (e+f x)+144 d^2 f^2 x^2 \sin (3 (e+f x))+972 i d^2 f x \sin (e+f x)-48 i d^2 f x \sin (3 (e+f x))+567 d^2 \sin (e+f x)-8 d^2 \sin (3 (e+f x))\right)}{6912 a^3 f^3 (\tan (e+f x)-i)^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,"((I/6912)*Sec[e + f*x]^3*(81*((24*I)*c^2*f^2 + 4*c*d*f*(5 + (12*I)*f*x) + d^2*(-9*I + 20*f*x + (24*I)*f^2*x^2))*Cos[e + f*x] + 8*(18*c^2*f^2*(I + 6*f*x) + 6*c*d*f*(1 + (6*I)*f*x + 18*f^2*x^2) + d^2*(-I + 6*f*x + (18*I)*f^2*x^2 + 36*f^3*x^3))*Cos[3*(e + f*x)] + 567*d^2*Sin[e + f*x] + (972*I)*c*d*f*Sin[e + f*x] - 648*c^2*f^2*Sin[e + f*x] + (972*I)*d^2*f*x*Sin[e + f*x] - 1296*c*d*f^2*x*Sin[e + f*x] - 648*d^2*f^2*x^2*Sin[e + f*x] - 8*d^2*Sin[3*(e + f*x)] - (48*I)*c*d*f*Sin[3*(e + f*x)] + 144*c^2*f^2*Sin[3*(e + f*x)] - (48*I)*d^2*f*x*Sin[3*(e + f*x)] + 288*c*d*f^2*x*Sin[3*(e + f*x)] + (864*I)*c^2*f^3*x*Sin[3*(e + f*x)] + 144*d^2*f^2*x^2*Sin[3*(e + f*x)] + (864*I)*c*d*f^3*x^2*Sin[3*(e + f*x)] + (288*I)*d^2*f^3*x^3*Sin[3*(e + f*x)]))/(a^3*f^3*(-I + Tan[e + f*x])^3)","A",1
31,1,205,209,0.9124622,"\int \frac{c+d x}{(a+i a \tan (e+f x))^3} \, dx","Integrate[(c + d*x)/(a + I*a*Tan[e + f*x])^3,x]","\frac{i \sec ^3(e+f x) \left(4 \left(6 c f (6 f x+i)+d \left(18 f^2 x^2+6 i f x+1\right)\right) \cos (3 (e+f x))+27 (12 i c f+d (5+12 i f x)) \cos (e+f x)+144 i c f^2 x \sin (3 (e+f x))-108 c f \sin (e+f x)+24 c f \sin (3 (e+f x))+72 i d f^2 x^2 \sin (3 (e+f x))-108 d f x \sin (e+f x)+24 d f x \sin (3 (e+f x))+81 i d \sin (e+f x)-4 i d \sin (3 (e+f x))\right)}{1152 a^3 f^2 (\tan (e+f x)-i)^3}","\frac{i (c+d x)}{8 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{x (c+d x)}{8 a^3}+\frac{11 d}{96 f^2 \left(a^3+i a^3 \tan (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 \tan (e+f x))^2}+\frac{i (c+d x)}{6 f (a+i a \tan (e+f x))^3}+\frac{5 d}{96 a f^2 (a+i a \tan (e+f x))^2}+\frac{d}{36 f^2 (a+i a \tan (e+f x))^3}",1,"((I/1152)*Sec[e + f*x]^3*(27*((12*I)*c*f + d*(5 + (12*I)*f*x))*Cos[e + f*x] + 4*(6*c*f*(I + 6*f*x) + d*(1 + (6*I)*f*x + 18*f^2*x^2))*Cos[3*(e + f*x)] + (81*I)*d*Sin[e + f*x] - 108*c*f*Sin[e + f*x] - 108*d*f*x*Sin[e + f*x] - (4*I)*d*Sin[3*(e + f*x)] + 24*c*f*Sin[3*(e + f*x)] + 24*d*f*x*Sin[3*(e + f*x)] + (144*I)*c*f^2*x*Sin[3*(e + f*x)] + (72*I)*d*f^2*x^2*Sin[3*(e + f*x)]))/(a^3*f^2*(-I + Tan[e + f*x])^3)","A",1
32,1,336,449,0.8019675,"\int \frac{1}{(c+d x) (a+i a \tan (e+f x))^3} \, dx","Integrate[1/((c + d*x)*(a + I*a*Tan[e + f*x])^3),x]","\frac{\sec ^3(e+f x) (\cos (f x)+i \sin (f x))^3 \left(\left(\cos \left(e-\frac{4 c f}{d}\right)-i \sin \left(e-\frac{4 c f}{d}\right)\right) \left(-i \text{Ci}\left(\frac{6 f (c+d x)}{d}\right) \sin \left(2 e-\frac{2 c f}{d}\right)+\text{Ci}\left(\frac{6 f (c+d x)}{d}\right) \cos \left(2 e-\frac{2 c f}{d}\right)+3 \text{Ci}\left(\frac{2 f (c+d x)}{d}\right) \left(\cos \left(2 e-\frac{2 c f}{d}\right)+i \sin \left(2 e-\frac{2 c f}{d}\right)\right)+3 \text{Ci}\left(\frac{4 f (c+d x)}{d}\right)+3 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(\frac{2 f (c+d x)}{d}\right)-\sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(\frac{6 f (c+d x)}{d}\right)-3 i \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(\frac{2 f (c+d x)}{d}\right)-i \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(\frac{6 f (c+d x)}{d}\right)-3 i \text{Si}\left(\frac{4 f (c+d x)}{d}\right)\right)+i \sin (3 e) \log (f (c+d x))+\cos (3 e) \log (f (c+d x))\right)}{8 d (a+i a \tan (e+f x))^3}","-\frac{3 i \text{Ci}\left(2 x f+\frac{2 c f}{d}\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{8 a^3 d}-\frac{i \text{Ci}\left(6 x f+\frac{6 c f}{d}\right) \sin \left(6 e-\frac{6 c f}{d}\right)}{8 a^3 d}-\frac{3 i \text{Ci}\left(4 x f+\frac{4 c f}{d}\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{8 a^3 d}+\frac{3 \text{Ci}\left(2 x f+\frac{2 c f}{d}\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{8 a^3 d}+\frac{3 \text{Ci}\left(4 x f+\frac{4 c f}{d}\right) \cos \left(4 e-\frac{4 c f}{d}\right)}{8 a^3 d}+\frac{\text{Ci}\left(6 x f+\frac{6 c f}{d}\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,"(Sec[e + f*x]^3*(Cos[f*x] + I*Sin[f*x])^3*(Cos[3*e]*Log[f*(c + d*x)] + I*Log[f*(c + d*x)]*Sin[3*e] + (Cos[e - (4*c*f)/d] - I*Sin[e - (4*c*f)/d])*(3*CosIntegral[(4*f*(c + d*x))/d] + Cos[2*e - (2*c*f)/d]*CosIntegral[(6*f*(c + d*x))/d] + 3*CosIntegral[(2*f*(c + d*x))/d]*(Cos[2*e - (2*c*f)/d] + I*Sin[2*e - (2*c*f)/d]) - I*CosIntegral[(6*f*(c + d*x))/d]*Sin[2*e - (2*c*f)/d] - (3*I)*Cos[2*e - (2*c*f)/d]*SinIntegral[(2*f*(c + d*x))/d] + 3*Sin[2*e - (2*c*f)/d]*SinIntegral[(2*f*(c + d*x))/d] - (3*I)*SinIntegral[(4*f*(c + d*x))/d] - I*Cos[2*e - (2*c*f)/d]*SinIntegral[(6*f*(c + d*x))/d] - Sin[2*e - (2*c*f)/d]*SinIntegral[(6*f*(c + d*x))/d])))/(8*d*(a + I*a*Tan[e + f*x])^3)","A",0
33,1,833,712,3.1571215,"\int \frac{1}{(c+d x)^2 (a+i a \tan (e+f x))^3} \, dx","Integrate[1/((c + d*x)^2*(a + I*a*Tan[e + f*x])^3),x]","\frac{\sec ^3(e+f x) \left(\sin \left(\frac{3 c f}{d}\right)-i \cos \left(\frac{3 c f}{d}\right)\right) \left(3 d \cos \left(e+f \left(x-\frac{3 c}{d}\right)\right)+d \cos \left(3 \left(e+f \left(x-\frac{c}{d}\right)\right)\right)+d \cos \left(3 \left(e+f \left(\frac{c}{d}+x\right)\right)\right)+3 d \cos \left(e+f \left(\frac{3 c}{d}+x\right)\right)+6 i c f \cos \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Ci}\left(\frac{6 f (c+d x)}{d}\right)+6 i d f x \cos \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Ci}\left(\frac{6 f (c+d x)}{d}\right)+6 i f (c+d x) \text{Ci}\left(\frac{2 f (c+d x)}{d}\right) \left(\cos \left(e-\frac{c f}{d}+3 f x\right)+i \sin \left(e-\frac{c f}{d}+3 f x\right)\right)+3 i d \sin \left(e+f \left(x-\frac{3 c}{d}\right)\right)+i d \sin \left(3 \left(e+f \left(x-\frac{c}{d}\right)\right)\right)-i d \sin \left(3 \left(e+f \left(\frac{c}{d}+x\right)\right)\right)-3 i d \sin \left(e+f \left(\frac{3 c}{d}+x\right)\right)+6 c f \text{Ci}\left(\frac{6 f (c+d x)}{d}\right) \sin \left(3 e-\frac{3 f (c+d x)}{d}\right)+6 d f x \text{Ci}\left(\frac{6 f (c+d x)}{d}\right) \sin \left(3 e-\frac{3 f (c+d x)}{d}\right)+12 f (c+d x) \text{Ci}\left(\frac{4 f (c+d x)}{d}\right) \left(i \cos \left(e-\frac{f (c+3 d x)}{d}\right)+\sin \left(e-\frac{f (c+3 d x)}{d}\right)\right)+6 c f \cos \left(e-\frac{c f}{d}+3 f x\right) \text{Si}\left(\frac{2 f (c+d x)}{d}\right)+6 d f x \cos \left(e-\frac{c f}{d}+3 f x\right) \text{Si}\left(\frac{2 f (c+d x)}{d}\right)+6 i c f \sin \left(e-\frac{c f}{d}+3 f x\right) \text{Si}\left(\frac{2 f (c+d x)}{d}\right)+6 i d f x \sin \left(e-\frac{c f}{d}+3 f x\right) \text{Si}\left(\frac{2 f (c+d x)}{d}\right)+12 c f \cos \left(e-\frac{f (c+3 d x)}{d}\right) \text{Si}\left(\frac{4 f (c+d x)}{d}\right)+12 d f x \cos \left(e-\frac{f (c+3 d x)}{d}\right) \text{Si}\left(\frac{4 f (c+d x)}{d}\right)-12 i c f \sin \left(e-\frac{f (c+3 d x)}{d}\right) \text{Si}\left(\frac{4 f (c+d x)}{d}\right)-12 i d f x \sin \left(e-\frac{f (c+3 d x)}{d}\right) \text{Si}\left(\frac{4 f (c+d x)}{d}\right)+6 c f \cos \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Si}\left(\frac{6 f (c+d x)}{d}\right)+6 d f x \cos \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Si}\left(\frac{6 f (c+d x)}{d}\right)-6 i c f \sin \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Si}\left(\frac{6 f (c+d x)}{d}\right)-6 i d f x \sin \left(3 e-\frac{3 f (c+d x)}{d}\right) \text{Si}\left(\frac{6 f (c+d x)}{d}\right)\right)}{8 a^3 d^2 (c+d x) (\tan (e+f x)-i)^3}","-\frac{3 f \text{Ci}\left(6 x f+\frac{6 c f}{d}\right) \sin \left(6 e-\frac{6 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \text{Ci}\left(4 x f+\frac{4 c f}{d}\right) \sin \left(4 e-\frac{4 c f}{d}\right)}{2 a^3 d^2}-\frac{3 f \text{Ci}\left(2 x f+\frac{2 c f}{d}\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 i f \text{Ci}\left(2 x f+\frac{2 c f}{d}\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 i f \text{Ci}\left(4 x f+\frac{4 c f}{d}\right) \cos \left(4 e-\frac{4 c f}{d}\right)}{2 a^3 d^2}-\frac{3 i f \text{Ci}\left(6 x f+\frac{6 c f}{d}\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,"(Sec[e + f*x]^3*((-I)*Cos[(3*c*f)/d] + Sin[(3*c*f)/d])*(3*d*Cos[e + f*((-3*c)/d + x)] + d*Cos[3*(e + f*(-(c/d) + x))] + d*Cos[3*(e + f*(c/d + x))] + 3*d*Cos[e + f*((3*c)/d + x)] + (6*I)*c*f*Cos[3*e - (3*f*(c + d*x))/d]*CosIntegral[(6*f*(c + d*x))/d] + (6*I)*d*f*x*Cos[3*e - (3*f*(c + d*x))/d]*CosIntegral[(6*f*(c + d*x))/d] + (6*I)*f*(c + d*x)*CosIntegral[(2*f*(c + d*x))/d]*(Cos[e - (c*f)/d + 3*f*x] + I*Sin[e - (c*f)/d + 3*f*x]) + (3*I)*d*Sin[e + f*((-3*c)/d + x)] + I*d*Sin[3*(e + f*(-(c/d) + x))] - I*d*Sin[3*(e + f*(c/d + x))] - (3*I)*d*Sin[e + f*((3*c)/d + x)] + 6*c*f*CosIntegral[(6*f*(c + d*x))/d]*Sin[3*e - (3*f*(c + d*x))/d] + 6*d*f*x*CosIntegral[(6*f*(c + d*x))/d]*Sin[3*e - (3*f*(c + d*x))/d] + 12*f*(c + d*x)*CosIntegral[(4*f*(c + d*x))/d]*(I*Cos[e - (f*(c + 3*d*x))/d] + Sin[e - (f*(c + 3*d*x))/d]) + 6*c*f*Cos[e - (c*f)/d + 3*f*x]*SinIntegral[(2*f*(c + d*x))/d] + 6*d*f*x*Cos[e - (c*f)/d + 3*f*x]*SinIntegral[(2*f*(c + d*x))/d] + (6*I)*c*f*Sin[e - (c*f)/d + 3*f*x]*SinIntegral[(2*f*(c + d*x))/d] + (6*I)*d*f*x*Sin[e - (c*f)/d + 3*f*x]*SinIntegral[(2*f*(c + d*x))/d] + 12*c*f*Cos[e - (f*(c + 3*d*x))/d]*SinIntegral[(4*f*(c + d*x))/d] + 12*d*f*x*Cos[e - (f*(c + 3*d*x))/d]*SinIntegral[(4*f*(c + d*x))/d] - (12*I)*c*f*Sin[e - (f*(c + 3*d*x))/d]*SinIntegral[(4*f*(c + d*x))/d] - (12*I)*d*f*x*Sin[e - (f*(c + 3*d*x))/d]*SinIntegral[(4*f*(c + d*x))/d] + 6*c*f*Cos[3*e - (3*f*(c + d*x))/d]*SinIntegral[(6*f*(c + d*x))/d] + 6*d*f*x*Cos[3*e - (3*f*(c + d*x))/d]*SinIntegral[(6*f*(c + d*x))/d] - (6*I)*c*f*Sin[3*e - (3*f*(c + d*x))/d]*SinIntegral[(6*f*(c + d*x))/d] - (6*I)*d*f*x*Sin[3*e - (3*f*(c + d*x))/d]*SinIntegral[(6*f*(c + d*x))/d]))/(8*a^3*d^2*(c + d*x)*(-I + Tan[e + f*x])^3)","A",0
34,0,0,26,39.4412495,"\int (c+d x)^m (a+i a \tan (e+f x))^2 \, dx","Integrate[(c + d*x)^m*(a + I*a*Tan[e + f*x])^2,x]","\int (c+d x)^m (a+i a \tan (e+f x))^2 \, dx","\text{Int}\left((c+d x)^m (a+i a \tan (e+f x))^2,x\right)",0,"Integrate[(c + d*x)^m*(a + I*a*Tan[e + f*x])^2, x]","A",-1
35,0,0,24,15.6110479,"\int (c+d x)^m (a+i a \tan (e+f x)) \, dx","Integrate[(c + d*x)^m*(a + I*a*Tan[e + f*x]),x]","\int (c+d x)^m (a+i a \tan (e+f x)) \, dx","\text{Int}\left((c+d x)^m (a+i a \tan (e+f x)),x\right)",0,"Integrate[(c + d*x)^m*(a + I*a*Tan[e + f*x]), x]","A",-1
36,1,205,98,1.3667393,"\int \frac{(c+d x)^m}{a+i a \tan (e+f x)} \, dx","Integrate[(c + d*x)^m/(a + I*a*Tan[e + f*x]),x]","\frac{2^{-m-2} (c+d x)^m \sec (e+f x) \left(-\frac{i f (c+d x)}{d}\right)^m \left(\frac{f^2 (c+d x)^2}{d^2}\right)^{-m} \left(\sin \left(f \left(\frac{c}{d}+x\right)\right)-i \cos \left(f \left(\frac{c}{d}+x\right)\right)\right) \left(f 2^{m+1} (c+d x) \left(\frac{i f (c+d x)}{d}\right)^m \left(\cos \left(e-\frac{c f}{d}\right)+i \sin \left(e-\frac{c f}{d}\right)\right)+d (m+1) \left(\sin \left(e-\frac{c f}{d}\right)+i \cos \left(e-\frac{c f}{d}\right)\right) \Gamma \left(m+1,\frac{2 i f (c+d x)}{d}\right)\right)}{a d f (m+1) (\tan (e+f x)-i)}","\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} \Gamma \left(m+1,\frac{2 i f (c+d x)}{d}\right)}{a f}",1,"(2^(-2 - m)*(c + d*x)^m*(((-I)*f*(c + d*x))/d)^m*Sec[e + f*x]*(2^(1 + m)*f*(c + d*x)*((I*f*(c + d*x))/d)^m*(Cos[e - (c*f)/d] + I*Sin[e - (c*f)/d]) + d*(1 + m)*Gamma[1 + m, ((2*I)*f*(c + d*x))/d]*(I*Cos[e - (c*f)/d] + Sin[e - (c*f)/d]))*((-I)*Cos[f*(c/d + x)] + Sin[f*(c/d + x)]))/(a*d*f*(1 + m)*((f^2*(c + d*x)^2)/d^2)^m*(-I + Tan[e + f*x]))","B",1
37,1,192,171,48.0686223,"\int \frac{(c+d x)^m}{(a+i a \tan (e+f x))^2} \, dx","Integrate[(c + d*x)^m/(a + I*a*Tan[e + f*x])^2,x]","\frac{(c+d x)^m \sec ^2(e+f x) (\cos (f x)+i \sin (f x))^2 \left(\frac{4 e^{2 i e} f (c+d x)}{d (m+1)}+i 4^{-m} e^{\frac{4 i c f}{d}-2 i e} \left(\frac{i f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{4 i f (c+d x)}{d}\right)+i 2^{2-m} e^{\frac{2 i c f}{d}} \left(\frac{i f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 i f (c+d x)}{d}\right)\right)}{16 f (a+i a \tan (e+f x))^2}","\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} \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} \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)^m*((4*E^((2*I)*e)*f*(c + d*x))/(d*(1 + m)) + (I*2^(2 - m)*E^(((2*I)*c*f)/d)*Gamma[1 + m, ((2*I)*f*(c + d*x))/d])/((I*f*(c + d*x))/d)^m + (I*E^((-2*I)*e + ((4*I)*c*f)/d)*Gamma[1 + m, ((4*I)*f*(c + d*x))/d])/(4^m*((I*f*(c + d*x))/d)^m))*Sec[e + f*x]^2*(Cos[f*x] + I*Sin[f*x])^2)/(16*f*(a + I*a*Tan[e + f*x])^2)","A",1
38,1,269,251,68.6981392,"\int \frac{(c+d x)^m}{(a+i a \tan (e+f x))^3} \, dx","Integrate[(c + d*x)^m/(a + I*a*Tan[e + f*x])^3,x]","\frac{e^{-3 i e} 2^{-2 m-5} 3^{-m-1} (c+d x)^m \sec ^3(e+f x) (\cos (f x)+i \sin (f x))^3 \left(\frac{i f (c+d x)}{d}\right)^{-m} \left(e^{6 i e} f 12^{m+1} (c+d x) \left(\frac{i f (c+d x)}{d}\right)^m+i d 2^{m+1} 3^{m+2} (m+1) e^{2 i \left(\frac{c f}{d}+2 e\right)} \Gamma \left(m+1,\frac{2 i f (c+d x)}{d}\right)+i d 3^{m+2} (m+1) e^{\frac{4 i c f}{d}+2 i e} \Gamma \left(m+1,\frac{4 i f (c+d x)}{d}\right)+i d 2^{m+1} (m+1) e^{\frac{6 i c f}{d}} \Gamma \left(m+1,\frac{6 i f (c+d x)}{d}\right)\right)}{d f (m+1) (a+i a \tan (e+f x))^3}","\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} \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} \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} \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,"(2^(-5 - 2*m)*3^(-1 - m)*(c + d*x)^m*(12^(1 + m)*E^((6*I)*e)*f*(c + d*x)*((I*f*(c + d*x))/d)^m + I*2^(1 + m)*3^(2 + m)*d*E^((2*I)*(2*e + (c*f)/d))*(1 + m)*Gamma[1 + m, ((2*I)*f*(c + d*x))/d] + I*3^(2 + m)*d*E^((2*I)*e + ((4*I)*c*f)/d)*(1 + m)*Gamma[1 + m, ((4*I)*f*(c + d*x))/d] + I*2^(1 + m)*d*E^(((6*I)*c*f)/d)*(1 + m)*Gamma[1 + m, ((6*I)*f*(c + d*x))/d])*Sec[e + f*x]^3*(Cos[f*x] + I*Sin[f*x])^3)/(d*E^((3*I)*e)*f*(1 + m)*((I*f*(c + d*x))/d)^m*(a + I*a*Tan[e + f*x])^3)","A",1
39,1,255,152,0.3583842,"\int (c+d x)^3 (a+b \tan (e+f x)) \, dx","Integrate[(c + d*x)^3*(a + b*Tan[e + f*x]),x]","\frac{1}{4} \left(4 a c^3 x+6 a c^2 d x^2+4 a c d^2 x^3+a d^3 x^4-\frac{4 b c^3 \log (\cos (e+f x))}{f}-\frac{12 b c^2 d x \log \left(1+e^{2 i (e+f x)}\right)}{f}+6 i b c^2 d x^2-\frac{6 b d^2 (c+d x) \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{f^3}-\frac{12 b c d^2 x^2 \log \left(1+e^{2 i (e+f x)}\right)}{f}+4 i b c d^2 x^3+\frac{6 i b d (c+d x)^2 \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^2}-\frac{3 i b d^3 \text{Li}_4\left(-e^{2 i (e+f x)}\right)}{f^4}-\frac{4 b d^3 x^3 \log \left(1+e^{2 i (e+f x)}\right)}{f}+i b d^3 x^4\right)","\frac{a (c+d x)^4}{4 d}-\frac{3 b d^2 (c+d x) \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{2 f^3}+\frac{3 i b d (c+d x)^2 \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{2 f^2}-\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 i b d^3 \text{Li}_4\left(-e^{2 i (e+f x)}\right)}{4 f^4}",1,"(4*a*c^3*x + 6*a*c^2*d*x^2 + (6*I)*b*c^2*d*x^2 + 4*a*c*d^2*x^3 + (4*I)*b*c*d^2*x^3 + a*d^3*x^4 + I*b*d^3*x^4 - (12*b*c^2*d*x*Log[1 + E^((2*I)*(e + f*x))])/f - (12*b*c*d^2*x^2*Log[1 + E^((2*I)*(e + f*x))])/f - (4*b*d^3*x^3*Log[1 + E^((2*I)*(e + f*x))])/f - (4*b*c^3*Log[Cos[e + f*x]])/f + ((6*I)*b*d*(c + d*x)^2*PolyLog[2, -E^((2*I)*(e + f*x))])/f^2 - (6*b*d^2*(c + d*x)*PolyLog[3, -E^((2*I)*(e + f*x))])/f^3 - ((3*I)*b*d^3*PolyLog[4, -E^((2*I)*(e + f*x))])/f^4)/4","A",1
40,1,191,115,0.1321709,"\int (c+d x)^2 (a+b \tan (e+f x)) \, dx","Integrate[(c + d*x)^2*(a + b*Tan[e + f*x]),x]","a c^2 x+a c d x^2+\frac{1}{3} a d^2 x^3-\frac{b c^2 \log (\cos (e+f x))}{f}+\frac{i b c d \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^2}-\frac{2 b c d x \log \left(1+e^{2 i (e+f x)}\right)}{f}+i b c d x^2-\frac{b d^2 \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{2 f^3}+\frac{i b d^2 x \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^2}-\frac{b d^2 x^2 \log \left(1+e^{2 i (e+f x)}\right)}{f}+\frac{1}{3} i b d^2 x^3","\frac{a (c+d x)^3}{3 d}+\frac{i b d (c+d x) \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^2}-\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{b d^2 \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{2 f^3}",1,"a*c^2*x + a*c*d*x^2 + I*b*c*d*x^2 + (a*d^2*x^3)/3 + (I/3)*b*d^2*x^3 - (2*b*c*d*x*Log[1 + E^((2*I)*(e + f*x))])/f - (b*d^2*x^2*Log[1 + E^((2*I)*(e + f*x))])/f - (b*c^2*Log[Cos[e + f*x]])/f + (I*b*c*d*PolyLog[2, -E^((2*I)*(e + f*x))])/f^2 + (I*b*d^2*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",1
41,1,87,84,0.0151355,"\int (c+d x) (a+b \tan (e+f x)) \, dx","Integrate[(c + d*x)*(a + b*Tan[e + f*x]),x]","a c x+\frac{1}{2} a d x^2-\frac{b c \log (\cos (e+f x))}{f}+\frac{i b d \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{2 f^2}-\frac{b d x \log \left(1+e^{2 i (e+f x)}\right)}{f}+\frac{1}{2} i b d x^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{Li}_2\left(-e^{2 i (e+f x)}\right)}{2 f^2}",1,"a*c*x + (a*d*x^2)/2 + (I/2)*b*d*x^2 - (b*d*x*Log[1 + E^((2*I)*(e + f*x))])/f - (b*c*Log[Cos[e + f*x]])/f + ((I/2)*b*d*PolyLog[2, -E^((2*I)*(e + f*x))])/f^2","A",1
42,0,0,21,2.1338424,"\int \frac{a+b \tan (e+f x)}{c+d x} \, dx","Integrate[(a + b*Tan[e + f*x])/(c + d*x),x]","\int \frac{a+b \tan (e+f x)}{c+d x} \, dx","\text{Int}\left(\frac{a+b \tan (e+f x)}{c+d x},x\right)",0,"Integrate[(a + b*Tan[e + f*x])/(c + d*x), x]","A",-1
43,0,0,21,6.1379345,"\int \frac{a+b \tan (e+f x)}{(c+d x)^2} \, dx","Integrate[(a + b*Tan[e + f*x])/(c + d*x)^2,x]","\int \frac{a+b \tan (e+f x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{a+b \tan (e+f x)}{(c+d x)^2},x\right)",0,"Integrate[(a + b*Tan[e + f*x])/(c + d*x)^2, x]","A",-1
44,1,1326,300,8.0392434,"\int (c+d x)^3 (a+b \tan (e+f x))^2 \, dx","Integrate[(c + d*x)^3*(a + b*Tan[e + f*x])^2,x]","-\frac{2 a b \sec (e) (\cos (e) \log (\cos (e) \cos (f x)-\sin (e) \sin (f x))+f x \sin (e)) c^3}{f \left(\cos ^2(e)+\sin ^2(e)\right)}-\frac{3 a b d \csc (e) \left(e^{-i \tan ^{-1}(\cot (e))} f^2 x^2-\frac{\cot (e) \left(i f x \left(-2 \tan ^{-1}(\cot (e))-\pi \right)-\pi  \log \left(1+e^{-2 i f x}\right)-2 \left(f x-\tan ^{-1}(\cot (e))\right) \log \left(1-e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)+\pi  \log (\cos (f x))-2 \tan ^{-1}(\cot (e)) \log \left(\sin \left(f x-\tan ^{-1}(\cot (e))\right)\right)+i \text{Li}_2\left(e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)\right)}{\sqrt{\cot ^2(e)+1}}\right) \sec (e) c^2}{f^2 \sqrt{\csc ^2(e) \left(\cos ^2(e)+\sin ^2(e)\right)}}+\frac{3 b^2 d \sec (e) (\cos (e) \log (\cos (e) \cos (f x)-\sin (e) \sin (f x))+f x \sin (e)) c^2}{f^2 \left(\cos ^2(e)+\sin ^2(e)\right)}-\frac{i a b d^2 e^{-i e} \left(2 f^2 \left(2 f x-3 i \left(1+e^{2 i e}\right) \log \left(1+e^{-2 i (e+f x)}\right)\right) x^2+6 \left(1+e^{2 i e}\right) f \text{Li}_2\left(-e^{-2 i (e+f x)}\right) x-3 i \left(1+e^{2 i e}\right) \text{Li}_3\left(-e^{-2 i (e+f x)}\right)\right) \sec (e) c}{2 f^3}+\frac{3 b^2 d^2 \csc (e) \left(e^{-i \tan ^{-1}(\cot (e))} f^2 x^2-\frac{\cot (e) \left(i f x \left(-2 \tan ^{-1}(\cot (e))-\pi \right)-\pi  \log \left(1+e^{-2 i f x}\right)-2 \left(f x-\tan ^{-1}(\cot (e))\right) \log \left(1-e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)+\pi  \log (\cos (f x))-2 \tan ^{-1}(\cot (e)) \log \left(\sin \left(f x-\tan ^{-1}(\cot (e))\right)\right)+i \text{Li}_2\left(e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)\right)}{\sqrt{\cot ^2(e)+1}}\right) \sec (e) c}{f^3 \sqrt{\csc ^2(e) \left(\cos ^2(e)+\sin ^2(e)\right)}}+\frac{i b^2 d^3 e^{-i e} \left(2 f^2 \left(2 f x-3 i \left(1+e^{2 i e}\right) \log \left(1+e^{-2 i (e+f x)}\right)\right) x^2+6 \left(1+e^{2 i e}\right) f \text{Li}_2\left(-e^{-2 i (e+f x)}\right) x-3 i \left(1+e^{2 i e}\right) \text{Li}_3\left(-e^{-2 i (e+f x)}\right)\right) \sec (e)}{4 f^4}-\frac{1}{4} i a b d^3 e^{i e} \left(2 e^{-2 i e} x^4-\frac{4 i \left(1+e^{-2 i e}\right) \log \left(1+e^{-2 i (e+f x)}\right) x^3}{f}+\frac{3 e^{-2 i e} \left(1+e^{2 i e}\right) \left(2 f^2 \text{Li}_2\left(-e^{-2 i (e+f x)}\right) x^2-2 i f \text{Li}_3\left(-e^{-2 i (e+f x)}\right) x-\text{Li}_4\left(-e^{-2 i (e+f x)}\right)\right)}{f^4}\right) \sec (e)+\frac{\sec (e) \sec (e+f x) \left(a^2 d^3 f \cos (f x) x^4-b^2 d^3 f \cos (f x) x^4+a^2 d^3 f \cos (2 e+f x) x^4-b^2 d^3 f \cos (2 e+f x) x^4-2 a b d^3 f \sin (f x) x^4+2 a b d^3 f \sin (2 e+f x) x^4+4 a^2 c d^2 f \cos (f x) x^3-4 b^2 c d^2 f \cos (f x) x^3+4 a^2 c d^2 f \cos (2 e+f x) x^3-4 b^2 c d^2 f \cos (2 e+f x) x^3+8 b^2 d^3 \sin (f x) x^3-8 a b c d^2 f \sin (f x) x^3+8 a b c d^2 f \sin (2 e+f x) x^3+6 a^2 c^2 d f \cos (f x) x^2-6 b^2 c^2 d f \cos (f x) x^2+6 a^2 c^2 d f \cos (2 e+f x) x^2-6 b^2 c^2 d f \cos (2 e+f x) x^2+24 b^2 c d^2 \sin (f x) x^2-12 a b c^2 d f \sin (f x) x^2+12 a b c^2 d f \sin (2 e+f x) x^2+4 a^2 c^3 f \cos (f x) x-4 b^2 c^3 f \cos (f x) x+4 a^2 c^3 f \cos (2 e+f x) x-4 b^2 c^3 f \cos (2 e+f x) x+24 b^2 c^2 d \sin (f x) x-8 a b c^3 f \sin (f x) x+8 a b c^3 f \sin (2 e+f x) x+8 b^2 c^3 \sin (f x)\right)}{8 f}","\frac{a^2 (c+d x)^4}{4 d}-\frac{3 a b d^2 (c+d x) \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{f^3}+\frac{3 i a b d (c+d x)^2 \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^2}-\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 i a b d^3 \text{Li}_4\left(-e^{2 i (e+f x)}\right)}{2 f^4}-\frac{3 i b^2 d^2 (c+d x) \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^3}+\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{b^2 (c+d x)^4}{4 d}+\frac{3 b^2 d^3 \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{2 f^4}",1,"((I/4)*b^2*d^3*(2*f^2*x^2*(2*f*x - (3*I)*(1 + E^((2*I)*e))*Log[1 + E^((-2*I)*(e + f*x))]) + 6*(1 + E^((2*I)*e))*f*x*PolyLog[2, -E^((-2*I)*(e + f*x))] - (3*I)*(1 + E^((2*I)*e))*PolyLog[3, -E^((-2*I)*(e + f*x))])*Sec[e])/(E^(I*e)*f^4) - ((I/2)*a*b*c*d^2*(2*f^2*x^2*(2*f*x - (3*I)*(1 + E^((2*I)*e))*Log[1 + E^((-2*I)*(e + f*x))]) + 6*(1 + E^((2*I)*e))*f*x*PolyLog[2, -E^((-2*I)*(e + f*x))] - (3*I)*(1 + E^((2*I)*e))*PolyLog[3, -E^((-2*I)*(e + f*x))])*Sec[e])/(E^(I*e)*f^3) - (I/4)*a*b*d^3*E^(I*e)*((2*x^4)/E^((2*I)*e) - ((4*I)*(1 + E^((-2*I)*e))*x^3*Log[1 + E^((-2*I)*(e + f*x))])/f + (3*(1 + E^((2*I)*e))*(2*f^2*x^2*PolyLog[2, -E^((-2*I)*(e + f*x))] - (2*I)*f*x*PolyLog[3, -E^((-2*I)*(e + f*x))] - PolyLog[4, -E^((-2*I)*(e + f*x))]))/(E^((2*I)*e)*f^4))*Sec[e] + (3*b^2*c^2*d*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f^2*(Cos[e]^2 + Sin[e]^2)) - (2*a*b*c^3*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f*(Cos[e]^2 + Sin[e]^2)) + (3*b^2*c*d^2*Csc[e]*((f^2*x^2)/E^(I*ArcTan[Cot[e]]) - (Cot[e]*(I*f*x*(-Pi - 2*ArcTan[Cot[e]]) - Pi*Log[1 + E^((-2*I)*f*x)] - 2*(f*x - ArcTan[Cot[e]])*Log[1 - E^((2*I)*(f*x - ArcTan[Cot[e]]))] + Pi*Log[Cos[f*x]] - 2*ArcTan[Cot[e]]*Log[Sin[f*x - ArcTan[Cot[e]]]] + I*PolyLog[2, E^((2*I)*(f*x - ArcTan[Cot[e]]))]))/Sqrt[1 + Cot[e]^2])*Sec[e])/(f^3*Sqrt[Csc[e]^2*(Cos[e]^2 + Sin[e]^2)]) - (3*a*b*c^2*d*Csc[e]*((f^2*x^2)/E^(I*ArcTan[Cot[e]]) - (Cot[e]*(I*f*x*(-Pi - 2*ArcTan[Cot[e]]) - Pi*Log[1 + E^((-2*I)*f*x)] - 2*(f*x - ArcTan[Cot[e]])*Log[1 - E^((2*I)*(f*x - ArcTan[Cot[e]]))] + Pi*Log[Cos[f*x]] - 2*ArcTan[Cot[e]]*Log[Sin[f*x - ArcTan[Cot[e]]]] + I*PolyLog[2, E^((2*I)*(f*x - ArcTan[Cot[e]]))]))/Sqrt[1 + Cot[e]^2])*Sec[e])/(f^2*Sqrt[Csc[e]^2*(Cos[e]^2 + Sin[e]^2)]) + (Sec[e]*Sec[e + f*x]*(4*a^2*c^3*f*x*Cos[f*x] - 4*b^2*c^3*f*x*Cos[f*x] + 6*a^2*c^2*d*f*x^2*Cos[f*x] - 6*b^2*c^2*d*f*x^2*Cos[f*x] + 4*a^2*c*d^2*f*x^3*Cos[f*x] - 4*b^2*c*d^2*f*x^3*Cos[f*x] + a^2*d^3*f*x^4*Cos[f*x] - b^2*d^3*f*x^4*Cos[f*x] + 4*a^2*c^3*f*x*Cos[2*e + f*x] - 4*b^2*c^3*f*x*Cos[2*e + f*x] + 6*a^2*c^2*d*f*x^2*Cos[2*e + f*x] - 6*b^2*c^2*d*f*x^2*Cos[2*e + f*x] + 4*a^2*c*d^2*f*x^3*Cos[2*e + f*x] - 4*b^2*c*d^2*f*x^3*Cos[2*e + f*x] + a^2*d^3*f*x^4*Cos[2*e + f*x] - b^2*d^3*f*x^4*Cos[2*e + f*x] + 8*b^2*c^3*Sin[f*x] + 24*b^2*c^2*d*x*Sin[f*x] - 8*a*b*c^3*f*x*Sin[f*x] + 24*b^2*c*d^2*x^2*Sin[f*x] - 12*a*b*c^2*d*f*x^2*Sin[f*x] + 8*b^2*d^3*x^3*Sin[f*x] - 8*a*b*c*d^2*f*x^3*Sin[f*x] - 2*a*b*d^3*f*x^4*Sin[f*x] + 8*a*b*c^3*f*x*Sin[2*e + f*x] + 12*a*b*c^2*d*f*x^2*Sin[2*e + f*x] + 8*a*b*c*d^2*f*x^3*Sin[2*e + f*x] + 2*a*b*d^3*f*x^4*Sin[2*e + f*x]))/(8*f)","B",0
45,1,649,229,7.1845824,"\int (c+d x)^2 (a+b \tan (e+f x))^2 \, dx","Integrate[(c + d*x)^2*(a + b*Tan[e + f*x])^2,x]","\frac{1}{3} x \sec (e) \left(3 c^2+3 c d x+d^2 x^2\right) \left(a^2 \cos (e)+2 a b \sin (e)-b^2 \cos (e)\right)-\frac{2 a b c^2 \sec (e) (f x \sin (e)+\cos (e) \log (\cos (e) \cos (f x)-\sin (e) \sin (f x)))}{f \left(\sin ^2(e)+\cos ^2(e)\right)}-\frac{2 a b c d \csc (e) \sec (e) \left(f^2 x^2 e^{-i \tan ^{-1}(\cot (e))}-\frac{\cot (e) \left(i \text{Li}_2\left(e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)+i f x \left(-2 \tan ^{-1}(\cot (e))-\pi \right)-2 \left(f x-\tan ^{-1}(\cot (e))\right) \log \left(1-e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)-2 \tan ^{-1}(\cot (e)) \log \left(\sin \left(f x-\tan ^{-1}(\cot (e))\right)\right)-\pi  \log \left(1+e^{-2 i f x}\right)+\pi  \log (\cos (f x))\right)}{\sqrt{\cot ^2(e)+1}}\right)}{f^2 \sqrt{\csc ^2(e) \left(\sin ^2(e)+\cos ^2(e)\right)}}-\frac{i a b d^2 e^{-i e} \sec (e) \left(2 f^2 x^2 \left(2 f x-3 i \left(1+e^{2 i e}\right) \log \left(1+e^{-2 i (e+f x)}\right)\right)+6 \left(1+e^{2 i e}\right) f x \text{Li}_2\left(-e^{-2 i (e+f x)}\right)-3 i \left(1+e^{2 i e}\right) \text{Li}_3\left(-e^{-2 i (e+f x)}\right)\right)}{6 f^3}+\frac{\sec (e) \sec (e+f x) \left(b^2 c^2 \sin (f x)+2 b^2 c d x \sin (f x)+b^2 d^2 x^2 \sin (f x)\right)}{f}+\frac{2 b^2 c d \sec (e) (f x \sin (e)+\cos (e) \log (\cos (e) \cos (f x)-\sin (e) \sin (f x)))}{f^2 \left(\sin ^2(e)+\cos ^2(e)\right)}+\frac{b^2 d^2 \csc (e) \sec (e) \left(f^2 x^2 e^{-i \tan ^{-1}(\cot (e))}-\frac{\cot (e) \left(i \text{Li}_2\left(e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)+i f x \left(-2 \tan ^{-1}(\cot (e))-\pi \right)-2 \left(f x-\tan ^{-1}(\cot (e))\right) \log \left(1-e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)-2 \tan ^{-1}(\cot (e)) \log \left(\sin \left(f x-\tan ^{-1}(\cot (e))\right)\right)-\pi  \log \left(1+e^{-2 i f x}\right)+\pi  \log (\cos (f x))\right)}{\sqrt{\cot ^2(e)+1}}\right)}{f^3 \sqrt{\csc ^2(e) \left(\sin ^2(e)+\cos ^2(e)\right)}}","\frac{a^2 (c+d x)^3}{3 d}+\frac{2 i a b d (c+d x) \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^2}-\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{a b d^2 \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{f^3}+\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{b^2 (c+d x)^3}{3 d}-\frac{i b^2 d^2 \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^3}",1,"((-1/6*I)*a*b*d^2*(2*f^2*x^2*(2*f*x - (3*I)*(1 + E^((2*I)*e))*Log[1 + E^((-2*I)*(e + f*x))]) + 6*(1 + E^((2*I)*e))*f*x*PolyLog[2, -E^((-2*I)*(e + f*x))] - (3*I)*(1 + E^((2*I)*e))*PolyLog[3, -E^((-2*I)*(e + f*x))])*Sec[e])/(E^(I*e)*f^3) + (x*(3*c^2 + 3*c*d*x + d^2*x^2)*Sec[e]*(a^2*Cos[e] - b^2*Cos[e] + 2*a*b*Sin[e]))/3 + (2*b^2*c*d*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f^2*(Cos[e]^2 + Sin[e]^2)) - (2*a*b*c^2*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f*(Cos[e]^2 + Sin[e]^2)) + (b^2*d^2*Csc[e]*((f^2*x^2)/E^(I*ArcTan[Cot[e]]) - (Cot[e]*(I*f*x*(-Pi - 2*ArcTan[Cot[e]]) - Pi*Log[1 + E^((-2*I)*f*x)] - 2*(f*x - ArcTan[Cot[e]])*Log[1 - E^((2*I)*(f*x - ArcTan[Cot[e]]))] + Pi*Log[Cos[f*x]] - 2*ArcTan[Cot[e]]*Log[Sin[f*x - ArcTan[Cot[e]]]] + I*PolyLog[2, E^((2*I)*(f*x - ArcTan[Cot[e]]))]))/Sqrt[1 + Cot[e]^2])*Sec[e])/(f^3*Sqrt[Csc[e]^2*(Cos[e]^2 + Sin[e]^2)]) - (2*a*b*c*d*Csc[e]*((f^2*x^2)/E^(I*ArcTan[Cot[e]]) - (Cot[e]*(I*f*x*(-Pi - 2*ArcTan[Cot[e]]) - Pi*Log[1 + E^((-2*I)*f*x)] - 2*(f*x - ArcTan[Cot[e]])*Log[1 - E^((2*I)*(f*x - ArcTan[Cot[e]]))] + Pi*Log[Cos[f*x]] - 2*ArcTan[Cot[e]]*Log[Sin[f*x - ArcTan[Cot[e]]]] + I*PolyLog[2, E^((2*I)*(f*x - ArcTan[Cot[e]]))]))/Sqrt[1 + Cot[e]^2])*Sec[e])/(f^2*Sqrt[Csc[e]^2*(Cos[e]^2 + Sin[e]^2)]) + (Sec[e]*Sec[e + f*x]*(b^2*c^2*Sin[f*x] + 2*b^2*c*d*x*Sin[f*x] + b^2*d^2*x^2*Sin[f*x]))/f","B",0
46,1,200,136,2.3205058,"\int (c+d x) (a+b \tan (e+f x))^2 \, dx","Integrate[(c + d*x)*(a + b*Tan[e + f*x])^2,x]","\frac{\cos (e+f x) (a+b \tan (e+f x))^2 \left(\cos (e+f x) \left(-\left((e+f x) \left(a^2 (-2 c f+d e-d f x)-2 i a b d (e+f x)+b^2 (2 c f-d e+d f x)\right)\right)+2 b \log (\cos (e+f x)) (-2 a c f+2 a d e+b d)-4 a b d (e+f x) \log \left(1+e^{2 i (e+f x)}\right)\right)+2 i a b d \text{Li}_2\left(-e^{2 i (e+f x)}\right) \cos (e+f x)+2 b^2 f (c+d x) \sin (e+f x)\right)}{2 f^2 (a \cos (e+f x)+b \sin (e+f x))^2}","\frac{a^2 (c+d x)^2}{2 d}-\frac{2 a b (c+d x) \log \left(1+e^{2 i (e+f x)}\right)}{f}+\frac{i a b (c+d x)^2}{d}+\frac{i a b d \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^2}+\frac{b^2 (c+d x) \tan (e+f x)}{f}-b^2 c x+\frac{b^2 d \log (\cos (e+f x))}{f^2}-\frac{1}{2} b^2 d x^2",1,"(Cos[e + f*x]*(Cos[e + f*x]*(-((e + f*x)*((-2*I)*a*b*d*(e + f*x) + a^2*(d*e - 2*c*f - d*f*x) + b^2*(-(d*e) + 2*c*f + d*f*x))) - 4*a*b*d*(e + f*x)*Log[1 + E^((2*I)*(e + f*x))] + 2*b*(b*d + 2*a*d*e - 2*a*c*f)*Log[Cos[e + f*x]]) + (2*I)*a*b*d*Cos[e + f*x]*PolyLog[2, -E^((2*I)*(e + f*x))] + 2*b^2*f*(c + d*x)*Sin[e + f*x])*(a + b*Tan[e + f*x])^2)/(2*f^2*(a*Cos[e + f*x] + b*Sin[e + f*x])^2)","A",1
47,0,0,23,20.2722228,"\int \frac{(a+b \tan (e+f x))^2}{c+d x} \, dx","Integrate[(a + b*Tan[e + f*x])^2/(c + d*x),x]","\int \frac{(a+b \tan (e+f x))^2}{c+d x} \, dx","\text{Int}\left(\frac{(a+b \tan (e+f x))^2}{c+d x},x\right)",0,"Integrate[(a + b*Tan[e + f*x])^2/(c + d*x), x]","A",-1
48,0,0,23,15.6906061,"\int \frac{(a+b \tan (e+f x))^2}{(c+d x)^2} \, dx","Integrate[(a + b*Tan[e + f*x])^2/(c + d*x)^2,x]","\int \frac{(a+b \tan (e+f x))^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{(a+b \tan (e+f x))^2}{(c+d x)^2},x\right)",0,"Integrate[(a + b*Tan[e + f*x])^2/(c + d*x)^2, x]","A",-1
49,1,2572,612,8.4763236,"\int (c+d x)^3 (a+b \tan (e+f x))^3 \, dx","Integrate[(c + d*x)^3*(a + b*Tan[e + f*x])^3,x]","\text{Result too large to show}","\frac{a^3 (c+d x)^4}{4 d}-\frac{9 a^2 b d^2 (c+d x) \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{2 f^3}+\frac{9 i a^2 b d (c+d x)^2 \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{2 f^2}-\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{9 i a^2 b d^3 \text{Li}_4\left(-e^{2 i (e+f x)}\right)}{4 f^4}-\frac{9 i a b^2 d^2 (c+d x) \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^3}+\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 \tan (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{9 a b^2 d^3 \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{2 f^4}+\frac{3 b^3 d^2 (c+d x) \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{2 f^3}-\frac{3 b^3 d^2 (c+d x) \log \left(1+e^{2 i (e+f x)}\right)}{f^3}-\frac{3 i b^3 d (c+d x)^2 \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{2 f^2}-\frac{3 b^3 d (c+d x)^2 \tan (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 \tan ^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{3 i b^3 d^3 \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{2 f^4}+\frac{3 i b^3 d^3 \text{Li}_4\left(-e^{2 i (e+f x)}\right)}{4 f^4}",1,"(((3*I)/4)*a*b^2*d^3*(2*f^2*x^2*(2*f*x - (3*I)*(1 + E^((2*I)*e))*Log[1 + E^((-2*I)*(e + f*x))]) + 6*(1 + E^((2*I)*e))*f*x*PolyLog[2, -E^((-2*I)*(e + f*x))] - (3*I)*(1 + E^((2*I)*e))*PolyLog[3, -E^((-2*I)*(e + f*x))])*Sec[e])/(E^(I*e)*f^4) - (((3*I)/4)*a^2*b*c*d^2*(2*f^2*x^2*(2*f*x - (3*I)*(1 + E^((2*I)*e))*Log[1 + E^((-2*I)*(e + f*x))]) + 6*(1 + E^((2*I)*e))*f*x*PolyLog[2, -E^((-2*I)*(e + f*x))] - (3*I)*(1 + E^((2*I)*e))*PolyLog[3, -E^((-2*I)*(e + f*x))])*Sec[e])/(E^(I*e)*f^3) + ((I/4)*b^3*c*d^2*(2*f^2*x^2*(2*f*x - (3*I)*(1 + E^((2*I)*e))*Log[1 + E^((-2*I)*(e + f*x))]) + 6*(1 + E^((2*I)*e))*f*x*PolyLog[2, -E^((-2*I)*(e + f*x))] - (3*I)*(1 + E^((2*I)*e))*PolyLog[3, -E^((-2*I)*(e + f*x))])*Sec[e])/(E^(I*e)*f^3) - ((3*I)/8)*a^2*b*d^3*E^(I*e)*((2*x^4)/E^((2*I)*e) - ((4*I)*(1 + E^((-2*I)*e))*x^3*Log[1 + E^((-2*I)*(e + f*x))])/f + (3*(1 + E^((2*I)*e))*(2*f^2*x^2*PolyLog[2, -E^((-2*I)*(e + f*x))] - (2*I)*f*x*PolyLog[3, -E^((-2*I)*(e + f*x))] - PolyLog[4, -E^((-2*I)*(e + f*x))]))/(E^((2*I)*e)*f^4))*Sec[e] + (I/8)*b^3*d^3*E^(I*e)*((2*x^4)/E^((2*I)*e) - ((4*I)*(1 + E^((-2*I)*e))*x^3*Log[1 + E^((-2*I)*(e + f*x))])/f + (3*(1 + E^((2*I)*e))*(2*f^2*x^2*PolyLog[2, -E^((-2*I)*(e + f*x))] - (2*I)*f*x*PolyLog[3, -E^((-2*I)*(e + f*x))] - PolyLog[4, -E^((-2*I)*(e + f*x))]))/(E^((2*I)*e)*f^4))*Sec[e] + ((b^3*c^3 + 3*b^3*c^2*d*x + 3*b^3*c*d^2*x^2 + b^3*d^3*x^3)*Sec[e + f*x]^2)/(2*f) - (3*b^3*c*d^2*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f^3*(Cos[e]^2 + Sin[e]^2)) + (9*a*b^2*c^2*d*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f^2*(Cos[e]^2 + Sin[e]^2)) - (3*a^2*b*c^3*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f*(Cos[e]^2 + Sin[e]^2)) + (b^3*c^3*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f*(Cos[e]^2 + Sin[e]^2)) - (3*b^3*d^3*Csc[e]*((f^2*x^2)/E^(I*ArcTan[Cot[e]]) - (Cot[e]*(I*f*x*(-Pi - 2*ArcTan[Cot[e]]) - Pi*Log[1 + E^((-2*I)*f*x)] - 2*(f*x - ArcTan[Cot[e]])*Log[1 - E^((2*I)*(f*x - ArcTan[Cot[e]]))] + Pi*Log[Cos[f*x]] - 2*ArcTan[Cot[e]]*Log[Sin[f*x - ArcTan[Cot[e]]]] + I*PolyLog[2, E^((2*I)*(f*x - ArcTan[Cot[e]]))]))/Sqrt[1 + Cot[e]^2])*Sec[e])/(2*f^4*Sqrt[Csc[e]^2*(Cos[e]^2 + Sin[e]^2)]) + (9*a*b^2*c*d^2*Csc[e]*((f^2*x^2)/E^(I*ArcTan[Cot[e]]) - (Cot[e]*(I*f*x*(-Pi - 2*ArcTan[Cot[e]]) - Pi*Log[1 + E^((-2*I)*f*x)] - 2*(f*x - ArcTan[Cot[e]])*Log[1 - E^((2*I)*(f*x - ArcTan[Cot[e]]))] + Pi*Log[Cos[f*x]] - 2*ArcTan[Cot[e]]*Log[Sin[f*x - ArcTan[Cot[e]]]] + I*PolyLog[2, E^((2*I)*(f*x - ArcTan[Cot[e]]))]))/Sqrt[1 + Cot[e]^2])*Sec[e])/(f^3*Sqrt[Csc[e]^2*(Cos[e]^2 + Sin[e]^2)]) - (9*a^2*b*c^2*d*Csc[e]*((f^2*x^2)/E^(I*ArcTan[Cot[e]]) - (Cot[e]*(I*f*x*(-Pi - 2*ArcTan[Cot[e]]) - Pi*Log[1 + E^((-2*I)*f*x)] - 2*(f*x - ArcTan[Cot[e]])*Log[1 - E^((2*I)*(f*x - ArcTan[Cot[e]]))] + Pi*Log[Cos[f*x]] - 2*ArcTan[Cot[e]]*Log[Sin[f*x - ArcTan[Cot[e]]]] + I*PolyLog[2, E^((2*I)*(f*x - ArcTan[Cot[e]]))]))/Sqrt[1 + Cot[e]^2])*Sec[e])/(2*f^2*Sqrt[Csc[e]^2*(Cos[e]^2 + Sin[e]^2)]) + (3*b^3*c^2*d*Csc[e]*((f^2*x^2)/E^(I*ArcTan[Cot[e]]) - (Cot[e]*(I*f*x*(-Pi - 2*ArcTan[Cot[e]]) - Pi*Log[1 + E^((-2*I)*f*x)] - 2*(f*x - ArcTan[Cot[e]])*Log[1 - E^((2*I)*(f*x - ArcTan[Cot[e]]))] + Pi*Log[Cos[f*x]] - 2*ArcTan[Cot[e]]*Log[Sin[f*x - ArcTan[Cot[e]]]] + I*PolyLog[2, E^((2*I)*(f*x - ArcTan[Cot[e]]))]))/Sqrt[1 + Cot[e]^2])*Sec[e])/(2*f^2*Sqrt[Csc[e]^2*(Cos[e]^2 + Sin[e]^2)]) + (3*x^2*(a^3*c^2*d + (3*I)*a^2*b*c^2*d - 3*a*b^2*c^2*d - I*b^3*c^2*d + a^3*c^2*d*Cos[2*e] - (3*I)*a^2*b*c^2*d*Cos[2*e] - 3*a*b^2*c^2*d*Cos[2*e] + I*b^3*c^2*d*Cos[2*e] + I*a^3*c^2*d*Sin[2*e] + 3*a^2*b*c^2*d*Sin[2*e] - (3*I)*a*b^2*c^2*d*Sin[2*e] - b^3*c^2*d*Sin[2*e]))/(2*(1 + Cos[2*e] + I*Sin[2*e])) + (x^3*(a^3*c*d^2 + (3*I)*a^2*b*c*d^2 - 3*a*b^2*c*d^2 - I*b^3*c*d^2 + a^3*c*d^2*Cos[2*e] - (3*I)*a^2*b*c*d^2*Cos[2*e] - 3*a*b^2*c*d^2*Cos[2*e] + I*b^3*c*d^2*Cos[2*e] + I*a^3*c*d^2*Sin[2*e] + 3*a^2*b*c*d^2*Sin[2*e] - (3*I)*a*b^2*c*d^2*Sin[2*e] - b^3*c*d^2*Sin[2*e]))/(1 + Cos[2*e] + I*Sin[2*e]) + (x^4*(a^3*d^3 + (3*I)*a^2*b*d^3 - 3*a*b^2*d^3 - I*b^3*d^3 + a^3*d^3*Cos[2*e] - (3*I)*a^2*b*d^3*Cos[2*e] - 3*a*b^2*d^3*Cos[2*e] + I*b^3*d^3*Cos[2*e] + I*a^3*d^3*Sin[2*e] + 3*a^2*b*d^3*Sin[2*e] - (3*I)*a*b^2*d^3*Sin[2*e] - b^3*d^3*Sin[2*e]))/(4*(1 + Cos[2*e] + I*Sin[2*e])) + x*(a^3*c^3 - 3*a*b^2*c^3 + ((3*I)*a^2*b*c^3)/(1 + Cos[2*e] + I*Sin[2*e]) + ((-3*I)*a^2*b*c^3*Cos[2*e] + 3*a^2*b*c^3*Sin[2*e])/(1 + Cos[2*e] + I*Sin[2*e]) + ((2*I)*b^3*c^3*Cos[2*e] - 2*b^3*c^3*Sin[2*e])/((1 + Cos[2*e] + I*Sin[2*e])*(1 - Cos[2*e] + Cos[4*e] - I*Sin[2*e] + I*Sin[4*e])) + ((-2*I)*b^3*c^3*Cos[4*e] + 2*b^3*c^3*Sin[4*e])/((1 + Cos[2*e] + I*Sin[2*e])*(1 - Cos[2*e] + Cos[4*e] - I*Sin[2*e] + I*Sin[4*e])) - (I*b^3*c^3)/(1 + Cos[6*e] + I*Sin[6*e]) + (I*b^3*c^3*Cos[6*e] - b^3*c^3*Sin[6*e])/(1 + Cos[6*e] + I*Sin[6*e])) + (3*Sec[e]*Sec[e + f*x]*(-(b^3*c^2*d*Sin[f*x]) + 2*a*b^2*c^3*f*Sin[f*x] - 2*b^3*c*d^2*x*Sin[f*x] + 6*a*b^2*c^2*d*f*x*Sin[f*x] - b^3*d^3*x^2*Sin[f*x] + 6*a*b^2*c*d^2*f*x^2*Sin[f*x] + 2*a*b^2*d^3*f*x^3*Sin[f*x]))/(2*f^2)","B",0
50,1,1846,436,7.8481041,"\int (c+d x)^2 (a+b \tan (e+f x))^3 \, dx","Integrate[(c + d*x)^2*(a + b*Tan[e + f*x])^3,x]","\frac{i d^2 e^{-i e} \left(2 f^2 \left(2 f x-3 i \left(1+e^{2 i e}\right) \log \left(1+e^{-2 i (e+f x)}\right)\right) x^2+6 \left(1+e^{2 i e}\right) f \text{Li}_2\left(-e^{-2 i (e+f x)}\right) x-3 i \left(1+e^{2 i e}\right) \text{Li}_3\left(-e^{-2 i (e+f x)}\right)\right) \sec (e) b^3}{12 f^3}+\frac{c d \csc (e) \left(e^{-i \tan ^{-1}(\cot (e))} f^2 x^2-\frac{\cot (e) \left(i f x \left(-2 \tan ^{-1}(\cot (e))-\pi \right)-\pi  \log \left(1+e^{-2 i f x}\right)-2 \left(f x-\tan ^{-1}(\cot (e))\right) \log \left(1-e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)+\pi  \log (\cos (f x))-2 \tan ^{-1}(\cot (e)) \log \left(\sin \left(f x-\tan ^{-1}(\cot (e))\right)\right)+i \text{Li}_2\left(e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)\right)}{\sqrt{\cot ^2(e)+1}}\right) \sec (e) b^3}{f^2 \sqrt{\csc ^2(e) \left(\cos ^2(e)+\sin ^2(e)\right)}}+\frac{c^2 \sec (e) (\cos (e) \log (\cos (e) \cos (f x)-\sin (e) \sin (f x))+f x \sin (e)) b^3}{f \left(\cos ^2(e)+\sin ^2(e)\right)}-\frac{d^2 \sec (e) (\cos (e) \log (\cos (e) \cos (f x)-\sin (e) \sin (f x))+f x \sin (e)) b^3}{f^3 \left(\cos ^2(e)+\sin ^2(e)\right)}+\frac{3 a d^2 \csc (e) \left(e^{-i \tan ^{-1}(\cot (e))} f^2 x^2-\frac{\cot (e) \left(i f x \left(-2 \tan ^{-1}(\cot (e))-\pi \right)-\pi  \log \left(1+e^{-2 i f x}\right)-2 \left(f x-\tan ^{-1}(\cot (e))\right) \log \left(1-e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)+\pi  \log (\cos (f x))-2 \tan ^{-1}(\cot (e)) \log \left(\sin \left(f x-\tan ^{-1}(\cot (e))\right)\right)+i \text{Li}_2\left(e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)\right)}{\sqrt{\cot ^2(e)+1}}\right) \sec (e) b^2}{f^3 \sqrt{\csc ^2(e) \left(\cos ^2(e)+\sin ^2(e)\right)}}+\frac{6 a c d \sec (e) (\cos (e) \log (\cos (e) \cos (f x)-\sin (e) \sin (f x))+f x \sin (e)) b^2}{f^2 \left(\cos ^2(e)+\sin ^2(e)\right)}-\frac{i a^2 d^2 e^{-i e} \left(2 f^2 \left(2 f x-3 i \left(1+e^{2 i e}\right) \log \left(1+e^{-2 i (e+f x)}\right)\right) x^2+6 \left(1+e^{2 i e}\right) f \text{Li}_2\left(-e^{-2 i (e+f x)}\right) x-3 i \left(1+e^{2 i e}\right) \text{Li}_3\left(-e^{-2 i (e+f x)}\right)\right) \sec (e) b}{4 f^3}-\frac{3 a^2 c d \csc (e) \left(e^{-i \tan ^{-1}(\cot (e))} f^2 x^2-\frac{\cot (e) \left(i f x \left(-2 \tan ^{-1}(\cot (e))-\pi \right)-\pi  \log \left(1+e^{-2 i f x}\right)-2 \left(f x-\tan ^{-1}(\cot (e))\right) \log \left(1-e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)+\pi  \log (\cos (f x))-2 \tan ^{-1}(\cot (e)) \log \left(\sin \left(f x-\tan ^{-1}(\cot (e))\right)\right)+i \text{Li}_2\left(e^{2 i \left(f x-\tan ^{-1}(\cot (e))\right)}\right)\right)}{\sqrt{\cot ^2(e)+1}}\right) \sec (e) b}{f^2 \sqrt{\csc ^2(e) \left(\cos ^2(e)+\sin ^2(e)\right)}}-\frac{3 a^2 c^2 \sec (e) (\cos (e) \log (\cos (e) \cos (f x)-\sin (e) \sin (f x))+f x \sin (e)) b}{f \left(\cos ^2(e)+\sin ^2(e)\right)}+\frac{\sec (e) \sec ^2(e+f x) \left(2 d^2 f^2 x^3 \cos (e) a^3+6 c d f^2 x^2 \cos (e) a^3+6 c^2 f^2 x \cos (e) a^3+d^2 f^2 x^3 \cos (e+2 f x) a^3+3 c d f^2 x^2 \cos (e+2 f x) a^3+3 c^2 f^2 x \cos (e+2 f x) a^3+d^2 f^2 x^3 \cos (3 e+2 f x) a^3+3 c d f^2 x^2 \cos (3 e+2 f x) a^3+3 c^2 f^2 x \cos (3 e+2 f x) a^3+6 b d^2 f^2 x^3 \sin (e) a^2+18 b c d f^2 x^2 \sin (e) a^2+18 b c^2 f^2 x \sin (e) a^2-3 b d^2 f^2 x^3 \sin (e+2 f x) a^2-9 b c d f^2 x^2 \sin (e+2 f x) a^2-9 b c^2 f^2 x \sin (e+2 f x) a^2+3 b d^2 f^2 x^3 \sin (3 e+2 f x) a^2+9 b c d f^2 x^2 \sin (3 e+2 f x) a^2+9 b c^2 f^2 x \sin (3 e+2 f x) a^2-6 b^2 d^2 f^2 x^3 \cos (e) a-18 b^2 c d f^2 x^2 \cos (e) a-18 b^2 c^2 f^2 x \cos (e) a-3 b^2 d^2 f^2 x^3 \cos (e+2 f x) a-9 b^2 c d f^2 x^2 \cos (e+2 f x) a-9 b^2 c^2 f^2 x \cos (e+2 f x) a-3 b^2 d^2 f^2 x^3 \cos (3 e+2 f x) a-9 b^2 c d f^2 x^2 \cos (3 e+2 f x) a-9 b^2 c^2 f^2 x \cos (3 e+2 f x) a-18 b^2 d^2 f x^2 \sin (e) a-18 b^2 c^2 f \sin (e) a-36 b^2 c d f x \sin (e) a+18 b^2 d^2 f x^2 \sin (e+2 f x) a+18 b^2 c^2 f \sin (e+2 f x) a+36 b^2 c d f x \sin (e+2 f x) a+6 b^3 d^2 f x^2 \cos (e)+6 b^3 c^2 f \cos (e)+12 b^3 c d f x \cos (e)-2 b^3 d^2 f^2 x^3 \sin (e)-6 b^3 c d f^2 x^2 \sin (e)+6 b^3 c d \sin (e)+6 b^3 d^2 x \sin (e)-6 b^3 c^2 f^2 x \sin (e)+b^3 d^2 f^2 x^3 \sin (e+2 f x)+3 b^3 c d f^2 x^2 \sin (e+2 f x)-6 b^3 c d \sin (e+2 f x)-6 b^3 d^2 x \sin (e+2 f x)+3 b^3 c^2 f^2 x \sin (e+2 f x)-b^3 d^2 f^2 x^3 \sin (3 e+2 f x)-3 b^3 c d f^2 x^2 \sin (3 e+2 f x)-3 b^3 c^2 f^2 x \sin (3 e+2 f x)\right)}{12 f^2}","\frac{a^3 (c+d x)^3}{3 d}+\frac{3 i a^2 b d (c+d x) \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^2}-\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{3 a^2 b d^2 \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{2 f^3}+\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 \tan (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{3 i a b^2 d^2 \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^3}-\frac{i b^3 d (c+d x) \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{f^2}-\frac{b^3 d (c+d x) \tan (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 \tan ^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 \text{Li}_3\left(-e^{2 i (e+f x)}\right)}{2 f^3}-\frac{b^3 d^2 \log (\cos (e+f x))}{f^3}+\frac{b^3 d^2 x^2}{2 f}",1,"((-1/4*I)*a^2*b*d^2*(2*f^2*x^2*(2*f*x - (3*I)*(1 + E^((2*I)*e))*Log[1 + E^((-2*I)*(e + f*x))]) + 6*(1 + E^((2*I)*e))*f*x*PolyLog[2, -E^((-2*I)*(e + f*x))] - (3*I)*(1 + E^((2*I)*e))*PolyLog[3, -E^((-2*I)*(e + f*x))])*Sec[e])/(E^(I*e)*f^3) + ((I/12)*b^3*d^2*(2*f^2*x^2*(2*f*x - (3*I)*(1 + E^((2*I)*e))*Log[1 + E^((-2*I)*(e + f*x))]) + 6*(1 + E^((2*I)*e))*f*x*PolyLog[2, -E^((-2*I)*(e + f*x))] - (3*I)*(1 + E^((2*I)*e))*PolyLog[3, -E^((-2*I)*(e + f*x))])*Sec[e])/(E^(I*e)*f^3) - (b^3*d^2*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f^3*(Cos[e]^2 + Sin[e]^2)) + (6*a*b^2*c*d*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f^2*(Cos[e]^2 + Sin[e]^2)) - (3*a^2*b*c^2*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f*(Cos[e]^2 + Sin[e]^2)) + (b^3*c^2*Sec[e]*(Cos[e]*Log[Cos[e]*Cos[f*x] - Sin[e]*Sin[f*x]] + f*x*Sin[e]))/(f*(Cos[e]^2 + Sin[e]^2)) + (3*a*b^2*d^2*Csc[e]*((f^2*x^2)/E^(I*ArcTan[Cot[e]]) - (Cot[e]*(I*f*x*(-Pi - 2*ArcTan[Cot[e]]) - Pi*Log[1 + E^((-2*I)*f*x)] - 2*(f*x - ArcTan[Cot[e]])*Log[1 - E^((2*I)*(f*x - ArcTan[Cot[e]]))] + Pi*Log[Cos[f*x]] - 2*ArcTan[Cot[e]]*Log[Sin[f*x - ArcTan[Cot[e]]]] + I*PolyLog[2, E^((2*I)*(f*x - ArcTan[Cot[e]]))]))/Sqrt[1 + Cot[e]^2])*Sec[e])/(f^3*Sqrt[Csc[e]^2*(Cos[e]^2 + Sin[e]^2)]) - (3*a^2*b*c*d*Csc[e]*((f^2*x^2)/E^(I*ArcTan[Cot[e]]) - (Cot[e]*(I*f*x*(-Pi - 2*ArcTan[Cot[e]]) - Pi*Log[1 + E^((-2*I)*f*x)] - 2*(f*x - ArcTan[Cot[e]])*Log[1 - E^((2*I)*(f*x - ArcTan[Cot[e]]))] + Pi*Log[Cos[f*x]] - 2*ArcTan[Cot[e]]*Log[Sin[f*x - ArcTan[Cot[e]]]] + I*PolyLog[2, E^((2*I)*(f*x - ArcTan[Cot[e]]))]))/Sqrt[1 + Cot[e]^2])*Sec[e])/(f^2*Sqrt[Csc[e]^2*(Cos[e]^2 + Sin[e]^2)]) + (b^3*c*d*Csc[e]*((f^2*x^2)/E^(I*ArcTan[Cot[e]]) - (Cot[e]*(I*f*x*(-Pi - 2*ArcTan[Cot[e]]) - Pi*Log[1 + E^((-2*I)*f*x)] - 2*(f*x - ArcTan[Cot[e]])*Log[1 - E^((2*I)*(f*x - ArcTan[Cot[e]]))] + Pi*Log[Cos[f*x]] - 2*ArcTan[Cot[e]]*Log[Sin[f*x - ArcTan[Cot[e]]]] + I*PolyLog[2, E^((2*I)*(f*x - ArcTan[Cot[e]]))]))/Sqrt[1 + Cot[e]^2])*Sec[e])/(f^2*Sqrt[Csc[e]^2*(Cos[e]^2 + Sin[e]^2)]) + (Sec[e]*Sec[e + f*x]^2*(6*b^3*c^2*f*Cos[e] + 12*b^3*c*d*f*x*Cos[e] + 6*a^3*c^2*f^2*x*Cos[e] - 18*a*b^2*c^2*f^2*x*Cos[e] + 6*b^3*d^2*f*x^2*Cos[e] + 6*a^3*c*d*f^2*x^2*Cos[e] - 18*a*b^2*c*d*f^2*x^2*Cos[e] + 2*a^3*d^2*f^2*x^3*Cos[e] - 6*a*b^2*d^2*f^2*x^3*Cos[e] + 3*a^3*c^2*f^2*x*Cos[e + 2*f*x] - 9*a*b^2*c^2*f^2*x*Cos[e + 2*f*x] + 3*a^3*c*d*f^2*x^2*Cos[e + 2*f*x] - 9*a*b^2*c*d*f^2*x^2*Cos[e + 2*f*x] + a^3*d^2*f^2*x^3*Cos[e + 2*f*x] - 3*a*b^2*d^2*f^2*x^3*Cos[e + 2*f*x] + 3*a^3*c^2*f^2*x*Cos[3*e + 2*f*x] - 9*a*b^2*c^2*f^2*x*Cos[3*e + 2*f*x] + 3*a^3*c*d*f^2*x^2*Cos[3*e + 2*f*x] - 9*a*b^2*c*d*f^2*x^2*Cos[3*e + 2*f*x] + a^3*d^2*f^2*x^3*Cos[3*e + 2*f*x] - 3*a*b^2*d^2*f^2*x^3*Cos[3*e + 2*f*x] + 6*b^3*c*d*Sin[e] - 18*a*b^2*c^2*f*Sin[e] + 6*b^3*d^2*x*Sin[e] - 36*a*b^2*c*d*f*x*Sin[e] + 18*a^2*b*c^2*f^2*x*Sin[e] - 6*b^3*c^2*f^2*x*Sin[e] - 18*a*b^2*d^2*f*x^2*Sin[e] + 18*a^2*b*c*d*f^2*x^2*Sin[e] - 6*b^3*c*d*f^2*x^2*Sin[e] + 6*a^2*b*d^2*f^2*x^3*Sin[e] - 2*b^3*d^2*f^2*x^3*Sin[e] - 6*b^3*c*d*Sin[e + 2*f*x] + 18*a*b^2*c^2*f*Sin[e + 2*f*x] - 6*b^3*d^2*x*Sin[e + 2*f*x] + 36*a*b^2*c*d*f*x*Sin[e + 2*f*x] - 9*a^2*b*c^2*f^2*x*Sin[e + 2*f*x] + 3*b^3*c^2*f^2*x*Sin[e + 2*f*x] + 18*a*b^2*d^2*f*x^2*Sin[e + 2*f*x] - 9*a^2*b*c*d*f^2*x^2*Sin[e + 2*f*x] + 3*b^3*c*d*f^2*x^2*Sin[e + 2*f*x] - 3*a^2*b*d^2*f^2*x^3*Sin[e + 2*f*x] + b^3*d^2*f^2*x^3*Sin[e + 2*f*x] + 9*a^2*b*c^2*f^2*x*Sin[3*e + 2*f*x] - 3*b^3*c^2*f^2*x*Sin[3*e + 2*f*x] + 9*a^2*b*c*d*f^2*x^2*Sin[3*e + 2*f*x] - 3*b^3*c*d*f^2*x^2*Sin[3*e + 2*f*x] + 3*a^2*b*d^2*f^2*x^3*Sin[3*e + 2*f*x] - b^3*d^2*f^2*x^3*Sin[3*e + 2*f*x]))/(12*f^2)","B",0
51,1,277,277,3.68627,"\int (c+d x) (a+b \tan (e+f x))^3 \, dx","Integrate[(c + d*x)*(a + b*Tan[e + f*x])^3,x]","\frac{\cos (e+f x) (a+b \tan (e+f x))^3 \left(-i b d \left(b^2-3 a^2\right) \text{Li}_2\left(-e^{2 i (e+f x)}\right) \cos ^2(e+f x)+\cos ^2(e+f x) \left(2 b \log (\cos (e+f x)) \left(3 a^2 (d e-c f)+3 a b d+b^2 (c f-d e)\right)+2 b d \left(b^2-3 a^2\right) (e+f x) \log \left(1+e^{2 i (e+f x)}\right)-\left((e+f x) \left(a^3 (d (e-f x)-2 c f)-3 i a^2 b d (e+f x)+3 a b^2 (2 c f-d e+d f x)+i b^3 d (e+f x)\right)\right)\right)+\frac{1}{2} b^2 (\sin (2 (e+f x)) (6 a f (c+d x)-b d)+2 b f (c+d x))\right)}{2 f^2 (a \cos (e+f x)+b \sin (e+f x))^3}","\frac{a^3 (c+d x)^2}{2 d}-\frac{3 a^2 b (c+d x) \log \left(1+e^{2 i (e+f x)}\right)}{f}+\frac{3 i a^2 b (c+d x)^2}{2 d}+\frac{3 i a^2 b d \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{2 f^2}+\frac{3 a b^2 (c+d x) \tan (e+f x)}{f}-3 a b^2 c x+\frac{3 a b^2 d \log (\cos (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) \tan ^2(e+f x)}{2 f}-\frac{i b^3 (c+d x)^2}{2 d}-\frac{i b^3 d \text{Li}_2\left(-e^{2 i (e+f x)}\right)}{2 f^2}-\frac{b^3 d \tan (e+f x)}{2 f^2}+\frac{b^3 d x}{2 f}",1,"(Cos[e + f*x]*(Cos[e + f*x]^2*(-((e + f*x)*((-3*I)*a^2*b*d*(e + f*x) + I*b^3*d*(e + f*x) + 3*a*b^2*(-(d*e) + 2*c*f + d*f*x) + a^3*(-2*c*f + d*(e - f*x)))) + 2*b*(-3*a^2 + b^2)*d*(e + f*x)*Log[1 + E^((2*I)*(e + f*x))] + 2*b*(3*a*b*d + 3*a^2*(d*e - c*f) + b^2*(-(d*e) + c*f))*Log[Cos[e + f*x]]) - I*b*(-3*a^2 + b^2)*d*Cos[e + f*x]^2*PolyLog[2, -E^((2*I)*(e + f*x))] + (b^2*(2*b*f*(c + d*x) + (-(b*d) + 6*a*f*(c + d*x))*Sin[2*(e + f*x)]))/2)*(a + b*Tan[e + f*x])^3)/(2*f^2*(a*Cos[e + f*x] + b*Sin[e + f*x])^3)","A",1
52,0,0,23,14.5717744,"\int \frac{(a+b \tan (e+f x))^3}{c+d x} \, dx","Integrate[(a + b*Tan[e + f*x])^3/(c + d*x),x]","\int \frac{(a+b \tan (e+f x))^3}{c+d x} \, dx","\text{Int}\left(\frac{(a+b \tan (e+f x))^3}{c+d x},x\right)",0,"Integrate[(a + b*Tan[e + f*x])^3/(c + d*x), x]","A",-1
53,0,0,23,20.1097721,"\int \frac{(a+b \tan (e+f x))^3}{(c+d x)^2} \, dx","Integrate[(a + b*Tan[e + f*x])^3/(c + d*x)^2,x]","\int \frac{(a+b \tan (e+f x))^3}{(c+d x)^2} \, dx","\text{Int}\left(\frac{(a+b \tan (e+f x))^3}{(c+d x)^2},x\right)",0,"Integrate[(a + b*Tan[e + f*x])^3/(c + d*x)^2, x]","A",-1
54,1,297,243,2.3149718,"\int \frac{(c+d x)^3}{a+b \tan (e+f x)} \, dx","Integrate[(c + d*x)^3/(a + b*Tan[e + f*x]),x]","\frac{x \cos (e) \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)}{4 (a \cos (e)+b \sin (e))}+\frac{1}{4} b \left(\frac{3 d \left(2 i f^2 (c+d x)^2 \text{Li}_2\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)+d \left(2 f (c+d x) \text{Li}_3\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)-i d \text{Li}_4\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)\right)\right)}{f^4 \left(a^2+b^2\right)}+\frac{4 (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{2 (c+d x)^4}{d (b+i a) \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right)}\right)","\frac{3 b d^2 (c+d x) \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i (e+f x)}}{(a+i b)^2}\right)}{2 f^3 \left(a^2+b^2\right)}-\frac{3 i b d (c+d x)^2 \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i (e+f x)}}{(a+i b)^2}\right)}{2 f^2 \left(a^2+b^2\right)}+\frac{b (c+d x)^3 \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i (e+f x)}}{(a+i b)^2}\right)}{f \left(a^2+b^2\right)}+\frac{3 i b d^3 \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i (e+f x)}}{(a+i b)^2}\right)}{4 f^4 \left(a^2+b^2\right)}+\frac{(c+d x)^4}{4 d (a+i b)}",1,"(b*((-2*(c + d*x)^4)/((I*a + b)*d*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))) + (4*(c + d*x)^3*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])/((a^2 + b^2)*f) + (3*d*((2*I)*f^2*(c + d*x)^2*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))] + d*(2*f*(c + d*x)*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))] - I*d*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])))/((a^2 + b^2)*f^4)))/4 + (x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Cos[e])/(4*(a*Cos[e] + b*Sin[e]))","A",1
55,1,236,181,1.8606764,"\int \frac{(c+d x)^2}{a+b \tan (e+f x)} \, dx","Integrate[(c + d*x)^2/(a + b*Tan[e + f*x]),x]","\frac{x \cos (e) \left(3 c^2+3 c d x+d^2 x^2\right)}{3 (a \cos (e)+b \sin (e))}+\frac{1}{6} b \left(\frac{3 d \left(2 i f (c+d x) \text{Li}_2\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)+d \text{Li}_3\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)\right)}{f^3 \left(a^2+b^2\right)}+\frac{6 (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{4 (c+d x)^3}{d (b+i a) \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right)}\right)","-\frac{i b d (c+d x) \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i (e+f x)}}{(a+i b)^2}\right)}{f^2 \left(a^2+b^2\right)}+\frac{b (c+d x)^2 \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i (e+f x)}}{(a+i b)^2}\right)}{f \left(a^2+b^2\right)}+\frac{b d^2 \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i (e+f x)}}{(a+i b)^2}\right)}{2 f^3 \left(a^2+b^2\right)}+\frac{(c+d x)^3}{3 d (a+i b)}",1,"(b*((-4*(c + d*x)^3)/((I*a + b)*d*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))) + (6*(c + d*x)^2*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])/((a^2 + b^2)*f) + (3*d*((2*I)*f*(c + d*x)*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))] + d*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))]))/((a^2 + b^2)*f^3)))/6 + (x*(3*c^2 + 3*c*d*x + d^2*x^2)*Cos[e])/(3*(a*Cos[e] + b*Sin[e]))","A",1
56,1,177,125,1.9167547,"\int \frac{c+d x}{a+b \tan (e+f x)} \, dx","Integrate[(c + d*x)/(a + b*Tan[e + f*x]),x]","\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{i b d \text{Li}_2\left(\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)^2}{d (a-i b) \left(-i a \left(1+e^{2 i e}\right)+b \left(-e^{2 i e}\right)+b\right)}+\frac{x \cos (e) (2 c+d x)}{2 (a \cos (e)+b \sin (e))}","\frac{b (c+d x) \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i (e+f x)}}{(a+i b)^2}\right)}{f \left(a^2+b^2\right)}-\frac{i b d \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i (e+f x)}}{(a+i b)^2}\right)}{2 f^2 \left(a^2+b^2\right)}+\frac{(c+d x)^2}{2 d (a+i b)}",1,"(b*(c + d*x)^2)/((a - I*b)*d*(b - b*E^((2*I)*e) - I*a*(1 + E^((2*I)*e)))) + (b*(c + d*x)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])/((a^2 + b^2)*f) + ((I/2)*b*d*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])/((a^2 + b^2)*f^2) + (x*(2*c + d*x)*Cos[e])/(2*(a*Cos[e] + b*Sin[e]))","A",1
57,0,0,23,1.9709077,"\int \frac{1}{(c+d x) (a+b \tan (e+f x))} \, dx","Integrate[1/((c + d*x)*(a + b*Tan[e + f*x])),x]","\int \frac{1}{(c+d x) (a+b \tan (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \tan (e+f x))},x\right)",0,"Integrate[1/((c + d*x)*(a + b*Tan[e + f*x])), x]","A",-1
58,0,0,23,4.9760407,"\int \frac{1}{(c+d x)^2 (a+b \tan (e+f x))} \, dx","Integrate[1/((c + d*x)^2*(a + b*Tan[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+b \tan (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \tan (e+f x))},x\right)",0,"Integrate[1/((c + d*x)^2*(a + b*Tan[e + f*x])), x]","A",-1
59,1,1673,848,10.8498481,"\int \frac{(c+d x)^3}{(a+b \tan (e+f x))^2} \, dx","Integrate[(c + d*x)^3/(a + b*Tan[e + f*x])^2,x]","\frac{\left(a d^3-i b d^3+a \cos (2 e) d^3+i b \cos (2 e) d^3+i a \sin (2 e) d^3-b \sin (2 e) d^3\right) x^4}{4 (a-i b) (a+i b) (\cos (2 e) a+i \sin (2 e) a+a+i b-i b \cos (2 e)+b \sin (2 e))}+\frac{\left(a c d^2-i b c d^2+a c \cos (2 e) d^2+i b c \cos (2 e) d^2+i a c \sin (2 e) d^2-b c \sin (2 e) d^2\right) x^3}{(a-i b) (a+i b) (\cos (2 e) a+i \sin (2 e) a+a+i b-i b \cos (2 e)+b \sin (2 e))}+\frac{3 \left(a d c^2-i b d c^2+a d \cos (2 e) c^2+i b d \cos (2 e) c^2+i a d \sin (2 e) c^2-b d \sin (2 e) c^2\right) x^2}{2 (a-i b) (a+i b) (\cos (2 e) a+i \sin (2 e) a+a+i b-i b \cos (2 e)+b \sin (2 e))}+\left(\frac{c^3}{\cos (4 e) a^2+i \sin (4 e) a^2+a^2+2 i b a-2 i b \cos (4 e) a+2 b \sin (4 e) a-b^2-b^2 \cos (4 e)-i b^2 \sin (4 e)}+\frac{\cos (4 e) c^3+i \sin (4 e) c^3}{\cos (4 e) a^2+i \sin (4 e) a^2+a^2+2 i b a-2 i b \cos (4 e) a+2 b \sin (4 e) a-b^2-b^2 \cos (4 e)-i b^2 \sin (4 e)}+\frac{(\cos (2 e) a+i \sin (2 e) a-a-i b-i b \cos (2 e)+b \sin (2 e)) \left(4 a b c^3 \sin (2 e)-4 i a b c^3 \cos (2 e)\right)}{(a-i b) (a+i b) (\cos (2 e) a+i \sin (2 e) a+a+i b-i b \cos (2 e)+b \sin (2 e)) \left(\cos (4 e) a^2+i \sin (4 e) a^2+a^2+2 i b a-2 i b \cos (4 e) a+2 b \sin (4 e) a-b^2-b^2 \cos (4 e)-i b^2 \sin (4 e)\right)}\right) x+\frac{b \left(\frac{2 a f (c+d x)^4}{(a-i b) d}+\frac{4 b (c+d x)^3}{a-i b}+\frac{4 a d^3 \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) x^3 \log \left(\frac{e^{-2 i (e+f x)} (a+i b)}{a-i b}+1\right)}{(a+i b) (i a+b)}+\frac{6 d^2 \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) (b d+2 a c f) x^2 \log \left(\frac{e^{-2 i (e+f x)} (a+i b)}{a-i b}+1\right)}{(a+i b) (i a+b) f}+\frac{12 c d \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) (b d+a c f) x \log \left(\frac{e^{-2 i (e+f x)} (a+i b)}{a-i b}+1\right)}{(a+i b) (i a+b) f}-\frac{2 c^2 \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) (3 b d+2 a c f) \left(2 f x+i \log \left(a+(a-i b) e^{2 i (e+f x)}+i b\right)\right)}{\left(a^2+b^2\right) f}+\frac{6 c d \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) (b d+a c f) \text{Li}_2\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)}{\left(a^2+b^2\right) f^2}+\frac{3 d^2 \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) (b d+2 a c f) \left(2 f x \text{Li}_2\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)-i \text{Li}_3\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)\right)}{\left(a^2+b^2\right) f^3}+\frac{3 a d^3 \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) \left(2 f^2 \text{Li}_2\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right) x^2-2 i f \text{Li}_3\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right) x-\text{Li}_4\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)\right)}{\left(a^2+b^2\right) f^3}\right)}{2 (a-i b) (a+i b) \left(-e^{2 i e} b+b-i a \left(1+e^{2 i e}\right)\right) f}+\frac{b^2 \sin (f x) c^3+3 b^2 d x \sin (f x) c^2+3 b^2 d^2 x^2 \sin (f x) c+b^2 d^3 x^3 \sin (f x)}{(a-i b) (a+i b) f (a \cos (e)+b \sin (e)) (a \cos (e+f x)+b \sin (e+f x))}","\frac{b (c+d x)^4}{(i a-b) (a-i b)^2 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(\frac{e^{2 i e+2 i f x} (a-i b)}{a+i b}+1\right) (c+d x)^3}{(a-i b)^2 (a+i b) f}-\frac{2 i b^2 \log \left(\frac{e^{2 i e+2 i f x} (a-i b)}{a+i b}+1\right) (c+d x)^3}{\left(a^2+b^2\right)^2 f}+\frac{2 b^2 (c+d x)^3}{(a+i b) (i a+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(\frac{e^{2 i e+2 i f x} (a-i b)}{a+i b}+1\right) (c+d x)^2}{\left(a^2+b^2\right)^2 f^2}+\frac{3 b d \text{Li}_2\left(-\frac{(a-i b) e^{2 i e+2 i f x}}{a+i b}\right) (c+d x)^2}{(i a-b) (a-i b)^2 f^2}-\frac{3 b^2 d \text{Li}_2\left(-\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{Li}_2\left(-\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{Li}_3\left(-\frac{(a-i b) e^{2 i e+2 i f x}}{a+i b}\right) (c+d x)}{(a-i b)^2 (a+i b) f^3}-\frac{3 i b^2 d^2 \text{Li}_3\left(-\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{Li}_3\left(-\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{Li}_4\left(-\frac{(a-i b) e^{2 i e+2 i f x}}{a+i b}\right)}{2 (i a-b) (a-i b)^2 f^4}+\frac{3 b^2 d^3 \text{Li}_4\left(-\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,"(b*((4*b*(c + d*x)^3)/(a - I*b) + (2*a*f*(c + d*x)^4)/((a - I*b)*d) + (12*c*d*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*(b*d + a*c*f)*x*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])/((a + I*b)*(I*a + b)*f) + (6*d^2*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*(b*d + 2*a*c*f)*x^2*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])/((a + I*b)*(I*a + b)*f) + (4*a*d^3*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*x^3*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])/((a + I*b)*(I*a + b)) - (2*c^2*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*(3*b*d + 2*a*c*f)*(2*f*x + I*Log[a + I*b + (a - I*b)*E^((2*I)*(e + f*x))]))/((a^2 + b^2)*f) + (6*c*d*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*(b*d + a*c*f)*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])/((a^2 + b^2)*f^2) + (3*d^2*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*(b*d + 2*a*c*f)*(2*f*x*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))] - I*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))]))/((a^2 + b^2)*f^3) + (3*a*d^3*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*(2*f^2*x^2*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))] - (2*I)*f*x*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))] - PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))]))/((a^2 + b^2)*f^3)))/(2*(a - I*b)*(a + I*b)*(b - b*E^((2*I)*e) - I*a*(1 + E^((2*I)*e)))*f) + (3*x^2*(a*c^2*d - I*b*c^2*d + a*c^2*d*Cos[2*e] + I*b*c^2*d*Cos[2*e] + I*a*c^2*d*Sin[2*e] - b*c^2*d*Sin[2*e]))/(2*(a - I*b)*(a + I*b)*(a + I*b + a*Cos[2*e] - I*b*Cos[2*e] + I*a*Sin[2*e] + b*Sin[2*e])) + (x^3*(a*c*d^2 - I*b*c*d^2 + a*c*d^2*Cos[2*e] + I*b*c*d^2*Cos[2*e] + I*a*c*d^2*Sin[2*e] - b*c*d^2*Sin[2*e]))/((a - I*b)*(a + I*b)*(a + I*b + a*Cos[2*e] - I*b*Cos[2*e] + I*a*Sin[2*e] + b*Sin[2*e])) + (x^4*(a*d^3 - I*b*d^3 + a*d^3*Cos[2*e] + I*b*d^3*Cos[2*e] + I*a*d^3*Sin[2*e] - b*d^3*Sin[2*e]))/(4*(a - I*b)*(a + I*b)*(a + I*b + a*Cos[2*e] - I*b*Cos[2*e] + I*a*Sin[2*e] + b*Sin[2*e])) + x*(c^3/(a^2 + (2*I)*a*b - b^2 + a^2*Cos[4*e] - (2*I)*a*b*Cos[4*e] - b^2*Cos[4*e] + I*a^2*Sin[4*e] + 2*a*b*Sin[4*e] - I*b^2*Sin[4*e]) + ((-a - I*b + a*Cos[2*e] - I*b*Cos[2*e] + I*a*Sin[2*e] + b*Sin[2*e])*((-4*I)*a*b*c^3*Cos[2*e] + 4*a*b*c^3*Sin[2*e]))/((a - I*b)*(a + I*b)*(a + I*b + a*Cos[2*e] - I*b*Cos[2*e] + I*a*Sin[2*e] + b*Sin[2*e])*(a^2 + (2*I)*a*b - b^2 + a^2*Cos[4*e] - (2*I)*a*b*Cos[4*e] - b^2*Cos[4*e] + I*a^2*Sin[4*e] + 2*a*b*Sin[4*e] - I*b^2*Sin[4*e])) + (c^3*Cos[4*e] + I*c^3*Sin[4*e])/(a^2 + (2*I)*a*b - b^2 + a^2*Cos[4*e] - (2*I)*a*b*Cos[4*e] - b^2*Cos[4*e] + I*a^2*Sin[4*e] + 2*a*b*Sin[4*e] - I*b^2*Sin[4*e])) + (b^2*c^3*Sin[f*x] + 3*b^2*c^2*d*x*Sin[f*x] + 3*b^2*c*d^2*x^2*Sin[f*x] + b^2*d^3*x^3*Sin[f*x])/((a - I*b)*(a + I*b)*f*(a*Cos[e] + b*Sin[e])*(a*Cos[e + f*x] + b*Sin[e + f*x]))","A",0
60,1,714,654,9.5970196,"\int \frac{(c+d x)^2}{(a+b \tan (e+f x))^2} \, dx","Integrate[(c + d*x)^2/(a + b*Tan[e + f*x])^2,x]","\frac{\frac{f x \left(a^2+b^2\right) \left(3 c^2+3 c d x+d^2 x^2\right) \cos (2 e+f x)+f x \left(a^2-b^2\right) \left(3 c^2+3 c d x+d^2 x^2\right) \cos (f x)+2 b \sin (f x) \left(a f x \left(3 c^2+3 c d x+d^2 x^2\right)+3 b (c+d x)^2\right)}{(a \cos (e)+b \sin (e)) (a \cos (e+f x)+b \sin (e+f x))}+\frac{2 b \left(\frac{3 d \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) (2 a c f+b d) \text{Li}_2\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)}{f^2 \left(a^2+b^2\right)}-\frac{6 c \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) (a c f+b d) \left(2 f x+i \log \left((a-i b) e^{2 i (e+f x)}+a+i b\right)\right)}{f \left(a^2+b^2\right)}+\frac{3 a d^2 \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) \left(2 f x \text{Li}_2\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)-i \text{Li}_3\left(\frac{(-a-i b) e^{-2 i (e+f x)}}{a-i b}\right)\right)}{f^2 \left(a^2+b^2\right)}+\frac{6 d x \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) (2 a c f+b d) \log \left(1+\frac{(a+i b) e^{-2 i (e+f x)}}{a-i b}\right)}{f (a+i b) (b+i a)}+\frac{6 d x^2 (2 a c f+b d)}{a-i b}+\frac{12 c x (a c f+b d)}{a-i b}+\frac{6 a d^2 x^2 \left(a \left(1+e^{2 i e}\right)-i b \left(-1+e^{2 i e}\right)\right) \log \left(1+\frac{(a+i b) e^{-2 i (e+f x)}}{a-i b}\right)}{(a+i b) (b+i a)}+\frac{4 a d^2 f x^3}{a-i b}\right)}{-i a \left(1+e^{2 i e}\right)+b \left(-e^{2 i e}\right)+b}}{6 f \left(a^2+b^2\right)}","-\frac{2 b^2 d (c+d x) \text{Li}_2\left(-\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 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{i b^2 d^2 \text{Li}_2\left(-\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{Li}_3\left(-\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^2 (c+d x)^2}{f (a+i b) (b+i a)^2 \left((b+i a) e^{2 i e+2 i f x}+i a-b\right)}+\frac{2 b d (c+d x) \text{Li}_2\left(-\frac{(a-i b) e^{2 i e+2 i f x}}{a+i b}\right)}{f^2 (-b+i a) (a-i b)^2}+\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)^2 (a+i b)}+\frac{4 b (c+d x)^3}{3 d (-b+i a) (a-i b)^2}+\frac{(c+d x)^3}{3 d (a-i b)^2}+\frac{b d^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i e+2 i f x}}{a+i b}\right)}{f^3 (a-i b)^2 (a+i b)}",1,"((2*b*((12*c*(b*d + a*c*f)*x)/(a - I*b) + (6*d*(b*d + 2*a*c*f)*x^2)/(a - I*b) + (4*a*d^2*f*x^3)/(a - I*b) + (6*d*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*(b*d + 2*a*c*f)*x*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])/((a + I*b)*(I*a + b)*f) + (6*a*d^2*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*x^2*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])/((a + I*b)*(I*a + b)) - (6*c*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*(b*d + a*c*f)*(2*f*x + I*Log[a + I*b + (a - I*b)*E^((2*I)*(e + f*x))]))/((a^2 + b^2)*f) + (3*d*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*(b*d + 2*a*c*f)*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))])/((a^2 + b^2)*f^2) + (3*a*d^2*((-I)*b*(-1 + E^((2*I)*e)) + a*(1 + E^((2*I)*e)))*(2*f*x*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))] - I*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(e + f*x)))]))/((a^2 + b^2)*f^2)))/(b - b*E^((2*I)*e) - I*a*(1 + E^((2*I)*e))) + ((a^2 - b^2)*f*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Cos[f*x] + (a^2 + b^2)*f*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Cos[2*e + f*x] + 2*b*(3*b*(c + d*x)^2 + a*f*x*(3*c^2 + 3*c*d*x + d^2*x^2))*Sin[f*x])/((a*Cos[e] + b*Sin[e])*(a*Cos[e + f*x] + b*Sin[e + f*x])))/(6*(a^2 + b^2)*f)","A",1
61,1,745,214,7.0746455,"\int \frac{c+d x}{(a+b \tan (e+f x))^2} \, dx","Integrate[(c + d*x)/(a + b*Tan[e + f*x])^2,x]","\frac{2 b c \sec ^2(e+f x) (a \cos (e+f x)+b \sin (e+f x))^2 (a \log (a \cos (e+f x)+b \sin (e+f x))-b (e+f x))}{f (a-i b) (a+i b) \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{d \sec ^2(e+f x) (a \cos (e+f x)+b \sin (e+f x))^2 \left(\frac{a \left(i \text{Li}_2\left(e^{2 i \left(e+f x+\tan ^{-1}\left(\frac{a}{b}\right)\right)}\right)+i \left(2 \tan ^{-1}\left(\frac{a}{b}\right)-\pi \right) (e+f x)-2 \left(\tan ^{-1}\left(\frac{a}{b}\right)+e+f x\right) \log \left(1-e^{2 i \left(\tan ^{-1}\left(\frac{a}{b}\right)+e+f x\right)}\right)+2 \tan ^{-1}\left(\frac{a}{b}\right) \log \left(\sin \left(\tan ^{-1}\left(\frac{a}{b}\right)+e+f x\right)\right)-\pi  \log \left(1+e^{-2 i (e+f x)}\right)+\pi  \log (\cos (e+f x))\right)}{b \sqrt{\frac{a^2}{b^2}+1}}+e^{i \tan ^{-1}\left(\frac{a}{b}\right)} (e+f x)^2\right)}{f^2 (a-i b) (a+i b) \sqrt{\frac{a^2+b^2}{b^2}} (a+b \tan (e+f x))^2}+\frac{b^2 d \sec ^2(e+f x) (a \cos (e+f x)+b \sin (e+f x))^2 (a \log (a \cos (e+f x)+b \sin (e+f x))-b (e+f x))}{a f^2 (a-i b) (a+i b) \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{2 b d e \sec ^2(e+f x) (a \cos (e+f x)+b \sin (e+f x))^2 (a \log (a \cos (e+f x)+b \sin (e+f x))-b (e+f x))}{f^2 (a-i b) (a+i b) \left(a^2+b^2\right) (a+b \tan (e+f x))^2}+\frac{\sec ^2(e+f x) (a \cos (e+f x)+b \sin (e+f x)) \left(b^2 c f \sin (e+f x)+b^2 (-d) e \sin (e+f x)+b^2 d (e+f x) \sin (e+f x)\right)}{a f^2 (a-i b) (a+i b) (a+b \tan (e+f x))^2}+\frac{(e+f x) \sec ^2(e+f x) (2 c f+d (e+f x)-2 d e) (a \cos (e+f x)+b \sin (e+f x))^2}{2 f^2 (a-i b) (a+i b) (a+b \tan (e+f x))^2}","\frac{b (2 a c f+2 a d f x+b d) \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i (e+f x)}}{(a+i b)^2}\right)}{f^2 \left(a^2+b^2\right)^2}-\frac{b (c+d x)}{f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{(2 a c f+2 a d f x+b d)^2}{4 a d f^2 (a+i b) \left(a^2+b^2\right)}-\frac{(c+d x)^2}{2 d \left(a^2+b^2\right)}-\frac{i a b d \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i (e+f x)}}{(a+i b)^2}\right)}{f^2 \left(a^2+b^2\right)^2}",1,"((e + f*x)*(-2*d*e + 2*c*f + d*(e + f*x))*Sec[e + f*x]^2*(a*Cos[e + f*x] + b*Sin[e + f*x])^2)/(2*(a - I*b)*(a + I*b)*f^2*(a + b*Tan[e + f*x])^2) + (b^2*d*(-(b*(e + f*x)) + a*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])*Sec[e + f*x]^2*(a*Cos[e + f*x] + b*Sin[e + f*x])^2)/(a*(a - I*b)*(a + I*b)*(a^2 + b^2)*f^2*(a + b*Tan[e + f*x])^2) - (2*b*d*e*(-(b*(e + f*x)) + a*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])*Sec[e + f*x]^2*(a*Cos[e + f*x] + b*Sin[e + f*x])^2)/((a - I*b)*(a + I*b)*(a^2 + b^2)*f^2*(a + b*Tan[e + f*x])^2) + (2*b*c*(-(b*(e + f*x)) + a*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])*Sec[e + f*x]^2*(a*Cos[e + f*x] + b*Sin[e + f*x])^2)/((a - I*b)*(a + I*b)*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2) - (d*(E^(I*ArcTan[a/b])*(e + f*x)^2 + (a*(I*(e + f*x)*(-Pi + 2*ArcTan[a/b]) - Pi*Log[1 + E^((-2*I)*(e + f*x))] - 2*(e + f*x + ArcTan[a/b])*Log[1 - E^((2*I)*(e + f*x + ArcTan[a/b]))] + Pi*Log[Cos[e + f*x]] + 2*ArcTan[a/b]*Log[Sin[e + f*x + ArcTan[a/b]]] + I*PolyLog[2, E^((2*I)*(e + f*x + ArcTan[a/b]))]))/(Sqrt[1 + a^2/b^2]*b))*Sec[e + f*x]^2*(a*Cos[e + f*x] + b*Sin[e + f*x])^2)/((a - I*b)*(a + I*b)*Sqrt[(a^2 + b^2)/b^2]*f^2*(a + b*Tan[e + f*x])^2) + (Sec[e + f*x]^2*(a*Cos[e + f*x] + b*Sin[e + f*x])*(-(b^2*d*e*Sin[e + f*x]) + b^2*c*f*Sin[e + f*x] + b^2*d*(e + f*x)*Sin[e + f*x]))/(a*(a - I*b)*(a + I*b)*f^2*(a + b*Tan[e + f*x])^2)","B",0
62,0,0,23,19.5237973,"\int \frac{1}{(c+d x) (a+b \tan (e+f x))^2} \, dx","Integrate[1/((c + d*x)*(a + b*Tan[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+b \tan (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \tan (e+f x))^2},x\right)",0,"Integrate[1/((c + d*x)*(a + b*Tan[e + f*x])^2), x]","A",-1
63,0,0,23,19.4149431,"\int \frac{1}{(c+d x)^2 (a+b \tan (e+f x))^2} \, dx","Integrate[1/((c + d*x)^2*(a + b*Tan[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+b \tan (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \tan (e+f x))^2},x\right)",0,"Integrate[1/((c + d*x)^2*(a + b*Tan[e + f*x])^2), x]","A",-1