1,1,72,0,0.2506494,"\int (c e+d e x)^3 \left(a+b \tan ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcTan[c + d*x]),x]","\frac{e^3 (c+d x)^4 \left(a+b \tan ^{-1}(c+d x)\right)}{4 d}-\frac{b e^3 (c+d x)^3}{12 d}-\frac{b e^3 \tan ^{-1}(c+d x)}{4 d}+\frac{1}{4} b e^3 x","\frac{e^3 (c+d x)^4 \left(a+b \tan ^{-1}(c+d x)\right)}{4 d}-\frac{b e^3 (c+d x)^3}{12 d}-\frac{b e^3 \tan ^{-1}(c+d x)}{4 d}+\frac{1}{4} b e^3 x",1,"(b*e^3*x)/4 - (b*e^3*(c + d*x)^3)/(12*d) - (b*e^3*ArcTan[c + d*x])/(4*d) + (e^3*(c + d*x)^4*(a + b*ArcTan[c + d*x]))/(4*d)","A",6,5,21,0.2381,1,"{5043, 12, 4852, 302, 203}"
2,1,67,0,0.0547487,"\int (c e+d e x)^2 \left(a+b \tan ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcTan[c + d*x]),x]","\frac{e^2 (c+d x)^3 \left(a+b \tan ^{-1}(c+d x)\right)}{3 d}-\frac{b e^2 (c+d x)^2}{6 d}+\frac{b e^2 \log \left((c+d x)^2+1\right)}{6 d}","\frac{e^2 (c+d x)^3 \left(a+b \tan ^{-1}(c+d x)\right)}{3 d}-\frac{b e^2 (c+d x)^2}{6 d}+\frac{b e^2 \log \left((c+d x)^2+1\right)}{6 d}",1,"-(b*e^2*(c + d*x)^2)/(6*d) + (e^2*(c + d*x)^3*(a + b*ArcTan[c + d*x]))/(3*d) + (b*e^2*Log[1 + (c + d*x)^2])/(6*d)","A",6,5,21,0.2381,1,"{5043, 12, 4852, 266, 43}"
3,1,48,0,0.0302586,"\int (c e+d e x) \left(a+b \tan ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)*(a + b*ArcTan[c + d*x]),x]","\frac{e (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)}{2 d}+\frac{b e \tan ^{-1}(c+d x)}{2 d}-\frac{b e x}{2}","\frac{e (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)}{2 d}+\frac{b e \tan ^{-1}(c+d x)}{2 d}-\frac{b e x}{2}",1,"-(b*e*x)/2 + (b*e*ArcTan[c + d*x])/(2*d) + (e*(c + d*x)^2*(a + b*ArcTan[c + d*x]))/(2*d)","A",5,5,19,0.2632,1,"{5043, 12, 4852, 321, 203}"
4,1,63,0,0.0579499,"\int \frac{a+b \tan ^{-1}(c+d x)}{c e+d e x} \, dx","Int[(a + b*ArcTan[c + d*x])/(c*e + d*e*x),x]","\frac{i b \text{PolyLog}(2,-i (c+d x))}{2 d e}-\frac{i b \text{PolyLog}(2,i (c+d x))}{2 d e}+\frac{a \log (c+d x)}{d e}","\frac{i b \text{PolyLog}(2,-i (c+d x))}{2 d e}-\frac{i b \text{PolyLog}(2,i (c+d x))}{2 d e}+\frac{a \log (c+d x)}{d e}",1,"(a*Log[c + d*x])/(d*e) + ((I/2)*b*PolyLog[2, (-I)*(c + d*x)])/(d*e) - ((I/2)*b*PolyLog[2, I*(c + d*x)])/(d*e)","A",5,4,21,0.1905,1,"{5043, 12, 4848, 2391}"
5,1,61,0,0.0472608,"\int \frac{a+b \tan ^{-1}(c+d x)}{(c e+d e x)^2} \, dx","Int[(a + b*ArcTan[c + d*x])/(c*e + d*e*x)^2,x]","-\frac{a+b \tan ^{-1}(c+d x)}{d e^2 (c+d x)}+\frac{b \log (c+d x)}{d e^2}-\frac{b \log \left((c+d x)^2+1\right)}{2 d e^2}","-\frac{a+b \tan ^{-1}(c+d x)}{d e^2 (c+d x)}+\frac{b \log (c+d x)}{d e^2}-\frac{b \log \left((c+d x)^2+1\right)}{2 d e^2}",1,"-((a + b*ArcTan[c + d*x])/(d*e^2*(c + d*x))) + (b*Log[c + d*x])/(d*e^2) - (b*Log[1 + (c + d*x)^2])/(2*d*e^2)","A",7,7,21,0.3333,1,"{5043, 12, 4852, 266, 36, 29, 31}"
6,1,63,0,0.0446105,"\int \frac{a+b \tan ^{-1}(c+d x)}{(c e+d e x)^3} \, dx","Int[(a + b*ArcTan[c + d*x])/(c*e + d*e*x)^3,x]","-\frac{a+b \tan ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}-\frac{b}{2 d e^3 (c+d x)}-\frac{b \tan ^{-1}(c+d x)}{2 d e^3}","-\frac{a+b \tan ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}-\frac{b}{2 d e^3 (c+d x)}-\frac{b \tan ^{-1}(c+d x)}{2 d e^3}",1,"-b/(2*d*e^3*(c + d*x)) - (b*ArcTan[c + d*x])/(2*d*e^3) - (a + b*ArcTan[c + d*x])/(2*d*e^3*(c + d*x)^2)","A",5,5,21,0.2381,1,"{5043, 12, 4852, 325, 203}"
7,1,157,0,0.2205897,"\int (c e+d e x)^3 \left(a+b \tan ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcTan[c + d*x])^2,x]","\frac{e^3 (c+d x)^4 \left(a+b \tan ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e^3 (c+d x)^3 \left(a+b \tan ^{-1}(c+d x)\right)}{6 d}-\frac{e^3 \left(a+b \tan ^{-1}(c+d x)\right)^2}{4 d}+\frac{1}{2} a b e^3 x+\frac{b^2 e^3 (c+d x)^2}{12 d}-\frac{b^2 e^3 \log \left((c+d x)^2+1\right)}{3 d}+\frac{b^2 e^3 (c+d x) \tan ^{-1}(c+d x)}{2 d}","\frac{e^3 (c+d x)^4 \left(a+b \tan ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e^3 (c+d x)^3 \left(a+b \tan ^{-1}(c+d x)\right)}{6 d}-\frac{e^3 \left(a+b \tan ^{-1}(c+d x)\right)^2}{4 d}+\frac{1}{2} a b e^3 x+\frac{b^2 e^3 (c+d x)^2}{12 d}-\frac{b^2 e^3 \log \left((c+d x)^2+1\right)}{3 d}+\frac{b^2 e^3 (c+d x) \tan ^{-1}(c+d x)}{2 d}",1,"(a*b*e^3*x)/2 + (b^2*e^3*(c + d*x)^2)/(12*d) + (b^2*e^3*(c + d*x)*ArcTan[c + d*x])/(2*d) - (b*e^3*(c + d*x)^3*(a + b*ArcTan[c + d*x]))/(6*d) - (e^3*(a + b*ArcTan[c + d*x])^2)/(4*d) + (e^3*(c + d*x)^4*(a + b*ArcTan[c + d*x])^2)/(4*d) - (b^2*e^3*Log[1 + (c + d*x)^2])/(3*d)","A",13,9,23,0.3913,1,"{5043, 12, 4852, 4916, 266, 43, 4846, 260, 4884}"
8,1,183,0,0.2211335,"\int (c e+d e x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcTan[c + d*x])^2,x]","-\frac{i b^2 e^2 \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{3 d}+\frac{e^2 (c+d x)^3 \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d}-\frac{b e^2 (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)}{3 d}-\frac{i e^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{3 d}-\frac{b^2 e^2 \tan ^{-1}(c+d x)}{3 d}+\frac{1}{3} b^2 e^2 x","-\frac{i b^2 e^2 \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{3 d}+\frac{e^2 (c+d x)^3 \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d}-\frac{b e^2 (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)}{3 d}-\frac{i e^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{3 d}-\frac{b^2 e^2 \tan ^{-1}(c+d x)}{3 d}+\frac{1}{3} b^2 e^2 x",1,"(b^2*e^2*x)/3 - (b^2*e^2*ArcTan[c + d*x])/(3*d) - (b*e^2*(c + d*x)^2*(a + b*ArcTan[c + d*x]))/(3*d) - ((I/3)*e^2*(a + b*ArcTan[c + d*x])^2)/d + (e^2*(c + d*x)^3*(a + b*ArcTan[c + d*x])^2)/(3*d) - (2*b*e^2*(a + b*ArcTan[c + d*x])*Log[2/(1 + I*(c + d*x))])/(3*d) - ((I/3)*b^2*e^2*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/d","A",11,10,23,0.4348,1,"{5043, 12, 4852, 4916, 321, 203, 4920, 4854, 2402, 2315}"
9,1,95,0,0.1194305,"\int (c e+d e x) \left(a+b \tan ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)*(a + b*ArcTan[c + d*x])^2,x]","\frac{e (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}+\frac{e \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}-a b e x+\frac{b^2 e \log \left((c+d x)^2+1\right)}{2 d}-\frac{b^2 e (c+d x) \tan ^{-1}(c+d x)}{d}","\frac{e (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}+\frac{e \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}-a b e x+\frac{b^2 e \log \left((c+d x)^2+1\right)}{2 d}-\frac{b^2 e (c+d x) \tan ^{-1}(c+d x)}{d}",1,"-(a*b*e*x) - (b^2*e*(c + d*x)*ArcTan[c + d*x])/d + (e*(a + b*ArcTan[c + d*x])^2)/(2*d) + (e*(c + d*x)^2*(a + b*ArcTan[c + d*x])^2)/(2*d) + (b^2*e*Log[1 + (c + d*x)^2])/(2*d)","A",8,7,21,0.3333,1,"{5043, 12, 4852, 4916, 4846, 260, 4884}"
10,1,183,0,0.3388794,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{c e+d e x} \, dx","Int[(a + b*ArcTan[c + d*x])^2/(c*e + d*e*x),x]","-\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e}+\frac{i b \text{PolyLog}\left(2,-1+\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right)}{2 d e}+\frac{b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i (c+d x)}\right)}{2 d e}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d e}","-\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e}+\frac{i b \text{PolyLog}\left(2,-1+\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right)}{2 d e}+\frac{b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i (c+d x)}\right)}{2 d e}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d e}",1,"(2*(a + b*ArcTan[c + d*x])^2*ArcTanh[1 - 2/(1 + I*(c + d*x))])/(d*e) - (I*b*(a + b*ArcTan[c + d*x])*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/(d*e) + (I*b*(a + b*ArcTan[c + d*x])*PolyLog[2, -1 + 2/(1 + I*(c + d*x))])/(d*e) - (b^2*PolyLog[3, 1 - 2/(1 + I*(c + d*x))])/(2*d*e) + (b^2*PolyLog[3, -1 + 2/(1 + I*(c + d*x))])/(2*d*e)","A",8,7,23,0.3043,1,"{5043, 12, 4850, 4988, 4884, 4994, 6610}"
11,1,119,0,0.1868536,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{(c e+d e x)^2} \, dx","Int[(a + b*ArcTan[c + d*x])^2/(c*e + d*e*x)^2,x]","-\frac{i b^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i (c+d x)}\right)}{d e^2}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{d e^2 (c+d x)}-\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^2}{d e^2}+\frac{2 b \log \left(2-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e^2}","-\frac{i b^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i (c+d x)}\right)}{d e^2}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{d e^2 (c+d x)}-\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^2}{d e^2}+\frac{2 b \log \left(2-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e^2}",1,"((-I)*(a + b*ArcTan[c + d*x])^2)/(d*e^2) - (a + b*ArcTan[c + d*x])^2/(d*e^2*(c + d*x)) + (2*b*(a + b*ArcTan[c + d*x])*Log[2 - 2/(1 - I*(c + d*x))])/(d*e^2) - (I*b^2*PolyLog[2, -1 + 2/(1 - I*(c + d*x))])/(d*e^2)","A",6,6,23,0.2609,1,"{5043, 12, 4852, 4924, 4868, 2447}"
12,1,117,0,0.1528436,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{(c e+d e x)^3} \, dx","Int[(a + b*ArcTan[c + d*x])^2/(c*e + d*e*x)^3,x]","-\frac{b \left(a+b \tan ^{-1}(c+d x)\right)}{d e^3 (c+d x)}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)^2}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^3}+\frac{b^2 \log (c+d x)}{d e^3}-\frac{b^2 \log \left((c+d x)^2+1\right)}{2 d e^3}","-\frac{b \left(a+b \tan ^{-1}(c+d x)\right)}{d e^3 (c+d x)}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)^2}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^3}+\frac{b^2 \log (c+d x)}{d e^3}-\frac{b^2 \log \left((c+d x)^2+1\right)}{2 d e^3}",1,"-((b*(a + b*ArcTan[c + d*x]))/(d*e^3*(c + d*x))) - (a + b*ArcTan[c + d*x])^2/(2*d*e^3) - (a + b*ArcTan[c + d*x])^2/(2*d*e^3*(c + d*x)^2) + (b^2*Log[c + d*x])/(d*e^3) - (b^2*Log[1 + (c + d*x)^2])/(2*d*e^3)","A",10,9,23,0.3913,1,"{5043, 12, 4852, 4918, 266, 36, 29, 31, 4884}"
13,1,194,0,0.2574462,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{(c e+d e x)^4} \, dx","Int[(a + b*ArcTan[c + d*x])^2/(c*e + d*e*x)^4,x]","\frac{i b^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i (c+d x)}\right)}{3 d e^4}-\frac{b \left(a+b \tan ^{-1}(c+d x)\right)}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d e^4 (c+d x)^3}+\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d e^4}-\frac{2 b \log \left(2-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{3 d e^4}-\frac{b^2}{3 d e^4 (c+d x)}-\frac{b^2 \tan ^{-1}(c+d x)}{3 d e^4}","\frac{i b^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i (c+d x)}\right)}{3 d e^4}-\frac{b \left(a+b \tan ^{-1}(c+d x)\right)}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d e^4 (c+d x)^3}+\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d e^4}-\frac{2 b \log \left(2-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{3 d e^4}-\frac{b^2}{3 d e^4 (c+d x)}-\frac{b^2 \tan ^{-1}(c+d x)}{3 d e^4}",1,"-b^2/(3*d*e^4*(c + d*x)) - (b^2*ArcTan[c + d*x])/(3*d*e^4) - (b*(a + b*ArcTan[c + d*x]))/(3*d*e^4*(c + d*x)^2) + ((I/3)*(a + b*ArcTan[c + d*x])^2)/(d*e^4) - (a + b*ArcTan[c + d*x])^2/(3*d*e^4*(c + d*x)^3) - (2*b*(a + b*ArcTan[c + d*x])*Log[2 - 2/(1 - I*(c + d*x))])/(3*d*e^4) + ((I/3)*b^2*PolyLog[2, -1 + 2/(1 - I*(c + d*x))])/(d*e^4)","A",10,9,23,0.3913,1,"{5043, 12, 4852, 4918, 325, 203, 4924, 4868, 2447}"
14,1,170,0,0.2267456,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{(c e+d e x)^5} \, dx","Int[(a + b*ArcTan[c + d*x])^2/(c*e + d*e*x)^5,x]","\frac{b \left(a+b \tan ^{-1}(c+d x)\right)}{2 d e^5 (c+d x)}-\frac{b \left(a+b \tan ^{-1}(c+d x)\right)}{6 d e^5 (c+d x)^3}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{4 d e^5 (c+d x)^4}+\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{4 d e^5}-\frac{b^2}{12 d e^5 (c+d x)^2}-\frac{2 b^2 \log (c+d x)}{3 d e^5}+\frac{b^2 \log \left((c+d x)^2+1\right)}{3 d e^5}","\frac{b \left(a+b \tan ^{-1}(c+d x)\right)}{2 d e^5 (c+d x)}-\frac{b \left(a+b \tan ^{-1}(c+d x)\right)}{6 d e^5 (c+d x)^3}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{4 d e^5 (c+d x)^4}+\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{4 d e^5}-\frac{b^2}{12 d e^5 (c+d x)^2}-\frac{2 b^2 \log (c+d x)}{3 d e^5}+\frac{b^2 \log \left((c+d x)^2+1\right)}{3 d e^5}",1,"-b^2/(12*d*e^5*(c + d*x)^2) - (b*(a + b*ArcTan[c + d*x]))/(6*d*e^5*(c + d*x)^3) + (b*(a + b*ArcTan[c + d*x]))/(2*d*e^5*(c + d*x)) + (a + b*ArcTan[c + d*x])^2/(4*d*e^5) - (a + b*ArcTan[c + d*x])^2/(4*d*e^5*(c + d*x)^4) - (2*b^2*Log[c + d*x])/(3*d*e^5) + (b^2*Log[1 + (c + d*x)^2])/(3*d*e^5)","A",15,10,23,0.4348,1,"{5043, 12, 4852, 4918, 266, 44, 36, 29, 31, 4884}"
15,1,271,0,0.4387062,"\int (c e+d e x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcTan[c + d*x])^3,x]","-\frac{i b^2 e^2 \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d}-\frac{b^3 e^2 \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right)}{2 d}+a b^2 e^2 x-\frac{b e^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}-\frac{b e^2 (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}+\frac{e^2 (c+d x)^3 \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d}-\frac{i e^2 \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d}-\frac{b e^2 \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d}-\frac{b^3 e^2 \log \left((c+d x)^2+1\right)}{2 d}+\frac{b^3 e^2 (c+d x) \tan ^{-1}(c+d x)}{d}","-\frac{i b^2 e^2 \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d}-\frac{b^3 e^2 \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right)}{2 d}+a b^2 e^2 x-\frac{b e^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}-\frac{b e^2 (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}+\frac{e^2 (c+d x)^3 \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d}-\frac{i e^2 \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d}-\frac{b e^2 \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d}-\frac{b^3 e^2 \log \left((c+d x)^2+1\right)}{2 d}+\frac{b^3 e^2 (c+d x) \tan ^{-1}(c+d x)}{d}",1,"a*b^2*e^2*x + (b^3*e^2*(c + d*x)*ArcTan[c + d*x])/d - (b*e^2*(a + b*ArcTan[c + d*x])^2)/(2*d) - (b*e^2*(c + d*x)^2*(a + b*ArcTan[c + d*x])^2)/(2*d) - ((I/3)*e^2*(a + b*ArcTan[c + d*x])^3)/d + (e^2*(c + d*x)^3*(a + b*ArcTan[c + d*x])^3)/(3*d) - (b*e^2*(a + b*ArcTan[c + d*x])^2*Log[2/(1 + I*(c + d*x))])/d - (b^3*e^2*Log[1 + (c + d*x)^2])/(2*d) - (I*b^2*e^2*(a + b*ArcTan[c + d*x])*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/d - (b^3*e^2*PolyLog[3, 1 - 2/(1 + I*(c + d*x))])/(2*d)","A",14,11,23,0.4783,1,"{5043, 12, 4852, 4916, 4846, 260, 4884, 4920, 4854, 4994, 6610}"
16,1,164,0,0.2431522,"\int (c e+d e x) \left(a+b \tan ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)*(a + b*ArcTan[c + d*x])^3,x]","-\frac{3 i b^3 e \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{2 d}-\frac{3 b^2 e \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d}-\frac{3 i b e \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}-\frac{3 b e (c+d x) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}+\frac{e (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^3}{2 d}+\frac{e \left(a+b \tan ^{-1}(c+d x)\right)^3}{2 d}","-\frac{3 i b^3 e \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{2 d}-\frac{3 b^2 e \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d}-\frac{3 i b e \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}-\frac{3 b e (c+d x) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d}+\frac{e (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^3}{2 d}+\frac{e \left(a+b \tan ^{-1}(c+d x)\right)^3}{2 d}",1,"(((-3*I)/2)*b*e*(a + b*ArcTan[c + d*x])^2)/d - (3*b*e*(c + d*x)*(a + b*ArcTan[c + d*x])^2)/(2*d) + (e*(a + b*ArcTan[c + d*x])^3)/(2*d) + (e*(c + d*x)^2*(a + b*ArcTan[c + d*x])^3)/(2*d) - (3*b^2*e*(a + b*ArcTan[c + d*x])*Log[2/(1 + I*(c + d*x))])/d - (((3*I)/2)*b^3*e*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/d","A",10,10,21,0.4762,1,"{5043, 12, 4852, 4916, 4846, 4920, 4854, 2402, 2315, 4884}"
17,1,279,0,0.4581658,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{c e+d e x} \, dx","Int[(a + b*ArcTan[c + d*x])^3/(c*e + d*e*x),x]","-\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{2 d e}+\frac{3 b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{2 d e}-\frac{3 i b \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e}+\frac{3 i b \text{PolyLog}\left(2,-1+\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e}+\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+i (c+d x)}\right)}{4 d e}-\frac{3 i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+i (c+d x)}\right)}{4 d e}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^3}{d e}","-\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{2 d e}+\frac{3 b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{2 d e}-\frac{3 i b \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e}+\frac{3 i b \text{PolyLog}\left(2,-1+\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e}+\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+i (c+d x)}\right)}{4 d e}-\frac{3 i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+i (c+d x)}\right)}{4 d e}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^3}{d e}",1,"(2*(a + b*ArcTan[c + d*x])^3*ArcTanh[1 - 2/(1 + I*(c + d*x))])/(d*e) - (((3*I)/2)*b*(a + b*ArcTan[c + d*x])^2*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/(d*e) + (((3*I)/2)*b*(a + b*ArcTan[c + d*x])^2*PolyLog[2, -1 + 2/(1 + I*(c + d*x))])/(d*e) - (3*b^2*(a + b*ArcTan[c + d*x])*PolyLog[3, 1 - 2/(1 + I*(c + d*x))])/(2*d*e) + (3*b^2*(a + b*ArcTan[c + d*x])*PolyLog[3, -1 + 2/(1 + I*(c + d*x))])/(2*d*e) + (((3*I)/4)*b^3*PolyLog[4, 1 - 2/(1 + I*(c + d*x))])/(d*e) - (((3*I)/4)*b^3*PolyLog[4, -1 + 2/(1 + I*(c + d*x))])/(d*e)","A",10,8,23,0.3478,1,"{5043, 12, 4850, 4988, 4884, 4994, 4998, 6610}"
18,1,163,0,0.2996231,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{(c e+d e x)^2} \, dx","Int[(a + b*ArcTan[c + d*x])^3/(c*e + d*e*x)^2,x]","-\frac{3 i b^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e^2}+\frac{3 b^3 \text{PolyLog}\left(3,-1+\frac{2}{1-i (c+d x)}\right)}{2 d e^2}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{d e^2 (c+d x)}-\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^3}{d e^2}+\frac{3 b \log \left(2-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d e^2}","-\frac{3 i b^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e^2}+\frac{3 b^3 \text{PolyLog}\left(3,-1+\frac{2}{1-i (c+d x)}\right)}{2 d e^2}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{d e^2 (c+d x)}-\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^3}{d e^2}+\frac{3 b \log \left(2-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d e^2}",1,"((-I)*(a + b*ArcTan[c + d*x])^3)/(d*e^2) - (a + b*ArcTan[c + d*x])^3/(d*e^2*(c + d*x)) + (3*b*(a + b*ArcTan[c + d*x])^2*Log[2 - 2/(1 - I*(c + d*x))])/(d*e^2) - ((3*I)*b^2*(a + b*ArcTan[c + d*x])*PolyLog[2, -1 + 2/(1 - I*(c + d*x))])/(d*e^2) + (3*b^3*PolyLog[3, -1 + 2/(1 - I*(c + d*x))])/(2*d*e^2)","A",7,8,23,0.3478,1,"{5043, 12, 4852, 4924, 4868, 4884, 4992, 6610}"
19,1,180,0,0.3185903,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{(c e+d e x)^3} \, dx","Int[(a + b*ArcTan[c + d*x])^3/(c*e + d*e*x)^3,x]","-\frac{3 i b^3 \text{PolyLog}\left(2,-1+\frac{2}{1-i (c+d x)}\right)}{2 d e^3}+\frac{3 b^2 \log \left(2-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e^3}-\frac{3 b \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)}-\frac{3 i b \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^3}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{2 d e^3 (c+d x)^2}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{2 d e^3}","-\frac{3 i b^3 \text{PolyLog}\left(2,-1+\frac{2}{1-i (c+d x)}\right)}{2 d e^3}+\frac{3 b^2 \log \left(2-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e^3}-\frac{3 b \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)}-\frac{3 i b \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^3}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{2 d e^3 (c+d x)^2}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{2 d e^3}",1,"(((-3*I)/2)*b*(a + b*ArcTan[c + d*x])^2)/(d*e^3) - (3*b*(a + b*ArcTan[c + d*x])^2)/(2*d*e^3*(c + d*x)) - (a + b*ArcTan[c + d*x])^3/(2*d*e^3) - (a + b*ArcTan[c + d*x])^3/(2*d*e^3*(c + d*x)^2) + (3*b^2*(a + b*ArcTan[c + d*x])*Log[2 - 2/(1 - I*(c + d*x))])/(d*e^3) - (((3*I)/2)*b^3*PolyLog[2, -1 + 2/(1 - I*(c + d*x))])/(d*e^3)","A",9,8,23,0.3478,1,"{5043, 12, 4852, 4918, 4924, 4868, 2447, 4884}"
20,1,287,0,0.4999244,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{(c e+d e x)^4} \, dx","Int[(a + b*ArcTan[c + d*x])^3/(c*e + d*e*x)^4,x]","\frac{i b^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e^4}-\frac{b^3 \text{PolyLog}\left(3,-1+\frac{2}{1-i (c+d x)}\right)}{2 d e^4}-\frac{b^2 \left(a+b \tan ^{-1}(c+d x)\right)}{d e^4 (c+d x)}-\frac{b \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^4 (c+d x)^2}-\frac{b \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^4}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^3}+\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d e^4}-\frac{b \log \left(2-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d e^4}+\frac{b^3 \log (c+d x)}{d e^4}-\frac{b^3 \log \left((c+d x)^2+1\right)}{2 d e^4}","\frac{i b^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d e^4}-\frac{b^3 \text{PolyLog}\left(3,-1+\frac{2}{1-i (c+d x)}\right)}{2 d e^4}-\frac{b^2 \left(a+b \tan ^{-1}(c+d x)\right)}{d e^4 (c+d x)}-\frac{b \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^4 (c+d x)^2}-\frac{b \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d e^4}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^3}+\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d e^4}-\frac{b \log \left(2-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d e^4}+\frac{b^3 \log (c+d x)}{d e^4}-\frac{b^3 \log \left((c+d x)^2+1\right)}{2 d e^4}",1,"-((b^2*(a + b*ArcTan[c + d*x]))/(d*e^4*(c + d*x))) - (b*(a + b*ArcTan[c + d*x])^2)/(2*d*e^4) - (b*(a + b*ArcTan[c + d*x])^2)/(2*d*e^4*(c + d*x)^2) + ((I/3)*(a + b*ArcTan[c + d*x])^3)/(d*e^4) - (a + b*ArcTan[c + d*x])^3/(3*d*e^4*(c + d*x)^3) + (b^3*Log[c + d*x])/(d*e^4) - (b^3*Log[1 + (c + d*x)^2])/(2*d*e^4) - (b*(a + b*ArcTan[c + d*x])^2*Log[2 - 2/(1 - I*(c + d*x))])/(d*e^4) + (I*b^2*(a + b*ArcTan[c + d*x])*PolyLog[2, -1 + 2/(1 - I*(c + d*x))])/(d*e^4) - (b^3*PolyLog[3, -1 + 2/(1 - I*(c + d*x))])/(2*d*e^4)","A",16,13,23,0.5652,1,"{5043, 12, 4852, 4918, 266, 36, 29, 31, 4884, 4924, 4868, 4992, 6610}"
21,1,31,0,0.0375427,"\int \frac{\tan ^{-1}(1+x)}{2+2 x} \, dx","Int[ArcTan[1 + x]/(2 + 2*x),x]","\frac{1}{4} i \text{PolyLog}(2,-i (x+1))-\frac{1}{4} i \text{PolyLog}(2,i (x+1))","\frac{1}{4} i \text{PolyLog}(2,-i (x+1))-\frac{1}{4} i \text{PolyLog}(2,i (x+1))",1,"(I/4)*PolyLog[2, (-I)*(1 + x)] - (I/4)*PolyLog[2, I*(1 + x)]","A",5,4,12,0.3333,1,"{5043, 12, 4848, 2391}"
22,1,41,0,0.0452878,"\int \frac{\tan ^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Int[ArcTan[a + b*x]/((a*d)/b + d*x),x]","\frac{i \text{PolyLog}(2,-i (a+b x))}{2 d}-\frac{i \text{PolyLog}(2,i (a+b x))}{2 d}","\frac{i \text{PolyLog}(2,-i (a+b x))}{2 d}-\frac{i \text{PolyLog}(2,i (a+b x))}{2 d}",1,"((I/2)*PolyLog[2, (-I)*(a + b*x)])/d - ((I/2)*PolyLog[2, I*(a + b*x)])/d","A",5,4,19,0.2105,1,"{5043, 12, 4848, 2391}"
23,0,0,0,0.0165432,"\int (a+b x)^2 \sqrt{\tan ^{-1}(a+b x)} \, dx","Int[(a + b*x)^2*Sqrt[ArcTan[a + b*x]],x]","\int (a+b x)^2 \sqrt{\tan ^{-1}(a+b x)} \, dx","\text{Int}\left((a+b x)^2 \sqrt{\tan ^{-1}(a+b x)},x\right)",0,"Defer[Int][(a + b*x)^2*Sqrt[ArcTan[a + b*x]], x]","A",0,0,0,0,-1,"{}"
24,1,233,0,0.3813393,"\int (e+f x)^3 \left(a+b \tan ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)^3*(a + b*ArcTan[c + d*x]),x]","\frac{(e+f x)^4 \left(a+b \tan ^{-1}(c+d x)\right)}{4 f}-\frac{b f x \left(-\left(1-6 c^2\right) f^2-12 c d e f+6 d^2 e^2\right)}{4 d^3}-\frac{b \left(-6 \left(1-c^2\right) d^2 e^2 f^2+4 c \left(3-c^2\right) d e f^3+\left(c^4-6 c^2+1\right) f^4-4 c d^3 e^3 f+d^4 e^4\right) \tan ^{-1}(c+d x)}{4 d^4 f}-\frac{b f^2 (c+d x)^2 (d e-c f)}{2 d^4}-\frac{b (d e-c f) (-c f+d e+f) (d e-(c+1) f) \log \left((c+d x)^2+1\right)}{2 d^4}-\frac{b f^3 (c+d x)^3}{12 d^4}","\frac{(e+f x)^4 \left(a+b \tan ^{-1}(c+d x)\right)}{4 f}-\frac{b f x \left(-\left(1-6 c^2\right) f^2-12 c d e f+6 d^2 e^2\right)}{4 d^3}-\frac{b \left(-6 \left(1-c^2\right) d^2 e^2 f^2+4 c \left(3-c^2\right) d e f^3+\left(c^4-6 c^2+1\right) f^4-4 c d^3 e^3 f+d^4 e^4\right) \tan ^{-1}(c+d x)}{4 d^4 f}-\frac{b f^2 (c+d x)^2 (d e-c f)}{2 d^4}-\frac{b (d e-c f) (-c f+d e+f) (d e-(c+1) f) \log \left((c+d x)^2+1\right)}{2 d^4}-\frac{b f^3 (c+d x)^3}{12 d^4}",1,"-(b*f*(6*d^2*e^2 - 12*c*d*e*f - (1 - 6*c^2)*f^2)*x)/(4*d^3) - (b*f^2*(d*e - c*f)*(c + d*x)^2)/(2*d^4) - (b*f^3*(c + d*x)^3)/(12*d^4) - (b*(d^4*e^4 - 4*c*d^3*e^3*f - 6*(1 - c^2)*d^2*e^2*f^2 + 4*c*(3 - c^2)*d*e*f^3 + (1 - 6*c^2 + c^4)*f^4)*ArcTan[c + d*x])/(4*d^4*f) + ((e + f*x)^4*(a + b*ArcTan[c + d*x]))/(4*f) - (b*(d*e - c*f)*(d*e + f - c*f)*(d*e - (1 + c)*f)*Log[1 + (c + d*x)^2])/(2*d^4)","A",7,6,18,0.3333,1,"{5047, 4862, 702, 635, 203, 260}"
25,1,155,0,0.1898194,"\int (e+f x)^2 \left(a+b \tan ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)^2*(a + b*ArcTan[c + d*x]),x]","\frac{(e+f x)^3 \left(a+b \tan ^{-1}(c+d x)\right)}{3 f}-\frac{b \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left((c+d x)^2+1\right)}{6 d^3}-\frac{b (d e-c f) \left(-\left(3-c^2\right) f^2-2 c d e f+d^2 e^2\right) \tan ^{-1}(c+d x)}{3 d^3 f}-\frac{b f x (d e-c f)}{d^2}-\frac{b f^2 (c+d x)^2}{6 d^3}","\frac{(e+f x)^3 \left(a+b \tan ^{-1}(c+d x)\right)}{3 f}-\frac{b \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left((c+d x)^2+1\right)}{6 d^3}-\frac{b (d e-c f) \left(-\left(3-c^2\right) f^2-2 c d e f+d^2 e^2\right) \tan ^{-1}(c+d x)}{3 d^3 f}-\frac{b f x (d e-c f)}{d^2}-\frac{b f^2 (c+d x)^2}{6 d^3}",1,"-((b*f*(d*e - c*f)*x)/d^2) - (b*f^2*(c + d*x)^2)/(6*d^3) - (b*(d*e - c*f)*(d^2*e^2 - 2*c*d*e*f - (3 - c^2)*f^2)*ArcTan[c + d*x])/(3*d^3*f) + ((e + f*x)^3*(a + b*ArcTan[c + d*x]))/(3*f) - (b*(3*d^2*e^2 - 6*c*d*e*f - (1 - 3*c^2)*f^2)*Log[1 + (c + d*x)^2])/(6*d^3)","A",7,6,18,0.3333,1,"{5047, 4862, 702, 635, 203, 260}"
26,1,97,0,0.1120684,"\int (e+f x) \left(a+b \tan ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)*(a + b*ArcTan[c + d*x]),x]","\frac{(e+f x)^2 \left(a+b \tan ^{-1}(c+d x)\right)}{2 f}-\frac{b (d e-c f) \log \left((c+d x)^2+1\right)}{2 d^2}-\frac{b (-c f+d e+f) (d e-(c+1) f) \tan ^{-1}(c+d x)}{2 d^2 f}-\frac{b f x}{2 d}","\frac{(e+f x)^2 \left(a+b \tan ^{-1}(c+d x)\right)}{2 f}-\frac{b (d e-c f) \log \left((c+d x)^2+1\right)}{2 d^2}-\frac{b (-c f+d e+f) (d e-(c+1) f) \tan ^{-1}(c+d x)}{2 d^2 f}-\frac{b f x}{2 d}",1,"-(b*f*x)/(2*d) - (b*(d*e + f - c*f)*(d*e - (1 + c)*f)*ArcTan[c + d*x])/(2*d^2*f) + ((e + f*x)^2*(a + b*ArcTan[c + d*x]))/(2*f) - (b*(d*e - c*f)*Log[1 + (c + d*x)^2])/(2*d^2)","A",7,6,16,0.3750,1,"{5047, 4862, 702, 635, 203, 260}"
27,1,38,0,0.0184687,"\int \left(a+b \tan ^{-1}(c+d x)\right) \, dx","Int[a + b*ArcTan[c + d*x],x]","a x-\frac{b \log \left((c+d x)^2+1\right)}{2 d}+\frac{b (c+d x) \tan ^{-1}(c+d x)}{d}","a x-\frac{b \log \left((c+d x)^2+1\right)}{2 d}+\frac{b (c+d x) \tan ^{-1}(c+d x)}{d}",1,"a*x + (b*(c + d*x)*ArcTan[c + d*x])/d - (b*Log[1 + (c + d*x)^2])/(2*d)","A",4,3,10,0.3000,1,"{5039, 4846, 260}"
28,1,162,0,0.1501324,"\int \frac{a+b \tan ^{-1}(c+d x)}{e+f x} \, dx","Int[(a + b*ArcTan[c + d*x])/(e + f*x),x]","-\frac{i b \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{2 f}+\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right)}{2 f}+\frac{\left(a+b \tan ^{-1}(c+d x)\right) \log \left(\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{f}-\frac{\log \left(\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{f}","-\frac{i b \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{2 f}+\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right)}{2 f}+\frac{\left(a+b \tan ^{-1}(c+d x)\right) \log \left(\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{f}-\frac{\log \left(\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{f}",1,"-(((a + b*ArcTan[c + d*x])*Log[2/(1 - I*(c + d*x))])/f) + ((a + b*ArcTan[c + d*x])*Log[(2*d*(e + f*x))/((d*e + I*f - c*f)*(1 - I*(c + d*x)))])/f + ((I/2)*b*PolyLog[2, 1 - 2/(1 - I*(c + d*x))])/f - ((I/2)*b*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + I*f - c*f)*(1 - I*(c + d*x)))])/f","A",5,5,18,0.2778,1,"{5047, 4856, 2402, 2315, 2447}"
29,1,151,0,0.1210519,"\int \frac{a+b \tan ^{-1}(c+d x)}{(e+f x)^2} \, dx","Int[(a + b*ArcTan[c + d*x])/(e + f*x)^2,x]","-\frac{a+b \tan ^{-1}(c+d x)}{f (e+f x)}-\frac{b d \log \left(c^2+2 c d x+d^2 x^2+1\right)}{2 \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)}+\frac{b d \log (e+f x)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{b d (d e-c f) \tan ^{-1}(c+d x)}{f \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)}","-\frac{a+b \tan ^{-1}(c+d x)}{f (e+f x)}-\frac{b d \log \left(c^2+2 c d x+d^2 x^2+1\right)}{2 \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)}+\frac{b d \log (e+f x)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{b d (d e-c f) \tan ^{-1}(c+d x)}{f \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)}",1,"(b*d*(d*e - c*f)*ArcTan[c + d*x])/(f*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)) - (a + b*ArcTan[c + d*x])/(f*(e + f*x)) + (b*d*Log[e + f*x])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) - (b*d*Log[1 + c^2 + 2*c*d*x + d^2*x^2])/(2*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2))","A",8,8,18,0.4444,1,"{5045, 1982, 705, 31, 634, 618, 204, 628}"
30,1,227,0,0.3030893,"\int \frac{a+b \tan ^{-1}(c+d x)}{(e+f x)^3} \, dx","Int[(a + b*ArcTan[c + d*x])/(e + f*x)^3,x]","-\frac{a+b \tan ^{-1}(c+d x)}{2 f (e+f x)^2}-\frac{b d^2 (d e-c f) \log \left(c^2+2 c d x+d^2 x^2+1\right)}{2 \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)^2}-\frac{b d}{2 (e+f x) \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)}+\frac{b d^2 (d e-c f) \log (e+f x)}{\left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)^2}+\frac{b d^2 (-c f+d e+f) (d e-(c+1) f) \tan ^{-1}(c+d x)}{2 f \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)^2}","-\frac{a+b \tan ^{-1}(c+d x)}{2 f (e+f x)^2}-\frac{b d^2 (d e-c f) \log \left(c^2+2 c d x+d^2 x^2+1\right)}{2 \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)^2}-\frac{b d}{2 (e+f x) \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)}+\frac{b d^2 (d e-c f) \log (e+f x)}{\left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)^2}+\frac{b d^2 (-c f+d e+f) (d e-(c+1) f) \tan ^{-1}(c+d x)}{2 f \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)^2}",1,"-(b*d)/(2*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)*(e + f*x)) + (b*d^2*(d*e + f - c*f)*(d*e - (1 + c)*f)*ArcTan[c + d*x])/(2*f*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)^2) - (a + b*ArcTan[c + d*x])/(2*f*(e + f*x)^2) + (b*d^2*(d*e - c*f)*Log[e + f*x])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)^2 - (b*d^2*(d*e - c*f)*Log[1 + c^2 + 2*c*d*x + d^2*x^2])/(2*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)^2)","A",9,8,18,0.4444,1,"{5045, 1982, 709, 800, 634, 618, 204, 628}"
31,1,382,0,0.5740531,"\int (e+f x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)^2*(a + b*ArcTan[c + d*x])^2,x]","\frac{i b^2 \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{3 d^3}+\frac{i \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d^3}-\frac{(d e-c f) \left(-\left(3-c^2\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d^3 f}+\frac{2 b \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{3 d^3}-\frac{2 a b f x (d e-c f)}{d^2}-\frac{b f^2 (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)}{3 d^3}+\frac{(e+f x)^3 \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 f}+\frac{b^2 f (d e-c f) \log \left((c+d x)^2+1\right)}{d^3}-\frac{2 b^2 f (c+d x) (d e-c f) \tan ^{-1}(c+d x)}{d^3}-\frac{b^2 f^2 \tan ^{-1}(c+d x)}{3 d^3}+\frac{b^2 f^2 x}{3 d^2}","\frac{i b^2 \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{3 d^3}+\frac{i \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d^3}-\frac{(d e-c f) \left(-\left(3-c^2\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 d^3 f}+\frac{2 b \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{3 d^3}-\frac{2 a b f x (d e-c f)}{d^2}-\frac{b f^2 (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)}{3 d^3}+\frac{(e+f x)^3 \left(a+b \tan ^{-1}(c+d x)\right)^2}{3 f}+\frac{b^2 f (d e-c f) \log \left((c+d x)^2+1\right)}{d^3}-\frac{2 b^2 f (c+d x) (d e-c f) \tan ^{-1}(c+d x)}{d^3}-\frac{b^2 f^2 \tan ^{-1}(c+d x)}{3 d^3}+\frac{b^2 f^2 x}{3 d^2}",1,"(b^2*f^2*x)/(3*d^2) - (2*a*b*f*(d*e - c*f)*x)/d^2 - (b^2*f^2*ArcTan[c + d*x])/(3*d^3) - (2*b^2*f*(d*e - c*f)*(c + d*x)*ArcTan[c + d*x])/d^3 - (b*f^2*(c + d*x)^2*(a + b*ArcTan[c + d*x]))/(3*d^3) + ((I/3)*(3*d^2*e^2 - 6*c*d*e*f - (1 - 3*c^2)*f^2)*(a + b*ArcTan[c + d*x])^2)/d^3 - ((d*e - c*f)*(d^2*e^2 - 2*c*d*e*f - (3 - c^2)*f^2)*(a + b*ArcTan[c + d*x])^2)/(3*d^3*f) + ((e + f*x)^3*(a + b*ArcTan[c + d*x])^2)/(3*f) + (2*b*(3*d^2*e^2 - 6*c*d*e*f - (1 - 3*c^2)*f^2)*(a + b*ArcTan[c + d*x])*Log[2/(1 + I*(c + d*x))])/(3*d^3) + (b^2*f*(d*e - c*f)*Log[1 + (c + d*x)^2])/d^3 + ((I/3)*b^2*(3*d^2*e^2 - 6*c*d*e*f - (1 - 3*c^2)*f^2)*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/d^3","A",16,13,20,0.6500,1,"{5047, 4864, 4846, 260, 4852, 321, 203, 4984, 4884, 4920, 4854, 2402, 2315}"
32,1,222,0,0.3731476,"\int (e+f x) \left(a+b \tan ^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)*(a + b*ArcTan[c + d*x])^2,x]","\frac{i b^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{d^2}+\frac{i (d e-c f) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d^2}-\frac{(-c f+d e+f) (d e-(c+1) f) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d^2 f}+\frac{2 b (d e-c f) \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d^2}+\frac{(e+f x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 f}-\frac{a b f x}{d}+\frac{b^2 f \log \left((c+d x)^2+1\right)}{2 d^2}-\frac{b^2 f (c+d x) \tan ^{-1}(c+d x)}{d^2}","\frac{i b^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{d^2}+\frac{i (d e-c f) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d^2}-\frac{(-c f+d e+f) (d e-(c+1) f) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d^2 f}+\frac{2 b (d e-c f) \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d^2}+\frac{(e+f x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 f}-\frac{a b f x}{d}+\frac{b^2 f \log \left((c+d x)^2+1\right)}{2 d^2}-\frac{b^2 f (c+d x) \tan ^{-1}(c+d x)}{d^2}",1,"-((a*b*f*x)/d) - (b^2*f*(c + d*x)*ArcTan[c + d*x])/d^2 + (I*(d*e - c*f)*(a + b*ArcTan[c + d*x])^2)/d^2 - ((d*e + f - c*f)*(d*e - (1 + c)*f)*(a + b*ArcTan[c + d*x])^2)/(2*d^2*f) + ((e + f*x)^2*(a + b*ArcTan[c + d*x])^2)/(2*f) + (2*b*(d*e - c*f)*(a + b*ArcTan[c + d*x])*Log[2/(1 + I*(c + d*x))])/d^2 + (b^2*f*Log[1 + (c + d*x)^2])/(2*d^2) + (I*b^2*(d*e - c*f)*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/d^2","A",13,10,18,0.5556,1,"{5047, 4864, 4846, 260, 4984, 4884, 4920, 4854, 2402, 2315}"
33,1,102,0,0.1069767,"\int \left(a+b \tan ^{-1}(c+d x)\right)^2 \, dx","Int[(a + b*ArcTan[c + d*x])^2,x]","\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{d}+\frac{(c+d x) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d}+\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^2}{d}+\frac{2 b \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d}","\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{d}+\frac{(c+d x) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d}+\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^2}{d}+\frac{2 b \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d}",1,"(I*(a + b*ArcTan[c + d*x])^2)/d + ((c + d*x)*(a + b*ArcTan[c + d*x])^2)/d + (2*b*(a + b*ArcTan[c + d*x])*Log[2/(1 + I*(c + d*x))])/d + (I*b^2*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/d","A",6,6,12,0.5000,1,"{5039, 4846, 4920, 4854, 2402, 2315}"
34,1,261,0,0.1646439,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{e+f x} \, dx","Int[(a + b*ArcTan[c + d*x])^2/(e + f*x),x]","-\frac{i b \left(a+b \tan ^{-1}(c+d x)\right) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{f}+\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{f}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{2 f}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-i (c+d x)}\right)}{2 f}+\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2 \log \left(\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{f}-\frac{\log \left(\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{f}","-\frac{i b \left(a+b \tan ^{-1}(c+d x)\right) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{f}+\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{f}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{2 f}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-i (c+d x)}\right)}{2 f}+\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2 \log \left(\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{f}-\frac{\log \left(\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{f}",1,"-(((a + b*ArcTan[c + d*x])^2*Log[2/(1 - I*(c + d*x))])/f) + ((a + b*ArcTan[c + d*x])^2*Log[(2*d*(e + f*x))/((d*e + I*f - c*f)*(1 - I*(c + d*x)))])/f + (I*b*(a + b*ArcTan[c + d*x])*PolyLog[2, 1 - 2/(1 - I*(c + d*x))])/f - (I*b*(a + b*ArcTan[c + d*x])*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + I*f - c*f)*(1 - I*(c + d*x)))])/f - (b^2*PolyLog[3, 1 - 2/(1 - I*(c + d*x))])/(2*f) + (b^2*PolyLog[3, 1 - (2*d*(e + f*x))/((d*e + I*f - c*f)*(1 - I*(c + d*x)))])/(2*f)","A",2,2,20,0.1000,1,"{5047, 4858}"
35,1,568,0,1.351028,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{(e+f x)^2} \, dx","Int[(a + b*ArcTan[c + d*x])^2/(e + f*x)^2,x]","\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}-\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (d e+(-c+i) f)}\right)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{2 a b d \log (e+f x)}{(d e-c f)^2+f^2}-\frac{a b d \log \left((c+d x)^2+1\right)}{(d e-c f)^2+f^2}+\frac{2 a b d (d e-c f) \tan ^{-1}(c+d x)}{f \left((d e-c f)^2+f^2\right)}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{f (e+f x)}+\frac{i b^2 d \tan ^{-1}(c+d x)^2}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{b^2 d (d e-c f) \tan ^{-1}(c+d x)^2}{f \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)}-\frac{2 b^2 d \log \left(\frac{2}{1-i (c+d x)}\right) \tan ^{-1}(c+d x)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{2 b^2 d \tan ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(1-i (c+d x)) (d e+(-c+i) f)}\right)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{2 b^2 d \log \left(\frac{2}{1+i (c+d x)}\right) \tan ^{-1}(c+d x)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}","\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}-\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{2 a b d \log (e+f x)}{(d e-c f)^2+f^2}-\frac{a b d \log \left((c+d x)^2+1\right)}{(d e-c f)^2+f^2}+\frac{2 a b d (d e-c f) \tan ^{-1}(c+d x)}{f \left((d e-c f)^2+f^2\right)}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^2}{f (e+f x)}+\frac{i b^2 d \tan ^{-1}(c+d x)^2}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{b^2 d (d e-c f) \tan ^{-1}(c+d x)^2}{f \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right)}-\frac{2 b^2 d \log \left(\frac{2}{1-i (c+d x)}\right) \tan ^{-1}(c+d x)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{2 b^2 d \tan ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+\frac{2 b^2 d \log \left(\frac{2}{1+i (c+d x)}\right) \tan ^{-1}(c+d x)}{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}",1,"(2*a*b*d*(d*e - c*f)*ArcTan[c + d*x])/(f*(f^2 + (d*e - c*f)^2)) + (I*b^2*d*ArcTan[c + d*x]^2)/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + (b^2*d*(d*e - c*f)*ArcTan[c + d*x]^2)/(f*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)) - (a + b*ArcTan[c + d*x])^2/(f*(e + f*x)) + (2*a*b*d*Log[e + f*x])/(f^2 + (d*e - c*f)^2) - (2*b^2*d*ArcTan[c + d*x]*Log[2/(1 - I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + (2*b^2*d*ArcTan[c + d*x]*Log[(2*d*(e + f*x))/((d*e + (I - c)*f)*(1 - I*(c + d*x)))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + (2*b^2*d*ArcTan[c + d*x]*Log[2/(1 + I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) - (a*b*d*Log[1 + (c + d*x)^2])/(f^2 + (d*e - c*f)^2) + (I*b^2*d*PolyLog[2, 1 - 2/(1 - I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) - (I*b^2*d*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + (I - c)*f)*(1 - I*(c + d*x)))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + (I*b^2*d*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)","A",25,25,20,1.250,1,"{5045, 1982, 705, 31, 634, 618, 204, 628, 6741, 5057, 706, 635, 203, 260, 6688, 12, 6725, 4856, 2402, 2315, 2447, 4984, 4884, 4920, 4854}"
36,1,564,0,0.9370823,"\int (e+f x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^3 \, dx","Int[(e + f*x)^2*(a + b*ArcTan[c + d*x])^3,x]","\frac{i b^2 \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d^3}+\frac{b^3 \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right)}{2 d^3}-\frac{3 i b^3 f (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{d^3}-\frac{6 b^2 f (d e-c f) \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d^3}+\frac{a b^2 f^2 x}{d^2}+\frac{i \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d^3}-\frac{(d e-c f) \left(-\left(3-c^2\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d^3 f}+\frac{b \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d^3}-\frac{3 i b f (d e-c f) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d^3}-\frac{3 b f (c+d x) (d e-c f) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d^3}-\frac{b f^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d^3}-\frac{b f^2 (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d^3}+\frac{(e+f x)^3 \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 f}-\frac{b^3 f^2 \log \left((c+d x)^2+1\right)}{2 d^3}+\frac{b^3 f^2 (c+d x) \tan ^{-1}(c+d x)}{d^3}","\frac{i b^2 \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d^3}+\frac{b^3 \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right)}{2 d^3}-\frac{3 i b^3 f (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{d^3}-\frac{6 b^2 f (d e-c f) \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d^3}+\frac{a b^2 f^2 x}{d^2}+\frac{i \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d^3}-\frac{(d e-c f) \left(-\left(3-c^2\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 d^3 f}+\frac{b \left(-\left(1-3 c^2\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d^3}-\frac{3 i b f (d e-c f) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d^3}-\frac{3 b f (c+d x) (d e-c f) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d^3}-\frac{b f^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d^3}-\frac{b f^2 (c+d x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d^3}+\frac{(e+f x)^3 \left(a+b \tan ^{-1}(c+d x)\right)^3}{3 f}-\frac{b^3 f^2 \log \left((c+d x)^2+1\right)}{2 d^3}+\frac{b^3 f^2 (c+d x) \tan ^{-1}(c+d x)}{d^3}",1,"(a*b^2*f^2*x)/d^2 + (b^3*f^2*(c + d*x)*ArcTan[c + d*x])/d^3 - (b*f^2*(a + b*ArcTan[c + d*x])^2)/(2*d^3) - ((3*I)*b*f*(d*e - c*f)*(a + b*ArcTan[c + d*x])^2)/d^3 - (3*b*f*(d*e - c*f)*(c + d*x)*(a + b*ArcTan[c + d*x])^2)/d^3 - (b*f^2*(c + d*x)^2*(a + b*ArcTan[c + d*x])^2)/(2*d^3) + ((I/3)*(3*d^2*e^2 - 6*c*d*e*f - (1 - 3*c^2)*f^2)*(a + b*ArcTan[c + d*x])^3)/d^3 - ((d*e - c*f)*(d^2*e^2 - 2*c*d*e*f - (3 - c^2)*f^2)*(a + b*ArcTan[c + d*x])^3)/(3*d^3*f) + ((e + f*x)^3*(a + b*ArcTan[c + d*x])^3)/(3*f) - (6*b^2*f*(d*e - c*f)*(a + b*ArcTan[c + d*x])*Log[2/(1 + I*(c + d*x))])/d^3 + (b*(3*d^2*e^2 - 6*c*d*e*f - (1 - 3*c^2)*f^2)*(a + b*ArcTan[c + d*x])^2*Log[2/(1 + I*(c + d*x))])/d^3 - (b^3*f^2*Log[1 + (c + d*x)^2])/(2*d^3) - ((3*I)*b^3*f*(d*e - c*f)*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/d^3 + (I*b^2*(3*d^2*e^2 - 6*c*d*e*f - (1 - 3*c^2)*f^2)*(a + b*ArcTan[c + d*x])*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/d^3 + (b^3*(3*d^2*e^2 - 6*c*d*e*f - (1 - 3*c^2)*f^2)*PolyLog[3, 1 - 2/(1 + I*(c + d*x))])/(2*d^3)","A",21,14,20,0.7000,1,"{5047, 4864, 4846, 4920, 4854, 2402, 2315, 4852, 4916, 260, 4884, 4984, 4994, 6610}"
37,1,337,0,0.6316833,"\int (e+f x) \left(a+b \tan ^{-1}(c+d x)\right)^3 \, dx","Int[(e + f*x)*(a + b*ArcTan[c + d*x])^3,x]","\frac{3 i b^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d^2}+\frac{3 b^3 (d e-c f) \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right)}{2 d^2}-\frac{3 i b^3 f \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{2 d^2}-\frac{3 b^2 f \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d^2}+\frac{i (d e-c f) \left(a+b \tan ^{-1}(c+d x)\right)^3}{d^2}-\frac{(-c f+d e+f) (d e-(c+1) f) \left(a+b \tan ^{-1}(c+d x)\right)^3}{2 d^2 f}+\frac{3 b (d e-c f) \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d^2}-\frac{3 i b f \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d^2}-\frac{3 b f (c+d x) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d^2}+\frac{(e+f x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^3}{2 f}","\frac{3 i b^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d^2}+\frac{3 b^3 (d e-c f) \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right)}{2 d^2}-\frac{3 i b^3 f \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right)}{2 d^2}-\frac{3 b^2 f \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d^2}+\frac{i (d e-c f) \left(a+b \tan ^{-1}(c+d x)\right)^3}{d^2}-\frac{(-c f+d e+f) (d e-(c+1) f) \left(a+b \tan ^{-1}(c+d x)\right)^3}{2 d^2 f}+\frac{3 b (d e-c f) \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d^2}-\frac{3 i b f \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d^2}-\frac{3 b f (c+d x) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 d^2}+\frac{(e+f x)^2 \left(a+b \tan ^{-1}(c+d x)\right)^3}{2 f}",1,"(((-3*I)/2)*b*f*(a + b*ArcTan[c + d*x])^2)/d^2 - (3*b*f*(c + d*x)*(a + b*ArcTan[c + d*x])^2)/(2*d^2) + (I*(d*e - c*f)*(a + b*ArcTan[c + d*x])^3)/d^2 - ((d*e + f - c*f)*(d*e - (1 + c)*f)*(a + b*ArcTan[c + d*x])^3)/(2*d^2*f) + ((e + f*x)^2*(a + b*ArcTan[c + d*x])^3)/(2*f) - (3*b^2*f*(a + b*ArcTan[c + d*x])*Log[2/(1 + I*(c + d*x))])/d^2 + (3*b*(d*e - c*f)*(a + b*ArcTan[c + d*x])^2*Log[2/(1 + I*(c + d*x))])/d^2 - (((3*I)/2)*b^3*f*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/d^2 + ((3*I)*b^2*(d*e - c*f)*(a + b*ArcTan[c + d*x])*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/d^2 + (3*b^3*(d*e - c*f)*PolyLog[3, 1 - 2/(1 + I*(c + d*x))])/(2*d^2)","A",15,11,18,0.6111,1,"{5047, 4864, 4846, 4920, 4854, 2402, 2315, 4984, 4884, 4994, 6610}"
38,1,143,0,0.2144052,"\int \left(a+b \tan ^{-1}(c+d x)\right)^3 \, dx","Int[(a + b*ArcTan[c + d*x])^3,x]","\frac{3 i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right)}{2 d}+\frac{(c+d x) \left(a+b \tan ^{-1}(c+d x)\right)^3}{d}+\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^3}{d}+\frac{3 b \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d}","\frac{3 i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{d}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1+i (c+d x)}\right)}{2 d}+\frac{(c+d x) \left(a+b \tan ^{-1}(c+d x)\right)^3}{d}+\frac{i \left(a+b \tan ^{-1}(c+d x)\right)^3}{d}+\frac{3 b \log \left(\frac{2}{1+i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{d}",1,"(I*(a + b*ArcTan[c + d*x])^3)/d + ((c + d*x)*(a + b*ArcTan[c + d*x])^3)/d + (3*b*(a + b*ArcTan[c + d*x])^2*Log[2/(1 + I*(c + d*x))])/d + ((3*I)*b^2*(a + b*ArcTan[c + d*x])*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/d + (3*b^3*PolyLog[3, 1 - 2/(1 + I*(c + d*x))])/(2*d)","A",6,7,12,0.5833,1,"{5039, 4846, 4920, 4854, 4884, 4994, 6610}"
39,1,372,0,0.2028201,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{e+f x} \, dx","Int[(a + b*ArcTan[c + d*x])^3/(e + f*x),x]","\frac{3 b^2 \left(a+b \tan ^{-1}(c+d x)\right) \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{2 f}-\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{2 f}-\frac{3 i b \left(a+b \tan ^{-1}(c+d x)\right)^2 \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{2 f}+\frac{3 i b \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 f}+\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{4 f}-\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2}{1-i (c+d x)}\right)}{4 f}+\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3 \log \left(\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{f}-\frac{\log \left(\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^3}{f}","\frac{3 b^2 \left(a+b \tan ^{-1}(c+d x)\right) \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{2 f}-\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)}{2 f}-\frac{3 i b \left(a+b \tan ^{-1}(c+d x)\right)^2 \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{2 f}+\frac{3 i b \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^2}{2 f}+\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{4 f}-\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2}{1-i (c+d x)}\right)}{4 f}+\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3 \log \left(\frac{2 d (e+f x)}{(1-i (c+d x)) (-c f+d e+i f)}\right)}{f}-\frac{\log \left(\frac{2}{1-i (c+d x)}\right) \left(a+b \tan ^{-1}(c+d x)\right)^3}{f}",1,"-(((a + b*ArcTan[c + d*x])^3*Log[2/(1 - I*(c + d*x))])/f) + ((a + b*ArcTan[c + d*x])^3*Log[(2*d*(e + f*x))/((d*e + I*f - c*f)*(1 - I*(c + d*x)))])/f + (((3*I)/2)*b*(a + b*ArcTan[c + d*x])^2*PolyLog[2, 1 - 2/(1 - I*(c + d*x))])/f - (((3*I)/2)*b*(a + b*ArcTan[c + d*x])^2*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + I*f - c*f)*(1 - I*(c + d*x)))])/f - (3*b^2*(a + b*ArcTan[c + d*x])*PolyLog[3, 1 - 2/(1 - I*(c + d*x))])/(2*f) + (3*b^2*(a + b*ArcTan[c + d*x])*PolyLog[3, 1 - (2*d*(e + f*x))/((d*e + I*f - c*f)*(1 - I*(c + d*x)))])/(2*f) - (((3*I)/4)*b^3*PolyLog[4, 1 - 2/(1 - I*(c + d*x))])/f + (((3*I)/4)*b^3*PolyLog[4, 1 - (2*d*(e + f*x))/((d*e + I*f - c*f)*(1 - I*(c + d*x)))])/f","A",2,2,20,0.1000,1,"{5047, 4860}"
40,1,1233,0,2.3107806,"\int \frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{(e+f x)^2} \, dx","Int[(a + b*ArcTan[c + d*x])^3/(e + f*x)^2,x]","\frac{i d \tan ^{-1}(c+d x)^3 b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{d (d e-c f) \tan ^{-1}(c+d x)^3 b^3}{f \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)}-\frac{3 d \tan ^{-1}(c+d x)^2 \log \left(\frac{2}{1-i (c+d x)}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 d \tan ^{-1}(c+d x)^2 \log \left(\frac{2 d (e+f x)}{(d e+(i-c) f) (1-i (c+d x))}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 d \tan ^{-1}(c+d x)^2 \log \left(\frac{2}{i (c+d x)+1}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 i d \tan ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}-\frac{3 i d \tan ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e+(i-c) f) (1-i (c+d x))}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 i d \tan ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{i (c+d x)+1}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}-\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{1-i (c+d x)}\right) b^3}{2 \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(d e+(i-c) f) (1-i (c+d x))}\right) b^3}{2 \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{i (c+d x)+1}\right) b^3}{2 \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)}+\frac{3 i a d \tan ^{-1}(c+d x)^2 b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 a d (d e-c f) \tan ^{-1}(c+d x)^2 b^2}{f \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)}-\frac{6 a d \tan ^{-1}(c+d x) \log \left(\frac{2}{1-i (c+d x)}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{6 a d \tan ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(d e+(i-c) f) (1-i (c+d x))}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{6 a d \tan ^{-1}(c+d x) \log \left(\frac{2}{i (c+d x)+1}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 i a d \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}-\frac{3 i a d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e+(i-c) f) (1-i (c+d x))}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 i a d \text{PolyLog}\left(2,1-\frac{2}{i (c+d x)+1}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 a^2 d (d e-c f) \tan ^{-1}(c+d x) b}{f \left(f^2+(d e-c f)^2\right)}+\frac{3 a^2 d \log (e+f x) b}{f^2+(d e-c f)^2}-\frac{3 a^2 d \log \left((c+d x)^2+1\right) b}{2 \left(f^2+(d e-c f)^2\right)}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{f (e+f x)}","\frac{i d \tan ^{-1}(c+d x)^3 b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{d (d e-c f) \tan ^{-1}(c+d x)^3 b^3}{f \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)}-\frac{3 d \tan ^{-1}(c+d x)^2 \log \left(\frac{2}{1-i (c+d x)}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 d \tan ^{-1}(c+d x)^2 \log \left(\frac{2 d (e+f x)}{(d e-c f+i f) (1-i (c+d x))}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 d \tan ^{-1}(c+d x)^2 \log \left(\frac{2}{i (c+d x)+1}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 i d \tan ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}-\frac{3 i d \tan ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e-c f+i f) (1-i (c+d x))}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 i d \tan ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{i (c+d x)+1}\right) b^3}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}-\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{1-i (c+d x)}\right) b^3}{2 \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(d e-c f+i f) (1-i (c+d x))}\right) b^3}{2 \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{i (c+d x)+1}\right) b^3}{2 \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)}+\frac{3 i a d \tan ^{-1}(c+d x)^2 b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 a d (d e-c f) \tan ^{-1}(c+d x)^2 b^2}{f \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)}-\frac{6 a d \tan ^{-1}(c+d x) \log \left(\frac{2}{1-i (c+d x)}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{6 a d \tan ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(d e-c f+i f) (1-i (c+d x))}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{6 a d \tan ^{-1}(c+d x) \log \left(\frac{2}{i (c+d x)+1}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 i a d \text{PolyLog}\left(2,1-\frac{2}{1-i (c+d x)}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}-\frac{3 i a d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e-c f+i f) (1-i (c+d x))}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 i a d \text{PolyLog}\left(2,1-\frac{2}{i (c+d x)+1}\right) b^2}{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}+\frac{3 a^2 d (d e-c f) \tan ^{-1}(c+d x) b}{f \left(f^2+(d e-c f)^2\right)}+\frac{3 a^2 d \log (e+f x) b}{f^2+(d e-c f)^2}-\frac{3 a^2 d \log \left((c+d x)^2+1\right) b}{2 \left(f^2+(d e-c f)^2\right)}-\frac{\left(a+b \tan ^{-1}(c+d x)\right)^3}{f (e+f x)}",1,"(3*a^2*b*d*(d*e - c*f)*ArcTan[c + d*x])/(f*(f^2 + (d*e - c*f)^2)) + ((3*I)*a*b^2*d*ArcTan[c + d*x]^2)/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + (3*a*b^2*d*(d*e - c*f)*ArcTan[c + d*x]^2)/(f*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)) + (I*b^3*d*ArcTan[c + d*x]^3)/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + (b^3*d*(d*e - c*f)*ArcTan[c + d*x]^3)/(f*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)) - (a + b*ArcTan[c + d*x])^3/(f*(e + f*x)) + (3*a^2*b*d*Log[e + f*x])/(f^2 + (d*e - c*f)^2) - (6*a*b^2*d*ArcTan[c + d*x]*Log[2/(1 - I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) - (3*b^3*d*ArcTan[c + d*x]^2*Log[2/(1 - I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + (6*a*b^2*d*ArcTan[c + d*x]*Log[(2*d*(e + f*x))/((d*e + (I - c)*f)*(1 - I*(c + d*x)))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + (3*b^3*d*ArcTan[c + d*x]^2*Log[(2*d*(e + f*x))/((d*e + (I - c)*f)*(1 - I*(c + d*x)))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + (6*a*b^2*d*ArcTan[c + d*x]*Log[2/(1 + I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + (3*b^3*d*ArcTan[c + d*x]^2*Log[2/(1 + I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) - (3*a^2*b*d*Log[1 + (c + d*x)^2])/(2*(f^2 + (d*e - c*f)^2)) + ((3*I)*a*b^2*d*PolyLog[2, 1 - 2/(1 - I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + ((3*I)*b^3*d*ArcTan[c + d*x]*PolyLog[2, 1 - 2/(1 - I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) - ((3*I)*a*b^2*d*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + (I - c)*f)*(1 - I*(c + d*x)))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) - ((3*I)*b^3*d*ArcTan[c + d*x]*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + (I - c)*f)*(1 - I*(c + d*x)))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + ((3*I)*a*b^2*d*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) + ((3*I)*b^3*d*ArcTan[c + d*x]*PolyLog[2, 1 - 2/(1 + I*(c + d*x))])/(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2) - (3*b^3*d*PolyLog[3, 1 - 2/(1 - I*(c + d*x))])/(2*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)) + (3*b^3*d*PolyLog[3, 1 - (2*d*(e + f*x))/((d*e + (I - c)*f)*(1 - I*(c + d*x)))])/(2*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)) + (3*b^3*d*PolyLog[3, 1 - 2/(1 + I*(c + d*x))])/(2*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2))","A",35,22,20,1.100,1,"{5045, 6741, 5057, 6688, 12, 6725, 706, 31, 635, 203, 260, 4856, 2402, 2315, 2447, 4984, 4884, 4920, 4854, 4858, 4994, 6610}"
41,1,177,0,0.2463237,"\int (e+f x)^m \left(a+b \tan ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)^m*(a + b*ArcTan[c + d*x]),x]","-\frac{i b d (e+f x)^{m+2} \text{Hypergeometric2F1}\left(1,m+2,m+3,\frac{d (e+f x)}{-c f+d e+i f}\right)}{2 f (m+1) (m+2) (d e+(-c+i) f)}+\frac{i b d (e+f x)^{m+2} \text{Hypergeometric2F1}\left(1,m+2,m+3,\frac{d (e+f x)}{d e-(c+i) f}\right)}{2 f (m+1) (m+2) (d e-(c+i) f)}+\frac{(e+f x)^{m+1} \left(a+b \tan ^{-1}(c+d x)\right)}{f (m+1)}","-\frac{i b d (e+f x)^{m+2} \text{Hypergeometric2F1}\left(1,m+2,m+3,\frac{d (e+f x)}{-c f+d e+i f}\right)}{2 f (m+1) (m+2) (d e+(-c+i) f)}+\frac{i b d (e+f x)^{m+2} \text{Hypergeometric2F1}\left(1,m+2,m+3,\frac{d (e+f x)}{d e-(c+i) f}\right)}{2 f (m+1) (m+2) (d e-(c+i) f)}+\frac{(e+f x)^{m+1} \left(a+b \tan ^{-1}(c+d x)\right)}{f (m+1)}",1,"((e + f*x)^(1 + m)*(a + b*ArcTan[c + d*x]))/(f*(1 + m)) - ((I/2)*b*d*(e + f*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (d*(e + f*x))/(d*e + I*f - c*f)])/(f*(d*e + (I - c)*f)*(1 + m)*(2 + m)) + ((I/2)*b*d*(e + f*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (d*(e + f*x))/(d*e - (I + c)*f)])/(f*(d*e - (I + c)*f)*(1 + m)*(2 + m))","A",6,4,18,0.2222,1,"{5047, 4862, 712, 68}"
42,0,0,0,0.057976,"\int (e+f x)^m \left(a+b \tan ^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)^m*(a + b*ArcTan[c + d*x])^2,x]","\int (e+f x)^m \left(a+b \tan ^{-1}(c+d x)\right)^2 \, dx","\text{Int}\left((e+f x)^m \left(a+b \tan ^{-1}(c+d x)\right)^2,x\right)",0,"Defer[Subst][Defer[Int][((d*e - c*f)/d + (f*x)/d)^m*(a + b*ArcTan[x])^2, x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
43,0,0,0,0.0564118,"\int (e+f x)^m \left(a+b \tan ^{-1}(c+d x)\right)^3 \, dx","Int[(e + f*x)^m*(a + b*ArcTan[c + d*x])^3,x]","\int (e+f x)^m \left(a+b \tan ^{-1}(c+d x)\right)^3 \, dx","\text{Int}\left((e+f x)^m \left(a+b \tan ^{-1}(c+d x)\right)^3,x\right)",0,"Defer[Subst][Defer[Int][((d*e - c*f)/d + (f*x)/d)^m*(a + b*ArcTan[x])^3, x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
44,1,106,0,0.1106337,"\int x^3 \tan ^{-1}(a+b x) \, dx","Int[x^3*ArcTan[a + b*x],x]","\frac{\left(1-6 a^2\right) x}{4 b^3}-\frac{a \left(1-a^2\right) \log \left((a+b x)^2+1\right)}{2 b^4}-\frac{\left(a^4-6 a^2+1\right) \tan ^{-1}(a+b x)}{4 b^4}-\frac{(a+b x)^3}{12 b^4}+\frac{a (a+b x)^2}{2 b^4}+\frac{1}{4} x^4 \tan ^{-1}(a+b x)","\frac{\left(1-6 a^2\right) x}{4 b^3}-\frac{a \left(1-a^2\right) \log \left((a+b x)^2+1\right)}{2 b^4}-\frac{\left(a^4-6 a^2+1\right) \tan ^{-1}(a+b x)}{4 b^4}-\frac{(a+b x)^3}{12 b^4}+\frac{a (a+b x)^2}{2 b^4}+\frac{1}{4} x^4 \tan ^{-1}(a+b x)",1,"((1 - 6*a^2)*x)/(4*b^3) + (a*(a + b*x)^2)/(2*b^4) - (a + b*x)^3/(12*b^4) - ((1 - 6*a^2 + a^4)*ArcTan[a + b*x])/(4*b^4) + (x^4*ArcTan[a + b*x])/4 - (a*(1 - a^2)*Log[1 + (a + b*x)^2])/(2*b^4)","A",7,6,10,0.6000,1,"{5047, 4862, 702, 635, 203, 260}"
45,1,79,0,0.0917566,"\int x^2 \tan ^{-1}(a+b x) \, dx","Int[x^2*ArcTan[a + b*x],x]","\frac{\left(1-3 a^2\right) \log \left((a+b x)^2+1\right)}{6 b^3}-\frac{a \left(3-a^2\right) \tan ^{-1}(a+b x)}{3 b^3}+\frac{a x}{b^2}-\frac{(a+b x)^2}{6 b^3}+\frac{1}{3} x^3 \tan ^{-1}(a+b x)","\frac{\left(1-3 a^2\right) \log \left((a+b x)^2+1\right)}{6 b^3}-\frac{a \left(3-a^2\right) \tan ^{-1}(a+b x)}{3 b^3}+\frac{a x}{b^2}-\frac{(a+b x)^2}{6 b^3}+\frac{1}{3} x^3 \tan ^{-1}(a+b x)",1,"(a*x)/b^2 - (a + b*x)^2/(6*b^3) - (a*(3 - a^2)*ArcTan[a + b*x])/(3*b^3) + (x^3*ArcTan[a + b*x])/3 + ((1 - 3*a^2)*Log[1 + (a + b*x)^2])/(6*b^3)","A",7,6,10,0.6000,1,"{5047, 4862, 702, 635, 203, 260}"
46,1,60,0,0.0546893,"\int x \tan ^{-1}(a+b x) \, dx","Int[x*ArcTan[a + b*x],x]","\frac{\left(1-a^2\right) \tan ^{-1}(a+b x)}{2 b^2}+\frac{a \log \left((a+b x)^2+1\right)}{2 b^2}+\frac{1}{2} x^2 \tan ^{-1}(a+b x)-\frac{x}{2 b}","\frac{\left(1-a^2\right) \tan ^{-1}(a+b x)}{2 b^2}+\frac{a \log \left((a+b x)^2+1\right)}{2 b^2}+\frac{1}{2} x^2 \tan ^{-1}(a+b x)-\frac{x}{2 b}",1,"-x/(2*b) + ((1 - a^2)*ArcTan[a + b*x])/(2*b^2) + (x^2*ArcTan[a + b*x])/2 + (a*Log[1 + (a + b*x)^2])/(2*b^2)","A",7,6,8,0.7500,1,"{5047, 4862, 702, 635, 203, 260}"
47,1,33,0,0.0113888,"\int \tan ^{-1}(a+b x) \, dx","Int[ArcTan[a + b*x],x]","\frac{(a+b x) \tan ^{-1}(a+b x)}{b}-\frac{\log \left((a+b x)^2+1\right)}{2 b}","\frac{(a+b x) \tan ^{-1}(a+b x)}{b}-\frac{\log \left((a+b x)^2+1\right)}{2 b}",1,"((a + b*x)*ArcTan[a + b*x])/b - Log[1 + (a + b*x)^2]/(2*b)","A",3,3,6,0.5000,1,"{5039, 4846, 260}"
48,1,120,0,0.1062469,"\int \frac{\tan ^{-1}(a+b x)}{x} \, dx","Int[ArcTan[a + b*x]/x,x]","\frac{1}{2} i \text{PolyLog}\left(2,1-\frac{2}{1-i (a+b x)}\right)-\frac{1}{2} i \text{PolyLog}\left(2,1-\frac{2 b x}{(-a+i) (1-i (a+b x))}\right)+\log \left(\frac{2}{1-i (a+b x)}\right) \left(-\tan ^{-1}(a+b x)\right)+\log \left(\frac{2 b x}{(-a+i) (1-i (a+b x))}\right) \tan ^{-1}(a+b x)","\frac{1}{2} i \text{PolyLog}\left(2,1-\frac{2}{1-i (a+b x)}\right)-\frac{1}{2} i \text{PolyLog}\left(2,1-\frac{2 b x}{(-a+i) (1-i (a+b x))}\right)+\log \left(\frac{2}{1-i (a+b x)}\right) \left(-\tan ^{-1}(a+b x)\right)+\log \left(\frac{2 b x}{(-a+i) (1-i (a+b x))}\right) \tan ^{-1}(a+b x)",1,"-(ArcTan[a + b*x]*Log[2/(1 - I*(a + b*x))]) + ArcTan[a + b*x]*Log[(2*b*x)/((I - a)*(1 - I*(a + b*x)))] + (I/2)*PolyLog[2, 1 - 2/(1 - I*(a + b*x))] - (I/2)*PolyLog[2, 1 - (2*b*x)/((I - a)*(1 - I*(a + b*x)))]","A",5,5,10,0.5000,1,"{5047, 4856, 2402, 2315, 2447}"
49,1,62,0,0.038679,"\int \frac{\tan ^{-1}(a+b x)}{x^2} \, dx","Int[ArcTan[a + b*x]/x^2,x]","\frac{b \log (x)}{a^2+1}-\frac{b \log \left((a+b x)^2+1\right)}{2 \left(a^2+1\right)}-\frac{a b \tan ^{-1}(a+b x)}{a^2+1}-\frac{\tan ^{-1}(a+b x)}{x}","\frac{b \log (x)}{a^2+1}-\frac{b \log \left((a+b x)^2+1\right)}{2 \left(a^2+1\right)}-\frac{a b \tan ^{-1}(a+b x)}{a^2+1}-\frac{\tan ^{-1}(a+b x)}{x}",1,"-((a*b*ArcTan[a + b*x])/(1 + a^2)) - ArcTan[a + b*x]/x + (b*Log[x])/(1 + a^2) - (b*Log[1 + (a + b*x)^2])/(2*(1 + a^2))","A",7,7,10,0.7000,1,"{5045, 371, 706, 31, 635, 203, 260}"
50,1,96,0,0.0833072,"\int \frac{\tan ^{-1}(a+b x)}{x^3} \, dx","Int[ArcTan[a + b*x]/x^3,x]","-\frac{a b^2 \log (x)}{\left(a^2+1\right)^2}+\frac{a b^2 \log \left((a+b x)^2+1\right)}{2 \left(a^2+1\right)^2}-\frac{\left(1-a^2\right) b^2 \tan ^{-1}(a+b x)}{2 \left(a^2+1\right)^2}-\frac{b}{2 \left(a^2+1\right) x}-\frac{\tan ^{-1}(a+b x)}{2 x^2}","-\frac{a b^2 \log (x)}{\left(a^2+1\right)^2}+\frac{a b^2 \log \left((a+b x)^2+1\right)}{2 \left(a^2+1\right)^2}-\frac{\left(1-a^2\right) b^2 \tan ^{-1}(a+b x)}{2 \left(a^2+1\right)^2}-\frac{b}{2 \left(a^2+1\right) x}-\frac{\tan ^{-1}(a+b x)}{2 x^2}",1,"-b/(2*(1 + a^2)*x) - ((1 - a^2)*b^2*ArcTan[a + b*x])/(2*(1 + a^2)^2) - ArcTan[a + b*x]/(2*x^2) - (a*b^2*Log[x])/(1 + a^2)^2 + (a*b^2*Log[1 + (a + b*x)^2])/(2*(1 + a^2)^2)","A",8,7,10,0.7000,1,"{5045, 371, 710, 801, 635, 203, 260}"
51,1,129,0,0.1143711,"\int \frac{\tan ^{-1}(a+b x)}{x^4} \, dx","Int[ArcTan[a + b*x]/x^4,x]","\frac{2 a b^2}{3 \left(a^2+1\right)^2 x}-\frac{\left(1-3 a^2\right) b^3 \log (x)}{3 \left(a^2+1\right)^3}+\frac{\left(1-3 a^2\right) b^3 \log \left((a+b x)^2+1\right)}{6 \left(a^2+1\right)^3}+\frac{a \left(3-a^2\right) b^3 \tan ^{-1}(a+b x)}{3 \left(a^2+1\right)^3}-\frac{b}{6 \left(a^2+1\right) x^2}-\frac{\tan ^{-1}(a+b x)}{3 x^3}","\frac{2 a b^2}{3 \left(a^2+1\right)^2 x}-\frac{\left(1-3 a^2\right) b^3 \log (x)}{3 \left(a^2+1\right)^3}+\frac{\left(1-3 a^2\right) b^3 \log \left((a+b x)^2+1\right)}{6 \left(a^2+1\right)^3}+\frac{a \left(3-a^2\right) b^3 \tan ^{-1}(a+b x)}{3 \left(a^2+1\right)^3}-\frac{b}{6 \left(a^2+1\right) x^2}-\frac{\tan ^{-1}(a+b x)}{3 x^3}",1,"-b/(6*(1 + a^2)*x^2) + (2*a*b^2)/(3*(1 + a^2)^2*x) + (a*(3 - a^2)*b^3*ArcTan[a + b*x])/(3*(1 + a^2)^3) - ArcTan[a + b*x]/(3*x^3) - ((1 - 3*a^2)*b^3*Log[x])/(3*(1 + a^2)^3) + ((1 - 3*a^2)*b^3*Log[1 + (a + b*x)^2])/(6*(1 + a^2)^3)","A",8,7,10,0.7000,1,"{5045, 371, 710, 801, 635, 203, 260}"
52,1,863,0,1.2069409,"\int \frac{\tan ^{-1}(a+b x)}{c+d x^3} \, dx","Int[ArcTan[a + b*x]/(c + d*x^3),x]","-\frac{i \log (i a+i b x+1) \log \left(\frac{b \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\sqrt[3]{d} (i-a)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{i \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{b \sqrt[3]{c}-(a+i) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\sqrt[6]{-1} \log (i a+i b x+1) \log \left(\frac{b \left(\sqrt[3]{c}-\sqrt[3]{-1} \sqrt[3]{d} x\right)}{b \sqrt[3]{c}-\sqrt[3]{-1} (i-a) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{\sqrt[6]{-1} \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt[3]{c}-\sqrt[3]{-1} \sqrt[3]{d} x\right)}{\sqrt[3]{-1} \sqrt[3]{d} (a+i)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{(-1)^{5/6} \log (i a+i b x+1) \log \left(\frac{b \left((-1)^{2/3} \sqrt[3]{d} x+\sqrt[3]{c}\right)}{(-1)^{2/3} \sqrt[3]{d} (i-a)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{(-1)^{5/6} \log (-i a-i b x+1) \log \left(\frac{b \left((-1)^{2/3} \sqrt[3]{d} x+\sqrt[3]{c}\right)}{\sqrt[6]{-1} \sqrt[3]{d} (1-i a)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{i \text{PolyLog}\left(2,\frac{\sqrt[3]{d} (-a-b x+i)}{\sqrt[3]{d} (i-a)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{(-1)^{5/6} \text{PolyLog}\left(2,-\frac{\sqrt[6]{-1} \sqrt[3]{d} (-a-b x+i)}{i b \sqrt[3]{c}-\sqrt[6]{-1} (i-a) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\sqrt[6]{-1} \text{PolyLog}\left(2,-\frac{\sqrt[3]{-1} \sqrt[3]{d} (-a-b x+i)}{b \sqrt[3]{c}-\sqrt[3]{-1} (i-a) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{i \text{PolyLog}\left(2,-\frac{\sqrt[3]{d} (a+b x+i)}{b \sqrt[3]{c}-(a+i) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{\sqrt[6]{-1} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{d} (a+b x+i)}{\sqrt[3]{-1} \sqrt[3]{d} (a+i)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{(-1)^{5/6} \text{PolyLog}\left(2,-\frac{(-1)^{2/3} \sqrt[3]{d} (a+b x+i)}{b \sqrt[3]{c}-(-1)^{2/3} (a+i) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}","-\frac{i \log (i a+i b x+1) \log \left(\frac{b \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\sqrt[3]{d} (i-a)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{i \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{b \sqrt[3]{c}-(a+i) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\sqrt[6]{-1} \log (i a+i b x+1) \log \left(\frac{b \left(\sqrt[3]{c}-\sqrt[3]{-1} \sqrt[3]{d} x\right)}{b \sqrt[3]{c}-\sqrt[3]{-1} (i-a) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{\sqrt[6]{-1} \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt[3]{c}-\sqrt[3]{-1} \sqrt[3]{d} x\right)}{\sqrt[3]{-1} \sqrt[3]{d} (a+i)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{(-1)^{5/6} \log (i a+i b x+1) \log \left(\frac{b \left((-1)^{2/3} \sqrt[3]{d} x+\sqrt[3]{c}\right)}{(-1)^{2/3} \sqrt[3]{d} (i-a)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{(-1)^{5/6} \log (-i a-i b x+1) \log \left(\frac{b \left((-1)^{2/3} \sqrt[3]{d} x+\sqrt[3]{c}\right)}{\sqrt[6]{-1} \sqrt[3]{d} (1-i a)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{i \text{PolyLog}\left(2,\frac{\sqrt[3]{d} (-a-b x+i)}{\sqrt[3]{d} (i-a)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{(-1)^{5/6} \text{PolyLog}\left(2,-\frac{\sqrt[6]{-1} \sqrt[3]{d} (-a-b x+i)}{i b \sqrt[3]{c}-\sqrt[6]{-1} (i-a) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\sqrt[6]{-1} \text{PolyLog}\left(2,-\frac{\sqrt[3]{-1} \sqrt[3]{d} (-a-b x+i)}{b \sqrt[3]{c}-\sqrt[3]{-1} (i-a) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{i \text{PolyLog}\left(2,-\frac{\sqrt[3]{d} (a+b x+i)}{b \sqrt[3]{c}-(a+i) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{\sqrt[6]{-1} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{d} (a+b x+i)}{\sqrt[3]{-1} \sqrt[3]{d} (a+i)+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{(-1)^{5/6} \text{PolyLog}\left(2,-\frac{(-1)^{2/3} \sqrt[3]{d} (a+b x+i)}{b \sqrt[3]{c}-(-1)^{2/3} (a+i) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}",1,"((-I/6)*Log[1 + I*a + I*b*x]*Log[(b*(c^(1/3) + d^(1/3)*x))/(b*c^(1/3) + (I - a)*d^(1/3))])/(c^(2/3)*d^(1/3)) + ((I/6)*Log[1 - I*a - I*b*x]*Log[(b*(c^(1/3) + d^(1/3)*x))/(b*c^(1/3) - (I + a)*d^(1/3))])/(c^(2/3)*d^(1/3)) + ((-1)^(1/6)*Log[1 + I*a + I*b*x]*Log[(b*(c^(1/3) - (-1)^(1/3)*d^(1/3)*x))/(b*c^(1/3) - (-1)^(1/3)*(I - a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) - ((-1)^(1/6)*Log[1 - I*a - I*b*x]*Log[(b*(c^(1/3) - (-1)^(1/3)*d^(1/3)*x))/(b*c^(1/3) + (-1)^(1/3)*(I + a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) + ((-1)^(5/6)*Log[1 + I*a + I*b*x]*Log[(b*(c^(1/3) + (-1)^(2/3)*d^(1/3)*x))/(b*c^(1/3) + (-1)^(2/3)*(I - a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) - ((-1)^(5/6)*Log[1 - I*a - I*b*x]*Log[(b*(c^(1/3) + (-1)^(2/3)*d^(1/3)*x))/(b*c^(1/3) + (-1)^(1/6)*(1 - I*a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) - ((I/6)*PolyLog[2, (d^(1/3)*(I - a - b*x))/(b*c^(1/3) + (I - a)*d^(1/3))])/(c^(2/3)*d^(1/3)) + ((-1)^(5/6)*PolyLog[2, -(((-1)^(1/6)*d^(1/3)*(I - a - b*x))/(I*b*c^(1/3) - (-1)^(1/6)*(I - a)*d^(1/3)))])/(6*c^(2/3)*d^(1/3)) + ((-1)^(1/6)*PolyLog[2, -(((-1)^(1/3)*d^(1/3)*(I - a - b*x))/(b*c^(1/3) - (-1)^(1/3)*(I - a)*d^(1/3)))])/(6*c^(2/3)*d^(1/3)) + ((I/6)*PolyLog[2, -((d^(1/3)*(I + a + b*x))/(b*c^(1/3) - (I + a)*d^(1/3)))])/(c^(2/3)*d^(1/3)) - ((-1)^(1/6)*PolyLog[2, ((-1)^(1/3)*d^(1/3)*(I + a + b*x))/(b*c^(1/3) + (-1)^(1/3)*(I + a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) - ((-1)^(5/6)*PolyLog[2, -(((-1)^(2/3)*d^(1/3)*(I + a + b*x))/(b*c^(1/3) - (-1)^(2/3)*(I + a)*d^(1/3)))])/(6*c^(2/3)*d^(1/3))","A",23,5,16,0.3125,1,"{5051, 2409, 2394, 2393, 2391}"
53,1,543,0,0.6073358,"\int \frac{\tan ^{-1}(a+b x)}{c+d x^2} \, dx","Int[ArcTan[a + b*x]/(c + d*x^2),x]","-\frac{i \text{PolyLog}\left(2,-\frac{\sqrt{d} (-a-b x+i)}{b \sqrt{-c}-(-a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{i \text{PolyLog}\left(2,\frac{\sqrt{d} (-a-b x+i)}{b \sqrt{-c}+(-a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{i \text{PolyLog}\left(2,-\frac{\sqrt{d} (a+b x+i)}{b \sqrt{-c}-(a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{i \text{PolyLog}\left(2,\frac{\sqrt{d} (a+b x+i)}{b \sqrt{-c}+(a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{i \log (i a+i b x+1) \log \left(\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{b \sqrt{-c}-(-a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{i \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{b \sqrt{-c}+(a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{i \log (i a+i b x+1) \log \left(\frac{b \left(\sqrt{-c}+\sqrt{d} x\right)}{b \sqrt{-c}+(-a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{i \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt{-c}+\sqrt{d} x\right)}{b \sqrt{-c}-(a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}","-\frac{i \text{PolyLog}\left(2,-\frac{\sqrt{d} (-a-b x+i)}{b \sqrt{-c}-(-a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{i \text{PolyLog}\left(2,\frac{\sqrt{d} (-a-b x+i)}{b \sqrt{-c}+(-a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{i \text{PolyLog}\left(2,-\frac{\sqrt{d} (a+b x+i)}{b \sqrt{-c}-(a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{i \text{PolyLog}\left(2,\frac{\sqrt{d} (a+b x+i)}{b \sqrt{-c}+(a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{i \log (i a+i b x+1) \log \left(\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{b \sqrt{-c}-(-a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{i \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{b \sqrt{-c}+(a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{i \log (i a+i b x+1) \log \left(\frac{b \left(\sqrt{-c}+\sqrt{d} x\right)}{b \sqrt{-c}+(-a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{i \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt{-c}+\sqrt{d} x\right)}{b \sqrt{-c}-(a+i) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}",1,"((-I/4)*Log[1 + I*a + I*b*x]*Log[(b*(Sqrt[-c] - Sqrt[d]*x))/(b*Sqrt[-c] - (I - a)*Sqrt[d])])/(Sqrt[-c]*Sqrt[d]) + ((I/4)*Log[1 - I*a - I*b*x]*Log[(b*(Sqrt[-c] - Sqrt[d]*x))/(b*Sqrt[-c] + (I + a)*Sqrt[d])])/(Sqrt[-c]*Sqrt[d]) + ((I/4)*Log[1 + I*a + I*b*x]*Log[(b*(Sqrt[-c] + Sqrt[d]*x))/(b*Sqrt[-c] + (I - a)*Sqrt[d])])/(Sqrt[-c]*Sqrt[d]) - ((I/4)*Log[1 - I*a - I*b*x]*Log[(b*(Sqrt[-c] + Sqrt[d]*x))/(b*Sqrt[-c] - (I + a)*Sqrt[d])])/(Sqrt[-c]*Sqrt[d]) - ((I/4)*PolyLog[2, -((Sqrt[d]*(I - a - b*x))/(b*Sqrt[-c] - (I - a)*Sqrt[d]))])/(Sqrt[-c]*Sqrt[d]) + ((I/4)*PolyLog[2, (Sqrt[d]*(I - a - b*x))/(b*Sqrt[-c] + (I - a)*Sqrt[d])])/(Sqrt[-c]*Sqrt[d]) - ((I/4)*PolyLog[2, -((Sqrt[d]*(I + a + b*x))/(b*Sqrt[-c] - (I + a)*Sqrt[d]))])/(Sqrt[-c]*Sqrt[d]) + ((I/4)*PolyLog[2, (Sqrt[d]*(I + a + b*x))/(b*Sqrt[-c] + (I + a)*Sqrt[d])])/(Sqrt[-c]*Sqrt[d])","A",17,5,16,0.3125,1,"{5051, 2409, 2394, 2393, 2391}"
54,1,152,0,0.1384459,"\int \frac{\tan ^{-1}(a+b x)}{c+d x} \, dx","Int[ArcTan[a + b*x]/(c + d*x),x]","-\frac{i \text{PolyLog}\left(2,1-\frac{2 b (c+d x)}{(1-i (a+b x)) (-a d+b c+i d)}\right)}{2 d}+\frac{i \text{PolyLog}\left(2,1-\frac{2}{1-i (a+b x)}\right)}{2 d}+\frac{\tan ^{-1}(a+b x) \log \left(\frac{2 b (c+d x)}{(1-i (a+b x)) (-a d+b c+i d)}\right)}{d}-\frac{\log \left(\frac{2}{1-i (a+b x)}\right) \tan ^{-1}(a+b x)}{d}","-\frac{i \text{PolyLog}\left(2,1-\frac{2 b (c+d x)}{(1-i (a+b x)) (-a d+b c+i d)}\right)}{2 d}+\frac{i \text{PolyLog}\left(2,1-\frac{2}{1-i (a+b x)}\right)}{2 d}+\frac{\tan ^{-1}(a+b x) \log \left(\frac{2 b (c+d x)}{(1-i (a+b x)) (-a d+b c+i d)}\right)}{d}-\frac{\log \left(\frac{2}{1-i (a+b x)}\right) \tan ^{-1}(a+b x)}{d}",1,"-((ArcTan[a + b*x]*Log[2/(1 - I*(a + b*x))])/d) + (ArcTan[a + b*x]*Log[(2*b*(c + d*x))/((b*c + I*d - a*d)*(1 - I*(a + b*x)))])/d + ((I/2)*PolyLog[2, 1 - 2/(1 - I*(a + b*x))])/d - ((I/2)*PolyLog[2, 1 - (2*b*(c + d*x))/((b*c + I*d - a*d)*(1 - I*(a + b*x)))])/d","A",5,5,14,0.3571,1,"{5047, 4856, 2402, 2315, 2447}"
55,1,244,0,0.2391314,"\int \frac{\tan ^{-1}(a+b x)}{c+\frac{d}{x}} \, dx","Int[ArcTan[a + b*x]/(c + d/x),x]","\frac{i d \text{PolyLog}\left(2,\frac{c (-a-b x+i)}{-a c+b d+i c}\right)}{2 c^2}-\frac{i d \text{PolyLog}\left(2,\frac{c (a+b x+i)}{-b d+(a+i) c}\right)}{2 c^2}+\frac{i d \log (i a+i b x+1) \log \left(\frac{b (c x+d)}{b d+(-a+i) c}\right)}{2 c^2}-\frac{i d \log (-i a-i b x+1) \log \left(-\frac{b (c x+d)}{-b d+(a+i) c}\right)}{2 c^2}-\frac{(i a+i b x+1) \log (i a+i b x+1)}{2 b c}-\frac{(-i a-i b x+1) \log (-i (a+b x+i))}{2 b c}","\frac{i d \text{PolyLog}\left(2,\frac{c (-a-b x+i)}{-a c+b d+i c}\right)}{2 c^2}-\frac{i d \text{PolyLog}\left(2,\frac{c (a+b x+i)}{-b d+(a+i) c}\right)}{2 c^2}+\frac{i d \log (i a+i b x+1) \log \left(\frac{b (c x+d)}{b d+(-a+i) c}\right)}{2 c^2}-\frac{i d \log (-i a-i b x+1) \log \left(-\frac{b (c x+d)}{-b d+(a+i) c}\right)}{2 c^2}-\frac{(i a+i b x+1) \log (i a+i b x+1)}{2 b c}-\frac{(-i a-i b x+1) \log (-i (a+b x+i))}{2 b c}",1,"-((1 + I*a + I*b*x)*Log[1 + I*a + I*b*x])/(2*b*c) - ((1 - I*a - I*b*x)*Log[(-I)*(I + a + b*x)])/(2*b*c) - ((I/2)*d*Log[1 - I*a - I*b*x]*Log[-((b*(d + c*x))/((I + a)*c - b*d))])/c^2 + ((I/2)*d*Log[1 + I*a + I*b*x]*Log[(b*(d + c*x))/((I - a)*c + b*d)])/c^2 + ((I/2)*d*PolyLog[2, (c*(I - a - b*x))/(I*c - a*c + b*d)])/c^2 - ((I/2)*d*PolyLog[2, (c*(I + a + b*x))/((I + a)*c - b*d)])/c^2","A",15,7,16,0.4375,1,"{5051, 2409, 2389, 2295, 2394, 2393, 2391}"
56,1,668,0,0.854872,"\int \frac{\tan ^{-1}(a+b x)}{c+\frac{d}{x^2}} \, dx","Int[ArcTan[a + b*x]/(c + d/x^2),x]","\frac{i \sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (-a-b x+i)}{a \left(-\sqrt{-c}\right)-b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{i \sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (i a+i b x+1)}{(1+i a) \sqrt{-c}-i b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{i \sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+i)}{a \sqrt{-c}-b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{i \sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+i)}{a \sqrt{-c}+b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}+\frac{i \sqrt{d} \log (i a+i b x+1) \log \left(-\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{a \left(-\sqrt{-c}\right)-b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{i \sqrt{d} \log (i a+i b x+1) \log \left(\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{a \left(-\sqrt{-c}\right)+b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{i \sqrt{d} \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{a \sqrt{-c}+b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}+\frac{i \sqrt{d} \log (-i a-i b x+1) \log \left(-\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{-b \sqrt{d}+(a+i) \sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{(i a+i b x+1) \log (i a+i b x+1)}{2 b c}-\frac{(-i a-i b x+1) \log (-i (a+b x+i))}{2 b c}","\frac{i \sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (-a-b x+i)}{a \left(-\sqrt{-c}\right)-b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{i \sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (i a+i b x+1)}{(1+i a) \sqrt{-c}-i b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{i \sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+i)}{a \sqrt{-c}-b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{i \sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+i)}{a \sqrt{-c}+b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}+\frac{i \sqrt{d} \log (i a+i b x+1) \log \left(-\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{a \left(-\sqrt{-c}\right)-b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{i \sqrt{d} \log (i a+i b x+1) \log \left(\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{a \left(-\sqrt{-c}\right)+b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{i \sqrt{d} \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{a \sqrt{-c}+b \sqrt{d}+i \sqrt{-c}}\right)}{4 (-c)^{3/2}}+\frac{i \sqrt{d} \log (-i a-i b x+1) \log \left(-\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{-b \sqrt{d}+(a+i) \sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{(i a+i b x+1) \log (i a+i b x+1)}{2 b c}-\frac{(-i a-i b x+1) \log (-i (a+b x+i))}{2 b c}",1,"-((1 + I*a + I*b*x)*Log[1 + I*a + I*b*x])/(2*b*c) - ((1 - I*a - I*b*x)*Log[(-I)*(I + a + b*x)])/(2*b*c) + ((I/4)*Sqrt[d]*Log[1 + I*a + I*b*x]*Log[-((b*(Sqrt[d] - Sqrt[-c]*x))/(I*Sqrt[-c] - a*Sqrt[-c] - b*Sqrt[d]))])/(-c)^(3/2) - ((I/4)*Sqrt[d]*Log[1 - I*a - I*b*x]*Log[(b*(Sqrt[d] - Sqrt[-c]*x))/(I*Sqrt[-c] + a*Sqrt[-c] + b*Sqrt[d])])/(-c)^(3/2) + ((I/4)*Sqrt[d]*Log[1 - I*a - I*b*x]*Log[-((b*(Sqrt[d] + Sqrt[-c]*x))/((I + a)*Sqrt[-c] - b*Sqrt[d]))])/(-c)^(3/2) - ((I/4)*Sqrt[d]*Log[1 + I*a + I*b*x]*Log[(b*(Sqrt[d] + Sqrt[-c]*x))/(I*Sqrt[-c] - a*Sqrt[-c] + b*Sqrt[d])])/(-c)^(3/2) + ((I/4)*Sqrt[d]*PolyLog[2, (Sqrt[-c]*(I - a - b*x))/(I*Sqrt[-c] - a*Sqrt[-c] - b*Sqrt[d])])/(-c)^(3/2) - ((I/4)*Sqrt[d]*PolyLog[2, (Sqrt[-c]*(1 + I*a + I*b*x))/((1 + I*a)*Sqrt[-c] - I*b*Sqrt[d])])/(-c)^(3/2) + ((I/4)*Sqrt[d]*PolyLog[2, (Sqrt[-c]*(I + a + b*x))/(I*Sqrt[-c] + a*Sqrt[-c] - b*Sqrt[d])])/(-c)^(3/2) - ((I/4)*Sqrt[d]*PolyLog[2, (Sqrt[-c]*(I + a + b*x))/(I*Sqrt[-c] + a*Sqrt[-c] + b*Sqrt[d])])/(-c)^(3/2)","A",25,7,16,0.4375,1,"{5051, 2409, 2389, 2295, 2394, 2393, 2391}"
57,1,933,0,1.3674334,"\int \frac{\tan ^{-1}(a+b x)}{c+\frac{d}{x^3}} \, dx","Int[ArcTan[a + b*x]/(c + d/x^3),x]","-\frac{(i a+i b x+1) \log (i a+i b x+1)}{2 b c}+\frac{i \sqrt[3]{d} \log \left(\frac{b \left(\sqrt[3]{c} x+\sqrt[3]{d}\right)}{\sqrt[3]{c} (i-a)+b \sqrt[3]{d}}\right) \log (i a+i b x+1)}{6 c^{4/3}}-\frac{\sqrt[6]{-1} \sqrt[3]{d} \log \left(-\frac{b \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{c} x\right)}{\sqrt[3]{-1} (i-a) \sqrt[3]{c}-b \sqrt[3]{d}}\right) \log (i a+i b x+1)}{6 c^{4/3}}-\frac{(-1)^{5/6} \sqrt[3]{d} \log \left(\frac{b \left((-1)^{2/3} \sqrt[3]{c} x+\sqrt[3]{d}\right)}{(-1)^{2/3} \sqrt[3]{c} (i-a)+b \sqrt[3]{d}}\right) \log (i a+i b x+1)}{6 c^{4/3}}-\frac{(-i a-i b x+1) \log (-i (a+b x+i))}{2 b c}-\frac{i \sqrt[3]{d} \log (-i a-i b x+1) \log \left(-\frac{b \left(\sqrt[3]{c} x+\sqrt[3]{d}\right)}{(a+i) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{\sqrt[6]{-1} \sqrt[3]{d} \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{c} x\right)}{\sqrt[3]{-1} \sqrt[3]{c} (a+i)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{(-1)^{5/6} \sqrt[3]{d} \log (-i a-i b x+1) \log \left(\frac{b \left((-1)^{2/3} \sqrt[3]{c} x+\sqrt[3]{d}\right)}{\sqrt[6]{-1} \sqrt[3]{c} (1-i a)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{\sqrt[6]{-1} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{c} (-a-b x+i)}{\sqrt[3]{-1} (i-a) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{(-1)^{5/6} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[6]{-1} \sqrt[3]{c} (-a-b x+i)}{\sqrt[6]{-1} (i-a) \sqrt[3]{c}-i b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{i \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (-a-b x+i)}{\sqrt[3]{c} (i-a)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{i \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (a+b x+i)}{(a+i) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{(-1)^{5/6} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{c} (a+b x+i)}{(-1)^{2/3} (a+i) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{\sqrt[6]{-1} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{c} (a+b x+i)}{\sqrt[3]{-1} \sqrt[3]{c} (a+i)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}","-\frac{(i a+i b x+1) \log (i a+i b x+1)}{2 b c}+\frac{i \sqrt[3]{d} \log \left(\frac{b \left(\sqrt[3]{c} x+\sqrt[3]{d}\right)}{\sqrt[3]{c} (i-a)+b \sqrt[3]{d}}\right) \log (i a+i b x+1)}{6 c^{4/3}}-\frac{\sqrt[6]{-1} \sqrt[3]{d} \log \left(-\frac{b \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{c} x\right)}{\sqrt[3]{-1} (i-a) \sqrt[3]{c}-b \sqrt[3]{d}}\right) \log (i a+i b x+1)}{6 c^{4/3}}-\frac{(-1)^{5/6} \sqrt[3]{d} \log \left(\frac{b \left((-1)^{2/3} \sqrt[3]{c} x+\sqrt[3]{d}\right)}{(-1)^{2/3} \sqrt[3]{c} (i-a)+b \sqrt[3]{d}}\right) \log (i a+i b x+1)}{6 c^{4/3}}-\frac{(-i a-i b x+1) \log (-i (a+b x+i))}{2 b c}-\frac{i \sqrt[3]{d} \log (-i a-i b x+1) \log \left(-\frac{b \left(\sqrt[3]{c} x+\sqrt[3]{d}\right)}{(a+i) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{\sqrt[6]{-1} \sqrt[3]{d} \log (-i a-i b x+1) \log \left(\frac{b \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{c} x\right)}{\sqrt[3]{-1} \sqrt[3]{c} (a+i)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{(-1)^{5/6} \sqrt[3]{d} \log (-i a-i b x+1) \log \left(\frac{b \left((-1)^{2/3} \sqrt[3]{c} x+\sqrt[3]{d}\right)}{\sqrt[6]{-1} \sqrt[3]{c} (1-i a)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{\sqrt[6]{-1} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{c} (-a-b x+i)}{\sqrt[3]{-1} (i-a) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{(-1)^{5/6} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[6]{-1} \sqrt[3]{c} (-a-b x+i)}{\sqrt[6]{-1} (i-a) \sqrt[3]{c}-i b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{i \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (-a-b x+i)}{\sqrt[3]{c} (i-a)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{i \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (a+b x+i)}{(a+i) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{(-1)^{5/6} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{c} (a+b x+i)}{(-1)^{2/3} (a+i) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{\sqrt[6]{-1} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{c} (a+b x+i)}{\sqrt[3]{-1} \sqrt[3]{c} (a+i)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}",1,"-((1 + I*a + I*b*x)*Log[1 + I*a + I*b*x])/(2*b*c) - ((1 - I*a - I*b*x)*Log[(-I)*(I + a + b*x)])/(2*b*c) - ((I/6)*d^(1/3)*Log[1 - I*a - I*b*x]*Log[-((b*(d^(1/3) + c^(1/3)*x))/((I + a)*c^(1/3) - b*d^(1/3)))])/c^(4/3) + ((I/6)*d^(1/3)*Log[1 + I*a + I*b*x]*Log[(b*(d^(1/3) + c^(1/3)*x))/((I - a)*c^(1/3) + b*d^(1/3))])/c^(4/3) - ((-1)^(1/6)*d^(1/3)*Log[1 + I*a + I*b*x]*Log[-((b*(d^(1/3) - (-1)^(1/3)*c^(1/3)*x))/((-1)^(1/3)*(I - a)*c^(1/3) - b*d^(1/3)))])/(6*c^(4/3)) + ((-1)^(1/6)*d^(1/3)*Log[1 - I*a - I*b*x]*Log[(b*(d^(1/3) - (-1)^(1/3)*c^(1/3)*x))/((-1)^(1/3)*(I + a)*c^(1/3) + b*d^(1/3))])/(6*c^(4/3)) - ((-1)^(5/6)*d^(1/3)*Log[1 + I*a + I*b*x]*Log[(b*(d^(1/3) + (-1)^(2/3)*c^(1/3)*x))/((-1)^(2/3)*(I - a)*c^(1/3) + b*d^(1/3))])/(6*c^(4/3)) + ((-1)^(5/6)*d^(1/3)*Log[1 - I*a - I*b*x]*Log[(b*(d^(1/3) + (-1)^(2/3)*c^(1/3)*x))/((-1)^(1/6)*(1 - I*a)*c^(1/3) + b*d^(1/3))])/(6*c^(4/3)) - ((-1)^(1/6)*d^(1/3)*PolyLog[2, ((-1)^(1/3)*c^(1/3)*(I - a - b*x))/((-1)^(1/3)*(I - a)*c^(1/3) - b*d^(1/3))])/(6*c^(4/3)) - ((-1)^(5/6)*d^(1/3)*PolyLog[2, ((-1)^(1/6)*c^(1/3)*(I - a - b*x))/((-1)^(1/6)*(I - a)*c^(1/3) - I*b*d^(1/3))])/(6*c^(4/3)) + ((I/6)*d^(1/3)*PolyLog[2, (c^(1/3)*(I - a - b*x))/((I - a)*c^(1/3) + b*d^(1/3))])/c^(4/3) - ((I/6)*d^(1/3)*PolyLog[2, (c^(1/3)*(I + a + b*x))/((I + a)*c^(1/3) - b*d^(1/3))])/c^(4/3) + ((-1)^(5/6)*d^(1/3)*PolyLog[2, ((-1)^(2/3)*c^(1/3)*(I + a + b*x))/((-1)^(2/3)*(I + a)*c^(1/3) - b*d^(1/3))])/(6*c^(4/3)) + ((-1)^(1/6)*d^(1/3)*PolyLog[2, ((-1)^(1/3)*c^(1/3)*(I + a + b*x))/((-1)^(1/3)*(I + a)*c^(1/3) + b*d^(1/3))])/(6*c^(4/3))","A",31,7,16,0.4375,1,"{5051, 2409, 2389, 2295, 2394, 2393, 2391}"
58,1,673,0,0.8984244,"\int \frac{\tan ^{-1}(a+b x)}{c+d \sqrt{x}} \, dx","Int[ArcTan[a + b*x]/(c + d*Sqrt[x]),x]","\frac{i c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a-i} d}\right)}{d^2}+\frac{i c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c+\sqrt{-a-i} d}\right)}{d^2}-\frac{i c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a+i} d}\right)}{d^2}-\frac{i c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c+\sqrt{-a+i} d}\right)}{d^2}+\frac{i c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(-\sqrt{b} \sqrt{x}+\sqrt{-a-i}\right)}{\sqrt{b} c+\sqrt{-a-i} d}\right)}{d^2}-\frac{i c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(-\sqrt{b} \sqrt{x}+\sqrt{-a+i}\right)}{\sqrt{b} c+\sqrt{-a+i} d}\right)}{d^2}+\frac{i c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{b} \sqrt{x}+\sqrt{-a-i}\right)}{\sqrt{b} c-\sqrt{-a-i} d}\right)}{d^2}-\frac{i c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{b} \sqrt{x}+\sqrt{-a+i}\right)}{\sqrt{b} c-\sqrt{-a+i} d}\right)}{d^2}-\frac{i c \log (-i a-i b x+1) \log \left(c+d \sqrt{x}\right)}{d^2}+\frac{i c \log (i a+i b x+1) \log \left(c+d \sqrt{x}\right)}{d^2}+\frac{i \sqrt{x} \log (-i a-i b x+1)}{d}-\frac{i \sqrt{x} \log (i a+i b x+1)}{d}+\frac{2 i \sqrt{a+i} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+i}}\right)}{\sqrt{b} d}-\frac{2 i \sqrt{-a+i} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{-a+i}}\right)}{\sqrt{b} d}","\frac{i c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a-i} d}\right)}{d^2}+\frac{i c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c+\sqrt{-a-i} d}\right)}{d^2}-\frac{i c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a+i} d}\right)}{d^2}-\frac{i c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c+\sqrt{-a+i} d}\right)}{d^2}+\frac{i c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(-\sqrt{b} \sqrt{x}+\sqrt{-a-i}\right)}{\sqrt{b} c+\sqrt{-a-i} d}\right)}{d^2}-\frac{i c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(-\sqrt{b} \sqrt{x}+\sqrt{-a+i}\right)}{\sqrt{b} c+\sqrt{-a+i} d}\right)}{d^2}+\frac{i c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{b} \sqrt{x}+\sqrt{-a-i}\right)}{\sqrt{b} c-\sqrt{-a-i} d}\right)}{d^2}-\frac{i c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{b} \sqrt{x}+\sqrt{-a+i}\right)}{\sqrt{b} c-\sqrt{-a+i} d}\right)}{d^2}-\frac{i c \log (-i a-i b x+1) \log \left(c+d \sqrt{x}\right)}{d^2}+\frac{i c \log (i a+i b x+1) \log \left(c+d \sqrt{x}\right)}{d^2}+\frac{i \sqrt{x} \log (-i a-i b x+1)}{d}-\frac{i \sqrt{x} \log (i a+i b x+1)}{d}+\frac{2 i \sqrt{a+i} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+i}}\right)}{\sqrt{b} d}-\frac{2 i \sqrt{-a+i} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{-a+i}}\right)}{\sqrt{b} d}",1,"((2*I)*Sqrt[I + a]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[I + a]])/(Sqrt[b]*d) - ((2*I)*Sqrt[I - a]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[I - a]])/(Sqrt[b]*d) + (I*c*Log[(d*(Sqrt[-I - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c + Sqrt[-I - a]*d)]*Log[c + d*Sqrt[x]])/d^2 - (I*c*Log[(d*(Sqrt[I - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c + Sqrt[I - a]*d)]*Log[c + d*Sqrt[x]])/d^2 + (I*c*Log[-((d*(Sqrt[-I - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c - Sqrt[-I - a]*d))]*Log[c + d*Sqrt[x]])/d^2 - (I*c*Log[-((d*(Sqrt[I - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c - Sqrt[I - a]*d))]*Log[c + d*Sqrt[x]])/d^2 + (I*Sqrt[x]*Log[1 - I*a - I*b*x])/d - (I*c*Log[c + d*Sqrt[x]]*Log[1 - I*a - I*b*x])/d^2 - (I*Sqrt[x]*Log[1 + I*a + I*b*x])/d + (I*c*Log[c + d*Sqrt[x]]*Log[1 + I*a + I*b*x])/d^2 + (I*c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c - Sqrt[-I - a]*d)])/d^2 + (I*c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c + Sqrt[-I - a]*d)])/d^2 - (I*c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c - Sqrt[I - a]*d)])/d^2 - (I*c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c + Sqrt[I - a]*d)])/d^2","A",31,13,18,0.7222,1,"{5051, 2408, 2466, 2448, 321, 205, 2462, 260, 2416, 2394, 2393, 2391, 208}"
59,1,770,0,0.9823775,"\int \frac{\tan ^{-1}(a+b x)}{c+\frac{d}{\sqrt{x}}} \, dx","Int[ArcTan[a + b*x]/(c + d/Sqrt[x]),x]","-\frac{i d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{-\sqrt{b} d+\sqrt{-a-i} c}\right)}{c^3}+\frac{i d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{-\sqrt{b} d+\sqrt{-a+i} c}\right)}{c^3}-\frac{i d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{b} d+\sqrt{-a-i} c}\right)}{c^3}+\frac{i d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{b} d+\sqrt{-a+i} c}\right)}{c^3}-\frac{i d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(-\sqrt{b} \sqrt{x}+\sqrt{-a-i}\right)}{\sqrt{b} d+\sqrt{-a-i} c}\right)}{c^3}+\frac{i d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(-\sqrt{b} \sqrt{x}+\sqrt{-a+i}\right)}{\sqrt{b} d+\sqrt{-a+i} c}\right)}{c^3}-\frac{i d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{b} \sqrt{x}+\sqrt{-a-i}\right)}{-\sqrt{b} d+\sqrt{-a-i} c}\right)}{c^3}+\frac{i d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{b} \sqrt{x}+\sqrt{-a+i}\right)}{-\sqrt{b} d+\sqrt{-a+i} c}\right)}{c^3}+\frac{i d^2 \log (-i a-i b x+1) \log \left(c \sqrt{x}+d\right)}{c^3}-\frac{i d^2 \log (i a+i b x+1) \log \left(c \sqrt{x}+d\right)}{c^3}-\frac{i d \sqrt{x} \log (-i a-i b x+1)}{c^2}+\frac{i d \sqrt{x} \log (i a+i b x+1)}{c^2}-\frac{2 i \sqrt{a+i} d \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+i}}\right)}{\sqrt{b} c^2}+\frac{2 i \sqrt{-a+i} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{-a+i}}\right)}{\sqrt{b} c^2}-\frac{(i a+i b x+1) \log (i a+i b x+1)}{2 b c}-\frac{(-i a-i b x+1) \log (-i (a+b x+i))}{2 b c}","-\frac{i d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{-\sqrt{b} d+\sqrt{-a-i} c}\right)}{c^3}+\frac{i d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{-\sqrt{b} d+\sqrt{-a+i} c}\right)}{c^3}-\frac{i d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{b} d+\sqrt{-a-i} c}\right)}{c^3}+\frac{i d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{b} d+\sqrt{-a+i} c}\right)}{c^3}-\frac{i d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(-\sqrt{b} \sqrt{x}+\sqrt{-a-i}\right)}{\sqrt{b} d+\sqrt{-a-i} c}\right)}{c^3}+\frac{i d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(-\sqrt{b} \sqrt{x}+\sqrt{-a+i}\right)}{\sqrt{b} d+\sqrt{-a+i} c}\right)}{c^3}-\frac{i d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{b} \sqrt{x}+\sqrt{-a-i}\right)}{-\sqrt{b} d+\sqrt{-a-i} c}\right)}{c^3}+\frac{i d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{b} \sqrt{x}+\sqrt{-a+i}\right)}{-\sqrt{b} d+\sqrt{-a+i} c}\right)}{c^3}+\frac{i d^2 \log (-i a-i b x+1) \log \left(c \sqrt{x}+d\right)}{c^3}-\frac{i d^2 \log (i a+i b x+1) \log \left(c \sqrt{x}+d\right)}{c^3}-\frac{i d \sqrt{x} \log (-i a-i b x+1)}{c^2}+\frac{i d \sqrt{x} \log (i a+i b x+1)}{c^2}-\frac{2 i \sqrt{a+i} d \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+i}}\right)}{\sqrt{b} c^2}+\frac{2 i \sqrt{-a+i} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{-a+i}}\right)}{\sqrt{b} c^2}-\frac{(i a+i b x+1) \log (i a+i b x+1)}{2 b c}-\frac{(-i a-i b x+1) \log (-i (a+b x+i))}{2 b c}",1,"((-2*I)*Sqrt[I + a]*d*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[I + a]])/(Sqrt[b]*c^2) + ((2*I)*Sqrt[I - a]*d*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[I - a]])/(Sqrt[b]*c^2) - (I*d^2*Log[(c*(Sqrt[-I - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-I - a]*c + Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 + (I*d^2*Log[(c*(Sqrt[I - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[I - a]*c + Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 - (I*d^2*Log[(c*(Sqrt[-I - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-I - a]*c - Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 + (I*d^2*Log[(c*(Sqrt[I - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[I - a]*c - Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 - (I*d*Sqrt[x]*Log[1 - I*a - I*b*x])/c^2 + (I*d^2*Log[d + c*Sqrt[x]]*Log[1 - I*a - I*b*x])/c^3 + (I*d*Sqrt[x]*Log[1 + I*a + I*b*x])/c^2 - ((1 + I*a + I*b*x)*Log[1 + I*a + I*b*x])/(2*b*c) - (I*d^2*Log[d + c*Sqrt[x]]*Log[1 + I*a + I*b*x])/c^3 - ((1 - I*a - I*b*x)*Log[(-I)*(I + a + b*x)])/(2*b*c) - (I*d^2*PolyLog[2, -((Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[-I - a]*c - Sqrt[b]*d))])/c^3 + (I*d^2*PolyLog[2, -((Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[I - a]*c - Sqrt[b]*d))])/c^3 - (I*d^2*PolyLog[2, (Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[-I - a]*c + Sqrt[b]*d)])/c^3 + (I*d^2*PolyLog[2, (Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[I - a]*c + Sqrt[b]*d)])/c^3","A",37,16,18,0.8889,1,"{5051, 2408, 2476, 2448, 321, 205, 2454, 2389, 2295, 2462, 260, 2416, 2394, 2393, 2391, 208}"
60,1,274,0,0.2706856,"\int \frac{\tan ^{-1}(a+b x)}{1+x^2} \, dx","Int[ArcTan[a + b*x]/(1 + x^2),x]","-\frac{1}{4} \text{PolyLog}\left(2,-\frac{-a-b x+i}{a-i (1-b)}\right)+\frac{1}{4} \text{PolyLog}\left(2,-\frac{-a-b x+i}{a-i (b+1)}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{a+b x+i}{a-i b+i}\right)+\frac{1}{4} \text{PolyLog}\left(2,\frac{a+b x+i}{a+i (b+1)}\right)+\frac{1}{4} \log \left(\frac{b (-x+i)}{a+i (b+1)}\right) \log (-i a-i b x+1)-\frac{1}{4} \log \left(-\frac{b (x+i)}{a+i (1-b)}\right) \log (-i a-i b x+1)-\frac{1}{4} \log \left(\frac{b (-x+i)}{a-i (1-b)}\right) \log (i a+i b x+1)+\frac{1}{4} \log \left(-\frac{b (x+i)}{a-i (b+1)}\right) \log (i a+i b x+1)","-\frac{1}{4} \text{PolyLog}\left(2,-\frac{-a-b x+i}{a-i (1-b)}\right)+\frac{1}{4} \text{PolyLog}\left(2,-\frac{-a-b x+i}{a-i (b+1)}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{a+b x+i}{a-i b+i}\right)+\frac{1}{4} \text{PolyLog}\left(2,\frac{a+b x+i}{a+i (b+1)}\right)+\frac{1}{4} \log \left(\frac{b (-x+i)}{a+i (b+1)}\right) \log (-i a-i b x+1)-\frac{1}{4} \log \left(-\frac{b (x+i)}{a+i (1-b)}\right) \log (-i a-i b x+1)-\frac{1}{4} \log \left(\frac{b (-x+i)}{a-i (1-b)}\right) \log (i a+i b x+1)+\frac{1}{4} \log \left(-\frac{b (x+i)}{a-i (b+1)}\right) \log (i a+i b x+1)",1,"(Log[(b*(I - x))/(a + I*(1 + b))]*Log[1 - I*a - I*b*x])/4 - (Log[-((b*(I + x))/(a + I*(1 - b)))]*Log[1 - I*a - I*b*x])/4 - (Log[(b*(I - x))/(a - I*(1 - b))]*Log[1 + I*a + I*b*x])/4 + (Log[-((b*(I + x))/(a - I*(1 + b)))]*Log[1 + I*a + I*b*x])/4 - PolyLog[2, -((I - a - b*x)/(a - I*(1 - b)))]/4 + PolyLog[2, -((I - a - b*x)/(a - I*(1 + b)))]/4 - PolyLog[2, (I + a + b*x)/(I + a - I*b)]/4 + PolyLog[2, (I + a + b*x)/(a + I*(1 + b))]/4","A",17,5,14,0.3571,1,"{5051, 2409, 2394, 2393, 2391}"
61,1,543,0,0.6001257,"\int \frac{\tan ^{-1}(d+e x)}{a+b x^2} \, dx","Int[ArcTan[d + e*x]/(a + b*x^2),x]","-\frac{i \text{PolyLog}\left(2,\frac{\sqrt{b} (-d-e x+i)}{-\sqrt{-a} e+\sqrt{b} (-d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{i \text{PolyLog}\left(2,\frac{\sqrt{b} (-d-e x+i)}{\sqrt{-a} e+\sqrt{b} (-d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{i \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x+i)}{-\sqrt{-a} e+\sqrt{b} (d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{i \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x+i)}{\sqrt{-a} e+\sqrt{b} (d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{i \log (-i d-i e x+1) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} (d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{i \log (-i d-i e x+1) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{-\sqrt{-a} e+\sqrt{b} (d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{i \log (i d+i e x+1) \log \left(-\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{-\sqrt{-a} e+\sqrt{b} (-d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{i \log (i d+i e x+1) \log \left(\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} (-d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}","-\frac{i \text{PolyLog}\left(2,\frac{\sqrt{b} (-d-e x+i)}{-\sqrt{-a} e+\sqrt{b} (-d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{i \text{PolyLog}\left(2,\frac{\sqrt{b} (-d-e x+i)}{\sqrt{-a} e+\sqrt{b} (-d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{i \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x+i)}{-\sqrt{-a} e+\sqrt{b} (d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{i \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x+i)}{\sqrt{-a} e+\sqrt{b} (d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{i \log (-i d-i e x+1) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} (d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{i \log (-i d-i e x+1) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{-\sqrt{-a} e+\sqrt{b} (d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{i \log (i d+i e x+1) \log \left(-\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{-\sqrt{-a} e+\sqrt{b} (-d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{i \log (i d+i e x+1) \log \left(\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} (-d+i)}\right)}{4 \sqrt{-a} \sqrt{b}}",1,"((I/4)*Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*(I + d) + Sqrt[-a]*e)]*Log[1 - I*d - I*e*x])/(Sqrt[-a]*Sqrt[b]) - ((I/4)*Log[-((e*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*(I + d) - Sqrt[-a]*e))]*Log[1 - I*d - I*e*x])/(Sqrt[-a]*Sqrt[b]) - ((I/4)*Log[-((e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*(I - d) - Sqrt[-a]*e))]*Log[1 + I*d + I*e*x])/(Sqrt[-a]*Sqrt[b]) + ((I/4)*Log[(e*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*(I - d) + Sqrt[-a]*e)]*Log[1 + I*d + I*e*x])/(Sqrt[-a]*Sqrt[b]) - ((I/4)*PolyLog[2, (Sqrt[b]*(I - d - e*x))/(Sqrt[b]*(I - d) - Sqrt[-a]*e)])/(Sqrt[-a]*Sqrt[b]) + ((I/4)*PolyLog[2, (Sqrt[b]*(I - d - e*x))/(Sqrt[b]*(I - d) + Sqrt[-a]*e)])/(Sqrt[-a]*Sqrt[b]) - ((I/4)*PolyLog[2, (Sqrt[b]*(I + d + e*x))/(Sqrt[b]*(I + d) - Sqrt[-a]*e)])/(Sqrt[-a]*Sqrt[b]) + ((I/4)*PolyLog[2, (Sqrt[b]*(I + d + e*x))/(Sqrt[b]*(I + d) + Sqrt[-a]*e)])/(Sqrt[-a]*Sqrt[b])","A",17,5,16,0.3125,1,"{5051, 2409, 2394, 2393, 2391}"
62,1,367,0,0.6727315,"\int \frac{\tan ^{-1}(d+e x)}{a+b x+c x^2} \, dx","Int[ArcTan[d + e*x]/(a + b*x + c*x^2),x]","-\frac{i \text{PolyLog}\left(2,1+\frac{2 \left(-e \left(b-\sqrt{b^2-4 a c}\right)-2 c (d+e x)+2 c d\right)}{(1-i (d+e x)) \left(-e \sqrt{b^2-4 a c}+b e-2 c d+2 i c\right)}\right)}{2 \sqrt{b^2-4 a c}}+\frac{i \text{PolyLog}\left(2,1+\frac{2 \left(-e \left(\sqrt{b^2-4 a c}+b\right)-2 c (d+e x)+2 c d\right)}{(1-i (d+e x)) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (-d+i)\right)}\right)}{2 \sqrt{b^2-4 a c}}+\frac{\tan ^{-1}(d+e x) \log \left(\frac{2 e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{(1-i (d+e x)) \left(e \left(b-\sqrt{b^2-4 a c}\right)+2 c (-d+i)\right)}\right)}{\sqrt{b^2-4 a c}}-\frac{\tan ^{-1}(d+e x) \log \left(\frac{2 e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{(1-i (d+e x)) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (-d+i)\right)}\right)}{\sqrt{b^2-4 a c}}","-\frac{i \text{PolyLog}\left(2,1+\frac{2 \left(-e \left(b-\sqrt{b^2-4 a c}\right)-2 c (d+e x)+2 c d\right)}{(1-i (d+e x)) \left(-e \sqrt{b^2-4 a c}+b e-2 c d+2 i c\right)}\right)}{2 \sqrt{b^2-4 a c}}+\frac{i \text{PolyLog}\left(2,1+\frac{2 \left(-e \left(\sqrt{b^2-4 a c}+b\right)-2 c (d+e x)+2 c d\right)}{(1-i (d+e x)) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (-d+i)\right)}\right)}{2 \sqrt{b^2-4 a c}}+\frac{\tan ^{-1}(d+e x) \log \left(\frac{2 e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{(1-i (d+e x)) \left(e \left(b-\sqrt{b^2-4 a c}\right)+2 c (-d+i)\right)}\right)}{\sqrt{b^2-4 a c}}-\frac{\tan ^{-1}(d+e x) \log \left(\frac{2 e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{(1-i (d+e x)) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (-d+i)\right)}\right)}{\sqrt{b^2-4 a c}}",1,"(ArcTan[d + e*x]*Log[(2*e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*(I - d) + (b - Sqrt[b^2 - 4*a*c])*e)*(1 - I*(d + e*x)))])/Sqrt[b^2 - 4*a*c] - (ArcTan[d + e*x]*Log[(2*e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*(I - d) + (b + Sqrt[b^2 - 4*a*c])*e)*(1 - I*(d + e*x)))])/Sqrt[b^2 - 4*a*c] - ((I/2)*PolyLog[2, 1 + (2*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e - 2*c*(d + e*x)))/(((2*I)*c - 2*c*d + b*e - Sqrt[b^2 - 4*a*c]*e)*(1 - I*(d + e*x)))])/Sqrt[b^2 - 4*a*c] + ((I/2)*PolyLog[2, 1 + (2*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e - 2*c*(d + e*x)))/((2*c*(I - d) + (b + Sqrt[b^2 - 4*a*c])*e)*(1 - I*(d + e*x)))])/Sqrt[b^2 - 4*a*c]","A",12,8,19,0.4211,1,"{618, 206, 6728, 5047, 4856, 2402, 2315, 2447}"
63,1,132,0,0.0962101,"\int \frac{\tan ^{-1}(a+b x)}{\sqrt{1+a^2+2 a b x+b^2 x^2}} \, dx","Int[ArcTan[a + b*x]/Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2],x]","\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b}-\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b}-\frac{2 i \tan ^{-1}(a+b x) \tan ^{-1}\left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b}","\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b}-\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b}-\frac{2 i \tan ^{-1}(a+b x) \tan ^{-1}\left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b}",1,"((-2*I)*ArcTan[a + b*x]*ArcTan[Sqrt[1 + I*(a + b*x)]/Sqrt[1 - I*(a + b*x)]])/b + (I*PolyLog[2, ((-I)*Sqrt[1 + I*(a + b*x)])/Sqrt[1 - I*(a + b*x)]])/b - (I*PolyLog[2, (I*Sqrt[1 + I*(a + b*x)])/Sqrt[1 - I*(a + b*x)]])/b","A",2,2,28,0.07143,1,"{5055, 4886}"
64,1,216,0,0.1622883,"\int \frac{\tan ^{-1}(a+b x)}{\sqrt{\left(1+a^2\right) c+2 a b c x+b^2 c x^2}} \, dx","Int[ArcTan[a + b*x]/Sqrt[(1 + a^2)*c + 2*a*b*c*x + b^2*c*x^2],x]","\frac{i \sqrt{(a+b x)^2+1} \text{PolyLog}\left(2,-\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b \sqrt{c (a+b x)^2+c}}-\frac{i \sqrt{(a+b x)^2+1} \text{PolyLog}\left(2,\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b \sqrt{c (a+b x)^2+c}}-\frac{2 i \sqrt{(a+b x)^2+1} \tan ^{-1}(a+b x) \tan ^{-1}\left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b \sqrt{c (a+b x)^2+c}}","\frac{i \sqrt{(a+b x)^2+1} \text{PolyLog}\left(2,-\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b \sqrt{c (a+b x)^2+c}}-\frac{i \sqrt{(a+b x)^2+1} \text{PolyLog}\left(2,\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b \sqrt{c (a+b x)^2+c}}-\frac{2 i \sqrt{(a+b x)^2+1} \tan ^{-1}(a+b x) \tan ^{-1}\left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{b \sqrt{c (a+b x)^2+c}}",1,"((-2*I)*Sqrt[1 + (a + b*x)^2]*ArcTan[a + b*x]*ArcTan[Sqrt[1 + I*(a + b*x)]/Sqrt[1 - I*(a + b*x)]])/(b*Sqrt[c + c*(a + b*x)^2]) + (I*Sqrt[1 + (a + b*x)^2]*PolyLog[2, ((-I)*Sqrt[1 + I*(a + b*x)])/Sqrt[1 - I*(a + b*x)]])/(b*Sqrt[c + c*(a + b*x)^2]) - (I*Sqrt[1 + (a + b*x)^2]*PolyLog[2, (I*Sqrt[1 + I*(a + b*x)])/Sqrt[1 - I*(a + b*x)]])/(b*Sqrt[c + c*(a + b*x)^2])","A",3,3,33,0.09091,1,"{5055, 4890, 4886}"
65,0,0,0,0.0379871,"\int \frac{\tan ^{-1}(a+b x)}{\sqrt[3]{1+a^2+2 a b x+b^2 x^2}} \, dx","Int[ArcTan[a + b*x]/(1 + a^2 + 2*a*b*x + b^2*x^2)^(1/3),x]","\int \frac{\tan ^{-1}(a+b x)}{\sqrt[3]{1+a^2+2 a b x+b^2 x^2}} \, dx","\text{Int}\left(\frac{\tan ^{-1}(a+b x)}{\sqrt[3]{(a+b x)^2+1}},x\right)",0,"Defer[Subst][Defer[Int][ArcTan[x]/(1 + x^2)^(1/3), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"
66,0,0,0,0.0505649,"\int \frac{\tan ^{-1}(a+b x)}{\sqrt[3]{\left(1+a^2\right) c+2 a b c x+b^2 c x^2}} \, dx","Int[ArcTan[a + b*x]/((1 + a^2)*c + 2*a*b*c*x + b^2*c*x^2)^(1/3),x]","\int \frac{\tan ^{-1}(a+b x)}{\sqrt[3]{\left(1+a^2\right) c+2 a b c x+b^2 c x^2}} \, dx","\text{Int}\left(\frac{\tan ^{-1}(a+b x)}{\sqrt[3]{c (a+b x)^2+c}},x\right)",0,"Defer[Subst][Defer[Int][ArcTan[x]/(c + c*x^2)^(1/3), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"
67,1,187,0,0.2157839,"\int \frac{(a+b x)^2 \tan ^{-1}(a+b x)}{\sqrt{1+a^2+2 a b x+b^2 x^2}} \, dx","Int[((a + b*x)^2*ArcTan[a + b*x])/Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2],x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{2 b}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{2 b}-\frac{\sqrt{(a+b x)^2+1}}{2 b}+\frac{i \tan ^{-1}\left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right) \tan ^{-1}(a+b x)}{b}+\frac{(a+b x) \sqrt{(a+b x)^2+1} \tan ^{-1}(a+b x)}{2 b}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{2 b}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{2 b}-\frac{\sqrt{(a+b x)^2+1}}{2 b}+\frac{i \tan ^{-1}\left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right) \tan ^{-1}(a+b x)}{b}+\frac{(a+b x) \sqrt{(a+b x)^2+1} \tan ^{-1}(a+b x)}{2 b}",1,"-Sqrt[1 + (a + b*x)^2]/(2*b) + ((a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcTan[a + b*x])/(2*b) + (I*ArcTan[a + b*x]*ArcTan[Sqrt[1 + I*(a + b*x)]/Sqrt[1 - I*(a + b*x)]])/b - ((I/2)*PolyLog[2, ((-I)*Sqrt[1 + I*(a + b*x)])/Sqrt[1 - I*(a + b*x)]])/b + ((I/2)*PolyLog[2, (I*Sqrt[1 + I*(a + b*x)])/Sqrt[1 - I*(a + b*x)]])/b","A",4,4,35,0.1143,1,"{5057, 4952, 261, 4886}"
68,1,281,0,0.3310048,"\int \frac{(a+b x)^2 \tan ^{-1}(a+b x)}{\sqrt{\left(1+a^2\right) c+2 a b c x+b^2 c x^2}} \, dx","Int[((a + b*x)^2*ArcTan[a + b*x])/Sqrt[(1 + a^2)*c + 2*a*b*c*x + b^2*c*x^2],x]","-\frac{i \sqrt{(a+b x)^2+1} \text{PolyLog}\left(2,-\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{2 b \sqrt{c (a+b x)^2+c}}+\frac{i \sqrt{(a+b x)^2+1} \text{PolyLog}\left(2,\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{2 b \sqrt{c (a+b x)^2+c}}-\frac{\sqrt{c (a+b x)^2+c}}{2 b c}+\frac{i \sqrt{(a+b x)^2+1} \tan ^{-1}\left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right) \tan ^{-1}(a+b x)}{b \sqrt{c (a+b x)^2+c}}+\frac{(a+b x) \sqrt{c (a+b x)^2+c} \tan ^{-1}(a+b x)}{2 b c}","-\frac{i \sqrt{(a+b x)^2+1} \text{PolyLog}\left(2,-\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{2 b \sqrt{c (a+b x)^2+c}}+\frac{i \sqrt{(a+b x)^2+1} \text{PolyLog}\left(2,\frac{i \sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right)}{2 b \sqrt{c (a+b x)^2+c}}-\frac{\sqrt{c (a+b x)^2+c}}{2 b c}+\frac{i \sqrt{(a+b x)^2+1} \tan ^{-1}\left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}\right) \tan ^{-1}(a+b x)}{b \sqrt{c (a+b x)^2+c}}+\frac{(a+b x) \sqrt{c (a+b x)^2+c} \tan ^{-1}(a+b x)}{2 b c}",1,"-Sqrt[c + c*(a + b*x)^2]/(2*b*c) + ((a + b*x)*Sqrt[c + c*(a + b*x)^2]*ArcTan[a + b*x])/(2*b*c) + (I*Sqrt[1 + (a + b*x)^2]*ArcTan[a + b*x]*ArcTan[Sqrt[1 + I*(a + b*x)]/Sqrt[1 - I*(a + b*x)]])/(b*Sqrt[c + c*(a + b*x)^2]) - ((I/2)*Sqrt[1 + (a + b*x)^2]*PolyLog[2, ((-I)*Sqrt[1 + I*(a + b*x)])/Sqrt[1 - I*(a + b*x)]])/(b*Sqrt[c + c*(a + b*x)^2]) + ((I/2)*Sqrt[1 + (a + b*x)^2]*PolyLog[2, (I*Sqrt[1 + I*(a + b*x)])/Sqrt[1 - I*(a + b*x)]])/(b*Sqrt[c + c*(a + b*x)^2])","A",5,5,40,0.1250,1,"{5057, 4952, 261, 4890, 4886}"
69,0,0,0,0.1311723,"\int \frac{(a+b x)^2 \tan ^{-1}(a+b x)}{\sqrt[3]{1+a^2+2 a b x+b^2 x^2}} \, dx","Int[((a + b*x)^2*ArcTan[a + b*x])/(1 + a^2 + 2*a*b*x + b^2*x^2)^(1/3),x]","\int \frac{(a+b x)^2 \tan ^{-1}(a+b x)}{\sqrt[3]{1+a^2+2 a b x+b^2 x^2}} \, dx","\text{Int}\left(\frac{(a+b x)^2 \tan ^{-1}(a+b x)}{\sqrt[3]{(a+b x)^2+1}},x\right)",0,"Defer[Subst][Defer[Int][(x^2*ArcTan[x])/(1 + x^2)^(1/3), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"
70,0,0,0,0.1790795,"\int \frac{(a+b x)^2 \tan ^{-1}(a+b x)}{\sqrt[3]{\left(1+a^2\right) c+2 a b c x+b^2 c x^2}} \, dx","Int[((a + b*x)^2*ArcTan[a + b*x])/((1 + a^2)*c + 2*a*b*c*x + b^2*c*x^2)^(1/3),x]","\int \frac{(a+b x)^2 \tan ^{-1}(a+b x)}{\sqrt[3]{\left(1+a^2\right) c+2 a b c x+b^2 c x^2}} \, dx","\text{Int}\left(\frac{(a+b x)^2 \tan ^{-1}(a+b x)}{\sqrt[3]{c (a+b x)^2+c}},x\right)",0,"Defer[Subst][Defer[Int][(x^2*ArcTan[x])/(c + c*x^2)^(1/3), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"