1,1,149,0,0.1405746,"\int (d+e x)^4 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[(d + e*x)^4*(a + b*ArcTanh[c*x]),x]","\frac{(d+e x)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 e}+\frac{b e^2 x^2 \left(10 c^2 d^2+e^2\right)}{10 c^3}+\frac{b d e x \left(2 c^2 d^2+e^2\right)}{c^3}-\frac{b (c d-e)^5 \log (c x+1)}{10 c^5 e}+\frac{b (c d+e)^5 \log (1-c x)}{10 c^5 e}+\frac{b d e^3 x^3}{3 c}+\frac{b e^4 x^4}{20 c}","\frac{(d+e x)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 e}+\frac{b e^2 x^2 \left(10 c^2 d^2+e^2\right)}{10 c^3}+\frac{b d e x \left(2 c^2 d^2+e^2\right)}{c^3}-\frac{b (c d-e)^5 \log (c x+1)}{10 c^5 e}+\frac{b (c d+e)^5 \log (1-c x)}{10 c^5 e}+\frac{b d e^3 x^3}{3 c}+\frac{b e^4 x^4}{20 c}",1,"(b*d*e*(2*c^2*d^2 + e^2)*x)/c^3 + (b*e^2*(10*c^2*d^2 + e^2)*x^2)/(10*c^3) + (b*d*e^3*x^3)/(3*c) + (b*e^4*x^4)/(20*c) + ((d + e*x)^5*(a + b*ArcTanh[c*x]))/(5*e) + (b*(c*d + e)^5*Log[1 - c*x])/(10*c^5*e) - (b*(c*d - e)^5*Log[1 + c*x])/(10*c^5*e)","A",6,4,16,0.2500,1,"{5926, 702, 633, 31}"
2,1,125,0,0.1410625,"\int (d+e x)^3 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(a + b*ArcTanh[c*x]),x]","\frac{(d+e x)^4 \left(a+b \tanh ^{-1}(c x)\right)}{4 e}+\frac{b e x \left(6 c^2 d^2+e^2\right)}{4 c^3}-\frac{b (c d-e)^4 \log (c x+1)}{8 c^4 e}+\frac{b (c d+e)^4 \log (1-c x)}{8 c^4 e}+\frac{b d e^2 x^2}{2 c}+\frac{b e^3 x^3}{12 c}","\frac{(d+e x)^4 \left(a+b \tanh ^{-1}(c x)\right)}{4 e}+\frac{b e x \left(6 c^2 d^2+e^2\right)}{4 c^3}-\frac{b (c d-e)^4 \log (c x+1)}{8 c^4 e}+\frac{b (c d+e)^4 \log (1-c x)}{8 c^4 e}+\frac{b d e^2 x^2}{2 c}+\frac{b e^3 x^3}{12 c}",1,"(b*e*(6*c^2*d^2 + e^2)*x)/(4*c^3) + (b*d*e^2*x^2)/(2*c) + (b*e^3*x^3)/(12*c) + ((d + e*x)^4*(a + b*ArcTanh[c*x]))/(4*e) + (b*(c*d + e)^4*Log[1 - c*x])/(8*c^4*e) - (b*(c*d - e)^4*Log[1 + c*x])/(8*c^4*e)","A",6,4,16,0.2500,1,"{5926, 702, 633, 31}"
3,1,96,0,0.1218525,"\int (d+e x)^2 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcTanh[c*x]),x]","\frac{(d+e x)^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 e}-\frac{b (c d-e)^3 \log (c x+1)}{6 c^3 e}+\frac{b (c d+e)^3 \log (1-c x)}{6 c^3 e}+\frac{b d e x}{c}+\frac{b e^2 x^2}{6 c}","\frac{(d+e x)^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 e}-\frac{b (c d-e)^3 \log (c x+1)}{6 c^3 e}+\frac{b (c d+e)^3 \log (1-c x)}{6 c^3 e}+\frac{b d e x}{c}+\frac{b e^2 x^2}{6 c}",1,"(b*d*e*x)/c + (b*e^2*x^2)/(6*c) + ((d + e*x)^3*(a + b*ArcTanh[c*x]))/(3*e) + (b*(c*d + e)^3*Log[1 - c*x])/(6*c^3*e) - (b*(c*d - e)^3*Log[1 + c*x])/(6*c^3*e)","A",6,4,16,0.2500,1,"{5926, 702, 633, 31}"
4,1,84,0,0.0762702,"\int (d+e x) \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[(d + e*x)*(a + b*ArcTanh[c*x]),x]","\frac{(d+e x)^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 e}-\frac{b (c d-e)^2 \log (c x+1)}{4 c^2 e}+\frac{b (c d+e)^2 \log (1-c x)}{4 c^2 e}+\frac{b e x}{2 c}","\frac{(d+e x)^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 e}-\frac{b (c d-e)^2 \log (c x+1)}{4 c^2 e}+\frac{b (c d+e)^2 \log (1-c x)}{4 c^2 e}+\frac{b e x}{2 c}",1,"(b*e*x)/(2*c) + ((d + e*x)^2*(a + b*ArcTanh[c*x]))/(2*e) + (b*(c*d + e)^2*Log[1 - c*x])/(4*c^2*e) - (b*(c*d - e)^2*Log[1 + c*x])/(4*c^2*e)","A",6,4,14,0.2857,1,"{5926, 702, 633, 31}"
5,1,114,0,0.0807015,"\int \frac{a+b \tanh ^{-1}(c x)}{d+e x} \, dx","Int[(a + b*ArcTanh[c*x])/(d + e*x),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 e}+\frac{\left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e}","-\frac{b \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 e}+\frac{\left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e}",1,"-(((a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/e) + ((a + b*ArcTanh[c*x])*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e + (b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*e) - (b*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*e)","A",4,4,16,0.2500,1,"{5920, 2402, 2315, 2447}"
6,1,93,0,0.0670172,"\int \frac{a+b \tanh ^{-1}(c x)}{(d+e x)^2} \, dx","Int[(a + b*ArcTanh[c*x])/(d + e*x)^2,x]","-\frac{a+b \tanh ^{-1}(c x)}{e (d+e x)}-\frac{b c \log (d+e x)}{c^2 d^2-e^2}-\frac{b c \log (1-c x)}{2 e (c d+e)}+\frac{b c \log (c x+1)}{2 e (c d-e)}","-\frac{a+b \tanh ^{-1}(c x)}{e (d+e x)}-\frac{b c \log (d+e x)}{c^2 d^2-e^2}-\frac{b c \log (1-c x)}{2 e (c d+e)}+\frac{b c \log (c x+1)}{2 e (c d-e)}",1,"-((a + b*ArcTanh[c*x])/(e*(d + e*x))) - (b*c*Log[1 - c*x])/(2*e*(c*d + e)) + (b*c*Log[1 + c*x])/(2*(c*d - e)*e) - (b*c*Log[d + e*x])/(c^2*d^2 - e^2)","A",6,4,16,0.2500,1,"{5926, 706, 31, 633}"
7,1,130,0,0.1294297,"\int \frac{a+b \tanh ^{-1}(c x)}{(d+e x)^3} \, dx","Int[(a + b*ArcTanh[c*x])/(d + e*x)^3,x]","-\frac{a+b \tanh ^{-1}(c x)}{2 e (d+e x)^2}+\frac{b c}{2 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{b c^3 d \log (d+e x)}{\left(c^2 d^2-e^2\right)^2}-\frac{b c^2 \log (1-c x)}{4 e (c d+e)^2}+\frac{b c^2 \log (c x+1)}{4 e (c d-e)^2}","-\frac{a+b \tanh ^{-1}(c x)}{2 e (d+e x)^2}+\frac{b c}{2 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{b c^3 d \log (d+e x)}{\left(c^2 d^2-e^2\right)^2}-\frac{b c^2 \log (1-c x)}{4 e (c d+e)^2}+\frac{b c^2 \log (c x+1)}{4 e (c d-e)^2}",1,"(b*c)/(2*(c^2*d^2 - e^2)*(d + e*x)) - (a + b*ArcTanh[c*x])/(2*e*(d + e*x)^2) - (b*c^2*Log[1 - c*x])/(4*e*(c*d + e)^2) + (b*c^2*Log[1 + c*x])/(4*(c*d - e)^2*e) - (b*c^3*d*Log[d + e*x])/(c^2*d^2 - e^2)^2","A",4,3,16,0.1875,1,"{5926, 710, 801}"
8,1,175,0,0.1884817,"\int \frac{a+b \tanh ^{-1}(c x)}{(d+e x)^4} \, dx","Int[(a + b*ArcTanh[c*x])/(d + e*x)^4,x]","-\frac{a+b \tanh ^{-1}(c x)}{3 e (d+e x)^3}+\frac{2 b c^3 d}{3 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c}{6 \left(c^2 d^2-e^2\right) (d+e x)^2}-\frac{b c^3 \left(3 c^2 d^2+e^2\right) \log (d+e x)}{3 (c d-e)^3 (c d+e)^3}-\frac{b c^3 \log (1-c x)}{6 e (c d+e)^3}+\frac{b c^3 \log (c x+1)}{6 e (c d-e)^3}","-\frac{a+b \tanh ^{-1}(c x)}{3 e (d+e x)^3}+\frac{2 b c^3 d}{3 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c}{6 \left(c^2 d^2-e^2\right) (d+e x)^2}-\frac{b c^3 \left(3 c^2 d^2+e^2\right) \log (d+e x)}{3 (c d-e)^3 (c d+e)^3}-\frac{b c^3 \log (1-c x)}{6 e (c d+e)^3}+\frac{b c^3 \log (c x+1)}{6 e (c d-e)^3}",1,"(b*c)/(6*(c^2*d^2 - e^2)*(d + e*x)^2) + (2*b*c^3*d)/(3*(c^2*d^2 - e^2)^2*(d + e*x)) - (a + b*ArcTanh[c*x])/(3*e*(d + e*x)^3) - (b*c^3*Log[1 - c*x])/(6*e*(c*d + e)^3) + (b*c^3*Log[1 + c*x])/(6*(c*d - e)^3*e) - (b*c^3*(3*c^2*d^2 + e^2)*Log[d + e*x])/(3*(c*d - e)^3*(c*d + e)^3)","A",4,3,16,0.1875,1,"{5926, 710, 801}"
9,1,359,0,0.533985,"\int (d+e x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^3*(a + b*ArcTanh[c*x])^2,x]","-\frac{b^2 d \left(c^2 d^2+e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^3}+\frac{a b e x \left(6 c^2 d^2+e^2\right)}{2 c^3}+\frac{d \left(c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3}-\frac{\left(6 c^2 d^2 e^2+c^4 d^4+e^4\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^4 e}-\frac{2 b d \left(c^2 d^2+e^2\right) \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3}+\frac{b d e^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{c}+\frac{(d+e x)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 e}+\frac{b e^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 c}+\frac{b^2 e \left(6 c^2 d^2+e^2\right) \log \left(1-c^2 x^2\right)}{4 c^4}+\frac{b^2 e x \left(6 c^2 d^2+e^2\right) \tanh ^{-1}(c x)}{2 c^3}+\frac{b^2 d e^2 x}{c^2}-\frac{b^2 d e^2 \tanh ^{-1}(c x)}{c^3}+\frac{b^2 e^3 x^2}{12 c^2}+\frac{b^2 e^3 \log \left(1-c^2 x^2\right)}{12 c^4}","-\frac{b^2 d \left(c^2 d^2+e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^3}+\frac{a b e x \left(6 c^2 d^2+e^2\right)}{2 c^3}+\frac{d \left(c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3}-\frac{\left(6 c^2 d^2 e^2+c^4 d^4+e^4\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^4 e}-\frac{2 b d \left(c^2 d^2+e^2\right) \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3}+\frac{b d e^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{c}+\frac{(d+e x)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 e}+\frac{b e^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 c}+\frac{b^2 e \left(6 c^2 d^2+e^2\right) \log \left(1-c^2 x^2\right)}{4 c^4}+\frac{b^2 e x \left(6 c^2 d^2+e^2\right) \tanh ^{-1}(c x)}{2 c^3}+\frac{b^2 d e^2 x}{c^2}-\frac{b^2 d e^2 \tanh ^{-1}(c x)}{c^3}+\frac{b^2 e^3 x^2}{12 c^2}+\frac{b^2 e^3 \log \left(1-c^2 x^2\right)}{12 c^4}",1,"(b^2*d*e^2*x)/c^2 + (a*b*e*(6*c^2*d^2 + e^2)*x)/(2*c^3) + (b^2*e^3*x^2)/(12*c^2) - (b^2*d*e^2*ArcTanh[c*x])/c^3 + (b^2*e*(6*c^2*d^2 + e^2)*x*ArcTanh[c*x])/(2*c^3) + (b*d*e^2*x^2*(a + b*ArcTanh[c*x]))/c + (b*e^3*x^3*(a + b*ArcTanh[c*x]))/(6*c) + (d*(c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])^2)/c^3 - ((c^4*d^4 + 6*c^2*d^2*e^2 + e^4)*(a + b*ArcTanh[c*x])^2)/(4*c^4*e) + ((d + e*x)^4*(a + b*ArcTanh[c*x])^2)/(4*e) - (2*b*d*(c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c^3 + (b^2*e^3*Log[1 - c^2*x^2])/(12*c^4) + (b^2*e*(6*c^2*d^2 + e^2)*Log[1 - c^2*x^2])/(4*c^4) - (b^2*d*(c^2*d^2 + e^2)*PolyLog[2, 1 - 2/(1 - c*x)])/c^3","A",19,14,18,0.7778,1,"{5928, 5910, 260, 5916, 321, 206, 266, 43, 6048, 5948, 5984, 5918, 2402, 2315}"
10,1,257,0,0.4085353,"\int (d+e x)^2 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^2*(a + b*ArcTanh[c*x])^2,x]","-\frac{b^2 \left(3 c^2 d^2+e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^3}+\frac{\left(3 c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{3 c^3}-\frac{d \left(\frac{3 e^2}{c^2}+d^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{3 e}-\frac{2 b \left(3 c^2 d^2+e^2\right) \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^3}+\frac{2 a b d e x}{c}+\frac{(d+e x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 e}+\frac{b e^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 c}+\frac{b^2 d e \log \left(1-c^2 x^2\right)}{c^2}+\frac{b^2 e^2 x}{3 c^2}-\frac{b^2 e^2 \tanh ^{-1}(c x)}{3 c^3}+\frac{2 b^2 d e x \tanh ^{-1}(c x)}{c}","-\frac{b^2 \left(3 c^2 d^2+e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^3}+\frac{\left(3 c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{3 c^3}-\frac{d \left(\frac{3 e^2}{c^2}+d^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{3 e}-\frac{2 b \left(3 c^2 d^2+e^2\right) \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^3}+\frac{2 a b d e x}{c}+\frac{(d+e x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 e}+\frac{b e^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 c}+\frac{b^2 d e \log \left(1-c^2 x^2\right)}{c^2}+\frac{b^2 e^2 x}{3 c^2}-\frac{b^2 e^2 \tanh ^{-1}(c x)}{3 c^3}+\frac{2 b^2 d e x \tanh ^{-1}(c x)}{c}",1,"(2*a*b*d*e*x)/c + (b^2*e^2*x)/(3*c^2) - (b^2*e^2*ArcTanh[c*x])/(3*c^3) + (2*b^2*d*e*x*ArcTanh[c*x])/c + (b*e^2*x^2*(a + b*ArcTanh[c*x]))/(3*c) + ((3*c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])^2)/(3*c^3) - (d*(d^2 + (3*e^2)/c^2)*(a + b*ArcTanh[c*x])^2)/(3*e) + ((d + e*x)^3*(a + b*ArcTanh[c*x])^2)/(3*e) - (2*b*(3*c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(3*c^3) + (b^2*d*e*Log[1 - c^2*x^2])/c^2 - (b^2*(3*c^2*d^2 + e^2)*PolyLog[2, 1 - 2/(1 - c*x)])/(3*c^3)","A",15,12,18,0.6667,1,"{5928, 5910, 260, 5916, 321, 206, 6048, 5948, 5984, 5918, 2402, 2315}"
11,1,160,0,0.3299081,"\int (d+e x) \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)*(a + b*ArcTanh[c*x])^2,x]","-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c}-\frac{\left(\frac{e^2}{c^2}+d^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e}+\frac{(d+e x)^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e}+\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{c}-\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+\frac{a b e x}{c}+\frac{b^2 e \log \left(1-c^2 x^2\right)}{2 c^2}+\frac{b^2 e x \tanh ^{-1}(c x)}{c}","-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c}-\frac{\left(\frac{e^2}{c^2}+d^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e}+\frac{(d+e x)^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e}+\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{c}-\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+\frac{a b e x}{c}+\frac{b^2 e \log \left(1-c^2 x^2\right)}{2 c^2}+\frac{b^2 e x \tanh ^{-1}(c x)}{c}",1,"(a*b*e*x)/c + (b^2*e*x*ArcTanh[c*x])/c + (d*(a + b*ArcTanh[c*x])^2)/c - ((d^2 + e^2/c^2)*(a + b*ArcTanh[c*x])^2)/(2*e) + ((d + e*x)^2*(a + b*ArcTanh[c*x])^2)/(2*e) - (2*b*d*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c + (b^2*e*Log[1 - c^2*x^2])/(2*c^2) - (b^2*d*PolyLog[2, 1 - 2/(1 - c*x)])/c","A",12,9,16,0.5625,1,"{5928, 5910, 260, 6048, 5948, 5984, 5918, 2402, 2315}"
12,1,188,0,0.0499903,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d+e x} \, dx","Int[(a + b*ArcTanh[c*x])^2/(d + e*x),x]","-\frac{b \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 e}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{e}","-\frac{b \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 e}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{e}",1,"-(((a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/e) + ((a + b*ArcTanh[c*x])^2*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e + (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/e - (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e + (b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*e) - (b^2*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*e)","A",1,1,18,0.05556,1,"{5922}"
13,1,321,0,0.3128568,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{(d+e x)^2} \, dx","Int[(a + b*ArcTanh[c*x])^2/(d + e*x)^2,x]","-\frac{b^2 c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{c^2 d^2-e^2}+\frac{b^2 c \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{c^2 d^2-e^2}+\frac{b^2 c \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{2 e (c d+e)}+\frac{b^2 c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 e (c d-e)}+\frac{2 b c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d^2-e^2}-\frac{2 b c \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{c^2 d^2-e^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{e (d+e x)}+\frac{b c \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e (c d+e)}-\frac{b c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e (c d-e)}","-\frac{b^2 c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{c^2 d^2-e^2}+\frac{b^2 c \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{c^2 d^2-e^2}+\frac{b^2 c \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{2 e (c d+e)}+\frac{b^2 c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 e (c d-e)}+\frac{2 b c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d^2-e^2}-\frac{2 b c \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{c^2 d^2-e^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{e (d+e x)}+\frac{b c \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e (c d+e)}-\frac{b c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e (c d-e)}",1,"-((a + b*ArcTanh[c*x])^2/(e*(d + e*x))) + (b*c*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(e*(c*d + e)) - (b*c*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/((c*d - e)*e) + (2*b*c*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(c^2*d^2 - e^2) - (2*b*c*(a + b*ArcTanh[c*x])*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(c^2*d^2 - e^2) + (b^2*c*PolyLog[2, 1 - 2/(1 - c*x)])/(2*e*(c*d + e)) + (b^2*c*PolyLog[2, 1 - 2/(1 + c*x)])/(2*(c*d - e)*e) - (b^2*c*PolyLog[2, 1 - 2/(1 + c*x)])/(c^2*d^2 - e^2) + (b^2*c*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(c^2*d^2 - e^2)","A",12,6,18,0.3333,1,"{5928, 5918, 2402, 2315, 5920, 2447}"
14,1,480,0,0.498787,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{(d+e x)^3} \, dx","Int[(a + b*ArcTanh[c*x])^2/(d + e*x)^3,x]","-\frac{b^2 c^3 d \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{(c d-e)^2 (c d+e)^2}+\frac{b^2 c^3 d \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{(c d-e)^2 (c d+e)^2}+\frac{b^2 c^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{4 e (c d+e)^2}+\frac{b^2 c^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{4 e (c d-e)^2}+\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{\left(c^2 d^2-e^2\right) (d+e x)}+\frac{2 b c^3 d \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{(c d-e)^2 (c d+e)^2}-\frac{2 b c^3 d \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{(c d-e)^2 (c d+e)^2}+\frac{b c^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 e (c d+e)^2}-\frac{b c^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 e (c d-e)^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 e (d+e x)^2}+\frac{b^2 c^2 \log (1-c x)}{2 (c d-e) (c d+e)^2}-\frac{b^2 c^2 \log (c x+1)}{2 (c d-e)^2 (c d+e)}+\frac{b^2 c^2 e \log (d+e x)}{(c d-e)^2 (c d+e)^2}","-\frac{b^2 c^3 d \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{(c d-e)^2 (c d+e)^2}+\frac{b^2 c^3 d \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{(c d-e)^2 (c d+e)^2}+\frac{b^2 c^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{4 e (c d+e)^2}+\frac{b^2 c^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{4 e (c d-e)^2}+\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{\left(c^2 d^2-e^2\right) (d+e x)}+\frac{2 b c^3 d \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{(c d-e)^2 (c d+e)^2}-\frac{2 b c^3 d \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{(c d-e)^2 (c d+e)^2}+\frac{b c^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 e (c d+e)^2}-\frac{b c^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 e (c d-e)^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 e (d+e x)^2}+\frac{b^2 c^2 \log (1-c x)}{2 (c d-e) (c d+e)^2}-\frac{b^2 c^2 \log (c x+1)}{2 (c d-e)^2 (c d+e)}+\frac{b^2 c^2 e \log (d+e x)}{(c d-e)^2 (c d+e)^2}",1,"(b*c*(a + b*ArcTanh[c*x]))/((c^2*d^2 - e^2)*(d + e*x)) - (a + b*ArcTanh[c*x])^2/(2*e*(d + e*x)^2) + (b*c^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(2*e*(c*d + e)^2) + (b^2*c^2*Log[1 - c*x])/(2*(c*d - e)*(c*d + e)^2) - (b*c^2*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(2*(c*d - e)^2*e) + (2*b*c^3*d*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/((c*d - e)^2*(c*d + e)^2) - (b^2*c^2*Log[1 + c*x])/(2*(c*d - e)^2*(c*d + e)) + (b^2*c^2*e*Log[d + e*x])/((c*d - e)^2*(c*d + e)^2) - (2*b*c^3*d*(a + b*ArcTanh[c*x])*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/((c*d - e)^2*(c*d + e)^2) + (b^2*c^2*PolyLog[2, 1 - 2/(1 - c*x)])/(4*e*(c*d + e)^2) + (b^2*c^2*PolyLog[2, 1 - 2/(1 + c*x)])/(4*(c*d - e)^2*e) - (b^2*c^3*d*PolyLog[2, 1 - 2/(1 + c*x)])/((c*d - e)^2*(c*d + e)^2) + (b^2*c^3*d*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/((c*d - e)^2*(c*d + e)^2)","A",18,10,18,0.5556,1,"{5928, 5918, 2402, 2315, 5926, 706, 31, 633, 5920, 2447}"
15,1,614,0,1.1828942,"\int (d+e x)^3 \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[(d + e*x)^3*(a + b*ArcTanh[c*x])^3,x]","-\frac{3 b^2 d \left(c^2 d^2+e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3}-\frac{3 b^3 e \left(6 c^2 d^2+e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{4 c^4}+\frac{3 b^3 d \left(c^2 d^2+e^2\right) \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c^3}-\frac{b^3 e^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{4 c^4}-\frac{3 b^2 e \left(6 c^2 d^2+e^2\right) \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 c^4}+\frac{3 a b^2 d e^2 x}{c^2}+\frac{b^2 e^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2}-\frac{b^2 e^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 c^4}+\frac{d \left(c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{c^3}-\frac{\left(6 c^2 d^2 e^2+c^4 d^4+e^4\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{4 c^4 e}+\frac{3 b e \left(6 c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^4}+\frac{3 b e x \left(6 c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^3}-\frac{3 b d \left(c^2 d^2+e^2\right) \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3}-\frac{3 b d e^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3}+\frac{b e^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^4}+\frac{3 b d e^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{(d+e x)^4 \left(a+b \tanh ^{-1}(c x)\right)^3}{4 e}+\frac{b e^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c}+\frac{3 b^3 d e^2 \log \left(1-c^2 x^2\right)}{2 c^3}+\frac{3 b^3 d e^2 x \tanh ^{-1}(c x)}{c^2}+\frac{b^3 e^3 x}{4 c^3}-\frac{b^3 e^3 \tanh ^{-1}(c x)}{4 c^4}","-\frac{3 b^2 d \left(c^2 d^2+e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3}-\frac{3 b^3 e \left(6 c^2 d^2+e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{4 c^4}+\frac{3 b^3 d \left(c^2 d^2+e^2\right) \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c^3}-\frac{b^3 e^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{4 c^4}-\frac{3 b^2 e \left(6 c^2 d^2+e^2\right) \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 c^4}+\frac{3 a b^2 d e^2 x}{c^2}+\frac{b^2 e^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2}-\frac{b^2 e^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 c^4}+\frac{d \left(c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{c^3}-\frac{\left(6 c^2 d^2 e^2+c^4 d^4+e^4\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{4 c^4 e}+\frac{3 b e \left(6 c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^4}+\frac{3 b e x \left(6 c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^3}-\frac{3 b d \left(c^2 d^2+e^2\right) \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3}-\frac{3 b d e^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3}+\frac{b e^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^4}+\frac{3 b d e^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{(d+e x)^4 \left(a+b \tanh ^{-1}(c x)\right)^3}{4 e}+\frac{b e^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c}+\frac{3 b^3 d e^2 \log \left(1-c^2 x^2\right)}{2 c^3}+\frac{3 b^3 d e^2 x \tanh ^{-1}(c x)}{c^2}+\frac{b^3 e^3 x}{4 c^3}-\frac{b^3 e^3 \tanh ^{-1}(c x)}{4 c^4}",1,"(3*a*b^2*d*e^2*x)/c^2 + (b^3*e^3*x)/(4*c^3) - (b^3*e^3*ArcTanh[c*x])/(4*c^4) + (3*b^3*d*e^2*x*ArcTanh[c*x])/c^2 + (b^2*e^3*x^2*(a + b*ArcTanh[c*x]))/(4*c^2) - (3*b*d*e^2*(a + b*ArcTanh[c*x])^2)/(2*c^3) + (b*e^3*(a + b*ArcTanh[c*x])^2)/(4*c^4) + (3*b*e*(6*c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])^2)/(4*c^4) + (3*b*e*(6*c^2*d^2 + e^2)*x*(a + b*ArcTanh[c*x])^2)/(4*c^3) + (3*b*d*e^2*x^2*(a + b*ArcTanh[c*x])^2)/(2*c) + (b*e^3*x^3*(a + b*ArcTanh[c*x])^2)/(4*c) + (d*(c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])^3)/c^3 - ((c^4*d^4 + 6*c^2*d^2*e^2 + e^4)*(a + b*ArcTanh[c*x])^3)/(4*c^4*e) + ((d + e*x)^4*(a + b*ArcTanh[c*x])^3)/(4*e) - (b^2*e^3*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(2*c^4) - (3*b^2*e*(6*c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(2*c^4) - (3*b*d*(c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/c^3 + (3*b^3*d*e^2*Log[1 - c^2*x^2])/(2*c^3) - (b^3*e^3*PolyLog[2, 1 - 2/(1 - c*x)])/(4*c^4) - (3*b^3*e*(6*c^2*d^2 + e^2)*PolyLog[2, 1 - 2/(1 - c*x)])/(4*c^4) - (3*b^2*d*(c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/c^3 + (3*b^3*d*(c^2*d^2 + e^2)*PolyLog[3, 1 - 2/(1 - c*x)])/(2*c^3)","A",29,15,18,0.8333,1,"{5928, 5910, 5984, 5918, 2402, 2315, 5916, 5980, 260, 5948, 321, 206, 6048, 6058, 6610}"
16,1,387,0,0.8037022,"\int (d+e x)^2 \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[(d + e*x)^2*(a + b*ArcTanh[c*x])^3,x]","-\frac{b^2 \left(3 c^2 d^2+e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3}+\frac{b^3 \left(3 c^2 d^2+e^2\right) \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c^3}-\frac{3 b^3 d e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^2}-\frac{6 b^2 d e \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2}+\frac{a b^2 e^2 x}{c^2}+\frac{\left(3 c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{3 c^3}-\frac{d \left(\frac{3 e^2}{c^2}+d^2\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{3 e}-\frac{b \left(3 c^2 d^2+e^2\right) \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3}+\frac{3 b d e \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2}-\frac{b e^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3}+\frac{3 b d e x \left(a+b \tanh ^{-1}(c x)\right)^2}{c}+\frac{(d+e x)^3 \left(a+b \tanh ^{-1}(c x)\right)^3}{3 e}+\frac{b e^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{b^3 e^2 \log \left(1-c^2 x^2\right)}{2 c^3}+\frac{b^3 e^2 x \tanh ^{-1}(c x)}{c^2}","-\frac{b^2 \left(3 c^2 d^2+e^2\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3}+\frac{b^3 \left(3 c^2 d^2+e^2\right) \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c^3}-\frac{3 b^3 d e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^2}-\frac{6 b^2 d e \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2}+\frac{a b^2 e^2 x}{c^2}+\frac{\left(3 c^2 d^2+e^2\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{3 c^3}-\frac{d \left(\frac{3 e^2}{c^2}+d^2\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{3 e}-\frac{b \left(3 c^2 d^2+e^2\right) \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3}+\frac{3 b d e \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2}-\frac{b e^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3}+\frac{3 b d e x \left(a+b \tanh ^{-1}(c x)\right)^2}{c}+\frac{(d+e x)^3 \left(a+b \tanh ^{-1}(c x)\right)^3}{3 e}+\frac{b e^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{b^3 e^2 \log \left(1-c^2 x^2\right)}{2 c^3}+\frac{b^3 e^2 x \tanh ^{-1}(c x)}{c^2}",1,"(a*b^2*e^2*x)/c^2 + (b^3*e^2*x*ArcTanh[c*x])/c^2 + (3*b*d*e*(a + b*ArcTanh[c*x])^2)/c^2 - (b*e^2*(a + b*ArcTanh[c*x])^2)/(2*c^3) + (3*b*d*e*x*(a + b*ArcTanh[c*x])^2)/c + (b*e^2*x^2*(a + b*ArcTanh[c*x])^2)/(2*c) + ((3*c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])^3)/(3*c^3) - (d*(d^2 + (3*e^2)/c^2)*(a + b*ArcTanh[c*x])^3)/(3*e) + ((d + e*x)^3*(a + b*ArcTanh[c*x])^3)/(3*e) - (6*b^2*d*e*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c^2 - (b*(3*c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/c^3 + (b^3*e^2*Log[1 - c^2*x^2])/(2*c^3) - (3*b^3*d*e*PolyLog[2, 1 - 2/(1 - c*x)])/c^2 - (b^2*(3*c^2*d^2 + e^2)*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/c^3 + (b^3*(3*c^2*d^2 + e^2)*PolyLog[3, 1 - 2/(1 - c*x)])/(2*c^3)","A",20,13,18,0.7222,1,"{5928, 5910, 5984, 5918, 2402, 2315, 5916, 5980, 260, 5948, 6048, 6058, 6610}"
17,1,244,0,0.6017917,"\int (d+e x) \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[(d + e*x)*(a + b*ArcTanh[c*x])^3,x]","-\frac{3 b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}-\frac{3 b^3 e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{2 c^2}+\frac{3 b^3 d \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c}-\frac{3 b^2 e \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2}-\frac{\left(\frac{e^2}{c^2}+d^2\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{2 e}+\frac{3 b e \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2}+\frac{(d+e x)^2 \left(a+b \tanh ^{-1}(c x)\right)^3}{2 e}+\frac{d \left(a+b \tanh ^{-1}(c x)\right)^3}{c}-\frac{3 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c}+\frac{3 b e x \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}","-\frac{3 b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}-\frac{3 b^3 e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{2 c^2}+\frac{3 b^3 d \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c}-\frac{3 b^2 e \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2}-\frac{\left(\frac{e^2}{c^2}+d^2\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{2 e}+\frac{3 b e \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2}+\frac{(d+e x)^2 \left(a+b \tanh ^{-1}(c x)\right)^3}{2 e}+\frac{d \left(a+b \tanh ^{-1}(c x)\right)^3}{c}-\frac{3 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c}+\frac{3 b e x \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}",1,"(3*b*e*(a + b*ArcTanh[c*x])^2)/(2*c^2) + (3*b*e*x*(a + b*ArcTanh[c*x])^2)/(2*c) + (d*(a + b*ArcTanh[c*x])^3)/c - ((d^2 + e^2/c^2)*(a + b*ArcTanh[c*x])^3)/(2*e) + ((d + e*x)^2*(a + b*ArcTanh[c*x])^3)/(2*e) - (3*b^2*e*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c^2 - (3*b*d*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/c - (3*b^3*e*PolyLog[2, 1 - 2/(1 - c*x)])/(2*c^2) - (3*b^2*d*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/c + (3*b^3*d*PolyLog[3, 1 - 2/(1 - c*x)])/(2*c)","A",14,10,16,0.6250,1,"{5928, 5910, 5984, 5918, 2402, 2315, 6048, 5948, 6058, 6610}"
18,1,272,0,0.0566941,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{d+e x} \, dx","Int[(a + b*ArcTanh[c*x])^3/(d + e*x),x]","-\frac{3 b^2 \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 e}-\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e}-\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{4 e}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{c x+1}\right)}{4 e}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{e}","-\frac{3 b^2 \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 e}-\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e}-\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{4 e}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{c x+1}\right)}{4 e}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{e}",1,"-(((a + b*ArcTanh[c*x])^3*Log[2/(1 + c*x)])/e) + ((a + b*ArcTanh[c*x])^3*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e + (3*b*(a + b*ArcTanh[c*x])^2*PolyLog[2, 1 - 2/(1 + c*x)])/(2*e) - (3*b*(a + b*ArcTanh[c*x])^2*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*e) + (3*b^2*(a + b*ArcTanh[c*x])*PolyLog[3, 1 - 2/(1 + c*x)])/(2*e) - (3*b^2*(a + b*ArcTanh[c*x])*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*e) + (3*b^3*PolyLog[4, 1 - 2/(1 + c*x)])/(4*e) - (3*b^3*PolyLog[4, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(4*e)","A",1,1,18,0.05556,1,"{5924}"
19,1,517,0,0.5248299,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{(d+e x)^2} \, dx","Int[(a + b*ArcTanh[c*x])^3/(d + e*x)^2,x]","-\frac{3 b^2 c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d^2-e^2}+\frac{3 b^2 c \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{c^2 d^2-e^2}+\frac{3 b^2 c \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 e (c d+e)}+\frac{3 b^2 c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 e (c d-e)}-\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 \left(c^2 d^2-e^2\right)}+\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 \left(c^2 d^2-e^2\right)}-\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{4 e (c d+e)}+\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{4 e (c d-e)}+\frac{3 b c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d^2-e^2}-\frac{3 b c \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{c^2 d^2-e^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{e (d+e x)}+\frac{3 b c \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e (c d+e)}-\frac{3 b c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e (c d-e)}","-\frac{3 b^2 c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d^2-e^2}+\frac{3 b^2 c \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{c^2 d^2-e^2}+\frac{3 b^2 c \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 e (c d+e)}+\frac{3 b^2 c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 e (c d-e)}-\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 \left(c^2 d^2-e^2\right)}+\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 \left(c^2 d^2-e^2\right)}-\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{4 e (c d+e)}+\frac{3 b^3 c \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{4 e (c d-e)}+\frac{3 b c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d^2-e^2}-\frac{3 b c \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{c^2 d^2-e^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{e (d+e x)}+\frac{3 b c \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e (c d+e)}-\frac{3 b c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e (c d-e)}",1,"-((a + b*ArcTanh[c*x])^3/(e*(d + e*x))) + (3*b*c*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/(2*e*(c*d + e)) - (3*b*c*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(2*(c*d - e)*e) + (3*b*c*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c^2*d^2 - e^2) - (3*b*c*(a + b*ArcTanh[c*x])^2*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(c^2*d^2 - e^2) + (3*b^2*c*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/(2*e*(c*d + e)) + (3*b^2*c*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(2*(c*d - e)*e) - (3*b^2*c*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c^2*d^2 - e^2) + (3*b^2*c*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(c^2*d^2 - e^2) - (3*b^3*c*PolyLog[3, 1 - 2/(1 - c*x)])/(4*e*(c*d + e)) + (3*b^3*c*PolyLog[3, 1 - 2/(1 + c*x)])/(4*(c*d - e)*e) - (3*b^3*c*PolyLog[3, 1 - 2/(1 + c*x)])/(2*(c^2*d^2 - e^2)) + (3*b^3*c*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*(c^2*d^2 - e^2))","A",9,7,18,0.3889,1,"{5928, 5918, 5948, 6058, 6610, 6056, 5922}"
20,1,953,0,1.0271261,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{(d+e x)^3} \, dx","Int[(a + b*ArcTanh[c*x])^3/(d + e*x)^3,x]","-\frac{3 c^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) b^3}{4 (c d-e) (c d+e)^2}-\frac{3 c^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) b^3}{4 (c d-e)^2 (c d+e)}+\frac{3 c^2 e \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) b^3}{2 (c d-e)^2 (c d+e)^2}-\frac{3 c^2 e \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c d+e) (c x+1)}\right) b^3}{2 (c d-e)^2 (c d+e)^2}-\frac{3 c^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right) b^3}{8 e (c d+e)^2}+\frac{3 c^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right) b^3}{8 (c d-e)^2 e}-\frac{3 c^3 d \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right) b^3}{2 (c d-e)^2 (c d+e)^2}+\frac{3 c^3 d \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c d+e) (c x+1)}\right) b^3}{2 (c d-e)^2 (c d+e)^2}-\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2}{1-c x}\right) b^2}{2 (c d-e) (c d+e)^2}+\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2}{c x+1}\right) b^2}{2 (c d-e)^2 (c d+e)}-\frac{3 c^2 e \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2}{c x+1}\right) b^2}{(c d-e)^2 (c d+e)^2}+\frac{3 c^2 e \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c d+e) (c x+1)}\right) b^2}{(c d-e)^2 (c d+e)^2}+\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) b^2}{4 e (c d+e)^2}+\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) b^2}{4 (c d-e)^2 e}-\frac{3 c^3 d \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) b^2}{(c d-e)^2 (c d+e)^2}+\frac{3 c^3 d \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c d+e) (c x+1)}\right) b^2}{(c d-e)^2 (c d+e)^2}+\frac{3 c \left(a+b \tanh ^{-1}(c x)\right)^2 b}{2 \left(c^2 d^2-e^2\right) (d+e x)}+\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2}{1-c x}\right) b}{4 e (c d+e)^2}-\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2}{c x+1}\right) b}{4 (c d-e)^2 e}+\frac{3 c^3 d \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2}{c x+1}\right) b}{(c d-e)^2 (c d+e)^2}-\frac{3 c^3 d \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(c d+e) (c x+1)}\right) b}{(c d-e)^2 (c d+e)^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{2 e (d+e x)^2}","-\frac{3 c^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) b^3}{4 (c d-e) (c d+e)^2}-\frac{3 c^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) b^3}{4 (c d-e)^2 (c d+e)}+\frac{3 c^2 e \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) b^3}{2 (c d-e)^2 (c d+e)^2}-\frac{3 c^2 e \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c d+e) (c x+1)}\right) b^3}{2 (c d-e)^2 (c d+e)^2}-\frac{3 c^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right) b^3}{8 e (c d+e)^2}+\frac{3 c^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right) b^3}{8 (c d-e)^2 e}-\frac{3 c^3 d \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right) b^3}{2 (c d-e)^2 (c d+e)^2}+\frac{3 c^3 d \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c d+e) (c x+1)}\right) b^3}{2 (c d-e)^2 (c d+e)^2}-\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2}{1-c x}\right) b^2}{2 (c d-e) (c d+e)^2}+\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2}{c x+1}\right) b^2}{2 (c d-e)^2 (c d+e)}-\frac{3 c^2 e \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2}{c x+1}\right) b^2}{(c d-e)^2 (c d+e)^2}+\frac{3 c^2 e \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c d+e) (c x+1)}\right) b^2}{(c d-e)^2 (c d+e)^2}+\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) b^2}{4 e (c d+e)^2}+\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) b^2}{4 (c d-e)^2 e}-\frac{3 c^3 d \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) b^2}{(c d-e)^2 (c d+e)^2}+\frac{3 c^3 d \left(a+b \tanh ^{-1}(c x)\right) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c d+e) (c x+1)}\right) b^2}{(c d-e)^2 (c d+e)^2}+\frac{3 c \left(a+b \tanh ^{-1}(c x)\right)^2 b}{2 \left(c^2 d^2-e^2\right) (d+e x)}+\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2}{1-c x}\right) b}{4 e (c d+e)^2}-\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2}{c x+1}\right) b}{4 (c d-e)^2 e}+\frac{3 c^3 d \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2}{c x+1}\right) b}{(c d-e)^2 (c d+e)^2}-\frac{3 c^3 d \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(c d+e) (c x+1)}\right) b}{(c d-e)^2 (c d+e)^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{2 e (d+e x)^2}",1,"(3*b*c*(a + b*ArcTanh[c*x])^2)/(2*(c^2*d^2 - e^2)*(d + e*x)) - (a + b*ArcTanh[c*x])^3/(2*e*(d + e*x)^2) - (3*b^2*c^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(2*(c*d - e)*(c*d + e)^2) + (3*b*c^2*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/(4*e*(c*d + e)^2) - (3*b^2*c^2*e*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/((c*d - e)^2*(c*d + e)^2) + (3*b^2*c^2*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(2*(c*d - e)^2*(c*d + e)) - (3*b*c^2*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(4*(c*d - e)^2*e) + (3*b*c^3*d*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/((c*d - e)^2*(c*d + e)^2) + (3*b^2*c^2*e*(a + b*ArcTanh[c*x])*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/((c*d - e)^2*(c*d + e)^2) - (3*b*c^3*d*(a + b*ArcTanh[c*x])^2*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/((c*d - e)^2*(c*d + e)^2) - (3*b^3*c^2*PolyLog[2, 1 - 2/(1 - c*x)])/(4*(c*d - e)*(c*d + e)^2) + (3*b^2*c^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/(4*e*(c*d + e)^2) + (3*b^3*c^2*e*PolyLog[2, 1 - 2/(1 + c*x)])/(2*(c*d - e)^2*(c*d + e)^2) - (3*b^3*c^2*PolyLog[2, 1 - 2/(1 + c*x)])/(4*(c*d - e)^2*(c*d + e)) + (3*b^2*c^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(4*(c*d - e)^2*e) - (3*b^2*c^3*d*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/((c*d - e)^2*(c*d + e)^2) - (3*b^3*c^2*e*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*(c*d - e)^2*(c*d + e)^2) + (3*b^2*c^3*d*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/((c*d - e)^2*(c*d + e)^2) - (3*b^3*c^2*PolyLog[3, 1 - 2/(1 - c*x)])/(8*e*(c*d + e)^2) + (3*b^3*c^2*PolyLog[3, 1 - 2/(1 + c*x)])/(8*(c*d - e)^2*e) - (3*b^3*c^3*d*PolyLog[3, 1 - 2/(1 + c*x)])/(2*(c*d - e)^2*(c*d + e)^2) + (3*b^3*c^3*d*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*(c*d - e)^2*(c*d + e)^2)","A",21,11,18,0.6111,1,"{5928, 5918, 5948, 6058, 6610, 6056, 2402, 2315, 5920, 2447, 5922}"
21,1,109,0,0.0697833,"\int \frac{a+b \tanh ^{-1}(c x)}{1+2 c x} \, dx","Int[(a + b*ArcTanh[c*x])/(1 + 2*c*x),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{4 c}-\frac{b \text{PolyLog}\left(2,1-\frac{2 (2 c x+1)}{3 (c x+1)}\right)}{4 c}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 c}+\frac{\log \left(\frac{2 (2 c x+1)}{3 (c x+1)}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 c}","-\frac{b \text{PolyLog}(2,-2 c x-1)}{4 c}+\frac{b \text{PolyLog}\left(2,\frac{1}{3} (2 c x+1)\right)}{4 c}+\frac{\left(a-b \tanh ^{-1}\left(\frac{1}{2}\right)\right) \log \left(-\frac{2 c x+1}{2 d}\right)}{2 c}",1,"-((a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(2*c) + ((a + b*ArcTanh[c*x])*Log[(2*(1 + 2*c*x))/(3*(1 + c*x))])/(2*c) + (b*PolyLog[2, 1 - 2/(1 + c*x)])/(4*c) - (b*PolyLog[2, 1 - (2*(1 + 2*c*x))/(3*(1 + c*x))])/(4*c)","A",4,4,17,0.2353,1,"{5920, 2402, 2315, 2447}"
22,1,108,0,0.0660324,"\int \frac{\tanh ^{-1}(x)}{1-\sqrt{2} x} \, dx","Int[ArcTanh[x]/(1 - Sqrt[2]*x),x]","-\frac{\text{PolyLog}\left(2,1-\frac{2}{x+1}\right)}{2 \sqrt{2}}+\frac{\text{PolyLog}\left(2,\frac{2 \left(1+\sqrt{2}\right) \left(1-\sqrt{2} x\right)}{x+1}+1\right)}{2 \sqrt{2}}+\frac{\log \left(\frac{2}{x+1}\right) \tanh ^{-1}(x)}{\sqrt{2}}-\frac{\log \left(-\frac{2 \left(1+\sqrt{2}\right) \left(1-\sqrt{2} x\right)}{x+1}\right) \tanh ^{-1}(x)}{\sqrt{2}}","-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{2}-2 x}{2-\sqrt{2}}\right)}{2 \sqrt{2}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{2}-2 x}{2+\sqrt{2}}\right)}{2 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{1}{\sqrt{2}}\right) \log \left(1-\sqrt{2} x\right)}{\sqrt{2}}",1,"(ArcTanh[x]*Log[2/(1 + x)])/Sqrt[2] - (ArcTanh[x]*Log[(-2*(1 + Sqrt[2])*(1 - Sqrt[2]*x))/(1 + x)])/Sqrt[2] - PolyLog[2, 1 - 2/(1 + x)]/(2*Sqrt[2]) + PolyLog[2, 1 + (2*(1 + Sqrt[2])*(1 - Sqrt[2]*x))/(1 + x)]/(2*Sqrt[2])","A",4,4,15,0.2667,1,"{5920, 2402, 2315, 2447}"
23,1,220,0,0.2226031,"\int (d+e x)^3 \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[(d + e*x)^3*(a + b*ArcTanh[c*x^2]),x]","\frac{a (d+e x)^4}{4 e}+\frac{3 b d^2 e \log \left(1-c^2 x^4\right)}{4 c}-\frac{b d e^2 \tan ^{-1}\left(\sqrt{c} x\right)}{c^{3/2}}-\frac{b d e^2 \tanh ^{-1}\left(\sqrt{c} x\right)}{c^{3/2}}-\frac{b e^3 \tanh ^{-1}\left(c x^2\right)}{4 c^2}+\frac{3}{2} b d^2 e x^2 \tanh ^{-1}\left(c x^2\right)+b d^3 x \tanh ^{-1}\left(c x^2\right)+\frac{b d^3 \tan ^{-1}\left(\sqrt{c} x\right)}{\sqrt{c}}-\frac{b d^3 \tanh ^{-1}\left(\sqrt{c} x\right)}{\sqrt{c}}+b d e^2 x^3 \tanh ^{-1}\left(c x^2\right)+\frac{2 b d e^2 x}{c}+\frac{b e^3 x^2}{4 c}+\frac{1}{4} b e^3 x^4 \tanh ^{-1}\left(c x^2\right)","\frac{(d+e x)^4 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{4 e}+\frac{b \left(c^2 d^4+6 c d^2 e^2+e^4\right) \log \left(1-c x^2\right)}{8 c^2 e}-\frac{b \left(c^2 d^4-6 c d^2 e^2+e^4\right) \log \left(c x^2+1\right)}{8 c^2 e}+\frac{b d \left(c d^2-e^2\right) \tan ^{-1}\left(\sqrt{c} x\right)}{c^{3/2}}-\frac{b d \left(c d^2+e^2\right) \tanh ^{-1}\left(\sqrt{c} x\right)}{c^{3/2}}+\frac{2 b d e^2 x}{c}+\frac{b e^3 x^2}{4 c}",1,"(2*b*d*e^2*x)/c + (b*e^3*x^2)/(4*c) + (a*(d + e*x)^4)/(4*e) + (b*d^3*ArcTan[Sqrt[c]*x])/Sqrt[c] - (b*d*e^2*ArcTan[Sqrt[c]*x])/c^(3/2) - (b*d^3*ArcTanh[Sqrt[c]*x])/Sqrt[c] - (b*d*e^2*ArcTanh[Sqrt[c]*x])/c^(3/2) - (b*e^3*ArcTanh[c*x^2])/(4*c^2) + b*d^3*x*ArcTanh[c*x^2] + (3*b*d^2*e*x^2*ArcTanh[c*x^2])/2 + b*d*e^2*x^3*ArcTanh[c*x^2] + (b*e^3*x^4*ArcTanh[c*x^2])/4 + (3*b*d^2*e*Log[1 - c^2*x^4])/(4*c)","A",19,10,18,0.5556,1,"{6742, 6091, 298, 203, 206, 6097, 260, 321, 212, 275}"
24,1,158,0,0.2103235,"\int (d+e x)^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcTanh[c*x^2]),x]","\frac{(d+e x)^3 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{3 e}+\frac{b \left(3 c d^2-e^2\right) \tan ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}-\frac{b \left(3 c d^2+e^2\right) \tanh ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}+\frac{b d \left(c d^2+3 e^2\right) \log \left(1-c x^2\right)}{6 c e}-\frac{b d \left(c d^2-3 e^2\right) \log \left(c x^2+1\right)}{6 c e}+\frac{2 b e^2 x}{3 c}","\frac{(d+e x)^3 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{3 e}+\frac{b \left(3 c d^2-e^2\right) \tan ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}-\frac{b \left(3 c d^2+e^2\right) \tanh ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}+\frac{b d \left(c d^2+3 e^2\right) \log \left(1-c x^2\right)}{6 c e}-\frac{b d \left(c d^2-3 e^2\right) \log \left(c x^2+1\right)}{6 c e}+\frac{2 b e^2 x}{3 c}",1,"(2*b*e^2*x)/(3*c) + (b*(3*c*d^2 - e^2)*ArcTan[Sqrt[c]*x])/(3*c^(3/2)) - (b*(3*c*d^2 + e^2)*ArcTanh[Sqrt[c]*x])/(3*c^(3/2)) + ((d + e*x)^3*(a + b*ArcTanh[c*x^2]))/(3*e) + (b*d*(c*d^2 + 3*e^2)*Log[1 - c*x^2])/(6*c*e) - (b*d*(c*d^2 - 3*e^2)*Log[1 + c*x^2])/(6*c*e)","A",12,10,18,0.5556,1,"{6273, 12, 1831, 1248, 633, 31, 1280, 1167, 205, 208}"
25,1,94,0,0.0930256,"\int (d+e x) \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[(d + e*x)*(a + b*ArcTanh[c*x^2]),x]","\frac{a (d+e x)^2}{2 e}+\frac{b e \log \left(1-c^2 x^4\right)}{4 c}+b d x \tanh ^{-1}\left(c x^2\right)+\frac{b d \tan ^{-1}\left(\sqrt{c} x\right)}{\sqrt{c}}-\frac{b d \tanh ^{-1}\left(\sqrt{c} x\right)}{\sqrt{c}}+\frac{1}{2} b e x^2 \tanh ^{-1}\left(c x^2\right)","\frac{(d+e x)^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{2 e}+\frac{b \left(c d^2+e^2\right) \log \left(1-c x^2\right)}{4 c e}-\frac{b \left(c d^2-e^2\right) \log \left(c x^2+1\right)}{4 c e}+\frac{b d \tan ^{-1}\left(\sqrt{c} x\right)}{\sqrt{c}}-\frac{b d \tanh ^{-1}\left(\sqrt{c} x\right)}{\sqrt{c}}",1,"(a*(d + e*x)^2)/(2*e) + (b*d*ArcTan[Sqrt[c]*x])/Sqrt[c] - (b*d*ArcTanh[Sqrt[c]*x])/Sqrt[c] + b*d*x*ArcTanh[c*x^2] + (b*e*x^2*ArcTanh[c*x^2])/2 + (b*e*Log[1 - c^2*x^4])/(4*c)","A",10,7,16,0.4375,1,"{6742, 6091, 298, 203, 206, 6097, 260}"
26,0,0,0,0.0626453,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{d+e x} \, dx","Int[(a + b*ArcTanh[c*x^2])/(d + e*x),x]","\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{d+e x} \, dx","-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{-c} (d+e x)}{\sqrt{-c} d-e}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-e}\right)}{2 e}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{-c} (d+e x)}{\sqrt{-c} d+e}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+e}\right)}{2 e}+\frac{\log (d+e x) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{e}-\frac{b \log (d+e x) \log \left(\frac{e \left(1-\sqrt{-c} x\right)}{\sqrt{-c} d+e}\right)}{2 e}-\frac{b \log (d+e x) \log \left(-\frac{e \left(\sqrt{-c} x+1\right)}{\sqrt{-c} d-e}\right)}{2 e}+\frac{b \log (d+e x) \log \left(\frac{e \left(1-\sqrt{c} x\right)}{\sqrt{c} d+e}\right)}{2 e}+\frac{b \log (d+e x) \log \left(-\frac{e \left(\sqrt{c} x+1\right)}{\sqrt{c} d-e}\right)}{2 e}",1,"(a*Log[d + e*x])/e + b*Defer[Int][ArcTanh[c*x^2]/(d + e*x), x]","F",0,0,0,0,-1,"{}"
27,1,166,0,0.2785951,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{(d+e x)^2} \, dx","Int[(a + b*ArcTanh[c*x^2])/(d + e*x)^2,x]","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{e (d+e x)}+\frac{2 b c d e \log (d+e x)}{c^2 d^4-e^4}-\frac{b c d \log \left(1-c x^2\right)}{2 e \left(c d^2-e^2\right)}+\frac{b c d \log \left(c x^2+1\right)}{2 e \left(c d^2+e^2\right)}+\frac{b \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right)}{c d^2+e^2}-\frac{b \sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right)}{c d^2-e^2}","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{e (d+e x)}+\frac{2 b c d e \log (d+e x)}{c^2 d^4-e^4}-\frac{b c d \log \left(1-c x^2\right)}{2 e \left(c d^2-e^2\right)}+\frac{b c d \log \left(c x^2+1\right)}{2 e \left(c d^2+e^2\right)}+\frac{b \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right)}{c d^2+e^2}-\frac{b \sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right)}{c d^2-e^2}",1,"(b*Sqrt[c]*ArcTan[Sqrt[c]*x])/(c*d^2 + e^2) - (b*Sqrt[c]*ArcTanh[Sqrt[c]*x])/(c*d^2 - e^2) - (a + b*ArcTanh[c*x^2])/(e*(d + e*x)) + (2*b*c*d*e*Log[d + e*x])/(c^2*d^4 - e^4) - (b*c*d*Log[1 - c*x^2])/(2*e*(c*d^2 - e^2)) + (b*c*d*Log[1 + c*x^2])/(2*e*(c*d^2 + e^2))","A",10,7,18,0.3889,1,"{6273, 12, 6725, 635, 207, 260, 203}"
28,0,0,0,0.0664324,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{(d+e x)^3} \, dx","Int[(a + b*ArcTanh[c*x^2])/(d + e*x)^3,x]","\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{(d+e x)^3} \, dx","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{2 e (d+e x)^2}-\frac{b c d e}{\left(c^2 d^4-e^4\right) (d+e x)}+\frac{b c e \left(3 c^2 d^4+e^4\right) \log (d+e x)}{\left(c^2 d^4-e^4\right)^2}+\frac{b c^{3/2} d \tan ^{-1}\left(\sqrt{c} x\right)}{\left(c d^2+e^2\right)^2}-\frac{b c^{3/2} d \tanh ^{-1}\left(\sqrt{c} x\right)}{\left(c d^2-e^2\right)^2}-\frac{b c \left(c d^2+e^2\right) \log \left(1-c x^2\right)}{4 e \left(c d^2-e^2\right)^2}+\frac{b c \left(c d^2-e^2\right) \log \left(c x^2+1\right)}{4 e \left(c d^2+e^2\right)^2}",1,"-a/(2*e*(d + e*x)^2) + b*Defer[Int][ArcTanh[c*x^2]/(d + e*x)^3, x]","F",0,0,0,0,-1,"{}"
29,1,1216,0,2.4380437,"\int (d+e x) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[(d + e*x)*(a + b*ArcTanh[c*x^2])^2,x]","\frac{i d \tan ^{-1}\left(\sqrt{c} x\right)^2 b^2}{\sqrt{c}}-\frac{d \tanh ^{-1}\left(\sqrt{c} x\right)^2 b^2}{\sqrt{c}}+\frac{1}{4} d x \log ^2\left(1-c x^2\right) b^2-\frac{e \left(1-c x^2\right) \log ^2\left(1-c x^2\right) b^2}{8 c}+\frac{1}{4} d x \log ^2\left(c x^2+1\right) b^2+\frac{e \left(c x^2+1\right) \log ^2\left(c x^2+1\right) b^2}{8 c}+\frac{2 d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right) b^2}{\sqrt{c}}-\frac{2 d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right) b^2}{\sqrt{c}}+\frac{d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) b^2}{\sqrt{c}}+\frac{2 d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right) b^2}{\sqrt{c}}-\frac{2 d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right) b^2}{\sqrt{c}}+\frac{d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2}{\sqrt{c}}+\frac{d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2}{\sqrt{c}}+\frac{d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) b^2}{\sqrt{c}}-\frac{d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right) b^2}{\sqrt{c}}+\frac{d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right) b^2}{\sqrt{c}}-\frac{e \log \left(1-c x^2\right) \log \left(\frac{1}{2} \left(c x^2+1\right)\right) b^2}{4 c}+\frac{d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) b^2}{\sqrt{c}}-\frac{d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) b^2}{\sqrt{c}}+\frac{e \log \left(\frac{1}{2} \left(1-c x^2\right)\right) \log \left(c x^2+1\right) b^2}{4 c}-\frac{1}{4} e x^2 \log \left(1-c x^2\right) \log \left(c x^2+1\right) b^2-\frac{1}{2} d x \log \left(1-c x^2\right) \log \left(c x^2+1\right) b^2-\frac{e \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^2\right)\right) b^2}{4 c}+\frac{e \text{PolyLog}\left(2,\frac{1}{2} \left(c x^2+1\right)\right) b^2}{4 c}+\frac{d \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right) b^2}{\sqrt{c}}+\frac{i d \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right) b^2}{\sqrt{c}}-\frac{i d \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) b^2}{2 \sqrt{c}}+\frac{i d \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right) b^2}{\sqrt{c}}+\frac{d \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right) b^2}{\sqrt{c}}-\frac{d \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right) b^2}{2 \sqrt{c}}-\frac{d \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2}{2 \sqrt{c}}-\frac{i d \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) b^2}{2 \sqrt{c}}+\frac{2 a d \tan ^{-1}\left(\sqrt{c} x\right) b}{\sqrt{c}}-\frac{2 a d \tanh ^{-1}\left(\sqrt{c} x\right) b}{\sqrt{c}}+a e x^2 \tanh ^{-1}\left(c x^2\right) b+2 a d x \tanh ^{-1}\left(c x^2\right) b+\frac{a e \log \left(1-c^2 x^4\right) b}{2 c}+\frac{a^2 (d+e x)^2}{2 e}","d x a^2+\frac{2 b d \tan ^{-1}\left(\sqrt{c} x\right) a}{\sqrt{c}}-\frac{2 b d \tanh ^{-1}\left(\sqrt{c} x\right) a}{\sqrt{c}}-b d x \log \left(1-c x^2\right) a+b d x \log \left(c x^2+1\right) a+\frac{i b^2 d \tan ^{-1}\left(\sqrt{c} x\right)^2}{\sqrt{c}}-\frac{b^2 d \tanh ^{-1}\left(\sqrt{c} x\right)^2}{\sqrt{c}}+\frac{1}{2} e x^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2+\frac{e \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{2 c}+\frac{1}{4} b^2 d x \log ^2\left(1-c x^2\right)+\frac{1}{4} b^2 d x \log ^2\left(c x^2+1\right)+\frac{2 b^2 d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right)}{\sqrt{c}}-\frac{2 b^2 d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right)}{\sqrt{c}}+\frac{b^2 d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{\sqrt{c}}+\frac{2 b^2 d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{2 b^2 d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{b^2 d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{\sqrt{c}}+\frac{b^2 d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{\sqrt{c}}+\frac{b^2 d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{\sqrt{c}}-\frac{b e \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \log \left(\frac{2}{1-c x^2}\right)}{c}-\frac{b^2 d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right)}{\sqrt{c}}+\frac{b^2 d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right)}{\sqrt{c}}+\frac{b^2 d \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{\sqrt{c}}-\frac{b^2 d \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{\sqrt{c}}-\frac{1}{2} b^2 d x \log \left(1-c x^2\right) \log \left(c x^2+1\right)+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right)}{\sqrt{c}}+\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right)}{\sqrt{c}}-\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{2 \sqrt{c}}+\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{b^2 d \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right)}{2 \sqrt{c}}-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{2 \sqrt{c}}-\frac{i b^2 d \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{2 \sqrt{c}}-\frac{b^2 e \text{PolyLog}\left(2,1-\frac{2}{1-c x^2}\right)}{2 c}",1,"(a^2*(d + e*x)^2)/(2*e) + (2*a*b*d*ArcTan[Sqrt[c]*x])/Sqrt[c] + (I*b^2*d*ArcTan[Sqrt[c]*x]^2)/Sqrt[c] - (2*a*b*d*ArcTanh[Sqrt[c]*x])/Sqrt[c] - (b^2*d*ArcTanh[Sqrt[c]*x]^2)/Sqrt[c] + 2*a*b*d*x*ArcTanh[c*x^2] + a*b*e*x^2*ArcTanh[c*x^2] + (2*b^2*d*ArcTanh[Sqrt[c]*x]*Log[2/(1 - Sqrt[c]*x)])/Sqrt[c] - (2*b^2*d*ArcTan[Sqrt[c]*x]*Log[2/(1 - I*Sqrt[c]*x)])/Sqrt[c] + (b^2*d*ArcTan[Sqrt[c]*x]*Log[((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/Sqrt[c] + (2*b^2*d*ArcTan[Sqrt[c]*x]*Log[2/(1 + I*Sqrt[c]*x)])/Sqrt[c] - (2*b^2*d*ArcTanh[Sqrt[c]*x]*Log[2/(1 + Sqrt[c]*x)])/Sqrt[c] + (b^2*d*ArcTanh[Sqrt[c]*x]*Log[(-2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/Sqrt[c] + (b^2*d*ArcTanh[Sqrt[c]*x]*Log[(2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/Sqrt[c] + (b^2*d*ArcTan[Sqrt[c]*x]*Log[((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/Sqrt[c] - (b^2*d*ArcTan[Sqrt[c]*x]*Log[1 - c*x^2])/Sqrt[c] + (b^2*d*ArcTanh[Sqrt[c]*x]*Log[1 - c*x^2])/Sqrt[c] + (b^2*d*x*Log[1 - c*x^2]^2)/4 - (b^2*e*(1 - c*x^2)*Log[1 - c*x^2]^2)/(8*c) - (b^2*e*Log[1 - c*x^2]*Log[(1 + c*x^2)/2])/(4*c) + (b^2*d*ArcTan[Sqrt[c]*x]*Log[1 + c*x^2])/Sqrt[c] - (b^2*d*ArcTanh[Sqrt[c]*x]*Log[1 + c*x^2])/Sqrt[c] + (b^2*e*Log[(1 - c*x^2)/2]*Log[1 + c*x^2])/(4*c) - (b^2*d*x*Log[1 - c*x^2]*Log[1 + c*x^2])/2 - (b^2*e*x^2*Log[1 - c*x^2]*Log[1 + c*x^2])/4 + (b^2*d*x*Log[1 + c*x^2]^2)/4 + (b^2*e*(1 + c*x^2)*Log[1 + c*x^2]^2)/(8*c) + (a*b*e*Log[1 - c^2*x^4])/(2*c) - (b^2*e*PolyLog[2, (1 - c*x^2)/2])/(4*c) + (b^2*e*PolyLog[2, (1 + c*x^2)/2])/(4*c) + (b^2*d*PolyLog[2, 1 - 2/(1 - Sqrt[c]*x)])/Sqrt[c] + (I*b^2*d*PolyLog[2, 1 - 2/(1 - I*Sqrt[c]*x)])/Sqrt[c] - ((I/2)*b^2*d*PolyLog[2, 1 - ((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/Sqrt[c] + (I*b^2*d*PolyLog[2, 1 - 2/(1 + I*Sqrt[c]*x)])/Sqrt[c] + (b^2*d*PolyLog[2, 1 - 2/(1 + Sqrt[c]*x)])/Sqrt[c] - (b^2*d*PolyLog[2, 1 + (2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/(2*Sqrt[c]) - (b^2*d*PolyLog[2, 1 - (2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/(2*Sqrt[c]) - ((I/2)*b^2*d*PolyLog[2, 1 - ((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/Sqrt[c]","A",104,39,18,2.167,0,"{6742, 6091, 298, 203, 206, 6097, 260, 6093, 2450, 2476, 2448, 321, 2470, 12, 5984, 5918, 2402, 2315, 2556, 5992, 5920, 2447, 4928, 4856, 4920, 4854, 6099, 2454, 2389, 2296, 2295, 30, 2557, 2475, 43, 2416, 2394, 2393, 2391}"
30,0,0,0,0.1188259,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{d+e x} \, dx","Int[(a + b*ArcTanh[c*x^2])^2/(d + e*x),x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{d+e x} \, dx","\text{Int}\left(\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{d+e x},x\right)",0,"(a^2*Log[d + e*x])/e + 2*a*b*Defer[Int][ArcTanh[c*x^2]/(d + e*x), x] + b^2*Defer[Int][ArcTanh[c*x^2]^2/(d + e*x), x]","A",0,0,0,0,-1,"{}"
31,0,0,0,0.3688422,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{(d+e x)^2} \, dx","Int[(a + b*ArcTanh[c*x^2])^2/(d + e*x)^2,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{(d+e x)^2} \, dx","\text{Int}\left(\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{(d+e x)^2},x\right)",0,"-(a^2/(e*(d + e*x))) + (2*a*b*Sqrt[c]*ArcTan[Sqrt[c]*x])/(c*d^2 + e^2) - (2*a*b*Sqrt[c]*ArcTanh[Sqrt[c]*x])/(c*d^2 - e^2) - (2*a*b*ArcTanh[c*x^2])/(e*(d + e*x)) + (4*a*b*c*d*e*Log[d + e*x])/(c^2*d^4 - e^4) - (a*b*c*d*Log[1 - c*x^2])/(e*(c*d^2 - e^2)) + (a*b*c*d*Log[1 + c*x^2])/(e*(c*d^2 + e^2)) + b^2*Defer[Int][ArcTanh[c*x^2]^2/(d + e*x)^2, x]","A",0,0,0,0,-1,"{}"
32,1,332,0,0.5108853,"\int (d+e x)^2 \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcTanh[c*x^3]),x]","\frac{a (d+e x)^3}{3 e}+\frac{b d^2 \log \left(1-c^{2/3} x^2\right)}{2 \sqrt[3]{c}}-\frac{b d^2 \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b d^2 \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}+\frac{b d e \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{4 c^{2/3}}-\frac{b d e \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{4 c^{2/3}}-\frac{\sqrt{3} b d e \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{2 c^{2/3}}+\frac{\sqrt{3} b d e \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 c^{2/3}}-\frac{b d e \tanh ^{-1}\left(\sqrt[3]{c} x\right)}{c^{2/3}}+\frac{b e^2 \log \left(1-c^2 x^6\right)}{6 c}+b d^2 x \tanh ^{-1}\left(c x^3\right)+b d e x^2 \tanh ^{-1}\left(c x^3\right)+\frac{1}{3} b e^2 x^3 \tanh ^{-1}\left(c x^3\right)","\frac{(d+e x)^3 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{3 e}+\frac{b d^2 \log \left(1-c^{2/3} x^2\right)}{2 \sqrt[3]{c}}-\frac{b d^2 \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b d^2 \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}+\frac{b d e \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{4 c^{2/3}}-\frac{b d e \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{4 c^{2/3}}-\frac{\sqrt{3} b d e \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{2 c^{2/3}}+\frac{\sqrt{3} b d e \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 c^{2/3}}-\frac{b d e \tanh ^{-1}\left(\sqrt[3]{c} x\right)}{c^{2/3}}+\frac{b \left(c d^3+e^3\right) \log \left(1-c x^3\right)}{6 c e}-\frac{b \left(c d^3-e^3\right) \log \left(c x^3+1\right)}{6 c e}",1,"(a*(d + e*x)^3)/(3*e) - (Sqrt[3]*b*d*e*ArcTan[1/Sqrt[3] - (2*c^(1/3)*x)/Sqrt[3]])/(2*c^(2/3)) + (Sqrt[3]*b*d*e*ArcTan[1/Sqrt[3] + (2*c^(1/3)*x)/Sqrt[3]])/(2*c^(2/3)) + (Sqrt[3]*b*d^2*ArcTan[(1 + 2*c^(2/3)*x^2)/Sqrt[3]])/(2*c^(1/3)) - (b*d*e*ArcTanh[c^(1/3)*x])/c^(2/3) + b*d^2*x*ArcTanh[c*x^3] + b*d*e*x^2*ArcTanh[c*x^3] + (b*e^2*x^3*ArcTanh[c*x^3])/3 + (b*d^2*Log[1 - c^(2/3)*x^2])/(2*c^(1/3)) + (b*d*e*Log[1 - c^(1/3)*x + c^(2/3)*x^2])/(4*c^(2/3)) - (b*d*e*Log[1 + c^(1/3)*x + c^(2/3)*x^2])/(4*c^(2/3)) - (b*d^2*Log[1 + c^(2/3)*x^2 + c^(4/3)*x^4])/(4*c^(1/3)) + (b*e^2*Log[1 - c^2*x^6])/(6*c)","A",25,14,18,0.7778,1,"{6742, 6091, 275, 292, 31, 634, 617, 204, 628, 6097, 296, 618, 206, 260}"
33,1,285,0,0.4515951,"\int (d+e x) \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[(d + e*x)*(a + b*ArcTanh[c*x^3]),x]","\frac{(d+e x)^2 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{2 e}+\frac{b d \log \left(1-c^{2/3} x^2\right)}{2 \sqrt[3]{c}}-\frac{b d \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b d \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}+\frac{b e \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{b e \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{\sqrt{3} b e \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{4 c^{2/3}}+\frac{\sqrt{3} b e \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{4 c^{2/3}}-\frac{b e \tanh ^{-1}\left(\sqrt[3]{c} x\right)}{2 c^{2/3}}-\frac{b d^2 \tanh ^{-1}\left(c x^3\right)}{2 e}","\frac{(d+e x)^2 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{2 e}+\frac{b d \log \left(1-c^{2/3} x^2\right)}{2 \sqrt[3]{c}}-\frac{b d \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b d \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}+\frac{b e \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{b e \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{\sqrt{3} b e \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{4 c^{2/3}}+\frac{\sqrt{3} b e \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{4 c^{2/3}}-\frac{b e \tanh ^{-1}\left(\sqrt[3]{c} x\right)}{2 c^{2/3}}-\frac{b d^2 \tanh ^{-1}\left(c x^3\right)}{2 e}",1,"-(Sqrt[3]*b*e*ArcTan[1/Sqrt[3] - (2*c^(1/3)*x)/Sqrt[3]])/(4*c^(2/3)) + (Sqrt[3]*b*e*ArcTan[1/Sqrt[3] + (2*c^(1/3)*x)/Sqrt[3]])/(4*c^(2/3)) + (Sqrt[3]*b*d*ArcTan[(1 + 2*c^(2/3)*x^2)/Sqrt[3]])/(2*c^(1/3)) - (b*e*ArcTanh[c^(1/3)*x])/(2*c^(2/3)) - (b*d^2*ArcTanh[c*x^3])/(2*e) + ((d + e*x)^2*(a + b*ArcTanh[c*x^3]))/(2*e) + (b*d*Log[1 - c^(2/3)*x^2])/(2*c^(1/3)) + (b*e*Log[1 - c^(1/3)*x + c^(2/3)*x^2])/(8*c^(2/3)) - (b*e*Log[1 + c^(1/3)*x + c^(2/3)*x^2])/(8*c^(2/3)) - (b*d*Log[1 + c^(2/3)*x^2 + c^(4/3)*x^4])/(4*c^(1/3))","A",23,13,16,0.8125,1,"{6273, 12, 1831, 275, 206, 292, 31, 634, 617, 204, 628, 296, 618}"
34,0,0,0,0.0615003,"\int \frac{a+b \tanh ^{-1}\left(c x^3\right)}{d+e x} \, dx","Int[(a + b*ArcTanh[c*x^3])/(d + e*x),x]","\int \frac{a+b \tanh ^{-1}\left(c x^3\right)}{d+e x} \, dx","-\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (d+e x)}{\sqrt[3]{c} d-e}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (d+e x)}{\sqrt[3]{c} d+e}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (d+e x)}{\sqrt[3]{c} d-\sqrt[3]{-1} e}\right)}{2 e}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (d+e x)}{\sqrt[3]{c} d+\sqrt[3]{-1} e}\right)}{2 e}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (d+e x)}{\sqrt[3]{c} d-(-1)^{2/3} e}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (d+e x)}{\sqrt[3]{c} d+(-1)^{2/3} e}\right)}{2 e}+\frac{\log (d+e x) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{e}+\frac{b \log (d+e x) \log \left(\frac{e \left(1-\sqrt[3]{c} x\right)}{\sqrt[3]{c} d+e}\right)}{2 e}-\frac{b \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{c} x+1\right)}{\sqrt[3]{c} d-e}\right)}{2 e}+\frac{b \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{c} x+\sqrt[3]{-1}\right)}{\sqrt[3]{c} d-\sqrt[3]{-1} e}\right)}{2 e}-\frac{b \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{c} x+(-1)^{2/3}\right)}{\sqrt[3]{c} d-(-1)^{2/3} e}\right)}{2 e}+\frac{b \log (d+e x) \log \left(\frac{(-1)^{2/3} e \left(\sqrt[3]{-1} \sqrt[3]{c} x+1\right)}{\sqrt[3]{c} d+(-1)^{2/3} e}\right)}{2 e}-\frac{b \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[3]{c} x+1\right)}{\sqrt[3]{c} d+\sqrt[3]{-1} e}\right)}{2 e}",1,"(a*Log[d + e*x])/e + b*Defer[Int][ArcTanh[c*x^3]/(d + e*x), x]","F",0,0,0,0,-1,"{}"
35,1,414,0,0.7726848,"\int \frac{a+b \tanh ^{-1}\left(c x^3\right)}{(d+e x)^2} \, dx","Int[(a + b*ArcTanh[c*x^3])/(d + e*x)^2,x]","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{e (d+e x)}-\frac{b \sqrt[3]{c} \left(\sqrt[3]{c} d+e\right) \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{4 \left(c d^3-e^3\right)}-\frac{b \sqrt[3]{c} \left(\sqrt[3]{c} d-e\right) \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{4 \left(c d^3+e^3\right)}-\frac{3 b c d^2 e^2 \log (d+e x)}{c^2 d^6-e^6}-\frac{\sqrt{3} b \sqrt[3]{c} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{2 \left(c^{2/3} d^2+\sqrt[3]{c} d e+e^2\right)}-\frac{b c d^2 \log \left(1-c x^3\right)}{2 e \left(c d^3+e^3\right)}+\frac{b c d^2 \log \left(c x^3+1\right)}{2 e \left(c d^3-e^3\right)}+\frac{b \sqrt[3]{c} \left(\sqrt[3]{c} d-e\right) \log \left(1-\sqrt[3]{c} x\right)}{2 \left(c d^3+e^3\right)}+\frac{b \sqrt[3]{c} \left(\sqrt[3]{c} d+e\right) \log \left(\sqrt[3]{c} x+1\right)}{2 \left(c d^3-e^3\right)}-\frac{\sqrt{3} b \sqrt[3]{c} \left(\sqrt[3]{c} d+e\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x+1}{\sqrt{3}}\right)}{2 \left(c d^3+e^3\right)}","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{e (d+e x)}-\frac{b \sqrt[3]{c} \left(\sqrt[3]{c} d+e\right) \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{4 \left(c d^3-e^3\right)}-\frac{b \sqrt[3]{c} \left(\sqrt[3]{c} d-e\right) \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{4 \left(c d^3+e^3\right)}-\frac{3 b c d^2 e^2 \log (d+e x)}{c^2 d^6-e^6}-\frac{\sqrt{3} b \sqrt[3]{c} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{2 \left(c^{2/3} d^2+\sqrt[3]{c} d e+e^2\right)}-\frac{b c d^2 \log \left(1-c x^3\right)}{2 e \left(c d^3+e^3\right)}+\frac{b c d^2 \log \left(c x^3+1\right)}{2 e \left(c d^3-e^3\right)}+\frac{b \sqrt[3]{c} \left(\sqrt[3]{c} d-e\right) \log \left(1-\sqrt[3]{c} x\right)}{2 \left(c d^3+e^3\right)}+\frac{b \sqrt[3]{c} \left(\sqrt[3]{c} d+e\right) \log \left(\sqrt[3]{c} x+1\right)}{2 \left(c d^3-e^3\right)}-\frac{\sqrt{3} b \sqrt[3]{c} \left(\sqrt[3]{c} d+e\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x+1}{\sqrt{3}}\right)}{2 \left(c d^3+e^3\right)}",1,"-(Sqrt[3]*b*c^(1/3)*ArcTan[(1 - 2*c^(1/3)*x)/Sqrt[3]])/(2*(c^(2/3)*d^2 + c^(1/3)*d*e + e^2)) - (Sqrt[3]*b*c^(1/3)*(c^(1/3)*d + e)*ArcTan[(1 + 2*c^(1/3)*x)/Sqrt[3]])/(2*(c*d^3 + e^3)) - (a + b*ArcTanh[c*x^3])/(e*(d + e*x)) + (b*c^(1/3)*(c^(1/3)*d - e)*Log[1 - c^(1/3)*x])/(2*(c*d^3 + e^3)) + (b*c^(1/3)*(c^(1/3)*d + e)*Log[1 + c^(1/3)*x])/(2*(c*d^3 - e^3)) - (3*b*c*d^2*e^2*Log[d + e*x])/(c^2*d^6 - e^6) - (b*c^(1/3)*(c^(1/3)*d + e)*Log[1 - c^(1/3)*x + c^(2/3)*x^2])/(4*(c*d^3 - e^3)) - (b*c^(1/3)*(c^(1/3)*d - e)*Log[1 + c^(1/3)*x + c^(2/3)*x^2])/(4*(c*d^3 + e^3)) - (b*c*d^2*Log[1 - c*x^3])/(2*e*(c*d^3 + e^3)) + (b*c*d^2*Log[1 + c*x^3])/(2*e*(c*d^3 - e^3))","A",20,12,18,0.6667,1,"{6273, 12, 6725, 1871, 1861, 31, 634, 617, 204, 628, 260, 1860}"
36,1,195,0,0.6007308,"\int \frac{x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{1-c^2 x} \, dx","Int[(x^3*(a + b*ArcTanh[c*Sqrt[x]]))/(1 - c^2*x),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{c^8}-\frac{x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{3 c^2}-\frac{x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{2 c^4}-\frac{x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^6}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b c^8}+\frac{2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^8}-\frac{b x^{5/2}}{15 c^3}-\frac{5 b x^{3/2}}{18 c^5}-\frac{11 b \sqrt{x}}{6 c^7}+\frac{11 b \tanh ^{-1}\left(c \sqrt{x}\right)}{6 c^8}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{c^8}-\frac{x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{3 c^2}-\frac{x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{2 c^4}-\frac{x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^6}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b c^8}+\frac{2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^8}-\frac{b x^{5/2}}{15 c^3}-\frac{5 b x^{3/2}}{18 c^5}-\frac{11 b \sqrt{x}}{6 c^7}+\frac{11 b \tanh ^{-1}\left(c \sqrt{x}\right)}{6 c^8}",1,"(-11*b*Sqrt[x])/(6*c^7) - (5*b*x^(3/2))/(18*c^5) - (b*x^(5/2))/(15*c^3) + (11*b*ArcTanh[c*Sqrt[x]])/(6*c^8) - (x*(a + b*ArcTanh[c*Sqrt[x]]))/c^6 - (x^2*(a + b*ArcTanh[c*Sqrt[x]]))/(2*c^4) - (x^3*(a + b*ArcTanh[c*Sqrt[x]]))/(3*c^2) - (a + b*ArcTanh[c*Sqrt[x]])^2/(b*c^8) + (2*(a + b*ArcTanh[c*Sqrt[x]])*Log[2/(1 - c*Sqrt[x])])/c^8 + (b*PolyLog[2, 1 - 2/(1 - c*Sqrt[x])])/c^8","A",19,10,26,0.3846,1,"{43, 5980, 5916, 302, 206, 321, 5984, 5918, 2402, 2315}"
37,1,160,0,0.4285668,"\int \frac{x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{1-c^2 x} \, dx","Int[(x^2*(a + b*ArcTanh[c*Sqrt[x]]))/(1 - c^2*x),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{c^6}-\frac{x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{2 c^2}-\frac{x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^4}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b c^6}+\frac{2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^6}-\frac{b x^{3/2}}{6 c^3}-\frac{3 b \sqrt{x}}{2 c^5}+\frac{3 b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 c^6}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{c^6}-\frac{x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{2 c^2}-\frac{x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^4}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b c^6}+\frac{2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^6}-\frac{b x^{3/2}}{6 c^3}-\frac{3 b \sqrt{x}}{2 c^5}+\frac{3 b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 c^6}",1,"(-3*b*Sqrt[x])/(2*c^5) - (b*x^(3/2))/(6*c^3) + (3*b*ArcTanh[c*Sqrt[x]])/(2*c^6) - (x*(a + b*ArcTanh[c*Sqrt[x]]))/c^4 - (x^2*(a + b*ArcTanh[c*Sqrt[x]]))/(2*c^2) - (a + b*ArcTanh[c*Sqrt[x]])^2/(b*c^6) + (2*(a + b*ArcTanh[c*Sqrt[x]])*Log[2/(1 - c*Sqrt[x])])/c^6 + (b*PolyLog[2, 1 - 2/(1 - c*Sqrt[x])])/c^6","A",14,10,26,0.3846,1,"{43, 5980, 5916, 302, 206, 321, 5984, 5918, 2402, 2315}"
38,1,120,0,0.259834,"\int \frac{x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{1-c^2 x} \, dx","Int[(x*(a + b*ArcTanh[c*Sqrt[x]]))/(1 - c^2*x),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{c^4}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b c^4}-\frac{x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^2}+\frac{2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^4}-\frac{b \sqrt{x}}{c^3}+\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{c^4}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{c^4}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b c^4}-\frac{x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^2}+\frac{2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^4}-\frac{b \sqrt{x}}{c^3}+\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{c^4}",1,"-((b*Sqrt[x])/c^3) + (b*ArcTanh[c*Sqrt[x]])/c^4 - (x*(a + b*ArcTanh[c*Sqrt[x]]))/c^2 - (a + b*ArcTanh[c*Sqrt[x]])^2/(b*c^4) + (2*(a + b*ArcTanh[c*Sqrt[x]])*Log[2/(1 - c*Sqrt[x])])/c^4 + (b*PolyLog[2, 1 - 2/(1 - c*Sqrt[x])])/c^4","A",9,9,24,0.3750,1,"{43, 5980, 5916, 321, 206, 5984, 5918, 2402, 2315}"
39,1,78,0,0.1252082,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{1-c^2 x} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/(1 - c^2*x),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{c^2}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b c^2}+\frac{2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^2}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{c^2}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b c^2}+\frac{2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^2}",1,"-((a + b*ArcTanh[c*Sqrt[x]])^2/(b*c^2)) + (2*(a + b*ArcTanh[c*Sqrt[x]])*Log[2/(1 - c*Sqrt[x])])/c^2 + (b*PolyLog[2, 1 - 2/(1 - c*Sqrt[x])])/c^2","A",5,4,23,0.1739,1,"{5984, 5918, 2402, 2315}"
40,1,69,0,0.2436304,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x \left(1-c^2 x\right)} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/(x*(1 - c^2*x)),x]","-b \text{PolyLog}\left(2,\frac{2}{c \sqrt{x}+1}-1\right)+\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b}+2 \log \left(2-\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)","-b \text{PolyLog}\left(2,\frac{2}{c \sqrt{x}+1}-1\right)+\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b}+2 \log \left(2-\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)",1,"(a + b*ArcTanh[c*Sqrt[x]])^2/b + 2*(a + b*ArcTanh[c*Sqrt[x]])*Log[2 - 2/(1 + c*Sqrt[x])] - b*PolyLog[2, -1 + 2/(1 + c*Sqrt[x])]","A",5,7,26,0.2692,1,"{36, 29, 31, 1593, 5988, 5932, 2447}"
41,1,117,0,0.3633586,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x^2 \left(1-c^2 x\right)} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/(x^2*(1 - c^2*x)),x]","-b c^2 \text{PolyLog}\left(2,\frac{2}{c \sqrt{x}+1}-1\right)+\frac{c^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b}+2 c^2 \log \left(2-\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x}+b c^2 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{\sqrt{x}}","-b c^2 \text{PolyLog}\left(2,\frac{2}{c \sqrt{x}+1}-1\right)+\frac{c^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b}+2 c^2 \log \left(2-\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x}+b c^2 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{\sqrt{x}}",1,"-((b*c)/Sqrt[x]) + b*c^2*ArcTanh[c*Sqrt[x]] - (a + b*ArcTanh[c*Sqrt[x]])/x + (c^2*(a + b*ArcTanh[c*Sqrt[x]])^2)/b + 2*c^2*(a + b*ArcTanh[c*Sqrt[x]])*Log[2 - 2/(1 + c*Sqrt[x])] - b*c^2*PolyLog[2, -1 + 2/(1 + c*Sqrt[x])]","A",9,9,26,0.3462,1,"{44, 1593, 5982, 5916, 325, 206, 5988, 5932, 2447}"
42,1,157,0,0.4558524,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x^3 \left(1-c^2 x\right)} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/(x^3*(1 - c^2*x)),x]","-b c^4 \text{PolyLog}\left(2,\frac{2}{c \sqrt{x}+1}-1\right)+\frac{c^4 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b}-\frac{c^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{x}+2 c^4 \log \left(2-\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 x^2}-\frac{3 b c^3}{2 \sqrt{x}}+\frac{3}{2} b c^4 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{6 x^{3/2}}","-b c^4 \text{PolyLog}\left(2,\frac{2}{c \sqrt{x}+1}-1\right)+\frac{c^4 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b}-\frac{c^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{x}+2 c^4 \log \left(2-\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 x^2}-\frac{3 b c^3}{2 \sqrt{x}}+\frac{3}{2} b c^4 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{6 x^{3/2}}",1,"-(b*c)/(6*x^(3/2)) - (3*b*c^3)/(2*Sqrt[x]) + (3*b*c^4*ArcTanh[c*Sqrt[x]])/2 - (a + b*ArcTanh[c*Sqrt[x]])/(2*x^2) - (c^2*(a + b*ArcTanh[c*Sqrt[x]]))/x + (c^4*(a + b*ArcTanh[c*Sqrt[x]])^2)/b + 2*c^4*(a + b*ArcTanh[c*Sqrt[x]])*Log[2 - 2/(1 + c*Sqrt[x])] - b*c^4*PolyLog[2, -1 + 2/(1 + c*Sqrt[x])]","A",14,9,26,0.3462,1,"{44, 1593, 5982, 5916, 325, 206, 5988, 5932, 2447}"
43,1,192,0,0.5711809,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x^4 \left(1-c^2 x\right)} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/(x^4*(1 - c^2*x)),x]","-b c^6 \text{PolyLog}\left(2,\frac{2}{c \sqrt{x}+1}-1\right)-\frac{c^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{2 x^2}+\frac{c^6 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b}-\frac{c^4 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{x}+2 c^6 \log \left(2-\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{3 x^3}-\frac{5 b c^3}{18 x^{3/2}}-\frac{11 b c^5}{6 \sqrt{x}}+\frac{11}{6} b c^6 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{15 x^{5/2}}","-b c^6 \text{PolyLog}\left(2,\frac{2}{c \sqrt{x}+1}-1\right)-\frac{c^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{2 x^2}+\frac{c^6 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{b}-\frac{c^4 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{x}+2 c^6 \log \left(2-\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{3 x^3}-\frac{5 b c^3}{18 x^{3/2}}-\frac{11 b c^5}{6 \sqrt{x}}+\frac{11}{6} b c^6 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{15 x^{5/2}}",1,"-(b*c)/(15*x^(5/2)) - (5*b*c^3)/(18*x^(3/2)) - (11*b*c^5)/(6*Sqrt[x]) + (11*b*c^6*ArcTanh[c*Sqrt[x]])/6 - (a + b*ArcTanh[c*Sqrt[x]])/(3*x^3) - (c^2*(a + b*ArcTanh[c*Sqrt[x]]))/(2*x^2) - (c^4*(a + b*ArcTanh[c*Sqrt[x]]))/x + (c^6*(a + b*ArcTanh[c*Sqrt[x]])^2)/b + 2*c^6*(a + b*ArcTanh[c*Sqrt[x]])*Log[2 - 2/(1 + c*Sqrt[x])] - b*c^6*PolyLog[2, -1 + 2/(1 + c*Sqrt[x])]","A",20,9,26,0.3462,1,"{44, 1593, 5982, 5916, 325, 206, 5988, 5932, 2447}"
44,1,460,0,0.7831225,"\int \frac{x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{d+e x} \, dx","Int[(x^2*(a + b*ArcTanh[c*Sqrt[x]]))/(d + e*x),x]","\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{e^3}-\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 e^3}-\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 e^3}-\frac{2 d^2 \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{e^3}+\frac{d^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{e^3}+\frac{d^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{e^3}-\frac{d x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{e^2}+\frac{x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{2 e}+\frac{b d \tanh ^{-1}\left(c \sqrt{x}\right)}{c^2 e^2}+\frac{b \sqrt{x}}{2 c^3 e}-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 c^4 e}-\frac{b d \sqrt{x}}{c e^2}+\frac{b x^{3/2}}{6 c e}","\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{e^3}-\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 e^3}-\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 e^3}-\frac{2 d^2 \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{e^3}+\frac{d^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{e^3}+\frac{d^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{e^3}-\frac{d x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{e^2}+\frac{x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{2 e}+\frac{b d \tanh ^{-1}\left(c \sqrt{x}\right)}{c^2 e^2}+\frac{b \sqrt{x}}{2 c^3 e}-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 c^4 e}-\frac{b d \sqrt{x}}{c e^2}+\frac{b x^{3/2}}{6 c e}",1,"-((b*d*Sqrt[x])/(c*e^2)) + (b*Sqrt[x])/(2*c^3*e) + (b*x^(3/2))/(6*c*e) + (b*d*ArcTanh[c*Sqrt[x]])/(c^2*e^2) - (b*ArcTanh[c*Sqrt[x]])/(2*c^4*e) - (d*x*(a + b*ArcTanh[c*Sqrt[x]]))/e^2 + (x^2*(a + b*ArcTanh[c*Sqrt[x]]))/(2*e) - (2*d^2*(a + b*ArcTanh[c*Sqrt[x]])*Log[2/(1 + c*Sqrt[x])])/e^3 + (d^2*(a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/e^3 + (d^2*(a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/e^3 + (b*d^2*PolyLog[2, 1 - 2/(1 + c*Sqrt[x])])/e^3 - (b*d^2*PolyLog[2, 1 - (2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/(2*e^3) - (b*d^2*PolyLog[2, 1 - (2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/(2*e^3)","A",20,11,23,0.4783,1,"{43, 5980, 5916, 302, 206, 321, 6044, 5920, 2402, 2315, 2447}"
45,1,374,0,0.4845963,"\int \frac{x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{d+e x} \, dx","Int[(x*(a + b*ArcTanh[c*Sqrt[x]]))/(d + e*x),x]","-\frac{b d \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{e^2}+\frac{b d \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 e^2}+\frac{b d \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 e^2}+\frac{2 d \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{e^2}-\frac{d \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{e^2}-\frac{d \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{e^2}+\frac{x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{e}-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{c^2 e}+\frac{b \sqrt{x}}{c e}","-\frac{b d \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{e^2}+\frac{b d \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 e^2}+\frac{b d \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 e^2}+\frac{2 d \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{e^2}-\frac{d \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{e^2}-\frac{d \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{e^2}+\frac{x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{e}-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{c^2 e}+\frac{b \sqrt{x}}{c e}",1,"(b*Sqrt[x])/(c*e) - (b*ArcTanh[c*Sqrt[x]])/(c^2*e) + (x*(a + b*ArcTanh[c*Sqrt[x]]))/e + (2*d*(a + b*ArcTanh[c*Sqrt[x]])*Log[2/(1 + c*Sqrt[x])])/e^2 - (d*(a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/e^2 - (d*(a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/e^2 - (b*d*PolyLog[2, 1 - 2/(1 + c*Sqrt[x])])/e^2 + (b*d*PolyLog[2, 1 - (2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/(2*e^2) + (b*d*PolyLog[2, 1 - (2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/(2*e^2)","A",15,10,21,0.4762,1,"{43, 5980, 5916, 321, 206, 6044, 5920, 2402, 2315, 2447}"
46,1,318,0,0.3215409,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{d+e x} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/(d + e*x),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 e}-\frac{b \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{e}+\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{e}+\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{e}-\frac{2 \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{e}","-\frac{b \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 e}-\frac{b \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{e}+\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{e}+\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{e}-\frac{2 \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{e}",1,"(-2*(a + b*ArcTanh[c*Sqrt[x]])*Log[2/(1 + c*Sqrt[x])])/e + ((a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/e + ((a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/e + (b*PolyLog[2, 1 - 2/(1 + c*Sqrt[x])])/e - (b*PolyLog[2, 1 - (2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/(2*e) - (b*PolyLog[2, 1 - (2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/(2*e)","A",11,5,20,0.2500,1,"{6044, 5920, 2402, 2315, 2447}"
47,1,358,0,0.5868099,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x (d+e x)} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/(x*(d + e*x)),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 d}+\frac{b \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{d}-\frac{b \text{PolyLog}\left(2,-c \sqrt{x}\right)}{d}+\frac{b \text{PolyLog}\left(2,c \sqrt{x}\right)}{d}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{d}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{d}+\frac{2 \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{d}+\frac{a \log (x)}{d}","\frac{b \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 d}+\frac{b \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{d}-\frac{b \text{PolyLog}\left(2,-c \sqrt{x}\right)}{d}+\frac{b \text{PolyLog}\left(2,c \sqrt{x}\right)}{d}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{d}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{d}+\frac{2 \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{d}+\frac{a \log (x)}{d}",1,"(2*(a + b*ArcTanh[c*Sqrt[x]])*Log[2/(1 + c*Sqrt[x])])/d - ((a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/d - ((a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/d + (a*Log[x])/d - (b*PolyLog[2, 1 - 2/(1 + c*Sqrt[x])])/d + (b*PolyLog[2, 1 - (2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/(2*d) + (b*PolyLog[2, 1 - (2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/(2*d) - (b*PolyLog[2, -(c*Sqrt[x])])/d + (b*PolyLog[2, c*Sqrt[x]])/d","A",15,11,23,0.4783,1,"{36, 29, 31, 1593, 5992, 5912, 6044, 5920, 2402, 2315, 2447}"
48,1,413,0,0.7200634,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x^2 (d+e x)} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/(x^2*(d + e*x)),x]","\frac{b e \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{d^2}-\frac{b e \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 d^2}-\frac{b e \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 d^2}+\frac{b e \text{PolyLog}\left(2,-c \sqrt{x}\right)}{d^2}-\frac{b e \text{PolyLog}\left(2,c \sqrt{x}\right)}{d^2}-\frac{2 e \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{d^2}+\frac{e \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{d^2}+\frac{e \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{d^2}-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{d x}-\frac{a e \log (x)}{d^2}+\frac{b c^2 \tanh ^{-1}\left(c \sqrt{x}\right)}{d}-\frac{b c}{d \sqrt{x}}","\frac{b e \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{d^2}-\frac{b e \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 d^2}-\frac{b e \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 d^2}+\frac{b e \text{PolyLog}\left(2,-c \sqrt{x}\right)}{d^2}-\frac{b e \text{PolyLog}\left(2,c \sqrt{x}\right)}{d^2}-\frac{2 e \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{d^2}+\frac{e \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{d^2}+\frac{e \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{d^2}-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{d x}-\frac{a e \log (x)}{d^2}+\frac{b c^2 \tanh ^{-1}\left(c \sqrt{x}\right)}{d}-\frac{b c}{d \sqrt{x}}",1,"-((b*c)/(d*Sqrt[x])) + (b*c^2*ArcTanh[c*Sqrt[x]])/d - (a + b*ArcTanh[c*Sqrt[x]])/(d*x) - (2*e*(a + b*ArcTanh[c*Sqrt[x]])*Log[2/(1 + c*Sqrt[x])])/d^2 + (e*(a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/d^2 + (e*(a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/d^2 - (a*e*Log[x])/d^2 + (b*e*PolyLog[2, 1 - 2/(1 + c*Sqrt[x])])/d^2 - (b*e*PolyLog[2, 1 - (2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/(2*d^2) - (b*e*PolyLog[2, 1 - (2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/(2*d^2) + (b*e*PolyLog[2, -(c*Sqrt[x])])/d^2 - (b*e*PolyLog[2, c*Sqrt[x]])/d^2","A",19,13,23,0.5652,1,"{44, 1593, 5982, 5916, 325, 206, 5992, 5912, 6044, 5920, 2402, 2315, 2447}"
49,1,506,0,0.8724009,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x^3 (d+e x)} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/(x^3*(d + e*x)),x]","-\frac{b e^2 \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{d^3}+\frac{b e^2 \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 d^3}+\frac{b e^2 \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 d^3}-\frac{b e^2 \text{PolyLog}\left(2,-c \sqrt{x}\right)}{d^3}+\frac{b e^2 \text{PolyLog}\left(2,c \sqrt{x}\right)}{d^3}+\frac{2 e^2 \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{d^3}-\frac{e^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{d^3}-\frac{e^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{d^3}+\frac{e \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{d^2 x}-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 d x^2}+\frac{a e^2 \log (x)}{d^3}-\frac{b c^2 e \tanh ^{-1}\left(c \sqrt{x}\right)}{d^2}-\frac{b c^3}{2 d \sqrt{x}}+\frac{b c^4 \tanh ^{-1}\left(c \sqrt{x}\right)}{2 d}+\frac{b c e}{d^2 \sqrt{x}}-\frac{b c}{6 d x^{3/2}}","-\frac{b e^2 \text{PolyLog}\left(2,1-\frac{2}{c \sqrt{x}+1}\right)}{d^3}+\frac{b e^2 \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{2 d^3}+\frac{b e^2 \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{2 d^3}-\frac{b e^2 \text{PolyLog}\left(2,-c \sqrt{x}\right)}{d^3}+\frac{b e^2 \text{PolyLog}\left(2,c \sqrt{x}\right)}{d^3}+\frac{2 e^2 \log \left(\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{d^3}-\frac{e^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}-\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}-\sqrt{e}\right)}\right)}{d^3}-\frac{e^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \log \left(\frac{2 c \left(\sqrt{-d}+\sqrt{e} \sqrt{x}\right)}{\left(c \sqrt{x}+1\right) \left(c \sqrt{-d}+\sqrt{e}\right)}\right)}{d^3}+\frac{e \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{d^2 x}-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 d x^2}+\frac{a e^2 \log (x)}{d^3}-\frac{b c^2 e \tanh ^{-1}\left(c \sqrt{x}\right)}{d^2}-\frac{b c^3}{2 d \sqrt{x}}+\frac{b c^4 \tanh ^{-1}\left(c \sqrt{x}\right)}{2 d}+\frac{b c e}{d^2 \sqrt{x}}-\frac{b c}{6 d x^{3/2}}",1,"-(b*c)/(6*d*x^(3/2)) - (b*c^3)/(2*d*Sqrt[x]) + (b*c*e)/(d^2*Sqrt[x]) + (b*c^4*ArcTanh[c*Sqrt[x]])/(2*d) - (b*c^2*e*ArcTanh[c*Sqrt[x]])/d^2 - (a + b*ArcTanh[c*Sqrt[x]])/(2*d*x^2) + (e*(a + b*ArcTanh[c*Sqrt[x]]))/(d^2*x) + (2*e^2*(a + b*ArcTanh[c*Sqrt[x]])*Log[2/(1 + c*Sqrt[x])])/d^3 - (e^2*(a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/d^3 - (e^2*(a + b*ArcTanh[c*Sqrt[x]])*Log[(2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/d^3 + (a*e^2*Log[x])/d^3 - (b*e^2*PolyLog[2, 1 - 2/(1 + c*Sqrt[x])])/d^3 + (b*e^2*PolyLog[2, 1 - (2*c*(Sqrt[-d] - Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] - Sqrt[e])*(1 + c*Sqrt[x]))])/(2*d^3) + (b*e^2*PolyLog[2, 1 - (2*c*(Sqrt[-d] + Sqrt[e]*Sqrt[x]))/((c*Sqrt[-d] + Sqrt[e])*(1 + c*Sqrt[x]))])/(2*d^3) - (b*e^2*PolyLog[2, -(c*Sqrt[x])])/d^3 + (b*e^2*PolyLog[2, c*Sqrt[x]])/d^3","A",24,13,23,0.5652,1,"{44, 1593, 5982, 5916, 325, 206, 5992, 5912, 6044, 5920, 2402, 2315, 2447}"