1,1,184,0,0.1428068,"\int (d+e x)^4 \left(a+b \tan ^{-1}(c x)\right) \, dx","Int[(d + e*x)^4*(a + b*ArcTan[c*x]),x]","\frac{(d+e x)^5 \left(a+b \tan ^{-1}(c x)\right)}{5 e}-\frac{b e^2 x^2 \left(10 c^2 d^2-e^2\right)}{10 c^3}-\frac{b \left(-10 c^2 d^2 e^2+5 c^4 d^4+e^4\right) \log \left(c^2 x^2+1\right)}{10 c^5}-\frac{b d e x \left(2 c^2 d^2-e^2\right)}{c^3}-\frac{b d \left(-10 c^2 d^2 e^2+c^4 d^4+5 e^4\right) \tan ^{-1}(c x)}{5 c^4 e}-\frac{b d e^3 x^3}{3 c}-\frac{b e^4 x^4}{20 c}","\frac{(d+e x)^5 \left(a+b \tan ^{-1}(c x)\right)}{5 e}-\frac{b e^2 x^2 \left(10 c^2 d^2-e^2\right)}{10 c^3}-\frac{b \left(-10 c^2 d^2 e^2+5 c^4 d^4+e^4\right) \log \left(c^2 x^2+1\right)}{10 c^5}-\frac{b d e x \left(2 c^2 d^2-e^2\right)}{c^3}-\frac{b d \left(-10 c^2 d^2 e^2+c^4 d^4+5 e^4\right) \tan ^{-1}(c x)}{5 c^4 e}-\frac{b d e^3 x^3}{3 c}-\frac{b e^4 x^4}{20 c}",1,"-((b*d*e*(2*c^2*d^2 - e^2)*x)/c^3) - (b*e^2*(10*c^2*d^2 - e^2)*x^2)/(10*c^3) - (b*d*e^3*x^3)/(3*c) - (b*e^4*x^4)/(20*c) - (b*d*(c^4*d^4 - 10*c^2*d^2*e^2 + 5*e^4)*ArcTan[c*x])/(5*c^4*e) + ((d + e*x)^5*(a + b*ArcTan[c*x]))/(5*e) - (b*(5*c^4*d^4 - 10*c^2*d^2*e^2 + e^4)*Log[1 + c^2*x^2])/(10*c^5)","A",6,5,16,0.3125,1,"{4862, 702, 635, 203, 260}"
2,1,144,0,0.122858,"\int (d+e x)^3 \left(a+b \tan ^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(a + b*ArcTan[c*x]),x]","\frac{(d+e x)^4 \left(a+b \tan ^{-1}(c x)\right)}{4 e}-\frac{b e x \left(6 c^2 d^2-e^2\right)}{4 c^3}-\frac{b \left(-6 c^2 d^2 e^2+c^4 d^4+e^4\right) \tan ^{-1}(c x)}{4 c^4 e}-\frac{b d (c d-e) (c d+e) \log \left(c^2 x^2+1\right)}{2 c^3}-\frac{b d e^2 x^2}{2 c}-\frac{b e^3 x^3}{12 c}","\frac{(d+e x)^4 \left(a+b \tan ^{-1}(c x)\right)}{4 e}-\frac{b e x \left(6 c^2 d^2-e^2\right)}{4 c^3}-\frac{b \left(-6 c^2 d^2 e^2+c^4 d^4+e^4\right) \tan ^{-1}(c x)}{4 c^4 e}-\frac{b d (c d-e) (c d+e) \log \left(c^2 x^2+1\right)}{2 c^3}-\frac{b d e^2 x^2}{2 c}-\frac{b e^3 x^3}{12 c}",1,"-(b*e*(6*c^2*d^2 - e^2)*x)/(4*c^3) - (b*d*e^2*x^2)/(2*c) - (b*e^3*x^3)/(12*c) - (b*(c^4*d^4 - 6*c^2*d^2*e^2 + e^4)*ArcTan[c*x])/(4*c^4*e) + ((d + e*x)^4*(a + b*ArcTan[c*x]))/(4*e) - (b*d*(c*d - e)*(c*d + e)*Log[1 + c^2*x^2])/(2*c^3)","A",6,5,16,0.3125,1,"{4862, 702, 635, 203, 260}"
3,1,103,0,0.0896576,"\int (d+e x)^2 \left(a+b \tan ^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcTan[c*x]),x]","\frac{(d+e x)^3 \left(a+b \tan ^{-1}(c x)\right)}{3 e}-\frac{b \left(3 c^2 d^2-e^2\right) \log \left(c^2 x^2+1\right)}{6 c^3}-\frac{b d \left(d^2-\frac{3 e^2}{c^2}\right) \tan ^{-1}(c x)}{3 e}-\frac{b d e x}{c}-\frac{b e^2 x^2}{6 c}","\frac{(d+e x)^3 \left(a+b \tan ^{-1}(c x)\right)}{3 e}-\frac{b \left(3 c^2 d^2-e^2\right) \log \left(c^2 x^2+1\right)}{6 c^3}-\frac{b d \left(d^2-\frac{3 e^2}{c^2}\right) \tan ^{-1}(c x)}{3 e}-\frac{b d e x}{c}-\frac{b e^2 x^2}{6 c}",1,"-((b*d*e*x)/c) - (b*e^2*x^2)/(6*c) - (b*d*(d^2 - (3*e^2)/c^2)*ArcTan[c*x])/(3*e) + ((d + e*x)^3*(a + b*ArcTan[c*x]))/(3*e) - (b*(3*c^2*d^2 - e^2)*Log[1 + c^2*x^2])/(6*c^3)","A",6,5,16,0.3125,1,"{4862, 702, 635, 203, 260}"
4,1,76,0,0.061302,"\int (d+e x) \left(a+b \tan ^{-1}(c x)\right) \, dx","Int[(d + e*x)*(a + b*ArcTan[c*x]),x]","\frac{(d+e x)^2 \left(a+b \tan ^{-1}(c x)\right)}{2 e}-\frac{b \left(d^2-\frac{e^2}{c^2}\right) \tan ^{-1}(c x)}{2 e}-\frac{b d \log \left(c^2 x^2+1\right)}{2 c}-\frac{b e x}{2 c}","\frac{(d+e x)^2 \left(a+b \tan ^{-1}(c x)\right)}{2 e}-\frac{b \left(d^2-\frac{e^2}{c^2}\right) \tan ^{-1}(c x)}{2 e}-\frac{b d \log \left(c^2 x^2+1\right)}{2 c}-\frac{b e x}{2 c}",1,"-(b*e*x)/(2*c) - (b*(d^2 - e^2/c^2)*ArcTan[c*x])/(2*e) + ((d + e*x)^2*(a + b*ArcTan[c*x]))/(2*e) - (b*d*Log[1 + c^2*x^2])/(2*c)","A",6,5,14,0.3571,1,"{4862, 702, 635, 203, 260}"
5,1,138,0,0.0832176,"\int \frac{a+b \tan ^{-1}(c x)}{d+e x} \, dx","Int[(a + b*ArcTan[c*x])/(d + e*x),x]","-\frac{i b \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{2 e}+\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right)}{2 e}+\frac{\left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{e}-\frac{\log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{e}","-\frac{i b \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{2 e}+\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right)}{2 e}+\frac{\left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{e}-\frac{\log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{e}",1,"-(((a + b*ArcTan[c*x])*Log[2/(1 - I*c*x)])/e) + ((a + b*ArcTan[c*x])*Log[(2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/e + ((I/2)*b*PolyLog[2, 1 - 2/(1 - I*c*x)])/e - ((I/2)*b*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/e","A",4,4,16,0.2500,1,"{4856, 2402, 2315, 2447}"
6,1,98,0,0.05334,"\int \frac{a+b \tan ^{-1}(c x)}{(d+e x)^2} \, dx","Int[(a + b*ArcTan[c*x])/(d + e*x)^2,x]","-\frac{a+b \tan ^{-1}(c x)}{e (d+e x)}-\frac{b c \log \left(c^2 x^2+1\right)}{2 \left(c^2 d^2+e^2\right)}+\frac{b c \log (d+e x)}{c^2 d^2+e^2}+\frac{b c^2 d \tan ^{-1}(c x)}{e \left(c^2 d^2+e^2\right)}","-\frac{a+b \tan ^{-1}(c x)}{e (d+e x)}-\frac{b c \log \left(c^2 x^2+1\right)}{2 \left(c^2 d^2+e^2\right)}+\frac{b c \log (d+e x)}{c^2 d^2+e^2}+\frac{b c^2 d \tan ^{-1}(c x)}{e \left(c^2 d^2+e^2\right)}",1,"(b*c^2*d*ArcTan[c*x])/(e*(c^2*d^2 + e^2)) - (a + b*ArcTan[c*x])/(e*(d + e*x)) + (b*c*Log[d + e*x])/(c^2*d^2 + e^2) - (b*c*Log[1 + c^2*x^2])/(2*(c^2*d^2 + e^2))","A",6,6,16,0.3750,1,"{4862, 706, 31, 635, 203, 260}"
7,1,146,0,0.1231106,"\int \frac{a+b \tan ^{-1}(c x)}{(d+e x)^3} \, dx","Int[(a + b*ArcTan[c*x])/(d + e*x)^3,x]","-\frac{a+b \tan ^{-1}(c x)}{2 e (d+e x)^2}-\frac{b c^3 d \log \left(c^2 x^2+1\right)}{2 \left(c^2 d^2+e^2\right)^2}-\frac{b c}{2 \left(c^2 d^2+e^2\right) (d+e x)}+\frac{b c^3 d \log (d+e x)}{\left(c^2 d^2+e^2\right)^2}+\frac{b c^2 (c d-e) (c d+e) \tan ^{-1}(c x)}{2 e \left(c^2 d^2+e^2\right)^2}","-\frac{a+b \tan ^{-1}(c x)}{2 e (d+e x)^2}-\frac{b c^3 d \log \left(c^2 x^2+1\right)}{2 \left(c^2 d^2+e^2\right)^2}-\frac{b c}{2 \left(c^2 d^2+e^2\right) (d+e x)}+\frac{b c^3 d \log (d+e x)}{\left(c^2 d^2+e^2\right)^2}+\frac{b c^2 (c d-e) (c d+e) \tan ^{-1}(c x)}{2 e \left(c^2 d^2+e^2\right)^2}",1,"-(b*c)/(2*(c^2*d^2 + e^2)*(d + e*x)) + (b*c^2*(c*d - e)*(c*d + e)*ArcTan[c*x])/(2*e*(c^2*d^2 + e^2)^2) - (a + b*ArcTan[c*x])/(2*e*(d + e*x)^2) + (b*c^3*d*Log[d + e*x])/(c^2*d^2 + e^2)^2 - (b*c^3*d*Log[1 + c^2*x^2])/(2*(c^2*d^2 + e^2)^2)","A",7,6,16,0.3750,1,"{4862, 710, 801, 635, 203, 260}"
8,1,206,0,0.1822228,"\int \frac{a+b \tan ^{-1}(c x)}{(d+e x)^4} \, dx","Int[(a + b*ArcTan[c*x])/(d + e*x)^4,x]","-\frac{a+b \tan ^{-1}(c x)}{3 e (d+e x)^3}-\frac{b c^3 \left(3 c^2 d^2-e^2\right) \log \left(c^2 x^2+1\right)}{6 \left(c^2 d^2+e^2\right)^3}-\frac{2 b c^3 d}{3 \left(c^2 d^2+e^2\right)^2 (d+e x)}-\frac{b c}{6 \left(c^2 d^2+e^2\right) (d+e x)^2}+\frac{b c^3 \left(3 c^2 d^2-e^2\right) \log (d+e x)}{3 \left(c^2 d^2+e^2\right)^3}+\frac{b c^4 d \left(c^2 d^2-3 e^2\right) \tan ^{-1}(c x)}{3 e \left(c^2 d^2+e^2\right)^3}","-\frac{a+b \tan ^{-1}(c x)}{3 e (d+e x)^3}-\frac{b c^3 \left(3 c^2 d^2-e^2\right) \log \left(c^2 x^2+1\right)}{6 \left(c^2 d^2+e^2\right)^3}-\frac{2 b c^3 d}{3 \left(c^2 d^2+e^2\right)^2 (d+e x)}-\frac{b c}{6 \left(c^2 d^2+e^2\right) (d+e x)^2}+\frac{b c^3 \left(3 c^2 d^2-e^2\right) \log (d+e x)}{3 \left(c^2 d^2+e^2\right)^3}+\frac{b c^4 d \left(c^2 d^2-3 e^2\right) \tan ^{-1}(c x)}{3 e \left(c^2 d^2+e^2\right)^3}",1,"-(b*c)/(6*(c^2*d^2 + e^2)*(d + e*x)^2) - (2*b*c^3*d)/(3*(c^2*d^2 + e^2)^2*(d + e*x)) + (b*c^4*d*(c^2*d^2 - 3*e^2)*ArcTan[c*x])/(3*e*(c^2*d^2 + e^2)^3) - (a + b*ArcTan[c*x])/(3*e*(d + e*x)^3) + (b*c^3*(3*c^2*d^2 - e^2)*Log[d + e*x])/(3*(c^2*d^2 + e^2)^3) - (b*c^3*(3*c^2*d^2 - e^2)*Log[1 + c^2*x^2])/(6*(c^2*d^2 + e^2)^3)","A",7,6,16,0.3750,1,"{4862, 710, 801, 635, 203, 260}"
9,1,376,0,0.5731627,"\int (d+e x)^3 \left(a+b \tan ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^3*(a + b*ArcTan[c*x])^2,x]","\frac{i b^2 d (c d-e) (c d+e) \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c^3}-\frac{a b e x \left(6 c^2 d^2-e^2\right)}{2 c^3}-\frac{\left(-6 c^2 d^2 e^2+c^4 d^4+e^4\right) \left(a+b \tan ^{-1}(c x)\right)^2}{4 c^4 e}+\frac{i d (c d-e) (c d+e) \left(a+b \tan ^{-1}(c x)\right)^2}{c^3}+\frac{2 b d (c d-e) (c d+e) \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^3}-\frac{b d e^2 x^2 \left(a+b \tan ^{-1}(c x)\right)}{c}+\frac{(d+e x)^4 \left(a+b \tan ^{-1}(c x)\right)^2}{4 e}-\frac{b e^3 x^3 \left(a+b \tan ^{-1}(c x)\right)}{6 c}+\frac{b^2 e \left(6 c^2 d^2-e^2\right) \log \left(c^2 x^2+1\right)}{4 c^4}-\frac{b^2 e x \left(6 c^2 d^2-e^2\right) \tan ^{-1}(c x)}{2 c^3}+\frac{b^2 d e^2 x}{c^2}-\frac{b^2 d e^2 \tan ^{-1}(c x)}{c^3}+\frac{b^2 e^3 x^2}{12 c^2}-\frac{b^2 e^3 \log \left(c^2 x^2+1\right)}{12 c^4}","\frac{i b^2 d (c d-e) (c d+e) \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c^3}-\frac{a b e x \left(6 c^2 d^2-e^2\right)}{2 c^3}-\frac{\left(-6 c^2 d^2 e^2+c^4 d^4+e^4\right) \left(a+b \tan ^{-1}(c x)\right)^2}{4 c^4 e}+\frac{i d (c d-e) (c d+e) \left(a+b \tan ^{-1}(c x)\right)^2}{c^3}+\frac{2 b d (c d-e) (c d+e) \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^3}-\frac{b d e^2 x^2 \left(a+b \tan ^{-1}(c x)\right)}{c}+\frac{(d+e x)^4 \left(a+b \tan ^{-1}(c x)\right)^2}{4 e}-\frac{b e^3 x^3 \left(a+b \tan ^{-1}(c x)\right)}{6 c}+\frac{b^2 e \left(6 c^2 d^2-e^2\right) \log \left(c^2 x^2+1\right)}{4 c^4}-\frac{b^2 e x \left(6 c^2 d^2-e^2\right) \tan ^{-1}(c x)}{2 c^3}+\frac{b^2 d e^2 x}{c^2}-\frac{b^2 d e^2 \tan ^{-1}(c x)}{c^3}+\frac{b^2 e^3 x^2}{12 c^2}-\frac{b^2 e^3 \log \left(c^2 x^2+1\right)}{12 c^4}",1,"(b^2*d*e^2*x)/c^2 - (a*b*e*(6*c^2*d^2 - e^2)*x)/(2*c^3) + (b^2*e^3*x^2)/(12*c^2) - (b^2*d*e^2*ArcTan[c*x])/c^3 - (b^2*e*(6*c^2*d^2 - e^2)*x*ArcTan[c*x])/(2*c^3) - (b*d*e^2*x^2*(a + b*ArcTan[c*x]))/c - (b*e^3*x^3*(a + b*ArcTan[c*x]))/(6*c) + (I*d*(c*d - e)*(c*d + e)*(a + b*ArcTan[c*x])^2)/c^3 - ((c^4*d^4 - 6*c^2*d^2*e^2 + e^4)*(a + b*ArcTan[c*x])^2)/(4*c^4*e) + ((d + e*x)^4*(a + b*ArcTan[c*x])^2)/(4*e) + (2*b*d*(c*d - e)*(c*d + e)*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/c^3 - (b^2*e^3*Log[1 + c^2*x^2])/(12*c^4) + (b^2*e*(6*c^2*d^2 - e^2)*Log[1 + c^2*x^2])/(4*c^4) + (I*b^2*d*(c*d - e)*(c*d + e)*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^3","A",19,14,18,0.7778,1,"{4864, 4846, 260, 4852, 321, 203, 266, 43, 4984, 4884, 4920, 4854, 2402, 2315}"
10,1,270,0,0.3986769,"\int (d+e x)^2 \left(a+b \tan ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^2*(a + b*ArcTan[c*x])^2,x]","\frac{i b^2 \left(3 c^2 d^2-e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{3 c^3}+\frac{i \left(3 c^2 d^2-e^2\right) \left(a+b \tan ^{-1}(c x)\right)^2}{3 c^3}-\frac{d \left(d^2-\frac{3 e^2}{c^2}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{3 e}+\frac{2 b \left(3 c^2 d^2-e^2\right) \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{3 c^3}-\frac{2 a b d e x}{c}+\frac{(d+e x)^3 \left(a+b \tan ^{-1}(c x)\right)^2}{3 e}-\frac{b e^2 x^2 \left(a+b \tan ^{-1}(c x)\right)}{3 c}+\frac{b^2 d e \log \left(c^2 x^2+1\right)}{c^2}+\frac{b^2 e^2 x}{3 c^2}-\frac{b^2 e^2 \tan ^{-1}(c x)}{3 c^3}-\frac{2 b^2 d e x \tan ^{-1}(c x)}{c}","\frac{i b^2 \left(3 c^2 d^2-e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{3 c^3}+\frac{i \left(3 c^2 d^2-e^2\right) \left(a+b \tan ^{-1}(c x)\right)^2}{3 c^3}-\frac{d \left(d^2-\frac{3 e^2}{c^2}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{3 e}+\frac{2 b \left(3 c^2 d^2-e^2\right) \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{3 c^3}-\frac{2 a b d e x}{c}+\frac{(d+e x)^3 \left(a+b \tan ^{-1}(c x)\right)^2}{3 e}-\frac{b e^2 x^2 \left(a+b \tan ^{-1}(c x)\right)}{3 c}+\frac{b^2 d e \log \left(c^2 x^2+1\right)}{c^2}+\frac{b^2 e^2 x}{3 c^2}-\frac{b^2 e^2 \tan ^{-1}(c x)}{3 c^3}-\frac{2 b^2 d e x \tan ^{-1}(c x)}{c}",1,"(-2*a*b*d*e*x)/c + (b^2*e^2*x)/(3*c^2) - (b^2*e^2*ArcTan[c*x])/(3*c^3) - (2*b^2*d*e*x*ArcTan[c*x])/c - (b*e^2*x^2*(a + b*ArcTan[c*x]))/(3*c) + ((I/3)*(3*c^2*d^2 - e^2)*(a + b*ArcTan[c*x])^2)/c^3 - (d*(d^2 - (3*e^2)/c^2)*(a + b*ArcTan[c*x])^2)/(3*e) + ((d + e*x)^3*(a + b*ArcTan[c*x])^2)/(3*e) + (2*b*(3*c^2*d^2 - e^2)*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/(3*c^3) + (b^2*d*e*Log[1 + c^2*x^2])/c^2 + ((I/3)*b^2*(3*c^2*d^2 - e^2)*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^3","A",15,12,18,0.6667,1,"{4864, 4846, 260, 4852, 321, 203, 4984, 4884, 4920, 4854, 2402, 2315}"
11,1,171,0,0.2977218,"\int (d+e x) \left(a+b \tan ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)*(a + b*ArcTan[c*x])^2,x]","\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c}-\frac{\left(d^2-\frac{e^2}{c^2}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{2 e}+\frac{(d+e x)^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 e}+\frac{i d \left(a+b \tan ^{-1}(c x)\right)^2}{c}+\frac{2 b d \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c}-\frac{a b e x}{c}+\frac{b^2 e \log \left(c^2 x^2+1\right)}{2 c^2}-\frac{b^2 e x \tan ^{-1}(c x)}{c}","\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c}-\frac{\left(d^2-\frac{e^2}{c^2}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{2 e}+\frac{(d+e x)^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 e}+\frac{i d \left(a+b \tan ^{-1}(c x)\right)^2}{c}+\frac{2 b d \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c}-\frac{a b e x}{c}+\frac{b^2 e \log \left(c^2 x^2+1\right)}{2 c^2}-\frac{b^2 e x \tan ^{-1}(c x)}{c}",1,"-((a*b*e*x)/c) - (b^2*e*x*ArcTan[c*x])/c + (I*d*(a + b*ArcTan[c*x])^2)/c - ((d^2 - e^2/c^2)*(a + b*ArcTan[c*x])^2)/(2*e) + ((d + e*x)^2*(a + b*ArcTan[c*x])^2)/(2*e) + (2*b*d*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/c + (b^2*e*Log[1 + c^2*x^2])/(2*c^2) + (I*b^2*d*PolyLog[2, 1 - 2/(1 + I*c*x)])/c","A",12,9,16,0.5625,1,"{4864, 4846, 260, 4984, 4884, 4920, 4854, 2402, 2315}"
12,1,223,0,0.0487754,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^2}{d+e x} \, dx","Int[(a + b*ArcTan[c*x])^2/(d + e*x),x]","-\frac{i b \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{e}+\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{e}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{2 e}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-i c x}\right)}{2 e}+\frac{\left(a+b \tan ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{e}-\frac{\log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{e}","-\frac{i b \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{e}+\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{e}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{2 e}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-i c x}\right)}{2 e}+\frac{\left(a+b \tan ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{e}-\frac{\log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{e}",1,"-(((a + b*ArcTan[c*x])^2*Log[2/(1 - I*c*x)])/e) + ((a + b*ArcTan[c*x])^2*Log[(2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/e + (I*b*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 - I*c*x)])/e - (I*b*(a + b*ArcTan[c*x])*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/e - (b^2*PolyLog[3, 1 - 2/(1 - I*c*x)])/(2*e) + (b^2*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(2*e)","A",1,1,18,0.05556,1,"{4858}"
13,1,341,0,0.3701001,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^2}{(d+e x)^2} \, dx","Int[(a + b*ArcTan[c*x])^2/(d + e*x)^2,x]","\frac{i b^2 c \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right)}{c^2 d^2+e^2}+\frac{i b^2 c \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c^2 d^2+e^2}-\frac{i b^2 c \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{c^2 d^2+e^2}+\frac{i c \left(a+b \tan ^{-1}(c x)\right)^2}{c^2 d^2+e^2}+\frac{c^2 d \left(a+b \tan ^{-1}(c x)\right)^2}{e \left(c^2 d^2+e^2\right)}-\frac{2 b c \log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2 d^2+e^2}+\frac{2 b c \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2 d^2+e^2}+\frac{2 b c \left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{c^2 d^2+e^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{e (d+e x)}","\frac{i b^2 c \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right)}{c^2 d^2+e^2}+\frac{i b^2 c \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c^2 d^2+e^2}-\frac{i b^2 c \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{c^2 d^2+e^2}+\frac{i c \left(a+b \tan ^{-1}(c x)\right)^2}{c^2 d^2+e^2}+\frac{c^2 d \left(a+b \tan ^{-1}(c x)\right)^2}{e \left(c^2 d^2+e^2\right)}-\frac{2 b c \log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2 d^2+e^2}+\frac{2 b c \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2 d^2+e^2}+\frac{2 b c \left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{c^2 d^2+e^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{e (d+e x)}",1,"(I*c*(a + b*ArcTan[c*x])^2)/(c^2*d^2 + e^2) + (c^2*d*(a + b*ArcTan[c*x])^2)/(e*(c^2*d^2 + e^2)) - (a + b*ArcTan[c*x])^2/(e*(d + e*x)) - (2*b*c*(a + b*ArcTan[c*x])*Log[2/(1 - I*c*x)])/(c^2*d^2 + e^2) + (2*b*c*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/(c^2*d^2 + e^2) + (2*b*c*(a + b*ArcTan[c*x])*Log[(2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(c^2*d^2 + e^2) + (I*b^2*c*PolyLog[2, 1 - 2/(1 - I*c*x)])/(c^2*d^2 + e^2) + (I*b^2*c*PolyLog[2, 1 - 2/(1 + I*c*x)])/(c^2*d^2 + e^2) - (I*b^2*c*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(c^2*d^2 + e^2)","A",13,9,18,0.5000,1,"{4864, 4856, 2402, 2315, 2447, 4984, 4884, 4920, 4854}"
14,1,496,0,0.538568,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^2}{(d+e x)^3} \, dx","Int[(a + b*ArcTan[c*x])^2/(d + e*x)^3,x]","\frac{i b^2 c^3 d \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right)}{\left(c^2 d^2+e^2\right)^2}+\frac{i b^2 c^3 d \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{\left(c^2 d^2+e^2\right)^2}-\frac{i b^2 c^3 d \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{\left(c^2 d^2+e^2\right)^2}+\frac{i c^3 d \left(a+b \tan ^{-1}(c x)\right)^2}{\left(c^2 d^2+e^2\right)^2}+\frac{c^2 (c d-e) (c d+e) \left(a+b \tan ^{-1}(c x)\right)^2}{2 e \left(c^2 d^2+e^2\right)^2}-\frac{b c \left(a+b \tan ^{-1}(c x)\right)}{\left(c^2 d^2+e^2\right) (d+e x)}-\frac{2 b c^3 d \log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{\left(c^2 d^2+e^2\right)^2}+\frac{2 b c^3 d \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{\left(c^2 d^2+e^2\right)^2}+\frac{2 b c^3 d \left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{\left(c^2 d^2+e^2\right)^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{2 e (d+e x)^2}-\frac{b^2 c^2 e \log \left(c^2 x^2+1\right)}{2 \left(c^2 d^2+e^2\right)^2}+\frac{b^2 c^2 e \log (d+e x)}{\left(c^2 d^2+e^2\right)^2}+\frac{b^2 c^3 d \tan ^{-1}(c x)}{\left(c^2 d^2+e^2\right)^2}","\frac{i b^2 c^3 d \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right)}{\left(c^2 d^2+e^2\right)^2}+\frac{i b^2 c^3 d \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{\left(c^2 d^2+e^2\right)^2}-\frac{i b^2 c^3 d \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{\left(c^2 d^2+e^2\right)^2}+\frac{i c^3 d \left(a+b \tan ^{-1}(c x)\right)^2}{\left(c^2 d^2+e^2\right)^2}+\frac{c^2 (c d-e) (c d+e) \left(a+b \tan ^{-1}(c x)\right)^2}{2 e \left(c^2 d^2+e^2\right)^2}-\frac{b c \left(a+b \tan ^{-1}(c x)\right)}{\left(c^2 d^2+e^2\right) (d+e x)}-\frac{2 b c^3 d \log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{\left(c^2 d^2+e^2\right)^2}+\frac{2 b c^3 d \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{\left(c^2 d^2+e^2\right)^2}+\frac{2 b c^3 d \left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{\left(c^2 d^2+e^2\right)^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{2 e (d+e x)^2}-\frac{b^2 c^2 e \log \left(c^2 x^2+1\right)}{2 \left(c^2 d^2+e^2\right)^2}+\frac{b^2 c^2 e \log (d+e x)}{\left(c^2 d^2+e^2\right)^2}+\frac{b^2 c^3 d \tan ^{-1}(c x)}{\left(c^2 d^2+e^2\right)^2}",1,"(b^2*c^3*d*ArcTan[c*x])/(c^2*d^2 + e^2)^2 - (b*c*(a + b*ArcTan[c*x]))/((c^2*d^2 + e^2)*(d + e*x)) + (I*c^3*d*(a + b*ArcTan[c*x])^2)/(c^2*d^2 + e^2)^2 + (c^2*(c*d - e)*(c*d + e)*(a + b*ArcTan[c*x])^2)/(2*e*(c^2*d^2 + e^2)^2) - (a + b*ArcTan[c*x])^2/(2*e*(d + e*x)^2) - (2*b*c^3*d*(a + b*ArcTan[c*x])*Log[2/(1 - I*c*x)])/(c^2*d^2 + e^2)^2 + (2*b*c^3*d*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/(c^2*d^2 + e^2)^2 + (b^2*c^2*e*Log[d + e*x])/(c^2*d^2 + e^2)^2 + (2*b*c^3*d*(a + b*ArcTan[c*x])*Log[(2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(c^2*d^2 + e^2)^2 - (b^2*c^2*e*Log[1 + c^2*x^2])/(2*(c^2*d^2 + e^2)^2) + (I*b^2*c^3*d*PolyLog[2, 1 - 2/(1 - I*c*x)])/(c^2*d^2 + e^2)^2 + (I*b^2*c^3*d*PolyLog[2, 1 - 2/(1 + I*c*x)])/(c^2*d^2 + e^2)^2 - (I*b^2*c^3*d*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(c^2*d^2 + e^2)^2","A",19,15,18,0.8333,1,"{4864, 4862, 706, 31, 635, 203, 260, 4856, 2402, 2315, 2447, 4984, 4884, 4920, 4854}"
15,1,652,0,1.2016654,"\int (d+e x)^3 \left(a+b \tan ^{-1}(c x)\right)^3 \, dx","Int[(d + e*x)^3*(a + b*ArcTan[c*x])^3,x]","\frac{3 i b^2 d (c d-e) (c d+e) \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^3}-\frac{3 i b^3 e \left(6 c^2 d^2-e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{4 c^4}+\frac{3 b^3 d (c d-e) (c d+e) \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 c^3}+\frac{i b^3 e^3 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{4 c^4}-\frac{3 b^2 e \left(6 c^2 d^2-e^2\right) \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{2 c^4}+\frac{3 a b^2 d e^2 x}{c^2}+\frac{b^2 e^3 x^2 \left(a+b \tan ^{-1}(c x)\right)}{4 c^2}+\frac{b^2 e^3 \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{2 c^4}-\frac{\left(-6 c^2 d^2 e^2+c^4 d^4+e^4\right) \left(a+b \tan ^{-1}(c x)\right)^3}{4 c^4 e}-\frac{3 i b e \left(6 c^2 d^2-e^2\right) \left(a+b \tan ^{-1}(c x)\right)^2}{4 c^4}-\frac{3 b e x \left(6 c^2 d^2-e^2\right) \left(a+b \tan ^{-1}(c x)\right)^2}{4 c^3}-\frac{3 b d e^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^3}+\frac{i d (c d-e) (c d+e) \left(a+b \tan ^{-1}(c x)\right)^3}{c^3}+\frac{3 b d (c d-e) (c d+e) \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c^3}+\frac{i b e^3 \left(a+b \tan ^{-1}(c x)\right)^2}{4 c^4}-\frac{3 b d e^2 x^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 c}+\frac{(d+e x)^4 \left(a+b \tan ^{-1}(c x)\right)^3}{4 e}-\frac{b e^3 x^3 \left(a+b \tan ^{-1}(c x)\right)^2}{4 c}-\frac{3 b^3 d e^2 \log \left(c^2 x^2+1\right)}{2 c^3}+\frac{3 b^3 d e^2 x \tan ^{-1}(c x)}{c^2}-\frac{b^3 e^3 x}{4 c^3}+\frac{b^3 e^3 \tan ^{-1}(c x)}{4 c^4}","\frac{3 i b^2 d (c d-e) (c d+e) \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^3}-\frac{3 i b^3 e \left(6 c^2 d^2-e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{4 c^4}+\frac{3 b^3 d (c d-e) (c d+e) \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 c^3}+\frac{i b^3 e^3 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{4 c^4}-\frac{3 b^2 e \left(6 c^2 d^2-e^2\right) \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{2 c^4}+\frac{3 a b^2 d e^2 x}{c^2}+\frac{b^2 e^3 x^2 \left(a+b \tan ^{-1}(c x)\right)}{4 c^2}+\frac{b^2 e^3 \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{2 c^4}-\frac{\left(-6 c^2 d^2 e^2+c^4 d^4+e^4\right) \left(a+b \tan ^{-1}(c x)\right)^3}{4 c^4 e}-\frac{3 i b e \left(6 c^2 d^2-e^2\right) \left(a+b \tan ^{-1}(c x)\right)^2}{4 c^4}-\frac{3 b e x \left(6 c^2 d^2-e^2\right) \left(a+b \tan ^{-1}(c x)\right)^2}{4 c^3}-\frac{3 b d e^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^3}+\frac{i d (c d-e) (c d+e) \left(a+b \tan ^{-1}(c x)\right)^3}{c^3}+\frac{3 b d (c d-e) (c d+e) \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c^3}+\frac{i b e^3 \left(a+b \tan ^{-1}(c x)\right)^2}{4 c^4}-\frac{3 b d e^2 x^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 c}+\frac{(d+e x)^4 \left(a+b \tan ^{-1}(c x)\right)^3}{4 e}-\frac{b e^3 x^3 \left(a+b \tan ^{-1}(c x)\right)^2}{4 c}-\frac{3 b^3 d e^2 \log \left(c^2 x^2+1\right)}{2 c^3}+\frac{3 b^3 d e^2 x \tan ^{-1}(c x)}{c^2}-\frac{b^3 e^3 x}{4 c^3}+\frac{b^3 e^3 \tan ^{-1}(c x)}{4 c^4}",1,"(3*a*b^2*d*e^2*x)/c^2 - (b^3*e^3*x)/(4*c^3) + (b^3*e^3*ArcTan[c*x])/(4*c^4) + (3*b^3*d*e^2*x*ArcTan[c*x])/c^2 + (b^2*e^3*x^2*(a + b*ArcTan[c*x]))/(4*c^2) - (3*b*d*e^2*(a + b*ArcTan[c*x])^2)/(2*c^3) + ((I/4)*b*e^3*(a + b*ArcTan[c*x])^2)/c^4 - (((3*I)/4)*b*e*(6*c^2*d^2 - e^2)*(a + b*ArcTan[c*x])^2)/c^4 - (3*b*e*(6*c^2*d^2 - e^2)*x*(a + b*ArcTan[c*x])^2)/(4*c^3) - (3*b*d*e^2*x^2*(a + b*ArcTan[c*x])^2)/(2*c) - (b*e^3*x^3*(a + b*ArcTan[c*x])^2)/(4*c) + (I*d*(c*d - e)*(c*d + e)*(a + b*ArcTan[c*x])^3)/c^3 - ((c^4*d^4 - 6*c^2*d^2*e^2 + e^4)*(a + b*ArcTan[c*x])^3)/(4*c^4*e) + ((d + e*x)^4*(a + b*ArcTan[c*x])^3)/(4*e) + (b^2*e^3*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/(2*c^4) - (3*b^2*e*(6*c^2*d^2 - e^2)*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/(2*c^4) + (3*b*d*(c*d - e)*(c*d + e)*(a + b*ArcTan[c*x])^2*Log[2/(1 + I*c*x)])/c^3 - (3*b^3*d*e^2*Log[1 + c^2*x^2])/(2*c^3) + ((I/4)*b^3*e^3*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^4 - (((3*I)/4)*b^3*e*(6*c^2*d^2 - e^2)*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^4 + ((3*I)*b^2*d*(c*d - e)*(c*d + e)*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^3 + (3*b^3*d*(c*d - e)*(c*d + e)*PolyLog[3, 1 - 2/(1 + I*c*x)])/(2*c^3)","A",29,15,18,0.8333,1,"{4864, 4846, 4920, 4854, 2402, 2315, 4852, 4916, 260, 4884, 321, 203, 4984, 4994, 6610}"
16,1,411,0,0.7741107,"\int (d+e x)^2 \left(a+b \tan ^{-1}(c x)\right)^3 \, dx","Int[(d + e*x)^2*(a + b*ArcTan[c*x])^3,x]","\frac{i b^2 \left(3 c^2 d^2-e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^3}+\frac{b^3 \left(3 c^2 d^2-e^2\right) \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 c^3}-\frac{3 i b^3 d e \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c^2}-\frac{6 b^2 d e \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2}+\frac{a b^2 e^2 x}{c^2}+\frac{i \left(3 c^2 d^2-e^2\right) \left(a+b \tan ^{-1}(c x)\right)^3}{3 c^3}-\frac{d \left(d^2-\frac{3 e^2}{c^2}\right) \left(a+b \tan ^{-1}(c x)\right)^3}{3 e}+\frac{b \left(3 c^2 d^2-e^2\right) \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c^3}-\frac{3 i b d e \left(a+b \tan ^{-1}(c x)\right)^2}{c^2}-\frac{b e^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^3}-\frac{3 b d e x \left(a+b \tan ^{-1}(c x)\right)^2}{c}+\frac{(d+e x)^3 \left(a+b \tan ^{-1}(c x)\right)^3}{3 e}-\frac{b e^2 x^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 c}-\frac{b^3 e^2 \log \left(c^2 x^2+1\right)}{2 c^3}+\frac{b^3 e^2 x \tan ^{-1}(c x)}{c^2}","\frac{i b^2 \left(3 c^2 d^2-e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^3}+\frac{b^3 \left(3 c^2 d^2-e^2\right) \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 c^3}-\frac{3 i b^3 d e \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c^2}-\frac{6 b^2 d e \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2}+\frac{a b^2 e^2 x}{c^2}+\frac{i \left(3 c^2 d^2-e^2\right) \left(a+b \tan ^{-1}(c x)\right)^3}{3 c^3}-\frac{d \left(d^2-\frac{3 e^2}{c^2}\right) \left(a+b \tan ^{-1}(c x)\right)^3}{3 e}+\frac{b \left(3 c^2 d^2-e^2\right) \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c^3}-\frac{3 i b d e \left(a+b \tan ^{-1}(c x)\right)^2}{c^2}-\frac{b e^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^3}-\frac{3 b d e x \left(a+b \tan ^{-1}(c x)\right)^2}{c}+\frac{(d+e x)^3 \left(a+b \tan ^{-1}(c x)\right)^3}{3 e}-\frac{b e^2 x^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 c}-\frac{b^3 e^2 \log \left(c^2 x^2+1\right)}{2 c^3}+\frac{b^3 e^2 x \tan ^{-1}(c x)}{c^2}",1,"(a*b^2*e^2*x)/c^2 + (b^3*e^2*x*ArcTan[c*x])/c^2 - ((3*I)*b*d*e*(a + b*ArcTan[c*x])^2)/c^2 - (b*e^2*(a + b*ArcTan[c*x])^2)/(2*c^3) - (3*b*d*e*x*(a + b*ArcTan[c*x])^2)/c - (b*e^2*x^2*(a + b*ArcTan[c*x])^2)/(2*c) + ((I/3)*(3*c^2*d^2 - e^2)*(a + b*ArcTan[c*x])^3)/c^3 - (d*(d^2 - (3*e^2)/c^2)*(a + b*ArcTan[c*x])^3)/(3*e) + ((d + e*x)^3*(a + b*ArcTan[c*x])^3)/(3*e) - (6*b^2*d*e*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/c^2 + (b*(3*c^2*d^2 - e^2)*(a + b*ArcTan[c*x])^2*Log[2/(1 + I*c*x)])/c^3 - (b^3*e^2*Log[1 + c^2*x^2])/(2*c^3) - ((3*I)*b^3*d*e*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^2 + (I*b^2*(3*c^2*d^2 - e^2)*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^3 + (b^3*(3*c^2*d^2 - e^2)*PolyLog[3, 1 - 2/(1 + I*c*x)])/(2*c^3)","A",20,13,18,0.7222,1,"{4864, 4846, 4920, 4854, 2402, 2315, 4852, 4916, 260, 4884, 4984, 4994, 6610}"
17,1,264,0,0.5800838,"\int (d+e x) \left(a+b \tan ^{-1}(c x)\right)^3 \, dx","Int[(d + e*x)*(a + b*ArcTan[c*x])^3,x]","\frac{3 i b^2 d \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c}-\frac{3 i b^3 e \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{2 c^2}+\frac{3 b^3 d \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 c}-\frac{3 b^2 e \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2}-\frac{\left(d^2-\frac{e^2}{c^2}\right) \left(a+b \tan ^{-1}(c x)\right)^3}{2 e}-\frac{3 i b e \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^2}+\frac{(d+e x)^2 \left(a+b \tan ^{-1}(c x)\right)^3}{2 e}+\frac{i d \left(a+b \tan ^{-1}(c x)\right)^3}{c}+\frac{3 b d \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c}-\frac{3 b e x \left(a+b \tan ^{-1}(c x)\right)^2}{2 c}","\frac{3 i b^2 d \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c}-\frac{3 i b^3 e \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{2 c^2}+\frac{3 b^3 d \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 c}-\frac{3 b^2 e \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2}-\frac{\left(d^2-\frac{e^2}{c^2}\right) \left(a+b \tan ^{-1}(c x)\right)^3}{2 e}-\frac{3 i b e \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^2}+\frac{(d+e x)^2 \left(a+b \tan ^{-1}(c x)\right)^3}{2 e}+\frac{i d \left(a+b \tan ^{-1}(c x)\right)^3}{c}+\frac{3 b d \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c}-\frac{3 b e x \left(a+b \tan ^{-1}(c x)\right)^2}{2 c}",1,"(((-3*I)/2)*b*e*(a + b*ArcTan[c*x])^2)/c^2 - (3*b*e*x*(a + b*ArcTan[c*x])^2)/(2*c) + (I*d*(a + b*ArcTan[c*x])^3)/c - ((d^2 - e^2/c^2)*(a + b*ArcTan[c*x])^3)/(2*e) + ((d + e*x)^2*(a + b*ArcTan[c*x])^3)/(2*e) - (3*b^2*e*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/c^2 + (3*b*d*(a + b*ArcTan[c*x])^2*Log[2/(1 + I*c*x)])/c - (((3*I)/2)*b^3*e*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^2 + ((3*I)*b^2*d*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 + I*c*x)])/c + (3*b^3*d*PolyLog[3, 1 - 2/(1 + I*c*x)])/(2*c)","A",14,10,16,0.6250,1,"{4864, 4846, 4920, 4854, 2402, 2315, 4984, 4884, 4994, 6610}"
18,1,320,0,0.0568978,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^3}{d+e x} \, dx","Int[(a + b*ArcTan[c*x])^3/(d + e*x),x]","\frac{3 b^2 \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{2 e}-\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{2 e}-\frac{3 i b \left(a+b \tan ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{2 e}+\frac{3 i b \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{2 e}+\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{4 e}-\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2}{1-i c x}\right)}{4 e}+\frac{\left(a+b \tan ^{-1}(c x)\right)^3 \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{e}-\frac{\log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^3}{e}","\frac{3 b^2 \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{2 e}-\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{2 e}-\frac{3 i b \left(a+b \tan ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{2 e}+\frac{3 i b \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{2 e}+\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{4 e}-\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2}{1-i c x}\right)}{4 e}+\frac{\left(a+b \tan ^{-1}(c x)\right)^3 \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{e}-\frac{\log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^3}{e}",1,"-(((a + b*ArcTan[c*x])^3*Log[2/(1 - I*c*x)])/e) + ((a + b*ArcTan[c*x])^3*Log[(2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/e + (((3*I)/2)*b*(a + b*ArcTan[c*x])^2*PolyLog[2, 1 - 2/(1 - I*c*x)])/e - (((3*I)/2)*b*(a + b*ArcTan[c*x])^2*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/e - (3*b^2*(a + b*ArcTan[c*x])*PolyLog[3, 1 - 2/(1 - I*c*x)])/(2*e) + (3*b^2*(a + b*ArcTan[c*x])*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(2*e) - (((3*I)/4)*b^3*PolyLog[4, 1 - 2/(1 - I*c*x)])/e + (((3*I)/4)*b^3*PolyLog[4, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/e","A",1,1,18,0.05556,1,"{4860}"
19,1,499,0,0.53011,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^3}{(d+e x)^2} \, dx","Int[(a + b*ArcTan[c*x])^3/(d + e*x)^2,x]","\frac{3 i b^2 c \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2 d^2+e^2}+\frac{3 i b^2 c \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2 d^2+e^2}-\frac{3 i b^2 c \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{c^2 d^2+e^2}-\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2}{1-i c x}\right)}{2 \left(c^2 d^2+e^2\right)}+\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 \left(c^2 d^2+e^2\right)}+\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{2 \left(c^2 d^2+e^2\right)}+\frac{i c \left(a+b \tan ^{-1}(c x)\right)^3}{c^2 d^2+e^2}+\frac{c^2 d \left(a+b \tan ^{-1}(c x)\right)^3}{e \left(c^2 d^2+e^2\right)}-\frac{3 b c \log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c^2 d^2+e^2}+\frac{3 b c \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c^2 d^2+e^2}+\frac{3 b c \left(a+b \tan ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{c^2 d^2+e^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{e (d+e x)}","\frac{3 i b^2 c \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2 d^2+e^2}+\frac{3 i b^2 c \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2 d^2+e^2}-\frac{3 i b^2 c \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{c^2 d^2+e^2}-\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2}{1-i c x}\right)}{2 \left(c^2 d^2+e^2\right)}+\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 \left(c^2 d^2+e^2\right)}+\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{2 \left(c^2 d^2+e^2\right)}+\frac{i c \left(a+b \tan ^{-1}(c x)\right)^3}{c^2 d^2+e^2}+\frac{c^2 d \left(a+b \tan ^{-1}(c x)\right)^3}{e \left(c^2 d^2+e^2\right)}-\frac{3 b c \log \left(\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c^2 d^2+e^2}+\frac{3 b c \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c^2 d^2+e^2}+\frac{3 b c \left(a+b \tan ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(1-i c x) (c d+i e)}\right)}{c^2 d^2+e^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{e (d+e x)}",1,"(I*c*(a + b*ArcTan[c*x])^3)/(c^2*d^2 + e^2) + (c^2*d*(a + b*ArcTan[c*x])^3)/(e*(c^2*d^2 + e^2)) - (a + b*ArcTan[c*x])^3/(e*(d + e*x)) - (3*b*c*(a + b*ArcTan[c*x])^2*Log[2/(1 - I*c*x)])/(c^2*d^2 + e^2) + (3*b*c*(a + b*ArcTan[c*x])^2*Log[2/(1 + I*c*x)])/(c^2*d^2 + e^2) + (3*b*c*(a + b*ArcTan[c*x])^2*Log[(2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(c^2*d^2 + e^2) + ((3*I)*b^2*c*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 - I*c*x)])/(c^2*d^2 + e^2) + ((3*I)*b^2*c*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 + I*c*x)])/(c^2*d^2 + e^2) - ((3*I)*b^2*c*(a + b*ArcTan[c*x])*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(c^2*d^2 + e^2) - (3*b^3*c*PolyLog[3, 1 - 2/(1 - I*c*x)])/(2*(c^2*d^2 + e^2)) + (3*b^3*c*PolyLog[3, 1 - 2/(1 + I*c*x)])/(2*(c^2*d^2 + e^2)) + (3*b^3*c*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(2*(c^2*d^2 + e^2))","A",10,8,18,0.4444,1,"{4864, 4858, 4984, 4884, 4920, 4854, 4994, 6610}"
20,1,936,0,1.0899199,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^3}{(d+e x)^3} \, dx","Int[(a + b*ArcTan[c*x])^3/(d + e*x)^3,x]","\frac{3 i c^2 e \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}+\frac{3 i c^2 e \text{PolyLog}\left(2,1-\frac{2}{i c x+1}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}-\frac{3 i c^2 e \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c d+i e) (1-i c x)}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}-\frac{3 c^3 d \text{PolyLog}\left(3,1-\frac{2}{1-i c x}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}+\frac{3 c^3 d \text{PolyLog}\left(3,1-\frac{2}{i c x+1}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}+\frac{3 c^3 d \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c d+i e) (1-i c x)}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}-\frac{3 c^2 e \left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2}{1-i c x}\right) b^2}{\left(c^2 d^2+e^2\right)^2}+\frac{3 c^2 e \left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2}{i c x+1}\right) b^2}{\left(c^2 d^2+e^2\right)^2}+\frac{3 c^2 e \left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c d+i e) (1-i c x)}\right) b^2}{\left(c^2 d^2+e^2\right)^2}+\frac{3 i c^3 d \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right) b^2}{\left(c^2 d^2+e^2\right)^2}+\frac{3 i c^3 d \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2}{i c x+1}\right) b^2}{\left(c^2 d^2+e^2\right)^2}-\frac{3 i c^3 d \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c d+i e) (1-i c x)}\right) b^2}{\left(c^2 d^2+e^2\right)^2}-\frac{3 c \left(a+b \tan ^{-1}(c x)\right)^2 b}{2 \left(c^2 d^2+e^2\right) (d+e x)}+\frac{3 c^3 d \left(a+b \tan ^{-1}(c x)\right)^2 b}{2 \left(c^2 d^2+e^2\right)^2}+\frac{3 i c^2 e \left(a+b \tan ^{-1}(c x)\right)^2 b}{2 \left(c^2 d^2+e^2\right)^2}-\frac{3 c^3 d \left(a+b \tan ^{-1}(c x)\right)^2 \log \left(\frac{2}{1-i c x}\right) b}{\left(c^2 d^2+e^2\right)^2}+\frac{3 c^3 d \left(a+b \tan ^{-1}(c x)\right)^2 \log \left(\frac{2}{i c x+1}\right) b}{\left(c^2 d^2+e^2\right)^2}+\frac{3 c^3 d \left(a+b \tan ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(c d+i e) (1-i c x)}\right) b}{\left(c^2 d^2+e^2\right)^2}+\frac{i c^3 d \left(a+b \tan ^{-1}(c x)\right)^3}{\left(c^2 d^2+e^2\right)^2}+\frac{c^2 (c d-e) (c d+e) \left(a+b \tan ^{-1}(c x)\right)^3}{2 e \left(c^2 d^2+e^2\right)^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{2 e (d+e x)^2}","\frac{3 i c^2 e \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}+\frac{3 i c^2 e \text{PolyLog}\left(2,1-\frac{2}{i c x+1}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}-\frac{3 i c^2 e \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c d+i e) (1-i c x)}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}-\frac{3 c^3 d \text{PolyLog}\left(3,1-\frac{2}{1-i c x}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}+\frac{3 c^3 d \text{PolyLog}\left(3,1-\frac{2}{i c x+1}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}+\frac{3 c^3 d \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c d+i e) (1-i c x)}\right) b^3}{2 \left(c^2 d^2+e^2\right)^2}-\frac{3 c^2 e \left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2}{1-i c x}\right) b^2}{\left(c^2 d^2+e^2\right)^2}+\frac{3 c^2 e \left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2}{i c x+1}\right) b^2}{\left(c^2 d^2+e^2\right)^2}+\frac{3 c^2 e \left(a+b \tan ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c d+i e) (1-i c x)}\right) b^2}{\left(c^2 d^2+e^2\right)^2}+\frac{3 i c^3 d \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2}{1-i c x}\right) b^2}{\left(c^2 d^2+e^2\right)^2}+\frac{3 i c^3 d \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2}{i c x+1}\right) b^2}{\left(c^2 d^2+e^2\right)^2}-\frac{3 i c^3 d \left(a+b \tan ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c d+i e) (1-i c x)}\right) b^2}{\left(c^2 d^2+e^2\right)^2}-\frac{3 c \left(a+b \tan ^{-1}(c x)\right)^2 b}{2 \left(c^2 d^2+e^2\right) (d+e x)}+\frac{3 c^3 d \left(a+b \tan ^{-1}(c x)\right)^2 b}{2 \left(c^2 d^2+e^2\right)^2}+\frac{3 i c^2 e \left(a+b \tan ^{-1}(c x)\right)^2 b}{2 \left(c^2 d^2+e^2\right)^2}-\frac{3 c^3 d \left(a+b \tan ^{-1}(c x)\right)^2 \log \left(\frac{2}{1-i c x}\right) b}{\left(c^2 d^2+e^2\right)^2}+\frac{3 c^3 d \left(a+b \tan ^{-1}(c x)\right)^2 \log \left(\frac{2}{i c x+1}\right) b}{\left(c^2 d^2+e^2\right)^2}+\frac{3 c^3 d \left(a+b \tan ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(c d+i e) (1-i c x)}\right) b}{\left(c^2 d^2+e^2\right)^2}+\frac{i c^3 d \left(a+b \tan ^{-1}(c x)\right)^3}{\left(c^2 d^2+e^2\right)^2}+\frac{c^2 (c d-e) (c d+e) \left(a+b \tan ^{-1}(c x)\right)^3}{2 e \left(c^2 d^2+e^2\right)^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{2 e (d+e x)^2}",1,"(3*b*c^3*d*(a + b*ArcTan[c*x])^2)/(2*(c^2*d^2 + e^2)^2) + (((3*I)/2)*b*c^2*e*(a + b*ArcTan[c*x])^2)/(c^2*d^2 + e^2)^2 - (3*b*c*(a + b*ArcTan[c*x])^2)/(2*(c^2*d^2 + e^2)*(d + e*x)) + (I*c^3*d*(a + b*ArcTan[c*x])^3)/(c^2*d^2 + e^2)^2 + (c^2*(c*d - e)*(c*d + e)*(a + b*ArcTan[c*x])^3)/(2*e*(c^2*d^2 + e^2)^2) - (a + b*ArcTan[c*x])^3/(2*e*(d + e*x)^2) - (3*b^2*c^2*e*(a + b*ArcTan[c*x])*Log[2/(1 - I*c*x)])/(c^2*d^2 + e^2)^2 - (3*b*c^3*d*(a + b*ArcTan[c*x])^2*Log[2/(1 - I*c*x)])/(c^2*d^2 + e^2)^2 + (3*b^2*c^2*e*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/(c^2*d^2 + e^2)^2 + (3*b*c^3*d*(a + b*ArcTan[c*x])^2*Log[2/(1 + I*c*x)])/(c^2*d^2 + e^2)^2 + (3*b^2*c^2*e*(a + b*ArcTan[c*x])*Log[(2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(c^2*d^2 + e^2)^2 + (3*b*c^3*d*(a + b*ArcTan[c*x])^2*Log[(2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(c^2*d^2 + e^2)^2 + (((3*I)/2)*b^3*c^2*e*PolyLog[2, 1 - 2/(1 - I*c*x)])/(c^2*d^2 + e^2)^2 + ((3*I)*b^2*c^3*d*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 - I*c*x)])/(c^2*d^2 + e^2)^2 + (((3*I)/2)*b^3*c^2*e*PolyLog[2, 1 - 2/(1 + I*c*x)])/(c^2*d^2 + e^2)^2 + ((3*I)*b^2*c^3*d*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 + I*c*x)])/(c^2*d^2 + e^2)^2 - (((3*I)/2)*b^3*c^2*e*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(c^2*d^2 + e^2)^2 - ((3*I)*b^2*c^3*d*(a + b*ArcTan[c*x])*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(c^2*d^2 + e^2)^2 - (3*b^3*c^3*d*PolyLog[3, 1 - 2/(1 - I*c*x)])/(2*(c^2*d^2 + e^2)^2) + (3*b^3*c^3*d*PolyLog[3, 1 - 2/(1 + I*c*x)])/(2*(c^2*d^2 + e^2)^2) + (3*b^3*c^3*d*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + I*e)*(1 - I*c*x))])/(2*(c^2*d^2 + e^2)^2)","A",23,12,18,0.6667,1,"{4864, 4856, 2402, 2315, 2447, 4984, 4884, 4920, 4854, 4858, 4994, 6610}"
21,1,250,0,0.3034772,"\int (d+e x)^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcTan[c*x^2]),x]","\frac{(d+e x)^3 \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{3 e}-\frac{b \left(3 c d^2+e^2\right) \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2} c^{3/2}}+\frac{b \left(3 c d^2+e^2\right) \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2} c^{3/2}}+\frac{b \left(3 c d^2-e^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{3 \sqrt{2} c^{3/2}}-\frac{b \left(3 c d^2-e^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{3 \sqrt{2} c^{3/2}}-\frac{b d e \log \left(c^2 x^4+1\right)}{2 c}-\frac{b d^3 \tan ^{-1}\left(c x^2\right)}{3 e}-\frac{2 b e^2 x}{3 c}","\frac{(d+e x)^3 \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{3 e}-\frac{b \left(3 c d^2+e^2\right) \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2} c^{3/2}}+\frac{b \left(3 c d^2+e^2\right) \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2} c^{3/2}}+\frac{b \left(3 c d^2-e^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{3 \sqrt{2} c^{3/2}}-\frac{b \left(3 c d^2-e^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{3 \sqrt{2} c^{3/2}}-\frac{b d e \log \left(c^2 x^4+1\right)}{2 c}-\frac{b d^3 \tan ^{-1}\left(c x^2\right)}{3 e}-\frac{2 b e^2 x}{3 c}",1,"(-2*b*e^2*x)/(3*c) - (b*d^3*ArcTan[c*x^2])/(3*e) + ((d + e*x)^3*(a + b*ArcTan[c*x^2]))/(3*e) + (b*(3*c*d^2 - e^2)*ArcTan[1 - Sqrt[2]*Sqrt[c]*x])/(3*Sqrt[2]*c^(3/2)) - (b*(3*c*d^2 - e^2)*ArcTan[1 + Sqrt[2]*Sqrt[c]*x])/(3*Sqrt[2]*c^(3/2)) - (b*(3*c*d^2 + e^2)*Log[1 - Sqrt[2]*Sqrt[c]*x + c*x^2])/(6*Sqrt[2]*c^(3/2)) + (b*(3*c*d^2 + e^2)*Log[1 + Sqrt[2]*Sqrt[c]*x + c*x^2])/(6*Sqrt[2]*c^(3/2)) - (b*d*e*Log[1 + c^2*x^4])/(2*c)","A",18,14,18,0.7778,1,"{5205, 12, 1831, 1248, 635, 203, 260, 1280, 1168, 1162, 617, 204, 1165, 628}"
22,1,191,0,0.2089943,"\int (d+e x) \left(a+b \tan ^{-1}\left(c x^2\right)\right) \, dx","Int[(d + e*x)*(a + b*ArcTan[c*x^2]),x]","\frac{a (d+e x)^2}{2 e}-\frac{b e \log \left(c^2 x^4+1\right)}{4 c}-\frac{b d \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \sqrt{c}}+\frac{b d \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \sqrt{c}}+b d x \tan ^{-1}\left(c x^2\right)+\frac{b d \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{\sqrt{2} \sqrt{c}}-\frac{b d \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{\sqrt{2} \sqrt{c}}+\frac{1}{2} b e x^2 \tan ^{-1}\left(c x^2\right)","\frac{(d+e x)^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{2 e}-\frac{b e \log \left(c^2 x^4+1\right)}{4 c}-\frac{b d^2 \tan ^{-1}\left(c x^2\right)}{2 e}-\frac{b d \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \sqrt{c}}+\frac{b d \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \sqrt{c}}+\frac{b d \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{\sqrt{2} \sqrt{c}}-\frac{b d \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{\sqrt{2} \sqrt{c}}",1,"(a*(d + e*x)^2)/(2*e) + b*d*x*ArcTan[c*x^2] + (b*e*x^2*ArcTan[c*x^2])/2 + (b*d*ArcTan[1 - Sqrt[2]*Sqrt[c]*x])/(Sqrt[2]*Sqrt[c]) - (b*d*ArcTan[1 + Sqrt[2]*Sqrt[c]*x])/(Sqrt[2]*Sqrt[c]) - (b*d*Log[1 - Sqrt[2]*Sqrt[c]*x + c*x^2])/(2*Sqrt[2]*Sqrt[c]) + (b*d*Log[1 + Sqrt[2]*Sqrt[c]*x + c*x^2])/(2*Sqrt[2]*Sqrt[c]) - (b*e*Log[1 + c^2*x^4])/(4*c)","A",16,10,16,0.6250,1,"{6742, 5027, 297, 1162, 617, 204, 1165, 628, 5033, 260}"
23,0,0,0,0.0637799,"\int \frac{a+b \tan ^{-1}\left(c x^2\right)}{d+e x} \, dx","Int[(a + b*ArcTan[c*x^2])/(d + e*x),x]","\int \frac{a+b \tan ^{-1}\left(c x^2\right)}{d+e x} \, dx","\frac{b c \text{PolyLog}\left(2,\frac{\sqrt[4]{-c^2} (d+e x)}{\sqrt[4]{-c^2} d-e}\right)}{2 \sqrt{-c^2} e}-\frac{b c \text{PolyLog}\left(2,\frac{\sqrt{-\sqrt{-c^2}} (d+e x)}{\sqrt{-\sqrt{-c^2}} d-e}\right)}{2 \sqrt{-c^2} e}+\frac{b c \text{PolyLog}\left(2,\frac{\sqrt[4]{-c^2} (d+e x)}{\sqrt[4]{-c^2} d+e}\right)}{2 \sqrt{-c^2} e}-\frac{b c \text{PolyLog}\left(2,\frac{\sqrt{-\sqrt{-c^2}} (d+e x)}{\sqrt{-\sqrt{-c^2}} d+e}\right)}{2 \sqrt{-c^2} e}+\frac{\log (d+e x) \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{e}+\frac{b c \log (d+e x) \log \left(\frac{e \left(1-\sqrt[4]{-c^2} x\right)}{\sqrt[4]{-c^2} d+e}\right)}{2 \sqrt{-c^2} e}+\frac{b c \log (d+e x) \log \left(-\frac{e \left(\sqrt[4]{-c^2} x+1\right)}{\sqrt[4]{-c^2} d-e}\right)}{2 \sqrt{-c^2} e}-\frac{b c \log (d+e x) \log \left(\frac{e \left(1-\sqrt{-\sqrt{-c^2}} x\right)}{\sqrt{-\sqrt{-c^2}} d+e}\right)}{2 \sqrt{-c^2} e}-\frac{b c \log (d+e x) \log \left(-\frac{e \left(\sqrt{-\sqrt{-c^2}} x+1\right)}{\sqrt{-\sqrt{-c^2}} d-e}\right)}{2 \sqrt{-c^2} e}",1,"(a*Log[d + e*x])/e + b*Defer[Int][ArcTan[c*x^2]/(d + e*x), x]","F",0,0,0,0,-1,"{}"
24,1,328,0,0.5221586,"\int \frac{a+b \tan ^{-1}\left(c x^2\right)}{(d+e x)^2} \, dx","Int[(a + b*ArcTan[c*x^2])/(d + e*x)^2,x]","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{e (d+e x)}+\frac{b c d e \log \left(c^2 x^4+1\right)}{2 \left(c^2 d^4+e^4\right)}-\frac{b \sqrt{c} \left(c d^2+e^2\right) \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \left(c^2 d^4+e^4\right)}+\frac{b \sqrt{c} \left(c d^2+e^2\right) \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \left(c^2 d^4+e^4\right)}+\frac{b c^2 d^3 \tan ^{-1}\left(c x^2\right)}{e \left(c^2 d^4+e^4\right)}-\frac{2 b c d e \log (d+e x)}{c^2 d^4+e^4}+\frac{b \sqrt{c} \left(c d^2-e^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{\sqrt{2} \left(c^2 d^4+e^4\right)}-\frac{b \sqrt{c} \left(c d^2-e^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{\sqrt{2} \left(c^2 d^4+e^4\right)}","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{e (d+e x)}+\frac{b c d e \log \left(c^2 x^4+1\right)}{2 \left(c^2 d^4+e^4\right)}-\frac{b \sqrt{c} \left(c d^2+e^2\right) \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \left(c^2 d^4+e^4\right)}+\frac{b \sqrt{c} \left(c d^2+e^2\right) \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \left(c^2 d^4+e^4\right)}+\frac{b c^2 d^3 \tan ^{-1}\left(c x^2\right)}{e \left(c^2 d^4+e^4\right)}-\frac{2 b c d e \log (d+e x)}{c^2 d^4+e^4}+\frac{b \sqrt{c} \left(c d^2-e^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{\sqrt{2} \left(c^2 d^4+e^4\right)}-\frac{b \sqrt{c} \left(c d^2-e^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{\sqrt{2} \left(c^2 d^4+e^4\right)}",1,"(b*c^2*d^3*ArcTan[c*x^2])/(e*(c^2*d^4 + e^4)) - (a + b*ArcTan[c*x^2])/(e*(d + e*x)) + (b*Sqrt[c]*(c*d^2 - e^2)*ArcTan[1 - Sqrt[2]*Sqrt[c]*x])/(Sqrt[2]*(c^2*d^4 + e^4)) - (b*Sqrt[c]*(c*d^2 - e^2)*ArcTan[1 + Sqrt[2]*Sqrt[c]*x])/(Sqrt[2]*(c^2*d^4 + e^4)) - (2*b*c*d*e*Log[d + e*x])/(c^2*d^4 + e^4) - (b*Sqrt[c]*(c*d^2 + e^2)*Log[1 - Sqrt[2]*Sqrt[c]*x + c*x^2])/(2*Sqrt[2]*(c^2*d^4 + e^4)) + (b*Sqrt[c]*(c*d^2 + e^2)*Log[1 + Sqrt[2]*Sqrt[c]*x + c*x^2])/(2*Sqrt[2]*(c^2*d^4 + e^4)) + (b*c*d*e*Log[1 + c^2*x^4])/(2*(c^2*d^4 + e^4))","A",19,14,18,0.7778,1,"{5205, 12, 6725, 1876, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 203, 260}"
25,1,1554,0,3.0988103,"\int (d+e x) \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[(d + e*x)*(a + b*ArcTan[c*x^2])^2,x]","\frac{(-1)^{3/4} d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 b^2}{\sqrt{c}}-\frac{\sqrt[4]{-1} d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 b^2}{\sqrt{c}}-\frac{1}{4} d x \log ^2\left(1-i c x^2\right) b^2-\frac{i e \left(1-i c x^2\right) \log ^2\left(1-i c x^2\right) b^2}{8 c}-\frac{1}{4} d x \log ^2\left(i c x^2+1\right) b^2+\frac{i e \left(i c x^2+1\right) \log ^2\left(i c x^2+1\right) b^2}{8 c}+\frac{2 \sqrt[4]{-1} d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) b^2}{\sqrt{c}}-\frac{2 \sqrt[4]{-1} d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2}{\sqrt{c}}+\frac{\sqrt[4]{-1} d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2}{\sqrt{c}}+\frac{2 \sqrt[4]{-1} d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) b^2}{\sqrt{c}}-\frac{2 \sqrt[4]{-1} d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2}{\sqrt{c}}+\frac{\sqrt[4]{-1} d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2}{\sqrt{c}}+\frac{\sqrt[4]{-1} d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2}{\sqrt{c}}+\frac{\sqrt[4]{-1} d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2}{\sqrt{c}}+\frac{\sqrt[4]{-1} d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right) b^2}{\sqrt{c}}-\frac{\sqrt[4]{-1} d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right) b^2}{\sqrt{c}}-\frac{i e \log \left(1-i c x^2\right) \log \left(\frac{1}{2} \left(i c x^2+1\right)\right) b^2}{4 c}-\frac{\sqrt[4]{-1} d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) b^2}{\sqrt{c}}+\frac{\sqrt[4]{-1} d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) b^2}{\sqrt{c}}+\frac{i e \log \left(\frac{1}{2} \left(1-i c x^2\right)\right) \log \left(i c x^2+1\right) b^2}{4 c}+\frac{1}{4} e x^2 \log \left(1-i c x^2\right) \log \left(i c x^2+1\right) b^2+\frac{1}{2} d x \log \left(1-i c x^2\right) \log \left(i c x^2+1\right) b^2-\frac{i e \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^2\right)\right) b^2}{4 c}+\frac{i e \text{PolyLog}\left(2,\frac{1}{2} \left(i c x^2+1\right)\right) b^2}{4 c}+\frac{(-1)^{3/4} d \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) b^2}{\sqrt{c}}+\frac{(-1)^{3/4} d \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2}{\sqrt{c}}-\frac{(-1)^{3/4} d \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2}{2 \sqrt{c}}+\frac{\sqrt[4]{-1} d \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) b^2}{\sqrt{c}}+\frac{\sqrt[4]{-1} d \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2}{\sqrt{c}}-\frac{\sqrt[4]{-1} d \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right) b^2}{2 \sqrt{c}}-\frac{\sqrt[4]{-1} d \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2}{2 \sqrt{c}}-\frac{(-1)^{3/4} d \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2}{2 \sqrt{c}}+a e x^2 \tan ^{-1}\left(c x^2\right) b+2 a d x \tan ^{-1}\left(c x^2\right) b+\frac{\sqrt{2} a d \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right) b}{\sqrt{c}}-\frac{\sqrt{2} a d \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right) b}{\sqrt{c}}-\frac{a d \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right) b}{\sqrt{2} \sqrt{c}}+\frac{a d \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right) b}{\sqrt{2} \sqrt{c}}-\frac{a e \log \left(c^2 x^4+1\right) b}{2 c}+\frac{a^2 (d+e x)^2}{2 e}","d x a^2-\frac{2 (-1)^{3/4} b d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) a}{\sqrt{c}}+\frac{2 (-1)^{3/4} b d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) a}{\sqrt{c}}+i b d x \log \left(1-i c x^2\right) a-i b d x \log \left(i c x^2+1\right) a+\frac{(-1)^{3/4} b^2 d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2}{\sqrt{c}}+\frac{1}{2} e x^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2+\frac{i e \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{2 c}-\frac{\sqrt[4]{-1} b^2 d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2}{\sqrt{c}}-\frac{1}{4} b^2 d x \log ^2\left(1-i c x^2\right)-\frac{1}{4} b^2 d x \log ^2\left(i c x^2+1\right)+\frac{2 \sqrt[4]{-1} b^2 d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right)}{\sqrt{c}}-\frac{2 \sqrt[4]{-1} b^2 d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{2 \sqrt[4]{-1} b^2 d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right)}{\sqrt{c}}-\frac{2 \sqrt[4]{-1} b^2 d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right)}{\sqrt{c}}-\frac{\sqrt[4]{-1} b^2 d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right)}{\sqrt{c}}+\frac{b e \left(a+b \tan ^{-1}\left(c x^2\right)\right) \log \left(\frac{2}{i c x^2+1}\right)}{c}-\frac{\sqrt[4]{-1} b^2 d \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 d \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right)}{\sqrt{c}}+\frac{1}{2} b^2 d x \log \left(1-i c x^2\right) \log \left(i c x^2+1\right)+\frac{(-1)^{3/4} b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right)}{\sqrt{c}}+\frac{(-1)^{3/4} b^2 d \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{(-1)^{3/4} b^2 d \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{2 \sqrt{c}}+\frac{\sqrt[4]{-1} b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 d \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{\sqrt[4]{-1} b^2 d \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right)}{2 \sqrt{c}}-\frac{\sqrt[4]{-1} b^2 d \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{2 \sqrt{c}}-\frac{(-1)^{3/4} b^2 d \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{2 \sqrt{c}}+\frac{i b^2 e \text{PolyLog}\left(2,1-\frac{2}{i c x^2+1}\right)}{2 c}",1,"(a^2*(d + e*x)^2)/(2*e) + ((-1)^(3/4)*b^2*d*ArcTan[(-1)^(3/4)*Sqrt[c]*x]^2)/Sqrt[c] + 2*a*b*d*x*ArcTan[c*x^2] + a*b*e*x^2*ArcTan[c*x^2] + (Sqrt[2]*a*b*d*ArcTan[1 - Sqrt[2]*Sqrt[c]*x])/Sqrt[c] - (Sqrt[2]*a*b*d*ArcTan[1 + Sqrt[2]*Sqrt[c]*x])/Sqrt[c] - ((-1)^(1/4)*b^2*d*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]^2)/Sqrt[c] + (2*(-1)^(1/4)*b^2*d*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] - (2*(-1)^(1/4)*b^2*d*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(1/4)*b^2*d*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[(Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] + (2*(-1)^(1/4)*b^2*d*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] - (2*(-1)^(1/4)*b^2*d*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(1/4)*b^2*d*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[-((Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x))])/Sqrt[c] + ((-1)^(1/4)*b^2*d*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(1/4)*b^2*d*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(1/4)*b^2*d*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[1 - I*c*x^2])/Sqrt[c] - ((-1)^(1/4)*b^2*d*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 - I*c*x^2])/Sqrt[c] - (b^2*d*x*Log[1 - I*c*x^2]^2)/4 - ((I/8)*b^2*e*(1 - I*c*x^2)*Log[1 - I*c*x^2]^2)/c - ((I/4)*b^2*e*Log[1 - I*c*x^2]*Log[(1 + I*c*x^2)/2])/c - ((-1)^(1/4)*b^2*d*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/Sqrt[c] + ((-1)^(1/4)*b^2*d*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/Sqrt[c] + ((I/4)*b^2*e*Log[(1 - I*c*x^2)/2]*Log[1 + I*c*x^2])/c + (b^2*d*x*Log[1 - I*c*x^2]*Log[1 + I*c*x^2])/2 + (b^2*e*x^2*Log[1 - I*c*x^2]*Log[1 + I*c*x^2])/4 - (b^2*d*x*Log[1 + I*c*x^2]^2)/4 + ((I/8)*b^2*e*(1 + I*c*x^2)*Log[1 + I*c*x^2]^2)/c - (a*b*d*Log[1 - Sqrt[2]*Sqrt[c]*x + c*x^2])/(Sqrt[2]*Sqrt[c]) + (a*b*d*Log[1 + Sqrt[2]*Sqrt[c]*x + c*x^2])/(Sqrt[2]*Sqrt[c]) - (a*b*e*Log[1 + c^2*x^4])/(2*c) - ((I/4)*b^2*e*PolyLog[2, (1 - I*c*x^2)/2])/c + ((I/4)*b^2*e*PolyLog[2, (1 + I*c*x^2)/2])/c + ((-1)^(3/4)*b^2*d*PolyLog[2, 1 - 2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(3/4)*b^2*d*PolyLog[2, 1 - 2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] - ((-1)^(3/4)*b^2*d*PolyLog[2, 1 - (Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(2*Sqrt[c]) + ((-1)^(1/4)*b^2*d*PolyLog[2, 1 - 2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(1/4)*b^2*d*PolyLog[2, 1 - 2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] - ((-1)^(1/4)*b^2*d*PolyLog[2, 1 + (Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(2*Sqrt[c]) - ((-1)^(1/4)*b^2*d*PolyLog[2, 1 - ((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(2*Sqrt[c]) - ((-1)^(3/4)*b^2*d*PolyLog[2, 1 - ((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(2*Sqrt[c])","A",110,46,18,2.556,0,"{6742, 5027, 297, 1162, 617, 204, 1165, 628, 5033, 260, 5029, 2450, 2476, 2448, 321, 203, 2470, 12, 4920, 4854, 2402, 2315, 206, 2556, 205, 4928, 4856, 2447, 208, 5992, 5920, 5984, 5918, 5035, 2454, 2389, 2296, 2295, 30, 2557, 2475, 43, 2416, 2394, 2393, 2391}"
26,0,0,0,0.1230236,"\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{d+e x} \, dx","Int[(a + b*ArcTan[c*x^2])^2/(d + e*x),x]","\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{d+e x} \, dx","\text{Int}\left(\frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{d+e x},x\right)",0,"(a^2*Log[d + e*x])/e + 2*a*b*Defer[Int][ArcTan[c*x^2]/(d + e*x), x] + b^2*Defer[Int][ArcTan[c*x^2]^2/(d + e*x), x]","A",0,0,0,0,-1,"{}"
27,0,0,0,0.6564502,"\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{(d+e x)^2} \, dx","Int[(a + b*ArcTan[c*x^2])^2/(d + e*x)^2,x]","\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{(d+e x)^2} \, dx","\text{Int}\left(\frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{(d+e x)^2},x\right)",0,"-(a^2/(e*(d + e*x))) + (2*a*b*c^2*d^3*ArcTan[c*x^2])/(e*(c^2*d^4 + e^4)) - (2*a*b*ArcTan[c*x^2])/(e*(d + e*x)) + (Sqrt[2]*a*b*Sqrt[c]*(c*d^2 - e^2)*ArcTan[1 - Sqrt[2]*Sqrt[c]*x])/(c^2*d^4 + e^4) - (Sqrt[2]*a*b*Sqrt[c]*(c*d^2 - e^2)*ArcTan[1 + Sqrt[2]*Sqrt[c]*x])/(c^2*d^4 + e^4) - (4*a*b*c*d*e*Log[d + e*x])/(c^2*d^4 + e^4) - (a*b*Sqrt[c]*(c*d^2 + e^2)*Log[1 - Sqrt[2]*Sqrt[c]*x + c*x^2])/(Sqrt[2]*(c^2*d^4 + e^4)) + (a*b*Sqrt[c]*(c*d^2 + e^2)*Log[1 + Sqrt[2]*Sqrt[c]*x + c*x^2])/(Sqrt[2]*(c^2*d^4 + e^4)) + (a*b*c*d*e*Log[1 + c^2*x^4])/(c^2*d^4 + e^4) + b^2*Defer[Int][ArcTan[c*x^2]^2/(d + e*x)^2, x]","A",0,0,0,0,-1,"{}"
28,1,331,0,0.7094877,"\int (d+e x)^2 \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcTan[c*x^3]),x]","\frac{a (d+e x)^3}{3 e}+\frac{b d^2 \log \left(c^{2/3} x^2+1\right)}{2 \sqrt[3]{c}}-\frac{b d^2 \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b d^2 \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}-\frac{\sqrt{3} b d e \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)}{4 c^{2/3}}+\frac{\sqrt{3} b d e \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)}{4 c^{2/3}}-\frac{b d e \tan ^{-1}\left(\sqrt[3]{c} x\right)}{c^{2/3}}+\frac{b d e \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)}{2 c^{2/3}}-\frac{b d e \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)}{2 c^{2/3}}-\frac{b e^2 \log \left(c^2 x^6+1\right)}{6 c}+b d^2 x \tan ^{-1}\left(c x^3\right)+b d e x^2 \tan ^{-1}\left(c x^3\right)+\frac{1}{3} b e^2 x^3 \tan ^{-1}\left(c x^3\right)","\frac{(d+e x)^3 \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{3 e}+\frac{b d^2 \log \left(c^{2/3} x^2+1\right)}{2 \sqrt[3]{c}}-\frac{b d^2 \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b d^2 \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}-\frac{\sqrt{3} b d e \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)}{4 c^{2/3}}+\frac{\sqrt{3} b d e \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)}{4 c^{2/3}}-\frac{b d e \tan ^{-1}\left(\sqrt[3]{c} x\right)}{c^{2/3}}+\frac{b d e \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)}{2 c^{2/3}}-\frac{b d e \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)}{2 c^{2/3}}-\frac{b e^2 \log \left(c^2 x^6+1\right)}{6 c}-\frac{b d^3 \tan ^{-1}\left(c x^3\right)}{3 e}",1,"(a*(d + e*x)^3)/(3*e) - (b*d*e*ArcTan[c^(1/3)*x])/c^(2/3) + b*d^2*x*ArcTan[c*x^3] + b*d*e*x^2*ArcTan[c*x^3] + (b*e^2*x^3*ArcTan[c*x^3])/3 + (b*d*e*ArcTan[Sqrt[3] - 2*c^(1/3)*x])/(2*c^(2/3)) - (b*d*e*ArcTan[Sqrt[3] + 2*c^(1/3)*x])/(2*c^(2/3)) + (Sqrt[3]*b*d^2*ArcTan[(1 - 2*c^(2/3)*x^2)/Sqrt[3]])/(2*c^(1/3)) + (b*d^2*Log[1 + c^(2/3)*x^2])/(2*c^(1/3)) - (Sqrt[3]*b*d*e*Log[1 - Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(4*c^(2/3)) + (Sqrt[3]*b*d*e*Log[1 + Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(4*c^(2/3)) - (b*d^2*Log[1 - c^(2/3)*x^2 + c^(4/3)*x^4])/(4*c^(1/3)) - (b*e^2*Log[1 + c^2*x^6])/(6*c)","A",25,14,18,0.7778,1,"{6742, 5027, 275, 292, 31, 634, 617, 204, 628, 5033, 295, 618, 203, 260}"
29,1,285,0,0.6026398,"\int (d+e x) \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[(d + e*x)*(a + b*ArcTan[c*x^3]),x]","\frac{(d+e x)^2 \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{2 e}+\frac{b d \log \left(c^{2/3} x^2+1\right)}{2 \sqrt[3]{c}}-\frac{b d \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b d \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}-\frac{\sqrt{3} b e \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)}{8 c^{2/3}}+\frac{\sqrt{3} b e \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{b e \tan ^{-1}\left(\sqrt[3]{c} x\right)}{2 c^{2/3}}+\frac{b e \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)}{4 c^{2/3}}-\frac{b e \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)}{4 c^{2/3}}-\frac{b d^2 \tan ^{-1}\left(c x^3\right)}{2 e}","\frac{(d+e x)^2 \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{2 e}+\frac{b d \log \left(c^{2/3} x^2+1\right)}{2 \sqrt[3]{c}}-\frac{b d \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b d \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}-\frac{\sqrt{3} b e \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)}{8 c^{2/3}}+\frac{\sqrt{3} b e \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{b e \tan ^{-1}\left(\sqrt[3]{c} x\right)}{2 c^{2/3}}+\frac{b e \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)}{4 c^{2/3}}-\frac{b e \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)}{4 c^{2/3}}-\frac{b d^2 \tan ^{-1}\left(c x^3\right)}{2 e}",1,"-(b*e*ArcTan[c^(1/3)*x])/(2*c^(2/3)) - (b*d^2*ArcTan[c*x^3])/(2*e) + ((d + e*x)^2*(a + b*ArcTan[c*x^3]))/(2*e) + (b*e*ArcTan[Sqrt[3] - 2*c^(1/3)*x])/(4*c^(2/3)) - (b*e*ArcTan[Sqrt[3] + 2*c^(1/3)*x])/(4*c^(2/3)) + (Sqrt[3]*b*d*ArcTan[(1 - 2*c^(2/3)*x^2)/Sqrt[3]])/(2*c^(1/3)) + (b*d*Log[1 + c^(2/3)*x^2])/(2*c^(1/3)) - (Sqrt[3]*b*e*Log[1 - Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(8*c^(2/3)) + (Sqrt[3]*b*e*Log[1 + Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(8*c^(2/3)) - (b*d*Log[1 - c^(2/3)*x^2 + c^(4/3)*x^4])/(4*c^(1/3))","A",23,13,16,0.8125,1,"{5205, 12, 1831, 275, 203, 292, 31, 634, 617, 204, 628, 295, 618}"
30,0,0,0,0.0625405,"\int \frac{a+b \tan ^{-1}\left(c x^3\right)}{d+e x} \, dx","Int[(a + b*ArcTan[c*x^3])/(d + e*x),x]","\int \frac{a+b \tan ^{-1}\left(c x^3\right)}{d+e x} \, dx","-\frac{b c \text{PolyLog}\left(2,\frac{\sqrt[6]{-c^2} (d+e x)}{\sqrt[6]{-c^2} d-e}\right)}{2 \sqrt{-c^2} e}+\frac{b c \text{PolyLog}\left(2,\frac{\sqrt[6]{-c^2} (d+e x)}{\sqrt[6]{-c^2} d+e}\right)}{2 \sqrt{-c^2} e}+\frac{b c \text{PolyLog}\left(2,\frac{\sqrt[6]{-c^2} (d+e x)}{\sqrt[6]{-c^2} d-\sqrt[3]{-1} e}\right)}{2 \sqrt{-c^2} e}-\frac{b c \text{PolyLog}\left(2,\frac{\sqrt[6]{-c^2} (d+e x)}{\sqrt[6]{-c^2} d+\sqrt[3]{-1} e}\right)}{2 \sqrt{-c^2} e}-\frac{b c \text{PolyLog}\left(2,\frac{\sqrt[6]{-c^2} (d+e x)}{\sqrt[6]{-c^2} d-(-1)^{2/3} e}\right)}{2 \sqrt{-c^2} e}+\frac{b c \text{PolyLog}\left(2,\frac{\sqrt[6]{-c^2} (d+e x)}{\sqrt[6]{-c^2} d+(-1)^{2/3} e}\right)}{2 \sqrt{-c^2} e}+\frac{\log (d+e x) \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{e}+\frac{b c \log (d+e x) \log \left(\frac{e \left(1-\sqrt[6]{-c^2} x\right)}{\sqrt[6]{-c^2} d+e}\right)}{2 \sqrt{-c^2} e}-\frac{b c \log (d+e x) \log \left(-\frac{e \left(\sqrt[6]{-c^2} x+1\right)}{\sqrt[6]{-c^2} d-e}\right)}{2 \sqrt{-c^2} e}+\frac{b c \log (d+e x) \log \left(-\frac{e \left(\sqrt[6]{-c^2} x+\sqrt[3]{-1}\right)}{\sqrt[6]{-c^2} d-\sqrt[3]{-1} e}\right)}{2 \sqrt{-c^2} e}-\frac{b c \log (d+e x) \log \left(-\frac{e \left(\sqrt[6]{-c^2} x+(-1)^{2/3}\right)}{\sqrt[6]{-c^2} d-(-1)^{2/3} e}\right)}{2 \sqrt{-c^2} e}+\frac{b c \log (d+e x) \log \left(\frac{(-1)^{2/3} e \left(\sqrt[3]{-1} \sqrt[6]{-c^2} x+1\right)}{\sqrt[6]{-c^2} d+(-1)^{2/3} e}\right)}{2 \sqrt{-c^2} e}-\frac{b c \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[6]{-c^2} x+1\right)}{\sqrt[6]{-c^2} d+\sqrt[3]{-1} e}\right)}{2 \sqrt{-c^2} e}",1,"(a*Log[d + e*x])/e + b*Defer[Int][ArcTan[c*x^3]/(d + e*x), x]","F",0,0,0,0,-1,"{}"
31,1,906,0,1.4837997,"\int \frac{a+b \tan ^{-1}\left(c x^3\right)}{(d+e x)^2} \, dx","Int[(a + b*ArcTan[c*x^3])/(d + e*x)^2,x]","\frac{b c^2 \tan ^{-1}\left(c x^3\right) d^5}{e \left(c^2 d^6+e^6\right)}+\frac{b c^{5/3} \log \left(c^{2/3} x^2+1\right) d^4}{2 \left(c^2 d^6+e^6\right)}+\frac{3 b c e^2 \log (d+e x) d^2}{c^2 d^6+e^6}-\frac{b c e^2 \log \left(c^2 x^6+1\right) d^2}{2 \left(c^2 d^6+e^6\right)}-\frac{b c^{2/3} e^3 \tan ^{-1}\left(\sqrt[3]{c} x\right) d}{c^2 d^6+e^6}+\frac{b c^{2/3} \left(\sqrt{3} c d^3+e^3\right) \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right) d}{2 \left(c^2 d^6+e^6\right)}+\frac{b c^{2/3} \left(\sqrt{3} c d^3-e^3\right) \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right) d}{2 \left(c^2 d^6+e^6\right)}-\frac{b c^{2/3} \left(c d^3-\sqrt{3} e^3\right) \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right) d}{4 \left(c^2 d^6+e^6\right)}-\frac{b c^{2/3} \left(c d^3+\sqrt{3} e^3\right) \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right) d}{4 \left(c^2 d^6+e^6\right)}-\frac{a+b \tan ^{-1}\left(c x^3\right)}{e (d+e x)}+\frac{\sqrt{3} b c^{5/3} e \left(\sqrt{-c^2} d^3+e^3\right) \tan ^{-1}\left(\frac{\frac{2 c^{2/3} x}{\sqrt[6]{-c^2}}+1}{\sqrt{3}}\right)}{2 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}-\frac{\sqrt{3} b c^{5/3} e \left(\sqrt{-c^2} d^3-e^3\right) \tan ^{-1}\left(\frac{c^{4/3}+2 \left(-c^2\right)^{5/6} x}{\sqrt{3} c^{4/3}}\right)}{2 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}+\frac{b c^{5/3} e \left(\sqrt{-c^2} d^3+e^3\right) \log \left(\sqrt[6]{-c^2}-c^{2/3} x\right)}{2 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}-\frac{b c^{5/3} e \left(\sqrt{-c^2} d^3-e^3\right) \log \left(c^{2/3} x+\sqrt[6]{-c^2}\right)}{2 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}+\frac{b c^{5/3} e \left(\sqrt{-c^2} d^3-e^3\right) \log \left(c^{4/3} x^2-c^{2/3} \sqrt[6]{-c^2} x+\sqrt[3]{-c^2}\right)}{4 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}-\frac{b c^{5/3} e \left(\sqrt{-c^2} d^3+e^3\right) \log \left(c^{4/3} x^2+c^{2/3} \sqrt[6]{-c^2} x+\sqrt[3]{-c^2}\right)}{4 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}","\frac{b c^2 \tan ^{-1}\left(c x^3\right) d^5}{e \left(c^2 d^6+e^6\right)}+\frac{b c^{5/3} \log \left(c^{2/3} x^2+1\right) d^4}{2 \left(c^2 d^6+e^6\right)}+\frac{3 b c e^2 \log (d+e x) d^2}{c^2 d^6+e^6}-\frac{b c e^2 \log \left(c^2 x^6+1\right) d^2}{2 \left(c^2 d^6+e^6\right)}-\frac{b c^{2/3} e^3 \tan ^{-1}\left(\sqrt[3]{c} x\right) d}{c^2 d^6+e^6}+\frac{b c^{2/3} \left(\sqrt{3} c d^3+e^3\right) \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right) d}{2 \left(c^2 d^6+e^6\right)}+\frac{b c^{2/3} \left(\sqrt{3} c d^3-e^3\right) \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right) d}{2 \left(c^2 d^6+e^6\right)}-\frac{b c^{2/3} \left(c d^3-\sqrt{3} e^3\right) \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right) d}{4 \left(c^2 d^6+e^6\right)}-\frac{b c^{2/3} \left(c d^3+\sqrt{3} e^3\right) \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right) d}{4 \left(c^2 d^6+e^6\right)}-\frac{a+b \tan ^{-1}\left(c x^3\right)}{e (d+e x)}+\frac{\sqrt{3} b c^{5/3} e \left(\sqrt{-c^2} d^3+e^3\right) \tan ^{-1}\left(\frac{\frac{2 c^{2/3} x}{\sqrt[6]{-c^2}}+1}{\sqrt{3}}\right)}{2 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}-\frac{\sqrt{3} b c^{5/3} e \left(\sqrt{-c^2} d^3-e^3\right) \tan ^{-1}\left(\frac{c^{4/3}+2 \left(-c^2\right)^{5/6} x}{\sqrt{3} c^{4/3}}\right)}{2 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}+\frac{b c^{5/3} e \left(\sqrt{-c^2} d^3+e^3\right) \log \left(\sqrt[6]{-c^2}-c^{2/3} x\right)}{2 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}-\frac{b c^{5/3} e \left(\sqrt{-c^2} d^3-e^3\right) \log \left(c^{2/3} x+\sqrt[6]{-c^2}\right)}{2 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}+\frac{b c^{5/3} e \left(\sqrt{-c^2} d^3-e^3\right) \log \left(c^{4/3} x^2-c^{2/3} \sqrt[6]{-c^2} x+\sqrt[3]{-c^2}\right)}{4 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}-\frac{b c^{5/3} e \left(\sqrt{-c^2} d^3+e^3\right) \log \left(c^{4/3} x^2+c^{2/3} \sqrt[6]{-c^2} x+\sqrt[3]{-c^2}\right)}{4 \left(-c^2\right)^{2/3} \left(c^2 d^6+e^6\right)}",1,"-((b*c^(2/3)*d*e^3*ArcTan[c^(1/3)*x])/(c^2*d^6 + e^6)) + (b*c^2*d^5*ArcTan[c*x^3])/(e*(c^2*d^6 + e^6)) - (a + b*ArcTan[c*x^3])/(e*(d + e*x)) + (b*c^(2/3)*d*(Sqrt[3]*c*d^3 + e^3)*ArcTan[Sqrt[3] - 2*c^(1/3)*x])/(2*(c^2*d^6 + e^6)) + (b*c^(2/3)*d*(Sqrt[3]*c*d^3 - e^3)*ArcTan[Sqrt[3] + 2*c^(1/3)*x])/(2*(c^2*d^6 + e^6)) + (Sqrt[3]*b*c^(5/3)*e*(Sqrt[-c^2]*d^3 + e^3)*ArcTan[(1 + (2*c^(2/3)*x)/(-c^2)^(1/6))/Sqrt[3]])/(2*(-c^2)^(2/3)*(c^2*d^6 + e^6)) - (Sqrt[3]*b*c^(5/3)*e*(Sqrt[-c^2]*d^3 - e^3)*ArcTan[(c^(4/3) + 2*(-c^2)^(5/6)*x)/(Sqrt[3]*c^(4/3))])/(2*(-c^2)^(2/3)*(c^2*d^6 + e^6)) + (b*c^(5/3)*e*(Sqrt[-c^2]*d^3 + e^3)*Log[(-c^2)^(1/6) - c^(2/3)*x])/(2*(-c^2)^(2/3)*(c^2*d^6 + e^6)) - (b*c^(5/3)*e*(Sqrt[-c^2]*d^3 - e^3)*Log[(-c^2)^(1/6) + c^(2/3)*x])/(2*(-c^2)^(2/3)*(c^2*d^6 + e^6)) + (3*b*c*d^2*e^2*Log[d + e*x])/(c^2*d^6 + e^6) + (b*c^(5/3)*d^4*Log[1 + c^(2/3)*x^2])/(2*(c^2*d^6 + e^6)) - (b*c^(2/3)*d*(c*d^3 - Sqrt[3]*e^3)*Log[1 - Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(4*(c^2*d^6 + e^6)) - (b*c^(2/3)*d*(c*d^3 + Sqrt[3]*e^3)*Log[1 + Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(4*(c^2*d^6 + e^6)) + (b*c^(5/3)*e*(Sqrt[-c^2]*d^3 - e^3)*Log[(-c^2)^(1/3) - c^(2/3)*(-c^2)^(1/6)*x + c^(4/3)*x^2])/(4*(-c^2)^(2/3)*(c^2*d^6 + e^6)) - (b*c^(5/3)*e*(Sqrt[-c^2]*d^3 + e^3)*Log[(-c^2)^(1/3) + c^(2/3)*(-c^2)^(1/6)*x + c^(4/3)*x^2])/(4*(-c^2)^(2/3)*(c^2*d^6 + e^6)) - (b*c*d^2*e^2*Log[1 + c^2*x^6])/(2*(c^2*d^6 + e^6))","A",35,16,18,0.8889,1,"{5205, 12, 6725, 1876, 1416, 635, 203, 260, 634, 617, 204, 628, 1511, 292, 31, 1469}"