1,1,108,0,0.096842,"\int x^3 (d+c d x) \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^3*(d + c*d*x)*(a + b*ArcTanh[c*x]),x]","\frac{1}{5} c d x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d x^2}{10 c^2}+\frac{b d x}{4 c^3}+\frac{9 b d \log (1-c x)}{40 c^4}-\frac{b d \log (c x+1)}{40 c^4}+\frac{b d x^3}{12 c}+\frac{1}{20} b d x^4","\frac{1}{5} c d x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d x^2}{10 c^2}+\frac{b d x}{4 c^3}+\frac{9 b d \log (1-c x)}{40 c^4}-\frac{b d \log (c x+1)}{40 c^4}+\frac{b d x^3}{12 c}+\frac{1}{20} b d x^4",1,"(b*d*x)/(4*c^3) + (b*d*x^2)/(10*c^2) + (b*d*x^3)/(12*c) + (b*d*x^4)/20 + (d*x^4*(a + b*ArcTanh[c*x]))/4 + (c*d*x^5*(a + b*ArcTanh[c*x]))/5 + (9*b*d*Log[1 - c*x])/(40*c^4) - (b*d*Log[1 + c*x])/(40*c^4)","A",7,6,18,0.3333,1,"{43, 5936, 12, 801, 633, 31}"
2,1,96,0,0.0974052,"\int x^2 (d+c d x) \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^2*(d + c*d*x)*(a + b*ArcTanh[c*x]),x]","\frac{1}{4} c d x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{3} d x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d x}{4 c^2}+\frac{7 b d \log (1-c x)}{24 c^3}+\frac{b d \log (c x+1)}{24 c^3}+\frac{b d x^2}{6 c}+\frac{1}{12} b d x^3","\frac{1}{4} c d x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{3} d x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d x}{4 c^2}+\frac{7 b d \log (1-c x)}{24 c^3}+\frac{b d \log (c x+1)}{24 c^3}+\frac{b d x^2}{6 c}+\frac{1}{12} b d x^3",1,"(b*d*x)/(4*c^2) + (b*d*x^2)/(6*c) + (b*d*x^3)/12 + (d*x^3*(a + b*ArcTanh[c*x]))/3 + (c*d*x^4*(a + b*ArcTanh[c*x]))/4 + (7*b*d*Log[1 - c*x])/(24*c^3) + (b*d*Log[1 + c*x])/(24*c^3)","A",7,6,18,0.3333,1,"{43, 5936, 12, 801, 633, 31}"
3,1,84,0,0.074793,"\int x (d+c d x) \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x*(d + c*d*x)*(a + b*ArcTanh[c*x]),x]","\frac{1}{3} c d x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} d x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{5 b d \log (1-c x)}{12 c^2}-\frac{b d \log (c x+1)}{12 c^2}+\frac{b d x}{2 c}+\frac{1}{6} b d x^2","\frac{1}{3} c d x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} d x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{5 b d \log (1-c x)}{12 c^2}-\frac{b d \log (c x+1)}{12 c^2}+\frac{b d x}{2 c}+\frac{1}{6} b d x^2",1,"(b*d*x)/(2*c) + (b*d*x^2)/6 + (d*x^2*(a + b*ArcTanh[c*x]))/2 + (c*d*x^3*(a + b*ArcTanh[c*x]))/3 + (5*b*d*Log[1 - c*x])/(12*c^2) - (b*d*Log[1 + c*x])/(12*c^2)","A",7,6,16,0.3750,1,"{43, 5936, 12, 801, 633, 31}"
4,1,44,0,0.0299195,"\int (d+c d x) \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[(d + c*d*x)*(a + b*ArcTanh[c*x]),x]","\frac{d (c x+1)^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c}+\frac{b d \log (1-c x)}{c}+\frac{b d x}{2}","\frac{d (c x+1)^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c}+\frac{b d \log (1-c x)}{c}+\frac{b d x}{2}",1,"(b*d*x)/2 + (d*(1 + c*x)^2*(a + b*ArcTanh[c*x]))/(2*c) + (b*d*Log[1 - c*x])/c","A",4,3,15,0.2000,1,"{5926, 627, 43}"
5,1,60,0,0.0693332,"\int \frac{(d+c d x) \left(a+b \tanh ^{-1}(c x)\right)}{x} \, dx","Int[((d + c*d*x)*(a + b*ArcTanh[c*x]))/x,x]","-\frac{1}{2} b d \text{PolyLog}(2,-c x)+\frac{1}{2} b d \text{PolyLog}(2,c x)+a c d x+a d \log (x)+\frac{1}{2} b d \log \left(1-c^2 x^2\right)+b c d x \tanh ^{-1}(c x)","-\frac{1}{2} b d \text{PolyLog}(2,-c x)+\frac{1}{2} b d \text{PolyLog}(2,c x)+a c d x+a d \log (x)+\frac{1}{2} b d \log \left(1-c^2 x^2\right)+b c d x \tanh ^{-1}(c x)",1,"a*c*d*x + b*c*d*x*ArcTanh[c*x] + a*d*Log[x] + (b*d*Log[1 - c^2*x^2])/2 - (b*d*PolyLog[2, -(c*x)])/2 + (b*d*PolyLog[2, c*x])/2","A",6,4,18,0.2222,1,"{5940, 5910, 260, 5912}"
6,1,70,0,0.0859438,"\int \frac{(d+c d x) \left(a+b \tanh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + c*d*x)*(a + b*ArcTanh[c*x]))/x^2,x]","-\frac{1}{2} b c d \text{PolyLog}(2,-c x)+\frac{1}{2} b c d \text{PolyLog}(2,c x)-\frac{d \left(a+b \tanh ^{-1}(c x)\right)}{x}+a c d \log (x)-\frac{1}{2} b c d \log \left(1-c^2 x^2\right)+b c d \log (x)","-\frac{1}{2} b c d \text{PolyLog}(2,-c x)+\frac{1}{2} b c d \text{PolyLog}(2,c x)-\frac{d \left(a+b \tanh ^{-1}(c x)\right)}{x}+a c d \log (x)-\frac{1}{2} b c d \log \left(1-c^2 x^2\right)+b c d \log (x)",1,"-((d*(a + b*ArcTanh[c*x]))/x) + a*c*d*Log[x] + b*c*d*Log[x] - (b*c*d*Log[1 - c^2*x^2])/2 - (b*c*d*PolyLog[2, -(c*x)])/2 + (b*c*d*PolyLog[2, c*x])/2","A",8,7,18,0.3889,1,"{5940, 5916, 266, 36, 29, 31, 5912}"
7,1,56,0,0.0540103,"\int \frac{(d+c d x) \left(a+b \tanh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + c*d*x)*(a + b*ArcTanh[c*x]))/x^3,x]","-\frac{d (c x+1)^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}+b c^2 d \log (x)-b c^2 d \log (1-c x)-\frac{b c d}{2 x}","-\frac{d (c x+1)^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}+b c^2 d \log (x)-b c^2 d \log (1-c x)-\frac{b c d}{2 x}",1,"-(b*c*d)/(2*x) - (d*(1 + c*x)^2*(a + b*ArcTanh[c*x]))/(2*x^2) + b*c^2*d*Log[x] - b*c^2*d*Log[1 - c*x]","A",4,4,18,0.2222,1,"{37, 5936, 12, 77}"
8,1,98,0,0.0866609,"\int \frac{(d+c d x) \left(a+b \tanh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + c*d*x)*(a + b*ArcTanh[c*x]))/x^4,x]","-\frac{c d \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{b c^2 d}{2 x}+\frac{1}{3} b c^3 d \log (x)-\frac{5}{12} b c^3 d \log (1-c x)+\frac{1}{12} b c^3 d \log (c x+1)-\frac{b c d}{6 x^2}","-\frac{c d \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{b c^2 d}{2 x}+\frac{1}{3} b c^3 d \log (x)-\frac{5}{12} b c^3 d \log (1-c x)+\frac{1}{12} b c^3 d \log (c x+1)-\frac{b c d}{6 x^2}",1,"-(b*c*d)/(6*x^2) - (b*c^2*d)/(2*x) - (d*(a + b*ArcTanh[c*x]))/(3*x^3) - (c*d*(a + b*ArcTanh[c*x]))/(2*x^2) + (b*c^3*d*Log[x])/3 - (5*b*c^3*d*Log[1 - c*x])/12 + (b*c^3*d*Log[1 + c*x])/12","A",4,4,18,0.2222,1,"{43, 5936, 12, 801}"
9,1,110,0,0.0924434,"\int \frac{(d+c d x) \left(a+b \tanh ^{-1}(c x)\right)}{x^5} \, dx","Int[((d + c*d*x)*(a + b*ArcTanh[c*x]))/x^5,x]","-\frac{c d \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)}{4 x^4}-\frac{b c^2 d}{6 x^2}-\frac{b c^3 d}{4 x}+\frac{1}{3} b c^4 d \log (x)-\frac{7}{24} b c^4 d \log (1-c x)-\frac{1}{24} b c^4 d \log (c x+1)-\frac{b c d}{12 x^3}","-\frac{c d \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)}{4 x^4}-\frac{b c^2 d}{6 x^2}-\frac{b c^3 d}{4 x}+\frac{1}{3} b c^4 d \log (x)-\frac{7}{24} b c^4 d \log (1-c x)-\frac{1}{24} b c^4 d \log (c x+1)-\frac{b c d}{12 x^3}",1,"-(b*c*d)/(12*x^3) - (b*c^2*d)/(6*x^2) - (b*c^3*d)/(4*x) - (d*(a + b*ArcTanh[c*x]))/(4*x^4) - (c*d*(a + b*ArcTanh[c*x]))/(3*x^3) + (b*c^4*d*Log[x])/3 - (7*b*c^4*d*Log[1 - c*x])/24 - (b*c^4*d*Log[1 + c*x])/24","A",4,4,18,0.2222,1,"{43, 5936, 12, 801}"
10,1,157,0,0.1678131,"\int x^3 (d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^3*(d + c*d*x)^2*(a + b*ArcTanh[c*x]),x]","\frac{1}{6} c^2 d^2 x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{2}{5} c d^2 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d^2 x^2}{5 c^2}+\frac{5 b d^2 x}{12 c^3}+\frac{49 b d^2 \log (1-c x)}{120 c^4}-\frac{b d^2 \log (c x+1)}{120 c^4}+\frac{1}{30} b c d^2 x^5+\frac{5 b d^2 x^3}{36 c}+\frac{1}{10} b d^2 x^4","\frac{1}{6} c^2 d^2 x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{2}{5} c d^2 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d^2 x^2}{5 c^2}+\frac{5 b d^2 x}{12 c^3}+\frac{49 b d^2 \log (1-c x)}{120 c^4}-\frac{b d^2 \log (c x+1)}{120 c^4}+\frac{1}{30} b c d^2 x^5+\frac{5 b d^2 x^3}{36 c}+\frac{1}{10} b d^2 x^4",1,"(5*b*d^2*x)/(12*c^3) + (b*d^2*x^2)/(5*c^2) + (5*b*d^2*x^3)/(36*c) + (b*d^2*x^4)/10 + (b*c*d^2*x^5)/30 + (d^2*x^4*(a + b*ArcTanh[c*x]))/4 + (2*c*d^2*x^5*(a + b*ArcTanh[c*x]))/5 + (c^2*d^2*x^6*(a + b*ArcTanh[c*x]))/6 + (49*b*d^2*Log[1 - c*x])/(120*c^4) - (b*d^2*Log[1 + c*x])/(120*c^4)","A",7,6,20,0.3000,1,"{43, 5936, 12, 1802, 633, 31}"
11,1,143,0,0.1544106,"\int x^2 (d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^2*(d + c*d*x)^2*(a + b*ArcTanh[c*x]),x]","\frac{1}{5} c^2 d^2 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} c d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{3} d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d^2 x}{2 c^2}+\frac{31 b d^2 \log (1-c x)}{60 c^3}+\frac{b d^2 \log (c x+1)}{60 c^3}+\frac{1}{20} b c d^2 x^4+\frac{4 b d^2 x^2}{15 c}+\frac{1}{6} b d^2 x^3","\frac{1}{5} c^2 d^2 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} c d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{3} d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d^2 x}{2 c^2}+\frac{31 b d^2 \log (1-c x)}{60 c^3}+\frac{b d^2 \log (c x+1)}{60 c^3}+\frac{1}{20} b c d^2 x^4+\frac{4 b d^2 x^2}{15 c}+\frac{1}{6} b d^2 x^3",1,"(b*d^2*x)/(2*c^2) + (4*b*d^2*x^2)/(15*c) + (b*d^2*x^3)/6 + (b*c*d^2*x^4)/20 + (d^2*x^3*(a + b*ArcTanh[c*x]))/3 + (c*d^2*x^4*(a + b*ArcTanh[c*x]))/2 + (c^2*d^2*x^5*(a + b*ArcTanh[c*x]))/5 + (31*b*d^2*Log[1 - c*x])/(60*c^3) + (b*d^2*Log[1 + c*x])/(60*c^3)","A",7,6,20,0.3000,1,"{43, 5936, 12, 1802, 633, 31}"
12,1,129,0,0.1302196,"\int x (d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x*(d + c*d*x)^2*(a + b*ArcTanh[c*x]),x]","\frac{1}{4} c^2 d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{2}{3} c d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{17 b d^2 \log (1-c x)}{24 c^2}-\frac{b d^2 \log (c x+1)}{24 c^2}+\frac{1}{12} b c d^2 x^3+\frac{3 b d^2 x}{4 c}+\frac{1}{3} b d^2 x^2","\frac{1}{4} c^2 d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{2}{3} c d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{17 b d^2 \log (1-c x)}{24 c^2}-\frac{b d^2 \log (c x+1)}{24 c^2}+\frac{1}{12} b c d^2 x^3+\frac{3 b d^2 x}{4 c}+\frac{1}{3} b d^2 x^2",1,"(3*b*d^2*x)/(4*c) + (b*d^2*x^2)/3 + (b*c*d^2*x^3)/12 + (d^2*x^2*(a + b*ArcTanh[c*x]))/2 + (2*c*d^2*x^3*(a + b*ArcTanh[c*x]))/3 + (c^2*d^2*x^4*(a + b*ArcTanh[c*x]))/4 + (17*b*d^2*Log[1 - c*x])/(24*c^2) - (b*d^2*Log[1 + c*x])/(24*c^2)","A",7,6,18,0.3333,1,"{43, 5936, 12, 1802, 633, 31}"
13,1,71,0,0.0425078,"\int (d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[(d + c*d*x)^2*(a + b*ArcTanh[c*x]),x]","\frac{d^2 (c x+1)^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 c}+\frac{b d^2 (c x+1)^2}{6 c}+\frac{4 b d^2 \log (1-c x)}{3 c}+\frac{2}{3} b d^2 x","\frac{d^2 (c x+1)^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 c}+\frac{b d^2 (c x+1)^2}{6 c}+\frac{4 b d^2 \log (1-c x)}{3 c}+\frac{2}{3} b d^2 x",1,"(2*b*d^2*x)/3 + (b*d^2*(1 + c*x)^2)/(6*c) + (d^2*(1 + c*x)^3*(a + b*ArcTanh[c*x]))/(3*c) + (4*b*d^2*Log[1 - c*x])/(3*c)","A",4,3,17,0.1765,1,"{5926, 627, 43}"
14,1,114,0,0.113866,"\int \frac{(d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)}{x} \, dx","Int[((d + c*d*x)^2*(a + b*ArcTanh[c*x]))/x,x]","-\frac{1}{2} b d^2 \text{PolyLog}(2,-c x)+\frac{1}{2} b d^2 \text{PolyLog}(2,c x)+\frac{1}{2} c^2 d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)+2 a c d^2 x+a d^2 \log (x)+b d^2 \log \left(1-c^2 x^2\right)+\frac{1}{2} b c d^2 x-\frac{1}{2} b d^2 \tanh ^{-1}(c x)+2 b c d^2 x \tanh ^{-1}(c x)","-\frac{1}{2} b d^2 \text{PolyLog}(2,-c x)+\frac{1}{2} b d^2 \text{PolyLog}(2,c x)+\frac{1}{2} c^2 d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)+2 a c d^2 x+a d^2 \log (x)+b d^2 \log \left(1-c^2 x^2\right)+\frac{1}{2} b c d^2 x-\frac{1}{2} b d^2 \tanh ^{-1}(c x)+2 b c d^2 x \tanh ^{-1}(c x)",1,"2*a*c*d^2*x + (b*c*d^2*x)/2 - (b*d^2*ArcTanh[c*x])/2 + 2*b*c*d^2*x*ArcTanh[c*x] + (c^2*d^2*x^2*(a + b*ArcTanh[c*x]))/2 + a*d^2*Log[x] + b*d^2*Log[1 - c^2*x^2] - (b*d^2*PolyLog[2, -(c*x)])/2 + (b*d^2*PolyLog[2, c*x])/2","A",9,7,20,0.3500,1,"{5940, 5910, 260, 5912, 5916, 321, 206}"
15,1,80,0,0.1258318,"\int \frac{(d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + c*d*x)^2*(a + b*ArcTanh[c*x]))/x^2,x]","-b c d^2 \text{PolyLog}(2,-c x)+b c d^2 \text{PolyLog}(2,c x)-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)}{x}+a c^2 d^2 x+2 a c d^2 \log (x)+b c^2 d^2 x \tanh ^{-1}(c x)+b c d^2 \log (x)","-b c d^2 \text{PolyLog}(2,-c x)+b c d^2 \text{PolyLog}(2,c x)+\frac{d^2 \left(c^2 x^2-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{x}+c d^2 (2 a+b) \log (x)",1,"a*c^2*d^2*x + b*c^2*d^2*x*ArcTanh[c*x] - (d^2*(a + b*ArcTanh[c*x]))/x + 2*a*c*d^2*Log[x] + b*c*d^2*Log[x] - b*c*d^2*PolyLog[2, -(c*x)] + b*c*d^2*PolyLog[2, c*x]","A",11,9,20,0.4500,1,"{5940, 5910, 260, 5916, 266, 36, 29, 31, 5912}"
16,1,137,0,0.139936,"\int \frac{(d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + c*d*x)^2*(a + b*ArcTanh[c*x]))/x^3,x]","-\frac{1}{2} b c^2 d^2 \text{PolyLog}(2,-c x)+\frac{1}{2} b c^2 d^2 \text{PolyLog}(2,c x)-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{2 c d^2 \left(a+b \tanh ^{-1}(c x)\right)}{x}+a c^2 d^2 \log (x)-b c^2 d^2 \log \left(1-c^2 x^2\right)+2 b c^2 d^2 \log (x)+\frac{1}{2} b c^2 d^2 \tanh ^{-1}(c x)-\frac{b c d^2}{2 x}","-\frac{1}{2} b c^2 d^2 \text{PolyLog}(2,-c x)+\frac{1}{2} b c^2 d^2 \text{PolyLog}(2,c x)-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{2 c d^2 \left(a+b \tanh ^{-1}(c x)\right)}{x}+a c^2 d^2 \log (x)-b c^2 d^2 \log \left(1-c^2 x^2\right)+2 b c^2 d^2 \log (x)+\frac{1}{2} b c^2 d^2 \tanh ^{-1}(c x)-\frac{b c d^2}{2 x}",1,"-(b*c*d^2)/(2*x) + (b*c^2*d^2*ArcTanh[c*x])/2 - (d^2*(a + b*ArcTanh[c*x]))/(2*x^2) - (2*c*d^2*(a + b*ArcTanh[c*x]))/x + a*c^2*d^2*Log[x] + 2*b*c^2*d^2*Log[x] - b*c^2*d^2*Log[1 - c^2*x^2] - (b*c^2*d^2*PolyLog[2, -(c*x)])/2 + (b*c^2*d^2*PolyLog[2, c*x])/2","A",11,9,20,0.4500,1,"{5940, 5916, 325, 206, 266, 36, 29, 31, 5912}"
17,1,81,0,0.0849651,"\int \frac{(d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + c*d*x)^2*(a + b*ArcTanh[c*x]))/x^4,x]","-\frac{d^2 (c x+1)^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{b c^2 d^2}{x}+\frac{4}{3} b c^3 d^2 \log (x)-\frac{4}{3} b c^3 d^2 \log (1-c x)-\frac{b c d^2}{6 x^2}","-\frac{d^2 (c x+1)^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{b c^2 d^2}{x}+\frac{4}{3} b c^3 d^2 \log (x)-\frac{4}{3} b c^3 d^2 \log (1-c x)-\frac{b c d^2}{6 x^2}",1,"-(b*c*d^2)/(6*x^2) - (b*c^2*d^2)/x - (d^2*(1 + c*x)^3*(a + b*ArcTanh[c*x]))/(3*x^3) + (4*b*c^3*d^2*Log[x])/3 - (4*b*c^3*d^2*Log[1 - c*x])/3","A",4,4,20,0.2000,1,"{37, 5936, 12, 88}"
18,1,147,0,0.149283,"\int \frac{(d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)}{x^5} \, dx","Int[((d + c*d*x)^2*(a + b*ArcTanh[c*x]))/x^5,x]","-\frac{c^2 d^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{2 c d^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)}{4 x^4}-\frac{b c^2 d^2}{3 x^2}-\frac{3 b c^3 d^2}{4 x}+\frac{2}{3} b c^4 d^2 \log (x)-\frac{17}{24} b c^4 d^2 \log (1-c x)+\frac{1}{24} b c^4 d^2 \log (c x+1)-\frac{b c d^2}{12 x^3}","-\frac{c^2 d^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{2 c d^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)}{4 x^4}-\frac{b c^2 d^2}{3 x^2}-\frac{3 b c^3 d^2}{4 x}+\frac{2}{3} b c^4 d^2 \log (x)-\frac{17}{24} b c^4 d^2 \log (1-c x)+\frac{1}{24} b c^4 d^2 \log (c x+1)-\frac{b c d^2}{12 x^3}",1,"-(b*c*d^2)/(12*x^3) - (b*c^2*d^2)/(3*x^2) - (3*b*c^3*d^2)/(4*x) - (d^2*(a + b*ArcTanh[c*x]))/(4*x^4) - (2*c*d^2*(a + b*ArcTanh[c*x]))/(3*x^3) - (c^2*d^2*(a + b*ArcTanh[c*x]))/(2*x^2) + (2*b*c^4*d^2*Log[x])/3 - (17*b*c^4*d^2*Log[1 - c*x])/24 + (b*c^4*d^2*Log[1 + c*x])/24","A",4,4,20,0.2000,1,"{43, 5936, 12, 1802}"
19,1,161,0,0.1602659,"\int \frac{(d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)}{x^6} \, dx","Int[((d + c*d*x)^2*(a + b*ArcTanh[c*x]))/x^6,x]","-\frac{c^2 d^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{c d^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^4}-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^5}-\frac{4 b c^3 d^2}{15 x^2}-\frac{b c^2 d^2}{6 x^3}-\frac{b c^4 d^2}{2 x}+\frac{8}{15} b c^5 d^2 \log (x)-\frac{31}{60} b c^5 d^2 \log (1-c x)-\frac{1}{60} b c^5 d^2 \log (c x+1)-\frac{b c d^2}{20 x^4}","-\frac{c^2 d^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{c d^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^4}-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^5}-\frac{4 b c^3 d^2}{15 x^2}-\frac{b c^2 d^2}{6 x^3}-\frac{b c^4 d^2}{2 x}+\frac{8}{15} b c^5 d^2 \log (x)-\frac{31}{60} b c^5 d^2 \log (1-c x)-\frac{1}{60} b c^5 d^2 \log (c x+1)-\frac{b c d^2}{20 x^4}",1,"-(b*c*d^2)/(20*x^4) - (b*c^2*d^2)/(6*x^3) - (4*b*c^3*d^2)/(15*x^2) - (b*c^4*d^2)/(2*x) - (d^2*(a + b*ArcTanh[c*x]))/(5*x^5) - (c*d^2*(a + b*ArcTanh[c*x]))/(2*x^4) - (c^2*d^2*(a + b*ArcTanh[c*x]))/(3*x^3) + (8*b*c^5*d^2*Log[x])/15 - (31*b*c^5*d^2*Log[1 - c*x])/60 - (b*c^5*d^2*Log[1 + c*x])/60","A",4,4,20,0.2000,1,"{43, 5936, 12, 1802}"
20,1,192,0,0.1814295,"\int x^3 (d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^3*(d + c*d*x)^3*(a + b*ArcTanh[c*x]),x]","\frac{1}{7} c^3 d^3 x^7 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} c^2 d^3 x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{5} c d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{42} b c^2 d^3 x^6+\frac{13 b d^3 x^2}{35 c^2}+\frac{3 b d^3 x}{4 c^3}+\frac{209 b d^3 \log (1-c x)}{280 c^4}-\frac{b d^3 \log (c x+1)}{280 c^4}+\frac{1}{10} b c d^3 x^5+\frac{b d^3 x^3}{4 c}+\frac{13}{70} b d^3 x^4","\frac{1}{7} c^3 d^3 x^7 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} c^2 d^3 x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{5} c d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{42} b c^2 d^3 x^6+\frac{13 b d^3 x^2}{35 c^2}+\frac{3 b d^3 x}{4 c^3}+\frac{209 b d^3 \log (1-c x)}{280 c^4}-\frac{b d^3 \log (c x+1)}{280 c^4}+\frac{1}{10} b c d^3 x^5+\frac{b d^3 x^3}{4 c}+\frac{13}{70} b d^3 x^4",1,"(3*b*d^3*x)/(4*c^3) + (13*b*d^3*x^2)/(35*c^2) + (b*d^3*x^3)/(4*c) + (13*b*d^3*x^4)/70 + (b*c*d^3*x^5)/10 + (b*c^2*d^3*x^6)/42 + (d^3*x^4*(a + b*ArcTanh[c*x]))/4 + (3*c*d^3*x^5*(a + b*ArcTanh[c*x]))/5 + (c^2*d^3*x^6*(a + b*ArcTanh[c*x]))/2 + (c^3*d^3*x^7*(a + b*ArcTanh[c*x]))/7 + (209*b*d^3*Log[1 - c*x])/(280*c^4) - (b*d^3*Log[1 + c*x])/(280*c^4)","A",7,6,20,0.3000,1,"{43, 5936, 12, 1802, 633, 31}"
21,1,178,0,0.1756644,"\int x^2 (d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^2*(d + c*d*x)^3*(a + b*ArcTanh[c*x]),x]","\frac{1}{6} c^3 d^3 x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{5} c^2 d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{4} c d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{30} b c^2 d^3 x^5+\frac{11 b d^3 x}{12 c^2}+\frac{37 b d^3 \log (1-c x)}{40 c^3}+\frac{b d^3 \log (c x+1)}{120 c^3}+\frac{3}{20} b c d^3 x^4+\frac{7 b d^3 x^2}{15 c}+\frac{11}{36} b d^3 x^3","\frac{1}{6} c^3 d^3 x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{5} c^2 d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{4} c d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{30} b c^2 d^3 x^5+\frac{11 b d^3 x}{12 c^2}+\frac{37 b d^3 \log (1-c x)}{40 c^3}+\frac{b d^3 \log (c x+1)}{120 c^3}+\frac{3}{20} b c d^3 x^4+\frac{7 b d^3 x^2}{15 c}+\frac{11}{36} b d^3 x^3",1,"(11*b*d^3*x)/(12*c^2) + (7*b*d^3*x^2)/(15*c) + (11*b*d^3*x^3)/36 + (3*b*c*d^3*x^4)/20 + (b*c^2*d^3*x^5)/30 + (d^3*x^3*(a + b*ArcTanh[c*x]))/3 + (3*c*d^3*x^4*(a + b*ArcTanh[c*x]))/4 + (3*c^2*d^3*x^5*(a + b*ArcTanh[c*x]))/5 + (c^3*d^3*x^6*(a + b*ArcTanh[c*x]))/6 + (37*b*d^3*Log[1 - c*x])/(40*c^3) + (b*d^3*Log[1 + c*x])/(120*c^3)","A",7,6,20,0.3000,1,"{43, 5936, 12, 1802, 633, 31}"
22,1,135,0,0.1011096,"\int x (d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x*(d + c*d*x)^3*(a + b*ArcTanh[c*x]),x]","\frac{d^3 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^2}-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2}+\frac{b d^3 (c x+1)^4}{20 c^2}+\frac{b d^3 (c x+1)^3}{20 c^2}+\frac{3 b d^3 (c x+1)^2}{20 c^2}+\frac{6 b d^3 \log (1-c x)}{5 c^2}+\frac{3 b d^3 x}{5 c}","\frac{d^3 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^2}-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2}+\frac{b d^3 (c x+1)^4}{20 c^2}+\frac{b d^3 (c x+1)^3}{20 c^2}+\frac{3 b d^3 (c x+1)^2}{20 c^2}+\frac{6 b d^3 \log (1-c x)}{5 c^2}+\frac{3 b d^3 x}{5 c}",1,"(3*b*d^3*x)/(5*c) + (3*b*d^3*(1 + c*x)^2)/(20*c^2) + (b*d^3*(1 + c*x)^3)/(20*c^2) + (b*d^3*(1 + c*x)^4)/(20*c^2) - (d^3*(1 + c*x)^4*(a + b*ArcTanh[c*x]))/(4*c^2) + (d^3*(1 + c*x)^5*(a + b*ArcTanh[c*x]))/(5*c^2) + (6*b*d^3*Log[1 - c*x])/(5*c^2)","A",4,4,18,0.2222,1,"{43, 5936, 12, 77}"
23,1,84,0,0.051169,"\int (d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[(d + c*d*x)^3*(a + b*ArcTanh[c*x]),x]","\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)}{4 c}+\frac{b d^3 (c x+1)^3}{12 c}+\frac{b d^3 (c x+1)^2}{4 c}+\frac{2 b d^3 \log (1-c x)}{c}+b d^3 x","\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)}{4 c}+\frac{b d^3 (c x+1)^3}{12 c}+\frac{b d^3 (c x+1)^2}{4 c}+\frac{2 b d^3 \log (1-c x)}{c}+b d^3 x",1,"b*d^3*x + (b*d^3*(1 + c*x)^2)/(4*c) + (b*d^3*(1 + c*x)^3)/(12*c) + (d^3*(1 + c*x)^4*(a + b*ArcTanh[c*x]))/(4*c) + (2*b*d^3*Log[1 - c*x])/c","A",4,3,17,0.1765,1,"{5926, 627, 43}"
24,1,152,0,0.1658906,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)}{x} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x]))/x,x]","-\frac{1}{2} b d^3 \text{PolyLog}(2,-c x)+\frac{1}{2} b d^3 \text{PolyLog}(2,c x)+\frac{1}{3} c^3 d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{2} c^2 d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)+3 a c d^3 x+a d^3 \log (x)+\frac{1}{6} b c^2 d^3 x^2+\frac{5}{3} b d^3 \log \left(1-c^2 x^2\right)+\frac{3}{2} b c d^3 x-\frac{3}{2} b d^3 \tanh ^{-1}(c x)+3 b c d^3 x \tanh ^{-1}(c x)","-\frac{1}{2} b d^3 \text{PolyLog}(2,-c x)+\frac{1}{2} b d^3 \text{PolyLog}(2,c x)+\frac{1}{3} c^3 d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{2} c^2 d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)+3 a c d^3 x+a d^3 \log (x)+\frac{1}{6} b c^2 d^3 x^2+\frac{5}{3} b d^3 \log \left(1-c^2 x^2\right)+\frac{3}{2} b c d^3 x-\frac{3}{2} b d^3 \tanh ^{-1}(c x)+3 b c d^3 x \tanh ^{-1}(c x)",1,"3*a*c*d^3*x + (3*b*c*d^3*x)/2 + (b*c^2*d^3*x^2)/6 - (3*b*d^3*ArcTanh[c*x])/2 + 3*b*c*d^3*x*ArcTanh[c*x] + (3*c^2*d^3*x^2*(a + b*ArcTanh[c*x]))/2 + (c^3*d^3*x^3*(a + b*ArcTanh[c*x]))/3 + a*d^3*Log[x] + (5*b*d^3*Log[1 - c^2*x^2])/3 - (b*d^3*PolyLog[2, -(c*x)])/2 + (b*d^3*PolyLog[2, c*x])/2","A",13,9,20,0.4500,1,"{5940, 5910, 260, 5912, 5916, 321, 206, 266, 43}"
25,1,150,0,0.1576284,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x]))/x^2,x]","-\frac{3}{2} b c d^3 \text{PolyLog}(2,-c x)+\frac{3}{2} b c d^3 \text{PolyLog}(2,c x)+\frac{1}{2} c^3 d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x}+3 a c^2 d^3 x+3 a c d^3 \log (x)+b c d^3 \log \left(1-c^2 x^2\right)+\frac{1}{2} b c^2 d^3 x+3 b c^2 d^3 x \tanh ^{-1}(c x)+b c d^3 \log (x)-\frac{1}{2} b c d^3 \tanh ^{-1}(c x)","-\frac{3}{2} b c d^3 \text{PolyLog}(2,-c x)+\frac{3}{2} b c d^3 \text{PolyLog}(2,c x)+\frac{1}{2} c^3 d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x}+3 a c^2 d^3 x+3 a c d^3 \log (x)+b c d^3 \log \left(1-c^2 x^2\right)+\frac{1}{2} b c^2 d^3 x+3 b c^2 d^3 x \tanh ^{-1}(c x)+b c d^3 \log (x)-\frac{1}{2} b c d^3 \tanh ^{-1}(c x)",1,"3*a*c^2*d^3*x + (b*c^2*d^3*x)/2 - (b*c*d^3*ArcTanh[c*x])/2 + 3*b*c^2*d^3*x*ArcTanh[c*x] - (d^3*(a + b*ArcTanh[c*x]))/x + (c^3*d^3*x^2*(a + b*ArcTanh[c*x]))/2 + 3*a*c*d^3*Log[x] + b*c*d^3*Log[x] + b*c*d^3*Log[1 - c^2*x^2] - (3*b*c*d^3*PolyLog[2, -(c*x)])/2 + (3*b*c*d^3*PolyLog[2, c*x])/2","A",14,11,20,0.5500,1,"{5940, 5910, 260, 5916, 266, 36, 29, 31, 5912, 321, 206}"
26,1,160,0,0.1679667,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x]))/x^3,x]","-\frac{3}{2} b c^2 d^3 \text{PolyLog}(2,-c x)+\frac{3}{2} b c^2 d^3 \text{PolyLog}(2,c x)-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x}+a c^3 d^3 x+3 a c^2 d^3 \log (x)-b c^2 d^3 \log \left(1-c^2 x^2\right)+3 b c^2 d^3 \log (x)+\frac{1}{2} b c^2 d^3 \tanh ^{-1}(c x)+b c^3 d^3 x \tanh ^{-1}(c x)-\frac{b c d^3}{2 x}","-\frac{3}{2} b c^2 d^3 \text{PolyLog}(2,-c x)+\frac{3}{2} b c^2 d^3 \text{PolyLog}(2,c x)-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x}+a c^3 d^3 x+3 a c^2 d^3 \log (x)-b c^2 d^3 \log \left(1-c^2 x^2\right)+3 b c^2 d^3 \log (x)+\frac{1}{2} b c^2 d^3 \tanh ^{-1}(c x)+b c^3 d^3 x \tanh ^{-1}(c x)-\frac{b c d^3}{2 x}",1,"-(b*c*d^3)/(2*x) + a*c^3*d^3*x + (b*c^2*d^3*ArcTanh[c*x])/2 + b*c^3*d^3*x*ArcTanh[c*x] - (d^3*(a + b*ArcTanh[c*x]))/(2*x^2) - (3*c*d^3*(a + b*ArcTanh[c*x]))/x + 3*a*c^2*d^3*Log[x] + 3*b*c^2*d^3*Log[x] - b*c^2*d^3*Log[1 - c^2*x^2] - (3*b*c^2*d^3*PolyLog[2, -(c*x)])/2 + (3*b*c^2*d^3*PolyLog[2, c*x])/2","A",14,11,20,0.5500,1,"{5940, 5910, 260, 5916, 325, 206, 266, 36, 29, 31, 5912}"
27,1,176,0,0.1942525,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x]))/x^4,x]","-\frac{1}{2} b c^3 d^3 \text{PolyLog}(2,-c x)+\frac{1}{2} b c^3 d^3 \text{PolyLog}(2,c x)-\frac{3 c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}+a c^3 d^3 \log (x)-\frac{5}{3} b c^3 d^3 \log \left(1-c^2 x^2\right)-\frac{3 b c^2 d^3}{2 x}+\frac{10}{3} b c^3 d^3 \log (x)+\frac{3}{2} b c^3 d^3 \tanh ^{-1}(c x)-\frac{b c d^3}{6 x^2}","-\frac{1}{2} b c^3 d^3 \text{PolyLog}(2,-c x)+\frac{1}{2} b c^3 d^3 \text{PolyLog}(2,c x)-\frac{3 c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}+a c^3 d^3 \log (x)-\frac{5}{3} b c^3 d^3 \log \left(1-c^2 x^2\right)-\frac{3 b c^2 d^3}{2 x}+\frac{10}{3} b c^3 d^3 \log (x)+\frac{3}{2} b c^3 d^3 \tanh ^{-1}(c x)-\frac{b c d^3}{6 x^2}",1,"-(b*c*d^3)/(6*x^2) - (3*b*c^2*d^3)/(2*x) + (3*b*c^3*d^3*ArcTanh[c*x])/2 - (d^3*(a + b*ArcTanh[c*x]))/(3*x^3) - (3*c*d^3*(a + b*ArcTanh[c*x]))/(2*x^2) - (3*c^2*d^3*(a + b*ArcTanh[c*x]))/x + a*c^3*d^3*Log[x] + (10*b*c^3*d^3*Log[x])/3 - (5*b*c^3*d^3*Log[1 - c^2*x^2])/3 - (b*c^3*d^3*PolyLog[2, -(c*x)])/2 + (b*c^3*d^3*PolyLog[2, c*x])/2","A",15,10,20,0.5000,1,"{5940, 5916, 266, 44, 325, 206, 36, 29, 31, 5912}"
28,1,93,0,0.0985638,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)}{x^5} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x]))/x^5,x]","-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)}{4 x^4}-\frac{b c^2 d^3}{2 x^2}-\frac{7 b c^3 d^3}{4 x}+2 b c^4 d^3 \log (x)-2 b c^4 d^3 \log (1-c x)-\frac{b c d^3}{12 x^3}","-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)}{4 x^4}-\frac{b c^2 d^3}{2 x^2}-\frac{7 b c^3 d^3}{4 x}+2 b c^4 d^3 \log (x)-2 b c^4 d^3 \log (1-c x)-\frac{b c d^3}{12 x^3}",1,"-(b*c*d^3)/(12*x^3) - (b*c^2*d^3)/(2*x^2) - (7*b*c^3*d^3)/(4*x) - (d^3*(1 + c*x)^4*(a + b*ArcTanh[c*x]))/(4*x^4) + 2*b*c^4*d^3*Log[x] - 2*b*c^4*d^3*Log[1 - c*x]","A",4,4,20,0.2000,1,"{37, 5936, 12, 88}"
29,1,137,0,0.1188442,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)}{x^6} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x]))/x^6,x]","\frac{c d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)}{20 x^4}-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^5}-\frac{3 b c^3 d^3}{5 x^2}-\frac{b c^2 d^3}{4 x^3}-\frac{5 b c^4 d^3}{4 x}+\frac{6}{5} b c^5 d^3 \log (x)-\frac{6}{5} b c^5 d^3 \log (1-c x)-\frac{b c d^3}{20 x^4}","\frac{c d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)}{20 x^4}-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^5}-\frac{3 b c^3 d^3}{5 x^2}-\frac{b c^2 d^3}{4 x^3}-\frac{5 b c^4 d^3}{4 x}+\frac{6}{5} b c^5 d^3 \log (x)-\frac{6}{5} b c^5 d^3 \log (1-c x)-\frac{b c d^3}{20 x^4}",1,"-(b*c*d^3)/(20*x^4) - (b*c^2*d^3)/(4*x^3) - (3*b*c^3*d^3)/(5*x^2) - (5*b*c^4*d^3)/(4*x) - (d^3*(1 + c*x)^4*(a + b*ArcTanh[c*x]))/(5*x^5) + (c*d^3*(1 + c*x)^4*(a + b*ArcTanh[c*x]))/(20*x^4) + (6*b*c^5*d^3*Log[x])/5 - (6*b*c^5*d^3*Log[1 - c*x])/5","A",4,5,20,0.2500,1,"{45, 37, 5936, 12, 148}"
30,1,196,0,0.1773125,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)}{x^7} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x]))/x^7,x]","-\frac{c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{3 c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{4 x^4}-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^5}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 x^6}-\frac{7 b c^4 d^3}{15 x^2}-\frac{11 b c^3 d^3}{36 x^3}-\frac{3 b c^2 d^3}{20 x^4}-\frac{11 b c^5 d^3}{12 x}+\frac{14}{15} b c^6 d^3 \log (x)-\frac{37}{40} b c^6 d^3 \log (1-c x)-\frac{1}{120} b c^6 d^3 \log (c x+1)-\frac{b c d^3}{30 x^5}","-\frac{c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{3 c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{4 x^4}-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^5}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 x^6}-\frac{7 b c^4 d^3}{15 x^2}-\frac{11 b c^3 d^3}{36 x^3}-\frac{3 b c^2 d^3}{20 x^4}-\frac{11 b c^5 d^3}{12 x}+\frac{14}{15} b c^6 d^3 \log (x)-\frac{37}{40} b c^6 d^3 \log (1-c x)-\frac{1}{120} b c^6 d^3 \log (c x+1)-\frac{b c d^3}{30 x^5}",1,"-(b*c*d^3)/(30*x^5) - (3*b*c^2*d^3)/(20*x^4) - (11*b*c^3*d^3)/(36*x^3) - (7*b*c^4*d^3)/(15*x^2) - (11*b*c^5*d^3)/(12*x) - (d^3*(a + b*ArcTanh[c*x]))/(6*x^6) - (3*c*d^3*(a + b*ArcTanh[c*x]))/(5*x^5) - (3*c^2*d^3*(a + b*ArcTanh[c*x]))/(4*x^4) - (c^3*d^3*(a + b*ArcTanh[c*x]))/(3*x^3) + (14*b*c^6*d^3*Log[x])/15 - (37*b*c^6*d^3*Log[1 - c*x])/40 - (b*c^6*d^3*Log[1 + c*x])/120","A",4,4,20,0.2000,1,"{43, 5936, 12, 1802}"
31,1,224,0,0.2134763,"\int x^3 (d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^3*(d + c*d*x)^4*(a + b*ArcTanh[c*x]),x]","\frac{1}{8} c^4 d^4 x^8 \left(a+b \tanh ^{-1}(c x)\right)+\frac{4}{7} c^3 d^4 x^7 \left(a+b \tanh ^{-1}(c x)\right)+c^2 d^4 x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{4}{5} c d^4 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d^4 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{56} b c^3 d^4 x^7+\frac{2}{21} b c^2 d^4 x^6+\frac{24 b d^4 x^2}{35 c^2}+\frac{11 b d^4 x}{8 c^3}+\frac{769 b d^4 \log (1-c x)}{560 c^4}-\frac{b d^4 \log (c x+1)}{560 c^4}+\frac{9}{40} b c d^4 x^5+\frac{11 b d^4 x^3}{24 c}+\frac{12}{35} b d^4 x^4","\frac{1}{8} c^4 d^4 x^8 \left(a+b \tanh ^{-1}(c x)\right)+\frac{4}{7} c^3 d^4 x^7 \left(a+b \tanh ^{-1}(c x)\right)+c^2 d^4 x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{4}{5} c d^4 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d^4 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{56} b c^3 d^4 x^7+\frac{2}{21} b c^2 d^4 x^6+\frac{24 b d^4 x^2}{35 c^2}+\frac{11 b d^4 x}{8 c^3}+\frac{769 b d^4 \log (1-c x)}{560 c^4}-\frac{b d^4 \log (c x+1)}{560 c^4}+\frac{9}{40} b c d^4 x^5+\frac{11 b d^4 x^3}{24 c}+\frac{12}{35} b d^4 x^4",1,"(11*b*d^4*x)/(8*c^3) + (24*b*d^4*x^2)/(35*c^2) + (11*b*d^4*x^3)/(24*c) + (12*b*d^4*x^4)/35 + (9*b*c*d^4*x^5)/40 + (2*b*c^2*d^4*x^6)/21 + (b*c^3*d^4*x^7)/56 + (d^4*x^4*(a + b*ArcTanh[c*x]))/4 + (4*c*d^4*x^5*(a + b*ArcTanh[c*x]))/5 + c^2*d^4*x^6*(a + b*ArcTanh[c*x]) + (4*c^3*d^4*x^7*(a + b*ArcTanh[c*x]))/7 + (c^4*d^4*x^8*(a + b*ArcTanh[c*x]))/8 + (769*b*d^4*Log[1 - c*x])/(560*c^4) - (b*d^4*Log[1 + c*x])/(560*c^4)","A",7,6,20,0.3000,1,"{43, 5936, 12, 1802, 633, 31}"
32,1,171,0,0.1805478,"\int x^2 (d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^2*(d + c*d*x)^4*(a + b*ArcTanh[c*x]),x]","\frac{d^4 (c x+1)^7 \left(a+b \tanh ^{-1}(c x)\right)}{7 c^3}-\frac{d^4 (c x+1)^6 \left(a+b \tanh ^{-1}(c x)\right)}{3 c^3}+\frac{d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^3}+\frac{1}{42} b c^3 d^4 x^6+\frac{2}{15} b c^2 d^4 x^5+\frac{5 b d^4 x}{3 c^2}+\frac{176 b d^4 \log (1-c x)}{105 c^3}+\frac{47}{140} b c d^4 x^4+\frac{88 b d^4 x^2}{105 c}+\frac{5}{9} b d^4 x^3","\frac{d^4 (c x+1)^7 \left(a+b \tanh ^{-1}(c x)\right)}{7 c^3}-\frac{d^4 (c x+1)^6 \left(a+b \tanh ^{-1}(c x)\right)}{3 c^3}+\frac{d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^3}+\frac{1}{42} b c^3 d^4 x^6+\frac{2}{15} b c^2 d^4 x^5+\frac{5 b d^4 x}{3 c^2}+\frac{176 b d^4 \log (1-c x)}{105 c^3}+\frac{47}{140} b c d^4 x^4+\frac{88 b d^4 x^2}{105 c}+\frac{5}{9} b d^4 x^3",1,"(5*b*d^4*x)/(3*c^2) + (88*b*d^4*x^2)/(105*c) + (5*b*d^4*x^3)/9 + (47*b*c*d^4*x^4)/140 + (2*b*c^2*d^4*x^5)/15 + (b*c^3*d^4*x^6)/42 + (d^4*(1 + c*x)^5*(a + b*ArcTanh[c*x]))/(5*c^3) - (d^4*(1 + c*x)^6*(a + b*ArcTanh[c*x]))/(3*c^3) + (d^4*(1 + c*x)^7*(a + b*ArcTanh[c*x]))/(7*c^3) + (176*b*d^4*Log[1 - c*x])/(105*c^3)","A",4,4,20,0.2000,1,"{43, 5936, 12, 893}"
33,1,153,0,0.1161789,"\int x (d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x*(d + c*d*x)^4*(a + b*ArcTanh[c*x]),x]","\frac{d^4 (c x+1)^6 \left(a+b \tanh ^{-1}(c x)\right)}{6 c^2}-\frac{d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^2}+\frac{b d^4 (c x+1)^5}{30 c^2}+\frac{b d^4 (c x+1)^4}{30 c^2}+\frac{4 b d^4 (c x+1)^3}{45 c^2}+\frac{4 b d^4 (c x+1)^2}{15 c^2}+\frac{32 b d^4 \log (1-c x)}{15 c^2}+\frac{16 b d^4 x}{15 c}","\frac{d^4 (c x+1)^6 \left(a+b \tanh ^{-1}(c x)\right)}{6 c^2}-\frac{d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^2}+\frac{b d^4 (c x+1)^5}{30 c^2}+\frac{b d^4 (c x+1)^4}{30 c^2}+\frac{4 b d^4 (c x+1)^3}{45 c^2}+\frac{4 b d^4 (c x+1)^2}{15 c^2}+\frac{32 b d^4 \log (1-c x)}{15 c^2}+\frac{16 b d^4 x}{15 c}",1,"(16*b*d^4*x)/(15*c) + (4*b*d^4*(1 + c*x)^2)/(15*c^2) + (4*b*d^4*(1 + c*x)^3)/(45*c^2) + (b*d^4*(1 + c*x)^4)/(30*c^2) + (b*d^4*(1 + c*x)^5)/(30*c^2) - (d^4*(1 + c*x)^5*(a + b*ArcTanh[c*x]))/(5*c^2) + (d^4*(1 + c*x)^6*(a + b*ArcTanh[c*x]))/(6*c^2) + (32*b*d^4*Log[1 - c*x])/(15*c^2)","A",4,4,18,0.2222,1,"{43, 5936, 12, 77}"
34,1,107,0,0.0548806,"\int (d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[(d + c*d*x)^4*(a + b*ArcTanh[c*x]),x]","\frac{d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 c}+\frac{b d^4 (c x+1)^4}{20 c}+\frac{2 b d^4 (c x+1)^3}{15 c}+\frac{2 b d^4 (c x+1)^2}{5 c}+\frac{16 b d^4 \log (1-c x)}{5 c}+\frac{8}{5} b d^4 x","\frac{d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 c}+\frac{b d^4 (c x+1)^4}{20 c}+\frac{2 b d^4 (c x+1)^3}{15 c}+\frac{2 b d^4 (c x+1)^2}{5 c}+\frac{16 b d^4 \log (1-c x)}{5 c}+\frac{8}{5} b d^4 x",1,"(8*b*d^4*x)/5 + (2*b*d^4*(1 + c*x)^2)/(5*c) + (2*b*d^4*(1 + c*x)^3)/(15*c) + (b*d^4*(1 + c*x)^4)/(20*c) + (d^4*(1 + c*x)^5*(a + b*ArcTanh[c*x]))/(5*c) + (16*b*d^4*Log[1 - c*x])/(5*c)","A",4,3,17,0.1765,1,"{5926, 627, 43}"
35,1,185,0,0.1970958,"\int \frac{(d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right)}{x} \, dx","Int[((d + c*d*x)^4*(a + b*ArcTanh[c*x]))/x,x]","-\frac{1}{2} b d^4 \text{PolyLog}(2,-c x)+\frac{1}{2} b d^4 \text{PolyLog}(2,c x)+\frac{1}{4} c^4 d^4 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{4}{3} c^3 d^4 x^3 \left(a+b \tanh ^{-1}(c x)\right)+3 c^2 d^4 x^2 \left(a+b \tanh ^{-1}(c x)\right)+4 a c d^4 x+a d^4 \log (x)+\frac{1}{12} b c^3 d^4 x^3+\frac{2}{3} b c^2 d^4 x^2+\frac{8}{3} b d^4 \log \left(1-c^2 x^2\right)+\frac{13}{4} b c d^4 x-\frac{13}{4} b d^4 \tanh ^{-1}(c x)+4 b c d^4 x \tanh ^{-1}(c x)","-\frac{1}{2} b d^4 \text{PolyLog}(2,-c x)+\frac{1}{2} b d^4 \text{PolyLog}(2,c x)+\frac{1}{4} c^4 d^4 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{4}{3} c^3 d^4 x^3 \left(a+b \tanh ^{-1}(c x)\right)+3 c^2 d^4 x^2 \left(a+b \tanh ^{-1}(c x)\right)+4 a c d^4 x+a d^4 \log (x)+\frac{1}{12} b c^3 d^4 x^3+\frac{2}{3} b c^2 d^4 x^2+\frac{8}{3} b d^4 \log \left(1-c^2 x^2\right)+\frac{13}{4} b c d^4 x-\frac{13}{4} b d^4 \tanh ^{-1}(c x)+4 b c d^4 x \tanh ^{-1}(c x)",1,"4*a*c*d^4*x + (13*b*c*d^4*x)/4 + (2*b*c^2*d^4*x^2)/3 + (b*c^3*d^4*x^3)/12 - (13*b*d^4*ArcTanh[c*x])/4 + 4*b*c*d^4*x*ArcTanh[c*x] + 3*c^2*d^4*x^2*(a + b*ArcTanh[c*x]) + (4*c^3*d^4*x^3*(a + b*ArcTanh[c*x]))/3 + (c^4*d^4*x^4*(a + b*ArcTanh[c*x]))/4 + a*d^4*Log[x] + (8*b*d^4*Log[1 - c^2*x^2])/3 - (b*d^4*PolyLog[2, -(c*x)])/2 + (b*d^4*PolyLog[2, c*x])/2","A",17,10,20,0.5000,1,"{5940, 5910, 260, 5912, 5916, 321, 206, 266, 43, 302}"
36,1,178,0,0.1998108,"\int \frac{(d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + c*d*x)^4*(a + b*ArcTanh[c*x]))/x^2,x]","-2 b c d^4 \text{PolyLog}(2,-c x)+2 b c d^4 \text{PolyLog}(2,c x)+\frac{1}{3} c^4 d^4 x^3 \left(a+b \tanh ^{-1}(c x)\right)+2 c^3 d^4 x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x}+6 a c^2 d^4 x+4 a c d^4 \log (x)+\frac{1}{6} b c^3 d^4 x^2+\frac{8}{3} b c d^4 \log \left(1-c^2 x^2\right)+2 b c^2 d^4 x+6 b c^2 d^4 x \tanh ^{-1}(c x)+b c d^4 \log (x)-2 b c d^4 \tanh ^{-1}(c x)","-2 b c d^4 \text{PolyLog}(2,-c x)+2 b c d^4 \text{PolyLog}(2,c x)+\frac{1}{3} c^4 d^4 x^3 \left(a+b \tanh ^{-1}(c x)\right)+2 c^3 d^4 x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x}+6 a c^2 d^4 x+4 a c d^4 \log (x)+\frac{1}{6} b c^3 d^4 x^2+\frac{8}{3} b c d^4 \log \left(1-c^2 x^2\right)+2 b c^2 d^4 x+6 b c^2 d^4 x \tanh ^{-1}(c x)+b c d^4 \log (x)-2 b c d^4 \tanh ^{-1}(c x)",1,"6*a*c^2*d^4*x + 2*b*c^2*d^4*x + (b*c^3*d^4*x^2)/6 - 2*b*c*d^4*ArcTanh[c*x] + 6*b*c^2*d^4*x*ArcTanh[c*x] - (d^4*(a + b*ArcTanh[c*x]))/x + 2*c^3*d^4*x^2*(a + b*ArcTanh[c*x]) + (c^4*d^4*x^3*(a + b*ArcTanh[c*x]))/3 + 4*a*c*d^4*Log[x] + b*c*d^4*Log[x] + (8*b*c*d^4*Log[1 - c^2*x^2])/3 - 2*b*c*d^4*PolyLog[2, -(c*x)] + 2*b*c*d^4*PolyLog[2, c*x]","A",18,12,20,0.6000,1,"{5940, 5910, 260, 5916, 266, 36, 29, 31, 5912, 321, 206, 43}"
37,1,156,0,0.1892879,"\int \frac{(d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + c*d*x)^4*(a + b*ArcTanh[c*x]))/x^3,x]","-3 b c^2 d^4 \text{PolyLog}(2,-c x)+3 b c^2 d^4 \text{PolyLog}(2,c x)+\frac{1}{2} c^4 d^4 x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{d^4 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{4 c d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x}+4 a c^3 d^4 x+6 a c^2 d^4 \log (x)+\frac{1}{2} b c^3 d^4 x+4 b c^2 d^4 \log (x)+4 b c^3 d^4 x \tanh ^{-1}(c x)-\frac{b c d^4}{2 x}","-3 b c^2 d^4 \text{PolyLog}(2,-c x)+3 b c^2 d^4 \text{PolyLog}(2,c x)+\frac{1}{2} c^4 d^4 x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{d^4 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^2}-\frac{4 c d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x}+4 a c^3 d^4 x+6 a c^2 d^4 \log (x)+\frac{1}{2} b c^3 d^4 x+4 b c^2 d^4 \log (x)+4 b c^3 d^4 x \tanh ^{-1}(c x)-\frac{b c d^4}{2 x}",1,"-(b*c*d^4)/(2*x) + 4*a*c^3*d^4*x + (b*c^3*d^4*x)/2 + 4*b*c^3*d^4*x*ArcTanh[c*x] - (d^4*(a + b*ArcTanh[c*x]))/(2*x^2) - (4*c*d^4*(a + b*ArcTanh[c*x]))/x + (c^4*d^4*x^2*(a + b*ArcTanh[c*x]))/2 + 6*a*c^2*d^4*Log[x] + 4*b*c^2*d^4*Log[x] - 3*b*c^2*d^4*PolyLog[2, -(c*x)] + 3*b*c^2*d^4*PolyLog[2, c*x]","A",17,12,20,0.6000,1,"{5940, 5910, 260, 5916, 325, 206, 266, 36, 29, 31, 5912, 321}"
38,1,189,0,0.2166419,"\int \frac{(d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + c*d*x)^4*(a + b*ArcTanh[c*x]))/x^4,x]","-2 b c^3 d^4 \text{PolyLog}(2,-c x)+2 b c^3 d^4 \text{PolyLog}(2,c x)-\frac{6 c^2 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{2 c d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^2}-\frac{d^4 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}+a c^4 d^4 x+4 a c^3 d^4 \log (x)-\frac{8}{3} b c^3 d^4 \log \left(1-c^2 x^2\right)-\frac{2 b c^2 d^4}{x}+\frac{19}{3} b c^3 d^4 \log (x)+2 b c^3 d^4 \tanh ^{-1}(c x)+b c^4 d^4 x \tanh ^{-1}(c x)-\frac{b c d^4}{6 x^2}","-2 b c^3 d^4 \text{PolyLog}(2,-c x)+2 b c^3 d^4 \text{PolyLog}(2,c x)-\frac{6 c^2 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{2 c d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^2}-\frac{d^4 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}+a c^4 d^4 x+4 a c^3 d^4 \log (x)-\frac{8}{3} b c^3 d^4 \log \left(1-c^2 x^2\right)-\frac{2 b c^2 d^4}{x}+\frac{19}{3} b c^3 d^4 \log (x)+2 b c^3 d^4 \tanh ^{-1}(c x)+b c^4 d^4 x \tanh ^{-1}(c x)-\frac{b c d^4}{6 x^2}",1,"-(b*c*d^4)/(6*x^2) - (2*b*c^2*d^4)/x + a*c^4*d^4*x + 2*b*c^3*d^4*ArcTanh[c*x] + b*c^4*d^4*x*ArcTanh[c*x] - (d^4*(a + b*ArcTanh[c*x]))/(3*x^3) - (2*c*d^4*(a + b*ArcTanh[c*x]))/x^2 - (6*c^2*d^4*(a + b*ArcTanh[c*x]))/x + 4*a*c^3*d^4*Log[x] + (19*b*c^3*d^4*Log[x])/3 - (8*b*c^3*d^4*Log[1 - c^2*x^2])/3 - 2*b*c^3*d^4*PolyLog[2, -(c*x)] + 2*b*c^3*d^4*PolyLog[2, c*x]","A",18,12,20,0.6000,1,"{5940, 5910, 260, 5916, 266, 44, 325, 206, 36, 29, 31, 5912}"
39,1,209,0,0.2291742,"\int \frac{(d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^5} \, dx","Int[((d + c*d*x)^4*(a + b*ArcTanh[c*x]))/x^5,x]","-\frac{1}{2} b c^4 d^4 \text{PolyLog}(2,-c x)+\frac{1}{2} b c^4 d^4 \text{PolyLog}(2,c x)-\frac{3 c^2 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^2}-\frac{4 c^3 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{4 c d^4 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{d^4 \left(a+b \tanh ^{-1}(c x)\right)}{4 x^4}+a c^4 d^4 \log (x)-\frac{2 b c^2 d^4}{3 x^2}-\frac{8}{3} b c^4 d^4 \log \left(1-c^2 x^2\right)-\frac{13 b c^3 d^4}{4 x}+\frac{16}{3} b c^4 d^4 \log (x)+\frac{13}{4} b c^4 d^4 \tanh ^{-1}(c x)-\frac{b c d^4}{12 x^3}","-\frac{1}{2} b c^4 d^4 \text{PolyLog}(2,-c x)+\frac{1}{2} b c^4 d^4 \text{PolyLog}(2,c x)-\frac{3 c^2 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^2}-\frac{4 c^3 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{4 c d^4 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{d^4 \left(a+b \tanh ^{-1}(c x)\right)}{4 x^4}+a c^4 d^4 \log (x)-\frac{2 b c^2 d^4}{3 x^2}-\frac{8}{3} b c^4 d^4 \log \left(1-c^2 x^2\right)-\frac{13 b c^3 d^4}{4 x}+\frac{16}{3} b c^4 d^4 \log (x)+\frac{13}{4} b c^4 d^4 \tanh ^{-1}(c x)-\frac{b c d^4}{12 x^3}",1,"-(b*c*d^4)/(12*x^3) - (2*b*c^2*d^4)/(3*x^2) - (13*b*c^3*d^4)/(4*x) + (13*b*c^4*d^4*ArcTanh[c*x])/4 - (d^4*(a + b*ArcTanh[c*x]))/(4*x^4) - (4*c*d^4*(a + b*ArcTanh[c*x]))/(3*x^3) - (3*c^2*d^4*(a + b*ArcTanh[c*x]))/x^2 - (4*c^3*d^4*(a + b*ArcTanh[c*x]))/x + a*c^4*d^4*Log[x] + (16*b*c^4*d^4*Log[x])/3 - (8*b*c^4*d^4*Log[1 - c^2*x^2])/3 - (b*c^4*d^4*PolyLog[2, -(c*x)])/2 + (b*c^4*d^4*PolyLog[2, c*x])/2","A",19,10,20,0.5000,1,"{5940, 5916, 325, 206, 266, 44, 36, 29, 31, 5912}"
40,1,109,0,0.1049587,"\int \frac{(d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^6} \, dx","Int[((d + c*d*x)^4*(a + b*ArcTanh[c*x]))/x^6,x]","-\frac{d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^5}-\frac{11 b c^3 d^4}{10 x^2}-\frac{b c^2 d^4}{3 x^3}-\frac{3 b c^4 d^4}{x}+\frac{16}{5} b c^5 d^4 \log (x)-\frac{16}{5} b c^5 d^4 \log (1-c x)-\frac{b c d^4}{20 x^4}","-\frac{d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^5}-\frac{11 b c^3 d^4}{10 x^2}-\frac{b c^2 d^4}{3 x^3}-\frac{3 b c^4 d^4}{x}+\frac{16}{5} b c^5 d^4 \log (x)-\frac{16}{5} b c^5 d^4 \log (1-c x)-\frac{b c d^4}{20 x^4}",1,"-(b*c*d^4)/(20*x^4) - (b*c^2*d^4)/(3*x^3) - (11*b*c^3*d^4)/(10*x^2) - (3*b*c^4*d^4)/x - (d^4*(1 + c*x)^5*(a + b*ArcTanh[c*x]))/(5*x^5) + (16*b*c^5*d^4*Log[x])/5 - (16*b*c^5*d^4*Log[1 - c*x])/5","A",4,4,20,0.2000,1,"{37, 5936, 12, 88}"
41,1,151,0,0.1254172,"\int \frac{(d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^7} \, dx","Int[((d + c*d*x)^4*(a + b*ArcTanh[c*x]))/x^7,x]","\frac{c d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{30 x^5}-\frac{d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{6 x^6}-\frac{16 b c^4 d^4}{15 x^2}-\frac{5 b c^3 d^4}{9 x^3}-\frac{b c^2 d^4}{5 x^4}-\frac{13 b c^5 d^4}{6 x}+\frac{32}{15} b c^6 d^4 \log (x)-\frac{32}{15} b c^6 d^4 \log (1-c x)-\frac{b c d^4}{30 x^5}","\frac{c d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{30 x^5}-\frac{d^4 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)}{6 x^6}-\frac{16 b c^4 d^4}{15 x^2}-\frac{5 b c^3 d^4}{9 x^3}-\frac{b c^2 d^4}{5 x^4}-\frac{13 b c^5 d^4}{6 x}+\frac{32}{15} b c^6 d^4 \log (x)-\frac{32}{15} b c^6 d^4 \log (1-c x)-\frac{b c d^4}{30 x^5}",1,"-(b*c*d^4)/(30*x^5) - (b*c^2*d^4)/(5*x^4) - (5*b*c^3*d^4)/(9*x^3) - (16*b*c^4*d^4)/(15*x^2) - (13*b*c^5*d^4)/(6*x) - (d^4*(1 + c*x)^5*(a + b*ArcTanh[c*x]))/(6*x^6) + (c*d^4*(1 + c*x)^5*(a + b*ArcTanh[c*x]))/(30*x^5) + (32*b*c^6*d^4*Log[x])/15 - (32*b*c^6*d^4*Log[1 - c*x])/15","A",4,5,20,0.2500,1,"{45, 37, 5936, 12, 148}"
42,1,229,0,0.196895,"\int \frac{(d+c d x)^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^8} \, dx","Int[((d + c*d*x)^4*(a + b*ArcTanh[c*x]))/x^8,x]","-\frac{c^4 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{c^3 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^4}-\frac{6 c^2 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^5}-\frac{2 c d^4 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^6}-\frac{d^4 \left(a+b \tanh ^{-1}(c x)\right)}{7 x^7}-\frac{88 b c^5 d^4}{105 x^2}-\frac{5 b c^4 d^4}{9 x^3}-\frac{47 b c^3 d^4}{140 x^4}-\frac{2 b c^2 d^4}{15 x^5}-\frac{5 b c^6 d^4}{3 x}+\frac{176}{105} b c^7 d^4 \log (x)-\frac{117}{70} b c^7 d^4 \log (1-c x)-\frac{1}{210} b c^7 d^4 \log (c x+1)-\frac{b c d^4}{42 x^6}","-\frac{c^4 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^3}-\frac{c^3 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{x^4}-\frac{6 c^2 d^4 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^5}-\frac{2 c d^4 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^6}-\frac{d^4 \left(a+b \tanh ^{-1}(c x)\right)}{7 x^7}-\frac{88 b c^5 d^4}{105 x^2}-\frac{5 b c^4 d^4}{9 x^3}-\frac{47 b c^3 d^4}{140 x^4}-\frac{2 b c^2 d^4}{15 x^5}-\frac{5 b c^6 d^4}{3 x}+\frac{176}{105} b c^7 d^4 \log (x)-\frac{117}{70} b c^7 d^4 \log (1-c x)-\frac{1}{210} b c^7 d^4 \log (c x+1)-\frac{b c d^4}{42 x^6}",1,"-(b*c*d^4)/(42*x^6) - (2*b*c^2*d^4)/(15*x^5) - (47*b*c^3*d^4)/(140*x^4) - (5*b*c^4*d^4)/(9*x^3) - (88*b*c^5*d^4)/(105*x^2) - (5*b*c^6*d^4)/(3*x) - (d^4*(a + b*ArcTanh[c*x]))/(7*x^7) - (2*c*d^4*(a + b*ArcTanh[c*x]))/(3*x^6) - (6*c^2*d^4*(a + b*ArcTanh[c*x]))/(5*x^5) - (c^3*d^4*(a + b*ArcTanh[c*x]))/x^4 - (c^4*d^4*(a + b*ArcTanh[c*x]))/(3*x^3) + (176*b*c^7*d^4*Log[x])/105 - (117*b*c^7*d^4*Log[1 - c*x])/70 - (b*c^7*d^4*Log[1 + c*x])/210","A",4,4,20,0.2000,1,"{43, 5936, 12, 1802}"
43,1,177,0,0.287424,"\int \frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)}{d+c d x} \, dx","Int[(x^3*(a + b*ArcTanh[c*x]))/(d + c*d*x),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^4 d}-\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c^2 d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d}+\frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 c d}+\frac{a x}{c^3 d}+\frac{b x^2}{6 c^2 d}+\frac{2 b \log \left(1-c^2 x^2\right)}{3 c^4 d}-\frac{b x}{2 c^3 d}+\frac{b x \tanh ^{-1}(c x)}{c^3 d}+\frac{b \tanh ^{-1}(c x)}{2 c^4 d}","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^4 d}-\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c^2 d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d}+\frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 c d}+\frac{a x}{c^3 d}+\frac{b x^2}{6 c^2 d}+\frac{2 b \log \left(1-c^2 x^2\right)}{3 c^4 d}-\frac{b x}{2 c^3 d}+\frac{b x \tanh ^{-1}(c x)}{c^3 d}+\frac{b \tanh ^{-1}(c x)}{2 c^4 d}",1,"(a*x)/(c^3*d) - (b*x)/(2*c^3*d) + (b*x^2)/(6*c^2*d) + (b*ArcTanh[c*x])/(2*c^4*d) + (b*x*ArcTanh[c*x])/(c^3*d) - (x^2*(a + b*ArcTanh[c*x]))/(2*c^2*d) + (x^3*(a + b*ArcTanh[c*x]))/(3*c*d) + ((a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(c^4*d) + (2*b*Log[1 - c^2*x^2])/(3*c^4*d) - (b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*c^4*d)","A",16,11,20,0.5500,1,"{5930, 5916, 266, 43, 321, 206, 5910, 260, 5918, 2402, 2315}"
44,1,145,0,0.1838067,"\int \frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{d+c d x} \, dx","Int[(x^2*(a + b*ArcTanh[c*x]))/(d + c*d*x),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^3 d}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c d}-\frac{a x}{c^2 d}-\frac{b \log \left(1-c^2 x^2\right)}{2 c^3 d}+\frac{b x}{2 c^2 d}-\frac{b x \tanh ^{-1}(c x)}{c^2 d}-\frac{b \tanh ^{-1}(c x)}{2 c^3 d}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^3 d}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c d}-\frac{a x}{c^2 d}-\frac{b \log \left(1-c^2 x^2\right)}{2 c^3 d}+\frac{b x}{2 c^2 d}-\frac{b x \tanh ^{-1}(c x)}{c^2 d}-\frac{b \tanh ^{-1}(c x)}{2 c^3 d}",1,"-((a*x)/(c^2*d)) + (b*x)/(2*c^2*d) - (b*ArcTanh[c*x])/(2*c^3*d) - (b*x*ArcTanh[c*x])/(c^2*d) + (x^2*(a + b*ArcTanh[c*x]))/(2*c*d) - ((a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(c^3*d) - (b*Log[1 - c^2*x^2])/(2*c^3*d) + (b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*c^3*d)","A",11,9,20,0.4500,1,"{5930, 5916, 321, 206, 5910, 260, 5918, 2402, 2315}"
45,1,94,0,0.1025197,"\int \frac{x \left(a+b \tanh ^{-1}(c x)\right)}{d+c d x} \, dx","Int[(x*(a + b*ArcTanh[c*x]))/(d + c*d*x),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^2 d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d}+\frac{a x}{c d}+\frac{b \log \left(1-c^2 x^2\right)}{2 c^2 d}+\frac{b x \tanh ^{-1}(c x)}{c d}","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^2 d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d}+\frac{a x}{c d}+\frac{b \log \left(1-c^2 x^2\right)}{2 c^2 d}+\frac{b x \tanh ^{-1}(c x)}{c d}",1,"(a*x)/(c*d) + (b*x*ArcTanh[c*x])/(c*d) + ((a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(c^2*d) + (b*Log[1 - c^2*x^2])/(2*c^2*d) - (b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*c^2*d)","A",7,6,18,0.3333,1,"{5930, 5910, 260, 5918, 2402, 2315}"
46,1,51,0,0.0477698,"\int \frac{a+b \tanh ^{-1}(c x)}{d+c d x} \, dx","Int[(a + b*ArcTanh[c*x])/(d + c*d*x),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c d}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c d}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c d}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c d}",1,"-(((a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(c*d)) + (b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*c*d)","A",3,3,17,0.1765,1,"{5918, 2402, 2315}"
47,1,46,0,0.0735335,"\int \frac{a+b \tanh ^{-1}(c x)}{x (d+c d x)} \, dx","Int[(a + b*ArcTanh[c*x])/(x*(d + c*d*x)),x]","\frac{\log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{b \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{2 d}","\frac{\log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{b \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{2 d}",1,"((a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/d - (b*PolyLog[2, -1 + 2/(1 + c*x)])/(2*d)","A",2,2,20,0.1000,1,"{5932, 2447}"
48,1,93,0,0.1531754,"\int \frac{a+b \tanh ^{-1}(c x)}{x^2 (d+c d x)} \, dx","Int[(a + b*ArcTanh[c*x])/(x^2*(d + c*d*x)),x]","\frac{b c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{2 d}-\frac{a+b \tanh ^{-1}(c x)}{d x}-\frac{c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{b c \log \left(1-c^2 x^2\right)}{2 d}+\frac{b c \log (x)}{d}","\frac{b c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{2 d}-\frac{a+b \tanh ^{-1}(c x)}{d x}-\frac{c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{b c \log \left(1-c^2 x^2\right)}{2 d}+\frac{b c \log (x)}{d}",1,"-((a + b*ArcTanh[c*x])/(d*x)) + (b*c*Log[x])/d - (b*c*Log[1 - c^2*x^2])/(2*d) - (c*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/d + (b*c*PolyLog[2, -1 + 2/(1 + c*x)])/(2*d)","A",8,8,20,0.4000,1,"{5934, 5916, 266, 36, 29, 31, 5932, 2447}"
49,1,146,0,0.2344774,"\int \frac{a+b \tanh ^{-1}(c x)}{x^3 (d+c d x)} \, dx","Int[(a + b*ArcTanh[c*x])/(x^3*(d + c*d*x)),x]","-\frac{b c^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{2 d}+\frac{c^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{a+b \tanh ^{-1}(c x)}{2 d x^2}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)}{d x}+\frac{b c^2 \log \left(1-c^2 x^2\right)}{2 d}-\frac{b c^2 \log (x)}{d}+\frac{b c^2 \tanh ^{-1}(c x)}{2 d}-\frac{b c}{2 d x}","-\frac{b c^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{2 d}+\frac{c^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{a+b \tanh ^{-1}(c x)}{2 d x^2}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)}{d x}+\frac{b c^2 \log \left(1-c^2 x^2\right)}{2 d}-\frac{b c^2 \log (x)}{d}+\frac{b c^2 \tanh ^{-1}(c x)}{2 d}-\frac{b c}{2 d x}",1,"-(b*c)/(2*d*x) + (b*c^2*ArcTanh[c*x])/(2*d) - (a + b*ArcTanh[c*x])/(2*d*x^2) + (c*(a + b*ArcTanh[c*x]))/(d*x) - (b*c^2*Log[x])/d + (b*c^2*Log[1 - c^2*x^2])/(2*d) + (c^2*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/d - (b*c^2*PolyLog[2, -1 + 2/(1 + c*x)])/(2*d)","A",12,10,20,0.5000,1,"{5934, 5916, 325, 206, 266, 36, 29, 31, 5932, 2447}"
50,1,185,0,0.3459083,"\int \frac{a+b \tanh ^{-1}(c x)}{x^4 (d+c d x)} \, dx","Int[(a + b*ArcTanh[c*x])/(x^4*(d + c*d*x)),x]","\frac{b c^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{2 d}-\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)}{d x}-\frac{c^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)}{2 d x^2}-\frac{a+b \tanh ^{-1}(c x)}{3 d x^3}-\frac{2 b c^3 \log \left(1-c^2 x^2\right)}{3 d}+\frac{b c^2}{2 d x}+\frac{4 b c^3 \log (x)}{3 d}-\frac{b c^3 \tanh ^{-1}(c x)}{2 d}-\frac{b c}{6 d x^2}","\frac{b c^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{2 d}-\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)}{d x}-\frac{c^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)}{2 d x^2}-\frac{a+b \tanh ^{-1}(c x)}{3 d x^3}-\frac{2 b c^3 \log \left(1-c^2 x^2\right)}{3 d}+\frac{b c^2}{2 d x}+\frac{4 b c^3 \log (x)}{3 d}-\frac{b c^3 \tanh ^{-1}(c x)}{2 d}-\frac{b c}{6 d x^2}",1,"-(b*c)/(6*d*x^2) + (b*c^2)/(2*d*x) - (b*c^3*ArcTanh[c*x])/(2*d) - (a + b*ArcTanh[c*x])/(3*d*x^3) + (c*(a + b*ArcTanh[c*x]))/(2*d*x^2) - (c^2*(a + b*ArcTanh[c*x]))/(d*x) + (4*b*c^3*Log[x])/(3*d) - (2*b*c^3*Log[1 - c^2*x^2])/(3*d) - (c^3*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/d + (b*c^3*PolyLog[2, -1 + 2/(1 + c*x)])/(2*d)","A",17,11,20,0.5500,1,"{5934, 5916, 266, 44, 325, 206, 36, 29, 31, 5932, 2447}"
51,1,181,0,0.2220014,"\int \frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)}{(d+c d x)^2} \, dx","Int[(x^3*(a + b*ArcTanh[c*x]))/(d + c*d*x)^2,x]","\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^4 d^2}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c^2 d^2}+\frac{a+b \tanh ^{-1}(c x)}{c^4 d^2 (c x+1)}-\frac{3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^2}-\frac{2 a x}{c^3 d^2}-\frac{b \log \left(1-c^2 x^2\right)}{c^4 d^2}+\frac{b x}{2 c^3 d^2}+\frac{b}{2 c^4 d^2 (c x+1)}-\frac{2 b x \tanh ^{-1}(c x)}{c^3 d^2}-\frac{b \tanh ^{-1}(c x)}{c^4 d^2}","\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^4 d^2}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c^2 d^2}+\frac{a+b \tanh ^{-1}(c x)}{c^4 d^2 (c x+1)}-\frac{3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^2}-\frac{2 a x}{c^3 d^2}-\frac{b \log \left(1-c^2 x^2\right)}{c^4 d^2}+\frac{b x}{2 c^3 d^2}+\frac{b}{2 c^4 d^2 (c x+1)}-\frac{2 b x \tanh ^{-1}(c x)}{c^3 d^2}-\frac{b \tanh ^{-1}(c x)}{c^4 d^2}",1,"(-2*a*x)/(c^3*d^2) + (b*x)/(2*c^3*d^2) + b/(2*c^4*d^2*(1 + c*x)) - (b*ArcTanh[c*x])/(c^4*d^2) - (2*b*x*ArcTanh[c*x])/(c^3*d^2) + (x^2*(a + b*ArcTanh[c*x]))/(2*c^2*d^2) + (a + b*ArcTanh[c*x])/(c^4*d^2*(1 + c*x)) - (3*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(c^4*d^2) - (b*Log[1 - c^2*x^2])/(c^4*d^2) + (3*b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*c^4*d^2)","A",16,13,20,0.6500,1,"{5940, 5910, 260, 5916, 321, 206, 5926, 627, 44, 207, 5918, 2402, 2315}"
52,1,149,0,0.1852357,"\int \frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{(d+c d x)^2} \, dx","Int[(x^2*(a + b*ArcTanh[c*x]))/(d + c*d*x)^2,x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{c^3 d^2}-\frac{a+b \tanh ^{-1}(c x)}{c^3 d^2 (c x+1)}+\frac{2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^2}+\frac{a x}{c^2 d^2}+\frac{b \log \left(1-c^2 x^2\right)}{2 c^3 d^2}-\frac{b}{2 c^3 d^2 (c x+1)}+\frac{b x \tanh ^{-1}(c x)}{c^2 d^2}+\frac{b \tanh ^{-1}(c x)}{2 c^3 d^2}","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{c^3 d^2}-\frac{a+b \tanh ^{-1}(c x)}{c^3 d^2 (c x+1)}+\frac{2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^2}+\frac{a x}{c^2 d^2}+\frac{b \log \left(1-c^2 x^2\right)}{2 c^3 d^2}-\frac{b}{2 c^3 d^2 (c x+1)}+\frac{b x \tanh ^{-1}(c x)}{c^2 d^2}+\frac{b \tanh ^{-1}(c x)}{2 c^3 d^2}",1,"(a*x)/(c^2*d^2) - b/(2*c^3*d^2*(1 + c*x)) + (b*ArcTanh[c*x])/(2*c^3*d^2) + (b*x*ArcTanh[c*x])/(c^2*d^2) - (a + b*ArcTanh[c*x])/(c^3*d^2*(1 + c*x)) + (2*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(c^3*d^2) + (b*Log[1 - c^2*x^2])/(2*c^3*d^2) - (b*PolyLog[2, 1 - 2/(1 + c*x)])/(c^3*d^2)","A",13,10,20,0.5000,1,"{5940, 5910, 260, 5926, 627, 44, 207, 5918, 2402, 2315}"
53,1,106,0,0.1431068,"\int \frac{x \left(a+b \tanh ^{-1}(c x)\right)}{(d+c d x)^2} \, dx","Int[(x*(a + b*ArcTanh[c*x]))/(d + c*d*x)^2,x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^2 d^2}+\frac{a+b \tanh ^{-1}(c x)}{c^2 d^2 (c x+1)}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d^2}+\frac{b}{2 c^2 d^2 (c x+1)}-\frac{b \tanh ^{-1}(c x)}{2 c^2 d^2}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^2 d^2}+\frac{a+b \tanh ^{-1}(c x)}{c^2 d^2 (c x+1)}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d^2}+\frac{b}{2 c^2 d^2 (c x+1)}-\frac{b \tanh ^{-1}(c x)}{2 c^2 d^2}",1,"b/(2*c^2*d^2*(1 + c*x)) - (b*ArcTanh[c*x])/(2*c^2*d^2) + (a + b*ArcTanh[c*x])/(c^2*d^2*(1 + c*x)) - ((a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(c^2*d^2) + (b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*c^2*d^2)","A",10,8,18,0.4444,1,"{5940, 5926, 627, 44, 207, 5918, 2402, 2315}"
54,1,57,0,0.0453211,"\int \frac{a+b \tanh ^{-1}(c x)}{(d+c d x)^2} \, dx","Int[(a + b*ArcTanh[c*x])/(d + c*d*x)^2,x]","-\frac{a+b \tanh ^{-1}(c x)}{c d^2 (c x+1)}-\frac{b}{2 c d^2 (c x+1)}+\frac{b \tanh ^{-1}(c x)}{2 c d^2}","-\frac{a+b \tanh ^{-1}(c x)}{c d^2 (c x+1)}-\frac{b}{2 c d^2 (c x+1)}+\frac{b \tanh ^{-1}(c x)}{2 c d^2}",1,"-b/(2*c*d^2*(1 + c*x)) + (b*ArcTanh[c*x])/(2*c*d^2) - (a + b*ArcTanh[c*x])/(c*d^2*(1 + c*x))","A",5,4,17,0.2353,1,"{5926, 627, 44, 207}"
55,1,124,0,0.174434,"\int \frac{a+b \tanh ^{-1}(c x)}{x (d+c d x)^2} \, dx","Int[(a + b*ArcTanh[c*x])/(x*(d + c*d*x)^2),x]","-\frac{b \text{PolyLog}(2,-c x)}{2 d^2}+\frac{b \text{PolyLog}(2,c x)}{2 d^2}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^2}+\frac{a+b \tanh ^{-1}(c x)}{d^2 (c x+1)}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{a \log (x)}{d^2}+\frac{b}{2 d^2 (c x+1)}-\frac{b \tanh ^{-1}(c x)}{2 d^2}","-\frac{b \text{PolyLog}(2,-c x)}{2 d^2}+\frac{b \text{PolyLog}(2,c x)}{2 d^2}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^2}+\frac{a+b \tanh ^{-1}(c x)}{d^2 (c x+1)}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{a \log (x)}{d^2}+\frac{b}{2 d^2 (c x+1)}-\frac{b \tanh ^{-1}(c x)}{2 d^2}",1,"b/(2*d^2*(1 + c*x)) - (b*ArcTanh[c*x])/(2*d^2) + (a + b*ArcTanh[c*x])/(d^2*(1 + c*x)) + (a*Log[x])/d^2 + ((a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/d^2 - (b*PolyLog[2, -(c*x)])/(2*d^2) + (b*PolyLog[2, c*x])/(2*d^2) - (b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*d^2)","A",11,9,20,0.4500,1,"{5940, 5912, 5926, 627, 44, 207, 5918, 2402, 2315}"
56,1,171,0,0.2210961,"\int \frac{a+b \tanh ^{-1}(c x)}{x^2 (d+c d x)^2} \, dx","Int[(a + b*ArcTanh[c*x])/(x^2*(d + c*d*x)^2),x]","\frac{b c \text{PolyLog}(2,-c x)}{d^2}-\frac{b c \text{PolyLog}(2,c x)}{d^2}+\frac{b c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{d^2}-\frac{c \left(a+b \tanh ^{-1}(c x)\right)}{d^2 (c x+1)}-\frac{a+b \tanh ^{-1}(c x)}{d^2 x}-\frac{2 c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{2 a c \log (x)}{d^2}-\frac{b c \log \left(1-c^2 x^2\right)}{2 d^2}-\frac{b c}{2 d^2 (c x+1)}+\frac{b c \log (x)}{d^2}+\frac{b c \tanh ^{-1}(c x)}{2 d^2}","\frac{b c \text{PolyLog}(2,-c x)}{d^2}-\frac{b c \text{PolyLog}(2,c x)}{d^2}+\frac{b c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{d^2}-\frac{c \left(a+b \tanh ^{-1}(c x)\right)}{d^2 (c x+1)}-\frac{a+b \tanh ^{-1}(c x)}{d^2 x}-\frac{2 c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{2 a c \log (x)}{d^2}-\frac{b c \log \left(1-c^2 x^2\right)}{2 d^2}-\frac{b c}{2 d^2 (c x+1)}+\frac{b c \log (x)}{d^2}+\frac{b c \tanh ^{-1}(c x)}{2 d^2}",1,"-(b*c)/(2*d^2*(1 + c*x)) + (b*c*ArcTanh[c*x])/(2*d^2) - (a + b*ArcTanh[c*x])/(d^2*x) - (c*(a + b*ArcTanh[c*x]))/(d^2*(1 + c*x)) - (2*a*c*Log[x])/d^2 + (b*c*Log[x])/d^2 - (2*c*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/d^2 - (b*c*Log[1 - c^2*x^2])/(2*d^2) + (b*c*PolyLog[2, -(c*x)])/d^2 - (b*c*PolyLog[2, c*x])/d^2 + (b*c*PolyLog[2, 1 - 2/(1 + c*x)])/d^2","A",16,14,20,0.7000,1,"{5940, 5916, 266, 36, 29, 31, 5912, 5926, 627, 44, 207, 5918, 2402, 2315}"
57,1,212,0,0.2573842,"\int \frac{a+b \tanh ^{-1}(c x)}{x^3 (d+c d x)^2} \, dx","Int[(a + b*ArcTanh[c*x])/(x^3*(d + c*d*x)^2),x]","-\frac{3 b c^2 \text{PolyLog}(2,-c x)}{2 d^2}+\frac{3 b c^2 \text{PolyLog}(2,c x)}{2 d^2}-\frac{3 b c^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^2}+\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)}{d^2 (c x+1)}+\frac{3 c^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{a+b \tanh ^{-1}(c x)}{2 d^2 x^2}+\frac{2 c \left(a+b \tanh ^{-1}(c x)\right)}{d^2 x}+\frac{3 a c^2 \log (x)}{d^2}+\frac{b c^2 \log \left(1-c^2 x^2\right)}{d^2}+\frac{b c^2}{2 d^2 (c x+1)}-\frac{2 b c^2 \log (x)}{d^2}-\frac{b c}{2 d^2 x}","-\frac{3 b c^2 \text{PolyLog}(2,-c x)}{2 d^2}+\frac{3 b c^2 \text{PolyLog}(2,c x)}{2 d^2}-\frac{3 b c^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^2}+\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)}{d^2 (c x+1)}+\frac{3 c^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{a+b \tanh ^{-1}(c x)}{2 d^2 x^2}+\frac{2 c \left(a+b \tanh ^{-1}(c x)\right)}{d^2 x}+\frac{3 a c^2 \log (x)}{d^2}+\frac{b c^2 \log \left(1-c^2 x^2\right)}{d^2}+\frac{b c^2}{2 d^2 (c x+1)}-\frac{2 b c^2 \log (x)}{d^2}-\frac{b c}{2 d^2 x}",1,"-(b*c)/(2*d^2*x) + (b*c^2)/(2*d^2*(1 + c*x)) - (a + b*ArcTanh[c*x])/(2*d^2*x^2) + (2*c*(a + b*ArcTanh[c*x]))/(d^2*x) + (c^2*(a + b*ArcTanh[c*x]))/(d^2*(1 + c*x)) + (3*a*c^2*Log[x])/d^2 - (2*b*c^2*Log[x])/d^2 + (3*c^2*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/d^2 + (b*c^2*Log[1 - c^2*x^2])/d^2 - (3*b*c^2*PolyLog[2, -(c*x)])/(2*d^2) + (3*b*c^2*PolyLog[2, c*x])/(2*d^2) - (3*b*c^2*PolyLog[2, 1 - 2/(1 + c*x)])/(2*d^2)","A",19,16,20,0.8000,1,"{5940, 5916, 325, 206, 266, 36, 29, 31, 5912, 5926, 627, 44, 207, 5918, 2402, 2315}"
58,1,227,0,0.2875837,"\int \frac{x^4 \left(a+b \tanh ^{-1}(c x)\right)}{(d+c d x)^3} \, dx","Int[(x^4*(a + b*ArcTanh[c*x]))/(d + c*d*x)^3,x]","\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{c^5 d^3}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c^3 d^3}+\frac{4 \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^3 (c x+1)}-\frac{a+b \tanh ^{-1}(c x)}{2 c^5 d^3 (c x+1)^2}-\frac{6 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^3}-\frac{3 a x}{c^4 d^3}-\frac{3 b \log \left(1-c^2 x^2\right)}{2 c^5 d^3}+\frac{b x}{2 c^4 d^3}+\frac{15 b}{8 c^5 d^3 (c x+1)}-\frac{b}{8 c^5 d^3 (c x+1)^2}-\frac{3 b x \tanh ^{-1}(c x)}{c^4 d^3}-\frac{19 b \tanh ^{-1}(c x)}{8 c^5 d^3}","\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{c^5 d^3}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c^3 d^3}+\frac{4 \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^3 (c x+1)}-\frac{a+b \tanh ^{-1}(c x)}{2 c^5 d^3 (c x+1)^2}-\frac{6 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^3}-\frac{3 a x}{c^4 d^3}-\frac{3 b \log \left(1-c^2 x^2\right)}{2 c^5 d^3}+\frac{b x}{2 c^4 d^3}+\frac{15 b}{8 c^5 d^3 (c x+1)}-\frac{b}{8 c^5 d^3 (c x+1)^2}-\frac{3 b x \tanh ^{-1}(c x)}{c^4 d^3}-\frac{19 b \tanh ^{-1}(c x)}{8 c^5 d^3}",1,"(-3*a*x)/(c^4*d^3) + (b*x)/(2*c^4*d^3) - b/(8*c^5*d^3*(1 + c*x)^2) + (15*b)/(8*c^5*d^3*(1 + c*x)) - (19*b*ArcTanh[c*x])/(8*c^5*d^3) - (3*b*x*ArcTanh[c*x])/(c^4*d^3) + (x^2*(a + b*ArcTanh[c*x]))/(2*c^3*d^3) - (a + b*ArcTanh[c*x])/(2*c^5*d^3*(1 + c*x)^2) + (4*(a + b*ArcTanh[c*x]))/(c^5*d^3*(1 + c*x)) - (6*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(c^5*d^3) - (3*b*Log[1 - c^2*x^2])/(2*c^5*d^3) + (3*b*PolyLog[2, 1 - 2/(1 + c*x)])/(c^5*d^3)","A",21,13,20,0.6500,1,"{5940, 5910, 260, 5916, 321, 206, 5926, 627, 44, 207, 5918, 2402, 2315}"
59,1,194,0,0.2479997,"\int \frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)}{(d+c d x)^3} \, dx","Int[(x^3*(a + b*ArcTanh[c*x]))/(d + c*d*x)^3,x]","-\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^4 d^3}-\frac{3 \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^3 (c x+1)}+\frac{a+b \tanh ^{-1}(c x)}{2 c^4 d^3 (c x+1)^2}+\frac{3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^3}+\frac{a x}{c^3 d^3}+\frac{b \log \left(1-c^2 x^2\right)}{2 c^4 d^3}-\frac{11 b}{8 c^4 d^3 (c x+1)}+\frac{b}{8 c^4 d^3 (c x+1)^2}+\frac{b x \tanh ^{-1}(c x)}{c^3 d^3}+\frac{11 b \tanh ^{-1}(c x)}{8 c^4 d^3}","-\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^4 d^3}-\frac{3 \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^3 (c x+1)}+\frac{a+b \tanh ^{-1}(c x)}{2 c^4 d^3 (c x+1)^2}+\frac{3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^3}+\frac{a x}{c^3 d^3}+\frac{b \log \left(1-c^2 x^2\right)}{2 c^4 d^3}-\frac{11 b}{8 c^4 d^3 (c x+1)}+\frac{b}{8 c^4 d^3 (c x+1)^2}+\frac{b x \tanh ^{-1}(c x)}{c^3 d^3}+\frac{11 b \tanh ^{-1}(c x)}{8 c^4 d^3}",1,"(a*x)/(c^3*d^3) + b/(8*c^4*d^3*(1 + c*x)^2) - (11*b)/(8*c^4*d^3*(1 + c*x)) + (11*b*ArcTanh[c*x])/(8*c^4*d^3) + (b*x*ArcTanh[c*x])/(c^3*d^3) + (a + b*ArcTanh[c*x])/(2*c^4*d^3*(1 + c*x)^2) - (3*(a + b*ArcTanh[c*x]))/(c^4*d^3*(1 + c*x)) + (3*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(c^4*d^3) + (b*Log[1 - c^2*x^2])/(2*c^4*d^3) - (3*b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*c^4*d^3)","A",18,10,20,0.5000,1,"{5940, 5910, 260, 5926, 627, 44, 207, 5918, 2402, 2315}"
60,1,150,0,0.2185943,"\int \frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{(d+c d x)^3} \, dx","Int[(x^2*(a + b*ArcTanh[c*x]))/(d + c*d*x)^3,x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^3 d^3}+\frac{2 \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^3 (c x+1)}-\frac{a+b \tanh ^{-1}(c x)}{2 c^3 d^3 (c x+1)^2}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^3}+\frac{7 b}{8 c^3 d^3 (c x+1)}-\frac{b}{8 c^3 d^3 (c x+1)^2}-\frac{7 b \tanh ^{-1}(c x)}{8 c^3 d^3}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^3 d^3}+\frac{2 \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^3 (c x+1)}-\frac{a+b \tanh ^{-1}(c x)}{2 c^3 d^3 (c x+1)^2}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^3}+\frac{7 b}{8 c^3 d^3 (c x+1)}-\frac{b}{8 c^3 d^3 (c x+1)^2}-\frac{7 b \tanh ^{-1}(c x)}{8 c^3 d^3}",1,"-b/(8*c^3*d^3*(1 + c*x)^2) + (7*b)/(8*c^3*d^3*(1 + c*x)) - (7*b*ArcTanh[c*x])/(8*c^3*d^3) - (a + b*ArcTanh[c*x])/(2*c^3*d^3*(1 + c*x)^2) + (2*(a + b*ArcTanh[c*x]))/(c^3*d^3*(1 + c*x)) - ((a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/(c^3*d^3) + (b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*c^3*d^3)","A",15,8,20,0.4000,1,"{5940, 5926, 627, 44, 207, 5918, 2402, 2315}"
61,1,77,0,0.0822645,"\int \frac{x \left(a+b \tanh ^{-1}(c x)\right)}{(d+c d x)^3} \, dx","Int[(x*(a + b*ArcTanh[c*x]))/(d + c*d*x)^3,x]","\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 d^3 (c x+1)^2}-\frac{3 b}{8 c^2 d^3 (c x+1)}+\frac{b}{8 c^2 d^3 (c x+1)^2}-\frac{b \tanh ^{-1}(c x)}{8 c^2 d^3}","\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 d^3 (c x+1)^2}-\frac{3 b}{8 c^2 d^3 (c x+1)}+\frac{b}{8 c^2 d^3 (c x+1)^2}-\frac{b \tanh ^{-1}(c x)}{8 c^2 d^3}",1,"b/(8*c^2*d^3*(1 + c*x)^2) - (3*b)/(8*c^2*d^3*(1 + c*x)) - (b*ArcTanh[c*x])/(8*c^2*d^3) + (x^2*(a + b*ArcTanh[c*x]))/(2*d^3*(1 + c*x)^2)","A",5,5,18,0.2778,1,"{37, 5936, 12, 88, 207}"
62,1,77,0,0.0550454,"\int \frac{a+b \tanh ^{-1}(c x)}{(d+c d x)^3} \, dx","Int[(a + b*ArcTanh[c*x])/(d + c*d*x)^3,x]","-\frac{a+b \tanh ^{-1}(c x)}{2 c d^3 (c x+1)^2}-\frac{b}{8 c d^3 (c x+1)}-\frac{b}{8 c d^3 (c x+1)^2}+\frac{b \tanh ^{-1}(c x)}{8 c d^3}","-\frac{a+b \tanh ^{-1}(c x)}{2 c d^3 (c x+1)^2}-\frac{b}{8 c d^3 (c x+1)}-\frac{b}{8 c d^3 (c x+1)^2}+\frac{b \tanh ^{-1}(c x)}{8 c d^3}",1,"-b/(8*c*d^3*(1 + c*x)^2) - b/(8*c*d^3*(1 + c*x)) + (b*ArcTanh[c*x])/(8*c*d^3) - (a + b*ArcTanh[c*x])/(2*c*d^3*(1 + c*x)^2)","A",5,4,17,0.2353,1,"{5926, 627, 44, 207}"
63,1,161,0,0.2273613,"\int \frac{a+b \tanh ^{-1}(c x)}{x (d+c d x)^3} \, dx","Int[(a + b*ArcTanh[c*x])/(x*(d + c*d*x)^3),x]","-\frac{b \text{PolyLog}(2,-c x)}{2 d^3}+\frac{b \text{PolyLog}(2,c x)}{2 d^3}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^3}+\frac{a+b \tanh ^{-1}(c x)}{d^3 (c x+1)}+\frac{a+b \tanh ^{-1}(c x)}{2 d^3 (c x+1)^2}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}+\frac{a \log (x)}{d^3}+\frac{5 b}{8 d^3 (c x+1)}+\frac{b}{8 d^3 (c x+1)^2}-\frac{5 b \tanh ^{-1}(c x)}{8 d^3}","-\frac{b \text{PolyLog}(2,-c x)}{2 d^3}+\frac{b \text{PolyLog}(2,c x)}{2 d^3}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^3}+\frac{a+b \tanh ^{-1}(c x)}{d^3 (c x+1)}+\frac{a+b \tanh ^{-1}(c x)}{2 d^3 (c x+1)^2}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}+\frac{a \log (x)}{d^3}+\frac{5 b}{8 d^3 (c x+1)}+\frac{b}{8 d^3 (c x+1)^2}-\frac{5 b \tanh ^{-1}(c x)}{8 d^3}",1,"b/(8*d^3*(1 + c*x)^2) + (5*b)/(8*d^3*(1 + c*x)) - (5*b*ArcTanh[c*x])/(8*d^3) + (a + b*ArcTanh[c*x])/(2*d^3*(1 + c*x)^2) + (a + b*ArcTanh[c*x])/(d^3*(1 + c*x)) + (a*Log[x])/d^3 + ((a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/d^3 - (b*PolyLog[2, -(c*x)])/(2*d^3) + (b*PolyLog[2, c*x])/(2*d^3) - (b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*d^3)","A",16,9,20,0.4500,1,"{5940, 5912, 5926, 627, 44, 207, 5918, 2402, 2315}"
64,1,218,0,0.2738215,"\int \frac{a+b \tanh ^{-1}(c x)}{x^2 (d+c d x)^3} \, dx","Int[(a + b*ArcTanh[c*x])/(x^2*(d + c*d*x)^3),x]","\frac{3 b c \text{PolyLog}(2,-c x)}{2 d^3}-\frac{3 b c \text{PolyLog}(2,c x)}{2 d^3}+\frac{3 b c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^3}-\frac{2 c \left(a+b \tanh ^{-1}(c x)\right)}{d^3 (c x+1)}-\frac{c \left(a+b \tanh ^{-1}(c x)\right)}{2 d^3 (c x+1)^2}-\frac{a+b \tanh ^{-1}(c x)}{d^3 x}-\frac{3 c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{3 a c \log (x)}{d^3}-\frac{b c \log \left(1-c^2 x^2\right)}{2 d^3}-\frac{9 b c}{8 d^3 (c x+1)}-\frac{b c}{8 d^3 (c x+1)^2}+\frac{b c \log (x)}{d^3}+\frac{9 b c \tanh ^{-1}(c x)}{8 d^3}","\frac{3 b c \text{PolyLog}(2,-c x)}{2 d^3}-\frac{3 b c \text{PolyLog}(2,c x)}{2 d^3}+\frac{3 b c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^3}-\frac{2 c \left(a+b \tanh ^{-1}(c x)\right)}{d^3 (c x+1)}-\frac{c \left(a+b \tanh ^{-1}(c x)\right)}{2 d^3 (c x+1)^2}-\frac{a+b \tanh ^{-1}(c x)}{d^3 x}-\frac{3 c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{3 a c \log (x)}{d^3}-\frac{b c \log \left(1-c^2 x^2\right)}{2 d^3}-\frac{9 b c}{8 d^3 (c x+1)}-\frac{b c}{8 d^3 (c x+1)^2}+\frac{b c \log (x)}{d^3}+\frac{9 b c \tanh ^{-1}(c x)}{8 d^3}",1,"-(b*c)/(8*d^3*(1 + c*x)^2) - (9*b*c)/(8*d^3*(1 + c*x)) + (9*b*c*ArcTanh[c*x])/(8*d^3) - (a + b*ArcTanh[c*x])/(d^3*x) - (c*(a + b*ArcTanh[c*x]))/(2*d^3*(1 + c*x)^2) - (2*c*(a + b*ArcTanh[c*x]))/(d^3*(1 + c*x)) - (3*a*c*Log[x])/d^3 + (b*c*Log[x])/d^3 - (3*c*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/d^3 - (b*c*Log[1 - c^2*x^2])/(2*d^3) + (3*b*c*PolyLog[2, -(c*x)])/(2*d^3) - (3*b*c*PolyLog[2, c*x])/(2*d^3) + (3*b*c*PolyLog[2, 1 - 2/(1 + c*x)])/(2*d^3)","A",21,14,20,0.7000,1,"{5940, 5916, 266, 36, 29, 31, 5912, 5926, 627, 44, 207, 5918, 2402, 2315}"
65,1,268,0,0.3169839,"\int \frac{a+b \tanh ^{-1}(c x)}{x^3 (d+c d x)^3} \, dx","Int[(a + b*ArcTanh[c*x])/(x^3*(d + c*d*x)^3),x]","-\frac{3 b c^2 \text{PolyLog}(2,-c x)}{d^3}+\frac{3 b c^2 \text{PolyLog}(2,c x)}{d^3}-\frac{3 b c^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{d^3}+\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right)}{d^3 (c x+1)}+\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 d^3 (c x+1)^2}+\frac{6 c^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{a+b \tanh ^{-1}(c x)}{2 d^3 x^2}+\frac{3 c \left(a+b \tanh ^{-1}(c x)\right)}{d^3 x}+\frac{6 a c^2 \log (x)}{d^3}+\frac{3 b c^2 \log \left(1-c^2 x^2\right)}{2 d^3}+\frac{13 b c^2}{8 d^3 (c x+1)}+\frac{b c^2}{8 d^3 (c x+1)^2}-\frac{3 b c^2 \log (x)}{d^3}-\frac{9 b c^2 \tanh ^{-1}(c x)}{8 d^3}-\frac{b c}{2 d^3 x}","-\frac{3 b c^2 \text{PolyLog}(2,-c x)}{d^3}+\frac{3 b c^2 \text{PolyLog}(2,c x)}{d^3}-\frac{3 b c^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{d^3}+\frac{3 c^2 \left(a+b \tanh ^{-1}(c x)\right)}{d^3 (c x+1)}+\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 d^3 (c x+1)^2}+\frac{6 c^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{a+b \tanh ^{-1}(c x)}{2 d^3 x^2}+\frac{3 c \left(a+b \tanh ^{-1}(c x)\right)}{d^3 x}+\frac{6 a c^2 \log (x)}{d^3}+\frac{3 b c^2 \log \left(1-c^2 x^2\right)}{2 d^3}+\frac{13 b c^2}{8 d^3 (c x+1)}+\frac{b c^2}{8 d^3 (c x+1)^2}-\frac{3 b c^2 \log (x)}{d^3}-\frac{9 b c^2 \tanh ^{-1}(c x)}{8 d^3}-\frac{b c}{2 d^3 x}",1,"-(b*c)/(2*d^3*x) + (b*c^2)/(8*d^3*(1 + c*x)^2) + (13*b*c^2)/(8*d^3*(1 + c*x)) - (9*b*c^2*ArcTanh[c*x])/(8*d^3) - (a + b*ArcTanh[c*x])/(2*d^3*x^2) + (3*c*(a + b*ArcTanh[c*x]))/(d^3*x) + (c^2*(a + b*ArcTanh[c*x]))/(2*d^3*(1 + c*x)^2) + (3*c^2*(a + b*ArcTanh[c*x]))/(d^3*(1 + c*x)) + (6*a*c^2*Log[x])/d^3 - (3*b*c^2*Log[x])/d^3 + (6*c^2*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/d^3 + (3*b*c^2*Log[1 - c^2*x^2])/(2*d^3) - (3*b*c^2*PolyLog[2, -(c*x)])/d^3 + (3*b*c^2*PolyLog[2, c*x])/d^3 - (3*b*c^2*PolyLog[2, 1 - 2/(1 + c*x)])/d^3","A",24,16,20,0.8000,1,"{5940, 5916, 325, 206, 266, 36, 29, 31, 5912, 5926, 627, 44, 207, 5918, 2402, 2315}"
66,1,80,0,0.053593,"\int \frac{a+b \tanh ^{-1}(c x)}{(1+c x)^4} \, dx","Int[(a + b*ArcTanh[c*x])/(1 + c*x)^4,x]","-\frac{a+b \tanh ^{-1}(c x)}{3 c (c x+1)^3}-\frac{b}{24 c (c x+1)}-\frac{b}{24 c (c x+1)^2}-\frac{b}{18 c (c x+1)^3}+\frac{b \tanh ^{-1}(c x)}{24 c}","-\frac{a+b \tanh ^{-1}(c x)}{3 c (c x+1)^3}-\frac{b}{24 c (c x+1)}-\frac{b}{24 c (c x+1)^2}-\frac{b}{18 c (c x+1)^3}+\frac{b \tanh ^{-1}(c x)}{24 c}",1,"-b/(18*c*(1 + c*x)^3) - b/(24*c*(1 + c*x)^2) - b/(24*c*(1 + c*x)) + (b*ArcTanh[c*x])/(24*c) - (a + b*ArcTanh[c*x])/(3*c*(1 + c*x)^3)","A",5,4,16,0.2500,1,"{5926, 627, 44, 207}"
67,1,41,0,0.0646014,"\int \frac{\tanh ^{-1}(a x)}{c x+a c x^2} \, dx","Int[ArcTanh[a*x]/(c*x + a*c*x^2),x]","\frac{\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)}{c}-\frac{\text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}","\frac{\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)}{c}-\frac{\text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}",1,"(ArcTanh[a*x]*Log[2 - 2/(1 + a*x)])/c - PolyLog[2, -1 + 2/(1 + a*x)]/(2*c)","A",3,3,17,0.1765,1,"{1593, 5932, 2447}"
68,1,270,0,0.649668,"\int x^3 (d+c d x) \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d + c*d*x)*(a + b*ArcTanh[c*x])^2,x]","-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{5 c^4}+\frac{b d x^2 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^2}+\frac{a b d x}{2 c^3}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{20 c^4}-\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{5 c^4}+\frac{1}{5} c d x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{4} d x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{10} b d x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d x^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 c}+\frac{b^2 d x^2}{12 c^2}+\frac{b^2 d \log \left(1-c^2 x^2\right)}{3 c^4}+\frac{3 b^2 d x}{10 c^3}+\frac{b^2 d x \tanh ^{-1}(c x)}{2 c^3}-\frac{3 b^2 d \tanh ^{-1}(c x)}{10 c^4}+\frac{b^2 d x^3}{30 c}","-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{5 c^4}+\frac{b d x^2 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^2}+\frac{a b d x}{2 c^3}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{20 c^4}-\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{5 c^4}+\frac{1}{5} c d x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{4} d x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{10} b d x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d x^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 c}+\frac{b^2 d x^2}{12 c^2}+\frac{b^2 d \log \left(1-c^2 x^2\right)}{3 c^4}+\frac{3 b^2 d x}{10 c^3}+\frac{b^2 d x \tanh ^{-1}(c x)}{2 c^3}-\frac{3 b^2 d \tanh ^{-1}(c x)}{10 c^4}+\frac{b^2 d x^3}{30 c}",1,"(a*b*d*x)/(2*c^3) + (3*b^2*d*x)/(10*c^3) + (b^2*d*x^2)/(12*c^2) + (b^2*d*x^3)/(30*c) - (3*b^2*d*ArcTanh[c*x])/(10*c^4) + (b^2*d*x*ArcTanh[c*x])/(2*c^3) + (b*d*x^2*(a + b*ArcTanh[c*x]))/(5*c^2) + (b*d*x^3*(a + b*ArcTanh[c*x]))/(6*c) + (b*d*x^4*(a + b*ArcTanh[c*x]))/10 - (d*(a + b*ArcTanh[c*x])^2)/(20*c^4) + (d*x^4*(a + b*ArcTanh[c*x])^2)/4 + (c*d*x^5*(a + b*ArcTanh[c*x])^2)/5 - (2*b*d*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(5*c^4) + (b^2*d*Log[1 - c^2*x^2])/(3*c^4) - (b^2*d*PolyLog[2, 1 - 2/(1 - c*x)])/(5*c^4)","A",27,15,20,0.7500,1,"{5940, 5916, 5980, 266, 43, 5910, 260, 5948, 302, 206, 321, 5984, 5918, 2402, 2315}"
69,1,236,0,0.5259703,"\int x^2 (d+c d x) \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d + c*d*x)*(a + b*ArcTanh[c*x])^2,x]","-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^3}+\frac{a b d x}{2 c^2}+\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{12 c^3}-\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^3}+\frac{1}{4} c d x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{3} d x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{6} b d x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d x^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 c}+\frac{b^2 d \log \left(1-c^2 x^2\right)}{3 c^3}+\frac{b^2 d x}{3 c^2}+\frac{b^2 d x \tanh ^{-1}(c x)}{2 c^2}-\frac{b^2 d \tanh ^{-1}(c x)}{3 c^3}+\frac{b^2 d x^2}{12 c}","-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^3}+\frac{a b d x}{2 c^2}+\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{12 c^3}-\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^3}+\frac{1}{4} c d x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{3} d x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{6} b d x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d x^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 c}+\frac{b^2 d \log \left(1-c^2 x^2\right)}{3 c^3}+\frac{b^2 d x}{3 c^2}+\frac{b^2 d x \tanh ^{-1}(c x)}{2 c^2}-\frac{b^2 d \tanh ^{-1}(c x)}{3 c^3}+\frac{b^2 d x^2}{12 c}",1,"(a*b*d*x)/(2*c^2) + (b^2*d*x)/(3*c^2) + (b^2*d*x^2)/(12*c) - (b^2*d*ArcTanh[c*x])/(3*c^3) + (b^2*d*x*ArcTanh[c*x])/(2*c^2) + (b*d*x^2*(a + b*ArcTanh[c*x]))/(3*c) + (b*d*x^3*(a + b*ArcTanh[c*x]))/6 + (d*(a + b*ArcTanh[c*x])^2)/(12*c^3) + (d*x^3*(a + b*ArcTanh[c*x])^2)/3 + (c*d*x^4*(a + b*ArcTanh[c*x])^2)/4 - (2*b*d*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(3*c^3) + (b^2*d*Log[1 - c^2*x^2])/(3*c^3) - (b^2*d*PolyLog[2, 1 - 2/(1 - c*x)])/(3*c^3)","A",22,14,20,0.7000,1,"{5940, 5916, 5980, 321, 206, 5984, 5918, 2402, 2315, 266, 43, 5910, 260, 5948}"
70,1,196,0,0.393827,"\int x (d+c d x) \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x*(d + c*d*x)*(a + b*ArcTanh[c*x])^2,x]","-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^2}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{6 c^2}-\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^2}+\frac{1}{3} c d x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{2} d x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{3} b d x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{a b d x}{c}+\frac{b^2 d \log \left(1-c^2 x^2\right)}{2 c^2}-\frac{b^2 d \tanh ^{-1}(c x)}{3 c^2}+\frac{b^2 d x}{3 c}+\frac{b^2 d x \tanh ^{-1}(c x)}{c}","-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^2}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{6 c^2}-\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^2}+\frac{1}{3} c d x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{2} d x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{3} b d x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{a b d x}{c}+\frac{b^2 d \log \left(1-c^2 x^2\right)}{2 c^2}-\frac{b^2 d \tanh ^{-1}(c x)}{3 c^2}+\frac{b^2 d x}{3 c}+\frac{b^2 d x \tanh ^{-1}(c x)}{c}",1,"(a*b*d*x)/c + (b^2*d*x)/(3*c) - (b^2*d*ArcTanh[c*x])/(3*c^2) + (b^2*d*x*ArcTanh[c*x])/c + (b*d*x^2*(a + b*ArcTanh[c*x]))/3 - (d*(a + b*ArcTanh[c*x])^2)/(6*c^2) + (d*x^2*(a + b*ArcTanh[c*x])^2)/2 + (c*d*x^3*(a + b*ArcTanh[c*x])^2)/3 - (2*b*d*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(3*c^2) + (b^2*d*Log[1 - c^2*x^2])/(2*c^2) - (b^2*d*PolyLog[2, 1 - 2/(1 - c*x)])/(3*c^2)","A",17,12,18,0.6667,1,"{5940, 5916, 5980, 5910, 260, 5948, 321, 206, 5984, 5918, 2402, 2315}"
71,1,112,0,0.1186837,"\int (d+c d x) \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[(d + c*d*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{d (c x+1)^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}-\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+a b d x+\frac{b^2 d \log \left(1-c^2 x^2\right)}{2 c}+b^2 d x \tanh ^{-1}(c x)","-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c}+\frac{d (c x+1)^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}-\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+a b d x+\frac{b^2 d \log \left(1-c^2 x^2\right)}{2 c}+b^2 d x \tanh ^{-1}(c x)",1,"a*b*d*x + b^2*d*x*ArcTanh[c*x] + (d*(1 + c*x)^2*(a + b*ArcTanh[c*x])^2)/(2*c) - (2*b*d*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c + (b^2*d*Log[1 - c^2*x^2])/(2*c) - (b^2*d*PolyLog[2, 1 - 2/(1 - c*x)])/c","A",9,7,17,0.4118,1,"{5928, 5910, 260, 1586, 5918, 2402, 2315}"
72,1,191,0,0.4506179,"\int \frac{(d+c d x) \left(a+b \tanh ^{-1}(c x)\right)^2}{x} \, dx","Int[((d + c*d*x)*(a + b*ArcTanh[c*x])^2)/x,x]","-b d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b d \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)+b^2 (-d) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{1}{2} b^2 d \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 d \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+d \left(a+b \tanh ^{-1}(c x)\right)^2+c d x \left(a+b \tanh ^{-1}(c x)\right)^2+2 d \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)","-b d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b d \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)+b^2 (-d) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{1}{2} b^2 d \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 d \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+d \left(a+b \tanh ^{-1}(c x)\right)^2+c d x \left(a+b \tanh ^{-1}(c x)\right)^2+2 d \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)",1,"d*(a + b*ArcTanh[c*x])^2 + c*d*x*(a + b*ArcTanh[c*x])^2 + 2*d*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)] - 2*b*d*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)] - b^2*d*PolyLog[2, 1 - 2/(1 - c*x)] - b*d*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)] + b*d*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)] + (b^2*d*PolyLog[3, 1 - 2/(1 - c*x)])/2 - (b^2*d*PolyLog[3, -1 + 2/(1 - c*x)])/2","A",13,11,20,0.5500,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5914, 6052, 5948, 6058, 6610}"
73,1,201,0,0.4840354,"\int \frac{(d+c d x) \left(a+b \tanh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d + c*d*x)*(a + b*ArcTanh[c*x])^2)/x^2,x]","-b c d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b c d \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)+b^2 (-c) d \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{1}{2} b^2 c d \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 c d \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+c d \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{x}+2 c d \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2+2 b c d \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)","-b c d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b c d \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)+b^2 (-c) d \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{1}{2} b^2 c d \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 c d \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+c d \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{x}+2 c d \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2+2 b c d \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)",1,"c*d*(a + b*ArcTanh[c*x])^2 - (d*(a + b*ArcTanh[c*x])^2)/x + 2*c*d*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)] + 2*b*c*d*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)] - b*c*d*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)] + b*c*d*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)] - b^2*c*d*PolyLog[2, -1 + 2/(1 + c*x)] + (b^2*c*d*PolyLog[3, 1 - 2/(1 - c*x)])/2 - (b^2*c*d*PolyLog[3, -1 + 2/(1 - c*x)])/2","A",12,10,20,0.5000,1,"{5940, 5916, 5988, 5932, 2447, 5914, 6052, 5948, 6058, 6610}"
74,1,151,0,0.3652707,"\int \frac{(d+c d x) \left(a+b \tanh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d + c*d*x)*(a + b*ArcTanh[c*x])^2)/x^3,x]","-b^2 c^2 d \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{3}{2} c^2 d \left(a+b \tanh ^{-1}(c x)\right)^2+2 b c^2 d \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{c d \left(a+b \tanh ^{-1}(c x)\right)^2}{x}-\frac{b c d \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{1}{2} b^2 c^2 d \log \left(1-c^2 x^2\right)+b^2 c^2 d \log (x)","-b^2 c^2 d \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{3}{2} c^2 d \left(a+b \tanh ^{-1}(c x)\right)^2+2 b c^2 d \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{c d \left(a+b \tanh ^{-1}(c x)\right)^2}{x}-\frac{b c d \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{1}{2} b^2 c^2 d \log \left(1-c^2 x^2\right)+b^2 c^2 d \log (x)",1,"-((b*c*d*(a + b*ArcTanh[c*x]))/x) + (3*c^2*d*(a + b*ArcTanh[c*x])^2)/2 - (d*(a + b*ArcTanh[c*x])^2)/(2*x^2) - (c*d*(a + b*ArcTanh[c*x])^2)/x + b^2*c^2*d*Log[x] - (b^2*c^2*d*Log[1 - c^2*x^2])/2 + 2*b*c^2*d*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)] - b^2*c^2*d*PolyLog[2, -1 + 2/(1 + c*x)]","A",14,11,20,0.5500,1,"{5940, 5916, 5982, 266, 36, 29, 31, 5948, 5988, 5932, 2447}"
75,1,206,0,0.4531182,"\int \frac{(d+c d x) \left(a+b \tanh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d + c*d*x)*(a + b*ArcTanh[c*x])^2)/x^4,x]","-\frac{1}{3} b^2 c^3 d \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{5}{6} c^3 d \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{b c^2 d \left(a+b \tanh ^{-1}(c x)\right)}{x}+\frac{2}{3} b c^3 d \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{c d \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{b c d \left(a+b \tanh ^{-1}(c x)\right)}{3 x^2}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{3 x^3}-\frac{1}{2} b^2 c^3 d \log \left(1-c^2 x^2\right)-\frac{b^2 c^2 d}{3 x}+b^2 c^3 d \log (x)+\frac{1}{3} b^2 c^3 d \tanh ^{-1}(c x)","-\frac{1}{3} b^2 c^3 d \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{5}{6} c^3 d \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{b c^2 d \left(a+b \tanh ^{-1}(c x)\right)}{x}+\frac{2}{3} b c^3 d \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{c d \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{b c d \left(a+b \tanh ^{-1}(c x)\right)}{3 x^2}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{3 x^3}-\frac{1}{2} b^2 c^3 d \log \left(1-c^2 x^2\right)-\frac{b^2 c^2 d}{3 x}+b^2 c^3 d \log (x)+\frac{1}{3} b^2 c^3 d \tanh ^{-1}(c x)",1,"-(b^2*c^2*d)/(3*x) + (b^2*c^3*d*ArcTanh[c*x])/3 - (b*c*d*(a + b*ArcTanh[c*x]))/(3*x^2) - (b*c^2*d*(a + b*ArcTanh[c*x]))/x + (5*c^3*d*(a + b*ArcTanh[c*x])^2)/6 - (d*(a + b*ArcTanh[c*x])^2)/(3*x^3) - (c*d*(a + b*ArcTanh[c*x])^2)/(2*x^2) + b^2*c^3*d*Log[x] - (b^2*c^3*d*Log[1 - c^2*x^2])/2 + (2*b*c^3*d*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/3 - (b^2*c^3*d*PolyLog[2, -1 + 2/(1 + c*x)])/3","A",18,13,20,0.6500,1,"{5940, 5916, 5982, 325, 206, 5988, 5932, 2447, 266, 36, 29, 31, 5948}"
76,1,356,0,1.0241632,"\int x^3 (d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d + c*d*x)^2*(a + b*ArcTanh[c*x])^2,x]","-\frac{2 b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{5 c^4}+\frac{1}{6} c^2 d^2 x^6 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{2 b d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^2}+\frac{5 a b d^2 x}{6 c^3}-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{60 c^4}-\frac{4 b d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{5 c^4}+\frac{2}{5} c d^2 x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{15} b c d^2 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{5} b d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{5 b d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)}{18 c}+\frac{31 b^2 d^2 x^2}{180 c^2}+\frac{53 b^2 d^2 \log \left(1-c^2 x^2\right)}{90 c^4}+\frac{3 b^2 d^2 x}{5 c^3}+\frac{5 b^2 d^2 x \tanh ^{-1}(c x)}{6 c^3}-\frac{3 b^2 d^2 \tanh ^{-1}(c x)}{5 c^4}+\frac{b^2 d^2 x^3}{15 c}+\frac{1}{60} b^2 d^2 x^4","-\frac{2 b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{5 c^4}+\frac{1}{6} c^2 d^2 x^6 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{2 b d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^2}+\frac{5 a b d^2 x}{6 c^3}-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{60 c^4}-\frac{4 b d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{5 c^4}+\frac{2}{5} c d^2 x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{15} b c d^2 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{5} b d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{5 b d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)}{18 c}+\frac{31 b^2 d^2 x^2}{180 c^2}+\frac{53 b^2 d^2 \log \left(1-c^2 x^2\right)}{90 c^4}+\frac{3 b^2 d^2 x}{5 c^3}+\frac{5 b^2 d^2 x \tanh ^{-1}(c x)}{6 c^3}-\frac{3 b^2 d^2 \tanh ^{-1}(c x)}{5 c^4}+\frac{b^2 d^2 x^3}{15 c}+\frac{1}{60} b^2 d^2 x^4",1,"(5*a*b*d^2*x)/(6*c^3) + (3*b^2*d^2*x)/(5*c^3) + (31*b^2*d^2*x^2)/(180*c^2) + (b^2*d^2*x^3)/(15*c) + (b^2*d^2*x^4)/60 - (3*b^2*d^2*ArcTanh[c*x])/(5*c^4) + (5*b^2*d^2*x*ArcTanh[c*x])/(6*c^3) + (2*b*d^2*x^2*(a + b*ArcTanh[c*x]))/(5*c^2) + (5*b*d^2*x^3*(a + b*ArcTanh[c*x]))/(18*c) + (b*d^2*x^4*(a + b*ArcTanh[c*x]))/5 + (b*c*d^2*x^5*(a + b*ArcTanh[c*x]))/15 - (d^2*(a + b*ArcTanh[c*x])^2)/(60*c^4) + (d^2*x^4*(a + b*ArcTanh[c*x])^2)/4 + (2*c*d^2*x^5*(a + b*ArcTanh[c*x])^2)/5 + (c^2*d^2*x^6*(a + b*ArcTanh[c*x])^2)/6 - (4*b*d^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(5*c^4) + (53*b^2*d^2*Log[1 - c^2*x^2])/(90*c^4) - (2*b^2*d^2*PolyLog[2, 1 - 2/(1 - c*x)])/(5*c^4)","A",43,15,22,0.6818,1,"{5940, 5916, 5980, 266, 43, 5910, 260, 5948, 302, 206, 321, 5984, 5918, 2402, 2315}"
77,1,312,0,0.8837281,"\int x^2 (d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d + c*d*x)^2*(a + b*ArcTanh[c*x])^2,x]","-\frac{8 b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{15 c^3}+\frac{1}{5} c^2 d^2 x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{a b d^2 x}{c^2}+\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{30 c^3}-\frac{16 b d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{15 c^3}+\frac{1}{2} c d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{10} b c d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{3} d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{3} b d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{8 b d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{15 c}+\frac{2 b^2 d^2 \log \left(1-c^2 x^2\right)}{3 c^3}+\frac{19 b^2 d^2 x}{30 c^2}+\frac{b^2 d^2 x \tanh ^{-1}(c x)}{c^2}-\frac{19 b^2 d^2 \tanh ^{-1}(c x)}{30 c^3}+\frac{b^2 d^2 x^2}{6 c}+\frac{1}{30} b^2 d^2 x^3","-\frac{8 b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{15 c^3}+\frac{1}{5} c^2 d^2 x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{a b d^2 x}{c^2}+\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{30 c^3}-\frac{16 b d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{15 c^3}+\frac{1}{2} c d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{10} b c d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{3} d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{3} b d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{8 b d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{15 c}+\frac{2 b^2 d^2 \log \left(1-c^2 x^2\right)}{3 c^3}+\frac{19 b^2 d^2 x}{30 c^2}+\frac{b^2 d^2 x \tanh ^{-1}(c x)}{c^2}-\frac{19 b^2 d^2 \tanh ^{-1}(c x)}{30 c^3}+\frac{b^2 d^2 x^2}{6 c}+\frac{1}{30} b^2 d^2 x^3",1,"(a*b*d^2*x)/c^2 + (19*b^2*d^2*x)/(30*c^2) + (b^2*d^2*x^2)/(6*c) + (b^2*d^2*x^3)/30 - (19*b^2*d^2*ArcTanh[c*x])/(30*c^3) + (b^2*d^2*x*ArcTanh[c*x])/c^2 + (8*b*d^2*x^2*(a + b*ArcTanh[c*x]))/(15*c) + (b*d^2*x^3*(a + b*ArcTanh[c*x]))/3 + (b*c*d^2*x^4*(a + b*ArcTanh[c*x]))/10 + (d^2*(a + b*ArcTanh[c*x])^2)/(30*c^3) + (d^2*x^3*(a + b*ArcTanh[c*x])^2)/3 + (c*d^2*x^4*(a + b*ArcTanh[c*x])^2)/2 + (c^2*d^2*x^5*(a + b*ArcTanh[c*x])^2)/5 - (16*b*d^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(15*c^3) + (2*b^2*d^2*Log[1 - c^2*x^2])/(3*c^3) - (8*b^2*d^2*PolyLog[2, 1 - 2/(1 - c*x)])/(15*c^3)","A",36,15,22,0.6818,1,"{5940, 5916, 5980, 321, 206, 5984, 5918, 2402, 2315, 266, 43, 5910, 260, 5948, 302}"
78,1,280,0,0.6521947,"\int x (d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x*(d + c*d*x)^2*(a + b*ArcTanh[c*x])^2,x]","-\frac{2 b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^2}+\frac{1}{4} c^2 d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{12 c^2}-\frac{4 b d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^2}+\frac{2}{3} c d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{6} b c d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{2}{3} b d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{3 a b d^2 x}{2 c}+\frac{5 b^2 d^2 \log \left(1-c^2 x^2\right)}{6 c^2}-\frac{2 b^2 d^2 \tanh ^{-1}(c x)}{3 c^2}+\frac{2 b^2 d^2 x}{3 c}+\frac{3 b^2 d^2 x \tanh ^{-1}(c x)}{2 c}+\frac{1}{12} b^2 d^2 x^2","-\frac{2 b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^2}+\frac{1}{4} c^2 d^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{12 c^2}-\frac{4 b d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^2}+\frac{2}{3} c d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{6} b c d^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{2}{3} b d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{3 a b d^2 x}{2 c}+\frac{5 b^2 d^2 \log \left(1-c^2 x^2\right)}{6 c^2}-\frac{2 b^2 d^2 \tanh ^{-1}(c x)}{3 c^2}+\frac{2 b^2 d^2 x}{3 c}+\frac{3 b^2 d^2 x \tanh ^{-1}(c x)}{2 c}+\frac{1}{12} b^2 d^2 x^2",1,"(3*a*b*d^2*x)/(2*c) + (2*b^2*d^2*x)/(3*c) + (b^2*d^2*x^2)/12 - (2*b^2*d^2*ArcTanh[c*x])/(3*c^2) + (3*b^2*d^2*x*ArcTanh[c*x])/(2*c) + (2*b*d^2*x^2*(a + b*ArcTanh[c*x]))/3 + (b*c*d^2*x^3*(a + b*ArcTanh[c*x]))/6 - (d^2*(a + b*ArcTanh[c*x])^2)/(12*c^2) + (d^2*x^2*(a + b*ArcTanh[c*x])^2)/2 + (2*c*d^2*x^3*(a + b*ArcTanh[c*x])^2)/3 + (c^2*d^2*x^4*(a + b*ArcTanh[c*x])^2)/4 - (4*b*d^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(3*c^2) + (5*b^2*d^2*Log[1 - c^2*x^2])/(6*c^2) - (2*b^2*d^2*PolyLog[2, 1 - 2/(1 - c*x)])/(3*c^2)","A",28,14,20,0.7000,1,"{5940, 5916, 5980, 5910, 260, 5948, 321, 206, 5984, 5918, 2402, 2315, 266, 43}"
79,1,175,0,0.1643858,"\int (d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[(d + c*d*x)^2*(a + b*ArcTanh[c*x])^2,x]","-\frac{4 b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c}+\frac{1}{3} b c d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{d^2 (c x+1)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 c}-\frac{8 b d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c}+2 a b d^2 x+\frac{b^2 d^2 \log \left(1-c^2 x^2\right)}{c}-\frac{b^2 d^2 \tanh ^{-1}(c x)}{3 c}+2 b^2 d^2 x \tanh ^{-1}(c x)+\frac{1}{3} b^2 d^2 x","-\frac{4 b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c}+\frac{1}{3} b c d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{d^2 (c x+1)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 c}-\frac{8 b d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c}+2 a b d^2 x+\frac{b^2 d^2 \log \left(1-c^2 x^2\right)}{c}-\frac{b^2 d^2 \tanh ^{-1}(c x)}{3 c}+2 b^2 d^2 x \tanh ^{-1}(c x)+\frac{1}{3} b^2 d^2 x",1,"2*a*b*d^2*x + (b^2*d^2*x)/3 - (b^2*d^2*ArcTanh[c*x])/(3*c) + 2*b^2*d^2*x*ArcTanh[c*x] + (b*c*d^2*x^2*(a + b*ArcTanh[c*x]))/3 + (d^2*(1 + c*x)^3*(a + b*ArcTanh[c*x])^2)/(3*c) - (8*b*d^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(3*c) + (b^2*d^2*Log[1 - c^2*x^2])/c - (4*b^2*d^2*PolyLog[2, 1 - 2/(1 - c*x)])/(3*c)","A",12,10,19,0.5263,1,"{5928, 5910, 260, 5916, 321, 206, 1586, 5918, 2402, 2315}"
80,1,278,0,0.5864043,"\int \frac{(d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{x} \, dx","Int[((d + c*d*x)^2*(a + b*ArcTanh[c*x])^2)/x,x]","-b d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b d^2 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-2 b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{1}{2} b^2 d^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 d^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{1}{2} c^2 d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+a b c d^2 x+2 c d^2 x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{2} d^2 \left(a+b \tanh ^{-1}(c x)\right)^2+2 d^2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-4 b d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} b^2 d^2 \log \left(1-c^2 x^2\right)+b^2 c d^2 x \tanh ^{-1}(c x)","-b d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b d^2 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-2 b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{1}{2} b^2 d^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 d^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{1}{2} c^2 d^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+a b c d^2 x+2 c d^2 x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{2} d^2 \left(a+b \tanh ^{-1}(c x)\right)^2+2 d^2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-4 b d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} b^2 d^2 \log \left(1-c^2 x^2\right)+b^2 c d^2 x \tanh ^{-1}(c x)",1,"a*b*c*d^2*x + b^2*c*d^2*x*ArcTanh[c*x] + (3*d^2*(a + b*ArcTanh[c*x])^2)/2 + 2*c*d^2*x*(a + b*ArcTanh[c*x])^2 + (c^2*d^2*x^2*(a + b*ArcTanh[c*x])^2)/2 + 2*d^2*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)] - 4*b*d^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)] + (b^2*d^2*Log[1 - c^2*x^2])/2 - 2*b^2*d^2*PolyLog[2, 1 - 2/(1 - c*x)] - b*d^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)] + b*d^2*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)] + (b^2*d^2*PolyLog[3, 1 - 2/(1 - c*x)])/2 - (b^2*d^2*PolyLog[3, -1 + 2/(1 - c*x)])/2","A",19,14,22,0.6364,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5914, 6052, 5948, 6058, 6610, 5916, 5980, 260}"
81,1,283,0,0.6291366,"\int \frac{(d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d + c*d*x)^2*(a + b*ArcTanh[c*x])^2)/x^2,x]","-2 b c d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+2 b c d^2 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-b^2 c d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-b^2 c d^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+b^2 c d^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-b^2 c d^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+c^2 d^2 x \left(a+b \tanh ^{-1}(c x)\right)^2+2 c d^2 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{x}+4 c d^2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-2 b c d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+2 b c d^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)","-2 b c d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+2 b c d^2 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-b^2 c d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-b^2 c d^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+b^2 c d^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-b^2 c d^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+c^2 d^2 x \left(a+b \tanh ^{-1}(c x)\right)^2+2 c d^2 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{x}+4 c d^2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-2 b c d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+2 b c d^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)",1,"2*c*d^2*(a + b*ArcTanh[c*x])^2 - (d^2*(a + b*ArcTanh[c*x])^2)/x + c^2*d^2*x*(a + b*ArcTanh[c*x])^2 + 4*c*d^2*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)] - 2*b*c*d^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)] + 2*b*c*d^2*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)] - b^2*c*d^2*PolyLog[2, 1 - 2/(1 - c*x)] - 2*b*c*d^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)] + 2*b*c*d^2*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)] - b^2*c*d^2*PolyLog[2, -1 + 2/(1 + c*x)] + b^2*c*d^2*PolyLog[3, 1 - 2/(1 - c*x)] - b^2*c*d^2*PolyLog[3, -1 + 2/(1 - c*x)]","A",17,15,22,0.6818,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5916, 5988, 5932, 2447, 5914, 6052, 5948, 6058, 6610}"
82,1,313,0,0.6733286,"\int \frac{(d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d + c*d*x)^2*(a + b*ArcTanh[c*x])^2)/x^3,x]","-b c^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b c^2 d^2 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-2 b^2 c^2 d^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{1}{2} b^2 c^2 d^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 c^2 d^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{5}{2} c^2 d^2 \left(a+b \tanh ^{-1}(c x)\right)^2+2 c^2 d^2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2+4 b c^2 d^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{2 c d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{x}-\frac{b c d^2 \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{1}{2} b^2 c^2 d^2 \log \left(1-c^2 x^2\right)+b^2 c^2 d^2 \log (x)","-b c^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b c^2 d^2 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-2 b^2 c^2 d^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{1}{2} b^2 c^2 d^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 c^2 d^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{5}{2} c^2 d^2 \left(a+b \tanh ^{-1}(c x)\right)^2+2 c^2 d^2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2+4 b c^2 d^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{2 c d^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{x}-\frac{b c d^2 \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{1}{2} b^2 c^2 d^2 \log \left(1-c^2 x^2\right)+b^2 c^2 d^2 \log (x)",1,"-((b*c*d^2*(a + b*ArcTanh[c*x]))/x) + (5*c^2*d^2*(a + b*ArcTanh[c*x])^2)/2 - (d^2*(a + b*ArcTanh[c*x])^2)/(2*x^2) - (2*c*d^2*(a + b*ArcTanh[c*x])^2)/x + 2*c^2*d^2*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)] + b^2*c^2*d^2*Log[x] - (b^2*c^2*d^2*Log[1 - c^2*x^2])/2 + 4*b*c^2*d^2*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)] - b*c^2*d^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)] + b*c^2*d^2*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)] - 2*b^2*c^2*d^2*PolyLog[2, -1 + 2/(1 + c*x)] + (b^2*c^2*d^2*PolyLog[3, 1 - 2/(1 - c*x)])/2 - (b^2*c^2*d^2*PolyLog[3, -1 + 2/(1 - c*x)])/2","A",20,15,22,0.6818,1,"{5940, 5916, 5982, 266, 36, 29, 31, 5948, 5988, 5932, 2447, 5914, 6052, 6058, 6610}"
83,1,244,0,0.2561344,"\int \frac{(d+c d x)^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d + c*d*x)^2*(a + b*ArcTanh[c*x])^2)/x^4,x]","-\frac{4}{3} b^2 c^3 d^2 \text{PolyLog}(2,-c x)+\frac{4}{3} b^2 c^3 d^2 \text{PolyLog}(2,c x)+\frac{4}{3} b^2 c^3 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{8}{3} a b c^3 d^2 \log (x)-\frac{2 b c^2 d^2 \left(a+b \tanh ^{-1}(c x)\right)}{x}+\frac{8}{3} b c^3 d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{b c d^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^2}-\frac{d^2 (c x+1)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 x^3}-b^2 c^3 d^2 \log \left(1-c^2 x^2\right)-\frac{b^2 c^2 d^2}{3 x}+2 b^2 c^3 d^2 \log (x)+\frac{1}{3} b^2 c^3 d^2 \tanh ^{-1}(c x)","-\frac{4}{3} b^2 c^3 d^2 \text{PolyLog}(2,-c x)+\frac{4}{3} b^2 c^3 d^2 \text{PolyLog}(2,c x)+\frac{4}{3} b^2 c^3 d^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{8}{3} a b c^3 d^2 \log (x)-\frac{2 b c^2 d^2 \left(a+b \tanh ^{-1}(c x)\right)}{x}+\frac{8}{3} b c^3 d^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{b c d^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^2}-\frac{d^2 (c x+1)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 x^3}-b^2 c^3 d^2 \log \left(1-c^2 x^2\right)-\frac{b^2 c^2 d^2}{3 x}+2 b^2 c^3 d^2 \log (x)+\frac{1}{3} b^2 c^3 d^2 \tanh ^{-1}(c x)",1,"-(b^2*c^2*d^2)/(3*x) + (b^2*c^3*d^2*ArcTanh[c*x])/3 - (b*c*d^2*(a + b*ArcTanh[c*x]))/(3*x^2) - (2*b*c^2*d^2*(a + b*ArcTanh[c*x]))/x - (d^2*(1 + c*x)^3*(a + b*ArcTanh[c*x])^2)/(3*x^3) + (8*a*b*c^3*d^2*Log[x])/3 + 2*b^2*c^3*d^2*Log[x] + (8*b*c^3*d^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/3 - b^2*c^3*d^2*Log[1 - c^2*x^2] - (4*b^2*c^3*d^2*PolyLog[2, -(c*x)])/3 + (4*b^2*c^3*d^2*PolyLog[2, c*x])/3 + (4*b^2*c^3*d^2*PolyLog[2, 1 - 2/(1 - c*x)])/3","A",14,13,22,0.5909,1,"{37, 5938, 5916, 325, 206, 266, 36, 29, 31, 5912, 5918, 2402, 2315}"
84,1,415,0,1.4590061,"\int x^3 (d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d + c*d*x)^3*(a + b*ArcTanh[c*x])^2,x]","-\frac{26 b^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{35 c^4}+\frac{1}{7} c^3 d^3 x^7 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{2} c^2 d^3 x^6 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{21} b c^2 d^3 x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{26 b d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{35 c^2}+\frac{3 a b d^3 x}{2 c^3}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{140 c^4}-\frac{52 b d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{35 c^4}+\frac{3}{5} c d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{5} b c d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{13}{35} b d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 c}+\frac{7 b^2 d^3 x^2}{20 c^2}+\frac{11 b^2 d^3 \log \left(1-c^2 x^2\right)}{10 c^4}+\frac{122 b^2 d^3 x}{105 c^3}+\frac{3 b^2 d^3 x \tanh ^{-1}(c x)}{2 c^3}-\frac{122 b^2 d^3 \tanh ^{-1}(c x)}{105 c^4}+\frac{1}{105} b^2 c d^3 x^5+\frac{44 b^2 d^3 x^3}{315 c}+\frac{1}{20} b^2 d^3 x^4","-\frac{26 b^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{35 c^4}+\frac{1}{7} c^3 d^3 x^7 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{2} c^2 d^3 x^6 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{21} b c^2 d^3 x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{26 b d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{35 c^2}+\frac{3 a b d^3 x}{2 c^3}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{140 c^4}-\frac{52 b d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{35 c^4}+\frac{3}{5} c d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{5} b c d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{13}{35} b d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 c}+\frac{7 b^2 d^3 x^2}{20 c^2}+\frac{11 b^2 d^3 \log \left(1-c^2 x^2\right)}{10 c^4}+\frac{122 b^2 d^3 x}{105 c^3}+\frac{3 b^2 d^3 x \tanh ^{-1}(c x)}{2 c^3}-\frac{122 b^2 d^3 \tanh ^{-1}(c x)}{105 c^4}+\frac{1}{105} b^2 c d^3 x^5+\frac{44 b^2 d^3 x^3}{315 c}+\frac{1}{20} b^2 d^3 x^4",1,"(3*a*b*d^3*x)/(2*c^3) + (122*b^2*d^3*x)/(105*c^3) + (7*b^2*d^3*x^2)/(20*c^2) + (44*b^2*d^3*x^3)/(315*c) + (b^2*d^3*x^4)/20 + (b^2*c*d^3*x^5)/105 - (122*b^2*d^3*ArcTanh[c*x])/(105*c^4) + (3*b^2*d^3*x*ArcTanh[c*x])/(2*c^3) + (26*b*d^3*x^2*(a + b*ArcTanh[c*x]))/(35*c^2) + (b*d^3*x^3*(a + b*ArcTanh[c*x]))/(2*c) + (13*b*d^3*x^4*(a + b*ArcTanh[c*x]))/35 + (b*c*d^3*x^5*(a + b*ArcTanh[c*x]))/5 + (b*c^2*d^3*x^6*(a + b*ArcTanh[c*x]))/21 - (d^3*(a + b*ArcTanh[c*x])^2)/(140*c^4) + (d^3*x^4*(a + b*ArcTanh[c*x])^2)/4 + (3*c*d^3*x^5*(a + b*ArcTanh[c*x])^2)/5 + (c^2*d^3*x^6*(a + b*ArcTanh[c*x])^2)/2 + (c^3*d^3*x^7*(a + b*ArcTanh[c*x])^2)/7 - (52*b*d^3*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(35*c^4) + (11*b^2*d^3*Log[1 - c^2*x^2])/(10*c^4) - (26*b^2*d^3*PolyLog[2, 1 - 2/(1 - c*x)])/(35*c^4)","A",62,15,22,0.6818,1,"{5940, 5916, 5980, 266, 43, 5910, 260, 5948, 302, 206, 321, 5984, 5918, 2402, 2315}"
85,1,377,0,1.2298114,"\int x^2 (d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d + c*d*x)^3*(a + b*ArcTanh[c*x])^2,x]","-\frac{14 b^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{15 c^3}+\frac{1}{6} c^3 d^3 x^6 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{5} c^2 d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{15} b c^2 d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{11 a b d^3 x}{6 c^2}+\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{60 c^3}-\frac{28 b d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{15 c^3}+\frac{3}{4} c d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{10} b c d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{11}{18} b d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{14 b d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{15 c}+\frac{113 b^2 d^3 \log \left(1-c^2 x^2\right)}{90 c^3}+\frac{37 b^2 d^3 x}{30 c^2}+\frac{11 b^2 d^3 x \tanh ^{-1}(c x)}{6 c^2}-\frac{37 b^2 d^3 \tanh ^{-1}(c x)}{30 c^3}+\frac{1}{60} b^2 c d^3 x^4+\frac{61 b^2 d^3 x^2}{180 c}+\frac{1}{10} b^2 d^3 x^3","-\frac{14 b^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{15 c^3}+\frac{1}{6} c^3 d^3 x^6 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{5} c^2 d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{15} b c^2 d^3 x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{11 a b d^3 x}{6 c^2}+\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{60 c^3}-\frac{28 b d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{15 c^3}+\frac{3}{4} c d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{10} b c d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{11}{18} b d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{14 b d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{15 c}+\frac{113 b^2 d^3 \log \left(1-c^2 x^2\right)}{90 c^3}+\frac{37 b^2 d^3 x}{30 c^2}+\frac{11 b^2 d^3 x \tanh ^{-1}(c x)}{6 c^2}-\frac{37 b^2 d^3 \tanh ^{-1}(c x)}{30 c^3}+\frac{1}{60} b^2 c d^3 x^4+\frac{61 b^2 d^3 x^2}{180 c}+\frac{1}{10} b^2 d^3 x^3",1,"(11*a*b*d^3*x)/(6*c^2) + (37*b^2*d^3*x)/(30*c^2) + (61*b^2*d^3*x^2)/(180*c) + (b^2*d^3*x^3)/10 + (b^2*c*d^3*x^4)/60 - (37*b^2*d^3*ArcTanh[c*x])/(30*c^3) + (11*b^2*d^3*x*ArcTanh[c*x])/(6*c^2) + (14*b*d^3*x^2*(a + b*ArcTanh[c*x]))/(15*c) + (11*b*d^3*x^3*(a + b*ArcTanh[c*x]))/18 + (3*b*c*d^3*x^4*(a + b*ArcTanh[c*x]))/10 + (b*c^2*d^3*x^5*(a + b*ArcTanh[c*x]))/15 + (d^3*(a + b*ArcTanh[c*x])^2)/(60*c^3) + (d^3*x^3*(a + b*ArcTanh[c*x])^2)/3 + (3*c*d^3*x^4*(a + b*ArcTanh[c*x])^2)/4 + (3*c^2*d^3*x^5*(a + b*ArcTanh[c*x])^2)/5 + (c^3*d^3*x^6*(a + b*ArcTanh[c*x])^2)/6 - (28*b*d^3*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(15*c^3) + (113*b^2*d^3*Log[1 - c^2*x^2])/(90*c^3) - (14*b^2*d^3*PolyLog[2, 1 - 2/(1 - c*x)])/(15*c^3)","A",52,15,22,0.6818,1,"{5940, 5916, 5980, 321, 206, 5984, 5918, 2402, 2315, 266, 43, 5910, 260, 5948, 302}"
86,1,286,0,0.597233,"\int x (d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x*(d + c*d*x)^3*(a + b*ArcTanh[c*x])^2,x]","-\frac{6 b^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{5 c^2}+\frac{1}{10} b c^2 d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{d^3 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)^2}{5 c^2}-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^2}-\frac{12 b d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{5 c^2}+\frac{1}{2} b c d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{6}{5} b d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{5 a b d^3 x}{2 c}+\frac{3 b^2 d^3 \log \left(1-c^2 x^2\right)}{2 c^2}-\frac{13 b^2 d^3 \tanh ^{-1}(c x)}{10 c^2}+\frac{1}{30} b^2 c d^3 x^3+\frac{13 b^2 d^3 x}{10 c}+\frac{5 b^2 d^3 x \tanh ^{-1}(c x)}{2 c}+\frac{1}{4} b^2 d^3 x^2","-\frac{6 b^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{5 c^2}+\frac{1}{10} b c^2 d^3 x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{d^3 (c x+1)^5 \left(a+b \tanh ^{-1}(c x)\right)^2}{5 c^2}-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^2}-\frac{12 b d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{5 c^2}+\frac{1}{2} b c d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{6}{5} b d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{5 a b d^3 x}{2 c}+\frac{3 b^2 d^3 \log \left(1-c^2 x^2\right)}{2 c^2}-\frac{13 b^2 d^3 \tanh ^{-1}(c x)}{10 c^2}+\frac{1}{30} b^2 c d^3 x^3+\frac{13 b^2 d^3 x}{10 c}+\frac{5 b^2 d^3 x \tanh ^{-1}(c x)}{2 c}+\frac{1}{4} b^2 d^3 x^2",1,"(5*a*b*d^3*x)/(2*c) + (13*b^2*d^3*x)/(10*c) + (b^2*d^3*x^2)/4 + (b^2*c*d^3*x^3)/30 - (13*b^2*d^3*ArcTanh[c*x])/(10*c^2) + (5*b^2*d^3*x*ArcTanh[c*x])/(2*c) + (6*b*d^3*x^2*(a + b*ArcTanh[c*x]))/5 + (b*c*d^3*x^3*(a + b*ArcTanh[c*x]))/2 + (b*c^2*d^3*x^4*(a + b*ArcTanh[c*x]))/10 - (d^3*(1 + c*x)^4*(a + b*ArcTanh[c*x])^2)/(4*c^2) + (d^3*(1 + c*x)^5*(a + b*ArcTanh[c*x])^2)/(5*c^2) - (12*b*d^3*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(5*c^2) + (3*b^2*d^3*Log[1 - c^2*x^2])/(2*c^2) - (6*b^2*d^3*PolyLog[2, 1 - 2/(1 - c*x)])/(5*c^2)","A",38,14,20,0.7000,1,"{5940, 5928, 5910, 260, 5916, 321, 206, 266, 43, 1586, 5918, 2402, 2315, 302}"
87,1,206,0,0.214082,"\int (d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[(d + c*d*x)^3*(a + b*ArcTanh[c*x])^2,x]","-\frac{2 b^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c}+\frac{1}{6} b c^2 d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)+b c d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c}-\frac{4 b d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+\frac{7}{2} a b d^3 x+\frac{11 b^2 d^3 \log \left(1-c^2 x^2\right)}{6 c}+\frac{1}{12} b^2 c d^3 x^2-\frac{b^2 d^3 \tanh ^{-1}(c x)}{c}+\frac{7}{2} b^2 d^3 x \tanh ^{-1}(c x)+b^2 d^3 x","-\frac{2 b^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c}+\frac{1}{6} b c^2 d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)+b c d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c}-\frac{4 b d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+\frac{7}{2} a b d^3 x+\frac{11 b^2 d^3 \log \left(1-c^2 x^2\right)}{6 c}+\frac{1}{12} b^2 c d^3 x^2-\frac{b^2 d^3 \tanh ^{-1}(c x)}{c}+\frac{7}{2} b^2 d^3 x \tanh ^{-1}(c x)+b^2 d^3 x",1,"(7*a*b*d^3*x)/2 + b^2*d^3*x + (b^2*c*d^3*x^2)/12 - (b^2*d^3*ArcTanh[c*x])/c + (7*b^2*d^3*x*ArcTanh[c*x])/2 + b*c*d^3*x^2*(a + b*ArcTanh[c*x]) + (b*c^2*d^3*x^3*(a + b*ArcTanh[c*x]))/6 + (d^3*(1 + c*x)^4*(a + b*ArcTanh[c*x])^2)/(4*c) - (4*b*d^3*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c + (11*b^2*d^3*Log[1 - c^2*x^2])/(6*c) - (2*b^2*d^3*PolyLog[2, 1 - 2/(1 - c*x)])/c","A",16,12,19,0.6316,1,"{5928, 5910, 260, 5916, 321, 206, 266, 43, 1586, 5918, 2402, 2315}"
88,1,355,0,0.8127872,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x])^2)/x,x]","-b d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b d^3 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{10}{3} b^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{1}{2} b^2 d^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 d^3 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{1}{3} c^3 d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{2} c^2 d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{3} b c^2 d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)+3 a b c d^3 x+3 c d^3 x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{11}{6} d^3 \left(a+b \tanh ^{-1}(c x)\right)^2+2 d^3 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{20}{3} b d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{2} b^2 d^3 \log \left(1-c^2 x^2\right)+\frac{1}{3} b^2 c d^3 x-\frac{1}{3} b^2 d^3 \tanh ^{-1}(c x)+3 b^2 c d^3 x \tanh ^{-1}(c x)","-b d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b d^3 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{10}{3} b^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{1}{2} b^2 d^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 d^3 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{1}{3} c^3 d^3 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{2} c^2 d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{3} b c^2 d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)+3 a b c d^3 x+3 c d^3 x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{11}{6} d^3 \left(a+b \tanh ^{-1}(c x)\right)^2+2 d^3 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{20}{3} b d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{2} b^2 d^3 \log \left(1-c^2 x^2\right)+\frac{1}{3} b^2 c d^3 x-\frac{1}{3} b^2 d^3 \tanh ^{-1}(c x)+3 b^2 c d^3 x \tanh ^{-1}(c x)",1,"3*a*b*c*d^3*x + (b^2*c*d^3*x)/3 - (b^2*d^3*ArcTanh[c*x])/3 + 3*b^2*c*d^3*x*ArcTanh[c*x] + (b*c^2*d^3*x^2*(a + b*ArcTanh[c*x]))/3 + (11*d^3*(a + b*ArcTanh[c*x])^2)/6 + 3*c*d^3*x*(a + b*ArcTanh[c*x])^2 + (3*c^2*d^3*x^2*(a + b*ArcTanh[c*x])^2)/2 + (c^3*d^3*x^3*(a + b*ArcTanh[c*x])^2)/3 + 2*d^3*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)] - (20*b*d^3*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/3 + (3*b^2*d^3*Log[1 - c^2*x^2])/2 - (10*b^2*d^3*PolyLog[2, 1 - 2/(1 - c*x)])/3 - b*d^3*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)] + b*d^3*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)] + (b^2*d^3*PolyLog[3, 1 - 2/(1 - c*x)])/2 - (b^2*d^3*PolyLog[3, -1 + 2/(1 - c*x)])/2","A",28,16,22,0.7273,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5914, 6052, 5948, 6058, 6610, 5916, 5980, 260, 321, 206}"
89,1,361,0,0.7761009,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x])^2)/x^2,x]","-3 b c d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+3 b c d^3 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-3 b^2 c d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-b^2 c d^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{3}{2} b^2 c d^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{3}{2} b^2 c d^3 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{1}{2} c^3 d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+a b c^2 d^3 x+3 c^2 d^3 x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{7}{2} c d^3 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x}+6 c d^3 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-6 b c d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+2 b c d^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} b^2 c d^3 \log \left(1-c^2 x^2\right)+b^2 c^2 d^3 x \tanh ^{-1}(c x)","-3 b c d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+3 b c d^3 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-3 b^2 c d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-b^2 c d^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{3}{2} b^2 c d^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{3}{2} b^2 c d^3 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{1}{2} c^3 d^3 x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+a b c^2 d^3 x+3 c^2 d^3 x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{7}{2} c d^3 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x}+6 c d^3 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-6 b c d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+2 b c d^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} b^2 c d^3 \log \left(1-c^2 x^2\right)+b^2 c^2 d^3 x \tanh ^{-1}(c x)",1,"a*b*c^2*d^3*x + b^2*c^2*d^3*x*ArcTanh[c*x] + (7*c*d^3*(a + b*ArcTanh[c*x])^2)/2 - (d^3*(a + b*ArcTanh[c*x])^2)/x + 3*c^2*d^3*x*(a + b*ArcTanh[c*x])^2 + (c^3*d^3*x^2*(a + b*ArcTanh[c*x])^2)/2 + 6*c*d^3*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)] - 6*b*c*d^3*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)] + (b^2*c*d^3*Log[1 - c^2*x^2])/2 + 2*b*c*d^3*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)] - 3*b^2*c*d^3*PolyLog[2, 1 - 2/(1 - c*x)] - 3*b*c*d^3*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)] + 3*b*c*d^3*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)] - b^2*c*d^3*PolyLog[2, -1 + 2/(1 + c*x)] + (3*b^2*c*d^3*PolyLog[3, 1 - 2/(1 - c*x)])/2 - (3*b^2*c*d^3*PolyLog[3, -1 + 2/(1 - c*x)])/2","A",23,17,22,0.7727,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5916, 5988, 5932, 2447, 5914, 6052, 5948, 6058, 6610, 5980, 260}"
90,1,385,0,0.7876503,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x])^2)/x^3,x]","-3 b c^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+3 b c^2 d^3 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-b^2 c^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-3 b^2 c^2 d^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{3}{2} b^2 c^2 d^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{3}{2} b^2 c^2 d^3 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{9}{2} c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)^2+c^3 d^3 x \left(a+b \tanh ^{-1}(c x)\right)^2+6 c^2 d^3 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-2 b c^2 d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+6 b c^2 d^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x}-\frac{b c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{1}{2} b^2 c^2 d^3 \log \left(1-c^2 x^2\right)+b^2 c^2 d^3 \log (x)","-3 b c^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+3 b c^2 d^3 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-b^2 c^2 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-3 b^2 c^2 d^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{3}{2} b^2 c^2 d^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{3}{2} b^2 c^2 d^3 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{9}{2} c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)^2+c^3 d^3 x \left(a+b \tanh ^{-1}(c x)\right)^2+6 c^2 d^3 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-2 b c^2 d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+6 b c^2 d^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x}-\frac{b c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{1}{2} b^2 c^2 d^3 \log \left(1-c^2 x^2\right)+b^2 c^2 d^3 \log (x)",1,"-((b*c*d^3*(a + b*ArcTanh[c*x]))/x) + (9*c^2*d^3*(a + b*ArcTanh[c*x])^2)/2 - (d^3*(a + b*ArcTanh[c*x])^2)/(2*x^2) - (3*c*d^3*(a + b*ArcTanh[c*x])^2)/x + c^3*d^3*x*(a + b*ArcTanh[c*x])^2 + 6*c^2*d^3*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)] + b^2*c^2*d^3*Log[x] - 2*b*c^2*d^3*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)] - (b^2*c^2*d^3*Log[1 - c^2*x^2])/2 + 6*b*c^2*d^3*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)] - b^2*c^2*d^3*PolyLog[2, 1 - 2/(1 - c*x)] - 3*b*c^2*d^3*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)] + 3*b*c^2*d^3*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)] - 3*b^2*c^2*d^3*PolyLog[2, -1 + 2/(1 + c*x)] + (3*b^2*c^2*d^3*PolyLog[3, 1 - 2/(1 - c*x)])/2 - (3*b^2*c^2*d^3*PolyLog[3, -1 + 2/(1 - c*x)])/2","A",25,20,22,0.9091,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5916, 5982, 266, 36, 29, 31, 5948, 5988, 5932, 2447, 5914, 6052, 6058, 6610}"
91,1,396,0,0.9269424,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x])^2)/x^4,x]","-b c^3 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b c^3 d^3 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{10}{3} b^2 c^3 d^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{1}{2} b^2 c^3 d^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 c^3 d^3 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{29}{6} c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{3 c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x}-\frac{3 b c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x}+2 c^3 d^3 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{20}{3} b c^3 d^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 x^3}-\frac{b c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^2}-\frac{3}{2} b^2 c^3 d^3 \log \left(1-c^2 x^2\right)-\frac{b^2 c^2 d^3}{3 x}+3 b^2 c^3 d^3 \log (x)+\frac{1}{3} b^2 c^3 d^3 \tanh ^{-1}(c x)","-b c^3 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b c^3 d^3 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{10}{3} b^2 c^3 d^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{1}{2} b^2 c^3 d^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 c^3 d^3 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+\frac{29}{6} c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{3 c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x}-\frac{3 b c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x}+2 c^3 d^3 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{20}{3} b c^3 d^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 x^3}-\frac{b c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 x^2}-\frac{3}{2} b^2 c^3 d^3 \log \left(1-c^2 x^2\right)-\frac{b^2 c^2 d^3}{3 x}+3 b^2 c^3 d^3 \log (x)+\frac{1}{3} b^2 c^3 d^3 \tanh ^{-1}(c x)",1,"-(b^2*c^2*d^3)/(3*x) + (b^2*c^3*d^3*ArcTanh[c*x])/3 - (b*c*d^3*(a + b*ArcTanh[c*x]))/(3*x^2) - (3*b*c^2*d^3*(a + b*ArcTanh[c*x]))/x + (29*c^3*d^3*(a + b*ArcTanh[c*x])^2)/6 - (d^3*(a + b*ArcTanh[c*x])^2)/(3*x^3) - (3*c*d^3*(a + b*ArcTanh[c*x])^2)/(2*x^2) - (3*c^2*d^3*(a + b*ArcTanh[c*x])^2)/x + 2*c^3*d^3*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)] + 3*b^2*c^3*d^3*Log[x] - (3*b^2*c^3*d^3*Log[1 - c^2*x^2])/2 + (20*b*c^3*d^3*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/3 - b*c^3*d^3*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)] + b*c^3*d^3*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)] - (10*b^2*c^3*d^3*PolyLog[2, -1 + 2/(1 + c*x)])/3 + (b^2*c^3*d^3*PolyLog[3, 1 - 2/(1 - c*x)])/2 - (b^2*c^3*d^3*PolyLog[3, -1 + 2/(1 - c*x)])/2","A",28,17,22,0.7727,1,"{5940, 5916, 5982, 325, 206, 5988, 5932, 2447, 266, 36, 29, 31, 5948, 5914, 6052, 6058, 6610}"
92,1,271,0,0.3078354,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x^5} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x])^2)/x^5,x]","-2 b^2 c^4 d^3 \text{PolyLog}(2,-c x)+2 b^2 c^4 d^3 \text{PolyLog}(2,c x)+2 b^2 c^4 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-\frac{b c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x^2}+4 a b c^4 d^3 \log (x)-\frac{7 b c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x}+4 b c^4 d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{b c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 x^3}-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 x^4}-\frac{b^2 c^2 d^3}{12 x^2}-\frac{11}{6} b^2 c^4 d^3 \log \left(1-c^2 x^2\right)-\frac{b^2 c^3 d^3}{x}+\frac{11}{3} b^2 c^4 d^3 \log (x)+b^2 c^4 d^3 \tanh ^{-1}(c x)","-2 b^2 c^4 d^3 \text{PolyLog}(2,-c x)+2 b^2 c^4 d^3 \text{PolyLog}(2,c x)+2 b^2 c^4 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-\frac{b c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{x^2}+4 a b c^4 d^3 \log (x)-\frac{7 b c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x}+4 b c^4 d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{b c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 x^3}-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 x^4}-\frac{b^2 c^2 d^3}{12 x^2}-\frac{11}{6} b^2 c^4 d^3 \log \left(1-c^2 x^2\right)-\frac{b^2 c^3 d^3}{x}+\frac{11}{3} b^2 c^4 d^3 \log (x)+b^2 c^4 d^3 \tanh ^{-1}(c x)",1,"-(b^2*c^2*d^3)/(12*x^2) - (b^2*c^3*d^3)/x + b^2*c^4*d^3*ArcTanh[c*x] - (b*c*d^3*(a + b*ArcTanh[c*x]))/(6*x^3) - (b*c^2*d^3*(a + b*ArcTanh[c*x]))/x^2 - (7*b*c^3*d^3*(a + b*ArcTanh[c*x]))/(2*x) - (d^3*(1 + c*x)^4*(a + b*ArcTanh[c*x])^2)/(4*x^4) + 4*a*b*c^4*d^3*Log[x] + (11*b^2*c^4*d^3*Log[x])/3 + 4*b*c^4*d^3*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)] - (11*b^2*c^4*d^3*Log[1 - c^2*x^2])/6 - 2*b^2*c^4*d^3*PolyLog[2, -(c*x)] + 2*b^2*c^4*d^3*PolyLog[2, c*x] + 2*b^2*c^4*d^3*PolyLog[2, 1 - 2/(1 - c*x)]","A",18,14,22,0.6364,1,"{37, 5938, 5916, 266, 44, 325, 206, 36, 29, 31, 5912, 5918, 2402, 2315}"
93,1,352,0,0.3681855,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x^6} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x])^2)/x^6,x]","-\frac{6}{5} b^2 c^5 d^3 \text{PolyLog}(2,-c x)+\frac{6}{5} b^2 c^5 d^3 \text{PolyLog}(2,c x)+\frac{6}{5} b^2 c^5 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-\frac{6 b c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^2}-\frac{b c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^3}+\frac{12}{5} a b c^5 d^3 \log (x)-\frac{5 b c^4 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x}+\frac{12}{5} b c^5 d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{c d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{20 x^4}-\frac{b c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{10 x^4}-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{5 x^5}-\frac{b^2 c^3 d^3}{4 x^2}-\frac{b^2 c^2 d^3}{30 x^3}-\frac{3}{2} b^2 c^5 d^3 \log \left(1-c^2 x^2\right)-\frac{13 b^2 c^4 d^3}{10 x}+3 b^2 c^5 d^3 \log (x)+\frac{13}{10} b^2 c^5 d^3 \tanh ^{-1}(c x)","-\frac{6}{5} b^2 c^5 d^3 \text{PolyLog}(2,-c x)+\frac{6}{5} b^2 c^5 d^3 \text{PolyLog}(2,c x)+\frac{6}{5} b^2 c^5 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-\frac{6 b c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{5 x^2}-\frac{b c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x^3}+\frac{12}{5} a b c^5 d^3 \log (x)-\frac{5 b c^4 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x}+\frac{12}{5} b c^5 d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{c d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{20 x^4}-\frac{b c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{10 x^4}-\frac{d^3 (c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{5 x^5}-\frac{b^2 c^3 d^3}{4 x^2}-\frac{b^2 c^2 d^3}{30 x^3}-\frac{3}{2} b^2 c^5 d^3 \log \left(1-c^2 x^2\right)-\frac{13 b^2 c^4 d^3}{10 x}+3 b^2 c^5 d^3 \log (x)+\frac{13}{10} b^2 c^5 d^3 \tanh ^{-1}(c x)",1,"-(b^2*c^2*d^3)/(30*x^3) - (b^2*c^3*d^3)/(4*x^2) - (13*b^2*c^4*d^3)/(10*x) + (13*b^2*c^5*d^3*ArcTanh[c*x])/10 - (b*c*d^3*(a + b*ArcTanh[c*x]))/(10*x^4) - (b*c^2*d^3*(a + b*ArcTanh[c*x]))/(2*x^3) - (6*b*c^3*d^3*(a + b*ArcTanh[c*x]))/(5*x^2) - (5*b*c^4*d^3*(a + b*ArcTanh[c*x]))/(2*x) - (d^3*(1 + c*x)^4*(a + b*ArcTanh[c*x])^2)/(5*x^5) + (c*d^3*(1 + c*x)^4*(a + b*ArcTanh[c*x])^2)/(20*x^4) + (12*a*b*c^5*d^3*Log[x])/5 + 3*b^2*c^5*d^3*Log[x] + (12*b*c^5*d^3*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/5 - (3*b^2*c^5*d^3*Log[1 - c^2*x^2])/2 - (6*b^2*c^5*d^3*PolyLog[2, -(c*x)])/5 + (6*b^2*c^5*d^3*PolyLog[2, c*x])/5 + (6*b^2*c^5*d^3*PolyLog[2, 1 - 2/(1 - c*x)])/5","A",22,15,22,0.6818,1,"{45, 37, 5938, 5916, 325, 206, 266, 44, 36, 29, 31, 5912, 5918, 2402, 2315}"
94,1,479,0,0.5091325,"\int \frac{(d+c d x)^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{x^7} \, dx","Int[((d + c*d*x)^3*(a + b*ArcTanh[c*x])^2)/x^7,x]","-\frac{14}{15} b^2 c^6 d^3 \text{PolyLog}(2,-c x)+\frac{14}{15} b^2 c^6 d^3 \text{PolyLog}(2,c x)+\frac{37}{40} b^2 c^6 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-\frac{1}{120} b^2 c^6 d^3 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)-\frac{14 b c^4 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{15 x^2}-\frac{c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 x^3}-\frac{11 b c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{18 x^3}-\frac{3 c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 x^4}-\frac{3 b c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{10 x^4}+\frac{28}{15} a b c^6 d^3 \log (x)-\frac{11 b c^5 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 x}+\frac{37}{20} b c^6 d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{60} b c^6 d^3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{5 x^5}-\frac{b c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{15 x^5}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{6 x^6}-\frac{61 b^2 c^4 d^3}{180 x^2}-\frac{b^2 c^3 d^3}{10 x^3}-\frac{b^2 c^2 d^3}{60 x^4}-\frac{113}{90} b^2 c^6 d^3 \log \left(1-c^2 x^2\right)-\frac{37 b^2 c^5 d^3}{30 x}+\frac{113}{45} b^2 c^6 d^3 \log (x)+\frac{37}{30} b^2 c^6 d^3 \tanh ^{-1}(c x)","-\frac{14}{15} b^2 c^6 d^3 \text{PolyLog}(2,-c x)+\frac{14}{15} b^2 c^6 d^3 \text{PolyLog}(2,c x)+\frac{37}{40} b^2 c^6 d^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)-\frac{1}{120} b^2 c^6 d^3 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)-\frac{14 b c^4 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{15 x^2}-\frac{c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 x^3}-\frac{11 b c^3 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{18 x^3}-\frac{3 c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 x^4}-\frac{3 b c^2 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{10 x^4}+\frac{28}{15} a b c^6 d^3 \log (x)-\frac{11 b c^5 d^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 x}+\frac{37}{20} b c^6 d^3 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{60} b c^6 d^3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{3 c d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{5 x^5}-\frac{b c d^3 \left(a+b \tanh ^{-1}(c x)\right)}{15 x^5}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{6 x^6}-\frac{61 b^2 c^4 d^3}{180 x^2}-\frac{b^2 c^3 d^3}{10 x^3}-\frac{b^2 c^2 d^3}{60 x^4}-\frac{113}{90} b^2 c^6 d^3 \log \left(1-c^2 x^2\right)-\frac{37 b^2 c^5 d^3}{30 x}+\frac{113}{45} b^2 c^6 d^3 \log (x)+\frac{37}{30} b^2 c^6 d^3 \tanh ^{-1}(c x)",1,"-(b^2*c^2*d^3)/(60*x^4) - (b^2*c^3*d^3)/(10*x^3) - (61*b^2*c^4*d^3)/(180*x^2) - (37*b^2*c^5*d^3)/(30*x) + (37*b^2*c^6*d^3*ArcTanh[c*x])/30 - (b*c*d^3*(a + b*ArcTanh[c*x]))/(15*x^5) - (3*b*c^2*d^3*(a + b*ArcTanh[c*x]))/(10*x^4) - (11*b*c^3*d^3*(a + b*ArcTanh[c*x]))/(18*x^3) - (14*b*c^4*d^3*(a + b*ArcTanh[c*x]))/(15*x^2) - (11*b*c^5*d^3*(a + b*ArcTanh[c*x]))/(6*x) - (d^3*(a + b*ArcTanh[c*x])^2)/(6*x^6) - (3*c*d^3*(a + b*ArcTanh[c*x])^2)/(5*x^5) - (3*c^2*d^3*(a + b*ArcTanh[c*x])^2)/(4*x^4) - (c^3*d^3*(a + b*ArcTanh[c*x])^2)/(3*x^3) + (28*a*b*c^6*d^3*Log[x])/15 + (113*b^2*c^6*d^3*Log[x])/45 + (37*b*c^6*d^3*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/20 + (b*c^6*d^3*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/60 - (113*b^2*c^6*d^3*Log[1 - c^2*x^2])/90 - (14*b^2*c^6*d^3*PolyLog[2, -(c*x)])/15 + (14*b^2*c^6*d^3*PolyLog[2, c*x])/15 + (37*b^2*c^6*d^3*PolyLog[2, 1 - 2/(1 - c*x)])/40 - (b^2*c^6*d^3*PolyLog[2, 1 - 2/(1 + c*x)])/120","A",29,14,22,0.6364,1,"{43, 5938, 5916, 266, 44, 325, 206, 36, 29, 31, 5912, 5918, 2402, 2315}"
95,1,329,0,0.8403503,"\int \frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{d+c d x} \, dx","Int[(x^3*(a + b*ArcTanh[c*x])^2)/(d + c*d*x),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d}-\frac{4 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^4 d}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^4 d}-\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2 d}+\frac{b x^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 c^2 d}-\frac{a b x}{c^3 d}+\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d}+\frac{11 \left(a+b \tanh ^{-1}(c x)\right)^2}{6 c^4 d}-\frac{8 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^4 d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d}+\frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 c d}-\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^4 d}+\frac{b^2 x}{3 c^3 d}-\frac{b^2 x \tanh ^{-1}(c x)}{c^3 d}-\frac{b^2 \tanh ^{-1}(c x)}{3 c^4 d}","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d}-\frac{4 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^4 d}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^4 d}-\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2 d}+\frac{b x^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 c^2 d}-\frac{a b x}{c^3 d}+\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d}+\frac{11 \left(a+b \tanh ^{-1}(c x)\right)^2}{6 c^4 d}-\frac{8 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^4 d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d}+\frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 c d}-\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^4 d}+\frac{b^2 x}{3 c^3 d}-\frac{b^2 x \tanh ^{-1}(c x)}{c^3 d}-\frac{b^2 \tanh ^{-1}(c x)}{3 c^4 d}",1,"-((a*b*x)/(c^3*d)) + (b^2*x)/(3*c^3*d) - (b^2*ArcTanh[c*x])/(3*c^4*d) - (b^2*x*ArcTanh[c*x])/(c^3*d) + (b*x^2*(a + b*ArcTanh[c*x]))/(3*c^2*d) + (11*(a + b*ArcTanh[c*x])^2)/(6*c^4*d) + (x*(a + b*ArcTanh[c*x])^2)/(c^3*d) - (x^2*(a + b*ArcTanh[c*x])^2)/(2*c^2*d) + (x^3*(a + b*ArcTanh[c*x])^2)/(3*c*d) - (8*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(3*c^4*d) + ((a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c^4*d) - (b^2*Log[1 - c^2*x^2])/(2*c^4*d) - (4*b^2*PolyLog[2, 1 - 2/(1 - c*x)])/(3*c^4*d) - (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c^4*d) - (b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*c^4*d)","A",26,14,22,0.6364,1,"{5930, 5916, 5980, 321, 206, 5984, 5918, 2402, 2315, 5910, 260, 5948, 6056, 6610}"
96,1,247,0,0.5331583,"\int \frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{d+c d x} \, dx","Int[(x^2*(a + b*ArcTanh[c*x])^2)/(d + c*d*x),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^3 d}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^3 d}+\frac{a b x}{c^2 d}-\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d}-\frac{3 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3 d}+\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c d}+\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^3 d}+\frac{b^2 x \tanh ^{-1}(c x)}{c^2 d}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^3 d}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^3 d}+\frac{a b x}{c^2 d}-\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d}-\frac{3 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3 d}+\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c d}+\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^3 d}+\frac{b^2 x \tanh ^{-1}(c x)}{c^2 d}",1,"(a*b*x)/(c^2*d) + (b^2*x*ArcTanh[c*x])/(c^2*d) - (3*(a + b*ArcTanh[c*x])^2)/(2*c^3*d) - (x*(a + b*ArcTanh[c*x])^2)/(c^2*d) + (x^2*(a + b*ArcTanh[c*x])^2)/(2*c*d) + (2*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(c^3*d) - ((a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c^3*d) + (b^2*Log[1 - c^2*x^2])/(2*c^3*d) + (b^2*PolyLog[2, 1 - 2/(1 - c*x)])/(c^3*d) + (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c^3*d) + (b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*c^3*d)","A",16,12,22,0.5455,1,"{5930, 5916, 5980, 5910, 260, 5948, 5984, 5918, 2402, 2315, 6056, 6610}"
97,1,172,0,0.3062901,"\int \frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{d+c d x} \, dx","Int[(x*(a + b*ArcTanh[c*x])^2)/(d + c*d*x),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^2 d}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^2 d}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d}+\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{c d}","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^2 d}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^2 d}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d}+\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{c d}",1,"(a + b*ArcTanh[c*x])^2/(c^2*d) + (x*(a + b*ArcTanh[c*x])^2)/(c*d) - (2*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(c^2*d) + ((a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c^2*d) - (b^2*PolyLog[2, 1 - 2/(1 - c*x)])/(c^2*d) - (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c^2*d) - (b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*c^2*d)","A",9,9,20,0.4500,1,"{5930, 5910, 5984, 5918, 2402, 2315, 5948, 6056, 6610}"
98,1,84,0,0.1456997,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d+c d x} \, dx","Int[(a + b*ArcTanh[c*x])^2/(d + c*d*x),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c d}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c d}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c d}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c d}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c d}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c d}",1,"-(((a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c*d)) + (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c*d) + (b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*c*d)","A",3,4,19,0.2105,1,"{5918, 5948, 6056, 6610}"
99,1,77,0,0.1657333,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x (d+c d x)} \, dx","Int[(a + b*ArcTanh[c*x])^2/(x*(d + c*d*x)),x]","-\frac{b \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)}{2 d}+\frac{\log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}","-\frac{b \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)}{2 d}+\frac{\log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}",1,"((a + b*ArcTanh[c*x])^2*Log[2 - 2/(1 + c*x)])/d - (b*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 + c*x)])/d - (b^2*PolyLog[3, -1 + 2/(1 + c*x)])/(2*d)","A",3,4,22,0.1818,1,"{5932, 5948, 6056, 6610}"
100,1,162,0,0.4120513,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x^2 (d+c d x)} \, dx","Int[(a + b*ArcTanh[c*x])^2/(x^2*(d + c*d*x)),x]","\frac{b c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{b^2 c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d}+\frac{b^2 c \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)}{2 d}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{d}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d x}+\frac{2 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}","\frac{b c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{b^2 c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d}+\frac{b^2 c \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)}{2 d}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{d}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d x}+\frac{2 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}",1,"(c*(a + b*ArcTanh[c*x])^2)/d - (a + b*ArcTanh[c*x])^2/(d*x) + (2*b*c*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/d - (c*(a + b*ArcTanh[c*x])^2*Log[2 - 2/(1 + c*x)])/d - (b^2*c*PolyLog[2, -1 + 2/(1 + c*x)])/d + (b*c*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 + c*x)])/d + (b^2*c*PolyLog[3, -1 + 2/(1 + c*x)])/(2*d)","A",8,8,22,0.3636,1,"{5934, 5916, 5988, 5932, 2447, 5948, 6056, 6610}"
101,1,250,0,0.6343454,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x^3 (d+c d x)} \, dx","Int[(a + b*ArcTanh[c*x])^2/(x^3*(d + c*d*x)),x]","-\frac{b c^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{b^2 c^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d}-\frac{b^2 c^2 \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)}{2 d}-\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 d}+\frac{c^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}-\frac{2 b c^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 d x^2}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{d x}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{d x}-\frac{b^2 c^2 \log \left(1-c^2 x^2\right)}{2 d}+\frac{b^2 c^2 \log (x)}{d}","-\frac{b c^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{b^2 c^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d}-\frac{b^2 c^2 \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)}{2 d}-\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 d}+\frac{c^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}-\frac{2 b c^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 d x^2}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{d x}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{d x}-\frac{b^2 c^2 \log \left(1-c^2 x^2\right)}{2 d}+\frac{b^2 c^2 \log (x)}{d}",1,"-((b*c*(a + b*ArcTanh[c*x]))/(d*x)) - (c^2*(a + b*ArcTanh[c*x])^2)/(2*d) - (a + b*ArcTanh[c*x])^2/(2*d*x^2) + (c*(a + b*ArcTanh[c*x])^2)/(d*x) + (b^2*c^2*Log[x])/d - (b^2*c^2*Log[1 - c^2*x^2])/(2*d) - (2*b*c^2*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/d + (c^2*(a + b*ArcTanh[c*x])^2*Log[2 - 2/(1 + c*x)])/d + (b^2*c^2*PolyLog[2, -1 + 2/(1 + c*x)])/d - (b*c^2*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 + c*x)])/d - (b^2*c^2*PolyLog[3, -1 + 2/(1 + c*x)])/(2*d)","A",17,13,22,0.5909,1,"{5934, 5916, 5982, 266, 36, 29, 31, 5948, 5988, 5932, 2447, 6056, 6610}"
102,1,334,0,0.9756303,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x^4 (d+c d x)} \, dx","Int[(a + b*ArcTanh[c*x])^2/(x^4*(d + c*d*x)),x]","\frac{b c^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{4 b^2 c^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{3 d}+\frac{b^2 c^3 \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)}{2 d}+\frac{5 c^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{6 d}-\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{d x}+\frac{b c^2 \left(a+b \tanh ^{-1}(c x)\right)}{d x}-\frac{c^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}+\frac{8 b c^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 d}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{2 d x^2}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{3 d x^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{3 d x^3}+\frac{b^2 c^3 \log \left(1-c^2 x^2\right)}{2 d}-\frac{b^2 c^2}{3 d x}-\frac{b^2 c^3 \log (x)}{d}+\frac{b^2 c^3 \tanh ^{-1}(c x)}{3 d}","\frac{b c^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{4 b^2 c^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{3 d}+\frac{b^2 c^3 \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)}{2 d}+\frac{5 c^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{6 d}-\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{d x}+\frac{b c^2 \left(a+b \tanh ^{-1}(c x)\right)}{d x}-\frac{c^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}+\frac{8 b c^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 d}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{2 d x^2}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{3 d x^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{3 d x^3}+\frac{b^2 c^3 \log \left(1-c^2 x^2\right)}{2 d}-\frac{b^2 c^2}{3 d x}-\frac{b^2 c^3 \log (x)}{d}+\frac{b^2 c^3 \tanh ^{-1}(c x)}{3 d}",1,"-(b^2*c^2)/(3*d*x) + (b^2*c^3*ArcTanh[c*x])/(3*d) - (b*c*(a + b*ArcTanh[c*x]))/(3*d*x^2) + (b*c^2*(a + b*ArcTanh[c*x]))/(d*x) + (5*c^3*(a + b*ArcTanh[c*x])^2)/(6*d) - (a + b*ArcTanh[c*x])^2/(3*d*x^3) + (c*(a + b*ArcTanh[c*x])^2)/(2*d*x^2) - (c^2*(a + b*ArcTanh[c*x])^2)/(d*x) - (b^2*c^3*Log[x])/d + (b^2*c^3*Log[1 - c^2*x^2])/(2*d) + (8*b*c^3*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/(3*d) - (c^3*(a + b*ArcTanh[c*x])^2*Log[2 - 2/(1 + c*x)])/d - (4*b^2*c^3*PolyLog[2, -1 + 2/(1 + c*x)])/(3*d) + (b*c^3*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 + c*x)])/d + (b^2*c^3*PolyLog[3, -1 + 2/(1 + c*x)])/(2*d)","A",26,15,22,0.6818,1,"{5934, 5916, 5982, 325, 206, 5988, 5932, 2447, 266, 36, 29, 31, 5948, 6056, 6610}"
103,1,394,0,0.8414048,"\int \frac{x^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{(d+c d x)^2} \, dx","Int[(x^4*(a + b*ArcTanh[c*x])^2)/(d + c*d*x)^2,x]","-\frac{4 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^2}-\frac{10 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^5 d^2}-\frac{2 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{c^5 d^2}+\frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 c^2 d^2}-\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^2}+\frac{b x^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 c^3 d^2}-\frac{2 a b x}{c^4 d^2}+\frac{3 x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c^5 d^2 (c x+1)}+\frac{29 \left(a+b \tanh ^{-1}(c x)\right)^2}{6 c^5 d^2}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^2 (c x+1)}-\frac{20 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^5 d^2}+\frac{4 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^5 d^2}-\frac{b^2 \log \left(1-c^2 x^2\right)}{c^5 d^2}+\frac{b^2 x}{3 c^4 d^2}-\frac{b^2}{2 c^5 d^2 (c x+1)}-\frac{2 b^2 x \tanh ^{-1}(c x)}{c^4 d^2}+\frac{b^2 \tanh ^{-1}(c x)}{6 c^5 d^2}","-\frac{4 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^2}-\frac{10 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^5 d^2}-\frac{2 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{c^5 d^2}+\frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{3 c^2 d^2}-\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^2}+\frac{b x^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 c^3 d^2}-\frac{2 a b x}{c^4 d^2}+\frac{3 x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c^5 d^2 (c x+1)}+\frac{29 \left(a+b \tanh ^{-1}(c x)\right)^2}{6 c^5 d^2}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^2 (c x+1)}-\frac{20 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^5 d^2}+\frac{4 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^5 d^2}-\frac{b^2 \log \left(1-c^2 x^2\right)}{c^5 d^2}+\frac{b^2 x}{3 c^4 d^2}-\frac{b^2}{2 c^5 d^2 (c x+1)}-\frac{2 b^2 x \tanh ^{-1}(c x)}{c^4 d^2}+\frac{b^2 \tanh ^{-1}(c x)}{6 c^5 d^2}",1,"(-2*a*b*x)/(c^4*d^2) + (b^2*x)/(3*c^4*d^2) - b^2/(2*c^5*d^2*(1 + c*x)) + (b^2*ArcTanh[c*x])/(6*c^5*d^2) - (2*b^2*x*ArcTanh[c*x])/(c^4*d^2) + (b*x^2*(a + b*ArcTanh[c*x]))/(3*c^3*d^2) - (b*(a + b*ArcTanh[c*x]))/(c^5*d^2*(1 + c*x)) + (29*(a + b*ArcTanh[c*x])^2)/(6*c^5*d^2) + (3*x*(a + b*ArcTanh[c*x])^2)/(c^4*d^2) - (x^2*(a + b*ArcTanh[c*x])^2)/(c^3*d^2) + (x^3*(a + b*ArcTanh[c*x])^2)/(3*c^2*d^2) - (a + b*ArcTanh[c*x])^2/(c^5*d^2*(1 + c*x)) - (20*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(3*c^5*d^2) + (4*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c^5*d^2) - (b^2*Log[1 - c^2*x^2])/(c^5*d^2) - (10*b^2*PolyLog[2, 1 - 2/(1 - c*x)])/(3*c^5*d^2) - (4*b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c^5*d^2) - (2*b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(c^5*d^2)","A",33,19,22,0.8636,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5916, 5980, 260, 5948, 321, 206, 5928, 5926, 627, 44, 207, 6056, 6610}"
104,1,331,0,0.62533,"\int \frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{(d+c d x)^2} \, dx","Int[(x^3*(a + b*ArcTanh[c*x])^2)/(d + c*d*x)^2,x]","\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^2}+\frac{2 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^4 d^2}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^4 d^2}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2 d^2}+\frac{a b x}{c^3 d^2}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^2 (c x+1)}-\frac{2 x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^2}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^2 (c x+1)}-\frac{3 \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^2}+\frac{4 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^2}-\frac{3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^2}+\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^4 d^2}+\frac{b^2}{2 c^4 d^2 (c x+1)}+\frac{b^2 x \tanh ^{-1}(c x)}{c^3 d^2}-\frac{b^2 \tanh ^{-1}(c x)}{2 c^4 d^2}","\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^2}+\frac{2 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^4 d^2}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^4 d^2}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2 d^2}+\frac{a b x}{c^3 d^2}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^2 (c x+1)}-\frac{2 x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^2}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^2 (c x+1)}-\frac{3 \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^2}+\frac{4 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^2}-\frac{3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^2}+\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^4 d^2}+\frac{b^2}{2 c^4 d^2 (c x+1)}+\frac{b^2 x \tanh ^{-1}(c x)}{c^3 d^2}-\frac{b^2 \tanh ^{-1}(c x)}{2 c^4 d^2}",1,"(a*b*x)/(c^3*d^2) + b^2/(2*c^4*d^2*(1 + c*x)) - (b^2*ArcTanh[c*x])/(2*c^4*d^2) + (b^2*x*ArcTanh[c*x])/(c^3*d^2) + (b*(a + b*ArcTanh[c*x]))/(c^4*d^2*(1 + c*x)) - (3*(a + b*ArcTanh[c*x])^2)/(c^4*d^2) - (2*x*(a + b*ArcTanh[c*x])^2)/(c^3*d^2) + (x^2*(a + b*ArcTanh[c*x])^2)/(2*c^2*d^2) + (a + b*ArcTanh[c*x])^2/(c^4*d^2*(1 + c*x)) + (4*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(c^4*d^2) - (3*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c^4*d^2) + (b^2*Log[1 - c^2*x^2])/(2*c^4*d^2) + (2*b^2*PolyLog[2, 1 - 2/(1 - c*x)])/(c^4*d^2) + (3*b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c^4*d^2) + (3*b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*c^4*d^2)","A",24,17,22,0.7727,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5916, 5980, 260, 5948, 5928, 5926, 627, 44, 207, 6056, 6610}"
105,1,260,0,0.4758915,"\int \frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{(d+c d x)^2} \, dx","Int[(x^2*(a + b*ArcTanh[c*x])^2)/(d + c*d*x)^2,x]","-\frac{2 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^2}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^3 d^2}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{c^3 d^2}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^2 (c x+1)}+\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^2 (c x+1)}+\frac{3 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3 d^2}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^2}+\frac{2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^2}-\frac{b^2}{2 c^3 d^2 (c x+1)}+\frac{b^2 \tanh ^{-1}(c x)}{2 c^3 d^2}","-\frac{2 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^2}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^3 d^2}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{c^3 d^2}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^2 (c x+1)}+\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^2 (c x+1)}+\frac{3 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3 d^2}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^2}+\frac{2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^2}-\frac{b^2}{2 c^3 d^2 (c x+1)}+\frac{b^2 \tanh ^{-1}(c x)}{2 c^3 d^2}",1,"-b^2/(2*c^3*d^2*(1 + c*x)) + (b^2*ArcTanh[c*x])/(2*c^3*d^2) - (b*(a + b*ArcTanh[c*x]))/(c^3*d^2*(1 + c*x)) + (3*(a + b*ArcTanh[c*x])^2)/(2*c^3*d^2) + (x*(a + b*ArcTanh[c*x])^2)/(c^2*d^2) - (a + b*ArcTanh[c*x])^2/(c^3*d^2*(1 + c*x)) - (2*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(c^3*d^2) + (2*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c^3*d^2) - (b^2*PolyLog[2, 1 - 2/(1 - c*x)])/(c^3*d^2) - (2*b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c^3*d^2) - (b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(c^3*d^2)","A",18,14,22,0.6364,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5928, 5926, 627, 44, 207, 5948, 6056, 6610}"
106,1,188,0,0.3425512,"\int \frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{(d+c d x)^2} \, dx","Int[(x*(a + b*ArcTanh[c*x])^2)/(d + c*d*x)^2,x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d^2}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^2 d^2}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d^2 (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d^2 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2 d^2}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d^2}+\frac{b^2}{2 c^2 d^2 (c x+1)}-\frac{b^2 \tanh ^{-1}(c x)}{2 c^2 d^2}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d^2}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^2 d^2}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{c^2 d^2 (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d^2 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2 d^2}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2 d^2}+\frac{b^2}{2 c^2 d^2 (c x+1)}-\frac{b^2 \tanh ^{-1}(c x)}{2 c^2 d^2}",1,"b^2/(2*c^2*d^2*(1 + c*x)) - (b^2*ArcTanh[c*x])/(2*c^2*d^2) + (b*(a + b*ArcTanh[c*x]))/(c^2*d^2*(1 + c*x)) - (a + b*ArcTanh[c*x])^2/(2*c^2*d^2) + (a + b*ArcTanh[c*x])^2/(c^2*d^2*(1 + c*x)) - ((a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c^2*d^2) + (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c^2*d^2) + (b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*c^2*d^2)","A",13,10,20,0.5000,1,"{5940, 5928, 5926, 627, 44, 207, 5948, 5918, 6056, 6610}"
107,1,107,0,0.1243759,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{(d+c d x)^2} \, dx","Int[(a + b*ArcTanh[c*x])^2/(d + c*d*x)^2,x]","-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{c d^2 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c d^2 (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c d^2}-\frac{b^2}{2 c d^2 (c x+1)}+\frac{b^2 \tanh ^{-1}(c x)}{2 c d^2}","-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{c d^2 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c d^2 (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c d^2}-\frac{b^2}{2 c d^2 (c x+1)}+\frac{b^2 \tanh ^{-1}(c x)}{2 c d^2}",1,"-b^2/(2*c*d^2*(1 + c*x)) + (b^2*ArcTanh[c*x])/(2*c*d^2) - (b*(a + b*ArcTanh[c*x]))/(c*d^2*(1 + c*x)) + (a + b*ArcTanh[c*x])^2/(2*c*d^2) - (a + b*ArcTanh[c*x])^2/(c*d^2*(1 + c*x))","A",8,6,19,0.3158,1,"{5928, 5926, 627, 44, 207, 5948}"
108,1,295,0,0.6404837,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x (d+c d x)^2} \, dx","Int[(a + b*ArcTanh[c*x])^2/(x*(d + c*d*x)^2),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{b \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d^2}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d^2}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d^2}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{d^2 (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d^2 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^2}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{b^2}{2 d^2 (c x+1)}-\frac{b^2 \tanh ^{-1}(c x)}{2 d^2}","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{b \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d^2}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d^2}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d^2}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{d^2 (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d^2 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^2}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{b^2}{2 d^2 (c x+1)}-\frac{b^2 \tanh ^{-1}(c x)}{2 d^2}",1,"b^2/(2*d^2*(1 + c*x)) - (b^2*ArcTanh[c*x])/(2*d^2) + (b*(a + b*ArcTanh[c*x]))/(d^2*(1 + c*x)) - (a + b*ArcTanh[c*x])^2/(2*d^2) + (a + b*ArcTanh[c*x])^2/(d^2*(1 + c*x)) + (2*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)])/d^2 + ((a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/d^2 - (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/d^2 + (b*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)])/d^2 - (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/d^2 + (b^2*PolyLog[3, 1 - 2/(1 - c*x)])/(2*d^2) - (b^2*PolyLog[3, -1 + 2/(1 - c*x)])/(2*d^2) - (b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*d^2)","A",19,13,22,0.5909,1,"{5940, 5914, 6052, 5948, 6058, 6610, 5928, 5926, 627, 44, 207, 5918, 6056}"
109,1,371,0,0.7972919,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x^2 (d+c d x)^2} \, dx","Int[(a + b*ArcTanh[c*x])^2/(x^2*(d + c*d*x)^2),x]","\frac{2 b c \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{2 b c \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{2 b c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{b^2 c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d^2}-\frac{b^2 c \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{d^2}+\frac{b^2 c \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{d^2}+\frac{b^2 c \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{d^2}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{d^2 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d^2 x}-\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2 (c x+1)}+\frac{3 c \left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^2}-\frac{4 c \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{2 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{2 c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}-\frac{b^2 c}{2 d^2 (c x+1)}+\frac{b^2 c \tanh ^{-1}(c x)}{2 d^2}","\frac{2 b c \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{2 b c \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{2 b c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{b^2 c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d^2}-\frac{b^2 c \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{d^2}+\frac{b^2 c \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{d^2}+\frac{b^2 c \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{d^2}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{d^2 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d^2 x}-\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2 (c x+1)}+\frac{3 c \left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^2}-\frac{4 c \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{2 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{2 c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}-\frac{b^2 c}{2 d^2 (c x+1)}+\frac{b^2 c \tanh ^{-1}(c x)}{2 d^2}",1,"-(b^2*c)/(2*d^2*(1 + c*x)) + (b^2*c*ArcTanh[c*x])/(2*d^2) - (b*c*(a + b*ArcTanh[c*x]))/(d^2*(1 + c*x)) + (3*c*(a + b*ArcTanh[c*x])^2)/(2*d^2) - (a + b*ArcTanh[c*x])^2/(d^2*x) - (c*(a + b*ArcTanh[c*x])^2)/(d^2*(1 + c*x)) - (4*c*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)])/d^2 - (2*c*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/d^2 + (2*b*c*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/d^2 + (2*b*c*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/d^2 - (2*b*c*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)])/d^2 + (2*b*c*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/d^2 - (b^2*c*PolyLog[2, -1 + 2/(1 + c*x)])/d^2 - (b^2*c*PolyLog[3, 1 - 2/(1 - c*x)])/d^2 + (b^2*c*PolyLog[3, -1 + 2/(1 - c*x)])/d^2 + (b^2*c*PolyLog[3, 1 - 2/(1 + c*x)])/d^2","A",23,17,22,0.7727,1,"{5940, 5916, 5988, 5932, 2447, 5914, 6052, 5948, 6058, 6610, 5928, 5926, 627, 44, 207, 5918, 6056}"
110,1,480,0,0.9530686,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x^3 (d+c d x)^2} \, dx","Int[(a + b*ArcTanh[c*x])^2/(x^3*(d + c*d*x)^2),x]","-\frac{3 b c^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{3 b c^2 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{3 b c^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{2 b^2 c^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d^2}+\frac{3 b^2 c^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d^2}-\frac{3 b^2 c^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d^2}-\frac{3 b^2 c^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d^2}+\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2 (c x+1)}-\frac{2 c^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{b c^2 \left(a+b \tanh ^{-1}(c x)\right)}{d^2 (c x+1)}+\frac{6 c^2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{3 c^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}-\frac{4 b c^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^2 x^2}+\frac{2 c \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2 x}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{d^2 x}-\frac{b^2 c^2 \log \left(1-c^2 x^2\right)}{2 d^2}+\frac{b^2 c^2}{2 d^2 (c x+1)}+\frac{b^2 c^2 \log (x)}{d^2}-\frac{b^2 c^2 \tanh ^{-1}(c x)}{2 d^2}","-\frac{3 b c^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{3 b c^2 \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{3 b c^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{2 b^2 c^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d^2}+\frac{3 b^2 c^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d^2}-\frac{3 b^2 c^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d^2}-\frac{3 b^2 c^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d^2}+\frac{c^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2 (c x+1)}-\frac{2 c^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{b c^2 \left(a+b \tanh ^{-1}(c x)\right)}{d^2 (c x+1)}+\frac{6 c^2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{3 c^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}-\frac{4 b c^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^2 x^2}+\frac{2 c \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2 x}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{d^2 x}-\frac{b^2 c^2 \log \left(1-c^2 x^2\right)}{2 d^2}+\frac{b^2 c^2}{2 d^2 (c x+1)}+\frac{b^2 c^2 \log (x)}{d^2}-\frac{b^2 c^2 \tanh ^{-1}(c x)}{2 d^2}",1,"(b^2*c^2)/(2*d^2*(1 + c*x)) - (b^2*c^2*ArcTanh[c*x])/(2*d^2) - (b*c*(a + b*ArcTanh[c*x]))/(d^2*x) + (b*c^2*(a + b*ArcTanh[c*x]))/(d^2*(1 + c*x)) - (2*c^2*(a + b*ArcTanh[c*x])^2)/d^2 - (a + b*ArcTanh[c*x])^2/(2*d^2*x^2) + (2*c*(a + b*ArcTanh[c*x])^2)/(d^2*x) + (c^2*(a + b*ArcTanh[c*x])^2)/(d^2*(1 + c*x)) + (6*c^2*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)])/d^2 + (b^2*c^2*Log[x])/d^2 + (3*c^2*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/d^2 - (b^2*c^2*Log[1 - c^2*x^2])/(2*d^2) - (4*b*c^2*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/d^2 - (3*b*c^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/d^2 + (3*b*c^2*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)])/d^2 - (3*b*c^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/d^2 + (2*b^2*c^2*PolyLog[2, -1 + 2/(1 + c*x)])/d^2 + (3*b^2*c^2*PolyLog[3, 1 - 2/(1 - c*x)])/(2*d^2) - (3*b^2*c^2*PolyLog[3, -1 + 2/(1 - c*x)])/(2*d^2) - (3*b^2*c^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*d^2)","A",31,22,22,1.000,1,"{5940, 5916, 5982, 266, 36, 29, 31, 5948, 5988, 5932, 2447, 5914, 6052, 6058, 6610, 5928, 5926, 627, 44, 207, 5918, 6056}"
111,1,408,0,0.8108645,"\int \frac{x^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{(d+c d x)^3} \, dx","Int[(x^4*(a + b*ArcTanh[c*x])^2)/(d + c*d*x)^3,x]","\frac{6 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^3}+\frac{3 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^5 d^3}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{c^5 d^3}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3 d^3}+\frac{a b x}{c^4 d^3}+\frac{15 b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^5 d^3 (c x+1)}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^5 d^3 (c x+1)^2}-\frac{3 x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^3}+\frac{4 \left(a+b \tanh ^{-1}(c x)\right)^2}{c^5 d^3 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^5 d^3 (c x+1)^2}-\frac{43 \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c^5 d^3}+\frac{6 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^3}-\frac{6 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^5 d^3}+\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^5 d^3}+\frac{29 b^2}{16 c^5 d^3 (c x+1)}-\frac{b^2}{16 c^5 d^3 (c x+1)^2}+\frac{b^2 x \tanh ^{-1}(c x)}{c^4 d^3}-\frac{29 b^2 \tanh ^{-1}(c x)}{16 c^5 d^3}","\frac{6 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^3}+\frac{3 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^5 d^3}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{c^5 d^3}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3 d^3}+\frac{a b x}{c^4 d^3}+\frac{15 b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^5 d^3 (c x+1)}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^5 d^3 (c x+1)^2}-\frac{3 x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^3}+\frac{4 \left(a+b \tanh ^{-1}(c x)\right)^2}{c^5 d^3 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^5 d^3 (c x+1)^2}-\frac{43 \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c^5 d^3}+\frac{6 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^5 d^3}-\frac{6 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^5 d^3}+\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^5 d^3}+\frac{29 b^2}{16 c^5 d^3 (c x+1)}-\frac{b^2}{16 c^5 d^3 (c x+1)^2}+\frac{b^2 x \tanh ^{-1}(c x)}{c^4 d^3}-\frac{29 b^2 \tanh ^{-1}(c x)}{16 c^5 d^3}",1,"(a*b*x)/(c^4*d^3) - b^2/(16*c^5*d^3*(1 + c*x)^2) + (29*b^2)/(16*c^5*d^3*(1 + c*x)) - (29*b^2*ArcTanh[c*x])/(16*c^5*d^3) + (b^2*x*ArcTanh[c*x])/(c^4*d^3) - (b*(a + b*ArcTanh[c*x]))/(4*c^5*d^3*(1 + c*x)^2) + (15*b*(a + b*ArcTanh[c*x]))/(4*c^5*d^3*(1 + c*x)) - (43*(a + b*ArcTanh[c*x])^2)/(8*c^5*d^3) - (3*x*(a + b*ArcTanh[c*x])^2)/(c^4*d^3) + (x^2*(a + b*ArcTanh[c*x])^2)/(2*c^3*d^3) - (a + b*ArcTanh[c*x])^2/(2*c^5*d^3*(1 + c*x)^2) + (4*(a + b*ArcTanh[c*x])^2)/(c^5*d^3*(1 + c*x)) + (6*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(c^5*d^3) - (6*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c^5*d^3) + (b^2*Log[1 - c^2*x^2])/(2*c^5*d^3) + (3*b^2*PolyLog[2, 1 - 2/(1 - c*x)])/(c^5*d^3) + (6*b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c^5*d^3) + (3*b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(c^5*d^3)","A",37,17,22,0.7727,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5916, 5980, 260, 5948, 5928, 5926, 627, 44, 207, 6056, 6610}"
112,1,337,0,0.6615554,"\int \frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{(d+c d x)^3} \, dx","Int[(x^3*(a + b*ArcTanh[c*x])^2)/(d + c*d*x)^3,x]","-\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^3}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^4 d^3}-\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^4 d^3}-\frac{11 b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^4 d^3 (c x+1)}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^4 d^3 (c x+1)^2}+\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^3}-\frac{3 \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^3 (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^4 d^3 (c x+1)^2}+\frac{19 \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c^4 d^3}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^3}+\frac{3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^3}-\frac{21 b^2}{16 c^4 d^3 (c x+1)}+\frac{b^2}{16 c^4 d^3 (c x+1)^2}+\frac{21 b^2 \tanh ^{-1}(c x)}{16 c^4 d^3}","-\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^3}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^4 d^3}-\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^4 d^3}-\frac{11 b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^4 d^3 (c x+1)}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^4 d^3 (c x+1)^2}+\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^3}-\frac{3 \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^3 (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^4 d^3 (c x+1)^2}+\frac{19 \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c^4 d^3}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4 d^3}+\frac{3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4 d^3}-\frac{21 b^2}{16 c^4 d^3 (c x+1)}+\frac{b^2}{16 c^4 d^3 (c x+1)^2}+\frac{21 b^2 \tanh ^{-1}(c x)}{16 c^4 d^3}",1,"b^2/(16*c^4*d^3*(1 + c*x)^2) - (21*b^2)/(16*c^4*d^3*(1 + c*x)) + (21*b^2*ArcTanh[c*x])/(16*c^4*d^3) + (b*(a + b*ArcTanh[c*x]))/(4*c^4*d^3*(1 + c*x)^2) - (11*b*(a + b*ArcTanh[c*x]))/(4*c^4*d^3*(1 + c*x)) + (19*(a + b*ArcTanh[c*x])^2)/(8*c^4*d^3) + (x*(a + b*ArcTanh[c*x])^2)/(c^3*d^3) + (a + b*ArcTanh[c*x])^2/(2*c^4*d^3*(1 + c*x)^2) - (3*(a + b*ArcTanh[c*x])^2)/(c^4*d^3*(1 + c*x)) - (2*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(c^4*d^3) + (3*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c^4*d^3) - (b^2*PolyLog[2, 1 - 2/(1 - c*x)])/(c^4*d^3) - (3*b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c^4*d^3) - (3*b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*c^4*d^3)","A",31,14,22,0.6364,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5928, 5926, 627, 44, 207, 5948, 6056, 6610}"
113,1,265,0,0.5435682,"\int \frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{(d+c d x)^3} \, dx","Int[(x^2*(a + b*ArcTanh[c*x])^2)/(d + c*d*x)^3,x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^3}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^3 d^3}+\frac{7 b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^3 d^3 (c x+1)}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^3 d^3 (c x+1)^2}+\frac{2 \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^3 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3 d^3 (c x+1)^2}-\frac{7 \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c^3 d^3}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^3}+\frac{13 b^2}{16 c^3 d^3 (c x+1)}-\frac{b^2}{16 c^3 d^3 (c x+1)^2}-\frac{13 b^2 \tanh ^{-1}(c x)}{16 c^3 d^3}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3 d^3}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 c^3 d^3}+\frac{7 b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^3 d^3 (c x+1)}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^3 d^3 (c x+1)^2}+\frac{2 \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^3 (c x+1)}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3 d^3 (c x+1)^2}-\frac{7 \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c^3 d^3}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3 d^3}+\frac{13 b^2}{16 c^3 d^3 (c x+1)}-\frac{b^2}{16 c^3 d^3 (c x+1)^2}-\frac{13 b^2 \tanh ^{-1}(c x)}{16 c^3 d^3}",1,"-b^2/(16*c^3*d^3*(1 + c*x)^2) + (13*b^2)/(16*c^3*d^3*(1 + c*x)) - (13*b^2*ArcTanh[c*x])/(16*c^3*d^3) - (b*(a + b*ArcTanh[c*x]))/(4*c^3*d^3*(1 + c*x)^2) + (7*b*(a + b*ArcTanh[c*x]))/(4*c^3*d^3*(1 + c*x)) - (7*(a + b*ArcTanh[c*x])^2)/(8*c^3*d^3) - (a + b*ArcTanh[c*x])^2/(2*c^3*d^3*(1 + c*x)^2) + (2*(a + b*ArcTanh[c*x])^2)/(c^3*d^3*(1 + c*x)) - ((a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/(c^3*d^3) + (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/(c^3*d^3) + (b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*c^3*d^3)","A",26,10,22,0.4545,1,"{5940, 5928, 5926, 627, 44, 207, 5948, 5918, 6056, 6610}"
114,1,157,0,0.2137703,"\int \frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{(d+c d x)^3} \, dx","Int[(x*(a + b*ArcTanh[c*x])^2)/(d + c*d*x)^3,x]","-\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2 d^3 (c x+1)}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2 d^3 (c x+1)^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{8 c^2 d^3}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^3 (c x+1)^2}-\frac{5 b^2}{16 c^2 d^3 (c x+1)}+\frac{b^2}{16 c^2 d^3 (c x+1)^2}+\frac{5 b^2 \tanh ^{-1}(c x)}{16 c^2 d^3}","-\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2 d^3 (c x+1)}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2 d^3 (c x+1)^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{8 c^2 d^3}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^3 (c x+1)^2}-\frac{5 b^2}{16 c^2 d^3 (c x+1)}+\frac{b^2}{16 c^2 d^3 (c x+1)^2}+\frac{5 b^2 \tanh ^{-1}(c x)}{16 c^2 d^3}",1,"b^2/(16*c^2*d^3*(1 + c*x)^2) - (5*b^2)/(16*c^2*d^3*(1 + c*x)) + (5*b^2*ArcTanh[c*x])/(16*c^2*d^3) + (b*(a + b*ArcTanh[c*x]))/(4*c^2*d^3*(1 + c*x)^2) - (3*b*(a + b*ArcTanh[c*x]))/(4*c^2*d^3*(1 + c*x)) - (a + b*ArcTanh[c*x])^2/(8*c^2*d^3) + (x^2*(a + b*ArcTanh[c*x])^2)/(2*d^3*(1 + c*x)^2)","A",13,7,20,0.3500,1,"{37, 5938, 5926, 627, 44, 207, 5948}"
115,1,157,0,0.1777486,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{(d+c d x)^3} \, dx","Int[(a + b*ArcTanh[c*x])^2/(d + c*d*x)^3,x]","-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c d^3 (c x+1)}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c d^3 (c x+1)^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c d^3 (c x+1)^2}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{8 c d^3}-\frac{3 b^2}{16 c d^3 (c x+1)}-\frac{b^2}{16 c d^3 (c x+1)^2}+\frac{3 b^2 \tanh ^{-1}(c x)}{16 c d^3}","-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c d^3 (c x+1)}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 c d^3 (c x+1)^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c d^3 (c x+1)^2}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{8 c d^3}-\frac{3 b^2}{16 c d^3 (c x+1)}-\frac{b^2}{16 c d^3 (c x+1)^2}+\frac{3 b^2 \tanh ^{-1}(c x)}{16 c d^3}",1,"-b^2/(16*c*d^3*(1 + c*x)^2) - (3*b^2)/(16*c*d^3*(1 + c*x)) + (3*b^2*ArcTanh[c*x])/(16*c*d^3) - (b*(a + b*ArcTanh[c*x]))/(4*c*d^3*(1 + c*x)^2) - (b*(a + b*ArcTanh[c*x]))/(4*c*d^3*(1 + c*x)) + (a + b*ArcTanh[c*x])^2/(8*c*d^3) - (a + b*ArcTanh[c*x])^2/(2*c*d^3*(1 + c*x)^2)","A",13,6,19,0.3158,1,"{5928, 5926, 627, 44, 207, 5948}"
116,1,362,0,0.8040011,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x (d+c d x)^3} \, dx","Int[(a + b*ArcTanh[c*x])^2/(x*(d + c*d*x)^3),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}+\frac{b \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d^3}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d^3}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d^3}+\frac{5 b \left(a+b \tanh ^{-1}(c x)\right)}{4 d^3 (c x+1)}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 d^3 (c x+1)^2}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d^3 (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^3 (c x+1)^2}-\frac{5 \left(a+b \tanh ^{-1}(c x)\right)^2}{8 d^3}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^3}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^3}+\frac{11 b^2}{16 d^3 (c x+1)}+\frac{b^2}{16 d^3 (c x+1)^2}-\frac{11 b^2 \tanh ^{-1}(c x)}{16 d^3}","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}+\frac{b \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d^3}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d^3}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d^3}+\frac{5 b \left(a+b \tanh ^{-1}(c x)\right)}{4 d^3 (c x+1)}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{4 d^3 (c x+1)^2}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d^3 (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^3 (c x+1)^2}-\frac{5 \left(a+b \tanh ^{-1}(c x)\right)^2}{8 d^3}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^3}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^3}+\frac{11 b^2}{16 d^3 (c x+1)}+\frac{b^2}{16 d^3 (c x+1)^2}-\frac{11 b^2 \tanh ^{-1}(c x)}{16 d^3}",1,"b^2/(16*d^3*(1 + c*x)^2) + (11*b^2)/(16*d^3*(1 + c*x)) - (11*b^2*ArcTanh[c*x])/(16*d^3) + (b*(a + b*ArcTanh[c*x]))/(4*d^3*(1 + c*x)^2) + (5*b*(a + b*ArcTanh[c*x]))/(4*d^3*(1 + c*x)) - (5*(a + b*ArcTanh[c*x])^2)/(8*d^3) + (a + b*ArcTanh[c*x])^2/(2*d^3*(1 + c*x)^2) + (a + b*ArcTanh[c*x])^2/(d^3*(1 + c*x)) + (2*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)])/d^3 + ((a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/d^3 - (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/d^3 + (b*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)])/d^3 - (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/d^3 + (b^2*PolyLog[3, 1 - 2/(1 - c*x)])/(2*d^3) - (b^2*PolyLog[3, -1 + 2/(1 - c*x)])/(2*d^3) - (b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*d^3)","A",32,13,22,0.5909,1,"{5940, 5914, 6052, 5948, 6058, 6610, 5928, 5926, 627, 44, 207, 5918, 6056}"
117,1,448,0,0.9827027,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x^2 (d+c d x)^3} \, dx","Int[(a + b*ArcTanh[c*x])^2/(x^2*(d + c*d*x)^3),x]","\frac{3 b c \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{3 b c \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}+\frac{3 b c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{b^2 c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d^3}-\frac{3 b^2 c \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d^3}+\frac{3 b^2 c \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d^3}+\frac{3 b^2 c \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d^3}-\frac{9 b c \left(a+b \tanh ^{-1}(c x)\right)}{4 d^3 (c x+1)}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{4 d^3 (c x+1)^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d^3 x}-\frac{2 c \left(a+b \tanh ^{-1}(c x)\right)^2}{d^3 (c x+1)}-\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^3 (c x+1)^2}+\frac{17 c \left(a+b \tanh ^{-1}(c x)\right)^2}{8 d^3}-\frac{6 c \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^3}+\frac{2 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{3 c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^3}-\frac{19 b^2 c}{16 d^3 (c x+1)}-\frac{b^2 c}{16 d^3 (c x+1)^2}+\frac{19 b^2 c \tanh ^{-1}(c x)}{16 d^3}","\frac{3 b c \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{3 b c \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}+\frac{3 b c \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{b^2 c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d^3}-\frac{3 b^2 c \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d^3}+\frac{3 b^2 c \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d^3}+\frac{3 b^2 c \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d^3}-\frac{9 b c \left(a+b \tanh ^{-1}(c x)\right)}{4 d^3 (c x+1)}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{4 d^3 (c x+1)^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d^3 x}-\frac{2 c \left(a+b \tanh ^{-1}(c x)\right)^2}{d^3 (c x+1)}-\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{2 d^3 (c x+1)^2}+\frac{17 c \left(a+b \tanh ^{-1}(c x)\right)^2}{8 d^3}-\frac{6 c \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^3}+\frac{2 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{3 c \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^3}-\frac{19 b^2 c}{16 d^3 (c x+1)}-\frac{b^2 c}{16 d^3 (c x+1)^2}+\frac{19 b^2 c \tanh ^{-1}(c x)}{16 d^3}",1,"-(b^2*c)/(16*d^3*(1 + c*x)^2) - (19*b^2*c)/(16*d^3*(1 + c*x)) + (19*b^2*c*ArcTanh[c*x])/(16*d^3) - (b*c*(a + b*ArcTanh[c*x]))/(4*d^3*(1 + c*x)^2) - (9*b*c*(a + b*ArcTanh[c*x]))/(4*d^3*(1 + c*x)) + (17*c*(a + b*ArcTanh[c*x])^2)/(8*d^3) - (a + b*ArcTanh[c*x])^2/(d^3*x) - (c*(a + b*ArcTanh[c*x])^2)/(2*d^3*(1 + c*x)^2) - (2*c*(a + b*ArcTanh[c*x])^2)/(d^3*(1 + c*x)) - (6*c*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)])/d^3 - (3*c*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/d^3 + (2*b*c*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/d^3 + (3*b*c*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/d^3 - (3*b*c*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)])/d^3 + (3*b*c*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/d^3 - (b^2*c*PolyLog[2, -1 + 2/(1 + c*x)])/d^3 - (3*b^2*c*PolyLog[3, 1 - 2/(1 - c*x)])/(2*d^3) + (3*b^2*c*PolyLog[3, -1 + 2/(1 - c*x)])/(2*d^3) + (3*b^2*c*PolyLog[3, 1 - 2/(1 + c*x)])/(2*d^3)","A",36,17,22,0.7727,1,"{5940, 5916, 5988, 5932, 2447, 5914, 6052, 5948, 6058, 6610, 5928, 5926, 627, 44, 207, 5918, 6056}"
118,1,176,0,0.2177569,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{(1+c x)^4} \, dx","Int[(a + b*ArcTanh[c*x])^2/(1 + c*x)^4,x]","-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{12 c (c x+1)}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{12 c (c x+1)^2}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{9 c (c x+1)^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{24 c}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{3 c (c x+1)^3}-\frac{11 b^2}{144 c (c x+1)}-\frac{5 b^2}{144 c (c x+1)^2}-\frac{b^2}{54 c (c x+1)^3}+\frac{11 b^2 \tanh ^{-1}(c x)}{144 c}","-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{12 c (c x+1)}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{12 c (c x+1)^2}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)}{9 c (c x+1)^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{24 c}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{3 c (c x+1)^3}-\frac{11 b^2}{144 c (c x+1)}-\frac{5 b^2}{144 c (c x+1)^2}-\frac{b^2}{54 c (c x+1)^3}+\frac{11 b^2 \tanh ^{-1}(c x)}{144 c}",1,"-b^2/(54*c*(1 + c*x)^3) - (5*b^2)/(144*c*(1 + c*x)^2) - (11*b^2)/(144*c*(1 + c*x)) + (11*b^2*ArcTanh[c*x])/(144*c) - (b*(a + b*ArcTanh[c*x]))/(9*c*(1 + c*x)^3) - (b*(a + b*ArcTanh[c*x]))/(12*c*(1 + c*x)^2) - (b*(a + b*ArcTanh[c*x]))/(12*c*(1 + c*x)) + (a + b*ArcTanh[c*x])^2/(24*c) - (a + b*ArcTanh[c*x])^2/(3*c*(1 + c*x)^3)","A",18,6,18,0.3333,1,"{5928, 5926, 627, 44, 207, 5948}"
119,1,67,0,0.1381053,"\int \frac{\tanh ^{-1}(a x)^2}{c x-a c x^2} \, dx","Int[ArcTanh[a*x]^2/(c*x - a*c*x^2),x]","-\frac{\text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)}{2 c}+\frac{\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)}{c}+\frac{\log \left(2-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{c}","-\frac{\text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)}{2 c}+\frac{\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)}{c}+\frac{\log \left(2-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{c}",1,"(ArcTanh[a*x]^2*Log[2 - 2/(1 - a*x)])/c + (ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 - a*x)])/c - PolyLog[3, -1 + 2/(1 - a*x)]/(2*c)","A",4,5,20,0.2500,1,"{1593, 5932, 5948, 6058, 6610}"
120,1,306,0,0.6582682,"\int (1+c x)^3 \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[(1 + c*x)^3*(a + b*ArcTanh[c*x])^3,x]","-\frac{6 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}-\frac{11 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{2 c}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{c}+\frac{1}{4} b^2 c x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{11 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+3 a b^2 x+\frac{1}{4} b c^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{2} b c x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{(c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^3}{4 c}+\frac{21}{4} b x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{4 b \left(a+b \tanh ^{-1}(c x)\right)^2}{c}-\frac{6 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c}+\frac{3 b^3 \log \left(1-c^2 x^2\right)}{2 c}+3 b^3 x \tanh ^{-1}(c x)-\frac{b^3 \tanh ^{-1}(c x)}{4 c}+\frac{b^3 x}{4}","-\frac{6 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}-\frac{11 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{2 c}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{c}+\frac{1}{4} b^2 c x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{11 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+3 a b^2 x+\frac{1}{4} b c^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{2} b c x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{(c x+1)^4 \left(a+b \tanh ^{-1}(c x)\right)^3}{4 c}+\frac{21}{4} b x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{4 b \left(a+b \tanh ^{-1}(c x)\right)^2}{c}-\frac{6 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c}+\frac{3 b^3 \log \left(1-c^2 x^2\right)}{2 c}+3 b^3 x \tanh ^{-1}(c x)-\frac{b^3 \tanh ^{-1}(c x)}{4 c}+\frac{b^3 x}{4}",1,"3*a*b^2*x + (b^3*x)/4 - (b^3*ArcTanh[c*x])/(4*c) + 3*b^3*x*ArcTanh[c*x] + (b^2*c*x^2*(a + b*ArcTanh[c*x]))/4 + (4*b*(a + b*ArcTanh[c*x])^2)/c + (21*b*x*(a + b*ArcTanh[c*x])^2)/4 + (3*b*c*x^2*(a + b*ArcTanh[c*x])^2)/2 + (b*c^2*x^3*(a + b*ArcTanh[c*x])^2)/4 + ((1 + c*x)^4*(a + b*ArcTanh[c*x])^3)/(4*c) - (11*b^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c - (6*b*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/c + (3*b^3*Log[1 - c^2*x^2])/(2*c) - (11*b^3*PolyLog[2, 1 - 2/(1 - c*x)])/(2*c) - (6*b^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/c + (3*b^3*PolyLog[3, 1 - 2/(1 - c*x)])/c","A",26,15,18,0.8333,1,"{5928, 5910, 5984, 5918, 2402, 2315, 5916, 5980, 260, 5948, 321, 206, 1586, 6058, 6610}"
121,1,240,0,0.4429612,"\int (1+c x)^2 \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[(1 + c*x)^2*(a + b*ArcTanh[c*x])^3,x]","-\frac{4 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}-\frac{3 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c}+\frac{2 b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{c}-\frac{6 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+a b^2 x+\frac{1}{2} b c x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+3 b x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{5 b \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{(c x+1)^3 \left(a+b \tanh ^{-1}(c x)\right)^3}{3 c}-\frac{4 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c}+\frac{b^3 \log \left(1-c^2 x^2\right)}{2 c}+b^3 x \tanh ^{-1}(c x)","-\frac{4 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}-\frac{3 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c}+\frac{2 b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{c}-\frac{6 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+a b^2 x+\frac{1}{2} b c x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+3 b x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{5 b \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{(c x+1)^3 \left(a+b \tanh ^{-1}(c x)\right)^3}{3 c}-\frac{4 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c}+\frac{b^3 \log \left(1-c^2 x^2\right)}{2 c}+b^3 x \tanh ^{-1}(c x)",1,"a*b^2*x + b^3*x*ArcTanh[c*x] + (5*b*(a + b*ArcTanh[c*x])^2)/(2*c) + 3*b*x*(a + b*ArcTanh[c*x])^2 + (b*c*x^2*(a + b*ArcTanh[c*x])^2)/2 + ((1 + c*x)^3*(a + b*ArcTanh[c*x])^3)/(3*c) - (6*b^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c - (4*b*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/c + (b^3*Log[1 - c^2*x^2])/(2*c) - (3*b^3*PolyLog[2, 1 - 2/(1 - c*x)])/c - (4*b^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/c + (2*b^3*PolyLog[3, 1 - 2/(1 - c*x)])/c","A",17,13,18,0.7222,1,"{5928, 5910, 5984, 5918, 2402, 2315, 5916, 5980, 260, 5948, 1586, 6058, 6610}"
122,1,191,0,0.3010052,"\int (1+c x) \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[(1 + c*x)*(a + b*ArcTanh[c*x])^3,x]","-\frac{3 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}-\frac{3 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{2 c}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c}-\frac{3 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+\frac{3}{2} b x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{(c x+1)^2 \left(a+b \tanh ^{-1}(c x)\right)^3}{2 c}-\frac{3 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c}","-\frac{3 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}-\frac{3 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{2 c}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c}-\frac{3 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}+\frac{3}{2} b x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{(c x+1)^2 \left(a+b \tanh ^{-1}(c x)\right)^3}{2 c}-\frac{3 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c}",1,"(3*b*(a + b*ArcTanh[c*x])^2)/(2*c) + (3*b*x*(a + b*ArcTanh[c*x])^2)/2 + ((1 + c*x)^2*(a + b*ArcTanh[c*x])^3)/(2*c) - (3*b^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c - (3*b*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/c - (3*b^3*PolyLog[2, 1 - 2/(1 - c*x)])/(2*c) - (3*b^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/c + (3*b^3*PolyLog[3, 1 - 2/(1 - c*x)])/(2*c)","A",11,10,16,0.6250,1,"{5928, 5910, 5984, 5918, 2402, 2315, 1586, 5948, 6058, 6610}"
123,1,111,0,0.2213378,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{1+c x} \, dx","Int[(a + b*ArcTanh[c*x])^3/(1 + c*x),x]","\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 c}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{c x+1}\right)}{4 c}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{c}","\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 c}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{c x+1}\right)}{4 c}-\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^3}{c}",1,"-(((a + b*ArcTanh[c*x])^3*Log[2/(1 + c*x)])/c) + (3*b*(a + b*ArcTanh[c*x])^2*PolyLog[2, 1 - 2/(1 + c*x)])/(2*c) + (3*b^2*(a + b*ArcTanh[c*x])*PolyLog[3, 1 - 2/(1 + c*x)])/(2*c) + (3*b^3*PolyLog[4, 1 - 2/(1 + c*x)])/(4*c)","A",4,5,18,0.2778,1,"{5918, 5948, 6056, 6060, 6610}"
124,1,139,0,0.1932271,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{(1+c x)^2} \, dx","Int[(a + b*ArcTanh[c*x])^3/(1 + c*x)^2,x]","-\frac{3 b^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c (c x+1)}+\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c}-\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{2 c}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{c (c x+1)}-\frac{3 b^3}{4 c (c x+1)}+\frac{3 b^3 \tanh ^{-1}(c x)}{4 c}","-\frac{3 b^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 c (c x+1)}+\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c}-\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c (c x+1)}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{2 c}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{c (c x+1)}-\frac{3 b^3}{4 c (c x+1)}+\frac{3 b^3 \tanh ^{-1}(c x)}{4 c}",1,"(-3*b^3)/(4*c*(1 + c*x)) + (3*b^3*ArcTanh[c*x])/(4*c) - (3*b^2*(a + b*ArcTanh[c*x]))/(2*c*(1 + c*x)) + (3*b*(a + b*ArcTanh[c*x])^2)/(4*c) - (3*b*(a + b*ArcTanh[c*x])^2)/(2*c*(1 + c*x)) + (a + b*ArcTanh[c*x])^3/(2*c) - (a + b*ArcTanh[c*x])^3/(c*(1 + c*x))","A",11,6,18,0.3333,1,"{5928, 5926, 627, 44, 207, 5948}"
125,1,208,0,0.3711692,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{(1+c x)^3} \, dx","Int[(a + b*ArcTanh[c*x])^3/(1 + c*x)^3,x]","-\frac{9 b^2 \left(a+b \tanh ^{-1}(c x)\right)}{16 c (c x+1)}-\frac{3 b^2 \left(a+b \tanh ^{-1}(c x)\right)}{16 c (c x+1)^2}+\frac{9 b \left(a+b \tanh ^{-1}(c x)\right)^2}{32 c}-\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c (c x+1)}-\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c (c x+1)^2}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{8 c}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{2 c (c x+1)^2}-\frac{21 b^3}{64 c (c x+1)}-\frac{3 b^3}{64 c (c x+1)^2}+\frac{21 b^3 \tanh ^{-1}(c x)}{64 c}","-\frac{9 b^2 \left(a+b \tanh ^{-1}(c x)\right)}{16 c (c x+1)}-\frac{3 b^2 \left(a+b \tanh ^{-1}(c x)\right)}{16 c (c x+1)^2}+\frac{9 b \left(a+b \tanh ^{-1}(c x)\right)^2}{32 c}-\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c (c x+1)}-\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c (c x+1)^2}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{8 c}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{2 c (c x+1)^2}-\frac{21 b^3}{64 c (c x+1)}-\frac{3 b^3}{64 c (c x+1)^2}+\frac{21 b^3 \tanh ^{-1}(c x)}{64 c}",1,"(-3*b^3)/(64*c*(1 + c*x)^2) - (21*b^3)/(64*c*(1 + c*x)) + (21*b^3*ArcTanh[c*x])/(64*c) - (3*b^2*(a + b*ArcTanh[c*x]))/(16*c*(1 + c*x)^2) - (9*b^2*(a + b*ArcTanh[c*x]))/(16*c*(1 + c*x)) + (9*b*(a + b*ArcTanh[c*x])^2)/(32*c) - (3*b*(a + b*ArcTanh[c*x])^2)/(8*c*(1 + c*x)^2) - (3*b*(a + b*ArcTanh[c*x])^2)/(8*c*(1 + c*x)) + (a + b*ArcTanh[c*x])^3/(8*c) - (a + b*ArcTanh[c*x])^3/(2*c*(1 + c*x)^2)","A",24,6,18,0.3333,1,"{5928, 5926, 627, 44, 207, 5948}"
126,1,275,0,0.6138646,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{(1+c x)^4} \, dx","Int[(a + b*ArcTanh[c*x])^3/(1 + c*x)^4,x]","-\frac{11 b^2 \left(a+b \tanh ^{-1}(c x)\right)}{48 c (c x+1)}-\frac{5 b^2 \left(a+b \tanh ^{-1}(c x)\right)}{48 c (c x+1)^2}-\frac{b^2 \left(a+b \tanh ^{-1}(c x)\right)}{18 c (c x+1)^3}+\frac{11 b \left(a+b \tanh ^{-1}(c x)\right)^2}{96 c}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c (c x+1)}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c (c x+1)^2}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)^2}{6 c (c x+1)^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{24 c}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{3 c (c x+1)^3}-\frac{85 b^3}{576 c (c x+1)}-\frac{19 b^3}{576 c (c x+1)^2}-\frac{b^3}{108 c (c x+1)^3}+\frac{85 b^3 \tanh ^{-1}(c x)}{576 c}","-\frac{11 b^2 \left(a+b \tanh ^{-1}(c x)\right)}{48 c (c x+1)}-\frac{5 b^2 \left(a+b \tanh ^{-1}(c x)\right)}{48 c (c x+1)^2}-\frac{b^2 \left(a+b \tanh ^{-1}(c x)\right)}{18 c (c x+1)^3}+\frac{11 b \left(a+b \tanh ^{-1}(c x)\right)^2}{96 c}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c (c x+1)}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)^2}{8 c (c x+1)^2}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)^2}{6 c (c x+1)^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{24 c}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{3 c (c x+1)^3}-\frac{85 b^3}{576 c (c x+1)}-\frac{19 b^3}{576 c (c x+1)^2}-\frac{b^3}{108 c (c x+1)^3}+\frac{85 b^3 \tanh ^{-1}(c x)}{576 c}",1,"-b^3/(108*c*(1 + c*x)^3) - (19*b^3)/(576*c*(1 + c*x)^2) - (85*b^3)/(576*c*(1 + c*x)) + (85*b^3*ArcTanh[c*x])/(576*c) - (b^2*(a + b*ArcTanh[c*x]))/(18*c*(1 + c*x)^3) - (5*b^2*(a + b*ArcTanh[c*x]))/(48*c*(1 + c*x)^2) - (11*b^2*(a + b*ArcTanh[c*x]))/(48*c*(1 + c*x)) + (11*b*(a + b*ArcTanh[c*x])^2)/(96*c) - (b*(a + b*ArcTanh[c*x])^2)/(6*c*(1 + c*x)^3) - (b*(a + b*ArcTanh[c*x])^2)/(8*c*(1 + c*x)^2) - (b*(a + b*ArcTanh[c*x])^2)/(8*c*(1 + c*x)) + (a + b*ArcTanh[c*x])^3/(24*c) - (a + b*ArcTanh[c*x])^3/(3*c*(1 + c*x)^3)","A",42,6,18,0.3333,1,"{5928, 5926, 627, 44, 207, 5948}"
127,1,309,0,0.6358567,"\int \frac{x^2 \tanh ^{-1}(a x)^3}{c+a c x} \, dx","Int[(x^2*ArcTanh[a*x]^3)/(c + a*c*x),x]","-\frac{3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^3 c}-\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^3 c}+\frac{3 \text{PolyLog}\left(4,1-\frac{2}{a x+1}\right)}{4 a^3 c}+\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{a x+1}\right)}{2 a^3 c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3 c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{a x+1}\right)}{2 a^3 c}-\frac{x \tanh ^{-1}(a x)^3}{a^2 c}-\frac{3 \tanh ^{-1}(a x)^3}{2 a^3 c}+\frac{3 x \tanh ^{-1}(a x)^2}{2 a^2 c}+\frac{3 \tanh ^{-1}(a x)^2}{2 a^3 c}-\frac{\log \left(\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{a^3 c}+\frac{3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^3 c}-\frac{3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^3 c}+\frac{x^2 \tanh ^{-1}(a x)^3}{2 a c}","-\frac{3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^3 c}-\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^3 c}+\frac{3 \text{PolyLog}\left(4,1-\frac{2}{a x+1}\right)}{4 a^3 c}+\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{a x+1}\right)}{2 a^3 c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3 c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{a x+1}\right)}{2 a^3 c}-\frac{x \tanh ^{-1}(a x)^3}{a^2 c}-\frac{3 \tanh ^{-1}(a x)^3}{2 a^3 c}+\frac{3 x \tanh ^{-1}(a x)^2}{2 a^2 c}+\frac{3 \tanh ^{-1}(a x)^2}{2 a^3 c}-\frac{\log \left(\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{a^3 c}+\frac{3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^3 c}-\frac{3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^3 c}+\frac{x^2 \tanh ^{-1}(a x)^3}{2 a c}",1,"(3*ArcTanh[a*x]^2)/(2*a^3*c) + (3*x*ArcTanh[a*x]^2)/(2*a^2*c) - (3*ArcTanh[a*x]^3)/(2*a^3*c) - (x*ArcTanh[a*x]^3)/(a^2*c) + (x^2*ArcTanh[a*x]^3)/(2*a*c) - (3*ArcTanh[a*x]*Log[2/(1 - a*x)])/(a^3*c) + (3*ArcTanh[a*x]^2*Log[2/(1 - a*x)])/(a^3*c) - (ArcTanh[a*x]^3*Log[2/(1 + a*x)])/(a^3*c) - (3*PolyLog[2, 1 - 2/(1 - a*x)])/(2*a^3*c) + (3*ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/(a^3*c) + (3*ArcTanh[a*x]^2*PolyLog[2, 1 - 2/(1 + a*x)])/(2*a^3*c) - (3*PolyLog[3, 1 - 2/(1 - a*x)])/(2*a^3*c) + (3*ArcTanh[a*x]*PolyLog[3, 1 - 2/(1 + a*x)])/(2*a^3*c) + (3*PolyLog[4, 1 - 2/(1 + a*x)])/(4*a^3*c)","A",19,13,18,0.7222,1,"{5930, 5916, 5980, 5910, 5984, 5918, 2402, 2315, 5948, 6058, 6610, 6056, 6060}"
128,1,205,0,0.3742016,"\int \frac{x \tanh ^{-1}(a x)^3}{c+a c x} \, dx","Int[(x*ArcTanh[a*x]^3)/(c + a*c*x),x]","\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^2 c}-\frac{3 \text{PolyLog}\left(4,1-\frac{2}{a x+1}\right)}{4 a^2 c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{a x+1}\right)}{2 a^2 c}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^2 c}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{a x+1}\right)}{2 a^2 c}+\frac{\tanh ^{-1}(a x)^3}{a^2 c}+\frac{\log \left(\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{a^2 c}-\frac{3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^2 c}+\frac{x \tanh ^{-1}(a x)^3}{a c}","\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^2 c}-\frac{3 \text{PolyLog}\left(4,1-\frac{2}{a x+1}\right)}{4 a^2 c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{a x+1}\right)}{2 a^2 c}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^2 c}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{a x+1}\right)}{2 a^2 c}+\frac{\tanh ^{-1}(a x)^3}{a^2 c}+\frac{\log \left(\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{a^2 c}-\frac{3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^2 c}+\frac{x \tanh ^{-1}(a x)^3}{a c}",1,"ArcTanh[a*x]^3/(a^2*c) + (x*ArcTanh[a*x]^3)/(a*c) - (3*ArcTanh[a*x]^2*Log[2/(1 - a*x)])/(a^2*c) + (ArcTanh[a*x]^3*Log[2/(1 + a*x)])/(a^2*c) - (3*ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/(a^2*c) - (3*ArcTanh[a*x]^2*PolyLog[2, 1 - 2/(1 + a*x)])/(2*a^2*c) + (3*PolyLog[3, 1 - 2/(1 - a*x)])/(2*a^2*c) - (3*ArcTanh[a*x]*PolyLog[3, 1 - 2/(1 + a*x)])/(2*a^2*c) - (3*PolyLog[4, 1 - 2/(1 + a*x)])/(4*a^2*c)","A",10,9,16,0.5625,1,"{5930, 5910, 5984, 5918, 5948, 6058, 6610, 6056, 6060}"
129,1,104,0,0.1641416,"\int \frac{\tanh ^{-1}(a x)^3}{c+a c x} \, dx","Int[ArcTanh[a*x]^3/(c + a*c*x),x]","\frac{3 \text{PolyLog}\left(4,1-\frac{2}{a x+1}\right)}{4 a c}+\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{a x+1}\right)}{2 a c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{a x+1}\right)}{2 a c}-\frac{\log \left(\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{a c}","\frac{3 \text{PolyLog}\left(4,1-\frac{2}{a x+1}\right)}{4 a c}+\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{a x+1}\right)}{2 a c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{a x+1}\right)}{2 a c}-\frac{\log \left(\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{a c}",1,"-((ArcTanh[a*x]^3*Log[2/(1 + a*x)])/(a*c)) + (3*ArcTanh[a*x]^2*PolyLog[2, 1 - 2/(1 + a*x)])/(2*a*c) + (3*ArcTanh[a*x]*PolyLog[3, 1 - 2/(1 + a*x)])/(2*a*c) + (3*PolyLog[4, 1 - 2/(1 + a*x)])/(4*a*c)","A",4,5,15,0.3333,1,"{5918, 5948, 6056, 6060, 6610}"
130,1,93,0,0.1716763,"\int \frac{\tanh ^{-1}(a x)^3}{x (c+a c x)} \, dx","Int[ArcTanh[a*x]^3/(x*(c + a*c*x)),x]","-\frac{3 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{4 c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}+\frac{\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}","-\frac{3 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{4 c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}+\frac{\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}",1,"(ArcTanh[a*x]^3*Log[2 - 2/(1 + a*x)])/c - (3*ArcTanh[a*x]^2*PolyLog[2, -1 + 2/(1 + a*x)])/(2*c) - (3*ArcTanh[a*x]*PolyLog[3, -1 + 2/(1 + a*x)])/(2*c) - (3*PolyLog[4, -1 + 2/(1 + a*x)])/(4*c)","A",4,5,18,0.2778,1,"{5932, 5948, 6056, 6060, 6610}"
131,1,93,0,0.1757078,"\int \frac{\tanh ^{-1}(a x)^3}{c x+a c x^2} \, dx","Int[ArcTanh[a*x]^3/(c*x + a*c*x^2),x]","-\frac{3 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{4 c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}+\frac{\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}","-\frac{3 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{4 c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}+\frac{\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}",1,"(ArcTanh[a*x]^3*Log[2 - 2/(1 + a*x)])/c - (3*ArcTanh[a*x]^2*PolyLog[2, -1 + 2/(1 + a*x)])/(2*c) - (3*ArcTanh[a*x]*PolyLog[3, -1 + 2/(1 + a*x)])/(2*c) - (3*PolyLog[4, -1 + 2/(1 + a*x)])/(4*c)","A",5,6,19,0.3158,1,"{1593, 5932, 5948, 6056, 6060, 6610}"
132,1,191,0,0.4633861,"\int \frac{\tanh ^{-1}(a x)^3}{x^2 (c+a c x)} \, dx","Int[ArcTanh[a*x]^3/(x^2*(c + a*c*x)),x]","-\frac{3 a \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}+\frac{3 a \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{4 c}+\frac{3 a \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}-\frac{3 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{c}+\frac{3 a \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}+\frac{a \tanh ^{-1}(a x)^3}{c}-\frac{\tanh ^{-1}(a x)^3}{c x}-\frac{a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}+\frac{3 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2}{c}","-\frac{3 a \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}+\frac{3 a \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{4 c}+\frac{3 a \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}-\frac{3 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{c}+\frac{3 a \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}+\frac{a \tanh ^{-1}(a x)^3}{c}-\frac{\tanh ^{-1}(a x)^3}{c x}-\frac{a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}+\frac{3 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2}{c}",1,"(a*ArcTanh[a*x]^3)/c - ArcTanh[a*x]^3/(c*x) + (3*a*ArcTanh[a*x]^2*Log[2 - 2/(1 + a*x)])/c - (a*ArcTanh[a*x]^3*Log[2 - 2/(1 + a*x)])/c - (3*a*ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 + a*x)])/c + (3*a*ArcTanh[a*x]^2*PolyLog[2, -1 + 2/(1 + a*x)])/(2*c) - (3*a*PolyLog[3, -1 + 2/(1 + a*x)])/(2*c) + (3*a*ArcTanh[a*x]*PolyLog[3, -1 + 2/(1 + a*x)])/(2*c) + (3*a*PolyLog[4, -1 + 2/(1 + a*x)])/(4*c)","A",10,8,18,0.4444,1,"{5934, 5916, 5988, 5932, 5948, 6056, 6610, 6060}"
133,1,305,0,0.7480831,"\int \frac{\tanh ^{-1}(a x)^3}{x^3 (c+a c x)} \, dx","Int[ArcTanh[a*x]^3/(x^3*(c + a*c*x)),x]","-\frac{3 a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}+\frac{3 a^2 \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}-\frac{3 a^2 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{4 c}-\frac{3 a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}+\frac{3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}-\frac{a^2 \tanh ^{-1}(a x)^3}{2 c}+\frac{3 a^2 \tanh ^{-1}(a x)^2}{2 c}+\frac{a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}-\frac{3 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2}{c}+\frac{3 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)}{c}-\frac{\tanh ^{-1}(a x)^3}{2 c x^2}+\frac{a \tanh ^{-1}(a x)^3}{c x}-\frac{3 a \tanh ^{-1}(a x)^2}{2 c x}","-\frac{3 a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}+\frac{3 a^2 \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}-\frac{3 a^2 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{4 c}-\frac{3 a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{2 c}+\frac{3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{2 c}-\frac{a^2 \tanh ^{-1}(a x)^3}{2 c}+\frac{3 a^2 \tanh ^{-1}(a x)^2}{2 c}+\frac{a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}-\frac{3 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2}{c}+\frac{3 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)}{c}-\frac{\tanh ^{-1}(a x)^3}{2 c x^2}+\frac{a \tanh ^{-1}(a x)^3}{c x}-\frac{3 a \tanh ^{-1}(a x)^2}{2 c x}",1,"(3*a^2*ArcTanh[a*x]^2)/(2*c) - (3*a*ArcTanh[a*x]^2)/(2*c*x) - (a^2*ArcTanh[a*x]^3)/(2*c) - ArcTanh[a*x]^3/(2*c*x^2) + (a*ArcTanh[a*x]^3)/(c*x) + (3*a^2*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)])/c - (3*a^2*ArcTanh[a*x]^2*Log[2 - 2/(1 + a*x)])/c + (a^2*ArcTanh[a*x]^3*Log[2 - 2/(1 + a*x)])/c - (3*a^2*PolyLog[2, -1 + 2/(1 + a*x)])/(2*c) + (3*a^2*ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 + a*x)])/c - (3*a^2*ArcTanh[a*x]^2*PolyLog[2, -1 + 2/(1 + a*x)])/(2*c) + (3*a^2*PolyLog[3, -1 + 2/(1 + a*x)])/(2*c) - (3*a^2*ArcTanh[a*x]*PolyLog[3, -1 + 2/(1 + a*x)])/(2*c) - (3*a^2*PolyLog[4, -1 + 2/(1 + a*x)])/(4*c)","A",18,10,18,0.5556,1,"{5934, 5916, 5982, 5988, 5932, 2447, 5948, 6056, 6610, 6060}"
134,1,384,0,0.8620024,"\int \frac{x^2 \tanh ^{-1}(a x)^4}{c-a c x} \, dx","Int[(x^2*ArcTanh[a*x]^4)/(c - a*c*x),x]","-\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a^3 c}+\frac{3 \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{a^3 c}-\frac{3 \text{PolyLog}\left(5,1-\frac{2}{1-a x}\right)}{2 a^3 c}+\frac{2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3 c}+\frac{6 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3 c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a^3 c}+\frac{6 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3 c}-\frac{6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a^3 c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{a^3 c}-\frac{x \tanh ^{-1}(a x)^4}{a^2 c}-\frac{\tanh ^{-1}(a x)^4}{2 a^3 c}-\frac{2 x \tanh ^{-1}(a x)^3}{a^2 c}-\frac{2 \tanh ^{-1}(a x)^3}{a^3 c}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{a^3 c}+\frac{4 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^3}{a^3 c}+\frac{6 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^3 c}-\frac{x^2 \tanh ^{-1}(a x)^4}{2 a c}","-\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a^3 c}+\frac{3 \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{a^3 c}-\frac{3 \text{PolyLog}\left(5,1-\frac{2}{1-a x}\right)}{2 a^3 c}+\frac{2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3 c}+\frac{6 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3 c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a^3 c}+\frac{6 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3 c}-\frac{6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a^3 c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{a^3 c}-\frac{x \tanh ^{-1}(a x)^4}{a^2 c}-\frac{\tanh ^{-1}(a x)^4}{2 a^3 c}-\frac{2 x \tanh ^{-1}(a x)^3}{a^2 c}-\frac{2 \tanh ^{-1}(a x)^3}{a^3 c}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{a^3 c}+\frac{4 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^3}{a^3 c}+\frac{6 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^3 c}-\frac{x^2 \tanh ^{-1}(a x)^4}{2 a c}",1,"(-2*ArcTanh[a*x]^3)/(a^3*c) - (2*x*ArcTanh[a*x]^3)/(a^2*c) - ArcTanh[a*x]^4/(2*a^3*c) - (x*ArcTanh[a*x]^4)/(a^2*c) - (x^2*ArcTanh[a*x]^4)/(2*a*c) + (6*ArcTanh[a*x]^2*Log[2/(1 - a*x)])/(a^3*c) + (4*ArcTanh[a*x]^3*Log[2/(1 - a*x)])/(a^3*c) + (ArcTanh[a*x]^4*Log[2/(1 - a*x)])/(a^3*c) + (6*ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/(a^3*c) + (6*ArcTanh[a*x]^2*PolyLog[2, 1 - 2/(1 - a*x)])/(a^3*c) + (2*ArcTanh[a*x]^3*PolyLog[2, 1 - 2/(1 - a*x)])/(a^3*c) - (3*PolyLog[3, 1 - 2/(1 - a*x)])/(a^3*c) - (6*ArcTanh[a*x]*PolyLog[3, 1 - 2/(1 - a*x)])/(a^3*c) - (3*ArcTanh[a*x]^2*PolyLog[3, 1 - 2/(1 - a*x)])/(a^3*c) + (3*PolyLog[4, 1 - 2/(1 - a*x)])/(a^3*c) + (3*ArcTanh[a*x]*PolyLog[4, 1 - 2/(1 - a*x)])/(a^3*c) - (3*PolyLog[5, 1 - 2/(1 - a*x)])/(2*a^3*c)","A",21,10,19,0.5263,1,"{5930, 5916, 5980, 5910, 5984, 5918, 5948, 6058, 6610, 6062}"
135,1,261,0,0.4981278,"\int \frac{x \tanh ^{-1}(a x)^4}{c-a c x} \, dx","Int[(x*ArcTanh[a*x]^4)/(c - a*c*x),x]","\frac{3 \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{a^2 c}-\frac{3 \text{PolyLog}\left(5,1-\frac{2}{1-a x}\right)}{2 a^2 c}+\frac{2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^2 c}+\frac{6 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^2 c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a^2 c}-\frac{6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a^2 c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{a^2 c}-\frac{\tanh ^{-1}(a x)^4}{a^2 c}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{a^2 c}+\frac{4 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^3}{a^2 c}-\frac{x \tanh ^{-1}(a x)^4}{a c}","\frac{3 \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{a^2 c}-\frac{3 \text{PolyLog}\left(5,1-\frac{2}{1-a x}\right)}{2 a^2 c}+\frac{2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^2 c}+\frac{6 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^2 c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a^2 c}-\frac{6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a^2 c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{a^2 c}-\frac{\tanh ^{-1}(a x)^4}{a^2 c}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{a^2 c}+\frac{4 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^3}{a^2 c}-\frac{x \tanh ^{-1}(a x)^4}{a c}",1,"-(ArcTanh[a*x]^4/(a^2*c)) - (x*ArcTanh[a*x]^4)/(a*c) + (4*ArcTanh[a*x]^3*Log[2/(1 - a*x)])/(a^2*c) + (ArcTanh[a*x]^4*Log[2/(1 - a*x)])/(a^2*c) + (6*ArcTanh[a*x]^2*PolyLog[2, 1 - 2/(1 - a*x)])/(a^2*c) + (2*ArcTanh[a*x]^3*PolyLog[2, 1 - 2/(1 - a*x)])/(a^2*c) - (6*ArcTanh[a*x]*PolyLog[3, 1 - 2/(1 - a*x)])/(a^2*c) - (3*ArcTanh[a*x]^2*PolyLog[3, 1 - 2/(1 - a*x)])/(a^2*c) + (3*PolyLog[4, 1 - 2/(1 - a*x)])/(a^2*c) + (3*ArcTanh[a*x]*PolyLog[4, 1 - 2/(1 - a*x)])/(a^2*c) - (3*PolyLog[5, 1 - 2/(1 - a*x)])/(2*a^2*c)","A",12,8,17,0.4706,1,"{5930, 5910, 5984, 5918, 5948, 6058, 6062, 6610}"
136,1,131,0,0.2144822,"\int \frac{\tanh ^{-1}(a x)^4}{c-a c x} \, dx","Int[ArcTanh[a*x]^4/(c - a*c*x),x]","-\frac{3 \text{PolyLog}\left(5,1-\frac{2}{1-a x}\right)}{2 a c}+\frac{2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{a c}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{a c}","-\frac{3 \text{PolyLog}\left(5,1-\frac{2}{1-a x}\right)}{2 a c}+\frac{2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{a c}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{a c}",1,"(ArcTanh[a*x]^4*Log[2/(1 - a*x)])/(a*c) + (2*ArcTanh[a*x]^3*PolyLog[2, 1 - 2/(1 - a*x)])/(a*c) - (3*ArcTanh[a*x]^2*PolyLog[3, 1 - 2/(1 - a*x)])/(a*c) + (3*ArcTanh[a*x]*PolyLog[4, 1 - 2/(1 - a*x)])/(a*c) - (3*PolyLog[5, 1 - 2/(1 - a*x)])/(2*a*c)","A",5,5,16,0.3125,1,"{5918, 5948, 6058, 6062, 6610}"
137,1,118,0,0.2206246,"\int \frac{\tanh ^{-1}(a x)^4}{x (c-a c x)} \, dx","Int[ArcTanh[a*x]^4/(x*(c - a*c*x)),x]","-\frac{3 \text{PolyLog}\left(5,\frac{2}{1-a x}-1\right)}{2 c}+\frac{2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)}{c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)}{c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(4,\frac{2}{1-a x}-1\right)}{c}+\frac{\log \left(2-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{c}","-\frac{3 \text{PolyLog}\left(5,\frac{2}{1-a x}-1\right)}{2 c}+\frac{2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)}{c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)}{c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(4,\frac{2}{1-a x}-1\right)}{c}+\frac{\log \left(2-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{c}",1,"(ArcTanh[a*x]^4*Log[2 - 2/(1 - a*x)])/c + (2*ArcTanh[a*x]^3*PolyLog[2, -1 + 2/(1 - a*x)])/c - (3*ArcTanh[a*x]^2*PolyLog[3, -1 + 2/(1 - a*x)])/c + (3*ArcTanh[a*x]*PolyLog[4, -1 + 2/(1 - a*x)])/c - (3*PolyLog[5, -1 + 2/(1 - a*x)])/(2*c)","A",5,5,19,0.2632,1,"{5932, 5948, 6058, 6062, 6610}"
138,1,118,0,0.2253952,"\int \frac{\tanh ^{-1}(a x)^4}{c x-a c x^2} \, dx","Int[ArcTanh[a*x]^4/(c*x - a*c*x^2),x]","-\frac{3 \text{PolyLog}\left(5,\frac{2}{1-a x}-1\right)}{2 c}+\frac{2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)}{c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)}{c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(4,\frac{2}{1-a x}-1\right)}{c}+\frac{\log \left(2-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{c}","-\frac{3 \text{PolyLog}\left(5,\frac{2}{1-a x}-1\right)}{2 c}+\frac{2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)}{c}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)}{c}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(4,\frac{2}{1-a x}-1\right)}{c}+\frac{\log \left(2-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{c}",1,"(ArcTanh[a*x]^4*Log[2 - 2/(1 - a*x)])/c + (2*ArcTanh[a*x]^3*PolyLog[2, -1 + 2/(1 - a*x)])/c - (3*ArcTanh[a*x]^2*PolyLog[3, -1 + 2/(1 - a*x)])/c + (3*ArcTanh[a*x]*PolyLog[4, -1 + 2/(1 - a*x)])/c - (3*PolyLog[5, -1 + 2/(1 - a*x)])/(2*c)","A",6,6,20,0.3000,1,"{1593, 5932, 5948, 6058, 6062, 6610}"
139,1,239,0,0.5487632,"\int \frac{\tanh ^{-1}(a x)^4}{x^2 (c-a c x)} \, dx","Int[ArcTanh[a*x]^4/(x^2*(c - a*c*x)),x]","-\frac{3 a \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a \text{PolyLog}\left(5,\frac{2}{1-a x}-1\right)}{2 c}+\frac{2 a \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)}{c}-\frac{6 a \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)}{c}-\frac{6 a \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{c}+\frac{3 a \tanh ^{-1}(a x) \text{PolyLog}\left(4,\frac{2}{1-a x}-1\right)}{c}+\frac{a \tanh ^{-1}(a x)^4}{c}-\frac{\tanh ^{-1}(a x)^4}{c x}+\frac{a \log \left(2-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{c}+\frac{4 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}","-\frac{3 a \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a \text{PolyLog}\left(5,\frac{2}{1-a x}-1\right)}{2 c}+\frac{2 a \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)}{c}-\frac{6 a \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)}{c}-\frac{6 a \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{c}+\frac{3 a \tanh ^{-1}(a x) \text{PolyLog}\left(4,\frac{2}{1-a x}-1\right)}{c}+\frac{a \tanh ^{-1}(a x)^4}{c}-\frac{\tanh ^{-1}(a x)^4}{c x}+\frac{a \log \left(2-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{c}+\frac{4 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}",1,"(a*ArcTanh[a*x]^4)/c - ArcTanh[a*x]^4/(c*x) + (a*ArcTanh[a*x]^4*Log[2 - 2/(1 - a*x)])/c + (4*a*ArcTanh[a*x]^3*Log[2 - 2/(1 + a*x)])/c + (2*a*ArcTanh[a*x]^3*PolyLog[2, -1 + 2/(1 - a*x)])/c - (6*a*ArcTanh[a*x]^2*PolyLog[2, -1 + 2/(1 + a*x)])/c - (3*a*ArcTanh[a*x]^2*PolyLog[3, -1 + 2/(1 - a*x)])/c - (6*a*ArcTanh[a*x]*PolyLog[3, -1 + 2/(1 + a*x)])/c + (3*a*ArcTanh[a*x]*PolyLog[4, -1 + 2/(1 - a*x)])/c - (3*a*PolyLog[4, -1 + 2/(1 + a*x)])/c - (3*a*PolyLog[5, -1 + 2/(1 - a*x)])/(2*c)","A",12,10,19,0.5263,1,"{5934, 5916, 5988, 5932, 5948, 6056, 6060, 6610, 6058, 6062}"
140,1,380,0,0.9555612,"\int \frac{\tanh ^{-1}(a x)^4}{x^3 (c-a c x)} \, dx","Int[ArcTanh[a*x]^4/(x^3*(c - a*c*x)),x]","-\frac{3 a^2 \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a^2 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a^2 \text{PolyLog}\left(5,\frac{2}{1-a x}-1\right)}{2 c}+\frac{2 a^2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)}{c}-\frac{6 a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)}{c}-\frac{6 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{c}-\frac{6 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{c}+\frac{3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(4,\frac{2}{1-a x}-1\right)}{c}+\frac{3 a^2 \tanh ^{-1}(a x)^4}{2 c}+\frac{2 a^2 \tanh ^{-1}(a x)^3}{c}+\frac{a^2 \log \left(2-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{c}+\frac{4 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}+\frac{6 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2}{c}-\frac{\tanh ^{-1}(a x)^4}{2 c x^2}-\frac{a \tanh ^{-1}(a x)^4}{c x}-\frac{2 a \tanh ^{-1}(a x)^3}{c x}","-\frac{3 a^2 \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a^2 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a^2 \text{PolyLog}\left(5,\frac{2}{1-a x}-1\right)}{2 c}+\frac{2 a^2 \tanh ^{-1}(a x)^3 \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)}{c}-\frac{6 a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{c}-\frac{3 a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)}{c}-\frac{6 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)}{c}-\frac{6 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)}{c}+\frac{3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(4,\frac{2}{1-a x}-1\right)}{c}+\frac{3 a^2 \tanh ^{-1}(a x)^4}{2 c}+\frac{2 a^2 \tanh ^{-1}(a x)^3}{c}+\frac{a^2 \log \left(2-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^4}{c}+\frac{4 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3}{c}+\frac{6 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2}{c}-\frac{\tanh ^{-1}(a x)^4}{2 c x^2}-\frac{a \tanh ^{-1}(a x)^4}{c x}-\frac{2 a \tanh ^{-1}(a x)^3}{c x}",1,"(2*a^2*ArcTanh[a*x]^3)/c - (2*a*ArcTanh[a*x]^3)/(c*x) + (3*a^2*ArcTanh[a*x]^4)/(2*c) - ArcTanh[a*x]^4/(2*c*x^2) - (a*ArcTanh[a*x]^4)/(c*x) + (a^2*ArcTanh[a*x]^4*Log[2 - 2/(1 - a*x)])/c + (6*a^2*ArcTanh[a*x]^2*Log[2 - 2/(1 + a*x)])/c + (4*a^2*ArcTanh[a*x]^3*Log[2 - 2/(1 + a*x)])/c + (2*a^2*ArcTanh[a*x]^3*PolyLog[2, -1 + 2/(1 - a*x)])/c - (6*a^2*ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 + a*x)])/c - (6*a^2*ArcTanh[a*x]^2*PolyLog[2, -1 + 2/(1 + a*x)])/c - (3*a^2*ArcTanh[a*x]^2*PolyLog[3, -1 + 2/(1 - a*x)])/c - (3*a^2*PolyLog[3, -1 + 2/(1 + a*x)])/c - (6*a^2*ArcTanh[a*x]*PolyLog[3, -1 + 2/(1 + a*x)])/c + (3*a^2*ArcTanh[a*x]*PolyLog[4, -1 + 2/(1 - a*x)])/c - (3*a^2*PolyLog[4, -1 + 2/(1 + a*x)])/c - (3*a^2*PolyLog[5, -1 + 2/(1 - a*x)])/(2*c)","A",21,11,19,0.5789,1,"{5934, 5916, 5982, 5988, 5932, 5948, 6056, 6610, 6060, 6058, 6062}"
141,0,0,0,0.0405899,"\int \frac{x}{(c+a c x) \tanh ^{-1}(a x)} \, dx","Int[x/((c + a*c*x)*ArcTanh[a*x]),x]","\int \frac{x}{(c+a c x) \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x}{(a c x+c) \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][x/((c + a*c*x)*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
142,0,0,0,0.0247666,"\int \frac{1}{(c+a c x) \tanh ^{-1}(a x)} \, dx","Int[1/((c + a*c*x)*ArcTanh[a*x]),x]","\int \frac{1}{(c+a c x) \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{(a c x+c) \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][1/((c + a*c*x)*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
143,0,0,0,0.0584234,"\int \frac{1}{x (c+a c x) \tanh ^{-1}(a x)} \, dx","Int[1/(x*(c + a*c*x)*ArcTanh[a*x]),x]","\int \frac{1}{x (c+a c x) \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x (a c x+c) \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x*(c + a*c*x)*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
144,0,0,0,0.0390449,"\int \frac{x}{(c+a c x) \tanh ^{-1}(a x)^2} \, dx","Int[x/((c + a*c*x)*ArcTanh[a*x]^2),x]","\int \frac{x}{(c+a c x) \tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{x}{(a c x+c) \tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][x/((c + a*c*x)*ArcTanh[a*x]^2), x]","A",0,0,0,0,-1,"{}"
145,0,0,0,0.0209782,"\int \frac{1}{(c+a c x) \tanh ^{-1}(a x)^2} \, dx","Int[1/((c + a*c*x)*ArcTanh[a*x]^2),x]","\int \frac{1}{(c+a c x) \tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{(a c x+c) \tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][1/((c + a*c*x)*ArcTanh[a*x]^2), x]","A",0,0,0,0,-1,"{}"
146,0,0,0,0.0551411,"\int \frac{1}{x (c+a c x) \tanh ^{-1}(a x)^2} \, dx","Int[1/(x*(c + a*c*x)*ArcTanh[a*x]^2),x]","\int \frac{1}{x (c+a c x) \tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{x (a c x+c) \tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][1/(x*(c + a*c*x)*ArcTanh[a*x]^2), x]","A",0,0,0,0,-1,"{}"
147,1,275,0,0.2557163,"\int \frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)}{d+e x} \, dx","Int[(x^3*(a + b*ArcTanh[c*x]))/(d + e*x),x]","-\frac{b d^3 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 e^4}+\frac{b d^3 \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e^4}+\frac{d^3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e^4}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e^4}-\frac{d x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 e^2}+\frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 e}+\frac{a d^2 x}{e^3}+\frac{b d^2 \log \left(1-c^2 x^2\right)}{2 c e^3}+\frac{b d \tanh ^{-1}(c x)}{2 c^2 e^2}+\frac{b \log \left(1-c^2 x^2\right)}{6 c^3 e}+\frac{b d^2 x \tanh ^{-1}(c x)}{e^3}-\frac{b d x}{2 c e^2}+\frac{b x^2}{6 c e}","-\frac{b d^3 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 e^4}+\frac{b d^3 \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e^4}+\frac{d^3 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e^4}-\frac{d^3 \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e^4}-\frac{d x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 e^2}+\frac{x^3 \left(a+b \tanh ^{-1}(c x)\right)}{3 e}+\frac{a d^2 x}{e^3}+\frac{b d^2 \log \left(1-c^2 x^2\right)}{2 c e^3}+\frac{b d \tanh ^{-1}(c x)}{2 c^2 e^2}+\frac{b \log \left(1-c^2 x^2\right)}{6 c^3 e}+\frac{b d^2 x \tanh ^{-1}(c x)}{e^3}-\frac{b d x}{2 c e^2}+\frac{b x^2}{6 c e}",1,"(a*d^2*x)/e^3 - (b*d*x)/(2*c*e^2) + (b*x^2)/(6*c*e) + (b*d*ArcTanh[c*x])/(2*c^2*e^2) + (b*d^2*x*ArcTanh[c*x])/e^3 - (d*x^2*(a + b*ArcTanh[c*x]))/(2*e^2) + (x^3*(a + b*ArcTanh[c*x]))/(3*e) + (d^3*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/e^4 - (d^3*(a + b*ArcTanh[c*x])*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e^4 + (b*d^2*Log[1 - c^2*x^2])/(2*c*e^3) + (b*Log[1 - c^2*x^2])/(6*c^3*e) - (b*d^3*PolyLog[2, 1 - 2/(1 + c*x)])/(2*e^4) + (b*d^3*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*e^4)","A",16,12,19,0.6316,1,"{5940, 5910, 260, 5916, 321, 206, 266, 43, 5920, 2402, 2315, 2447}"
148,1,214,0,0.1996717,"\int \frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{d+e x} \, dx","Int[(x^2*(a + b*ArcTanh[c*x]))/(d + e*x),x]","\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 e^3}-\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e^3}-\frac{d^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e^3}+\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e^3}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 e}-\frac{a d x}{e^2}-\frac{b d \log \left(1-c^2 x^2\right)}{2 c e^2}-\frac{b \tanh ^{-1}(c x)}{2 c^2 e}-\frac{b d x \tanh ^{-1}(c x)}{e^2}+\frac{b x}{2 c e}","\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 e^3}-\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e^3}-\frac{d^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e^3}+\frac{d^2 \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e^3}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)}{2 e}-\frac{a d x}{e^2}-\frac{b d \log \left(1-c^2 x^2\right)}{2 c e^2}-\frac{b \tanh ^{-1}(c x)}{2 c^2 e}-\frac{b d x \tanh ^{-1}(c x)}{e^2}+\frac{b x}{2 c e}",1,"-((a*d*x)/e^2) + (b*x)/(2*c*e) - (b*ArcTanh[c*x])/(2*c^2*e) - (b*d*x*ArcTanh[c*x])/e^2 + (x^2*(a + b*ArcTanh[c*x]))/(2*e) - (d^2*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/e^3 + (d^2*(a + b*ArcTanh[c*x])*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e^3 - (b*d*Log[1 - c^2*x^2])/(2*c*e^2) + (b*d^2*PolyLog[2, 1 - 2/(1 + c*x)])/(2*e^3) - (b*d^2*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*e^3)","A",12,10,19,0.5263,1,"{5940, 5910, 260, 5916, 321, 206, 5920, 2402, 2315, 2447}"
149,1,156,0,0.1538314,"\int \frac{x \left(a+b \tanh ^{-1}(c x)\right)}{d+e x} \, dx","Int[(x*(a + b*ArcTanh[c*x]))/(d + e*x),x]","-\frac{b d \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 e^2}+\frac{b d \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e^2}+\frac{d \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e^2}-\frac{d \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e^2}+\frac{a x}{e}+\frac{b \log \left(1-c^2 x^2\right)}{2 c e}+\frac{b x \tanh ^{-1}(c x)}{e}","-\frac{b d \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 e^2}+\frac{b d \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e^2}+\frac{d \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e^2}-\frac{d \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e^2}+\frac{a x}{e}+\frac{b \log \left(1-c^2 x^2\right)}{2 c e}+\frac{b x \tanh ^{-1}(c x)}{e}",1,"(a*x)/e + (b*x*ArcTanh[c*x])/e + (d*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/e^2 - (d*(a + b*ArcTanh[c*x])*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e^2 + (b*Log[1 - c^2*x^2])/(2*c*e) - (b*d*PolyLog[2, 1 - 2/(1 + c*x)])/(2*e^2) + (b*d*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*e^2)","A",9,7,17,0.4118,1,"{5940, 5910, 260, 5920, 2402, 2315, 2447}"
150,1,114,0,0.0708463,"\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}"
151,1,148,0,0.1637113,"\int \frac{a+b \tanh ^{-1}(c x)}{x (d+e x)} \, dx","Int[(a + b*ArcTanh[c*x])/(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 d}-\frac{b \text{PolyLog}(2,-c x)}{2 d}+\frac{b \text{PolyLog}(2,c x)}{2 d}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d}-\frac{\left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{a \log (x)}{d}","\frac{b \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 d}-\frac{b \text{PolyLog}(2,-c x)}{2 d}+\frac{b \text{PolyLog}(2,c x)}{2 d}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d}-\frac{\left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{a \log (x)}{d}",1,"(a*Log[x])/d + ((a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/d - ((a + b*ArcTanh[c*x])*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/d - (b*PolyLog[2, -(c*x)])/(2*d) + (b*PolyLog[2, c*x])/(2*d) - (b*PolyLog[2, 1 - 2/(1 + c*x)])/(2*d) + (b*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*d)","A",7,6,19,0.3158,1,"{5940, 5912, 5920, 2402, 2315, 2447}"
152,1,200,0,0.2037203,"\int \frac{a+b \tanh ^{-1}(c x)}{x^2 (d+e x)} \, dx","Int[(a + b*ArcTanh[c*x])/(x^2*(d + e*x)),x]","\frac{b e \text{PolyLog}(2,-c x)}{2 d^2}-\frac{b e \text{PolyLog}(2,c x)}{2 d^2}+\frac{b e \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^2}-\frac{b e \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 d^2}-\frac{e \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{e \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d^2}-\frac{a+b \tanh ^{-1}(c x)}{d x}-\frac{a e \log (x)}{d^2}-\frac{b c \log \left(1-c^2 x^2\right)}{2 d}+\frac{b c \log (x)}{d}","\frac{b e \text{PolyLog}(2,-c x)}{2 d^2}-\frac{b e \text{PolyLog}(2,c x)}{2 d^2}+\frac{b e \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^2}-\frac{b e \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 d^2}-\frac{e \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{e \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d^2}-\frac{a+b \tanh ^{-1}(c x)}{d x}-\frac{a e \log (x)}{d^2}-\frac{b c \log \left(1-c^2 x^2\right)}{2 d}+\frac{b c \log (x)}{d}",1,"-((a + b*ArcTanh[c*x])/(d*x)) + (b*c*Log[x])/d - (a*e*Log[x])/d^2 - (e*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/d^2 + (e*(a + b*ArcTanh[c*x])*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/d^2 - (b*c*Log[1 - c^2*x^2])/(2*d) + (b*e*PolyLog[2, -(c*x)])/(2*d^2) - (b*e*PolyLog[2, c*x])/(2*d^2) + (b*e*PolyLog[2, 1 - 2/(1 + c*x)])/(2*d^2) - (b*e*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*d^2)","A",12,11,19,0.5789,1,"{5940, 5916, 266, 36, 29, 31, 5912, 5920, 2402, 2315, 2447}"
153,1,261,0,0.245221,"\int \frac{a+b \tanh ^{-1}(c x)}{x^3 (d+e x)} \, dx","Int[(a + b*ArcTanh[c*x])/(x^3*(d + e*x)),x]","-\frac{b e^2 \text{PolyLog}(2,-c x)}{2 d^3}+\frac{b e^2 \text{PolyLog}(2,c x)}{2 d^3}-\frac{b e^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^3}+\frac{b e^2 \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 d^3}+\frac{e^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{e^2 \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d^3}+\frac{e \left(a+b \tanh ^{-1}(c x)\right)}{d^2 x}-\frac{a+b \tanh ^{-1}(c x)}{2 d x^2}+\frac{a e^2 \log (x)}{d^3}+\frac{b c e \log \left(1-c^2 x^2\right)}{2 d^2}+\frac{b c^2 \tanh ^{-1}(c x)}{2 d}-\frac{b c e \log (x)}{d^2}-\frac{b c}{2 d x}","-\frac{b e^2 \text{PolyLog}(2,-c x)}{2 d^3}+\frac{b e^2 \text{PolyLog}(2,c x)}{2 d^3}-\frac{b e^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 d^3}+\frac{b e^2 \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 d^3}+\frac{e^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^3}-\frac{e^2 \left(a+b \tanh ^{-1}(c x)\right) \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d^3}+\frac{e \left(a+b \tanh ^{-1}(c x)\right)}{d^2 x}-\frac{a+b \tanh ^{-1}(c x)}{2 d x^2}+\frac{a e^2 \log (x)}{d^3}+\frac{b c e \log \left(1-c^2 x^2\right)}{2 d^2}+\frac{b c^2 \tanh ^{-1}(c x)}{2 d}-\frac{b c e \log (x)}{d^2}-\frac{b c}{2 d x}",1,"-(b*c)/(2*d*x) + (b*c^2*ArcTanh[c*x])/(2*d) - (a + b*ArcTanh[c*x])/(2*d*x^2) + (e*(a + b*ArcTanh[c*x]))/(d^2*x) - (b*c*e*Log[x])/d^2 + (a*e^2*Log[x])/d^3 + (e^2*(a + b*ArcTanh[c*x])*Log[2/(1 + c*x)])/d^3 - (e^2*(a + b*ArcTanh[c*x])*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/d^3 + (b*c*e*Log[1 - c^2*x^2])/(2*d^2) - (b*e^2*PolyLog[2, -(c*x)])/(2*d^3) + (b*e^2*PolyLog[2, c*x])/(2*d^3) - (b*e^2*PolyLog[2, 1 - 2/(1 + c*x)])/(2*d^3) + (b*e^2*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*d^3)","A",15,13,19,0.6842,1,"{5940, 5916, 325, 206, 266, 36, 29, 31, 5912, 5920, 2402, 2315, 2447}"
154,1,385,0,0.4271473,"\int \frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{d+e x} \, dx","Int[(x^2*(a + b*ArcTanh[c*x])^2)/(d + e*x),x]","\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e^3}-\frac{b d^2 \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^3}+\frac{b^2 d^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 e^3}-\frac{b^2 d^2 \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e^3}+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c e^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2 e}-\frac{d^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{e^3}+\frac{d^2 \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^3}-\frac{d x \left(a+b \tanh ^{-1}(c x)\right)^2}{e^2}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{c e^2}+\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c e^2}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e}+\frac{a b x}{c e}+\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^2 e}+\frac{b^2 x \tanh ^{-1}(c x)}{c e}","\frac{b d^2 \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e^3}-\frac{b d^2 \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^3}+\frac{b^2 d^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 e^3}-\frac{b^2 d^2 \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e^3}+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c e^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2 e}-\frac{d^2 \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{e^3}+\frac{d^2 \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^3}-\frac{d x \left(a+b \tanh ^{-1}(c x)\right)^2}{e^2}-\frac{d \left(a+b \tanh ^{-1}(c x)\right)^2}{c e^2}+\frac{2 b d \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c e^2}+\frac{x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 e}+\frac{a b x}{c e}+\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^2 e}+\frac{b^2 x \tanh ^{-1}(c x)}{c e}",1,"(a*b*x)/(c*e) + (b^2*x*ArcTanh[c*x])/(c*e) - (d*(a + b*ArcTanh[c*x])^2)/(c*e^2) - (a + b*ArcTanh[c*x])^2/(2*c^2*e) - (d*x*(a + b*ArcTanh[c*x])^2)/e^2 + (x^2*(a + b*ArcTanh[c*x])^2)/(2*e) + (2*b*d*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(c*e^2) - (d^2*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/e^3 + (d^2*(a + b*ArcTanh[c*x])^2*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e^3 + (b^2*Log[1 - c^2*x^2])/(2*c^2*e) + (b^2*d*PolyLog[2, 1 - 2/(1 - c*x)])/(c*e^2) + (b*d^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/e^3 - (b*d^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e^3 + (b^2*d^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*e^3) - (b^2*d^2*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*e^3)","A",14,11,21,0.5238,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5916, 5980, 260, 5948, 5922}"
155,1,279,0,0.2575851,"\int \frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{d+e x} \, dx","Int[(x*(a + b*ArcTanh[c*x])^2)/(d + e*x),x]","-\frac{b d \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e^2}+\frac{b d \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^2}-\frac{b^2 d \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 e^2}+\frac{b^2 d \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e^2}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c e}+\frac{d \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{e^2}-\frac{d \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^2}+\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{e}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c e}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c e}","-\frac{b d \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{e^2}+\frac{b d \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^2}-\frac{b^2 d \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 e^2}+\frac{b^2 d \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e^2}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c e}+\frac{d \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{e^2}-\frac{d \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^2}+\frac{x \left(a+b \tanh ^{-1}(c x)\right)^2}{e}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c e}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c e}",1,"(a + b*ArcTanh[c*x])^2/(c*e) + (x*(a + b*ArcTanh[c*x])^2)/e - (2*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(c*e) + (d*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/e^2 - (d*(a + b*ArcTanh[c*x])^2*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e^2 - (b^2*PolyLog[2, 1 - 2/(1 - c*x)])/(c*e) - (b*d*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/e^2 + (b*d*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e^2 - (b^2*d*PolyLog[3, 1 - 2/(1 + c*x)])/(2*e^2) + (b^2*d*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*e^2)","A",8,7,19,0.3684,1,"{5940, 5910, 5984, 5918, 2402, 2315, 5922}"
156,1,188,0,0.0466511,"\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}"
157,1,319,0,0.4305971,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x (d+e x)} \, dx","Int[(a + b*ArcTanh[c*x])^2/(x*(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)}{d}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{b \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 d}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d}-\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)}{d}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}","\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)}{d}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{b \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 d}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d}-\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)}{d}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}+\frac{\log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d}",1,"(2*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)])/d + ((a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/d - ((a + b*ArcTanh[c*x])^2*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/d - (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/d + (b*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)])/d - (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/d + (b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/d + (b^2*PolyLog[3, 1 - 2/(1 - c*x)])/(2*d) - (b^2*PolyLog[3, -1 + 2/(1 - c*x)])/(2*d) - (b^2*PolyLog[3, 1 - 2/(1 + c*x)])/(2*d) + (b^2*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*d)","A",9,7,21,0.3333,1,"{5940, 5914, 6052, 5948, 6058, 6610, 5922}"
158,1,412,0,0.6037659,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x^2 (d+e x)} \, dx","Int[(a + b*ArcTanh[c*x])^2/(x^2*(d + e*x)),x]","\frac{b e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{b e \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{b e \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{b e \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)}{d^2}-\frac{b^2 e \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d^2}+\frac{b^2 e \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d^2}+\frac{b^2 e \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d^2}-\frac{b^2 e \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 d^2}-\frac{b^2 c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d}-\frac{2 e \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}-\frac{e \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{e \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d^2}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{d}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d x}+\frac{2 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}","\frac{b e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{b e \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}+\frac{b e \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d^2}-\frac{b e \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)}{d^2}-\frac{b^2 e \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d^2}+\frac{b^2 e \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d^2}+\frac{b^2 e \text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d^2}-\frac{b^2 e \text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 d^2}-\frac{b^2 c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)}{d}-\frac{2 e \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}-\frac{e \log \left(\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{d^2}+\frac{e \left(a+b \tanh ^{-1}(c x)\right)^2 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d^2}+\frac{c \left(a+b \tanh ^{-1}(c x)\right)^2}{d}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{d x}+\frac{2 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)}{d}",1,"(c*(a + b*ArcTanh[c*x])^2)/d - (a + b*ArcTanh[c*x])^2/(d*x) - (2*e*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)])/d^2 - (e*(a + b*ArcTanh[c*x])^2*Log[2/(1 + c*x)])/d^2 + (e*(a + b*ArcTanh[c*x])^2*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/d^2 + (2*b*c*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/d + (b*e*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/d^2 - (b*e*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)])/d^2 + (b*e*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 + c*x)])/d^2 - (b^2*c*PolyLog[2, -1 + 2/(1 + c*x)])/d - (b*e*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/d^2 - (b^2*e*PolyLog[3, 1 - 2/(1 - c*x)])/(2*d^2) + (b^2*e*PolyLog[3, -1 + 2/(1 - c*x)])/(2*d^2) + (b^2*e*PolyLog[3, 1 - 2/(1 + c*x)])/(2*d^2) - (b^2*e*PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/(2*d^2)","A",13,11,21,0.5238,1,"{5940, 5916, 5988, 5932, 2447, 5914, 6052, 5948, 6058, 6610, 5922}"
159,1,275,0,0.3356813,"\int \frac{\tanh ^{-1}(c x)^2}{x (d+e x)} \, dx","Int[ArcTanh[c*x]^2/(x*(d + e*x)),x]","\frac{\text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 d}+\frac{\tanh ^{-1}(c x) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d}+\frac{\text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d}-\frac{\text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d}-\frac{\text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d}-\frac{\tanh ^{-1}(c x) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{d}+\frac{\tanh ^{-1}(c x) \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right)}{d}-\frac{\tanh ^{-1}(c x) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{d}-\frac{\tanh ^{-1}(c x)^2 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \tanh ^{-1}(c x)^2}{d}+\frac{\log \left(\frac{2}{c x+1}\right) \tanh ^{-1}(c x)^2}{d}","\frac{\text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 d}+\frac{\tanh ^{-1}(c x) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d}+\frac{\text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 d}-\frac{\text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)}{2 d}-\frac{\text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 d}-\frac{\tanh ^{-1}(c x) \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{d}+\frac{\tanh ^{-1}(c x) \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right)}{d}-\frac{\tanh ^{-1}(c x) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{d}-\frac{\tanh ^{-1}(c x)^2 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{d}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \tanh ^{-1}(c x)^2}{d}+\frac{\log \left(\frac{2}{c x+1}\right) \tanh ^{-1}(c x)^2}{d}",1,"(2*ArcTanh[c*x]^2*ArcTanh[1 - 2/(1 - c*x)])/d + (ArcTanh[c*x]^2*Log[2/(1 + c*x)])/d - (ArcTanh[c*x]^2*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/d - (ArcTanh[c*x]*PolyLog[2, 1 - 2/(1 - c*x)])/d + (ArcTanh[c*x]*PolyLog[2, -1 + 2/(1 - c*x)])/d - (ArcTanh[c*x]*PolyLog[2, 1 - 2/(1 + c*x)])/d + (ArcTanh[c*x]*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/d + PolyLog[3, 1 - 2/(1 - c*x)]/(2*d) - PolyLog[3, -1 + 2/(1 - c*x)]/(2*d) - PolyLog[3, 1 - 2/(1 + c*x)]/(2*d) + PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))]/(2*d)","A",9,7,17,0.4118,1,"{5940, 5914, 6052, 5948, 6058, 6610, 5922}"
160,0,0,0,0.0306718,"\int \frac{1}{(d+e x) \left(a+b \tan ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x)*(a + b*ArcTan[c*x])),x]","\int \frac{1}{(d+e x) \left(a+b \tan ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{(d+e x) \left(a+b \tan ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x)*(a + b*ArcTan[c*x])), x]","A",0,0,0,0,-1,"{}"
161,1,72,0,0.1072748,"\int x^4 \left(1-a^2 x^2\right) \tanh ^{-1}(a x) \, dx","Int[x^4*(1 - a^2*x^2)*ArcTanh[a*x],x]","\frac{x^2}{35 a^3}+\frac{\log \left(1-a^2 x^2\right)}{35 a^5}-\frac{1}{7} a^2 x^7 \tanh ^{-1}(a x)-\frac{a x^6}{42}+\frac{x^4}{70 a}+\frac{1}{5} x^5 \tanh ^{-1}(a x)","\frac{x^2}{35 a^3}+\frac{\log \left(1-a^2 x^2\right)}{35 a^5}-\frac{1}{7} a^2 x^7 \tanh ^{-1}(a x)-\frac{a x^6}{42}+\frac{x^4}{70 a}+\frac{1}{5} x^5 \tanh ^{-1}(a x)",1,"x^2/(35*a^3) + x^4/(70*a) - (a*x^6)/42 + (x^5*ArcTanh[a*x])/5 - (a^2*x^7*ArcTanh[a*x])/7 + Log[1 - a^2*x^2]/(35*a^5)","A",9,4,18,0.2222,1,"{6014, 5916, 266, 43}"
162,1,63,0,0.0807167,"\int x^3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x) \, dx","Int[x^3*(1 - a^2*x^2)*ArcTanh[a*x],x]","-\frac{1}{6} a^2 x^6 \tanh ^{-1}(a x)+\frac{x}{12 a^3}-\frac{\tanh ^{-1}(a x)}{12 a^4}-\frac{a x^5}{30}+\frac{x^3}{36 a}+\frac{1}{4} x^4 \tanh ^{-1}(a x)","-\frac{1}{6} a^2 x^6 \tanh ^{-1}(a x)+\frac{x}{12 a^3}-\frac{\tanh ^{-1}(a x)}{12 a^4}-\frac{a x^5}{30}+\frac{x^3}{36 a}+\frac{1}{4} x^4 \tanh ^{-1}(a x)",1,"x/(12*a^3) + x^3/(36*a) - (a*x^5)/30 - ArcTanh[a*x]/(12*a^4) + (x^4*ArcTanh[a*x])/4 - (a^2*x^6*ArcTanh[a*x])/6","A",9,4,18,0.2222,1,"{6014, 5916, 302, 206}"
163,1,62,0,0.0874176,"\int x^2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x) \, dx","Int[x^2*(1 - a^2*x^2)*ArcTanh[a*x],x]","\frac{\log \left(1-a^2 x^2\right)}{15 a^3}-\frac{1}{5} a^2 x^5 \tanh ^{-1}(a x)-\frac{a x^4}{20}+\frac{x^2}{15 a}+\frac{1}{3} x^3 \tanh ^{-1}(a x)","\frac{\log \left(1-a^2 x^2\right)}{15 a^3}-\frac{1}{5} a^2 x^5 \tanh ^{-1}(a x)-\frac{a x^4}{20}+\frac{x^2}{15 a}+\frac{1}{3} x^3 \tanh ^{-1}(a x)",1,"x^2/(15*a) - (a*x^4)/20 + (x^3*ArcTanh[a*x])/3 - (a^2*x^5*ArcTanh[a*x])/5 + Log[1 - a^2*x^2]/(15*a^3)","A",9,4,18,0.2222,1,"{6014, 5916, 266, 43}"
164,1,40,0,0.0215924,"\int x \left(1-a^2 x^2\right) \tanh ^{-1}(a x) \, dx","Int[x*(1 - a^2*x^2)*ArcTanh[a*x],x]","-\frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{4 a^2}-\frac{a x^3}{12}+\frac{x}{4 a}","-\frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{4 a^2}-\frac{a x^3}{12}+\frac{x}{4 a}",1,"x/(4*a) - (a*x^3)/12 - ((1 - a^2*x^2)^2*ArcTanh[a*x])/(4*a^2)","A",2,1,16,0.06250,1,"{5994}"
165,1,64,0,0.0212375,"\int \left(1-a^2 x^2\right) \tanh ^{-1}(a x) \, dx","Int[(1 - a^2*x^2)*ArcTanh[a*x],x]","\frac{1-a^2 x^2}{6 a}+\frac{\log \left(1-a^2 x^2\right)}{3 a}+\frac{1}{3} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)+\frac{2}{3} x \tanh ^{-1}(a x)","\frac{1-a^2 x^2}{6 a}+\frac{\log \left(1-a^2 x^2\right)}{3 a}+\frac{1}{3} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)+\frac{2}{3} x \tanh ^{-1}(a x)",1,"(1 - a^2*x^2)/(6*a) + (2*x*ArcTanh[a*x])/3 + (x*(1 - a^2*x^2)*ArcTanh[a*x])/3 + Log[1 - a^2*x^2]/(3*a)","A",3,3,15,0.2000,1,"{5942, 5910, 260}"
166,1,48,0,0.0473091,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{x} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x])/x,x]","-\frac{1}{2} \text{PolyLog}(2,-a x)+\frac{1}{2} \text{PolyLog}(2,a x)-\frac{1}{2} a^2 x^2 \tanh ^{-1}(a x)-\frac{a x}{2}+\frac{1}{2} \tanh ^{-1}(a x)","-\frac{1}{2} \text{PolyLog}(2,-a x)+\frac{1}{2} \text{PolyLog}(2,a x)-\frac{1}{2} a^2 x^2 \tanh ^{-1}(a x)-\frac{a x}{2}+\frac{1}{2} \tanh ^{-1}(a x)",1,"-(a*x)/2 + ArcTanh[a*x]/2 - (a^2*x^2*ArcTanh[a*x])/2 - PolyLog[2, -(a*x)]/2 + PolyLog[2, a*x]/2","A",5,5,18,0.2778,1,"{6014, 5912, 5916, 321, 206}"
167,1,38,0,0.0511531,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{x^2} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x])/x^2,x]","-a \log \left(1-a^2 x^2\right)+a^2 (-x) \tanh ^{-1}(a x)+a \log (x)-\frac{\tanh ^{-1}(a x)}{x}","-a \log \left(1-a^2 x^2\right)+a^2 (-x) \tanh ^{-1}(a x)+a \log (x)-\frac{\tanh ^{-1}(a x)}{x}",1,"-(ArcTanh[a*x]/x) - a^2*x*ArcTanh[a*x] + a*Log[x] - a*Log[1 - a^2*x^2]","A",8,8,18,0.4444,1,"{6014, 5916, 266, 36, 29, 31, 5910, 260}"
168,1,56,0,0.0509202,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{x^3} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x])/x^3,x]","\frac{1}{2} a^2 \text{PolyLog}(2,-a x)-\frac{1}{2} a^2 \text{PolyLog}(2,a x)+\frac{1}{2} a^2 \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)}{2 x^2}-\frac{a}{2 x}","\frac{1}{2} a^2 \text{PolyLog}(2,-a x)-\frac{1}{2} a^2 \text{PolyLog}(2,a x)+\frac{1}{2} a^2 \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)}{2 x^2}-\frac{a}{2 x}",1,"-a/(2*x) + (a^2*ArcTanh[a*x])/2 - ArcTanh[a*x]/(2*x^2) + (a^2*PolyLog[2, -(a*x)])/2 - (a^2*PolyLog[2, a*x])/2","A",5,5,18,0.2778,1,"{6014, 5916, 325, 206, 5912}"
169,1,58,0,0.0763112,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{x^4} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x])/x^4,x]","\frac{1}{3} a^3 \log \left(1-a^2 x^2\right)-\frac{2}{3} a^3 \log (x)+\frac{a^2 \tanh ^{-1}(a x)}{x}-\frac{a}{6 x^2}-\frac{\tanh ^{-1}(a x)}{3 x^3}","\frac{1}{3} a^3 \log \left(1-a^2 x^2\right)-\frac{2}{3} a^3 \log (x)+\frac{a^2 \tanh ^{-1}(a x)}{x}-\frac{a}{6 x^2}-\frac{\tanh ^{-1}(a x)}{3 x^3}",1,"-a/(6*x^2) - ArcTanh[a*x]/(3*x^3) + (a^2*ArcTanh[a*x])/x - (2*a^3*Log[x])/3 + (a^3*Log[1 - a^2*x^2])/3","A",10,7,18,0.3889,1,"{6014, 5916, 266, 44, 36, 29, 31}"
170,1,42,0,0.0302711,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{x^5} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x])/x^5,x]","-\frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{4 x^4}+\frac{a^3}{4 x}-\frac{a}{12 x^3}","-\frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{4 x^4}+\frac{a^3}{4 x}-\frac{a}{12 x^3}",1,"-a/(12*x^3) + a^3/(4*x) - ((1 - a^2*x^2)^2*ArcTanh[a*x])/(4*x^4)","A",3,2,18,0.1111,1,"{6008, 14}"
171,1,71,0,0.0876415,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{x^6} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x])/x^6,x]","\frac{a^3}{15 x^2}+\frac{1}{15} a^5 \log \left(1-a^2 x^2\right)+\frac{a^2 \tanh ^{-1}(a x)}{3 x^3}-\frac{2}{15} a^5 \log (x)-\frac{a}{20 x^4}-\frac{\tanh ^{-1}(a x)}{5 x^5}","\frac{a^3}{15 x^2}+\frac{1}{15} a^5 \log \left(1-a^2 x^2\right)+\frac{a^2 \tanh ^{-1}(a x)}{3 x^3}-\frac{2}{15} a^5 \log (x)-\frac{a}{20 x^4}-\frac{\tanh ^{-1}(a x)}{5 x^5}",1,"-a/(20*x^4) + a^3/(15*x^2) - ArcTanh[a*x]/(5*x^5) + (a^2*ArcTanh[a*x])/(3*x^3) - (2*a^5*Log[x])/15 + (a^5*Log[1 - a^2*x^2])/15","A",9,4,18,0.2222,1,"{6014, 5916, 266, 44}"
172,1,162,0,0.5794926,"\int x^4 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2 \, dx","Int[x^4*(1 - a^2*x^2)*ArcTanh[a*x]^2,x]","-\frac{2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{35 a^5}-\frac{2 x^3}{315 a^2}-\frac{1}{7} a^2 x^7 \tanh ^{-1}(a x)^2+\frac{2 x^2 \tanh ^{-1}(a x)}{35 a^3}+\frac{4 x}{105 a^4}+\frac{2 \tanh ^{-1}(a x)^2}{35 a^5}-\frac{4 \tanh ^{-1}(a x)}{105 a^5}-\frac{4 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{35 a^5}-\frac{1}{21} a x^6 \tanh ^{-1}(a x)+\frac{1}{5} x^5 \tanh ^{-1}(a x)^2+\frac{x^4 \tanh ^{-1}(a x)}{35 a}-\frac{x^5}{105}","-\frac{2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{35 a^5}-\frac{2 x^3}{315 a^2}-\frac{1}{7} a^2 x^7 \tanh ^{-1}(a x)^2+\frac{2 x^2 \tanh ^{-1}(a x)}{35 a^3}+\frac{4 x}{105 a^4}+\frac{2 \tanh ^{-1}(a x)^2}{35 a^5}-\frac{4 \tanh ^{-1}(a x)}{105 a^5}-\frac{4 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{35 a^5}-\frac{1}{21} a x^6 \tanh ^{-1}(a x)+\frac{1}{5} x^5 \tanh ^{-1}(a x)^2+\frac{x^4 \tanh ^{-1}(a x)}{35 a}-\frac{x^5}{105}",1,"(4*x)/(105*a^4) - (2*x^3)/(315*a^2) - x^5/105 - (4*ArcTanh[a*x])/(105*a^5) + (2*x^2*ArcTanh[a*x])/(35*a^3) + (x^4*ArcTanh[a*x])/(35*a) - (a*x^6*ArcTanh[a*x])/21 + (2*ArcTanh[a*x]^2)/(35*a^5) + (x^5*ArcTanh[a*x]^2)/5 - (a^2*x^7*ArcTanh[a*x]^2)/7 - (4*ArcTanh[a*x]*Log[2/(1 - a*x)])/(35*a^5) - (2*PolyLog[2, 1 - 2/(1 - a*x)])/(35*a^5)","A",34,10,20,0.5000,1,"{6014, 5916, 5980, 302, 206, 321, 5984, 5918, 2402, 2315}"
173,1,116,0,0.4398779,"\int x^3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2 \, dx","Int[x^3*(1 - a^2*x^2)*ArcTanh[a*x]^2,x]","-\frac{x^2}{180 a^2}+\frac{7 \log \left(1-a^2 x^2\right)}{90 a^4}-\frac{1}{6} a^2 x^6 \tanh ^{-1}(a x)^2+\frac{x \tanh ^{-1}(a x)}{6 a^3}-\frac{\tanh ^{-1}(a x)^2}{12 a^4}-\frac{1}{15} a x^5 \tanh ^{-1}(a x)+\frac{1}{4} x^4 \tanh ^{-1}(a x)^2+\frac{x^3 \tanh ^{-1}(a x)}{18 a}-\frac{x^4}{60}","-\frac{x^2}{180 a^2}+\frac{7 \log \left(1-a^2 x^2\right)}{90 a^4}-\frac{1}{6} a^2 x^6 \tanh ^{-1}(a x)^2+\frac{x \tanh ^{-1}(a x)}{6 a^3}-\frac{\tanh ^{-1}(a x)^2}{12 a^4}-\frac{1}{15} a x^5 \tanh ^{-1}(a x)+\frac{1}{4} x^4 \tanh ^{-1}(a x)^2+\frac{x^3 \tanh ^{-1}(a x)}{18 a}-\frac{x^4}{60}",1,"-x^2/(180*a^2) - x^4/60 + (x*ArcTanh[a*x])/(6*a^3) + (x^3*ArcTanh[a*x])/(18*a) - (a*x^5*ArcTanh[a*x])/15 - ArcTanh[a*x]^2/(12*a^4) + (x^4*ArcTanh[a*x]^2)/4 - (a^2*x^6*ArcTanh[a*x]^2)/6 + (7*Log[1 - a^2*x^2])/(90*a^4)","A",26,8,20,0.4000,1,"{6014, 5916, 5980, 266, 43, 5910, 260, 5948}"
174,1,138,0,0.4134876,"\int x^2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2 \, dx","Int[x^2*(1 - a^2*x^2)*ArcTanh[a*x]^2,x]","-\frac{2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{15 a^3}-\frac{1}{5} a^2 x^5 \tanh ^{-1}(a x)^2+\frac{x}{30 a^2}+\frac{2 \tanh ^{-1}(a x)^2}{15 a^3}-\frac{\tanh ^{-1}(a x)}{30 a^3}-\frac{4 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{15 a^3}-\frac{1}{10} a x^4 \tanh ^{-1}(a x)+\frac{1}{3} x^3 \tanh ^{-1}(a x)^2+\frac{2 x^2 \tanh ^{-1}(a x)}{15 a}-\frac{x^3}{30}","-\frac{2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{15 a^3}-\frac{1}{5} a^2 x^5 \tanh ^{-1}(a x)^2+\frac{x}{30 a^2}+\frac{2 \tanh ^{-1}(a x)^2}{15 a^3}-\frac{\tanh ^{-1}(a x)}{30 a^3}-\frac{4 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{15 a^3}-\frac{1}{10} a x^4 \tanh ^{-1}(a x)+\frac{1}{3} x^3 \tanh ^{-1}(a x)^2+\frac{2 x^2 \tanh ^{-1}(a x)}{15 a}-\frac{x^3}{30}",1,"x/(30*a^2) - x^3/30 - ArcTanh[a*x]/(30*a^3) + (2*x^2*ArcTanh[a*x])/(15*a) - (a*x^4*ArcTanh[a*x])/10 + (2*ArcTanh[a*x]^2)/(15*a^3) + (x^3*ArcTanh[a*x]^2)/3 - (a^2*x^5*ArcTanh[a*x]^2)/5 - (4*ArcTanh[a*x]*Log[2/(1 - a*x)])/(15*a^3) - (2*PolyLog[2, 1 - 2/(1 - a*x)])/(15*a^3)","A",24,10,20,0.5000,1,"{6014, 5916, 5980, 321, 206, 5984, 5918, 2402, 2315, 302}"
175,1,95,0,0.0486081,"\int x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2 \, dx","Int[x*(1 - a^2*x^2)*ArcTanh[a*x]^2,x]","\frac{1-a^2 x^2}{12 a^2}+\frac{\log \left(1-a^2 x^2\right)}{6 a^2}-\frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{4 a^2}+\frac{x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{6 a}+\frac{x \tanh ^{-1}(a x)}{3 a}","\frac{1-a^2 x^2}{12 a^2}+\frac{\log \left(1-a^2 x^2\right)}{6 a^2}-\frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{4 a^2}+\frac{x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{6 a}+\frac{x \tanh ^{-1}(a x)}{3 a}",1,"(1 - a^2*x^2)/(12*a^2) + (x*ArcTanh[a*x])/(3*a) + (x*(1 - a^2*x^2)*ArcTanh[a*x])/(6*a) - ((1 - a^2*x^2)^2*ArcTanh[a*x]^2)/(4*a^2) + Log[1 - a^2*x^2]/(6*a^2)","A",4,4,18,0.2222,1,"{5994, 5942, 5910, 260}"
176,1,115,0,0.1032599,"\int \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2 \, dx","Int[(1 - a^2*x^2)*ArcTanh[a*x]^2,x]","-\frac{2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{3 a}+\frac{1}{3} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2+\frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{3 a}+\frac{2}{3} x \tanh ^{-1}(a x)^2+\frac{2 \tanh ^{-1}(a x)^2}{3 a}-\frac{4 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{3 a}-\frac{x}{3}","-\frac{2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{3 a}+\frac{1}{3} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2+\frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{3 a}+\frac{2}{3} x \tanh ^{-1}(a x)^2+\frac{2 \tanh ^{-1}(a x)^2}{3 a}-\frac{4 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{3 a}-\frac{x}{3}",1,"-x/3 + ((1 - a^2*x^2)*ArcTanh[a*x])/(3*a) + (2*ArcTanh[a*x]^2)/(3*a) + (2*x*ArcTanh[a*x]^2)/3 + (x*(1 - a^2*x^2)*ArcTanh[a*x]^2)/3 - (4*ArcTanh[a*x]*Log[2/(1 - a*x)])/(3*a) - (2*PolyLog[2, 1 - 2/(1 - a*x)])/(3*a)","A",7,7,17,0.4118,1,"{5944, 5910, 5984, 5918, 2402, 2315, 8}"
177,1,146,0,0.3118798,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{x} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x]^2)/x,x]","\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)-\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)-\tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)+\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)-\frac{1}{2} \log \left(1-a^2 x^2\right)-\frac{1}{2} a^2 x^2 \tanh ^{-1}(a x)^2+2 \tanh ^{-1}\left(1-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2+\frac{1}{2} \tanh ^{-1}(a x)^2-a x \tanh ^{-1}(a x)","\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)-\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)-\tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)+\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)-\frac{1}{2} \log \left(1-a^2 x^2\right)-\frac{1}{2} a^2 x^2 \tanh ^{-1}(a x)^2+2 \tanh ^{-1}\left(1-\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2+\frac{1}{2} \tanh ^{-1}(a x)^2-a x \tanh ^{-1}(a x)",1,"-(a*x*ArcTanh[a*x]) + ArcTanh[a*x]^2/2 - (a^2*x^2*ArcTanh[a*x]^2)/2 + 2*ArcTanh[a*x]^2*ArcTanh[1 - 2/(1 - a*x)] - Log[1 - a^2*x^2]/2 - ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)] + ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 - a*x)] + PolyLog[3, 1 - 2/(1 - a*x)]/2 - PolyLog[3, -1 + 2/(1 - a*x)]/2","A",12,10,20,0.5000,1,"{6014, 5914, 6052, 5948, 6058, 6610, 5916, 5980, 5910, 260}"
178,1,93,0,0.2179106,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{x^2} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x]^2)/x^2,x]","a \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-a^2 x \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{x}+2 a \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)+2 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)","a \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-a^2 x \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{x}+2 a \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)+2 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)",1,"-(ArcTanh[a*x]^2/x) - a^2*x*ArcTanh[a*x]^2 + 2*a*ArcTanh[a*x]*Log[2/(1 - a*x)] + 2*a*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] + a*PolyLog[2, 1 - 2/(1 - a*x)] - a*PolyLog[2, -1 + 2/(1 + a*x)]","A",10,10,20,0.5000,1,"{6014, 5916, 5988, 5932, 2447, 5910, 5984, 5918, 2402, 2315}"
179,1,172,0,0.3344927,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{x^3} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x]^2)/x^3,x]","-\frac{1}{2} a^2 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)+\frac{1}{2} a^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)+a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)-a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)-\frac{1}{2} a^2 \log \left(1-a^2 x^2\right)+a^2 \log (x)+\frac{1}{2} a^2 \tanh ^{-1}(a x)^2-2 a^2 \tanh ^{-1}(a x)^2 \tanh ^{-1}\left(1-\frac{2}{1-a x}\right)-\frac{\tanh ^{-1}(a x)^2}{2 x^2}-\frac{a \tanh ^{-1}(a x)}{x}","-\frac{1}{2} a^2 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)+\frac{1}{2} a^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)+a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)-a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)-\frac{1}{2} a^2 \log \left(1-a^2 x^2\right)+a^2 \log (x)+\frac{1}{2} a^2 \tanh ^{-1}(a x)^2-2 a^2 \tanh ^{-1}(a x)^2 \tanh ^{-1}\left(1-\frac{2}{1-a x}\right)-\frac{\tanh ^{-1}(a x)^2}{2 x^2}-\frac{a \tanh ^{-1}(a x)}{x}",1,"-((a*ArcTanh[a*x])/x) + (a^2*ArcTanh[a*x]^2)/2 - ArcTanh[a*x]^2/(2*x^2) - 2*a^2*ArcTanh[a*x]^2*ArcTanh[1 - 2/(1 - a*x)] + a^2*Log[x] - (a^2*Log[1 - a^2*x^2])/2 + a^2*ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)] - a^2*ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 - a*x)] - (a^2*PolyLog[3, 1 - 2/(1 - a*x)])/2 + (a^2*PolyLog[3, -1 + 2/(1 - a*x)])/2","A",15,12,20,0.6000,1,"{6014, 5916, 5982, 266, 36, 29, 31, 5948, 5914, 6052, 6058, 6610}"
180,1,116,0,0.3075881,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{x^4} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x]^2)/x^4,x]","\frac{2}{3} a^3 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2}{3 x}-\frac{2}{3} a^3 \tanh ^{-1}(a x)^2+\frac{1}{3} a^3 \tanh ^{-1}(a x)+\frac{a^2 \tanh ^{-1}(a x)^2}{x}-\frac{4}{3} a^3 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{a \tanh ^{-1}(a x)}{3 x^2}-\frac{\tanh ^{-1}(a x)^2}{3 x^3}","\frac{2}{3} a^3 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2}{3 x}-\frac{2}{3} a^3 \tanh ^{-1}(a x)^2+\frac{1}{3} a^3 \tanh ^{-1}(a x)+\frac{a^2 \tanh ^{-1}(a x)^2}{x}-\frac{4}{3} a^3 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{a \tanh ^{-1}(a x)}{3 x^2}-\frac{\tanh ^{-1}(a x)^2}{3 x^3}",1,"-a^2/(3*x) + (a^3*ArcTanh[a*x])/3 - (a*ArcTanh[a*x])/(3*x^2) - (2*a^3*ArcTanh[a*x]^2)/3 - ArcTanh[a*x]^2/(3*x^3) + (a^2*ArcTanh[a*x]^2)/x - (4*a^3*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)])/3 + (2*a^3*PolyLog[2, -1 + 2/(1 + a*x)])/3","A",13,8,20,0.4000,1,"{6014, 5916, 5982, 325, 206, 5988, 5932, 2447}"
181,1,89,0,0.1078311,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{x^5} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x]^2)/x^5,x]","-\frac{a^2}{12 x^2}+\frac{1}{6} a^4 \log \left(1-a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{4 x^4}-\frac{1}{3} a^4 \log (x)+\frac{a^3 \tanh ^{-1}(a x)}{2 x}-\frac{a \tanh ^{-1}(a x)}{6 x^3}","-\frac{a^2}{12 x^2}+\frac{1}{6} a^4 \log \left(1-a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{4 x^4}-\frac{1}{3} a^4 \log (x)+\frac{a^3 \tanh ^{-1}(a x)}{2 x}-\frac{a \tanh ^{-1}(a x)}{6 x^3}",1,"-a^2/(12*x^2) - (a*ArcTanh[a*x])/(6*x^3) + (a^3*ArcTanh[a*x])/(2*x) - ((1 - a^2*x^2)^2*ArcTanh[a*x]^2)/(4*x^4) - (a^4*Log[x])/3 + (a^4*Log[1 - a^2*x^2])/6","A",11,8,20,0.4000,1,"{6008, 6014, 5916, 266, 44, 36, 29, 31}"
182,1,143,0,0.4453566,"\int \frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{x^6} \, dx","Int[((1 - a^2*x^2)*ArcTanh[a*x]^2)/x^6,x]","\frac{2}{15} a^5 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2}{30 x^3}+\frac{2 a^3 \tanh ^{-1}(a x)}{15 x^2}+\frac{a^2 \tanh ^{-1}(a x)^2}{3 x^3}+\frac{a^4}{30 x}-\frac{2}{15} a^5 \tanh ^{-1}(a x)^2-\frac{1}{30} a^5 \tanh ^{-1}(a x)-\frac{4}{15} a^5 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{a \tanh ^{-1}(a x)}{10 x^4}-\frac{\tanh ^{-1}(a x)^2}{5 x^5}","\frac{2}{15} a^5 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2}{30 x^3}+\frac{2 a^3 \tanh ^{-1}(a x)}{15 x^2}+\frac{a^2 \tanh ^{-1}(a x)^2}{3 x^3}+\frac{a^4}{30 x}-\frac{2}{15} a^5 \tanh ^{-1}(a x)^2-\frac{1}{30} a^5 \tanh ^{-1}(a x)-\frac{4}{15} a^5 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{a \tanh ^{-1}(a x)}{10 x^4}-\frac{\tanh ^{-1}(a x)^2}{5 x^5}",1,"-a^2/(30*x^3) + a^4/(30*x) - (a^5*ArcTanh[a*x])/30 - (a*ArcTanh[a*x])/(10*x^4) + (2*a^3*ArcTanh[a*x])/(15*x^2) - (2*a^5*ArcTanh[a*x]^2)/15 - ArcTanh[a*x]^2/(5*x^5) + (a^2*ArcTanh[a*x]^2)/(3*x^3) - (4*a^5*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)])/15 + (2*a^5*PolyLog[2, -1 + 2/(1 + a*x)])/15","A",22,8,20,0.4000,1,"{6014, 5916, 5982, 325, 206, 5988, 5932, 2447}"
183,1,157,0,0.1921045,"\int \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3 \, dx","Int[(1 - a^2*x^2)*ArcTanh[a*x]^3,x]","\frac{\text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a}-\frac{2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a}-\frac{\log \left(1-a^2 x^2\right)}{2 a}+\frac{1}{3} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3+\frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{2 a}+\frac{2}{3} x \tanh ^{-1}(a x)^3+\frac{2 \tanh ^{-1}(a x)^3}{3 a}-x \tanh ^{-1}(a x)-\frac{2 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a}","\frac{\text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{a}-\frac{2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a}-\frac{\log \left(1-a^2 x^2\right)}{2 a}+\frac{1}{3} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3+\frac{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{2 a}+\frac{2}{3} x \tanh ^{-1}(a x)^3+\frac{2 \tanh ^{-1}(a x)^3}{3 a}-x \tanh ^{-1}(a x)-\frac{2 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a}",1,"-(x*ArcTanh[a*x]) + ((1 - a^2*x^2)*ArcTanh[a*x]^2)/(2*a) + (2*ArcTanh[a*x]^3)/(3*a) + (2*x*ArcTanh[a*x]^3)/3 + (x*(1 - a^2*x^2)*ArcTanh[a*x]^3)/3 - (2*ArcTanh[a*x]^2*Log[2/(1 - a*x)])/a - Log[1 - a^2*x^2]/(2*a) - (2*ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/a + PolyLog[3, 1 - 2/(1 - a*x)]/a","A",8,8,17,0.4706,1,"{5944, 5910, 5984, 5918, 5948, 6058, 6610, 260}"
184,1,193,0,0.2265026,"\int \frac{x \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{1-x^2} \, dx","Int[(x*ArcTanh[x/Sqrt[2]])/(1 - x^2),x]","-\frac{1}{2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{2}}{x+\sqrt{2}}\right)+\frac{1}{4} \text{PolyLog}\left(2,\frac{4 (1-x)}{\left(2-\sqrt{2}\right) \left(x+\sqrt{2}\right)}+1\right)+\frac{1}{4} \text{PolyLog}\left(2,1-\frac{4 (x+1)}{\left(2+\sqrt{2}\right) \left(x+\sqrt{2}\right)}\right)+\log \left(\frac{2 \sqrt{2}}{x+\sqrt{2}}\right) \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)-\frac{1}{2} \log \left(-\frac{4 (1-x)}{\left(2-\sqrt{2}\right) \left(x+\sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)-\frac{1}{2} \log \left(\frac{4 (x+1)}{\left(2+\sqrt{2}\right) \left(x+\sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)","-\frac{1}{2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{2}}{x+\sqrt{2}}\right)+\frac{1}{4} \text{PolyLog}\left(2,\frac{4 (1-x)}{\left(2-\sqrt{2}\right) \left(x+\sqrt{2}\right)}+1\right)+\frac{1}{4} \text{PolyLog}\left(2,1-\frac{4 (x+1)}{\left(2+\sqrt{2}\right) \left(x+\sqrt{2}\right)}\right)+\log \left(\frac{2 \sqrt{2}}{x+\sqrt{2}}\right) \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)-\frac{1}{2} \log \left(-\frac{4 (1-x)}{\left(2-\sqrt{2}\right) \left(x+\sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)-\frac{1}{2} \log \left(\frac{4 (x+1)}{\left(2+\sqrt{2}\right) \left(x+\sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"ArcTanh[x/Sqrt[2]]*Log[(2*Sqrt[2])/(Sqrt[2] + x)] - (ArcTanh[x/Sqrt[2]]*Log[(-4*(1 - x))/((2 - Sqrt[2])*(Sqrt[2] + x))])/2 - (ArcTanh[x/Sqrt[2]]*Log[(4*(1 + x))/((2 + Sqrt[2])*(Sqrt[2] + x))])/2 - PolyLog[2, 1 - (2*Sqrt[2])/(Sqrt[2] + x)]/2 + PolyLog[2, 1 + (4*(1 - x))/((2 - Sqrt[2])*(Sqrt[2] + x))]/4 + PolyLog[2, 1 - (4*(1 + x))/((2 + Sqrt[2])*(Sqrt[2] + x))]/4","A",10,5,19,0.2632,1,"{5992, 5920, 2402, 2315, 2447}"
185,0,0,0,0.0250282,"\int \frac{x \left(1-a^2 x^2\right)}{\tanh ^{-1}(a x)} \, dx","Int[(x*(1 - a^2*x^2))/ArcTanh[a*x],x]","\int \frac{x \left(1-a^2 x^2\right)}{\tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x \left(1-a^2 x^2\right)}{\tanh ^{-1}(a x)},x\right)",0,"Defer[Int][(x*(1 - a^2*x^2))/ArcTanh[a*x], x]","A",0,0,0,0,-1,"{}"
186,0,0,0,0.0144755,"\int \frac{1-a^2 x^2}{\tanh ^{-1}(a x)} \, dx","Int[(1 - a^2*x^2)/ArcTanh[a*x],x]","\int \frac{1-a^2 x^2}{\tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1-a^2 x^2}{\tanh ^{-1}(a x)},x\right)",0,"Defer[Int][(1 - a^2*x^2)/ArcTanh[a*x], x]","A",0,0,0,0,-1,"{}"
187,0,0,0,0.0365073,"\int \frac{1-a^2 x^2}{x \tanh ^{-1}(a x)} \, dx","Int[(1 - a^2*x^2)/(x*ArcTanh[a*x]),x]","\int \frac{1-a^2 x^2}{x \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1-a^2 x^2}{x \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][(1 - a^2*x^2)/(x*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
188,0,0,0,0.0243652,"\int \frac{x \left(1-a^2 x^2\right)}{\tanh ^{-1}(a x)^2} \, dx","Int[(x*(1 - a^2*x^2))/ArcTanh[a*x]^2,x]","\int \frac{x \left(1-a^2 x^2\right)}{\tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{x \left(1-a^2 x^2\right)}{\tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][(x*(1 - a^2*x^2))/ArcTanh[a*x]^2, x]","A",0,0,0,0,-1,"{}"
189,0,0,0,0.013154,"\int \frac{1-a^2 x^2}{\tanh ^{-1}(a x)^2} \, dx","Int[(1 - a^2*x^2)/ArcTanh[a*x]^2,x]","\int \frac{1-a^2 x^2}{\tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1-a^2 x^2}{\tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][(1 - a^2*x^2)/ArcTanh[a*x]^2, x]","A",0,0,0,0,-1,"{}"
190,0,0,0,0.0338011,"\int \frac{1-a^2 x^2}{x \tanh ^{-1}(a x)^2} \, dx","Int[(1 - a^2*x^2)/(x*ArcTanh[a*x]^2),x]","\int \frac{1-a^2 x^2}{x \tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1-a^2 x^2}{x \tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][(1 - a^2*x^2)/(x*ArcTanh[a*x]^2), x]","A",0,0,0,0,-1,"{}"
191,0,0,0,0.0132488,"\int \frac{1-a^2 x^2}{\tanh ^{-1}(a x)^3} \, dx","Int[(1 - a^2*x^2)/ArcTanh[a*x]^3,x]","\int \frac{1-a^2 x^2}{\tanh ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{1-a^2 x^2}{\tanh ^{-1}(a x)^3},x\right)",0,"Defer[Int][(1 - a^2*x^2)/ArcTanh[a*x]^3, x]","A",0,0,0,0,-1,"{}"
192,1,96,0,0.1888286,"\int x^4 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x) \, dx","Int[x^4*(1 - a^2*x^2)^2*ArcTanh[a*x],x]","\frac{a^3 x^8}{72}+\frac{4 x^2}{315 a^3}+\frac{4 \log \left(1-a^2 x^2\right)}{315 a^5}+\frac{1}{9} a^4 x^9 \tanh ^{-1}(a x)-\frac{2}{7} a^2 x^7 \tanh ^{-1}(a x)-\frac{11 a x^6}{378}+\frac{2 x^4}{315 a}+\frac{1}{5} x^5 \tanh ^{-1}(a x)","\frac{a^3 x^8}{72}+\frac{4 x^2}{315 a^3}+\frac{4 \log \left(1-a^2 x^2\right)}{315 a^5}+\frac{1}{9} a^4 x^9 \tanh ^{-1}(a x)-\frac{2}{7} a^2 x^7 \tanh ^{-1}(a x)-\frac{11 a x^6}{378}+\frac{2 x^4}{315 a}+\frac{1}{5} x^5 \tanh ^{-1}(a x)",1,"(4*x^2)/(315*a^3) + (2*x^4)/(315*a) - (11*a*x^6)/378 + (a^3*x^8)/72 + (x^5*ArcTanh[a*x])/5 - (2*a^2*x^7*ArcTanh[a*x])/7 + (a^4*x^9*ArcTanh[a*x])/9 + (4*Log[1 - a^2*x^2])/(315*a^5)","A",14,4,20,0.2000,1,"{6012, 5916, 266, 43}"
193,1,87,0,0.1374941,"\int x^3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x) \, dx","Int[x^3*(1 - a^2*x^2)^2*ArcTanh[a*x],x]","\frac{a^3 x^7}{56}+\frac{1}{8} a^4 x^8 \tanh ^{-1}(a x)-\frac{1}{3} a^2 x^6 \tanh ^{-1}(a x)+\frac{x}{24 a^3}-\frac{\tanh ^{-1}(a x)}{24 a^4}-\frac{a x^5}{24}+\frac{x^3}{72 a}+\frac{1}{4} x^4 \tanh ^{-1}(a x)","\frac{a^3 x^7}{56}+\frac{1}{8} a^4 x^8 \tanh ^{-1}(a x)-\frac{1}{3} a^2 x^6 \tanh ^{-1}(a x)+\frac{x}{24 a^3}-\frac{\tanh ^{-1}(a x)}{24 a^4}-\frac{a x^5}{24}+\frac{x^3}{72 a}+\frac{1}{4} x^4 \tanh ^{-1}(a x)",1,"x/(24*a^3) + x^3/(72*a) - (a*x^5)/24 + (a^3*x^7)/56 - ArcTanh[a*x]/(24*a^4) + (x^4*ArcTanh[a*x])/4 - (a^2*x^6*ArcTanh[a*x])/3 + (a^4*x^8*ArcTanh[a*x])/8","A",14,4,20,0.2000,1,"{6012, 5916, 302, 206}"
194,1,86,0,0.1614475,"\int x^2 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x) \, dx","Int[x^2*(1 - a^2*x^2)^2*ArcTanh[a*x],x]","\frac{a^3 x^6}{42}+\frac{4 \log \left(1-a^2 x^2\right)}{105 a^3}+\frac{1}{7} a^4 x^7 \tanh ^{-1}(a x)-\frac{2}{5} a^2 x^5 \tanh ^{-1}(a x)-\frac{9 a x^4}{140}+\frac{4 x^2}{105 a}+\frac{1}{3} x^3 \tanh ^{-1}(a x)","\frac{a^3 x^6}{42}+\frac{4 \log \left(1-a^2 x^2\right)}{105 a^3}+\frac{1}{7} a^4 x^7 \tanh ^{-1}(a x)-\frac{2}{5} a^2 x^5 \tanh ^{-1}(a x)-\frac{9 a x^4}{140}+\frac{4 x^2}{105 a}+\frac{1}{3} x^3 \tanh ^{-1}(a x)",1,"(4*x^2)/(105*a) - (9*a*x^4)/140 + (a^3*x^6)/42 + (x^3*ArcTanh[a*x])/3 - (2*a^2*x^5*ArcTanh[a*x])/5 + (a^4*x^7*ArcTanh[a*x])/7 + (4*Log[1 - a^2*x^2])/(105*a^3)","A",14,4,20,0.2000,1,"{6012, 5916, 266, 43}"
195,1,50,0,0.0370326,"\int x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x) \, dx","Int[x*(1 - a^2*x^2)^2*ArcTanh[a*x],x]","\frac{a^3 x^5}{30}-\frac{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}{6 a^2}-\frac{a x^3}{9}+\frac{x}{6 a}","\frac{a^3 x^5}{30}-\frac{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}{6 a^2}-\frac{a x^3}{9}+\frac{x}{6 a}",1,"x/(6*a) - (a*x^3)/9 + (a^3*x^5)/30 - ((1 - a^2*x^2)^3*ArcTanh[a*x])/(6*a^2)","A",3,2,18,0.1111,1,"{5994, 194}"
196,1,104,0,0.0437777,"\int \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x) \, dx","Int[(1 - a^2*x^2)^2*ArcTanh[a*x],x]","\frac{\left(1-a^2 x^2\right)^2}{20 a}+\frac{2 \left(1-a^2 x^2\right)}{15 a}+\frac{4 \log \left(1-a^2 x^2\right)}{15 a}+\frac{1}{5} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)+\frac{4}{15} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)+\frac{8}{15} x \tanh ^{-1}(a x)","\frac{\left(1-a^2 x^2\right)^2}{20 a}+\frac{2 \left(1-a^2 x^2\right)}{15 a}+\frac{4 \log \left(1-a^2 x^2\right)}{15 a}+\frac{1}{5} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)+\frac{4}{15} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)+\frac{8}{15} x \tanh ^{-1}(a x)",1,"(2*(1 - a^2*x^2))/(15*a) + (1 - a^2*x^2)^2/(20*a) + (8*x*ArcTanh[a*x])/15 + (4*x*(1 - a^2*x^2)*ArcTanh[a*x])/15 + (x*(1 - a^2*x^2)^2*ArcTanh[a*x])/5 + (4*Log[1 - a^2*x^2])/(15*a)","A",4,3,17,0.1765,1,"{5942, 5910, 260}"
197,1,70,0,0.0974804,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{x} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x])/x,x]","-\frac{1}{2} \text{PolyLog}(2,-a x)+\frac{1}{2} \text{PolyLog}(2,a x)+\frac{a^3 x^3}{12}+\frac{1}{4} a^4 x^4 \tanh ^{-1}(a x)-a^2 x^2 \tanh ^{-1}(a x)-\frac{3 a x}{4}+\frac{3}{4} \tanh ^{-1}(a x)","-\frac{1}{2} \text{PolyLog}(2,-a x)+\frac{1}{2} \text{PolyLog}(2,a x)+\frac{a^3 x^3}{12}+\frac{1}{4} a^4 x^4 \tanh ^{-1}(a x)-a^2 x^2 \tanh ^{-1}(a x)-\frac{3 a x}{4}+\frac{3}{4} \tanh ^{-1}(a x)",1,"(-3*a*x)/4 + (a^3*x^3)/12 + (3*ArcTanh[a*x])/4 - a^2*x^2*ArcTanh[a*x] + (a^4*x^4*ArcTanh[a*x])/4 - PolyLog[2, -(a*x)]/2 + PolyLog[2, a*x]/2","A",10,6,20,0.3000,1,"{6012, 5912, 5916, 321, 206, 302}"
198,1,64,0,0.1114578,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{x^2} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x])/x^2,x]","\frac{a^3 x^2}{6}-\frac{4}{3} a \log \left(1-a^2 x^2\right)+\frac{1}{3} a^4 x^3 \tanh ^{-1}(a x)-2 a^2 x \tanh ^{-1}(a x)+a \log (x)-\frac{\tanh ^{-1}(a x)}{x}","\frac{a^3 x^2}{6}-\frac{4}{3} a \log \left(1-a^2 x^2\right)+\frac{1}{3} a^4 x^3 \tanh ^{-1}(a x)-2 a^2 x \tanh ^{-1}(a x)+a \log (x)-\frac{\tanh ^{-1}(a x)}{x}",1,"(a^3*x^2)/6 - ArcTanh[a*x]/x - 2*a^2*x*ArcTanh[a*x] + (a^4*x^3*ArcTanh[a*x])/3 + a*Log[x] - (4*a*Log[1 - a^2*x^2])/3","A",13,9,20,0.4500,1,"{6012, 5910, 260, 5916, 266, 36, 29, 31, 43}"
199,1,62,0,0.0941136,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{x^3} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x])/x^3,x]","a^2 \text{PolyLog}(2,-a x)-a^2 \text{PolyLog}(2,a x)+\frac{1}{2} a^4 x^2 \tanh ^{-1}(a x)+\frac{a^3 x}{2}-\frac{\tanh ^{-1}(a x)}{2 x^2}-\frac{a}{2 x}","a^2 \text{PolyLog}(2,-a x)-a^2 \text{PolyLog}(2,a x)+\frac{1}{2} a^4 x^2 \tanh ^{-1}(a x)+\frac{a^3 x}{2}-\frac{\tanh ^{-1}(a x)}{2 x^2}-\frac{a}{2 x}",1,"-a/(2*x) + (a^3*x)/2 - ArcTanh[a*x]/(2*x^2) + (a^4*x^2*ArcTanh[a*x])/2 + a^2*PolyLog[2, -(a*x)] - a^2*PolyLog[2, a*x]","A",9,6,20,0.3000,1,"{6012, 5916, 325, 206, 5912, 321}"
200,1,68,0,0.1097642,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{x^4} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x])/x^4,x]","\frac{4}{3} a^3 \log \left(1-a^2 x^2\right)-\frac{5}{3} a^3 \log (x)+a^4 x \tanh ^{-1}(a x)+\frac{2 a^2 \tanh ^{-1}(a x)}{x}-\frac{a}{6 x^2}-\frac{\tanh ^{-1}(a x)}{3 x^3}","\frac{4}{3} a^3 \log \left(1-a^2 x^2\right)-\frac{5}{3} a^3 \log (x)+a^4 x \tanh ^{-1}(a x)+\frac{2 a^2 \tanh ^{-1}(a x)}{x}-\frac{a}{6 x^2}-\frac{\tanh ^{-1}(a x)}{3 x^3}",1,"-a/(6*x^2) - ArcTanh[a*x]/(3*x^3) + (2*a^2*ArcTanh[a*x])/x + a^4*x*ArcTanh[a*x] - (5*a^3*Log[x])/3 + (4*a^3*Log[1 - a^2*x^2])/3","A",13,9,20,0.4500,1,"{6012, 5910, 260, 5916, 266, 44, 36, 29, 31}"
201,1,77,0,0.1009284,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{x^5} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x])/x^5,x]","-\frac{1}{2} a^4 \text{PolyLog}(2,-a x)+\frac{1}{2} a^4 \text{PolyLog}(2,a x)+\frac{a^2 \tanh ^{-1}(a x)}{x^2}+\frac{3 a^3}{4 x}-\frac{3}{4} a^4 \tanh ^{-1}(a x)-\frac{a}{12 x^3}-\frac{\tanh ^{-1}(a x)}{4 x^4}","-\frac{1}{2} a^4 \text{PolyLog}(2,-a x)+\frac{1}{2} a^4 \text{PolyLog}(2,a x)+\frac{a^2 \tanh ^{-1}(a x)}{x^2}+\frac{3 a^3}{4 x}-\frac{3}{4} a^4 \tanh ^{-1}(a x)-\frac{a}{12 x^3}-\frac{\tanh ^{-1}(a x)}{4 x^4}",1,"-a/(12*x^3) + (3*a^3)/(4*x) - (3*a^4*ArcTanh[a*x])/4 - ArcTanh[a*x]/(4*x^4) + (a^2*ArcTanh[a*x])/x^2 - (a^4*PolyLog[2, -(a*x)])/2 + (a^4*PolyLog[2, a*x])/2","A",10,5,20,0.2500,1,"{6012, 5916, 325, 206, 5912}"
202,1,83,0,0.1379518,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{x^6} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x])/x^6,x]","\frac{7 a^3}{30 x^2}-\frac{4}{15} a^5 \log \left(1-a^2 x^2\right)+\frac{2 a^2 \tanh ^{-1}(a x)}{3 x^3}+\frac{8}{15} a^5 \log (x)-\frac{a^4 \tanh ^{-1}(a x)}{x}-\frac{a}{20 x^4}-\frac{\tanh ^{-1}(a x)}{5 x^5}","\frac{7 a^3}{30 x^2}-\frac{4}{15} a^5 \log \left(1-a^2 x^2\right)+\frac{2 a^2 \tanh ^{-1}(a x)}{3 x^3}+\frac{8}{15} a^5 \log (x)-\frac{a^4 \tanh ^{-1}(a x)}{x}-\frac{a}{20 x^4}-\frac{\tanh ^{-1}(a x)}{5 x^5}",1,"-a/(20*x^4) + (7*a^3)/(30*x^2) - ArcTanh[a*x]/(5*x^5) + (2*a^2*ArcTanh[a*x])/(3*x^3) - (a^4*ArcTanh[a*x])/x + (8*a^5*Log[x])/15 - (4*a^5*Log[1 - a^2*x^2])/15","A",15,7,20,0.3500,1,"{6012, 5916, 266, 44, 36, 29, 31}"
203,1,202,0,1.0245533,"\int x^4 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2 \, dx","Int[x^4*(1 - a^2*x^2)^2*ArcTanh[a*x]^2,x]","-\frac{8 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{315 a^5}+\frac{a^2 x^7}{252}-\frac{67 x^3}{11340 a^2}+\frac{1}{9} a^4 x^9 \tanh ^{-1}(a x)^2+\frac{1}{36} a^3 x^8 \tanh ^{-1}(a x)-\frac{2}{7} a^2 x^7 \tanh ^{-1}(a x)^2+\frac{8 x^2 \tanh ^{-1}(a x)}{315 a^3}+\frac{29 x}{3780 a^4}+\frac{8 \tanh ^{-1}(a x)^2}{315 a^5}-\frac{29 \tanh ^{-1}(a x)}{3780 a^5}-\frac{16 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{315 a^5}-\frac{11}{189} a x^6 \tanh ^{-1}(a x)+\frac{1}{5} x^5 \tanh ^{-1}(a x)^2+\frac{4 x^4 \tanh ^{-1}(a x)}{315 a}-\frac{23 x^5}{3780}","-\frac{8 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{315 a^5}+\frac{a^2 x^7}{252}-\frac{67 x^3}{11340 a^2}+\frac{1}{9} a^4 x^9 \tanh ^{-1}(a x)^2+\frac{1}{36} a^3 x^8 \tanh ^{-1}(a x)-\frac{2}{7} a^2 x^7 \tanh ^{-1}(a x)^2+\frac{8 x^2 \tanh ^{-1}(a x)}{315 a^3}+\frac{29 x}{3780 a^4}+\frac{8 \tanh ^{-1}(a x)^2}{315 a^5}-\frac{29 \tanh ^{-1}(a x)}{3780 a^5}-\frac{16 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{315 a^5}-\frac{11}{189} a x^6 \tanh ^{-1}(a x)+\frac{1}{5} x^5 \tanh ^{-1}(a x)^2+\frac{4 x^4 \tanh ^{-1}(a x)}{315 a}-\frac{23 x^5}{3780}",1,"(29*x)/(3780*a^4) - (67*x^3)/(11340*a^2) - (23*x^5)/3780 + (a^2*x^7)/252 - (29*ArcTanh[a*x])/(3780*a^5) + (8*x^2*ArcTanh[a*x])/(315*a^3) + (4*x^4*ArcTanh[a*x])/(315*a) - (11*a*x^6*ArcTanh[a*x])/189 + (a^3*x^8*ArcTanh[a*x])/36 + (8*ArcTanh[a*x]^2)/(315*a^5) + (x^5*ArcTanh[a*x]^2)/5 - (2*a^2*x^7*ArcTanh[a*x]^2)/7 + (a^4*x^9*ArcTanh[a*x]^2)/9 - (16*ArcTanh[a*x]*Log[2/(1 - a*x)])/(315*a^5) - (8*PolyLog[2, 1 - 2/(1 - a*x)])/(315*a^5)","A",59,10,22,0.4545,1,"{6012, 5916, 5980, 302, 206, 321, 5984, 5918, 2402, 2315}"
204,1,156,0,0.8191826,"\int x^3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2 \, dx","Int[x^3*(1 - a^2*x^2)^2*ArcTanh[a*x]^2,x]","\frac{a^2 x^6}{168}-\frac{5 x^2}{504 a^2}+\frac{2 \log \left(1-a^2 x^2\right)}{63 a^4}+\frac{1}{8} a^4 x^8 \tanh ^{-1}(a x)^2+\frac{1}{28} a^3 x^7 \tanh ^{-1}(a x)-\frac{1}{3} a^2 x^6 \tanh ^{-1}(a x)^2+\frac{x \tanh ^{-1}(a x)}{12 a^3}-\frac{\tanh ^{-1}(a x)^2}{24 a^4}-\frac{1}{12} a x^5 \tanh ^{-1}(a x)+\frac{1}{4} x^4 \tanh ^{-1}(a x)^2+\frac{x^3 \tanh ^{-1}(a x)}{36 a}-\frac{x^4}{84}","\frac{a^2 x^6}{168}-\frac{5 x^2}{504 a^2}+\frac{2 \log \left(1-a^2 x^2\right)}{63 a^4}+\frac{1}{8} a^4 x^8 \tanh ^{-1}(a x)^2+\frac{1}{28} a^3 x^7 \tanh ^{-1}(a x)-\frac{1}{3} a^2 x^6 \tanh ^{-1}(a x)^2+\frac{x \tanh ^{-1}(a x)}{12 a^3}-\frac{\tanh ^{-1}(a x)^2}{24 a^4}-\frac{1}{12} a x^5 \tanh ^{-1}(a x)+\frac{1}{4} x^4 \tanh ^{-1}(a x)^2+\frac{x^3 \tanh ^{-1}(a x)}{36 a}-\frac{x^4}{84}",1,"(-5*x^2)/(504*a^2) - x^4/84 + (a^2*x^6)/168 + (x*ArcTanh[a*x])/(12*a^3) + (x^3*ArcTanh[a*x])/(36*a) - (a*x^5*ArcTanh[a*x])/12 + (a^3*x^7*ArcTanh[a*x])/28 - ArcTanh[a*x]^2/(24*a^4) + (x^4*ArcTanh[a*x]^2)/4 - (a^2*x^6*ArcTanh[a*x]^2)/3 + (a^4*x^8*ArcTanh[a*x]^2)/8 + (2*Log[1 - a^2*x^2])/(63*a^4)","A",47,8,22,0.3636,1,"{6012, 5916, 5980, 266, 43, 5910, 260, 5948}"
205,1,178,0,0.7792308,"\int x^2 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2 \, dx","Int[x^2*(1 - a^2*x^2)^2*ArcTanh[a*x]^2,x]","-\frac{8 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{105 a^3}+\frac{a^2 x^5}{105}+\frac{1}{7} a^4 x^7 \tanh ^{-1}(a x)^2+\frac{1}{21} a^3 x^6 \tanh ^{-1}(a x)-\frac{2}{5} a^2 x^5 \tanh ^{-1}(a x)^2-\frac{x}{210 a^2}+\frac{8 \tanh ^{-1}(a x)^2}{105 a^3}+\frac{\tanh ^{-1}(a x)}{210 a^3}-\frac{16 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{105 a^3}-\frac{9}{70} a x^4 \tanh ^{-1}(a x)+\frac{1}{3} x^3 \tanh ^{-1}(a x)^2+\frac{8 x^2 \tanh ^{-1}(a x)}{105 a}-\frac{17 x^3}{630}","-\frac{8 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{105 a^3}+\frac{a^2 x^5}{105}+\frac{1}{7} a^4 x^7 \tanh ^{-1}(a x)^2+\frac{1}{21} a^3 x^6 \tanh ^{-1}(a x)-\frac{2}{5} a^2 x^5 \tanh ^{-1}(a x)^2-\frac{x}{210 a^2}+\frac{8 \tanh ^{-1}(a x)^2}{105 a^3}+\frac{\tanh ^{-1}(a x)}{210 a^3}-\frac{16 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{105 a^3}-\frac{9}{70} a x^4 \tanh ^{-1}(a x)+\frac{1}{3} x^3 \tanh ^{-1}(a x)^2+\frac{8 x^2 \tanh ^{-1}(a x)}{105 a}-\frac{17 x^3}{630}",1,"-x/(210*a^2) - (17*x^3)/630 + (a^2*x^5)/105 + ArcTanh[a*x]/(210*a^3) + (8*x^2*ArcTanh[a*x])/(105*a) - (9*a*x^4*ArcTanh[a*x])/70 + (a^3*x^6*ArcTanh[a*x])/21 + (8*ArcTanh[a*x]^2)/(105*a^3) + (x^3*ArcTanh[a*x]^2)/3 - (2*a^2*x^5*ArcTanh[a*x]^2)/5 + (a^4*x^7*ArcTanh[a*x]^2)/7 - (16*ArcTanh[a*x]*Log[2/(1 - a*x)])/(105*a^3) - (8*PolyLog[2, 1 - 2/(1 - a*x)])/(105*a^3)","A",44,10,22,0.4545,1,"{6012, 5916, 5980, 321, 206, 5984, 5918, 2402, 2315, 302}"
206,1,138,0,0.088121,"\int x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2 \, dx","Int[x*(1 - a^2*x^2)^2*ArcTanh[a*x]^2,x]","\frac{\left(1-a^2 x^2\right)^2}{60 a^2}+\frac{2 \left(1-a^2 x^2\right)}{45 a^2}+\frac{4 \log \left(1-a^2 x^2\right)}{45 a^2}-\frac{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2}{6 a^2}+\frac{x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{15 a}+\frac{4 x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{45 a}+\frac{8 x \tanh ^{-1}(a x)}{45 a}","\frac{\left(1-a^2 x^2\right)^2}{60 a^2}+\frac{2 \left(1-a^2 x^2\right)}{45 a^2}+\frac{4 \log \left(1-a^2 x^2\right)}{45 a^2}-\frac{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2}{6 a^2}+\frac{x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{15 a}+\frac{4 x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{45 a}+\frac{8 x \tanh ^{-1}(a x)}{45 a}",1,"(2*(1 - a^2*x^2))/(45*a^2) + (1 - a^2*x^2)^2/(60*a^2) + (8*x*ArcTanh[a*x])/(45*a) + (4*x*(1 - a^2*x^2)*ArcTanh[a*x])/(45*a) + (x*(1 - a^2*x^2)^2*ArcTanh[a*x])/(15*a) - ((1 - a^2*x^2)^3*ArcTanh[a*x]^2)/(6*a^2) + (4*Log[1 - a^2*x^2])/(45*a^2)","A",5,4,20,0.2000,1,"{5994, 5942, 5910, 260}"
207,1,171,0,0.1334532,"\int \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2 \, dx","Int[(1 - a^2*x^2)^2*ArcTanh[a*x]^2,x]","-\frac{8 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{15 a}+\frac{a^2 x^3}{30}+\frac{1}{5} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2+\frac{4}{15} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2+\frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{10 a}+\frac{4 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{15 a}+\frac{8}{15} x \tanh ^{-1}(a x)^2+\frac{8 \tanh ^{-1}(a x)^2}{15 a}-\frac{16 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{15 a}-\frac{11 x}{30}","-\frac{8 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{15 a}+\frac{a^2 x^3}{30}+\frac{1}{5} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2+\frac{4}{15} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2+\frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{10 a}+\frac{4 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{15 a}+\frac{8}{15} x \tanh ^{-1}(a x)^2+\frac{8 \tanh ^{-1}(a x)^2}{15 a}-\frac{16 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{15 a}-\frac{11 x}{30}",1,"(-11*x)/30 + (a^2*x^3)/30 + (4*(1 - a^2*x^2)*ArcTanh[a*x])/(15*a) + ((1 - a^2*x^2)^2*ArcTanh[a*x])/(10*a) + (8*ArcTanh[a*x]^2)/(15*a) + (8*x*ArcTanh[a*x]^2)/15 + (4*x*(1 - a^2*x^2)*ArcTanh[a*x]^2)/15 + (x*(1 - a^2*x^2)^2*ArcTanh[a*x]^2)/5 - (16*ArcTanh[a*x]*Log[2/(1 - a*x)])/(15*a) - (8*PolyLog[2, 1 - 2/(1 - a*x)])/(15*a)","A",9,7,19,0.3684,1,"{5944, 5910, 5984, 5918, 2402, 2315, 8}"
208,1,186,0,0.52983,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{x} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x]^2)/x,x]","\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)-\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)-\tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)+\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)+\frac{a^2 x^2}{12}-\frac{2}{3} \log \left(1-a^2 x^2\right)+\frac{1}{4} a^4 x^4 \tanh ^{-1}(a x)^2+\frac{1}{6} a^3 x^3 \tanh ^{-1}(a x)-a^2 x^2 \tanh ^{-1}(a x)^2-\frac{3}{2} a x \tanh ^{-1}(a x)+\frac{3}{4} \tanh ^{-1}(a x)^2+2 \tanh ^{-1}(a x)^2 \tanh ^{-1}\left(1-\frac{2}{1-a x}\right)","\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)-\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)-\tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)+\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)+\frac{a^2 x^2}{12}-\frac{2}{3} \log \left(1-a^2 x^2\right)+\frac{1}{4} a^4 x^4 \tanh ^{-1}(a x)^2+\frac{1}{6} a^3 x^3 \tanh ^{-1}(a x)-a^2 x^2 \tanh ^{-1}(a x)^2-\frac{3}{2} a x \tanh ^{-1}(a x)+\frac{3}{4} \tanh ^{-1}(a x)^2+2 \tanh ^{-1}(a x)^2 \tanh ^{-1}\left(1-\frac{2}{1-a x}\right)",1,"(a^2*x^2)/12 - (3*a*x*ArcTanh[a*x])/2 + (a^3*x^3*ArcTanh[a*x])/6 + (3*ArcTanh[a*x]^2)/4 - a^2*x^2*ArcTanh[a*x]^2 + (a^4*x^4*ArcTanh[a*x]^2)/4 + 2*ArcTanh[a*x]^2*ArcTanh[1 - 2/(1 - a*x)] - (2*Log[1 - a^2*x^2])/3 - ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)] + ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 - a*x)] + PolyLog[3, 1 - 2/(1 - a*x)]/2 - PolyLog[3, -1 + 2/(1 - a*x)]/2","A",23,12,22,0.5455,1,"{6012, 5914, 6052, 5948, 6058, 6610, 5916, 5980, 5910, 260, 266, 43}"
209,1,156,0,0.418459,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{x^2} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x]^2)/x^2,x]","\frac{5}{3} a \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{3} a^4 x^3 \tanh ^{-1}(a x)^2+\frac{1}{3} a^3 x^2 \tanh ^{-1}(a x)+\frac{a^2 x}{3}-2 a^2 x \tanh ^{-1}(a x)^2-\frac{2}{3} a \tanh ^{-1}(a x)^2-\frac{1}{3} a \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)^2}{x}+\frac{10}{3} a \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)+2 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)","\frac{5}{3} a \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{3} a^4 x^3 \tanh ^{-1}(a x)^2+\frac{1}{3} a^3 x^2 \tanh ^{-1}(a x)+\frac{a^2 x}{3}-2 a^2 x \tanh ^{-1}(a x)^2-\frac{2}{3} a \tanh ^{-1}(a x)^2-\frac{1}{3} a \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)^2}{x}+\frac{10}{3} a \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)+2 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)",1,"(a^2*x)/3 - (a*ArcTanh[a*x])/3 + (a^3*x^2*ArcTanh[a*x])/3 - (2*a*ArcTanh[a*x]^2)/3 - ArcTanh[a*x]^2/x - 2*a^2*x*ArcTanh[a*x]^2 + (a^4*x^3*ArcTanh[a*x]^2)/3 + (10*a*ArcTanh[a*x]*Log[2/(1 - a*x)])/3 + 2*a*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] + (5*a*PolyLog[2, 1 - 2/(1 - a*x)])/3 - a*PolyLog[2, -1 + 2/(1 + a*x)]","A",20,13,22,0.5909,1,"{6012, 5910, 5984, 5918, 2402, 2315, 5916, 5988, 5932, 2447, 5980, 321, 206}"
210,1,162,0,0.4611156,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{x^3} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x]^2)/x^3,x]","-a^2 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)+a^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)+2 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)-2 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)+\frac{1}{2} a^4 x^2 \tanh ^{-1}(a x)^2+a^2 \log (x)+a^3 x \tanh ^{-1}(a x)-4 a^2 \tanh ^{-1}(a x)^2 \tanh ^{-1}\left(1-\frac{2}{1-a x}\right)-\frac{\tanh ^{-1}(a x)^2}{2 x^2}-\frac{a \tanh ^{-1}(a x)}{x}","-a^2 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)+a^2 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)+2 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)-2 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)+\frac{1}{2} a^4 x^2 \tanh ^{-1}(a x)^2+a^2 \log (x)+a^3 x \tanh ^{-1}(a x)-4 a^2 \tanh ^{-1}(a x)^2 \tanh ^{-1}\left(1-\frac{2}{1-a x}\right)-\frac{\tanh ^{-1}(a x)^2}{2 x^2}-\frac{a \tanh ^{-1}(a x)}{x}",1,"-((a*ArcTanh[a*x])/x) + a^3*x*ArcTanh[a*x] - ArcTanh[a*x]^2/(2*x^2) + (a^4*x^2*ArcTanh[a*x]^2)/2 - 4*a^2*ArcTanh[a*x]^2*ArcTanh[1 - 2/(1 - a*x)] + a^2*Log[x] + 2*a^2*ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)] - 2*a^2*ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 - a*x)] - a^2*PolyLog[3, 1 - 2/(1 - a*x)] + a^2*PolyLog[3, -1 + 2/(1 - a*x)]","A",21,15,22,0.6818,1,"{6012, 5916, 5982, 266, 36, 29, 31, 5948, 5914, 6052, 6058, 6610, 5980, 5910, 260}"
211,1,167,0,0.4304518,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{x^4} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x]^2)/x^4,x]","-a^3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)+\frac{5}{3} a^3 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2}{3 x}+a^4 x \tanh ^{-1}(a x)^2-\frac{2}{3} a^3 \tanh ^{-1}(a x)^2+\frac{1}{3} a^3 \tanh ^{-1}(a x)+\frac{2 a^2 \tanh ^{-1}(a x)^2}{x}-2 a^3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)-\frac{10}{3} a^3 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{a \tanh ^{-1}(a x)}{3 x^2}-\frac{\tanh ^{-1}(a x)^2}{3 x^3}","-a^3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)+\frac{5}{3} a^3 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2}{3 x}+a^4 x \tanh ^{-1}(a x)^2-\frac{2}{3} a^3 \tanh ^{-1}(a x)^2+\frac{1}{3} a^3 \tanh ^{-1}(a x)+\frac{2 a^2 \tanh ^{-1}(a x)^2}{x}-2 a^3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)-\frac{10}{3} a^3 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{a \tanh ^{-1}(a x)}{3 x^2}-\frac{\tanh ^{-1}(a x)^2}{3 x^3}",1,"-a^2/(3*x) + (a^3*ArcTanh[a*x])/3 - (a*ArcTanh[a*x])/(3*x^2) - (2*a^3*ArcTanh[a*x]^2)/3 - ArcTanh[a*x]^2/(3*x^3) + (2*a^2*ArcTanh[a*x]^2)/x + a^4*x*ArcTanh[a*x]^2 - 2*a^3*ArcTanh[a*x]*Log[2/(1 - a*x)] - (10*a^3*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)])/3 - a^3*PolyLog[2, 1 - 2/(1 - a*x)] + (5*a^3*PolyLog[2, -1 + 2/(1 + a*x)])/3","A",19,13,22,0.5909,1,"{6012, 5910, 5984, 5918, 2402, 2315, 5916, 5982, 325, 206, 5988, 5932, 2447}"
212,1,214,0,0.5494013,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{x^5} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x]^2)/x^5,x]","\frac{1}{2} a^4 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)-\frac{1}{2} a^4 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)-a^4 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)+a^4 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)-\frac{a^2}{12 x^2}+\frac{2}{3} a^4 \log \left(1-a^2 x^2\right)+\frac{a^2 \tanh ^{-1}(a x)^2}{x^2}-\frac{4}{3} a^4 \log (x)-\frac{3}{4} a^4 \tanh ^{-1}(a x)^2+2 a^4 \tanh ^{-1}(a x)^2 \tanh ^{-1}\left(1-\frac{2}{1-a x}\right)+\frac{3 a^3 \tanh ^{-1}(a x)}{2 x}-\frac{a \tanh ^{-1}(a x)}{6 x^3}-\frac{\tanh ^{-1}(a x)^2}{4 x^4}","\frac{1}{2} a^4 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)-\frac{1}{2} a^4 \text{PolyLog}\left(3,\frac{2}{1-a x}-1\right)-a^4 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)+a^4 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{1-a x}-1\right)-\frac{a^2}{12 x^2}+\frac{2}{3} a^4 \log \left(1-a^2 x^2\right)+\frac{a^2 \tanh ^{-1}(a x)^2}{x^2}-\frac{4}{3} a^4 \log (x)-\frac{3}{4} a^4 \tanh ^{-1}(a x)^2+2 a^4 \tanh ^{-1}(a x)^2 \tanh ^{-1}\left(1-\frac{2}{1-a x}\right)+\frac{3 a^3 \tanh ^{-1}(a x)}{2 x}-\frac{a \tanh ^{-1}(a x)}{6 x^3}-\frac{\tanh ^{-1}(a x)^2}{4 x^4}",1,"-a^2/(12*x^2) - (a*ArcTanh[a*x])/(6*x^3) + (3*a^3*ArcTanh[a*x])/(2*x) - (3*a^4*ArcTanh[a*x]^2)/4 - ArcTanh[a*x]^2/(4*x^4) + (a^2*ArcTanh[a*x]^2)/x^2 + 2*a^4*ArcTanh[a*x]^2*ArcTanh[1 - 2/(1 - a*x)] - (4*a^4*Log[x])/3 + (2*a^4*Log[1 - a^2*x^2])/3 - a^4*ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)] + a^4*ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 - a*x)] + (a^4*PolyLog[3, 1 - 2/(1 - a*x)])/2 - (a^4*PolyLog[3, -1 + 2/(1 - a*x)])/2","A",29,13,22,0.5909,1,"{6012, 5916, 5982, 266, 44, 36, 29, 31, 5948, 5914, 6052, 6058, 6610}"
213,1,157,0,0.5944635,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{x^6} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x]^2)/x^6,x]","-\frac{8}{15} a^5 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2}{30 x^3}+\frac{7 a^3 \tanh ^{-1}(a x)}{15 x^2}+\frac{2 a^2 \tanh ^{-1}(a x)^2}{3 x^3}+\frac{11 a^4}{30 x}+\frac{8}{15} a^5 \tanh ^{-1}(a x)^2-\frac{11}{30} a^5 \tanh ^{-1}(a x)-\frac{a^4 \tanh ^{-1}(a x)^2}{x}+\frac{16}{15} a^5 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{a \tanh ^{-1}(a x)}{10 x^4}-\frac{\tanh ^{-1}(a x)^2}{5 x^5}","-\frac{8}{15} a^5 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2}{30 x^3}+\frac{7 a^3 \tanh ^{-1}(a x)}{15 x^2}+\frac{2 a^2 \tanh ^{-1}(a x)^2}{3 x^3}+\frac{11 a^4}{30 x}+\frac{8}{15} a^5 \tanh ^{-1}(a x)^2-\frac{11}{30} a^5 \tanh ^{-1}(a x)-\frac{a^4 \tanh ^{-1}(a x)^2}{x}+\frac{16}{15} a^5 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{a \tanh ^{-1}(a x)}{10 x^4}-\frac{\tanh ^{-1}(a x)^2}{5 x^5}",1,"-a^2/(30*x^3) + (11*a^4)/(30*x) - (11*a^5*ArcTanh[a*x])/30 - (a*ArcTanh[a*x])/(10*x^4) + (7*a^3*ArcTanh[a*x])/(15*x^2) + (8*a^5*ArcTanh[a*x]^2)/15 - ArcTanh[a*x]^2/(5*x^5) + (2*a^2*ArcTanh[a*x]^2)/(3*x^3) - (a^4*ArcTanh[a*x]^2)/x + (16*a^5*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)])/15 - (8*a^5*PolyLog[2, -1 + 2/(1 + a*x)])/15","A",27,8,22,0.3636,1,"{6012, 5916, 5982, 325, 206, 5988, 5932, 2447}"
214,1,113,0,0.1943072,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{x^7} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x]^2)/x^7,x]","\frac{7 a^4}{90 x^2}-\frac{a^2}{60 x^4}-\frac{4}{45} a^6 \log \left(1-a^2 x^2\right)+\frac{2 a^3 \tanh ^{-1}(a x)}{9 x^3}-\frac{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2}{6 x^6}+\frac{8}{45} a^6 \log (x)-\frac{a^5 \tanh ^{-1}(a x)}{3 x}-\frac{a \tanh ^{-1}(a x)}{15 x^5}","\frac{7 a^4}{90 x^2}-\frac{a^2}{60 x^4}-\frac{4}{45} a^6 \log \left(1-a^2 x^2\right)+\frac{2 a^3 \tanh ^{-1}(a x)}{9 x^3}-\frac{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2}{6 x^6}+\frac{8}{45} a^6 \log (x)-\frac{a^5 \tanh ^{-1}(a x)}{3 x}-\frac{a \tanh ^{-1}(a x)}{15 x^5}",1,"-a^2/(60*x^4) + (7*a^4)/(90*x^2) - (a*ArcTanh[a*x])/(15*x^5) + (2*a^3*ArcTanh[a*x])/(9*x^3) - (a^5*ArcTanh[a*x])/(3*x) - ((1 - a^2*x^2)^3*ArcTanh[a*x]^2)/(6*x^6) + (8*a^6*Log[x])/45 - (4*a^6*Log[1 - a^2*x^2])/45","A",16,8,22,0.3636,1,"{6008, 6012, 5916, 266, 44, 36, 29, 31}"
215,1,183,0,0.8161701,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{x^8} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x]^2)/x^8,x]","-\frac{8}{105} a^7 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{17 a^4}{630 x^3}-\frac{a^2}{105 x^5}-\frac{8 a^5 \tanh ^{-1}(a x)}{105 x^2}-\frac{a^4 \tanh ^{-1}(a x)^2}{3 x^3}+\frac{9 a^3 \tanh ^{-1}(a x)}{70 x^4}+\frac{2 a^2 \tanh ^{-1}(a x)^2}{5 x^5}+\frac{a^6}{210 x}+\frac{8}{105} a^7 \tanh ^{-1}(a x)^2-\frac{1}{210} a^7 \tanh ^{-1}(a x)+\frac{16}{105} a^7 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{a \tanh ^{-1}(a x)}{21 x^6}-\frac{\tanh ^{-1}(a x)^2}{7 x^7}","-\frac{8}{105} a^7 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{17 a^4}{630 x^3}-\frac{a^2}{105 x^5}-\frac{8 a^5 \tanh ^{-1}(a x)}{105 x^2}-\frac{a^4 \tanh ^{-1}(a x)^2}{3 x^3}+\frac{9 a^3 \tanh ^{-1}(a x)}{70 x^4}+\frac{2 a^2 \tanh ^{-1}(a x)^2}{5 x^5}+\frac{a^6}{210 x}+\frac{8}{105} a^7 \tanh ^{-1}(a x)^2-\frac{1}{210} a^7 \tanh ^{-1}(a x)+\frac{16}{105} a^7 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{a \tanh ^{-1}(a x)}{21 x^6}-\frac{\tanh ^{-1}(a x)^2}{7 x^7}",1,"-a^2/(105*x^5) + (17*a^4)/(630*x^3) + a^6/(210*x) - (a^7*ArcTanh[a*x])/210 - (a*ArcTanh[a*x])/(21*x^6) + (9*a^3*ArcTanh[a*x])/(70*x^4) - (8*a^5*ArcTanh[a*x])/(105*x^2) + (8*a^7*ArcTanh[a*x]^2)/105 - ArcTanh[a*x]^2/(7*x^7) + (2*a^2*ArcTanh[a*x]^2)/(5*x^5) - (a^4*ArcTanh[a*x]^2)/(3*x^3) + (16*a^7*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)])/105 - (8*a^7*PolyLog[2, -1 + 2/(1 + a*x)])/105","A",42,8,22,0.3636,1,"{6012, 5916, 5982, 325, 206, 5988, 5932, 2447}"
216,1,170,0,0.840865,"\int \frac{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{x^9} \, dx","Int[((1 - a^2*x^2)^2*ArcTanh[a*x]^2)/x^9,x]","\frac{5 a^6}{504 x^2}+\frac{a^4}{84 x^4}-\frac{a^2}{168 x^6}-\frac{2}{63} a^8 \log \left(1-a^2 x^2\right)-\frac{a^5 \tanh ^{-1}(a x)}{36 x^3}-\frac{a^4 \tanh ^{-1}(a x)^2}{4 x^4}+\frac{a^3 \tanh ^{-1}(a x)}{12 x^5}+\frac{a^2 \tanh ^{-1}(a x)^2}{3 x^6}+\frac{4}{63} a^8 \log (x)+\frac{1}{24} a^8 \tanh ^{-1}(a x)^2-\frac{a^7 \tanh ^{-1}(a x)}{12 x}-\frac{a \tanh ^{-1}(a x)}{28 x^7}-\frac{\tanh ^{-1}(a x)^2}{8 x^8}","\frac{5 a^6}{504 x^2}+\frac{a^4}{84 x^4}-\frac{a^2}{168 x^6}-\frac{2}{63} a^8 \log \left(1-a^2 x^2\right)-\frac{a^5 \tanh ^{-1}(a x)}{36 x^3}-\frac{a^4 \tanh ^{-1}(a x)^2}{4 x^4}+\frac{a^3 \tanh ^{-1}(a x)}{12 x^5}+\frac{a^2 \tanh ^{-1}(a x)^2}{3 x^6}+\frac{4}{63} a^8 \log (x)+\frac{1}{24} a^8 \tanh ^{-1}(a x)^2-\frac{a^7 \tanh ^{-1}(a x)}{12 x}-\frac{a \tanh ^{-1}(a x)}{28 x^7}-\frac{\tanh ^{-1}(a x)^2}{8 x^8}",1,"-a^2/(168*x^6) + a^4/(84*x^4) + (5*a^6)/(504*x^2) - (a*ArcTanh[a*x])/(28*x^7) + (a^3*ArcTanh[a*x])/(12*x^5) - (a^5*ArcTanh[a*x])/(36*x^3) - (a^7*ArcTanh[a*x])/(12*x) + (a^8*ArcTanh[a*x]^2)/24 - ArcTanh[a*x]^2/(8*x^8) + (a^2*ArcTanh[a*x]^2)/(3*x^6) - (a^4*ArcTanh[a*x]^2)/(4*x^4) + (4*a^8*Log[x])/63 - (2*a^8*Log[1 - a^2*x^2])/63","A",56,9,22,0.4091,1,"{6012, 5916, 5982, 266, 44, 36, 29, 31, 5948}"
217,1,248,0,0.2515645,"\int \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3 \, dx","Int[(1 - a^2*x^2)^2*ArcTanh[a*x]^3,x]","\frac{4 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{5 a}-\frac{8 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{5 a}-\frac{1-a^2 x^2}{20 a}-\frac{\log \left(1-a^2 x^2\right)}{2 a}+\frac{1}{5} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3+\frac{4}{15} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3+\frac{3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{20 a}+\frac{2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{5 a}-\frac{1}{10} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)+\frac{8}{15} x \tanh ^{-1}(a x)^3+\frac{8 \tanh ^{-1}(a x)^3}{15 a}-x \tanh ^{-1}(a x)-\frac{8 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{5 a}","\frac{4 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{5 a}-\frac{8 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{5 a}-\frac{1-a^2 x^2}{20 a}-\frac{\log \left(1-a^2 x^2\right)}{2 a}+\frac{1}{5} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3+\frac{4}{15} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3+\frac{3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{20 a}+\frac{2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{5 a}-\frac{1}{10} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)+\frac{8}{15} x \tanh ^{-1}(a x)^3+\frac{8 \tanh ^{-1}(a x)^3}{15 a}-x \tanh ^{-1}(a x)-\frac{8 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{5 a}",1,"-(1 - a^2*x^2)/(20*a) - x*ArcTanh[a*x] - (x*(1 - a^2*x^2)*ArcTanh[a*x])/10 + (2*(1 - a^2*x^2)*ArcTanh[a*x]^2)/(5*a) + (3*(1 - a^2*x^2)^2*ArcTanh[a*x]^2)/(20*a) + (8*ArcTanh[a*x]^3)/(15*a) + (8*x*ArcTanh[a*x]^3)/15 + (4*x*(1 - a^2*x^2)*ArcTanh[a*x]^3)/15 + (x*(1 - a^2*x^2)^2*ArcTanh[a*x]^3)/5 - (8*ArcTanh[a*x]^2*Log[2/(1 - a*x)])/(5*a) - Log[1 - a^2*x^2]/(2*a) - (8*ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/(5*a) + (4*PolyLog[3, 1 - 2/(1 - a*x)])/(5*a)","A",12,9,19,0.4737,1,"{5944, 5910, 5984, 5918, 5948, 6058, 6610, 260, 5942}"
218,0,0,0,0.036213,"\int \frac{x \left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)} \, dx","Int[(x*(1 - a^2*x^2)^2)/ArcTanh[a*x],x]","\int \frac{x \left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x \left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)},x\right)",0,"Defer[Int][(x*(1 - a^2*x^2)^2)/ArcTanh[a*x], x]","A",0,0,0,0,-1,"{}"
219,0,0,0,0.0226321,"\int \frac{\left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)} \, dx","Int[(1 - a^2*x^2)^2/ArcTanh[a*x],x]","\int \frac{\left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{\left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)},x\right)",0,"Defer[Int][(1 - a^2*x^2)^2/ArcTanh[a*x], x]","A",0,0,0,0,-1,"{}"
220,0,0,0,0.0514779,"\int \frac{\left(1-a^2 x^2\right)^2}{x \tanh ^{-1}(a x)} \, dx","Int[(1 - a^2*x^2)^2/(x*ArcTanh[a*x]),x]","\int \frac{\left(1-a^2 x^2\right)^2}{x \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{\left(1-a^2 x^2\right)^2}{x \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][(1 - a^2*x^2)^2/(x*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
221,0,0,0,0.0357664,"\int \frac{x \left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)^2} \, dx","Int[(x*(1 - a^2*x^2)^2)/ArcTanh[a*x]^2,x]","\int \frac{x \left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{x \left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][(x*(1 - a^2*x^2)^2)/ArcTanh[a*x]^2, x]","A",0,0,0,0,-1,"{}"
222,0,0,0,0.0209154,"\int \frac{\left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)^2} \, dx","Int[(1 - a^2*x^2)^2/ArcTanh[a*x]^2,x]","\int \frac{\left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{\left(1-a^2 x^2\right)^2}{\tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][(1 - a^2*x^2)^2/ArcTanh[a*x]^2, x]","A",0,0,0,0,-1,"{}"
223,0,0,0,0.0480228,"\int \frac{\left(1-a^2 x^2\right)^2}{x \tanh ^{-1}(a x)^2} \, dx","Int[(1 - a^2*x^2)^2/(x*ArcTanh[a*x]^2),x]","\int \frac{\left(1-a^2 x^2\right)^2}{x \tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{\left(1-a^2 x^2\right)^2}{x \tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][(1 - a^2*x^2)^2/(x*ArcTanh[a*x]^2), x]","A",0,0,0,0,-1,"{}"
224,1,144,0,0.0674981,"\int \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x) \, dx","Int[(1 - a^2*x^2)^3*ArcTanh[a*x],x]","\frac{\left(1-a^2 x^2\right)^3}{42 a}+\frac{3 \left(1-a^2 x^2\right)^2}{70 a}+\frac{4 \left(1-a^2 x^2\right)}{35 a}+\frac{8 \log \left(1-a^2 x^2\right)}{35 a}+\frac{1}{7} x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)+\frac{6}{35} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)+\frac{8}{35} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)+\frac{16}{35} x \tanh ^{-1}(a x)","\frac{\left(1-a^2 x^2\right)^3}{42 a}+\frac{3 \left(1-a^2 x^2\right)^2}{70 a}+\frac{4 \left(1-a^2 x^2\right)}{35 a}+\frac{8 \log \left(1-a^2 x^2\right)}{35 a}+\frac{1}{7} x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)+\frac{6}{35} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)+\frac{8}{35} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)+\frac{16}{35} x \tanh ^{-1}(a x)",1,"(4*(1 - a^2*x^2))/(35*a) + (3*(1 - a^2*x^2)^2)/(70*a) + (1 - a^2*x^2)^3/(42*a) + (16*x*ArcTanh[a*x])/35 + (8*x*(1 - a^2*x^2)*ArcTanh[a*x])/35 + (6*x*(1 - a^2*x^2)^2*ArcTanh[a*x])/35 + (x*(1 - a^2*x^2)^3*ArcTanh[a*x])/7 + (8*Log[1 - a^2*x^2])/(35*a)","A",5,3,17,0.1765,1,"{5942, 5910, 260}"
225,1,227,0,0.1712779,"\int \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2 \, dx","Int[(1 - a^2*x^2)^3*ArcTanh[a*x]^2,x]","-\frac{16 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{35 a}-\frac{1}{105} a^4 x^5+\frac{19 a^2 x^3}{315}+\frac{1}{7} x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2+\frac{6}{35} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2+\frac{8}{35} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2+\frac{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}{21 a}+\frac{3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{35 a}+\frac{8 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{35 a}+\frac{16}{35} x \tanh ^{-1}(a x)^2+\frac{16 \tanh ^{-1}(a x)^2}{35 a}-\frac{32 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{35 a}-\frac{38 x}{105}","-\frac{16 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{35 a}-\frac{1}{105} a^4 x^5+\frac{19 a^2 x^3}{315}+\frac{1}{7} x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2+\frac{6}{35} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2+\frac{8}{35} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2+\frac{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}{21 a}+\frac{3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}{35 a}+\frac{8 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}{35 a}+\frac{16}{35} x \tanh ^{-1}(a x)^2+\frac{16 \tanh ^{-1}(a x)^2}{35 a}-\frac{32 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{35 a}-\frac{38 x}{105}",1,"(-38*x)/105 + (19*a^2*x^3)/315 - (a^4*x^5)/105 + (8*(1 - a^2*x^2)*ArcTanh[a*x])/(35*a) + (3*(1 - a^2*x^2)^2*ArcTanh[a*x])/(35*a) + ((1 - a^2*x^2)^3*ArcTanh[a*x])/(21*a) + (16*ArcTanh[a*x]^2)/(35*a) + (16*x*ArcTanh[a*x]^2)/35 + (8*x*(1 - a^2*x^2)*ArcTanh[a*x]^2)/35 + (6*x*(1 - a^2*x^2)^2*ArcTanh[a*x]^2)/35 + (x*(1 - a^2*x^2)^3*ArcTanh[a*x]^2)/7 - (32*ArcTanh[a*x]*Log[2/(1 - a*x)])/(35*a) - (16*PolyLog[2, 1 - 2/(1 - a*x)])/(35*a)","A",12,8,19,0.4211,1,"{5944, 5910, 5984, 5918, 2402, 2315, 8, 194}"
226,1,338,0,0.3334083,"\int \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^3 \, dx","Int[(1 - a^2*x^2)^3*ArcTanh[a*x]^3,x]","\frac{24 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{35 a}-\frac{48 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{35 a}-\frac{\left(1-a^2 x^2\right)^2}{140 a}-\frac{13 \left(1-a^2 x^2\right)}{210 a}-\frac{7 \log \left(1-a^2 x^2\right)}{15 a}+\frac{1}{7} x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^3+\frac{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2}{14 a}+\frac{6}{35} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3+\frac{9 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{70 a}-\frac{1}{35} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)+\frac{8}{35} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3+\frac{12 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{35 a}-\frac{13}{105} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)+\frac{16}{35} x \tanh ^{-1}(a x)^3+\frac{16 \tanh ^{-1}(a x)^3}{35 a}-\frac{14}{15} x \tanh ^{-1}(a x)-\frac{48 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{35 a}","\frac{24 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{35 a}-\frac{48 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{35 a}-\frac{\left(1-a^2 x^2\right)^2}{140 a}-\frac{13 \left(1-a^2 x^2\right)}{210 a}-\frac{7 \log \left(1-a^2 x^2\right)}{15 a}+\frac{1}{7} x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^3+\frac{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2}{14 a}+\frac{6}{35} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3+\frac{9 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}{70 a}-\frac{1}{35} x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)+\frac{8}{35} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3+\frac{12 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}{35 a}-\frac{13}{105} x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)+\frac{16}{35} x \tanh ^{-1}(a x)^3+\frac{16 \tanh ^{-1}(a x)^3}{35 a}-\frac{14}{15} x \tanh ^{-1}(a x)-\frac{48 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{35 a}",1,"(-13*(1 - a^2*x^2))/(210*a) - (1 - a^2*x^2)^2/(140*a) - (14*x*ArcTanh[a*x])/15 - (13*x*(1 - a^2*x^2)*ArcTanh[a*x])/105 - (x*(1 - a^2*x^2)^2*ArcTanh[a*x])/35 + (12*(1 - a^2*x^2)*ArcTanh[a*x]^2)/(35*a) + (9*(1 - a^2*x^2)^2*ArcTanh[a*x]^2)/(70*a) + ((1 - a^2*x^2)^3*ArcTanh[a*x]^2)/(14*a) + (16*ArcTanh[a*x]^3)/(35*a) + (16*x*ArcTanh[a*x]^3)/35 + (8*x*(1 - a^2*x^2)*ArcTanh[a*x]^3)/35 + (6*x*(1 - a^2*x^2)^2*ArcTanh[a*x]^3)/35 + (x*(1 - a^2*x^2)^3*ArcTanh[a*x]^3)/7 - (48*ArcTanh[a*x]^2*Log[2/(1 - a*x)])/(35*a) - (7*Log[1 - a^2*x^2])/(15*a) - (48*ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/(35*a) + (24*PolyLog[3, 1 - 2/(1 - a*x)])/(35*a)","A",17,9,19,0.4737,1,"{5944, 5910, 5984, 5918, 5948, 6058, 6610, 260, 5942}"
227,1,87,0,0.1328829,"\int \frac{x^3 \tanh ^{-1}(a x)}{1-a^2 x^2} \, dx","Int[(x^3*ArcTanh[a*x])/(1 - a^2*x^2),x]","\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{x^2 \tanh ^{-1}(a x)}{2 a^2}-\frac{x}{2 a^3}-\frac{\tanh ^{-1}(a x)^2}{2 a^4}+\frac{\tanh ^{-1}(a x)}{2 a^4}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^4}","\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{x^2 \tanh ^{-1}(a x)}{2 a^2}-\frac{x}{2 a^3}-\frac{\tanh ^{-1}(a x)^2}{2 a^4}+\frac{\tanh ^{-1}(a x)}{2 a^4}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^4}",1,"-x/(2*a^3) + ArcTanh[a*x]/(2*a^4) - (x^2*ArcTanh[a*x])/(2*a^2) - ArcTanh[a*x]^2/(2*a^4) + (ArcTanh[a*x]*Log[2/(1 - a*x)])/a^4 + PolyLog[2, 1 - 2/(1 - a*x)]/(2*a^4)","A",8,8,20,0.4000,1,"{5980, 5916, 321, 206, 5984, 5918, 2402, 2315}"
228,1,42,0,0.0692734,"\int \frac{x^2 \tanh ^{-1}(a x)}{1-a^2 x^2} \, dx","Int[(x^2*ArcTanh[a*x])/(1 - a^2*x^2),x]","-\frac{\log \left(1-a^2 x^2\right)}{2 a^3}+\frac{\tanh ^{-1}(a x)^2}{2 a^3}-\frac{x \tanh ^{-1}(a x)}{a^2}","-\frac{\log \left(1-a^2 x^2\right)}{2 a^3}+\frac{\tanh ^{-1}(a x)^2}{2 a^3}-\frac{x \tanh ^{-1}(a x)}{a^2}",1,"-((x*ArcTanh[a*x])/a^2) + ArcTanh[a*x]^2/(2*a^3) - Log[1 - a^2*x^2]/(2*a^3)","A",4,4,20,0.2000,1,"{5980, 5910, 260, 5948}"
229,1,54,0,0.0706783,"\int \frac{x \tanh ^{-1}(a x)}{1-a^2 x^2} \, dx","Int[(x*ArcTanh[a*x])/(1 - a^2*x^2),x]","\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^2}-\frac{\tanh ^{-1}(a x)^2}{2 a^2}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^2}","\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^2}-\frac{\tanh ^{-1}(a x)^2}{2 a^2}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^2}",1,"-ArcTanh[a*x]^2/(2*a^2) + (ArcTanh[a*x]*Log[2/(1 - a*x)])/a^2 + PolyLog[2, 1 - 2/(1 - a*x)]/(2*a^2)","A",4,4,18,0.2222,1,"{5984, 5918, 2402, 2315}"
230,1,13,0,0.0157754,"\int \frac{\tanh ^{-1}(a x)}{1-a^2 x^2} \, dx","Int[ArcTanh[a*x]/(1 - a^2*x^2),x]","\frac{\tanh ^{-1}(a x)^2}{2 a}","\frac{\tanh ^{-1}(a x)^2}{2 a}",1,"ArcTanh[a*x]^2/(2*a)","A",1,1,17,0.05882,1,"{5948}"
231,1,45,0,0.0870035,"\int \frac{\tanh ^{-1}(a x)}{x \left(1-a^2 x^2\right)} \, dx","Int[ArcTanh[a*x]/(x*(1 - a^2*x^2)),x]","-\frac{1}{2} \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{2} \tanh ^{-1}(a x)^2+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)","-\frac{1}{2} \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{2} \tanh ^{-1}(a x)^2+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)",1,"ArcTanh[a*x]^2/2 + ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] - PolyLog[2, -1 + 2/(1 + a*x)]/2","A",3,3,20,0.1500,1,"{5988, 5932, 2447}"
232,1,41,0,0.077544,"\int \frac{\tanh ^{-1}(a x)}{x^2 \left(1-a^2 x^2\right)} \, dx","Int[ArcTanh[a*x]/(x^2*(1 - a^2*x^2)),x]","-\frac{1}{2} a \log \left(1-a^2 x^2\right)+a \log (x)+\frac{1}{2} a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)}{x}","-\frac{1}{2} a \log \left(1-a^2 x^2\right)+a \log (x)+\frac{1}{2} a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)}{x}",1,"-(ArcTanh[a*x]/x) + (a*ArcTanh[a*x]^2)/2 + a*Log[x] - (a*Log[1 - a^2*x^2])/2","A",7,7,20,0.3500,1,"{5982, 5916, 266, 36, 29, 31, 5948}"
233,1,84,0,0.1545843,"\int \frac{\tanh ^{-1}(a x)}{x^3 \left(1-a^2 x^2\right)} \, dx","Int[ArcTanh[a*x]/(x^3*(1 - a^2*x^2)),x]","-\frac{1}{2} a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{2} a^2 \tanh ^{-1}(a x)^2+\frac{1}{2} a^2 \tanh ^{-1}(a x)+a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)}{2 x^2}-\frac{a}{2 x}","-\frac{1}{2} a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{2} a^2 \tanh ^{-1}(a x)^2+\frac{1}{2} a^2 \tanh ^{-1}(a x)+a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)}{2 x^2}-\frac{a}{2 x}",1,"-a/(2*x) + (a^2*ArcTanh[a*x])/2 - ArcTanh[a*x]/(2*x^2) + (a^2*ArcTanh[a*x]^2)/2 + a^2*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] - (a^2*PolyLog[2, -1 + 2/(1 + a*x)])/2","A",7,7,20,0.3500,1,"{5982, 5916, 325, 206, 5988, 5932, 2447}"
234,1,135,0,0.3022685,"\int \frac{x^3 \tanh ^{-1}(a x)^2}{1-a^2 x^2} \, dx","Int[(x^3*ArcTanh[a*x]^2)/(1 - a^2*x^2),x]","-\frac{\text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^4}+\frac{\tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^4}-\frac{\log \left(1-a^2 x^2\right)}{2 a^4}-\frac{x^2 \tanh ^{-1}(a x)^2}{2 a^2}-\frac{\tanh ^{-1}(a x)^3}{3 a^4}+\frac{\tanh ^{-1}(a x)^2}{2 a^4}-\frac{x \tanh ^{-1}(a x)}{a^3}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^4}","-\frac{\text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^4}+\frac{\tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^4}-\frac{\log \left(1-a^2 x^2\right)}{2 a^4}-\frac{x^2 \tanh ^{-1}(a x)^2}{2 a^2}-\frac{\tanh ^{-1}(a x)^3}{3 a^4}+\frac{\tanh ^{-1}(a x)^2}{2 a^4}-\frac{x \tanh ^{-1}(a x)}{a^3}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^4}",1,"-((x*ArcTanh[a*x])/a^3) + ArcTanh[a*x]^2/(2*a^4) - (x^2*ArcTanh[a*x]^2)/(2*a^2) - ArcTanh[a*x]^3/(3*a^4) + (ArcTanh[a*x]^2*Log[2/(1 - a*x)])/a^4 - Log[1 - a^2*x^2]/(2*a^4) + (ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/a^4 - PolyLog[3, 1 - 2/(1 - a*x)]/(2*a^4)","A",10,9,22,0.4091,1,"{5980, 5916, 5910, 260, 5948, 5984, 5918, 6058, 6610}"
235,1,75,0,0.1685858,"\int \frac{x^2 \tanh ^{-1}(a x)^2}{1-a^2 x^2} \, dx","Int[(x^2*ArcTanh[a*x]^2)/(1 - a^2*x^2),x]","\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3}+\frac{\tanh ^{-1}(a x)^3}{3 a^3}-\frac{x \tanh ^{-1}(a x)^2}{a^2}-\frac{\tanh ^{-1}(a x)^2}{a^3}+\frac{2 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^3}","\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3}+\frac{\tanh ^{-1}(a x)^3}{3 a^3}-\frac{x \tanh ^{-1}(a x)^2}{a^2}-\frac{\tanh ^{-1}(a x)^2}{a^3}+\frac{2 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^3}",1,"-(ArcTanh[a*x]^2/a^3) - (x*ArcTanh[a*x]^2)/a^2 + ArcTanh[a*x]^3/(3*a^3) + (2*ArcTanh[a*x]*Log[2/(1 - a*x)])/a^3 + PolyLog[2, 1 - 2/(1 - a*x)]/a^3","A",7,7,22,0.3182,1,"{5980, 5910, 5984, 5918, 2402, 2315, 5948}"
236,1,78,0,0.1572777,"\int \frac{x \tanh ^{-1}(a x)^2}{1-a^2 x^2} \, dx","Int[(x*ArcTanh[a*x]^2)/(1 - a^2*x^2),x]","-\frac{\text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^2}+\frac{\tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^2}-\frac{\tanh ^{-1}(a x)^3}{3 a^2}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^2}","-\frac{\text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^2}+\frac{\tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^2}-\frac{\tanh ^{-1}(a x)^3}{3 a^2}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^2}",1,"-ArcTanh[a*x]^3/(3*a^2) + (ArcTanh[a*x]^2*Log[2/(1 - a*x)])/a^2 + (ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/a^2 - PolyLog[3, 1 - 2/(1 - a*x)]/(2*a^2)","A",4,5,20,0.2500,1,"{5984, 5918, 5948, 6058, 6610}"
237,1,13,0,0.0261026,"\int \frac{\tanh ^{-1}(a x)^2}{1-a^2 x^2} \, dx","Int[ArcTanh[a*x]^2/(1 - a^2*x^2),x]","\frac{\tanh ^{-1}(a x)^3}{3 a}","\frac{\tanh ^{-1}(a x)^3}{3 a}",1,"ArcTanh[a*x]^3/(3*a)","A",1,1,19,0.05263,1,"{5948}"
238,1,66,0,0.1808566,"\int \frac{\tanh ^{-1}(a x)^2}{x \left(1-a^2 x^2\right)} \, dx","Int[ArcTanh[a*x]^2/(x*(1 - a^2*x^2)),x]","-\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{3} \tanh ^{-1}(a x)^3+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2","-\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{3} \tanh ^{-1}(a x)^3+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2",1,"ArcTanh[a*x]^3/3 + ArcTanh[a*x]^2*Log[2 - 2/(1 + a*x)] - ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 + a*x)] - PolyLog[3, -1 + 2/(1 + a*x)]/2","A",4,5,22,0.2273,1,"{5988, 5932, 5948, 6056, 6610}"
239,1,66,0,0.2147676,"\int \frac{\tanh ^{-1}(a x)^2}{x^2 \left(1-a^2 x^2\right)} \, dx","Int[ArcTanh[a*x]^2/(x^2*(1 - a^2*x^2)),x]","-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{3} a \tanh ^{-1}(a x)^3+a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{x}+2 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)","-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{3} a \tanh ^{-1}(a x)^3+a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{x}+2 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)",1,"a*ArcTanh[a*x]^2 - ArcTanh[a*x]^2/x + (a*ArcTanh[a*x]^3)/3 + 2*a*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] - a*PolyLog[2, -1 + 2/(1 + a*x)]","A",6,6,22,0.2727,1,"{5982, 5916, 5988, 5932, 2447, 5948}"
240,1,138,0,0.3571814,"\int \frac{\tanh ^{-1}(a x)^2}{x^3 \left(1-a^2 x^2\right)} \, dx","Int[ArcTanh[a*x]^2/(x^3*(1 - a^2*x^2)),x]","-\frac{1}{2} a^2 \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{1}{2} a^2 \log \left(1-a^2 x^2\right)+a^2 \log (x)+\frac{1}{3} a^2 \tanh ^{-1}(a x)^3+\frac{1}{2} a^2 \tanh ^{-1}(a x)^2+a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{2 x^2}-\frac{a \tanh ^{-1}(a x)}{x}","-\frac{1}{2} a^2 \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{1}{2} a^2 \log \left(1-a^2 x^2\right)+a^2 \log (x)+\frac{1}{3} a^2 \tanh ^{-1}(a x)^3+\frac{1}{2} a^2 \tanh ^{-1}(a x)^2+a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{2 x^2}-\frac{a \tanh ^{-1}(a x)}{x}",1,"-((a*ArcTanh[a*x])/x) + (a^2*ArcTanh[a*x]^2)/2 - ArcTanh[a*x]^2/(2*x^2) + (a^2*ArcTanh[a*x]^3)/3 + a^2*Log[x] - (a^2*Log[1 - a^2*x^2])/2 + a^2*ArcTanh[a*x]^2*Log[2 - 2/(1 + a*x)] - a^2*ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 + a*x)] - (a^2*PolyLog[3, -1 + 2/(1 + a*x)])/2","A",13,11,22,0.5000,1,"{5982, 5916, 266, 36, 29, 31, 5948, 5988, 5932, 6056, 6610}"
241,1,205,0,0.4694769,"\int \frac{x^3 \tanh ^{-1}(a x)^3}{1-a^2 x^2} \, dx","Int[(x^3*ArcTanh[a*x]^3)/(1 - a^2*x^2),x]","\frac{3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^4}+\frac{3 \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{4 a^4}+\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{x^2 \tanh ^{-1}(a x)^3}{2 a^2}-\frac{\tanh ^{-1}(a x)^4}{4 a^4}+\frac{\tanh ^{-1}(a x)^3}{2 a^4}-\frac{3 x \tanh ^{-1}(a x)^2}{2 a^3}-\frac{3 \tanh ^{-1}(a x)^2}{2 a^4}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^3}{a^4}+\frac{3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^4}","\frac{3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^4}+\frac{3 \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{4 a^4}+\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{x^2 \tanh ^{-1}(a x)^3}{2 a^2}-\frac{\tanh ^{-1}(a x)^4}{4 a^4}+\frac{\tanh ^{-1}(a x)^3}{2 a^4}-\frac{3 x \tanh ^{-1}(a x)^2}{2 a^3}-\frac{3 \tanh ^{-1}(a x)^2}{2 a^4}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^3}{a^4}+\frac{3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^4}",1,"(-3*ArcTanh[a*x]^2)/(2*a^4) - (3*x*ArcTanh[a*x]^2)/(2*a^3) + ArcTanh[a*x]^3/(2*a^4) - (x^2*ArcTanh[a*x]^3)/(2*a^2) - ArcTanh[a*x]^4/(4*a^4) + (3*ArcTanh[a*x]*Log[2/(1 - a*x)])/a^4 + (ArcTanh[a*x]^3*Log[2/(1 - a*x)])/a^4 + (3*PolyLog[2, 1 - 2/(1 - a*x)])/(2*a^4) + (3*ArcTanh[a*x]^2*PolyLog[2, 1 - 2/(1 - a*x)])/(2*a^4) - (3*ArcTanh[a*x]*PolyLog[3, 1 - 2/(1 - a*x)])/(2*a^4) + (3*PolyLog[4, 1 - 2/(1 - a*x)])/(4*a^4)","A",14,11,22,0.5000,1,"{5980, 5916, 5910, 5984, 5918, 2402, 2315, 5948, 6058, 6062, 6610}"
242,1,103,0,0.2690132,"\int \frac{x^2 \tanh ^{-1}(a x)^3}{1-a^2 x^2} \, dx","Int[(x^2*ArcTanh[a*x]^3)/(1 - a^2*x^2),x]","-\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^3}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3}+\frac{\tanh ^{-1}(a x)^4}{4 a^3}-\frac{x \tanh ^{-1}(a x)^3}{a^2}-\frac{\tanh ^{-1}(a x)^3}{a^3}+\frac{3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^3}","-\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^3}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3}+\frac{\tanh ^{-1}(a x)^4}{4 a^3}-\frac{x \tanh ^{-1}(a x)^3}{a^2}-\frac{\tanh ^{-1}(a x)^3}{a^3}+\frac{3 \log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^3}",1,"-(ArcTanh[a*x]^3/a^3) - (x*ArcTanh[a*x]^3)/a^2 + ArcTanh[a*x]^4/(4*a^3) + (3*ArcTanh[a*x]^2*Log[2/(1 - a*x)])/a^3 + (3*ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/a^3 - (3*PolyLog[3, 1 - 2/(1 - a*x)])/(2*a^3)","A",7,7,22,0.3182,1,"{5980, 5910, 5984, 5918, 5948, 6058, 6610}"
243,1,108,0,0.2064636,"\int \frac{x \tanh ^{-1}(a x)^3}{1-a^2 x^2} \, dx","Int[(x*ArcTanh[a*x]^3)/(1 - a^2*x^2),x]","\frac{3 \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{4 a^2}+\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^2}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^2}-\frac{\tanh ^{-1}(a x)^4}{4 a^2}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^3}{a^2}","\frac{3 \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{4 a^2}+\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^2}-\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^2}-\frac{\tanh ^{-1}(a x)^4}{4 a^2}+\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^3}{a^2}",1,"-ArcTanh[a*x]^4/(4*a^2) + (ArcTanh[a*x]^3*Log[2/(1 - a*x)])/a^2 + (3*ArcTanh[a*x]^2*PolyLog[2, 1 - 2/(1 - a*x)])/(2*a^2) - (3*ArcTanh[a*x]*PolyLog[3, 1 - 2/(1 - a*x)])/(2*a^2) + (3*PolyLog[4, 1 - 2/(1 - a*x)])/(4*a^2)","A",5,6,20,0.3000,1,"{5984, 5918, 5948, 6058, 6062, 6610}"
244,1,13,0,0.0234723,"\int \frac{\tanh ^{-1}(a x)^3}{1-a^2 x^2} \, dx","Int[ArcTanh[a*x]^3/(1 - a^2*x^2),x]","\frac{\tanh ^{-1}(a x)^4}{4 a}","\frac{\tanh ^{-1}(a x)^4}{4 a}",1,"ArcTanh[a*x]^4/(4*a)","A",1,1,19,0.05263,1,"{5948}"
245,1,91,0,0.2211865,"\int \frac{\tanh ^{-1}(a x)^3}{x \left(1-a^2 x^2\right)} \, dx","Int[ArcTanh[a*x]^3/(x*(1 - a^2*x^2)),x]","-\frac{3}{4} \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)+\frac{1}{4} \tanh ^{-1}(a x)^4+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3","-\frac{3}{4} \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)+\frac{1}{4} \tanh ^{-1}(a x)^4+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3",1,"ArcTanh[a*x]^4/4 + ArcTanh[a*x]^3*Log[2 - 2/(1 + a*x)] - (3*ArcTanh[a*x]^2*PolyLog[2, -1 + 2/(1 + a*x)])/2 - (3*ArcTanh[a*x]*PolyLog[3, -1 + 2/(1 + a*x)])/2 - (3*PolyLog[4, -1 + 2/(1 + a*x)])/4","A",5,6,22,0.2727,1,"{5988, 5932, 5948, 6056, 6060, 6610}"
246,1,90,0,0.2727364,"\int \frac{\tanh ^{-1}(a x)^3}{x^2 \left(1-a^2 x^2\right)} \, dx","Int[ArcTanh[a*x]^3/(x^2*(1 - a^2*x^2)),x]","-\frac{3}{2} a \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-3 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{4} a \tanh ^{-1}(a x)^4+a \tanh ^{-1}(a x)^3-\frac{\tanh ^{-1}(a x)^3}{x}+3 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2","-\frac{3}{2} a \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-3 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{4} a \tanh ^{-1}(a x)^4+a \tanh ^{-1}(a x)^3-\frac{\tanh ^{-1}(a x)^3}{x}+3 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2",1,"a*ArcTanh[a*x]^3 - ArcTanh[a*x]^3/x + (a*ArcTanh[a*x]^4)/4 + 3*a*ArcTanh[a*x]^2*Log[2 - 2/(1 + a*x)] - 3*a*ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 + a*x)] - (3*a*PolyLog[3, -1 + 2/(1 + a*x)])/2","A",7,7,22,0.3182,1,"{5982, 5916, 5988, 5932, 5948, 6056, 6610}"
247,1,200,0,0.4956399,"\int \frac{\tanh ^{-1}(a x)^3}{x^3 \left(1-a^2 x^2\right)} \, dx","Int[ArcTanh[a*x]^3/(x^3*(1 - a^2*x^2)),x]","-\frac{3}{2} a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{4} a^2 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)-\frac{3}{2} a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{2} a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)+\frac{1}{4} a^2 \tanh ^{-1}(a x)^4+\frac{1}{2} a^2 \tanh ^{-1}(a x)^3+\frac{3}{2} a^2 \tanh ^{-1}(a x)^2+a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3+3 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)^3}{2 x^2}-\frac{3 a \tanh ^{-1}(a x)^2}{2 x}","-\frac{3}{2} a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{4} a^2 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)-\frac{3}{2} a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{2} a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)+\frac{1}{4} a^2 \tanh ^{-1}(a x)^4+\frac{1}{2} a^2 \tanh ^{-1}(a x)^3+\frac{3}{2} a^2 \tanh ^{-1}(a x)^2+a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3+3 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)^3}{2 x^2}-\frac{3 a \tanh ^{-1}(a x)^2}{2 x}",1,"(3*a^2*ArcTanh[a*x]^2)/2 - (3*a*ArcTanh[a*x]^2)/(2*x) + (a^2*ArcTanh[a*x]^3)/2 - ArcTanh[a*x]^3/(2*x^2) + (a^2*ArcTanh[a*x]^4)/4 + 3*a^2*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] + a^2*ArcTanh[a*x]^3*Log[2 - 2/(1 + a*x)] - (3*a^2*PolyLog[2, -1 + 2/(1 + a*x)])/2 - (3*a^2*ArcTanh[a*x]^2*PolyLog[2, -1 + 2/(1 + a*x)])/2 - (3*a^2*ArcTanh[a*x]*PolyLog[3, -1 + 2/(1 + a*x)])/2 - (3*a^2*PolyLog[4, -1 + 2/(1 + a*x)])/4","A",13,9,22,0.4091,1,"{5982, 5916, 5988, 5932, 2447, 5948, 6056, 6060, 6610}"
248,1,15,0,0.024674,"\int \frac{\sqrt{\tanh ^{-1}(a x)}}{1-a^2 x^2} \, dx","Int[Sqrt[ArcTanh[a*x]]/(1 - a^2*x^2),x]","\frac{2 \tanh ^{-1}(a x)^{3/2}}{3 a}","\frac{2 \tanh ^{-1}(a x)^{3/2}}{3 a}",1,"(2*ArcTanh[a*x]^(3/2))/(3*a)","A",1,1,21,0.04762,1,"{5948}"
249,0,0,0,0.0440452,"\int \frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)} \, dx","Int[x/((1 - a^2*x^2)*ArcTanh[a*x]),x]","\int \frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][x/((1 - a^2*x^2)*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
250,1,9,0,0.0275559,"\int \frac{1}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)} \, dx","Int[1/((1 - a^2*x^2)*ArcTanh[a*x]),x]","\frac{\log \left(\tanh ^{-1}(a x)\right)}{a}","\frac{\log \left(\tanh ^{-1}(a x)\right)}{a}",1,"Log[ArcTanh[a*x]]/a","A",1,1,19,0.05263,1,"{5946}"
251,0,0,0,0.0643657,"\int \frac{1}{x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)} \, dx","Int[1/(x*(1 - a^2*x^2)*ArcTanh[a*x]),x]","\int \frac{1}{x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x*(1 - a^2*x^2)*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
252,0,0,0,0.0467729,"\int \frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2} \, dx","Int[x/((1 - a^2*x^2)*ArcTanh[a*x]^2),x]","\int \frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2} \, dx","\frac{\text{Int}\left(\frac{1}{\tanh ^{-1}(a x)},x\right)}{a}-\frac{x}{a \tanh ^{-1}(a x)}",0,"-(x/(a*ArcTanh[a*x])) + Defer[Int][ArcTanh[a*x]^(-1), x]/a","A",0,0,0,0,-1,"{}"
253,1,11,0,0.0247837,"\int \frac{1}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2} \, dx","Int[1/((1 - a^2*x^2)*ArcTanh[a*x]^2),x]","-\frac{1}{a \tanh ^{-1}(a x)}","-\frac{1}{a \tanh ^{-1}(a x)}",1,"-(1/(a*ArcTanh[a*x]))","A",1,1,19,0.05263,1,"{5948}"
254,0,0,0,0.0777517,"\int \frac{1}{x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2} \, dx","Int[1/(x*(1 - a^2*x^2)*ArcTanh[a*x]^2),x]","\int \frac{1}{x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \tanh ^{-1}(a x)},x\right)}{a}-\frac{1}{a x \tanh ^{-1}(a x)}",0,"-(1/(a*x*ArcTanh[a*x])) - Defer[Int][1/(x^2*ArcTanh[a*x]), x]/a","A",0,0,0,0,-1,"{}"
255,0,0,0,0.0486874,"\int \frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3} \, dx","Int[x/((1 - a^2*x^2)*ArcTanh[a*x]^3),x]","\int \frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3} \, dx","\frac{\text{Int}\left(\frac{1}{\tanh ^{-1}(a x)^2},x\right)}{2 a}-\frac{x}{2 a \tanh ^{-1}(a x)^2}",0,"-x/(2*a*ArcTanh[a*x]^2) + Defer[Int][ArcTanh[a*x]^(-2), x]/(2*a)","A",0,0,0,0,-1,"{}"
256,1,13,0,0.0257797,"\int \frac{1}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3} \, dx","Int[1/((1 - a^2*x^2)*ArcTanh[a*x]^3),x]","-\frac{1}{2 a \tanh ^{-1}(a x)^2}","-\frac{1}{2 a \tanh ^{-1}(a x)^2}",1,"-1/(2*a*ArcTanh[a*x]^2)","A",1,1,19,0.05263,1,"{5948}"
257,0,0,0,0.0784743,"\int \frac{1}{x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3} \, dx","Int[1/(x*(1 - a^2*x^2)*ArcTanh[a*x]^3),x]","\int \frac{1}{x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \tanh ^{-1}(a x)^2},x\right)}{2 a}-\frac{1}{2 a x \tanh ^{-1}(a x)^2}",0,"-1/(2*a*x*ArcTanh[a*x]^2) - Defer[Int][1/(x^2*ArcTanh[a*x]^2), x]/(2*a)","A",0,0,0,0,-1,"{}"
258,1,17,0,0.0309873,"\int \frac{\tanh ^{-1}(a x)^p}{1-a^2 x^2} \, dx","Int[ArcTanh[a*x]^p/(1 - a^2*x^2),x]","\frac{\tanh ^{-1}(a x)^{p+1}}{a (p+1)}","\frac{\tanh ^{-1}(a x)^{p+1}}{a (p+1)}",1,"ArcTanh[a*x]^(1 + p)/(a*(1 + p))","A",1,1,19,0.05263,1,"{5948}"
259,1,109,0,0.1604543,"\int \frac{x^3 \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^2} \, dx","Int[(x^3*ArcTanh[a*x])/(1 - a^2*x^2)^2,x]","-\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{x}{4 a^3 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)}{2 a^4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{2 a^4}-\frac{\tanh ^{-1}(a x)}{4 a^4}-\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^4}","-\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{x}{4 a^3 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)}{2 a^4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{2 a^4}-\frac{\tanh ^{-1}(a x)}{4 a^4}-\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)}{a^4}",1,"-x/(4*a^3*(1 - a^2*x^2)) - ArcTanh[a*x]/(4*a^4) + ArcTanh[a*x]/(2*a^4*(1 - a^2*x^2)) + ArcTanh[a*x]^2/(2*a^4) - (ArcTanh[a*x]*Log[2/(1 - a*x)])/a^4 - PolyLog[2, 1 - 2/(1 - a*x)]/(2*a^4)","A",8,8,20,0.4000,1,"{6028, 5984, 5918, 2402, 2315, 5994, 199, 206}"
260,1,57,0,0.0628238,"\int \frac{x^2 \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^2} \, dx","Int[(x^2*ArcTanh[a*x])/(1 - a^2*x^2)^2,x]","-\frac{1}{4 a^3 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)}{2 a^2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)^2}{4 a^3}","-\frac{1}{4 a^3 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)}{2 a^2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)^2}{4 a^3}",1,"-1/(4*a^3*(1 - a^2*x^2)) + (x*ArcTanh[a*x])/(2*a^2*(1 - a^2*x^2)) - ArcTanh[a*x]^2/(4*a^3)","A",2,2,20,0.1000,1,"{5998, 5948}"
261,1,55,0,0.0376937,"\int \frac{x \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^2} \, dx","Int[(x*ArcTanh[a*x])/(1 - a^2*x^2)^2,x]","-\frac{x}{4 a \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)}{2 a^2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)}{4 a^2}","-\frac{x}{4 a \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)}{2 a^2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)}{4 a^2}",1,"-x/(4*a*(1 - a^2*x^2)) - ArcTanh[a*x]/(4*a^2) + ArcTanh[a*x]/(2*a^2*(1 - a^2*x^2))","A",3,3,18,0.1667,1,"{5994, 199, 206}"
262,1,54,0,0.0221565,"\int \frac{\tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]/(1 - a^2*x^2)^2,x]","-\frac{1}{4 a \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{4 a}","-\frac{1}{4 a \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{4 a}",1,"-1/(4*a*(1 - a^2*x^2)) + (x*ArcTanh[a*x])/(2*(1 - a^2*x^2)) + ArcTanh[a*x]^2/(4*a)","A",2,2,17,0.1176,1,"{5956, 261}"
263,1,91,0,0.1640753,"\int \frac{\tanh ^{-1}(a x)}{x \left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]/(x*(1 - a^2*x^2)^2),x]","-\frac{1}{2} \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a x}{4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{1}{2} \tanh ^{-1}(a x)^2-\frac{1}{4} \tanh ^{-1}(a x)+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)","-\frac{1}{2} \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a x}{4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{1}{2} \tanh ^{-1}(a x)^2-\frac{1}{4} \tanh ^{-1}(a x)+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)",1,"-(a*x)/(4*(1 - a^2*x^2)) - ArcTanh[a*x]/4 + ArcTanh[a*x]/(2*(1 - a^2*x^2)) + ArcTanh[a*x]^2/2 + ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] - PolyLog[2, -1 + 2/(1 + a*x)]/2","A",7,7,20,0.3500,1,"{6030, 5988, 5932, 2447, 5994, 199, 206}"
264,1,82,0,0.1453594,"\int \frac{\tanh ^{-1}(a x)}{x^2 \left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]/(x^2*(1 - a^2*x^2)^2),x]","-\frac{a}{4 \left(1-a^2 x^2\right)}-\frac{1}{2} a \log \left(1-a^2 x^2\right)+\frac{a^2 x \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+a \log (x)+\frac{3}{4} a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)}{x}","-\frac{a}{4 \left(1-a^2 x^2\right)}-\frac{1}{2} a \log \left(1-a^2 x^2\right)+\frac{a^2 x \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+a \log (x)+\frac{3}{4} a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)}{x}",1,"-a/(4*(1 - a^2*x^2)) - ArcTanh[a*x]/x + (a^2*x*ArcTanh[a*x])/(2*(1 - a^2*x^2)) + (3*a*ArcTanh[a*x]^2)/4 + a*Log[x] - (a*Log[1 - a^2*x^2])/2","A",10,10,20,0.5000,1,"{6030, 5982, 5916, 266, 36, 29, 31, 5948, 5956, 261}"
265,1,123,0,0.3583715,"\int \frac{\tanh ^{-1}(a x)}{x^3 \left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]/(x^3*(1 - a^2*x^2)^2),x]","-a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^3 x}{4 \left(1-a^2 x^2\right)}+\frac{a^2 \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+a^2 \tanh ^{-1}(a x)^2+\frac{1}{4} a^2 \tanh ^{-1}(a x)+2 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)}{2 x^2}-\frac{a}{2 x}","-a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^3 x}{4 \left(1-a^2 x^2\right)}+\frac{a^2 \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+a^2 \tanh ^{-1}(a x)^2+\frac{1}{4} a^2 \tanh ^{-1}(a x)+2 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)}{2 x^2}-\frac{a}{2 x}",1,"-a/(2*x) - (a^3*x)/(4*(1 - a^2*x^2)) + (a^2*ArcTanh[a*x])/4 - ArcTanh[a*x]/(2*x^2) + (a^2*ArcTanh[a*x])/(2*(1 - a^2*x^2)) + a^2*ArcTanh[a*x]^2 + 2*a^2*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] - a^2*PolyLog[2, -1 + 2/(1 + a*x)]","A",15,10,20,0.5000,1,"{6030, 5982, 5916, 325, 206, 5988, 5932, 2447, 5994, 199}"
266,1,161,0,0.2911783,"\int \frac{x^3 \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^2} \, dx","Int[(x^3*ArcTanh[a*x]^2)/(1 - a^2*x^2)^2,x]","\frac{\text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{\tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^4}+\frac{1}{4 a^4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{2 a^4 \left(1-a^2 x^2\right)}-\frac{x \tanh ^{-1}(a x)}{2 a^3 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{3 a^4}-\frac{\tanh ^{-1}(a x)^2}{4 a^4}-\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^4}","\frac{\text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{\tanh ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^4}+\frac{1}{4 a^4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{2 a^4 \left(1-a^2 x^2\right)}-\frac{x \tanh ^{-1}(a x)}{2 a^3 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{3 a^4}-\frac{\tanh ^{-1}(a x)^2}{4 a^4}-\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^2}{a^4}",1,"1/(4*a^4*(1 - a^2*x^2)) - (x*ArcTanh[a*x])/(2*a^3*(1 - a^2*x^2)) - ArcTanh[a*x]^2/(4*a^4) + ArcTanh[a*x]^2/(2*a^4*(1 - a^2*x^2)) + ArcTanh[a*x]^3/(3*a^4) - (ArcTanh[a*x]^2*Log[2/(1 - a*x)])/a^4 - (ArcTanh[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/a^4 + PolyLog[3, 1 - 2/(1 - a*x)]/(2*a^4)","A",8,9,22,0.4091,1,"{6028, 5984, 5918, 5948, 6058, 6610, 5994, 5956, 261}"
267,1,94,0,0.1026588,"\int \frac{x^2 \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^2} \, dx","Int[(x^2*ArcTanh[a*x]^2)/(1 - a^2*x^2)^2,x]","\frac{x}{4 a^2 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^2}{2 a^2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)}{2 a^3 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)^3}{6 a^3}+\frac{\tanh ^{-1}(a x)}{4 a^3}","\frac{x}{4 a^2 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^2}{2 a^2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)}{2 a^3 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)^3}{6 a^3}+\frac{\tanh ^{-1}(a x)}{4 a^3}",1,"x/(4*a^2*(1 - a^2*x^2)) + ArcTanh[a*x]/(4*a^3) - ArcTanh[a*x]/(2*a^3*(1 - a^2*x^2)) + (x*ArcTanh[a*x]^2)/(2*a^2*(1 - a^2*x^2)) - ArcTanh[a*x]^3/(6*a^3)","A",4,4,22,0.1818,1,"{6000, 5994, 199, 206}"
268,1,82,0,0.0679388,"\int \frac{x \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^2} \, dx","Int[(x*ArcTanh[a*x]^2)/(1 - a^2*x^2)^2,x]","\frac{1}{4 a^2 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{2 a^2 \left(1-a^2 x^2\right)}-\frac{x \tanh ^{-1}(a x)}{2 a \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)^2}{4 a^2}","\frac{1}{4 a^2 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{2 a^2 \left(1-a^2 x^2\right)}-\frac{x \tanh ^{-1}(a x)}{2 a \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)^2}{4 a^2}",1,"1/(4*a^2*(1 - a^2*x^2)) - (x*ArcTanh[a*x])/(2*a*(1 - a^2*x^2)) - ArcTanh[a*x]^2/(4*a^2) + ArcTanh[a*x]^2/(2*a^2*(1 - a^2*x^2))","A",3,3,20,0.1500,1,"{5994, 5956, 261}"
269,1,88,0,0.0639225,"\int \frac{\tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]^2/(1 - a^2*x^2)^2,x]","\frac{x}{4 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^2}{2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)}{2 a \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{6 a}+\frac{\tanh ^{-1}(a x)}{4 a}","\frac{x}{4 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^2}{2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)}{2 a \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{6 a}+\frac{\tanh ^{-1}(a x)}{4 a}",1,"x/(4*(1 - a^2*x^2)) + ArcTanh[a*x]/(4*a) - ArcTanh[a*x]/(2*a*(1 - a^2*x^2)) + (x*ArcTanh[a*x]^2)/(2*(1 - a^2*x^2)) + ArcTanh[a*x]^3/(6*a)","A",4,4,19,0.2105,1,"{5956, 5994, 199, 206}"
270,1,136,0,0.2920173,"\int \frac{\tanh ^{-1}(a x)^2}{x \left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]^2/(x*(1 - a^2*x^2)^2),x]","-\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{2 \left(1-a^2 x^2\right)}-\frac{a x \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{1}{3} \tanh ^{-1}(a x)^3-\frac{1}{4} \tanh ^{-1}(a x)^2+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2","-\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{2 \left(1-a^2 x^2\right)}-\frac{a x \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{1}{3} \tanh ^{-1}(a x)^3-\frac{1}{4} \tanh ^{-1}(a x)^2+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2",1,"1/(4*(1 - a^2*x^2)) - (a*x*ArcTanh[a*x])/(2*(1 - a^2*x^2)) - ArcTanh[a*x]^2/4 + ArcTanh[a*x]^2/(2*(1 - a^2*x^2)) + ArcTanh[a*x]^3/3 + ArcTanh[a*x]^2*Log[2 - 2/(1 + a*x)] - ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 + a*x)] - PolyLog[3, -1 + 2/(1 + a*x)]/2","A",8,9,22,0.4091,1,"{6030, 5988, 5932, 5948, 6056, 6610, 5994, 5956, 261}"
271,1,142,0,0.3150691,"\int \frac{\tanh ^{-1}(a x)^2}{x^2 \left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]^2/(x^2*(1 - a^2*x^2)^2),x]","-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{a^2 x}{4 \left(1-a^2 x^2\right)}+\frac{a^2 x \tanh ^{-1}(a x)^2}{2 \left(1-a^2 x^2\right)}-\frac{a \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{1}{2} a \tanh ^{-1}(a x)^3+a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{x}+\frac{1}{4} a \tanh ^{-1}(a x)+2 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)","-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{a^2 x}{4 \left(1-a^2 x^2\right)}+\frac{a^2 x \tanh ^{-1}(a x)^2}{2 \left(1-a^2 x^2\right)}-\frac{a \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{1}{2} a \tanh ^{-1}(a x)^3+a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{x}+\frac{1}{4} a \tanh ^{-1}(a x)+2 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)",1,"(a^2*x)/(4*(1 - a^2*x^2)) + (a*ArcTanh[a*x])/4 - (a*ArcTanh[a*x])/(2*(1 - a^2*x^2)) + a*ArcTanh[a*x]^2 - ArcTanh[a*x]^2/x + (a^2*x*ArcTanh[a*x]^2)/(2*(1 - a^2*x^2)) + (a*ArcTanh[a*x]^3)/2 + 2*a*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] - a*PolyLog[2, -1 + 2/(1 + a*x)]","A",11,11,22,0.5000,1,"{6030, 5982, 5916, 5988, 5932, 2447, 5948, 5956, 5994, 199, 206}"
272,1,205,0,0.6956333,"\int \frac{\tanh ^{-1}(a x)^2}{x^3 \left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]^2/(x^3*(1 - a^2*x^2)^2),x]","-a^2 \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-2 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{a^2}{4 \left(1-a^2 x^2\right)}-\frac{1}{2} a^2 \log \left(1-a^2 x^2\right)-\frac{a^3 x \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{a^2 \tanh ^{-1}(a x)^2}{2 \left(1-a^2 x^2\right)}+a^2 \log (x)+\frac{2}{3} a^2 \tanh ^{-1}(a x)^3+\frac{1}{4} a^2 \tanh ^{-1}(a x)^2+2 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{2 x^2}-\frac{a \tanh ^{-1}(a x)}{x}","-a^2 \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-2 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{a^2}{4 \left(1-a^2 x^2\right)}-\frac{1}{2} a^2 \log \left(1-a^2 x^2\right)-\frac{a^3 x \tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{a^2 \tanh ^{-1}(a x)^2}{2 \left(1-a^2 x^2\right)}+a^2 \log (x)+\frac{2}{3} a^2 \tanh ^{-1}(a x)^3+\frac{1}{4} a^2 \tanh ^{-1}(a x)^2+2 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{2 x^2}-\frac{a \tanh ^{-1}(a x)}{x}",1,"a^2/(4*(1 - a^2*x^2)) - (a*ArcTanh[a*x])/x - (a^3*x*ArcTanh[a*x])/(2*(1 - a^2*x^2)) + (a^2*ArcTanh[a*x]^2)/4 - ArcTanh[a*x]^2/(2*x^2) + (a^2*ArcTanh[a*x]^2)/(2*(1 - a^2*x^2)) + (2*a^2*ArcTanh[a*x]^3)/3 + a^2*Log[x] - (a^2*Log[1 - a^2*x^2])/2 + 2*a^2*ArcTanh[a*x]^2*Log[2 - 2/(1 + a*x)] - 2*a^2*ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 + a*x)] - a^2*PolyLog[3, -1 + 2/(1 + a*x)]","A",22,15,22,0.6818,1,"{6030, 5982, 5916, 266, 36, 29, 31, 5948, 5988, 5932, 6056, 6610, 5994, 5956, 261}"
273,1,227,0,0.4027905,"\int \frac{x^3 \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^2} \, dx","Int[(x^3*ArcTanh[a*x]^3)/(1 - a^2*x^2)^2,x]","-\frac{3 \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{4 a^4}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^4}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{3 x}{8 a^3 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{2 a^4 \left(1-a^2 x^2\right)}-\frac{3 x \tanh ^{-1}(a x)^2}{4 a^3 \left(1-a^2 x^2\right)}+\frac{3 \tanh ^{-1}(a x)}{4 a^4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^4}{4 a^4}-\frac{\tanh ^{-1}(a x)^3}{4 a^4}-\frac{3 \tanh ^{-1}(a x)}{8 a^4}-\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^3}{a^4}","-\frac{3 \text{PolyLog}\left(4,1-\frac{2}{1-a x}\right)}{4 a^4}-\frac{3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^4}+\frac{3 \tanh ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^4}-\frac{3 x}{8 a^3 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{2 a^4 \left(1-a^2 x^2\right)}-\frac{3 x \tanh ^{-1}(a x)^2}{4 a^3 \left(1-a^2 x^2\right)}+\frac{3 \tanh ^{-1}(a x)}{4 a^4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^4}{4 a^4}-\frac{\tanh ^{-1}(a x)^3}{4 a^4}-\frac{3 \tanh ^{-1}(a x)}{8 a^4}-\frac{\log \left(\frac{2}{1-a x}\right) \tanh ^{-1}(a x)^3}{a^4}",1,"(-3*x)/(8*a^3*(1 - a^2*x^2)) - (3*ArcTanh[a*x])/(8*a^4) + (3*ArcTanh[a*x])/(4*a^4*(1 - a^2*x^2)) - (3*x*ArcTanh[a*x]^2)/(4*a^3*(1 - a^2*x^2)) - ArcTanh[a*x]^3/(4*a^4) + ArcTanh[a*x]^3/(2*a^4*(1 - a^2*x^2)) + ArcTanh[a*x]^4/(4*a^4) - (ArcTanh[a*x]^3*Log[2/(1 - a*x)])/a^4 - (3*ArcTanh[a*x]^2*PolyLog[2, 1 - 2/(1 - a*x)])/(2*a^4) + (3*ArcTanh[a*x]*PolyLog[3, 1 - 2/(1 - a*x)])/(2*a^4) - (3*PolyLog[4, 1 - 2/(1 - a*x)])/(4*a^4)","A",11,11,22,0.5000,1,"{6028, 5984, 5918, 5948, 6058, 6062, 6610, 5994, 5956, 199, 206}"
274,1,121,0,0.1335747,"\int \frac{x^2 \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^2} \, dx","Int[(x^2*ArcTanh[a*x]^3)/(1 - a^2*x^2)^2,x]","-\frac{3}{8 a^3 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^3}{2 a^2 \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^2}{4 a^3 \left(1-a^2 x^2\right)}+\frac{3 x \tanh ^{-1}(a x)}{4 a^2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)^4}{8 a^3}+\frac{3 \tanh ^{-1}(a x)^2}{8 a^3}","-\frac{3}{8 a^3 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^3}{2 a^2 \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^2}{4 a^3 \left(1-a^2 x^2\right)}+\frac{3 x \tanh ^{-1}(a x)}{4 a^2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)^4}{8 a^3}+\frac{3 \tanh ^{-1}(a x)^2}{8 a^3}",1,"-3/(8*a^3*(1 - a^2*x^2)) + (3*x*ArcTanh[a*x])/(4*a^2*(1 - a^2*x^2)) + (3*ArcTanh[a*x]^2)/(8*a^3) - (3*ArcTanh[a*x]^2)/(4*a^3*(1 - a^2*x^2)) + (x*ArcTanh[a*x]^3)/(2*a^2*(1 - a^2*x^2)) - ArcTanh[a*x]^4/(8*a^3)","A",4,4,22,0.1818,1,"{6000, 5994, 5956, 261}"
275,1,119,0,0.1117129,"\int \frac{x \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^2} \, dx","Int[(x*ArcTanh[a*x]^3)/(1 - a^2*x^2)^2,x]","-\frac{3 x}{8 a \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{2 a^2 \left(1-a^2 x^2\right)}-\frac{3 x \tanh ^{-1}(a x)^2}{4 a \left(1-a^2 x^2\right)}+\frac{3 \tanh ^{-1}(a x)}{4 a^2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)^3}{4 a^2}-\frac{3 \tanh ^{-1}(a x)}{8 a^2}","-\frac{3 x}{8 a \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{2 a^2 \left(1-a^2 x^2\right)}-\frac{3 x \tanh ^{-1}(a x)^2}{4 a \left(1-a^2 x^2\right)}+\frac{3 \tanh ^{-1}(a x)}{4 a^2 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)^3}{4 a^2}-\frac{3 \tanh ^{-1}(a x)}{8 a^2}",1,"(-3*x)/(8*a*(1 - a^2*x^2)) - (3*ArcTanh[a*x])/(8*a^2) + (3*ArcTanh[a*x])/(4*a^2*(1 - a^2*x^2)) - (3*x*ArcTanh[a*x]^2)/(4*a*(1 - a^2*x^2)) - ArcTanh[a*x]^3/(4*a^2) + ArcTanh[a*x]^3/(2*a^2*(1 - a^2*x^2))","A",5,4,20,0.2000,1,"{5994, 5956, 199, 206}"
276,1,115,0,0.0962471,"\int \frac{\tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]^3/(1 - a^2*x^2)^2,x]","-\frac{3}{8 a \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^3}{2 \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^2}{4 a \left(1-a^2 x^2\right)}+\frac{3 x \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^4}{8 a}+\frac{3 \tanh ^{-1}(a x)^2}{8 a}","-\frac{3}{8 a \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^3}{2 \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^2}{4 a \left(1-a^2 x^2\right)}+\frac{3 x \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^4}{8 a}+\frac{3 \tanh ^{-1}(a x)^2}{8 a}",1,"-3/(8*a*(1 - a^2*x^2)) + (3*x*ArcTanh[a*x])/(4*(1 - a^2*x^2)) + (3*ArcTanh[a*x]^2)/(8*a) - (3*ArcTanh[a*x]^2)/(4*a*(1 - a^2*x^2)) + (x*ArcTanh[a*x]^3)/(2*(1 - a^2*x^2)) + ArcTanh[a*x]^4/(8*a)","A",4,3,19,0.1579,1,"{5956, 5994, 261}"
277,1,193,0,0.3882592,"\int \frac{\tanh ^{-1}(a x)^3}{x \left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]^3/(x*(1 - a^2*x^2)^2),x]","-\frac{3}{4} \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\frac{3 a x}{8 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{2 \left(1-a^2 x^2\right)}-\frac{3 a x \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)}+\frac{3 \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)}+\frac{1}{4} \tanh ^{-1}(a x)^4-\frac{1}{4} \tanh ^{-1}(a x)^3-\frac{3}{8} \tanh ^{-1}(a x)+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3","-\frac{3}{4} \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\frac{3 a x}{8 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{2 \left(1-a^2 x^2\right)}-\frac{3 a x \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)}+\frac{3 \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)}+\frac{1}{4} \tanh ^{-1}(a x)^4-\frac{1}{4} \tanh ^{-1}(a x)^3-\frac{3}{8} \tanh ^{-1}(a x)+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3",1,"(-3*a*x)/(8*(1 - a^2*x^2)) - (3*ArcTanh[a*x])/8 + (3*ArcTanh[a*x])/(4*(1 - a^2*x^2)) - (3*a*x*ArcTanh[a*x]^2)/(4*(1 - a^2*x^2)) - ArcTanh[a*x]^3/4 + ArcTanh[a*x]^3/(2*(1 - a^2*x^2)) + ArcTanh[a*x]^4/4 + ArcTanh[a*x]^3*Log[2 - 2/(1 + a*x)] - (3*ArcTanh[a*x]^2*PolyLog[2, -1 + 2/(1 + a*x)])/2 - (3*ArcTanh[a*x]*PolyLog[3, -1 + 2/(1 + a*x)])/2 - (3*PolyLog[4, -1 + 2/(1 + a*x)])/4","A",11,11,22,0.5000,1,"{6030, 5988, 5932, 5948, 6056, 6060, 6610, 5994, 5956, 199, 206}"
278,1,191,0,0.4350965,"\int \frac{\tanh ^{-1}(a x)^3}{x^2 \left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]^3/(x^2*(1 - a^2*x^2)^2),x]","-\frac{3}{2} a \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-3 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3 a}{8 \left(1-a^2 x^2\right)}+\frac{a^2 x \tanh ^{-1}(a x)^3}{2 \left(1-a^2 x^2\right)}-\frac{3 a \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)}+\frac{3 a^2 x \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)}+\frac{3}{8} a \tanh ^{-1}(a x)^4+a \tanh ^{-1}(a x)^3-\frac{\tanh ^{-1}(a x)^3}{x}+\frac{3}{8} a \tanh ^{-1}(a x)^2+3 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2","-\frac{3}{2} a \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-3 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3 a}{8 \left(1-a^2 x^2\right)}+\frac{a^2 x \tanh ^{-1}(a x)^3}{2 \left(1-a^2 x^2\right)}-\frac{3 a \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)}+\frac{3 a^2 x \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)}+\frac{3}{8} a \tanh ^{-1}(a x)^4+a \tanh ^{-1}(a x)^3-\frac{\tanh ^{-1}(a x)^3}{x}+\frac{3}{8} a \tanh ^{-1}(a x)^2+3 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2",1,"(-3*a)/(8*(1 - a^2*x^2)) + (3*a^2*x*ArcTanh[a*x])/(4*(1 - a^2*x^2)) + (3*a*ArcTanh[a*x]^2)/8 - (3*a*ArcTanh[a*x]^2)/(4*(1 - a^2*x^2)) + a*ArcTanh[a*x]^3 - ArcTanh[a*x]^3/x + (a^2*x*ArcTanh[a*x]^3)/(2*(1 - a^2*x^2)) + (3*a*ArcTanh[a*x]^4)/8 + 3*a*ArcTanh[a*x]^2*Log[2 - 2/(1 + a*x)] - 3*a*ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 + a*x)] - (3*a*PolyLog[3, -1 + 2/(1 + a*x)])/2","A",12,11,22,0.5000,1,"{6030, 5982, 5916, 5988, 5932, 5948, 6056, 6610, 5956, 5994, 261}"
279,1,302,0,0.955259,"\int \frac{\tanh ^{-1}(a x)^3}{x^3 \left(1-a^2 x^2\right)^2} \, dx","Int[ArcTanh[a*x]^3/(x^3*(1 - a^2*x^2)^2),x]","-\frac{3}{2} a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{2} a^2 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)-3 a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\frac{3 a^3 x}{8 \left(1-a^2 x^2\right)}+\frac{a^2 \tanh ^{-1}(a x)^3}{2 \left(1-a^2 x^2\right)}-\frac{3 a^3 x \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)}+\frac{3 a^2 \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)}+\frac{1}{2} a^2 \tanh ^{-1}(a x)^4+\frac{1}{4} a^2 \tanh ^{-1}(a x)^3+\frac{3}{2} a^2 \tanh ^{-1}(a x)^2-\frac{3}{8} a^2 \tanh ^{-1}(a x)+2 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3+3 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)^3}{2 x^2}-\frac{3 a \tanh ^{-1}(a x)^2}{2 x}","-\frac{3}{2} a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{2} a^2 \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)-3 a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\frac{3 a^3 x}{8 \left(1-a^2 x^2\right)}+\frac{a^2 \tanh ^{-1}(a x)^3}{2 \left(1-a^2 x^2\right)}-\frac{3 a^3 x \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)}+\frac{3 a^2 \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)}+\frac{1}{2} a^2 \tanh ^{-1}(a x)^4+\frac{1}{4} a^2 \tanh ^{-1}(a x)^3+\frac{3}{2} a^2 \tanh ^{-1}(a x)^2-\frac{3}{8} a^2 \tanh ^{-1}(a x)+2 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3+3 a^2 \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)-\frac{\tanh ^{-1}(a x)^3}{2 x^2}-\frac{3 a \tanh ^{-1}(a x)^2}{2 x}",1,"(-3*a^3*x)/(8*(1 - a^2*x^2)) - (3*a^2*ArcTanh[a*x])/8 + (3*a^2*ArcTanh[a*x])/(4*(1 - a^2*x^2)) + (3*a^2*ArcTanh[a*x]^2)/2 - (3*a*ArcTanh[a*x]^2)/(2*x) - (3*a^3*x*ArcTanh[a*x]^2)/(4*(1 - a^2*x^2)) + (a^2*ArcTanh[a*x]^3)/4 - ArcTanh[a*x]^3/(2*x^2) + (a^2*ArcTanh[a*x]^3)/(2*(1 - a^2*x^2)) + (a^2*ArcTanh[a*x]^4)/2 + 3*a^2*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] + 2*a^2*ArcTanh[a*x]^3*Log[2 - 2/(1 + a*x)] - (3*a^2*PolyLog[2, -1 + 2/(1 + a*x)])/2 - 3*a^2*ArcTanh[a*x]^2*PolyLog[2, -1 + 2/(1 + a*x)] - 3*a^2*ArcTanh[a*x]*PolyLog[3, -1 + 2/(1 + a*x)] - (3*a^2*PolyLog[4, -1 + 2/(1 + a*x)])/2","A",25,14,22,0.6364,1,"{6030, 5982, 5916, 5988, 5932, 2447, 5948, 6056, 6060, 6610, 5994, 5956, 199, 206}"
280,1,103,0,0.1443363,"\int \frac{\sqrt{\tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^2} \, dx","Int[Sqrt[ArcTanh[a*x]]/(1 - a^2*x^2)^2,x]","\frac{x \sqrt{\tanh ^{-1}(a x)}}{2 \left(1-a^2 x^2\right)}+\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{16 a}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{16 a}+\frac{\tanh ^{-1}(a x)^{3/2}}{3 a}","\frac{x \sqrt{\tanh ^{-1}(a x)}}{2 \left(1-a^2 x^2\right)}+\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{16 a}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{16 a}+\frac{\tanh ^{-1}(a x)^{3/2}}{3 a}",1,"(x*Sqrt[ArcTanh[a*x]])/(2*(1 - a^2*x^2)) + ArcTanh[a*x]^(3/2)/(3*a) + (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcTanh[a*x]]])/(16*a) - (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcTanh[a*x]]])/(16*a)","A",9,8,21,0.3810,1,"{5956, 6034, 5448, 12, 3308, 2180, 2204, 2205}"
281,0,0,0,0.0635334,"\int \frac{x^4}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)} \, dx","Int[x^4/((1 - a^2*x^2)^2*ArcTanh[a*x]),x]","\int \frac{x^4}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)} \, dx","\frac{\text{Int}\left(\frac{1}{\tanh ^{-1}(a x)},x\right)}{a^4}+\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^5}-\frac{3 \log \left(\tanh ^{-1}(a x)\right)}{2 a^5}",0,"Defer[Int][x^4/((1 - a^2*x^2)^2*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
282,0,0,0,0.0629171,"\int \frac{x^3}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)} \, dx","Int[x^3/((1 - a^2*x^2)^2*ArcTanh[a*x]),x]","\int \frac{x^3}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)} \, dx","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^4}-\frac{\text{Int}\left(\frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)},x\right)}{a^2}",0,"Defer[Int][x^3/((1 - a^2*x^2)^2*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
283,1,27,0,0.1030398,"\int \frac{x^2}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)} \, dx","Int[x^2/((1 - a^2*x^2)^2*ArcTanh[a*x]),x]","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^3}-\frac{\log \left(\tanh ^{-1}(a x)\right)}{2 a^3}","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^3}-\frac{\log \left(\tanh ^{-1}(a x)\right)}{2 a^3}",1,"CoshIntegral[2*ArcTanh[a*x]]/(2*a^3) - Log[ArcTanh[a*x]]/(2*a^3)","A",4,3,22,0.1364,1,"{6034, 3312, 3301}"
284,1,14,0,0.0696786,"\int \frac{x}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)} \, dx","Int[x/((1 - a^2*x^2)^2*ArcTanh[a*x]),x]","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^2}","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^2}",1,"SinhIntegral[2*ArcTanh[a*x]]/(2*a^2)","A",4,4,20,0.2000,1,"{6034, 5448, 12, 3298}"
285,1,27,0,0.0662723,"\int \frac{1}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)} \, dx","Int[1/((1 - a^2*x^2)^2*ArcTanh[a*x]),x]","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a}+\frac{\log \left(\tanh ^{-1}(a x)\right)}{2 a}","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a}+\frac{\log \left(\tanh ^{-1}(a x)\right)}{2 a}",1,"CoshIntegral[2*ArcTanh[a*x]]/(2*a) + Log[ArcTanh[a*x]]/(2*a)","A",4,3,19,0.1579,1,"{5968, 3312, 3301}"
286,0,0,0,0.0748869,"\int \frac{1}{x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)} \, dx","Int[1/(x*(1 - a^2*x^2)^2*ArcTanh[a*x]),x]","\int \frac{1}{x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \left(1-a^2 x^2\right) \tanh ^{-1}(a x)},x\right)+\frac{1}{2} \text{Shi}\left(2 \tanh ^{-1}(a x)\right)",0,"Defer[Int][1/(x*(1 - a^2*x^2)^2*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
287,0,0,0,0.3162601,"\int \frac{x^3}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2} \, dx","Int[x^3/((1 - a^2*x^2)^2*ArcTanh[a*x]^2),x]","\int \frac{x^3}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2} \, dx","-\frac{\text{Int}\left(\frac{1}{\tanh ^{-1}(a x)},x\right)}{a^3}+\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{a^4}-\frac{x}{a^3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}+\frac{x}{a^3 \tanh ^{-1}(a x)}",0,"x/(a^3*ArcTanh[a*x]) - x/(a^3*(1 - a^2*x^2)*ArcTanh[a*x]) + CoshIntegral[2*ArcTanh[a*x]]/a^4 - Defer[Int][ArcTanh[a*x]^(-1), x]/a^3","A",0,0,0,0,-1,"{}"
288,1,38,0,0.1333154,"\int \frac{x^2}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2} \, dx","Int[x^2/((1 - a^2*x^2)^2*ArcTanh[a*x]^2),x]","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{a^3}-\frac{x^2}{a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{a^3}-\frac{x^2}{a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}",1,"-(x^2/(a*(1 - a^2*x^2)*ArcTanh[a*x])) + SinhIntegral[2*ArcTanh[a*x]]/a^3","A",5,5,22,0.2273,1,"{6006, 6034, 5448, 12, 3298}"
289,1,36,0,0.2072556,"\int \frac{x}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2} \, dx","Int[x/((1 - a^2*x^2)^2*ArcTanh[a*x]^2),x]","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{a^2}-\frac{x}{a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{a^2}-\frac{x}{a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}",1,"-(x/(a*(1 - a^2*x^2)*ArcTanh[a*x])) + CoshIntegral[2*ArcTanh[a*x]]/a^2","A",9,5,20,0.2500,1,"{6032, 6034, 3312, 3301, 5968}"
290,1,35,0,0.0945495,"\int \frac{1}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2} \, dx","Int[1/((1 - a^2*x^2)^2*ArcTanh[a*x]^2),x]","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{a}-\frac{1}{a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{a}-\frac{1}{a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}",1,"-(1/(a*(1 - a^2*x^2)*ArcTanh[a*x])) + SinhIntegral[2*ArcTanh[a*x]]/a","A",5,5,19,0.2632,1,"{5966, 6034, 5448, 12, 3298}"
291,0,0,0,0.3419745,"\int \frac{1}{x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2} \, dx","Int[1/(x*(1 - a^2*x^2)^2*ArcTanh[a*x]^2),x]","\int \frac{1}{x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \tanh ^{-1}(a x)},x\right)}{a}-\frac{a x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}+\text{Chi}\left(2 \tanh ^{-1}(a x)\right)-\frac{1}{a x \tanh ^{-1}(a x)}",0,"-(1/(a*x*ArcTanh[a*x])) - (a*x)/((1 - a^2*x^2)*ArcTanh[a*x]) + CoshIntegral[2*ArcTanh[a*x]] - Defer[Int][1/(x^2*ArcTanh[a*x]), x]/a","A",0,0,0,0,-1,"{}"
292,0,0,0,0.2248697,"\int \frac{x^3}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3} \, dx","Int[x^3/((1 - a^2*x^2)^2*ArcTanh[a*x]^3),x]","\int \frac{x^3}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3} \, dx","-\frac{\text{Int}\left(\frac{1}{\tanh ^{-1}(a x)^2},x\right)}{2 a^3}+\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{a^4}-\frac{x}{2 a^3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{a^2 x^2+1}{2 a^4 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}+\frac{x}{2 a^3 \tanh ^{-1}(a x)^2}",0,"x/(2*a^3*ArcTanh[a*x]^2) - x/(2*a^3*(1 - a^2*x^2)*ArcTanh[a*x]^2) - (1 + a^2*x^2)/(2*a^4*(1 - a^2*x^2)*ArcTanh[a*x]) + SinhIntegral[2*ArcTanh[a*x]]/a^4 - Defer[Int][ArcTanh[a*x]^(-2), x]/(2*a^3)","A",0,0,0,0,-1,"{}"
293,1,64,0,0.2718108,"\int \frac{x^2}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3} \, dx","Int[x^2/((1 - a^2*x^2)^2*ArcTanh[a*x]^3),x]","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{a^3}-\frac{x^2}{2 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{x}{a^2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{a^3}-\frac{x^2}{2 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{x}{a^2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}",1,"-x^2/(2*a*(1 - a^2*x^2)*ArcTanh[a*x]^2) - x/(a^2*(1 - a^2*x^2)*ArcTanh[a*x]) + CoshIntegral[2*ArcTanh[a*x]]/a^3","A",10,6,22,0.2727,1,"{6006, 6032, 6034, 3312, 3301, 5968}"
294,1,72,0,0.112101,"\int \frac{x}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3} \, dx","Int[x/((1 - a^2*x^2)^2*ArcTanh[a*x]^3),x]","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{a^2}-\frac{x}{2 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{a^2 x^2+1}{2 a^2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{a^2}-\frac{x}{2 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{a^2 x^2+1}{2 a^2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}",1,"-x/(2*a*(1 - a^2*x^2)*ArcTanh[a*x]^2) - (1 + a^2*x^2)/(2*a^2*(1 - a^2*x^2)*ArcTanh[a*x]) + SinhIntegral[2*ArcTanh[a*x]]/a^2","A",5,5,20,0.2500,1,"{5996, 6034, 5448, 12, 3298}"
295,1,58,0,0.2344603,"\int \frac{1}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3} \, dx","Int[1/((1 - a^2*x^2)^2*ArcTanh[a*x]^3),x]","-\frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}+\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{a}","-\frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}+\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{a}",1,"-1/(2*a*(1 - a^2*x^2)*ArcTanh[a*x]^2) - x/((1 - a^2*x^2)*ArcTanh[a*x]) + CoshIntegral[2*ArcTanh[a*x]]/a","A",10,6,19,0.3158,1,"{5966, 6032, 6034, 3312, 3301, 5968}"
296,0,0,0,0.2471909,"\int \frac{1}{x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3} \, dx","Int[1/(x*(1 - a^2*x^2)^2*ArcTanh[a*x]^3),x]","\int \frac{1}{x \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \tanh ^{-1}(a x)^2},x\right)}{2 a}-\frac{a x}{2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{a^2 x^2+1}{2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}+\text{Shi}\left(2 \tanh ^{-1}(a x)\right)-\frac{1}{2 a x \tanh ^{-1}(a x)^2}",0,"-1/(2*a*x*ArcTanh[a*x]^2) - (a*x)/(2*(1 - a^2*x^2)*ArcTanh[a*x]^2) - (1 + a^2*x^2)/(2*(1 - a^2*x^2)*ArcTanh[a*x]) + SinhIntegral[2*ArcTanh[a*x]] - Defer[Int][1/(x^2*ArcTanh[a*x]^2), x]/(2*a)","A",0,0,0,0,-1,"{}"
297,1,97,0,0.1430653,"\int \frac{1}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^4} \, dx","Int[1/((1 - a^2*x^2)^2*ArcTanh[a*x]^4),x]","-\frac{x}{3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{a^2 x^2+1}{3 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{1}{3 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}+\frac{2 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{3 a}","-\frac{x}{3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{a^2 x^2+1}{3 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{1}{3 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}+\frac{2 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{3 a}",1,"-1/(3*a*(1 - a^2*x^2)*ArcTanh[a*x]^3) - x/(3*(1 - a^2*x^2)*ArcTanh[a*x]^2) - (1 + a^2*x^2)/(3*a*(1 - a^2*x^2)*ArcTanh[a*x]) + (2*SinhIntegral[2*ArcTanh[a*x]])/(3*a)","A",6,6,19,0.3158,1,"{5966, 5996, 6034, 5448, 12, 3298}"
298,1,120,0,0.2899937,"\int \frac{1}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^5} \, dx","Int[1/((1 - a^2*x^2)^2*ArcTanh[a*x]^5),x]","-\frac{x}{3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{x}{6 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}-\frac{a^2 x^2+1}{12 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{1}{4 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^4}+\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{3 a}","-\frac{x}{3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{x}{6 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}-\frac{a^2 x^2+1}{12 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{1}{4 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^4}+\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{3 a}",1,"-1/(4*a*(1 - a^2*x^2)*ArcTanh[a*x]^4) - x/(6*(1 - a^2*x^2)*ArcTanh[a*x]^3) - (1 + a^2*x^2)/(12*a*(1 - a^2*x^2)*ArcTanh[a*x]^2) - x/(3*(1 - a^2*x^2)*ArcTanh[a*x]) + CoshIntegral[2*ArcTanh[a*x]]/(3*a)","A",11,7,19,0.3684,1,"{5966, 5996, 6032, 6034, 3312, 3301, 5968}"
299,1,154,0,0.1955727,"\int \frac{1}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^6} \, dx","Int[1/((1 - a^2*x^2)^2*ArcTanh[a*x]^6),x]","-\frac{x}{15 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{x}{10 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^4}-\frac{a^2 x^2+1}{15 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{a^2 x^2+1}{30 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}-\frac{1}{5 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^5}+\frac{2 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{15 a}","-\frac{x}{15 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{x}{10 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^4}-\frac{a^2 x^2+1}{15 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{a^2 x^2+1}{30 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}-\frac{1}{5 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^5}+\frac{2 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{15 a}",1,"-1/(5*a*(1 - a^2*x^2)*ArcTanh[a*x]^5) - x/(10*(1 - a^2*x^2)*ArcTanh[a*x]^4) - (1 + a^2*x^2)/(30*a*(1 - a^2*x^2)*ArcTanh[a*x]^3) - x/(15*(1 - a^2*x^2)*ArcTanh[a*x]^2) - (1 + a^2*x^2)/(15*a*(1 - a^2*x^2)*ArcTanh[a*x]) + (2*SinhIntegral[2*ArcTanh[a*x]])/(15*a)","A",7,6,19,0.3158,1,"{5966, 5996, 6034, 5448, 12, 3298}"
300,1,177,0,0.3441564,"\int \frac{1}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^7} \, dx","Int[1/((1 - a^2*x^2)^2*ArcTanh[a*x]^7),x]","-\frac{2 x}{45 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{x}{45 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}-\frac{x}{15 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^5}-\frac{a^2 x^2+1}{90 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{a^2 x^2+1}{60 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^4}-\frac{1}{6 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^6}+\frac{2 \text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{45 a}","-\frac{2 x}{45 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{x}{45 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}-\frac{x}{15 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^5}-\frac{a^2 x^2+1}{90 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{a^2 x^2+1}{60 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^4}-\frac{1}{6 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^6}+\frac{2 \text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{45 a}",1,"-1/(6*a*(1 - a^2*x^2)*ArcTanh[a*x]^6) - x/(15*(1 - a^2*x^2)*ArcTanh[a*x]^5) - (1 + a^2*x^2)/(60*a*(1 - a^2*x^2)*ArcTanh[a*x]^4) - x/(45*(1 - a^2*x^2)*ArcTanh[a*x]^3) - (1 + a^2*x^2)/(90*a*(1 - a^2*x^2)*ArcTanh[a*x]^2) - (2*x)/(45*(1 - a^2*x^2)*ArcTanh[a*x]) + (2*CoshIntegral[2*ArcTanh[a*x]])/(45*a)","A",12,7,19,0.3684,1,"{5966, 5996, 6032, 6034, 3312, 3301, 5968}"
301,1,211,0,0.2559074,"\int \frac{1}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^8} \, dx","Int[1/((1 - a^2*x^2)^2*ArcTanh[a*x]^8),x]","-\frac{2 x}{315 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{x}{105 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^4}-\frac{x}{21 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^6}-\frac{2 \left(a^2 x^2+1\right)}{315 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{a^2 x^2+1}{315 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}-\frac{a^2 x^2+1}{105 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^5}-\frac{1}{7 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^7}+\frac{4 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{315 a}","-\frac{2 x}{315 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{x}{105 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^4}-\frac{x}{21 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^6}-\frac{2 \left(a^2 x^2+1\right)}{315 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{a^2 x^2+1}{315 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}-\frac{a^2 x^2+1}{105 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^5}-\frac{1}{7 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^7}+\frac{4 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{315 a}",1,"-1/(7*a*(1 - a^2*x^2)*ArcTanh[a*x]^7) - x/(21*(1 - a^2*x^2)*ArcTanh[a*x]^6) - (1 + a^2*x^2)/(105*a*(1 - a^2*x^2)*ArcTanh[a*x]^5) - x/(105*(1 - a^2*x^2)*ArcTanh[a*x]^4) - (1 + a^2*x^2)/(315*a*(1 - a^2*x^2)*ArcTanh[a*x]^3) - (2*x)/(315*(1 - a^2*x^2)*ArcTanh[a*x]^2) - (2*(1 + a^2*x^2))/(315*a*(1 - a^2*x^2)*ArcTanh[a*x]) + (4*SinhIntegral[2*ArcTanh[a*x]])/(315*a)","A",8,6,19,0.3158,1,"{5966, 5996, 6034, 5448, 12, 3298}"
302,1,77,0,0.0627185,"\int \frac{x^3 \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^3} \, dx","Int[(x^3*ArcTanh[a*x])/(1 - a^2*x^2)^3,x]","-\frac{x^3}{16 a \left(1-a^2 x^2\right)^2}+\frac{3 x}{32 a^3 \left(1-a^2 x^2\right)}+\frac{x^4 \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)^2}-\frac{3 \tanh ^{-1}(a x)}{32 a^4}","-\frac{x^3}{16 a \left(1-a^2 x^2\right)^2}+\frac{3 x}{32 a^3 \left(1-a^2 x^2\right)}+\frac{x^4 \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)^2}-\frac{3 \tanh ^{-1}(a x)}{32 a^4}",1,"-x^3/(16*a*(1 - a^2*x^2)^2) + (3*x)/(32*a^3*(1 - a^2*x^2)) - (3*ArcTanh[a*x])/(32*a^4) + (x^4*ArcTanh[a*x])/(4*(1 - a^2*x^2)^2)","A",4,3,20,0.1500,1,"{6008, 288, 206}"
303,1,100,0,0.071921,"\int \frac{x^2 \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^3} \, dx","Int[(x^2*ArcTanh[a*x])/(1 - a^2*x^2)^3,x]","\frac{1}{16 a^3 \left(1-a^2 x^2\right)}-\frac{1}{16 a^3 \left(1-a^2 x^2\right)^2}-\frac{x \tanh ^{-1}(a x)}{8 a^2 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)}{4 a^2 \left(1-a^2 x^2\right)^2}-\frac{\tanh ^{-1}(a x)^2}{16 a^3}","\frac{1}{16 a^3 \left(1-a^2 x^2\right)}-\frac{1}{16 a^3 \left(1-a^2 x^2\right)^2}-\frac{x \tanh ^{-1}(a x)}{8 a^2 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)}{4 a^2 \left(1-a^2 x^2\right)^2}-\frac{\tanh ^{-1}(a x)^2}{16 a^3}",1,"-1/(16*a^3*(1 - a^2*x^2)^2) + 1/(16*a^3*(1 - a^2*x^2)) + (x*ArcTanh[a*x])/(4*a^2*(1 - a^2*x^2)^2) - (x*ArcTanh[a*x])/(8*a^2*(1 - a^2*x^2)) - ArcTanh[a*x]^2/(16*a^3)","A",3,3,20,0.1500,1,"{5998, 5956, 261}"
304,1,75,0,0.0469405,"\int \frac{x \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^3} \, dx","Int[(x*ArcTanh[a*x])/(1 - a^2*x^2)^3,x]","-\frac{3 x}{32 a \left(1-a^2 x^2\right)}-\frac{x}{16 a \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)}{4 a^2 \left(1-a^2 x^2\right)^2}-\frac{3 \tanh ^{-1}(a x)}{32 a^2}","-\frac{3 x}{32 a \left(1-a^2 x^2\right)}-\frac{x}{16 a \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)}{4 a^2 \left(1-a^2 x^2\right)^2}-\frac{3 \tanh ^{-1}(a x)}{32 a^2}",1,"-x/(16*a*(1 - a^2*x^2)^2) - (3*x)/(32*a*(1 - a^2*x^2)) - (3*ArcTanh[a*x])/(32*a^2) + ArcTanh[a*x]/(4*a^2*(1 - a^2*x^2)^2)","A",4,3,18,0.1667,1,"{5994, 199, 206}"
305,1,94,0,0.0448151,"\int \frac{\tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^3} \, dx","Int[ArcTanh[a*x]/(1 - a^2*x^2)^3,x]","-\frac{3}{16 a \left(1-a^2 x^2\right)}-\frac{1}{16 a \left(1-a^2 x^2\right)^2}+\frac{3 x \tanh ^{-1}(a x)}{8 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)^2}+\frac{3 \tanh ^{-1}(a x)^2}{16 a}","-\frac{3}{16 a \left(1-a^2 x^2\right)}-\frac{1}{16 a \left(1-a^2 x^2\right)^2}+\frac{3 x \tanh ^{-1}(a x)}{8 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)^2}+\frac{3 \tanh ^{-1}(a x)^2}{16 a}",1,"-1/(16*a*(1 - a^2*x^2)^2) - 3/(16*a*(1 - a^2*x^2)) + (x*ArcTanh[a*x])/(4*(1 - a^2*x^2)^2) + (3*x*ArcTanh[a*x])/(8*(1 - a^2*x^2)) + (3*ArcTanh[a*x]^2)/(16*a)","A",3,3,17,0.1765,1,"{5960, 5956, 261}"
306,1,129,0,0.2496409,"\int \frac{\tanh ^{-1}(a x)}{x \left(1-a^2 x^2\right)^3} \, dx","Int[ArcTanh[a*x]/(x*(1 - a^2*x^2)^3),x]","-\frac{1}{2} \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{11 a x}{32 \left(1-a^2 x^2\right)}-\frac{a x}{16 \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)^2}+\frac{1}{2} \tanh ^{-1}(a x)^2-\frac{11}{32} \tanh ^{-1}(a x)+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)","-\frac{1}{2} \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{11 a x}{32 \left(1-a^2 x^2\right)}-\frac{a x}{16 \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)}{2 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)^2}+\frac{1}{2} \tanh ^{-1}(a x)^2-\frac{11}{32} \tanh ^{-1}(a x)+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)",1,"-(a*x)/(16*(1 - a^2*x^2)^2) - (11*a*x)/(32*(1 - a^2*x^2)) - (11*ArcTanh[a*x])/32 + ArcTanh[a*x]/(4*(1 - a^2*x^2)^2) + ArcTanh[a*x]/(2*(1 - a^2*x^2)) + ArcTanh[a*x]^2/2 + ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] - PolyLog[2, -1 + 2/(1 + a*x)]/2","A",12,7,20,0.3500,1,"{6030, 5988, 5932, 2447, 5994, 199, 206}"
307,1,123,0,0.2351483,"\int \frac{\tanh ^{-1}(a x)}{x^2 \left(1-a^2 x^2\right)^3} \, dx","Int[ArcTanh[a*x]/(x^2*(1 - a^2*x^2)^3),x]","-\frac{7 a}{16 \left(1-a^2 x^2\right)}-\frac{a}{16 \left(1-a^2 x^2\right)^2}-\frac{1}{2} a \log \left(1-a^2 x^2\right)+\frac{7 a^2 x \tanh ^{-1}(a x)}{8 \left(1-a^2 x^2\right)}+\frac{a^2 x \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)^2}+a \log (x)+\frac{15}{16} a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)}{x}","-\frac{7 a}{16 \left(1-a^2 x^2\right)}-\frac{a}{16 \left(1-a^2 x^2\right)^2}-\frac{1}{2} a \log \left(1-a^2 x^2\right)+\frac{7 a^2 x \tanh ^{-1}(a x)}{8 \left(1-a^2 x^2\right)}+\frac{a^2 x \tanh ^{-1}(a x)}{4 \left(1-a^2 x^2\right)^2}+a \log (x)+\frac{15}{16} a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)}{x}",1,"-a/(16*(1 - a^2*x^2)^2) - (7*a)/(16*(1 - a^2*x^2)) - ArcTanh[a*x]/x + (a^2*x*ArcTanh[a*x])/(4*(1 - a^2*x^2)^2) + (7*a^2*x*ArcTanh[a*x])/(8*(1 - a^2*x^2)) + (15*a*ArcTanh[a*x]^2)/16 + a*Log[x] - (a*Log[1 - a^2*x^2])/2","A",14,11,20,0.5500,1,"{6030, 5982, 5916, 266, 36, 29, 31, 5948, 5956, 261, 5960}"
308,1,127,0,0.1835272,"\int \frac{x^3 \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^3} \, dx","Int[(x^3*ArcTanh[a*x]^2)/(1 - a^2*x^2)^3,x]","\frac{x^4}{32 \left(1-a^2 x^2\right)^2}-\frac{3}{32 a^4 \left(1-a^2 x^2\right)}+\frac{x^4 \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)^2}-\frac{x^3 \tanh ^{-1}(a x)}{8 a \left(1-a^2 x^2\right)^2}+\frac{3 x \tanh ^{-1}(a x)}{16 a^3 \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^2}{32 a^4}","\frac{x^4}{32 \left(1-a^2 x^2\right)^2}-\frac{3}{32 a^4 \left(1-a^2 x^2\right)}+\frac{x^4 \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)^2}-\frac{x^3 \tanh ^{-1}(a x)}{8 a \left(1-a^2 x^2\right)^2}+\frac{3 x \tanh ^{-1}(a x)}{16 a^3 \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^2}{32 a^4}",1,"x^4/(32*(1 - a^2*x^2)^2) - 3/(32*a^4*(1 - a^2*x^2)) - (x^3*ArcTanh[a*x])/(8*a*(1 - a^2*x^2)^2) + (3*x*ArcTanh[a*x])/(16*a^3*(1 - a^2*x^2)) - (3*ArcTanh[a*x]^2)/(32*a^4) + (x^4*ArcTanh[a*x]^2)/(4*(1 - a^2*x^2)^2)","A",4,4,22,0.1818,1,"{6008, 6002, 5998, 5948}"
309,1,163,0,0.2503924,"\int \frac{x^2 \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^3} \, dx","Int[(x^2*ArcTanh[a*x]^2)/(1 - a^2*x^2)^3,x]","-\frac{x}{64 a^2 \left(1-a^2 x^2\right)}+\frac{x}{32 a^2 \left(1-a^2 x^2\right)^2}-\frac{x \tanh ^{-1}(a x)^2}{8 a^2 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^2}{4 a^2 \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)}{8 a^3 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)}{8 a^3 \left(1-a^2 x^2\right)^2}-\frac{\tanh ^{-1}(a x)^3}{24 a^3}-\frac{\tanh ^{-1}(a x)}{64 a^3}","-\frac{x}{64 a^2 \left(1-a^2 x^2\right)}+\frac{x}{32 a^2 \left(1-a^2 x^2\right)^2}-\frac{x \tanh ^{-1}(a x)^2}{8 a^2 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^2}{4 a^2 \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)}{8 a^3 \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)}{8 a^3 \left(1-a^2 x^2\right)^2}-\frac{\tanh ^{-1}(a x)^3}{24 a^3}-\frac{\tanh ^{-1}(a x)}{64 a^3}",1,"x/(32*a^2*(1 - a^2*x^2)^2) - x/(64*a^2*(1 - a^2*x^2)) - ArcTanh[a*x]/(64*a^3) - ArcTanh[a*x]/(8*a^3*(1 - a^2*x^2)^2) + ArcTanh[a*x]/(8*a^3*(1 - a^2*x^2)) + (x*ArcTanh[a*x]^2)/(4*a^2*(1 - a^2*x^2)^2) - (x*ArcTanh[a*x]^2)/(8*a^2*(1 - a^2*x^2)) - ArcTanh[a*x]^3/(24*a^3)","A",13,6,22,0.2727,1,"{6028, 5956, 5994, 199, 206, 5964}"
310,1,125,0,0.093837,"\int \frac{x \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^3} \, dx","Int[(x*ArcTanh[a*x]^2)/(1 - a^2*x^2)^3,x]","\frac{3}{32 a^2 \left(1-a^2 x^2\right)}+\frac{1}{32 a^2 \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)^2}{4 a^2 \left(1-a^2 x^2\right)^2}-\frac{3 x \tanh ^{-1}(a x)}{16 a \left(1-a^2 x^2\right)}-\frac{x \tanh ^{-1}(a x)}{8 a \left(1-a^2 x^2\right)^2}-\frac{3 \tanh ^{-1}(a x)^2}{32 a^2}","\frac{3}{32 a^2 \left(1-a^2 x^2\right)}+\frac{1}{32 a^2 \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)^2}{4 a^2 \left(1-a^2 x^2\right)^2}-\frac{3 x \tanh ^{-1}(a x)}{16 a \left(1-a^2 x^2\right)}-\frac{x \tanh ^{-1}(a x)}{8 a \left(1-a^2 x^2\right)^2}-\frac{3 \tanh ^{-1}(a x)^2}{32 a^2}",1,"1/(32*a^2*(1 - a^2*x^2)^2) + 3/(32*a^2*(1 - a^2*x^2)) - (x*ArcTanh[a*x])/(8*a*(1 - a^2*x^2)^2) - (3*x*ArcTanh[a*x])/(16*a*(1 - a^2*x^2)) - (3*ArcTanh[a*x]^2)/(32*a^2) + ArcTanh[a*x]^2/(4*a^2*(1 - a^2*x^2)^2)","A",4,4,20,0.2000,1,"{5994, 5960, 5956, 261}"
311,1,151,0,0.1104227,"\int \frac{\tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^3} \, dx","Int[ArcTanh[a*x]^2/(1 - a^2*x^2)^3,x]","\frac{15 x}{64 \left(1-a^2 x^2\right)}+\frac{x}{32 \left(1-a^2 x^2\right)^2}+\frac{3 x \tanh ^{-1}(a x)^2}{8 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)^2}-\frac{3 \tanh ^{-1}(a x)}{8 a \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)}{8 a \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)^3}{8 a}+\frac{15 \tanh ^{-1}(a x)}{64 a}","\frac{15 x}{64 \left(1-a^2 x^2\right)}+\frac{x}{32 \left(1-a^2 x^2\right)^2}+\frac{3 x \tanh ^{-1}(a x)^2}{8 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)^2}-\frac{3 \tanh ^{-1}(a x)}{8 a \left(1-a^2 x^2\right)}-\frac{\tanh ^{-1}(a x)}{8 a \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)^3}{8 a}+\frac{15 \tanh ^{-1}(a x)}{64 a}",1,"x/(32*(1 - a^2*x^2)^2) + (15*x)/(64*(1 - a^2*x^2)) + (15*ArcTanh[a*x])/(64*a) - ArcTanh[a*x]/(8*a*(1 - a^2*x^2)^2) - (3*ArcTanh[a*x])/(8*a*(1 - a^2*x^2)) + (x*ArcTanh[a*x]^2)/(4*(1 - a^2*x^2)^2) + (3*x*ArcTanh[a*x]^2)/(8*(1 - a^2*x^2)) + ArcTanh[a*x]^3/(8*a)","A",8,5,19,0.2632,1,"{5964, 5956, 5994, 199, 206}"
312,1,196,0,0.4492438,"\int \frac{\tanh ^{-1}(a x)^2}{x \left(1-a^2 x^2\right)^3} \, dx","Int[ArcTanh[a*x]^2/(x*(1 - a^2*x^2)^3),x]","-\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{11}{32 \left(1-a^2 x^2\right)}+\frac{1}{32 \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)^2}{2 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)^2}-\frac{11 a x \tanh ^{-1}(a x)}{16 \left(1-a^2 x^2\right)}-\frac{a x \tanh ^{-1}(a x)}{8 \left(1-a^2 x^2\right)^2}+\frac{1}{3} \tanh ^{-1}(a x)^3-\frac{11}{32} \tanh ^{-1}(a x)^2+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2","-\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{11}{32 \left(1-a^2 x^2\right)}+\frac{1}{32 \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)^2}{2 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)^2}-\frac{11 a x \tanh ^{-1}(a x)}{16 \left(1-a^2 x^2\right)}-\frac{a x \tanh ^{-1}(a x)}{8 \left(1-a^2 x^2\right)^2}+\frac{1}{3} \tanh ^{-1}(a x)^3-\frac{11}{32} \tanh ^{-1}(a x)^2+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2",1,"1/(32*(1 - a^2*x^2)^2) + 11/(32*(1 - a^2*x^2)) - (a*x*ArcTanh[a*x])/(8*(1 - a^2*x^2)^2) - (11*a*x*ArcTanh[a*x])/(16*(1 - a^2*x^2)) - (11*ArcTanh[a*x]^2)/32 + ArcTanh[a*x]^2/(4*(1 - a^2*x^2)^2) + ArcTanh[a*x]^2/(2*(1 - a^2*x^2)) + ArcTanh[a*x]^3/3 + ArcTanh[a*x]^2*Log[2 - 2/(1 + a*x)] - ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 + a*x)] - PolyLog[3, -1 + 2/(1 + a*x)]/2","A",13,10,22,0.4545,1,"{6030, 5988, 5932, 5948, 6056, 6610, 5994, 5956, 261, 5960}"
313,1,209,0,0.4921155,"\int \frac{\tanh ^{-1}(a x)^2}{x^2 \left(1-a^2 x^2\right)^3} \, dx","Int[ArcTanh[a*x]^2/(x^2*(1 - a^2*x^2)^3),x]","-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{31 a^2 x}{64 \left(1-a^2 x^2\right)}+\frac{a^2 x}{32 \left(1-a^2 x^2\right)^2}+\frac{7 a^2 x \tanh ^{-1}(a x)^2}{8 \left(1-a^2 x^2\right)}+\frac{a^2 x \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)^2}-\frac{7 a \tanh ^{-1}(a x)}{8 \left(1-a^2 x^2\right)}-\frac{a \tanh ^{-1}(a x)}{8 \left(1-a^2 x^2\right)^2}+\frac{5}{8} a \tanh ^{-1}(a x)^3+a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{x}+\frac{31}{64} a \tanh ^{-1}(a x)+2 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)","-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{31 a^2 x}{64 \left(1-a^2 x^2\right)}+\frac{a^2 x}{32 \left(1-a^2 x^2\right)^2}+\frac{7 a^2 x \tanh ^{-1}(a x)^2}{8 \left(1-a^2 x^2\right)}+\frac{a^2 x \tanh ^{-1}(a x)^2}{4 \left(1-a^2 x^2\right)^2}-\frac{7 a \tanh ^{-1}(a x)}{8 \left(1-a^2 x^2\right)}-\frac{a \tanh ^{-1}(a x)}{8 \left(1-a^2 x^2\right)^2}+\frac{5}{8} a \tanh ^{-1}(a x)^3+a \tanh ^{-1}(a x)^2-\frac{\tanh ^{-1}(a x)^2}{x}+\frac{31}{64} a \tanh ^{-1}(a x)+2 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)",1,"(a^2*x)/(32*(1 - a^2*x^2)^2) + (31*a^2*x)/(64*(1 - a^2*x^2)) + (31*a*ArcTanh[a*x])/64 - (a*ArcTanh[a*x])/(8*(1 - a^2*x^2)^2) - (7*a*ArcTanh[a*x])/(8*(1 - a^2*x^2)) + a*ArcTanh[a*x]^2 - ArcTanh[a*x]^2/x + (a^2*x*ArcTanh[a*x]^2)/(4*(1 - a^2*x^2)^2) + (7*a^2*x*ArcTanh[a*x]^2)/(8*(1 - a^2*x^2)) + (5*a*ArcTanh[a*x]^3)/8 + 2*a*ArcTanh[a*x]*Log[2 - 2/(1 + a*x)] - a*PolyLog[2, -1 + 2/(1 + a*x)]","A",20,12,22,0.5455,1,"{6030, 5982, 5916, 5988, 5932, 2447, 5948, 5956, 5994, 199, 206, 5964}"
314,1,192,0,0.2679073,"\int \frac{x^3 \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^3} \, dx","Int[(x^3*ArcTanh[a*x]^3)/(1 - a^2*x^2)^3,x]","-\frac{3 x^3}{128 a \left(1-a^2 x^2\right)^2}+\frac{45 x}{256 a^3 \left(1-a^2 x^2\right)}+\frac{x^4 \tanh ^{-1}(a x)^3}{4 \left(1-a^2 x^2\right)^2}+\frac{3 x^4 \tanh ^{-1}(a x)}{32 \left(1-a^2 x^2\right)^2}-\frac{3 x^3 \tanh ^{-1}(a x)^2}{16 a \left(1-a^2 x^2\right)^2}+\frac{9 x \tanh ^{-1}(a x)^2}{32 a^3 \left(1-a^2 x^2\right)}-\frac{9 \tanh ^{-1}(a x)}{32 a^4 \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^3}{32 a^4}+\frac{27 \tanh ^{-1}(a x)}{256 a^4}","-\frac{3 x^3}{128 a \left(1-a^2 x^2\right)^2}+\frac{45 x}{256 a^3 \left(1-a^2 x^2\right)}+\frac{x^4 \tanh ^{-1}(a x)^3}{4 \left(1-a^2 x^2\right)^2}+\frac{3 x^4 \tanh ^{-1}(a x)}{32 \left(1-a^2 x^2\right)^2}-\frac{3 x^3 \tanh ^{-1}(a x)^2}{16 a \left(1-a^2 x^2\right)^2}+\frac{9 x \tanh ^{-1}(a x)^2}{32 a^3 \left(1-a^2 x^2\right)}-\frac{9 \tanh ^{-1}(a x)}{32 a^4 \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^3}{32 a^4}+\frac{27 \tanh ^{-1}(a x)}{256 a^4}",1,"(-3*x^3)/(128*a*(1 - a^2*x^2)^2) + (45*x)/(256*a^3*(1 - a^2*x^2)) + (27*ArcTanh[a*x])/(256*a^4) + (3*x^4*ArcTanh[a*x])/(32*(1 - a^2*x^2)^2) - (9*ArcTanh[a*x])/(32*a^4*(1 - a^2*x^2)) - (3*x^3*ArcTanh[a*x]^2)/(16*a*(1 - a^2*x^2)^2) + (9*x*ArcTanh[a*x]^2)/(32*a^3*(1 - a^2*x^2)) - (3*ArcTanh[a*x]^3)/(32*a^4) + (x^4*ArcTanh[a*x]^3)/(4*(1 - a^2*x^2)^2)","A",9,7,22,0.3182,1,"{6008, 6004, 6000, 5994, 199, 206, 288}"
315,1,215,0,0.3588173,"\int \frac{x^2 \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^3} \, dx","Int[(x^2*ArcTanh[a*x]^3)/(1 - a^2*x^2)^3,x]","\frac{3}{128 a^3 \left(1-a^2 x^2\right)}-\frac{3}{128 a^3 \left(1-a^2 x^2\right)^2}-\frac{x \tanh ^{-1}(a x)^3}{8 a^2 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^3}{4 a^2 \left(1-a^2 x^2\right)^2}+\frac{3 \tanh ^{-1}(a x)^2}{16 a^3 \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^2}{16 a^3 \left(1-a^2 x^2\right)^2}-\frac{3 x \tanh ^{-1}(a x)}{64 a^2 \left(1-a^2 x^2\right)}+\frac{3 x \tanh ^{-1}(a x)}{32 a^2 \left(1-a^2 x^2\right)^2}-\frac{\tanh ^{-1}(a x)^4}{32 a^3}-\frac{3 \tanh ^{-1}(a x)^2}{128 a^3}","\frac{3}{128 a^3 \left(1-a^2 x^2\right)}-\frac{3}{128 a^3 \left(1-a^2 x^2\right)^2}-\frac{x \tanh ^{-1}(a x)^3}{8 a^2 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^3}{4 a^2 \left(1-a^2 x^2\right)^2}+\frac{3 \tanh ^{-1}(a x)^2}{16 a^3 \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^2}{16 a^3 \left(1-a^2 x^2\right)^2}-\frac{3 x \tanh ^{-1}(a x)}{64 a^2 \left(1-a^2 x^2\right)}+\frac{3 x \tanh ^{-1}(a x)}{32 a^2 \left(1-a^2 x^2\right)^2}-\frac{\tanh ^{-1}(a x)^4}{32 a^3}-\frac{3 \tanh ^{-1}(a x)^2}{128 a^3}",1,"-3/(128*a^3*(1 - a^2*x^2)^2) + 3/(128*a^3*(1 - a^2*x^2)) + (3*x*ArcTanh[a*x])/(32*a^2*(1 - a^2*x^2)^2) - (3*x*ArcTanh[a*x])/(64*a^2*(1 - a^2*x^2)) - (3*ArcTanh[a*x]^2)/(128*a^3) - (3*ArcTanh[a*x]^2)/(16*a^3*(1 - a^2*x^2)^2) + (3*ArcTanh[a*x]^2)/(16*a^3*(1 - a^2*x^2)) + (x*ArcTanh[a*x]^3)/(4*a^2*(1 - a^2*x^2)^2) - (x*ArcTanh[a*x]^3)/(8*a^2*(1 - a^2*x^2)) - ArcTanh[a*x]^4/(32*a^3)","A",13,6,22,0.2727,1,"{6028, 5956, 5994, 261, 5964, 5960}"
316,1,188,0,0.1636465,"\int \frac{x \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^3} \, dx","Int[(x*ArcTanh[a*x]^3)/(1 - a^2*x^2)^3,x]","-\frac{45 x}{256 a \left(1-a^2 x^2\right)}-\frac{3 x}{128 a \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)^3}{4 a^2 \left(1-a^2 x^2\right)^2}-\frac{9 x \tanh ^{-1}(a x)^2}{32 a \left(1-a^2 x^2\right)}-\frac{3 x \tanh ^{-1}(a x)^2}{16 a \left(1-a^2 x^2\right)^2}+\frac{9 \tanh ^{-1}(a x)}{32 a^2 \left(1-a^2 x^2\right)}+\frac{3 \tanh ^{-1}(a x)}{32 a^2 \left(1-a^2 x^2\right)^2}-\frac{3 \tanh ^{-1}(a x)^3}{32 a^2}-\frac{45 \tanh ^{-1}(a x)}{256 a^2}","-\frac{45 x}{256 a \left(1-a^2 x^2\right)}-\frac{3 x}{128 a \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)^3}{4 a^2 \left(1-a^2 x^2\right)^2}-\frac{9 x \tanh ^{-1}(a x)^2}{32 a \left(1-a^2 x^2\right)}-\frac{3 x \tanh ^{-1}(a x)^2}{16 a \left(1-a^2 x^2\right)^2}+\frac{9 \tanh ^{-1}(a x)}{32 a^2 \left(1-a^2 x^2\right)}+\frac{3 \tanh ^{-1}(a x)}{32 a^2 \left(1-a^2 x^2\right)^2}-\frac{3 \tanh ^{-1}(a x)^3}{32 a^2}-\frac{45 \tanh ^{-1}(a x)}{256 a^2}",1,"(-3*x)/(128*a*(1 - a^2*x^2)^2) - (45*x)/(256*a*(1 - a^2*x^2)) - (45*ArcTanh[a*x])/(256*a^2) + (3*ArcTanh[a*x])/(32*a^2*(1 - a^2*x^2)^2) + (9*ArcTanh[a*x])/(32*a^2*(1 - a^2*x^2)) - (3*x*ArcTanh[a*x]^2)/(16*a*(1 - a^2*x^2)^2) - (9*x*ArcTanh[a*x]^2)/(32*a*(1 - a^2*x^2)) - (3*ArcTanh[a*x]^3)/(32*a^2) + ArcTanh[a*x]^3/(4*a^2*(1 - a^2*x^2)^2)","A",9,5,20,0.2500,1,"{5994, 5964, 5956, 199, 206}"
317,1,203,0,0.1773035,"\int \frac{\tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^3} \, dx","Int[ArcTanh[a*x]^3/(1 - a^2*x^2)^3,x]","-\frac{45}{128 a \left(1-a^2 x^2\right)}-\frac{3}{128 a \left(1-a^2 x^2\right)^2}+\frac{3 x \tanh ^{-1}(a x)^3}{8 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^3}{4 \left(1-a^2 x^2\right)^2}-\frac{9 \tanh ^{-1}(a x)^2}{16 a \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^2}{16 a \left(1-a^2 x^2\right)^2}+\frac{45 x \tanh ^{-1}(a x)}{64 \left(1-a^2 x^2\right)}+\frac{3 x \tanh ^{-1}(a x)}{32 \left(1-a^2 x^2\right)^2}+\frac{3 \tanh ^{-1}(a x)^4}{32 a}+\frac{45 \tanh ^{-1}(a x)^2}{128 a}","-\frac{45}{128 a \left(1-a^2 x^2\right)}-\frac{3}{128 a \left(1-a^2 x^2\right)^2}+\frac{3 x \tanh ^{-1}(a x)^3}{8 \left(1-a^2 x^2\right)}+\frac{x \tanh ^{-1}(a x)^3}{4 \left(1-a^2 x^2\right)^2}-\frac{9 \tanh ^{-1}(a x)^2}{16 a \left(1-a^2 x^2\right)}-\frac{3 \tanh ^{-1}(a x)^2}{16 a \left(1-a^2 x^2\right)^2}+\frac{45 x \tanh ^{-1}(a x)}{64 \left(1-a^2 x^2\right)}+\frac{3 x \tanh ^{-1}(a x)}{32 \left(1-a^2 x^2\right)^2}+\frac{3 \tanh ^{-1}(a x)^4}{32 a}+\frac{45 \tanh ^{-1}(a x)^2}{128 a}",1,"-3/(128*a*(1 - a^2*x^2)^2) - 45/(128*a*(1 - a^2*x^2)) + (3*x*ArcTanh[a*x])/(32*(1 - a^2*x^2)^2) + (45*x*ArcTanh[a*x])/(64*(1 - a^2*x^2)) + (45*ArcTanh[a*x]^2)/(128*a) - (3*ArcTanh[a*x]^2)/(16*a*(1 - a^2*x^2)^2) - (9*ArcTanh[a*x]^2)/(16*a*(1 - a^2*x^2)) + (x*ArcTanh[a*x]^3)/(4*(1 - a^2*x^2)^2) + (3*x*ArcTanh[a*x]^3)/(8*(1 - a^2*x^2)) + (3*ArcTanh[a*x]^4)/(32*a)","A",8,5,19,0.2632,1,"{5964, 5956, 5994, 261, 5960}"
318,1,277,0,0.6260808,"\int \frac{\tanh ^{-1}(a x)^3}{x \left(1-a^2 x^2\right)^3} \, dx","Int[ArcTanh[a*x]^3/(x*(1 - a^2*x^2)^3),x]","-\frac{3}{4} \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\frac{141 a x}{256 \left(1-a^2 x^2\right)}-\frac{3 a x}{128 \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)^3}{2 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{4 \left(1-a^2 x^2\right)^2}-\frac{33 a x \tanh ^{-1}(a x)^2}{32 \left(1-a^2 x^2\right)}-\frac{3 a x \tanh ^{-1}(a x)^2}{16 \left(1-a^2 x^2\right)^2}+\frac{33 \tanh ^{-1}(a x)}{32 \left(1-a^2 x^2\right)}+\frac{3 \tanh ^{-1}(a x)}{32 \left(1-a^2 x^2\right)^2}+\frac{1}{4} \tanh ^{-1}(a x)^4-\frac{11}{32} \tanh ^{-1}(a x)^3-\frac{141}{256} \tanh ^{-1}(a x)+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3","-\frac{3}{4} \text{PolyLog}\left(4,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{3}{2} \tanh ^{-1}(a x) \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-\frac{141 a x}{256 \left(1-a^2 x^2\right)}-\frac{3 a x}{128 \left(1-a^2 x^2\right)^2}+\frac{\tanh ^{-1}(a x)^3}{2 \left(1-a^2 x^2\right)}+\frac{\tanh ^{-1}(a x)^3}{4 \left(1-a^2 x^2\right)^2}-\frac{33 a x \tanh ^{-1}(a x)^2}{32 \left(1-a^2 x^2\right)}-\frac{3 a x \tanh ^{-1}(a x)^2}{16 \left(1-a^2 x^2\right)^2}+\frac{33 \tanh ^{-1}(a x)}{32 \left(1-a^2 x^2\right)}+\frac{3 \tanh ^{-1}(a x)}{32 \left(1-a^2 x^2\right)^2}+\frac{1}{4} \tanh ^{-1}(a x)^4-\frac{11}{32} \tanh ^{-1}(a x)^3-\frac{141}{256} \tanh ^{-1}(a x)+\log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^3",1,"(-3*a*x)/(128*(1 - a^2*x^2)^2) - (141*a*x)/(256*(1 - a^2*x^2)) - (141*ArcTanh[a*x])/256 + (3*ArcTanh[a*x])/(32*(1 - a^2*x^2)^2) + (33*ArcTanh[a*x])/(32*(1 - a^2*x^2)) - (3*a*x*ArcTanh[a*x]^2)/(16*(1 - a^2*x^2)^2) - (33*a*x*ArcTanh[a*x]^2)/(32*(1 - a^2*x^2)) - (11*ArcTanh[a*x]^3)/32 + ArcTanh[a*x]^3/(4*(1 - a^2*x^2)^2) + ArcTanh[a*x]^3/(2*(1 - a^2*x^2)) + ArcTanh[a*x]^4/4 + ArcTanh[a*x]^3*Log[2 - 2/(1 + a*x)] - (3*ArcTanh[a*x]^2*PolyLog[2, -1 + 2/(1 + a*x)])/2 - (3*ArcTanh[a*x]*PolyLog[3, -1 + 2/(1 + a*x)])/2 - (3*PolyLog[4, -1 + 2/(1 + a*x)])/4","A",21,12,22,0.5455,1,"{6030, 5988, 5932, 5948, 6056, 6060, 6610, 5994, 5956, 199, 206, 5964}"
319,1,281,0,0.6902371,"\int \frac{\tanh ^{-1}(a x)^3}{x^2 \left(1-a^2 x^2\right)^3} \, dx","Int[ArcTanh[a*x]^3/(x^2*(1 - a^2*x^2)^3),x]","-\frac{3}{2} a \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-3 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{93 a}{128 \left(1-a^2 x^2\right)}-\frac{3 a}{128 \left(1-a^2 x^2\right)^2}+\frac{7 a^2 x \tanh ^{-1}(a x)^3}{8 \left(1-a^2 x^2\right)}+\frac{a^2 x \tanh ^{-1}(a x)^3}{4 \left(1-a^2 x^2\right)^2}-\frac{21 a \tanh ^{-1}(a x)^2}{16 \left(1-a^2 x^2\right)}-\frac{3 a \tanh ^{-1}(a x)^2}{16 \left(1-a^2 x^2\right)^2}+\frac{93 a^2 x \tanh ^{-1}(a x)}{64 \left(1-a^2 x^2\right)}+\frac{3 a^2 x \tanh ^{-1}(a x)}{32 \left(1-a^2 x^2\right)^2}+\frac{15}{32} a \tanh ^{-1}(a x)^4+a \tanh ^{-1}(a x)^3-\frac{\tanh ^{-1}(a x)^3}{x}+\frac{93}{128} a \tanh ^{-1}(a x)^2+3 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2","-\frac{3}{2} a \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-3 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{93 a}{128 \left(1-a^2 x^2\right)}-\frac{3 a}{128 \left(1-a^2 x^2\right)^2}+\frac{7 a^2 x \tanh ^{-1}(a x)^3}{8 \left(1-a^2 x^2\right)}+\frac{a^2 x \tanh ^{-1}(a x)^3}{4 \left(1-a^2 x^2\right)^2}-\frac{21 a \tanh ^{-1}(a x)^2}{16 \left(1-a^2 x^2\right)}-\frac{3 a \tanh ^{-1}(a x)^2}{16 \left(1-a^2 x^2\right)^2}+\frac{93 a^2 x \tanh ^{-1}(a x)}{64 \left(1-a^2 x^2\right)}+\frac{3 a^2 x \tanh ^{-1}(a x)}{32 \left(1-a^2 x^2\right)^2}+\frac{15}{32} a \tanh ^{-1}(a x)^4+a \tanh ^{-1}(a x)^3-\frac{\tanh ^{-1}(a x)^3}{x}+\frac{93}{128} a \tanh ^{-1}(a x)^2+3 a \log \left(2-\frac{2}{a x+1}\right) \tanh ^{-1}(a x)^2",1,"(-3*a)/(128*(1 - a^2*x^2)^2) - (93*a)/(128*(1 - a^2*x^2)) + (3*a^2*x*ArcTanh[a*x])/(32*(1 - a^2*x^2)^2) + (93*a^2*x*ArcTanh[a*x])/(64*(1 - a^2*x^2)) + (93*a*ArcTanh[a*x]^2)/128 - (3*a*ArcTanh[a*x]^2)/(16*(1 - a^2*x^2)^2) - (21*a*ArcTanh[a*x]^2)/(16*(1 - a^2*x^2)) + a*ArcTanh[a*x]^3 - ArcTanh[a*x]^3/x + (a^2*x*ArcTanh[a*x]^3)/(4*(1 - a^2*x^2)^2) + (7*a^2*x*ArcTanh[a*x]^3)/(8*(1 - a^2*x^2)) + (15*a*ArcTanh[a*x]^4)/32 + 3*a*ArcTanh[a*x]^2*Log[2 - 2/(1 + a*x)] - 3*a*ArcTanh[a*x]*PolyLog[2, -1 + 2/(1 + a*x)] - (3*a*PolyLog[3, -1 + 2/(1 + a*x)])/2","A",21,13,22,0.5909,1,"{6030, 5982, 5916, 5988, 5932, 5948, 6056, 6610, 5956, 5994, 261, 5964, 5960}"
320,1,168,0,0.1952438,"\int \frac{\sqrt{\tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^3} \, dx","Int[Sqrt[ArcTanh[a*x]]/(1 - a^2*x^2)^3,x]","\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\tanh ^{-1}(a x)}\right)}{256 a}+\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{16 a}-\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\tanh ^{-1}(a x)}\right)}{256 a}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{16 a}+\frac{\tanh ^{-1}(a x)^{3/2}}{4 a}+\frac{\sqrt{\tanh ^{-1}(a x)} \sinh \left(2 \tanh ^{-1}(a x)\right)}{4 a}+\frac{\sqrt{\tanh ^{-1}(a x)} \sinh \left(4 \tanh ^{-1}(a x)\right)}{32 a}","\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\tanh ^{-1}(a x)}\right)}{256 a}+\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{16 a}-\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\tanh ^{-1}(a x)}\right)}{256 a}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{16 a}+\frac{\tanh ^{-1}(a x)^{3/2}}{4 a}+\frac{\sqrt{\tanh ^{-1}(a x)} \sinh \left(2 \tanh ^{-1}(a x)\right)}{4 a}+\frac{\sqrt{\tanh ^{-1}(a x)} \sinh \left(4 \tanh ^{-1}(a x)\right)}{32 a}",1,"ArcTanh[a*x]^(3/2)/(4*a) + (Sqrt[Pi]*Erf[2*Sqrt[ArcTanh[a*x]]])/(256*a) + (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcTanh[a*x]]])/(16*a) - (Sqrt[Pi]*Erfi[2*Sqrt[ArcTanh[a*x]]])/(256*a) - (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcTanh[a*x]]])/(16*a) + (Sqrt[ArcTanh[a*x]]*Sinh[2*ArcTanh[a*x]])/(4*a) + (Sqrt[ArcTanh[a*x]]*Sinh[4*ArcTanh[a*x]])/(32*a)","A",15,7,21,0.3333,1,"{5968, 3312, 3296, 3308, 2180, 2204, 2205}"
321,0,0,0,0.0688041,"\int \frac{x^6}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)} \, dx","Int[x^6/((1 - a^2*x^2)^3*ArcTanh[a*x]),x]","\int \frac{x^6}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x^6}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][x^6/((1 - a^2*x^2)^3*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
322,0,0,0,0.0688522,"\int \frac{x^5}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)} \, dx","Int[x^5/((1 - a^2*x^2)^3*ArcTanh[a*x]),x]","\int \frac{x^5}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x^5}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][x^5/((1 - a^2*x^2)^3*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
323,1,41,0,0.121805,"\int \frac{x^4}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)} \, dx","Int[x^4/((1 - a^2*x^2)^3*ArcTanh[a*x]),x]","-\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^5}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^5}+\frac{3 \log \left(\tanh ^{-1}(a x)\right)}{8 a^5}","-\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^5}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^5}+\frac{3 \log \left(\tanh ^{-1}(a x)\right)}{8 a^5}",1,"-CoshIntegral[2*ArcTanh[a*x]]/(2*a^5) + CoshIntegral[4*ArcTanh[a*x]]/(8*a^5) + (3*Log[ArcTanh[a*x]])/(8*a^5)","A",5,3,22,0.1364,1,"{6034, 3312, 3301}"
324,1,29,0,0.11822,"\int \frac{x^3}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)} \, dx","Int[x^3/((1 - a^2*x^2)^3*ArcTanh[a*x]),x]","\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^4}-\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{4 a^4}","\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^4}-\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{4 a^4}",1,"-SinhIntegral[2*ArcTanh[a*x]]/(4*a^4) + SinhIntegral[4*ArcTanh[a*x]]/(8*a^4)","A",5,3,22,0.1364,1,"{6034, 5448, 3298}"
325,1,27,0,0.1125698,"\int \frac{x^2}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)} \, dx","Int[x^2/((1 - a^2*x^2)^3*ArcTanh[a*x]),x]","\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^3}-\frac{\log \left(\tanh ^{-1}(a x)\right)}{8 a^3}","\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^3}-\frac{\log \left(\tanh ^{-1}(a x)\right)}{8 a^3}",1,"CoshIntegral[4*ArcTanh[a*x]]/(8*a^3) - Log[ArcTanh[a*x]]/(8*a^3)","A",4,3,22,0.1364,1,"{6034, 5448, 3301}"
326,1,29,0,0.0941661,"\int \frac{x}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)} \, dx","Int[x/((1 - a^2*x^2)^3*ArcTanh[a*x]),x]","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{4 a^2}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^2}","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{4 a^2}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^2}",1,"SinhIntegral[2*ArcTanh[a*x]]/(4*a^2) + SinhIntegral[4*ArcTanh[a*x]]/(8*a^2)","A",5,3,20,0.1500,1,"{6034, 5448, 3298}"
327,1,41,0,0.0831106,"\int \frac{1}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)} \, dx","Int[1/((1 - a^2*x^2)^3*ArcTanh[a*x]),x]","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{8 a}+\frac{3 \log \left(\tanh ^{-1}(a x)\right)}{8 a}","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{8 a}+\frac{3 \log \left(\tanh ^{-1}(a x)\right)}{8 a}",1,"CoshIntegral[2*ArcTanh[a*x]]/(2*a) + CoshIntegral[4*ArcTanh[a*x]]/(8*a) + (3*Log[ArcTanh[a*x]])/(8*a)","A",5,3,19,0.1579,1,"{5968, 3312, 3301}"
328,0,0,0,0.0636374,"\int \frac{1}{x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)} \, dx","Int[1/(x*(1 - a^2*x^2)^3*ArcTanh[a*x]),x]","\int \frac{1}{x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)} \, dx","-\text{Int}\left(\frac{1}{x \left(a^2 x^2-1\right) \tanh ^{-1}(a x)},x\right)+\frac{3}{4} \text{Shi}\left(2 \tanh ^{-1}(a x)\right)+\frac{1}{8} \text{Shi}\left(4 \tanh ^{-1}(a x)\right)",0,"Defer[Int][1/(x*(1 - a^2*x^2)^3*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
329,0,0,0,0.9045769,"\int \frac{x^5}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2} \, dx","Int[x^5/((1 - a^2*x^2)^3*ArcTanh[a*x]^2),x]","\int \frac{x^5}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2} \, dx","\frac{\text{Int}\left(\frac{1}{\tanh ^{-1}(a x)},x\right)}{a^5}-\frac{3 \text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^6}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{2 a^6}+\frac{2 x}{a^5 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{x}{a^5 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}-\frac{x}{a^5 \tanh ^{-1}(a x)}",0,"-(x/(a^5*ArcTanh[a*x])) - x/(a^5*(1 - a^2*x^2)^2*ArcTanh[a*x]) + (2*x)/(a^5*(1 - a^2*x^2)*ArcTanh[a*x]) - (3*CoshIntegral[2*ArcTanh[a*x]])/(2*a^6) + CoshIntegral[4*ArcTanh[a*x]]/(2*a^6) + Defer[Int][ArcTanh[a*x]^(-1), x]/a^5","A",0,0,0,0,-1,"{}"
330,1,53,0,0.1863285,"\int \frac{x^4}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2} \, dx","Int[x^4/((1 - a^2*x^2)^3*ArcTanh[a*x]^2),x]","-\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{a^5}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{2 a^5}-\frac{x^4}{a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}","-\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{a^5}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{2 a^5}-\frac{x^4}{a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}",1,"-(x^4/(a*(1 - a^2*x^2)^2*ArcTanh[a*x])) - SinhIntegral[2*ArcTanh[a*x]]/a^5 + SinhIntegral[4*ArcTanh[a*x]]/(2*a^5)","A",6,4,22,0.1818,1,"{6006, 6034, 5448, 3298}"
331,1,76,0,0.5206008,"\int \frac{x^3}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2} \, dx","Int[x^3/((1 - a^2*x^2)^3*ArcTanh[a*x]^2),x]","-\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{2 a^4}+\frac{x}{a^3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{x}{a^3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}","-\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{2 a^4}-\frac{x^3}{a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}",1,"-(x/(a^3*(1 - a^2*x^2)^2*ArcTanh[a*x])) + x/(a^3*(1 - a^2*x^2)*ArcTanh[a*x]) - CoshIntegral[2*ArcTanh[a*x]]/(2*a^4) + CoshIntegral[4*ArcTanh[a*x]]/(2*a^4)","A",20,7,22,0.3182,1,"{6028, 6032, 6034, 3312, 3301, 5968, 5448}"
332,1,60,0,0.2872687,"\int \frac{x^2}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2} \, dx","Int[x^2/((1 - a^2*x^2)^3*ArcTanh[a*x]^2),x]","\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{2 a^3}+\frac{1}{a^3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{1}{a^3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}","\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{2 a^3}-\frac{x^2}{a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}",1,"-(1/(a^3*(1 - a^2*x^2)^2*ArcTanh[a*x])) + 1/(a^3*(1 - a^2*x^2)*ArcTanh[a*x]) + SinhIntegral[4*ArcTanh[a*x]]/(2*a^3)","A",12,6,22,0.2727,1,"{6028, 5966, 6034, 5448, 12, 3298}"
333,1,53,0,0.2451512,"\int \frac{x}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2} \, dx","Int[x/((1 - a^2*x^2)^3*ArcTanh[a*x]^2),x]","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^2}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{2 a^2}-\frac{x}{a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}","\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^2}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{2 a^2}-\frac{x}{a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}",1,"-(x/(a*(1 - a^2*x^2)^2*ArcTanh[a*x])) + CoshIntegral[2*ArcTanh[a*x]]/(2*a^2) + CoshIntegral[4*ArcTanh[a*x]]/(2*a^2)","A",10,6,20,0.3000,1,"{6032, 6034, 5448, 3301, 5968, 3312}"
334,1,49,0,0.1205319,"\int \frac{1}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2} \, dx","Int[1/((1 - a^2*x^2)^3*ArcTanh[a*x]^2),x]","-\frac{1}{a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}+\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{a}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{2 a}","-\frac{1}{a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}+\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{a}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{2 a}",1,"-(1/(a*(1 - a^2*x^2)^2*ArcTanh[a*x])) + SinhIntegral[2*ArcTanh[a*x]]/a + SinhIntegral[4*ArcTanh[a*x]]/(2*a)","A",6,4,19,0.2105,1,"{5966, 6034, 5448, 3298}"
335,0,0,0,0.6501638,"\int \frac{1}{x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2} \, dx","Int[1/(x*(1 - a^2*x^2)^3*ArcTanh[a*x]^2),x]","\int \frac{1}{x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \tanh ^{-1}(a x)},x\right)}{a}-\frac{a x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{a x}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}+\frac{3}{2} \text{Chi}\left(2 \tanh ^{-1}(a x)\right)+\frac{1}{2} \text{Chi}\left(4 \tanh ^{-1}(a x)\right)-\frac{1}{a x \tanh ^{-1}(a x)}",0,"-(1/(a*x*ArcTanh[a*x])) - (a*x)/((1 - a^2*x^2)^2*ArcTanh[a*x]) - (a*x)/((1 - a^2*x^2)*ArcTanh[a*x]) + (3*CoshIntegral[2*ArcTanh[a*x]])/2 + CoshIntegral[4*ArcTanh[a*x]]/2 - Defer[Int][1/(x^2*ArcTanh[a*x]), x]/a","A",0,0,0,0,-1,"{}"
336,1,100,0,0.5941999,"\int \frac{x^4}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^3} \, dx","Int[x^4/((1 - a^2*x^2)^3*ArcTanh[a*x]^3),x]","-\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{a^5}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{a^5}-\frac{x^4}{2 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}+\frac{2 x}{a^4 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{2 x}{a^4 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}","-\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{a^5}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{a^5}-\frac{x^4}{2 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}+\frac{2 x}{a^4 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{2 x}{a^4 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}",1,"-x^4/(2*a*(1 - a^2*x^2)^2*ArcTanh[a*x]^2) - (2*x)/(a^4*(1 - a^2*x^2)^2*ArcTanh[a*x]) + (2*x)/(a^4*(1 - a^2*x^2)*ArcTanh[a*x]) - CoshIntegral[2*ArcTanh[a*x]]/a^5 + CoshIntegral[4*ArcTanh[a*x]]/a^5","A",21,8,22,0.3636,1,"{6006, 6028, 6032, 6034, 3312, 3301, 5968, 5448}"
337,1,160,0,0.6547197,"\int \frac{x^3}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^3} \, dx","Int[x^3/((1 - a^2*x^2)^3*ArcTanh[a*x]^3),x]","-\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{a^4}+\frac{x}{2 a^3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{x}{2 a^3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}+\frac{a^2 x^2+1}{2 a^4 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}+\frac{3}{2 a^4 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{2}{a^4 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}","-\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{a^4}-\frac{x^4}{2 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}-\frac{x^3}{2 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}-\frac{3 x^2}{2 a^2 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}",1,"-x/(2*a^3*(1 - a^2*x^2)^2*ArcTanh[a*x]^2) + x/(2*a^3*(1 - a^2*x^2)*ArcTanh[a*x]^2) - 2/(a^4*(1 - a^2*x^2)^2*ArcTanh[a*x]) + 3/(2*a^4*(1 - a^2*x^2)*ArcTanh[a*x]) + (1 + a^2*x^2)/(2*a^4*(1 - a^2*x^2)*ArcTanh[a*x]) - SinhIntegral[2*ArcTanh[a*x]]/(2*a^4) + SinhIntegral[4*ArcTanh[a*x]]/a^4","A",25,8,22,0.3636,1,"{6028, 5996, 6034, 5448, 12, 3298, 6032, 5966}"
338,1,109,0,0.5856631,"\int \frac{x^2}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^3} \, dx","Int[x^2/((1 - a^2*x^2)^3*ArcTanh[a*x]^3),x]","\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{a^3}+\frac{x}{a^2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{2 x}{a^2 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}+\frac{1}{2 a^3 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{1}{2 a^3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}","\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{a^3}-\frac{x^2}{2 a \left(a^2 x^2-1\right)^2 \tanh ^{-1}(a x)^2}+\frac{x}{a^2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{2 x}{a^2 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}",1,"-1/(2*a^3*(1 - a^2*x^2)^2*ArcTanh[a*x]^2) + 1/(2*a^3*(1 - a^2*x^2)*ArcTanh[a*x]^2) - (2*x)/(a^2*(1 - a^2*x^2)^2*ArcTanh[a*x]) + x/(a^2*(1 - a^2*x^2)*ArcTanh[a*x]) + CoshIntegral[4*ArcTanh[a*x]]/a^3","A",22,8,22,0.3636,1,"{6028, 5966, 6032, 6034, 3312, 3301, 5968, 5448}"
339,1,100,0,0.4640655,"\int \frac{x}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^3} \, dx","Int[x/((1 - a^2*x^2)^3*ArcTanh[a*x]^3),x]","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^2}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{a^2}-\frac{x}{2 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}+\frac{3}{2 a^2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{2}{a^2 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}","\frac{\text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{2 a^2}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{a^2}-\frac{x}{2 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}+\frac{3}{2 a^2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{2}{a^2 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}",1,"-x/(2*a*(1 - a^2*x^2)^2*ArcTanh[a*x]^2) - 2/(a^2*(1 - a^2*x^2)^2*ArcTanh[a*x]) + 3/(2*a^2*(1 - a^2*x^2)*ArcTanh[a*x]) + SinhIntegral[2*ArcTanh[a*x]]/(2*a^2) + SinhIntegral[4*ArcTanh[a*x]]/a^2","A",19,7,20,0.3500,1,"{6032, 6028, 5966, 6034, 5448, 12, 3298}"
340,1,69,0,0.27001,"\int \frac{1}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^3} \, dx","Int[1/((1 - a^2*x^2)^3*ArcTanh[a*x]^3),x]","-\frac{2 x}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}+\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{a}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{a}","-\frac{2 x}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}+\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{a}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{a}",1,"-1/(2*a*(1 - a^2*x^2)^2*ArcTanh[a*x]^2) - (2*x)/((1 - a^2*x^2)^2*ArcTanh[a*x]) + CoshIntegral[2*ArcTanh[a*x]]/a + CoshIntegral[4*ArcTanh[a*x]]/a","A",11,7,19,0.3684,1,"{5966, 6032, 6034, 5448, 3301, 5968, 3312}"
341,0,0,0,0.7666912,"\int \frac{1}{x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^3} \, dx","Int[1/(x*(1 - a^2*x^2)^3*ArcTanh[a*x]^3),x]","\int \frac{1}{x \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^3} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \tanh ^{-1}(a x)^2},x\right)}{2 a}-\frac{a x}{2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{a x}{2 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}-\frac{a^2 x^2+1}{2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}+\frac{3}{2 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{2}{\left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}+\frac{3}{2} \text{Shi}\left(2 \tanh ^{-1}(a x)\right)+\text{Shi}\left(4 \tanh ^{-1}(a x)\right)-\frac{1}{2 a x \tanh ^{-1}(a x)^2}",0,"-1/(2*a*x*ArcTanh[a*x]^2) - (a*x)/(2*(1 - a^2*x^2)^2*ArcTanh[a*x]^2) - (a*x)/(2*(1 - a^2*x^2)*ArcTanh[a*x]^2) - 2/((1 - a^2*x^2)^2*ArcTanh[a*x]) + 3/(2*(1 - a^2*x^2)*ArcTanh[a*x]) - (1 + a^2*x^2)/(2*(1 - a^2*x^2)*ArcTanh[a*x]) + (3*SinhIntegral[2*ArcTanh[a*x]])/2 + SinhIntegral[4*ArcTanh[a*x]] - Defer[Int][1/(x^2*ArcTanh[a*x]^2), x]/(2*a)","A",0,0,0,0,-1,"{}"
342,1,125,0,0.4999484,"\int \frac{1}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^4} \, dx","Int[1/((1 - a^2*x^2)^3*ArcTanh[a*x]^4),x]","-\frac{2 x}{3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}+\frac{2}{a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{8}{3 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}-\frac{1}{3 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3}+\frac{2 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{3 a}+\frac{4 \text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{3 a}","-\frac{2 x}{3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}+\frac{2}{a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{8}{3 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}-\frac{1}{3 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3}+\frac{2 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{3 a}+\frac{4 \text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{3 a}",1,"-1/(3*a*(1 - a^2*x^2)^2*ArcTanh[a*x]^3) - (2*x)/(3*(1 - a^2*x^2)^2*ArcTanh[a*x]^2) - 8/(3*a*(1 - a^2*x^2)^2*ArcTanh[a*x]) + 2/(a*(1 - a^2*x^2)*ArcTanh[a*x]) + (2*SinhIntegral[2*ArcTanh[a*x]])/(3*a) + (4*SinhIntegral[4*ArcTanh[a*x]])/(3*a)","A",20,7,19,0.3684,1,"{5966, 6032, 6028, 6034, 5448, 12, 3298}"
343,1,170,0,0.9633583,"\int \frac{1}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^5} \, dx","Int[1/((1 - a^2*x^2)^3*ArcTanh[a*x]^5),x]","\frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{8 x}{3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}-\frac{x}{3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3}+\frac{1}{2 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{2}{3 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}-\frac{1}{4 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^4}+\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{3 a}+\frac{4 \text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{3 a}","\frac{x}{\left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{8 x}{3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}-\frac{x}{3 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3}+\frac{1}{2 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{2}{3 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}-\frac{1}{4 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^4}+\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{3 a}+\frac{4 \text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{3 a}",1,"-1/(4*a*(1 - a^2*x^2)^2*ArcTanh[a*x]^4) - x/(3*(1 - a^2*x^2)^2*ArcTanh[a*x]^3) - 2/(3*a*(1 - a^2*x^2)^2*ArcTanh[a*x]^2) + 1/(2*a*(1 - a^2*x^2)*ArcTanh[a*x]^2) - (8*x)/(3*(1 - a^2*x^2)^2*ArcTanh[a*x]) + x/((1 - a^2*x^2)*ArcTanh[a*x]) + CoshIntegral[2*ArcTanh[a*x]]/(3*a) + (4*CoshIntegral[4*ArcTanh[a*x]])/(3*a)","A",35,8,19,0.4211,1,"{5966, 6032, 6028, 6034, 3312, 3301, 5968, 5448}"
344,1,257,0,1.3490493,"\int \frac{1}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^6} \, dx","Int[1/((1 - a^2*x^2)^3*ArcTanh[a*x]^6),x]","\frac{x}{5 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{8 x}{15 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}-\frac{x}{5 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^4}+\frac{a^2 x^2+1}{5 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}+\frac{8}{5 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{32}{15 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}+\frac{1}{5 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}-\frac{4}{15 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3}-\frac{1}{5 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^5}+\frac{2 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{15 a}+\frac{16 \text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{15 a}","\frac{x}{5 \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^2}-\frac{8 x}{15 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^2}-\frac{x}{5 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^4}+\frac{a^2 x^2+1}{5 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}+\frac{8}{5 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)}-\frac{32}{15 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}+\frac{1}{5 a \left(1-a^2 x^2\right) \tanh ^{-1}(a x)^3}-\frac{4}{15 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^3}-\frac{1}{5 a \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)^5}+\frac{2 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{15 a}+\frac{16 \text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{15 a}",1,"-1/(5*a*(1 - a^2*x^2)^2*ArcTanh[a*x]^5) - x/(5*(1 - a^2*x^2)^2*ArcTanh[a*x]^4) - 4/(15*a*(1 - a^2*x^2)^2*ArcTanh[a*x]^3) + 1/(5*a*(1 - a^2*x^2)*ArcTanh[a*x]^3) - (8*x)/(15*(1 - a^2*x^2)^2*ArcTanh[a*x]^2) + x/(5*(1 - a^2*x^2)*ArcTanh[a*x]^2) - 32/(15*a*(1 - a^2*x^2)^2*ArcTanh[a*x]) + 8/(5*a*(1 - a^2*x^2)*ArcTanh[a*x]) + (1 + a^2*x^2)/(5*a*(1 - a^2*x^2)*ArcTanh[a*x]) + (2*SinhIntegral[2*ArcTanh[a*x]])/(15*a) + (16*SinhIntegral[4*ArcTanh[a*x]])/(15*a)","A",49,8,19,0.4211,1,"{5966, 6032, 6028, 5996, 6034, 5448, 12, 3298}"
345,1,134,0,0.0738376,"\int \frac{\tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^4} \, dx","Int[ArcTanh[a*x]/(1 - a^2*x^2)^4,x]","-\frac{5}{32 a \left(1-a^2 x^2\right)}-\frac{5}{96 a \left(1-a^2 x^2\right)^2}-\frac{1}{36 a \left(1-a^2 x^2\right)^3}+\frac{5 x \tanh ^{-1}(a x)}{16 \left(1-a^2 x^2\right)}+\frac{5 x \tanh ^{-1}(a x)}{24 \left(1-a^2 x^2\right)^2}+\frac{x \tanh ^{-1}(a x)}{6 \left(1-a^2 x^2\right)^3}+\frac{5 \tanh ^{-1}(a x)^2}{32 a}","-\frac{5}{32 a \left(1-a^2 x^2\right)}-\frac{5}{96 a \left(1-a^2 x^2\right)^2}-\frac{1}{36 a \left(1-a^2 x^2\right)^3}+\frac{5 x \tanh ^{-1}(a x)}{16 \left(1-a^2 x^2\right)}+\frac{5 x \tanh ^{-1}(a x)}{24 \left(1-a^2 x^2\right)^2}+\frac{x \tanh ^{-1}(a x)}{6 \left(1-a^2 x^2\right)^3}+\frac{5 \tanh ^{-1}(a x)^2}{32 a}",1,"-1/(36*a*(1 - a^2*x^2)^3) - 5/(96*a*(1 - a^2*x^2)^2) - 5/(32*a*(1 - a^2*x^2)) + (x*ArcTanh[a*x])/(6*(1 - a^2*x^2)^3) + (5*x*ArcTanh[a*x])/(24*(1 - a^2*x^2)^2) + (5*x*ArcTanh[a*x])/(16*(1 - a^2*x^2)) + (5*ArcTanh[a*x]^2)/(32*a)","A",4,3,17,0.1765,1,"{5960, 5956, 261}"
346,1,214,0,0.1688869,"\int \frac{\tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^4} \, dx","Int[ArcTanh[a*x]^2/(1 - a^2*x^2)^4,x]","\frac{245 x}{1152 \left(1-a^2 x^2\right)}+\frac{65 x}{1728 \left(1-a^2 x^2\right)^2}+\frac{x}{108 \left(1-a^2 x^2\right)^3}+\frac{5 x \tanh ^{-1}(a x)^2}{16 \left(1-a^2 x^2\right)}+\frac{5 x \tanh ^{-1}(a x)^2}{24 \left(1-a^2 x^2\right)^2}+\frac{x \tanh ^{-1}(a x)^2}{6 \left(1-a^2 x^2\right)^3}-\frac{5 \tanh ^{-1}(a x)}{16 a \left(1-a^2 x^2\right)}-\frac{5 \tanh ^{-1}(a x)}{48 a \left(1-a^2 x^2\right)^2}-\frac{\tanh ^{-1}(a x)}{18 a \left(1-a^2 x^2\right)^3}+\frac{5 \tanh ^{-1}(a x)^3}{48 a}+\frac{245 \tanh ^{-1}(a x)}{1152 a}","\frac{245 x}{1152 \left(1-a^2 x^2\right)}+\frac{65 x}{1728 \left(1-a^2 x^2\right)^2}+\frac{x}{108 \left(1-a^2 x^2\right)^3}+\frac{5 x \tanh ^{-1}(a x)^2}{16 \left(1-a^2 x^2\right)}+\frac{5 x \tanh ^{-1}(a x)^2}{24 \left(1-a^2 x^2\right)^2}+\frac{x \tanh ^{-1}(a x)^2}{6 \left(1-a^2 x^2\right)^3}-\frac{5 \tanh ^{-1}(a x)}{16 a \left(1-a^2 x^2\right)}-\frac{5 \tanh ^{-1}(a x)}{48 a \left(1-a^2 x^2\right)^2}-\frac{\tanh ^{-1}(a x)}{18 a \left(1-a^2 x^2\right)^3}+\frac{5 \tanh ^{-1}(a x)^3}{48 a}+\frac{245 \tanh ^{-1}(a x)}{1152 a}",1,"x/(108*(1 - a^2*x^2)^3) + (65*x)/(1728*(1 - a^2*x^2)^2) + (245*x)/(1152*(1 - a^2*x^2)) + (245*ArcTanh[a*x])/(1152*a) - ArcTanh[a*x]/(18*a*(1 - a^2*x^2)^3) - (5*ArcTanh[a*x])/(48*a*(1 - a^2*x^2)^2) - (5*ArcTanh[a*x])/(16*a*(1 - a^2*x^2)) + (x*ArcTanh[a*x]^2)/(6*(1 - a^2*x^2)^3) + (5*x*ArcTanh[a*x]^2)/(24*(1 - a^2*x^2)^2) + (5*x*ArcTanh[a*x]^2)/(16*(1 - a^2*x^2)) + (5*ArcTanh[a*x]^3)/(48*a)","A",13,5,19,0.2632,1,"{5964, 5956, 5994, 199, 206}"
347,1,291,0,0.3267917,"\int \frac{\tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^4} \, dx","Int[ArcTanh[a*x]^3/(1 - a^2*x^2)^4,x]","-\frac{245}{768 a \left(1-a^2 x^2\right)}-\frac{65}{2304 a \left(1-a^2 x^2\right)^2}-\frac{1}{216 a \left(1-a^2 x^2\right)^3}+\frac{5 x \tanh ^{-1}(a x)^3}{16 \left(1-a^2 x^2\right)}+\frac{5 x \tanh ^{-1}(a x)^3}{24 \left(1-a^2 x^2\right)^2}+\frac{x \tanh ^{-1}(a x)^3}{6 \left(1-a^2 x^2\right)^3}-\frac{15 \tanh ^{-1}(a x)^2}{32 a \left(1-a^2 x^2\right)}-\frac{5 \tanh ^{-1}(a x)^2}{32 a \left(1-a^2 x^2\right)^2}-\frac{\tanh ^{-1}(a x)^2}{12 a \left(1-a^2 x^2\right)^3}+\frac{245 x \tanh ^{-1}(a x)}{384 \left(1-a^2 x^2\right)}+\frac{65 x \tanh ^{-1}(a x)}{576 \left(1-a^2 x^2\right)^2}+\frac{x \tanh ^{-1}(a x)}{36 \left(1-a^2 x^2\right)^3}+\frac{5 \tanh ^{-1}(a x)^4}{64 a}+\frac{245 \tanh ^{-1}(a x)^2}{768 a}","-\frac{245}{768 a \left(1-a^2 x^2\right)}-\frac{65}{2304 a \left(1-a^2 x^2\right)^2}-\frac{1}{216 a \left(1-a^2 x^2\right)^3}+\frac{5 x \tanh ^{-1}(a x)^3}{16 \left(1-a^2 x^2\right)}+\frac{5 x \tanh ^{-1}(a x)^3}{24 \left(1-a^2 x^2\right)^2}+\frac{x \tanh ^{-1}(a x)^3}{6 \left(1-a^2 x^2\right)^3}-\frac{15 \tanh ^{-1}(a x)^2}{32 a \left(1-a^2 x^2\right)}-\frac{5 \tanh ^{-1}(a x)^2}{32 a \left(1-a^2 x^2\right)^2}-\frac{\tanh ^{-1}(a x)^2}{12 a \left(1-a^2 x^2\right)^3}+\frac{245 x \tanh ^{-1}(a x)}{384 \left(1-a^2 x^2\right)}+\frac{65 x \tanh ^{-1}(a x)}{576 \left(1-a^2 x^2\right)^2}+\frac{x \tanh ^{-1}(a x)}{36 \left(1-a^2 x^2\right)^3}+\frac{5 \tanh ^{-1}(a x)^4}{64 a}+\frac{245 \tanh ^{-1}(a x)^2}{768 a}",1,"-1/(216*a*(1 - a^2*x^2)^3) - 65/(2304*a*(1 - a^2*x^2)^2) - 245/(768*a*(1 - a^2*x^2)) + (x*ArcTanh[a*x])/(36*(1 - a^2*x^2)^3) + (65*x*ArcTanh[a*x])/(576*(1 - a^2*x^2)^2) + (245*x*ArcTanh[a*x])/(384*(1 - a^2*x^2)) + (245*ArcTanh[a*x]^2)/(768*a) - ArcTanh[a*x]^2/(12*a*(1 - a^2*x^2)^3) - (5*ArcTanh[a*x]^2)/(32*a*(1 - a^2*x^2)^2) - (15*ArcTanh[a*x]^2)/(32*a*(1 - a^2*x^2)) + (x*ArcTanh[a*x]^3)/(6*(1 - a^2*x^2)^3) + (5*x*ArcTanh[a*x]^3)/(24*(1 - a^2*x^2)^2) + (5*x*ArcTanh[a*x]^3)/(16*(1 - a^2*x^2)) + (5*ArcTanh[a*x]^4)/(64*a)","A",13,5,19,0.2632,1,"{5964, 5956, 5994, 261, 5960}"
348,1,252,0,0.3006401,"\int \frac{\sqrt{\tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^4} \, dx","Int[Sqrt[ArcTanh[a*x]]/(1 - a^2*x^2)^4,x]","\frac{3 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\tanh ^{-1}(a x)}\right)}{512 a}+\frac{15 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{256 a}+\frac{\sqrt{\frac{\pi }{6}} \text{Erf}\left(\sqrt{6} \sqrt{\tanh ^{-1}(a x)}\right)}{768 a}-\frac{3 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\tanh ^{-1}(a x)}\right)}{512 a}-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{256 a}-\frac{\sqrt{\frac{\pi }{6}} \text{Erfi}\left(\sqrt{6} \sqrt{\tanh ^{-1}(a x)}\right)}{768 a}+\frac{5 \tanh ^{-1}(a x)^{3/2}}{24 a}+\frac{15 \sqrt{\tanh ^{-1}(a x)} \sinh \left(2 \tanh ^{-1}(a x)\right)}{64 a}+\frac{3 \sqrt{\tanh ^{-1}(a x)} \sinh \left(4 \tanh ^{-1}(a x)\right)}{64 a}+\frac{\sqrt{\tanh ^{-1}(a x)} \sinh \left(6 \tanh ^{-1}(a x)\right)}{192 a}","\frac{3 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\tanh ^{-1}(a x)}\right)}{512 a}+\frac{15 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{256 a}+\frac{\sqrt{\frac{\pi }{6}} \text{Erf}\left(\sqrt{6} \sqrt{\tanh ^{-1}(a x)}\right)}{768 a}-\frac{3 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\tanh ^{-1}(a x)}\right)}{512 a}-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\tanh ^{-1}(a x)}\right)}{256 a}-\frac{\sqrt{\frac{\pi }{6}} \text{Erfi}\left(\sqrt{6} \sqrt{\tanh ^{-1}(a x)}\right)}{768 a}+\frac{5 \tanh ^{-1}(a x)^{3/2}}{24 a}+\frac{15 \sqrt{\tanh ^{-1}(a x)} \sinh \left(2 \tanh ^{-1}(a x)\right)}{64 a}+\frac{3 \sqrt{\tanh ^{-1}(a x)} \sinh \left(4 \tanh ^{-1}(a x)\right)}{64 a}+\frac{\sqrt{\tanh ^{-1}(a x)} \sinh \left(6 \tanh ^{-1}(a x)\right)}{192 a}",1,"(5*ArcTanh[a*x]^(3/2))/(24*a) + (3*Sqrt[Pi]*Erf[2*Sqrt[ArcTanh[a*x]]])/(512*a) + (15*Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcTanh[a*x]]])/(256*a) + (Sqrt[Pi/6]*Erf[Sqrt[6]*Sqrt[ArcTanh[a*x]]])/(768*a) - (3*Sqrt[Pi]*Erfi[2*Sqrt[ArcTanh[a*x]]])/(512*a) - (15*Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcTanh[a*x]]])/(256*a) - (Sqrt[Pi/6]*Erfi[Sqrt[6]*Sqrt[ArcTanh[a*x]]])/(768*a) + (15*Sqrt[ArcTanh[a*x]]*Sinh[2*ArcTanh[a*x]])/(64*a) + (3*Sqrt[ArcTanh[a*x]]*Sinh[4*ArcTanh[a*x]])/(64*a) + (Sqrt[ArcTanh[a*x]]*Sinh[6*ArcTanh[a*x]])/(192*a)","A",21,7,21,0.3333,1,"{5968, 3312, 3296, 3308, 2180, 2204, 2205}"
349,0,0,0,0.067944,"\int \frac{x^8}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","Int[x^8/((1 - a^2*x^2)^4*ArcTanh[a*x]),x]","\int \frac{x^8}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x^8}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][x^8/((1 - a^2*x^2)^4*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
350,0,0,0,0.0665811,"\int \frac{x^7}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","Int[x^7/((1 - a^2*x^2)^4*ArcTanh[a*x]),x]","\int \frac{x^7}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x^7}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][x^7/((1 - a^2*x^2)^4*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
351,1,55,0,0.1451565,"\int \frac{x^6}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","Int[x^6/((1 - a^2*x^2)^4*ArcTanh[a*x]),x]","\frac{15 \text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^7}-\frac{3 \text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{16 a^7}+\frac{\text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^7}-\frac{5 \log \left(\tanh ^{-1}(a x)\right)}{16 a^7}","\frac{15 \text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^7}-\frac{3 \text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{16 a^7}+\frac{\text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^7}-\frac{5 \log \left(\tanh ^{-1}(a x)\right)}{16 a^7}",1,"(15*CoshIntegral[2*ArcTanh[a*x]])/(32*a^7) - (3*CoshIntegral[4*ArcTanh[a*x]])/(16*a^7) + CoshIntegral[6*ArcTanh[a*x]]/(32*a^7) - (5*Log[ArcTanh[a*x]])/(16*a^7)","A",6,3,22,0.1364,1,"{6034, 3312, 3301}"
352,1,43,0,0.1437126,"\int \frac{x^5}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","Int[x^5/((1 - a^2*x^2)^4*ArcTanh[a*x]),x]","\frac{5 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^6}-\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^6}+\frac{\text{Shi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^6}","\frac{5 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^6}-\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^6}+\frac{\text{Shi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^6}",1,"(5*SinhIntegral[2*ArcTanh[a*x]])/(32*a^6) - SinhIntegral[4*ArcTanh[a*x]]/(8*a^6) + SinhIntegral[6*ArcTanh[a*x]]/(32*a^6)","A",6,3,22,0.1364,1,"{6034, 5448, 3298}"
353,1,55,0,0.154642,"\int \frac{x^4}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","Int[x^4/((1 - a^2*x^2)^4*ArcTanh[a*x]),x]","-\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^5}-\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{16 a^5}+\frac{\text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^5}+\frac{\log \left(\tanh ^{-1}(a x)\right)}{16 a^5}","-\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^5}-\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{16 a^5}+\frac{\text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^5}+\frac{\log \left(\tanh ^{-1}(a x)\right)}{16 a^5}",1,"-CoshIntegral[2*ArcTanh[a*x]]/(32*a^5) - CoshIntegral[4*ArcTanh[a*x]]/(16*a^5) + CoshIntegral[6*ArcTanh[a*x]]/(32*a^5) + Log[ArcTanh[a*x]]/(16*a^5)","A",6,3,22,0.1364,1,"{6034, 5448, 3301}"
354,1,29,0,0.1250316,"\int \frac{x^3}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","Int[x^3/((1 - a^2*x^2)^4*ArcTanh[a*x]),x]","\frac{\text{Shi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^4}-\frac{3 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^4}","\frac{\text{Shi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^4}-\frac{3 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^4}",1,"(-3*SinhIntegral[2*ArcTanh[a*x]])/(32*a^4) + SinhIntegral[6*ArcTanh[a*x]]/(32*a^4)","A",5,3,22,0.1364,1,"{6034, 5448, 3298}"
355,1,55,0,0.1421121,"\int \frac{x^2}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","Int[x^2/((1 - a^2*x^2)^4*ArcTanh[a*x]),x]","-\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^3}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{16 a^3}+\frac{\text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^3}-\frac{\log \left(\tanh ^{-1}(a x)\right)}{16 a^3}","-\frac{\text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^3}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{16 a^3}+\frac{\text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^3}-\frac{\log \left(\tanh ^{-1}(a x)\right)}{16 a^3}",1,"-CoshIntegral[2*ArcTanh[a*x]]/(32*a^3) + CoshIntegral[4*ArcTanh[a*x]]/(16*a^3) + CoshIntegral[6*ArcTanh[a*x]]/(32*a^3) - Log[ArcTanh[a*x]]/(16*a^3)","A",6,3,22,0.1364,1,"{6034, 5448, 3301}"
356,1,43,0,0.1123117,"\int \frac{x}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","Int[x/((1 - a^2*x^2)^4*ArcTanh[a*x]),x]","\frac{5 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^2}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^2}+\frac{\text{Shi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^2}","\frac{5 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{32 a^2}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{8 a^2}+\frac{\text{Shi}\left(6 \tanh ^{-1}(a x)\right)}{32 a^2}",1,"(5*SinhIntegral[2*ArcTanh[a*x]])/(32*a^2) + SinhIntegral[4*ArcTanh[a*x]]/(8*a^2) + SinhIntegral[6*ArcTanh[a*x]]/(32*a^2)","A",6,3,20,0.1500,1,"{6034, 5448, 3298}"
357,1,55,0,0.1034712,"\int \frac{1}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","Int[1/((1 - a^2*x^2)^4*ArcTanh[a*x]),x]","\frac{15 \text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{32 a}+\frac{3 \text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{16 a}+\frac{\text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{32 a}+\frac{5 \log \left(\tanh ^{-1}(a x)\right)}{16 a}","\frac{15 \text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{32 a}+\frac{3 \text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{16 a}+\frac{\text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{32 a}+\frac{5 \log \left(\tanh ^{-1}(a x)\right)}{16 a}",1,"(15*CoshIntegral[2*ArcTanh[a*x]])/(32*a) + (3*CoshIntegral[4*ArcTanh[a*x]])/(16*a) + CoshIntegral[6*ArcTanh[a*x]]/(32*a) + (5*Log[ArcTanh[a*x]])/(16*a)","A",6,3,19,0.1579,1,"{5968, 3312, 3301}"
358,0,0,0,0.061957,"\int \frac{1}{x \left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","Int[1/(x*(1 - a^2*x^2)^4*ArcTanh[a*x]),x]","\int \frac{1}{x \left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x*(1 - a^2*x^2)^4*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
359,0,0,0,0.0704338,"\int \frac{1}{x^2 \left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","Int[1/(x^2*(1 - a^2*x^2)^4*ArcTanh[a*x]),x]","\int \frac{1}{x^2 \left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x^2*(1 - a^2*x^2)^4*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
360,1,67,0,0.3068926,"\int \frac{x}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)^2} \, dx","Int[x/((1 - a^2*x^2)^4*ArcTanh[a*x]^2),x]","\frac{5 \text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{16 a^2}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{2 a^2}+\frac{3 \text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{16 a^2}-\frac{x}{a \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}","\frac{5 \text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{16 a^2}+\frac{\text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{2 a^2}+\frac{3 \text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{16 a^2}-\frac{x}{a \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}",1,"-(x/(a*(1 - a^2*x^2)^3*ArcTanh[a*x])) + (5*CoshIntegral[2*ArcTanh[a*x]])/(16*a^2) + CoshIntegral[4*ArcTanh[a*x]]/(2*a^2) + (3*CoshIntegral[6*ArcTanh[a*x]])/(16*a^2)","A",13,6,20,0.3000,1,"{6032, 6034, 5448, 3301, 5968, 3312}"
361,1,66,0,0.1428411,"\int \frac{1}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)^2} \, dx","Int[1/((1 - a^2*x^2)^4*ArcTanh[a*x]^2),x]","-\frac{1}{a \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}+\frac{15 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{16 a}+\frac{3 \text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{4 a}+\frac{3 \text{Shi}\left(6 \tanh ^{-1}(a x)\right)}{16 a}","-\frac{1}{a \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}+\frac{15 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{16 a}+\frac{3 \text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{4 a}+\frac{3 \text{Shi}\left(6 \tanh ^{-1}(a x)\right)}{16 a}",1,"-(1/(a*(1 - a^2*x^2)^3*ArcTanh[a*x])) + (15*SinhIntegral[2*ArcTanh[a*x]])/(16*a) + (3*SinhIntegral[4*ArcTanh[a*x]])/(4*a) + (3*SinhIntegral[6*ArcTanh[a*x]])/(16*a)","A",7,4,19,0.2105,1,"{5966, 6034, 5448, 3298}"
362,1,114,0,0.5850435,"\int \frac{x}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)^3} \, dx","Int[x/((1 - a^2*x^2)^4*ArcTanh[a*x]^3),x]","\frac{5 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{16 a^2}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{a^2}+\frac{9 \text{Shi}\left(6 \tanh ^{-1}(a x)\right)}{16 a^2}-\frac{x}{2 a \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2}+\frac{5}{2 a^2 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}-\frac{3}{a^2 \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}","\frac{5 \text{Shi}\left(2 \tanh ^{-1}(a x)\right)}{16 a^2}+\frac{\text{Shi}\left(4 \tanh ^{-1}(a x)\right)}{a^2}+\frac{9 \text{Shi}\left(6 \tanh ^{-1}(a x)\right)}{16 a^2}-\frac{x}{2 a \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2}+\frac{5}{2 a^2 \left(1-a^2 x^2\right)^2 \tanh ^{-1}(a x)}-\frac{3}{a^2 \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}",1,"-x/(2*a*(1 - a^2*x^2)^3*ArcTanh[a*x]^2) - 3/(a^2*(1 - a^2*x^2)^3*ArcTanh[a*x]) + 5/(2*a^2*(1 - a^2*x^2)^2*ArcTanh[a*x]) + (5*SinhIntegral[2*ArcTanh[a*x]])/(16*a^2) + SinhIntegral[4*ArcTanh[a*x]]/a^2 + (9*SinhIntegral[6*ArcTanh[a*x]])/(16*a^2)","A",22,6,20,0.3000,1,"{6032, 6028, 5966, 6034, 5448, 3298}"
363,1,89,0,0.386036,"\int \frac{1}{\left(1-a^2 x^2\right)^4 \tanh ^{-1}(a x)^3} \, dx","Int[1/((1 - a^2*x^2)^4*ArcTanh[a*x]^3),x]","-\frac{3 x}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2}+\frac{15 \text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{16 a}+\frac{3 \text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{2 a}+\frac{9 \text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{16 a}","-\frac{3 x}{\left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right)^3 \tanh ^{-1}(a x)^2}+\frac{15 \text{Chi}\left(2 \tanh ^{-1}(a x)\right)}{16 a}+\frac{3 \text{Chi}\left(4 \tanh ^{-1}(a x)\right)}{2 a}+\frac{9 \text{Chi}\left(6 \tanh ^{-1}(a x)\right)}{16 a}",1,"-1/(2*a*(1 - a^2*x^2)^3*ArcTanh[a*x]^2) - (3*x)/((1 - a^2*x^2)^3*ArcTanh[a*x]) + (15*CoshIntegral[2*ArcTanh[a*x]])/(16*a) + (3*CoshIntegral[4*ArcTanh[a*x]])/(2*a) + (9*CoshIntegral[6*ArcTanh[a*x]])/(16*a)","A",14,7,19,0.3684,1,"{5966, 6032, 6034, 5448, 3301, 5968, 3312}"
364,1,139,0,0.2348395,"\int \frac{x^5 \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^5*ArcTanh[a*x])/Sqrt[1 - a^2*x^2],x]","-\frac{x^3 \sqrt{1-a^2 x^2}}{20 a^3}-\frac{5 x \sqrt{1-a^2 x^2}}{24 a^5}-\frac{x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{5 a^2}-\frac{4 x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 a^4}-\frac{8 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 a^6}+\frac{89 \sin ^{-1}(a x)}{120 a^6}","-\frac{x^3 \sqrt{1-a^2 x^2}}{20 a^3}-\frac{5 x \sqrt{1-a^2 x^2}}{24 a^5}-\frac{x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{5 a^2}-\frac{4 x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 a^4}-\frac{8 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 a^6}+\frac{89 \sin ^{-1}(a x)}{120 a^6}",1,"(-5*x*Sqrt[1 - a^2*x^2])/(24*a^5) - (x^3*Sqrt[1 - a^2*x^2])/(20*a^3) + (89*ArcSin[a*x])/(120*a^6) - (8*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(15*a^6) - (4*x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(15*a^4) - (x^4*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(5*a^2)","A",9,4,22,0.1818,1,"{6016, 321, 216, 5994}"
365,1,197,0,0.216797,"\int \frac{x^4 \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^4*ArcTanh[a*x])/Sqrt[1 - a^2*x^2],x]","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a^5}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a^5}+\frac{\left(1-a^2 x^2\right)^{3/2}}{12 a^5}-\frac{5 \sqrt{1-a^2 x^2}}{8 a^5}-\frac{x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{4 a^2}-\frac{3 x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 a^4}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a^5}","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a^5}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a^5}+\frac{\left(1-a^2 x^2\right)^{3/2}}{12 a^5}-\frac{5 \sqrt{1-a^2 x^2}}{8 a^5}-\frac{x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{4 a^2}-\frac{3 x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 a^4}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a^5}",1,"(-5*Sqrt[1 - a^2*x^2])/(8*a^5) + (1 - a^2*x^2)^(3/2)/(12*a^5) - (3*x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(8*a^4) - (x^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(4*a^2) - (3*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(4*a^5) - (((3*I)/8)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^5 + (((3*I)/8)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^5","A",7,5,22,0.2273,1,"{6016, 266, 43, 261, 5950}"
366,1,87,0,0.1242374,"\int \frac{x^3 \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^3*ArcTanh[a*x])/Sqrt[1 - a^2*x^2],x]","-\frac{x \sqrt{1-a^2 x^2}}{6 a^3}-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{3 a^4}+\frac{5 \sin ^{-1}(a x)}{6 a^4}","-\frac{x \sqrt{1-a^2 x^2}}{6 a^3}-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{3 a^4}+\frac{5 \sin ^{-1}(a x)}{6 a^4}",1,"-(x*Sqrt[1 - a^2*x^2])/(6*a^3) + (5*ArcSin[a*x])/(6*a^4) - (2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(3*a^4) - (x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(3*a^2)","A",5,4,22,0.1818,1,"{6016, 321, 216, 5994}"
367,1,146,0,0.1045879,"\int \frac{x^2 \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^2*ArcTanh[a*x])/Sqrt[1 - a^2*x^2],x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a^3}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a^3}-\frac{\sqrt{1-a^2 x^2}}{2 a^3}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 a^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a^3}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a^3}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a^3}-\frac{\sqrt{1-a^2 x^2}}{2 a^3}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 a^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a^3}",1,"-Sqrt[1 - a^2*x^2]/(2*a^3) - (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(2*a^2) - (ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/a^3 - ((I/2)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^3 + ((I/2)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^3","A",3,3,22,0.1364,1,"{6016, 261, 5950}"
368,1,32,0,0.0469097,"\int \frac{x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x*ArcTanh[a*x])/Sqrt[1 - a^2*x^2],x]","\frac{\sin ^{-1}(a x)}{a^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a^2}","\frac{\sin ^{-1}(a x)}{a^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a^2}",1,"ArcSin[a*x]/a^2 - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/a^2","A",2,2,20,0.1000,1,"{5994, 216}"
369,1,95,0,0.0264132,"\int \frac{\tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]/Sqrt[1 - a^2*x^2],x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a}",1,"(-2*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/a - (I*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a + (I*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a","A",1,1,19,0.05263,1,"{5950}"
370,1,75,0,0.0650753,"\int \frac{\tanh ^{-1}(a x)}{x \sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]/(x*Sqrt[1 - a^2*x^2]),x]","\text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","\text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-2*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] + PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])] - PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]]","A",1,1,22,0.04545,1,"{6018}"
371,1,42,0,0.0758943,"\int \frac{\tanh ^{-1}(a x)}{x^2 \sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]/(x^2*Sqrt[1 - a^2*x^2]),x]","-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-((Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x) - a*ArcTanh[Sqrt[1 - a^2*x^2]]","A",4,4,22,0.1818,1,"{6008, 266, 63, 208}"
372,1,137,0,0.1356539,"\int \frac{\tanh ^{-1}(a x)}{x^3 \sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]/(x^3*Sqrt[1 - a^2*x^2]),x]","\frac{1}{2} a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{1}{2} a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a \sqrt{1-a^2 x^2}}{2 x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 x^2}+a^2 \left(-\tanh ^{-1}(a x)\right) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","\frac{1}{2} a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{1}{2} a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a \sqrt{1-a^2 x^2}}{2 x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 x^2}+a^2 \left(-\tanh ^{-1}(a x)\right) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-(a*Sqrt[1 - a^2*x^2])/(2*x) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(2*x^2) - a^2*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] + (a^2*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])])/2 - (a^2*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]])/2","A",3,3,22,0.1364,1,"{6026, 264, 6018}"
373,1,205,0,0.3136177,"\int \frac{x^3 \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^3*ArcTanh[a*x]^2)/Sqrt[1 - a^2*x^2],x]","-\frac{5 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{3 a^4}+\frac{5 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{3 a^4}-\frac{\sqrt{1-a^2 x^2}}{3 a^4}-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{3 a^4}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{3 a^3}-\frac{10 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{3 a^4}","-\frac{5 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{3 a^4}+\frac{5 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{3 a^4}-\frac{\sqrt{1-a^2 x^2}}{3 a^4}-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{3 a^4}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{3 a^3}-\frac{10 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{3 a^4}",1,"-Sqrt[1 - a^2*x^2]/(3*a^4) - (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(3*a^3) - (10*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(3*a^4) - (2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(3*a^4) - (x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(3*a^2) - (((5*I)/3)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^4 + (((5*I)/3)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^4","A",6,4,24,0.1667,1,"{6016, 261, 5950, 5994}"
374,1,161,0,0.2545203,"\int \frac{x^2 \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^2*ArcTanh[a*x]^2)/Sqrt[1 - a^2*x^2],x]","-\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 a^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a^3}+\frac{\sin ^{-1}(a x)}{a^3}+\frac{\tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^3}","-\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 a^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a^3}+\frac{\sin ^{-1}(a x)}{a^3}+\frac{\tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^3}",1,"ArcSin[a*x]/a^3 - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/a^3 - (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(2*a^2) + (ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^2)/a^3 - (I*ArcTanh[a*x]*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a^3 + (I*ArcTanh[a*x]*PolyLog[2, I*E^ArcTanh[a*x]])/a^3 + (I*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a^3 - (I*PolyLog[3, I*E^ArcTanh[a*x]])/a^3","A",11,8,24,0.3333,1,"{6016, 5994, 216, 5952, 4180, 2531, 2282, 6589}"
375,1,120,0,0.0988155,"\int \frac{x \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x*ArcTanh[a*x]^2)/Sqrt[1 - a^2*x^2],x]","-\frac{2 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^2}+\frac{2 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{a^2}-\frac{4 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a^2}","-\frac{2 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^2}+\frac{2 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{a^2}-\frac{4 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a^2}",1,"(-4*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/a^2 - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/a^2 - ((2*I)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^2 + ((2*I)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^2","A",2,2,22,0.09091,1,"{5994, 5950}"
376,1,103,0,0.0978629,"\int \frac{\tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]^2/Sqrt[1 - a^2*x^2],x]","-\frac{2 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{2 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{2 i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{2 i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{2 \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a}","-\frac{2 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{2 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{2 i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{2 i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{2 \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a}",1,"(2*ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^2)/a - ((2*I)*ArcTanh[a*x]*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a + ((2*I)*ArcTanh[a*x]*PolyLog[2, I*E^ArcTanh[a*x]])/a + ((2*I)*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a - ((2*I)*PolyLog[3, I*E^ArcTanh[a*x]])/a","A",8,5,21,0.2381,1,"{5952, 4180, 2531, 2282, 6589}"
377,1,68,0,0.1412894,"\int \frac{\tanh ^{-1}(a x)^2}{x \sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]^2/(x*Sqrt[1 - a^2*x^2]),x]","-2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2","-2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2",1,"-2*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^2 - 2*ArcTanh[a*x]*PolyLog[2, -E^ArcTanh[a*x]] + 2*ArcTanh[a*x]*PolyLog[2, E^ArcTanh[a*x]] + 2*PolyLog[3, -E^ArcTanh[a*x]] - 2*PolyLog[3, E^ArcTanh[a*x]]","A",8,5,24,0.2083,1,"{6020, 4182, 2531, 2282, 6589}"
378,1,105,0,0.1665001,"\int \frac{\tanh ^{-1}(a x)^2}{x^2 \sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]^2/(x^2*Sqrt[1 - a^2*x^2]),x]","2 a \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 a \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{x}-4 a \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)","2 a \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 a \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{x}-4 a \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)",1,"-((Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/x) - 4*a*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] + 2*a*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])] - 2*a*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]]","A",2,2,24,0.08333,1,"{6008, 6018}"
379,1,152,0,0.4153482,"\int \frac{\tanh ^{-1}(a x)^2}{x^3 \sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]^2/(x^3*Sqrt[1 - a^2*x^2]),x]","-a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+a^2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-a^2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 x^2}+a^2 \left(-\tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)\right) \tanh ^{-1}(a x)^2","-a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+a^2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-a^2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 x^2}+a^2 \left(-\tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)\right) \tanh ^{-1}(a x)^2",1,"-((a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(2*x^2) - a^2*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^2 - a^2*ArcTanh[Sqrt[1 - a^2*x^2]] - a^2*ArcTanh[a*x]*PolyLog[2, -E^ArcTanh[a*x]] + a^2*ArcTanh[a*x]*PolyLog[2, E^ArcTanh[a*x]] + a^2*PolyLog[3, -E^ArcTanh[a*x]] - a^2*PolyLog[3, E^ArcTanh[a*x]]","A",13,10,24,0.4167,1,"{6026, 6008, 266, 63, 208, 6020, 4182, 2531, 2282, 6589}"
380,1,219,0,0.5695952,"\int \frac{x^3 \tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^3*ArcTanh[a*x]^3)/Sqrt[1 - a^2*x^2],x]","-\frac{5 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^4}+\frac{5 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^4}+\frac{5 i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^4}-\frac{5 i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^4}-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{3 a^4}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 a^3}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a^4}+\frac{\sin ^{-1}(a x)}{a^4}+\frac{5 \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^4}","-\frac{5 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^4}+\frac{5 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^4}+\frac{5 i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^4}-\frac{5 i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^4}-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{3 a^4}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 a^3}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a^4}+\frac{\sin ^{-1}(a x)}{a^4}+\frac{5 \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^4}",1,"ArcSin[a*x]/a^4 - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/a^4 - (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(2*a^3) + (5*ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^2)/a^4 - (2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3)/(3*a^4) - (x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3)/(3*a^2) - ((5*I)*ArcTanh[a*x]*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a^4 + ((5*I)*ArcTanh[a*x]*PolyLog[2, I*E^ArcTanh[a*x]])/a^4 + ((5*I)*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a^4 - ((5*I)*PolyLog[3, I*E^ArcTanh[a*x]])/a^4","A",21,8,24,0.3333,1,"{6016, 5994, 216, 5952, 4180, 2531, 2282, 6589}"
381,1,305,0,0.3398739,"\int \frac{x^2 \tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^2*ArcTanh[a*x]^3)/Sqrt[1 - a^2*x^2],x]","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^3}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^3}-\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{2 a^3}+\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{2 a^3}+\frac{3 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{3 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{3 i \text{PolyLog}\left(4,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{3 i \text{PolyLog}\left(4,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{2 a^2}-\frac{3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 a^3}+\frac{\tanh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{6 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a^3}","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^3}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^3}-\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{2 a^3}+\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{2 a^3}+\frac{3 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{3 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{3 i \text{PolyLog}\left(4,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{3 i \text{PolyLog}\left(4,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{2 a^2}-\frac{3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 a^3}+\frac{\tanh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{6 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a^3}",1,"(-6*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/a^3 - (3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(2*a^3) - (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3)/(2*a^2) + (ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^3)/a^3 - (((3*I)/2)*ArcTanh[a*x]^2*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a^3 + (((3*I)/2)*ArcTanh[a*x]^2*PolyLog[2, I*E^ArcTanh[a*x]])/a^3 - ((3*I)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^3 + ((3*I)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^3 + ((3*I)*ArcTanh[a*x]*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a^3 - ((3*I)*ArcTanh[a*x]*PolyLog[3, I*E^ArcTanh[a*x]])/a^3 - ((3*I)*PolyLog[4, (-I)*E^ArcTanh[a*x]])/a^3 + ((3*I)*PolyLog[4, I*E^ArcTanh[a*x]])/a^3","A",13,9,24,0.3750,1,"{6016, 5994, 5950, 5952, 4180, 2531, 6609, 2282, 6589}"
382,1,128,0,0.176988,"\int \frac{x \tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x*ArcTanh[a*x]^3)/Sqrt[1 - a^2*x^2],x]","-\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^2}+\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^2}+\frac{6 i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^2}-\frac{6 i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{a^2}+\frac{6 \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^2}","-\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^2}+\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^2}+\frac{6 i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^2}-\frac{6 i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{a^2}+\frac{6 \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^2}",1,"(6*ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^2)/a^2 - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3)/a^2 - ((6*I)*ArcTanh[a*x]*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a^2 + ((6*I)*ArcTanh[a*x]*PolyLog[2, I*E^ArcTanh[a*x]])/a^2 + ((6*I)*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a^2 - ((6*I)*PolyLog[3, I*E^ArcTanh[a*x]])/a^2","A",9,6,22,0.2727,1,"{5994, 5952, 4180, 2531, 2282, 6589}"
383,1,153,0,0.1330996,"\int \frac{\tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]^3/Sqrt[1 - a^2*x^2],x]","-\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{6 i \text{PolyLog}\left(4,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{6 i \text{PolyLog}\left(4,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{2 \tanh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a}","-\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{6 i \text{PolyLog}\left(4,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{6 i \text{PolyLog}\left(4,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{2 \tanh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a}",1,"(2*ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^3)/a - ((3*I)*ArcTanh[a*x]^2*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a + ((3*I)*ArcTanh[a*x]^2*PolyLog[2, I*E^ArcTanh[a*x]])/a + ((6*I)*ArcTanh[a*x]*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a - ((6*I)*ArcTanh[a*x]*PolyLog[3, I*E^ArcTanh[a*x]])/a - ((6*I)*PolyLog[4, (-I)*E^ArcTanh[a*x]])/a + ((6*I)*PolyLog[4, I*E^ArcTanh[a*x]])/a","A",10,6,21,0.2857,1,"{5952, 4180, 2531, 6609, 2282, 6589}"
384,1,102,0,0.1730595,"\int \frac{\tanh ^{-1}(a x)^3}{x \sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]^3/(x*Sqrt[1 - a^2*x^2]),x]","-3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-6 \text{PolyLog}\left(4,-e^{\tanh ^{-1}(a x)}\right)+6 \text{PolyLog}\left(4,e^{\tanh ^{-1}(a x)}\right)-2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^3","-3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-6 \text{PolyLog}\left(4,-e^{\tanh ^{-1}(a x)}\right)+6 \text{PolyLog}\left(4,e^{\tanh ^{-1}(a x)}\right)-2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^3",1,"-2*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^3 - 3*ArcTanh[a*x]^2*PolyLog[2, -E^ArcTanh[a*x]] + 3*ArcTanh[a*x]^2*PolyLog[2, E^ArcTanh[a*x]] + 6*ArcTanh[a*x]*PolyLog[3, -E^ArcTanh[a*x]] - 6*ArcTanh[a*x]*PolyLog[3, E^ArcTanh[a*x]] - 6*PolyLog[4, -E^ArcTanh[a*x]] + 6*PolyLog[4, E^ArcTanh[a*x]]","A",10,6,24,0.2500,1,"{6020, 4182, 2531, 6609, 2282, 6589}"
385,1,98,0,0.2485154,"\int \frac{\tanh ^{-1}(a x)^3}{x^2 \sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]^3/(x^2*Sqrt[1 - a^2*x^2]),x]","-6 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+6 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+6 a \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-6 a \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{x}-6 a \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2","-6 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+6 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+6 a \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-6 a \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{x}-6 a \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2",1,"-6*a*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^2 - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3)/x - 6*a*ArcTanh[a*x]*PolyLog[2, -E^ArcTanh[a*x]] + 6*a*ArcTanh[a*x]*PolyLog[2, E^ArcTanh[a*x]] + 6*a*PolyLog[3, -E^ArcTanh[a*x]] - 6*a*PolyLog[3, E^ArcTanh[a*x]]","A",9,6,24,0.2500,1,"{6008, 6020, 4182, 2531, 2282, 6589}"
386,1,267,0,0.4470527,"\int \frac{\tanh ^{-1}(a x)^3}{x^3 \sqrt{1-a^2 x^2}} \, dx","Int[ArcTanh[a*x]^3/(x^3*Sqrt[1 - a^2*x^2]),x]","3 a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-3 a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{3}{2} a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+\frac{3}{2} a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-3 a^2 \text{PolyLog}\left(4,-e^{\tanh ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(4,e^{\tanh ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{2 x^2}-\frac{3 a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 x}-a^2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^3-6 a^2 \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)","3 a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-3 a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{3}{2} a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+\frac{3}{2} a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-3 a^2 \text{PolyLog}\left(4,-e^{\tanh ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(4,e^{\tanh ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{2 x^2}-\frac{3 a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 x}-a^2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^3-6 a^2 \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)",1,"(-3*a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(2*x) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3)/(2*x^2) - a^2*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^3 - 6*a^2*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] - (3*a^2*ArcTanh[a*x]^2*PolyLog[2, -E^ArcTanh[a*x]])/2 + (3*a^2*ArcTanh[a*x]^2*PolyLog[2, E^ArcTanh[a*x]])/2 + 3*a^2*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])] - 3*a^2*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]] + 3*a^2*ArcTanh[a*x]*PolyLog[3, -E^ArcTanh[a*x]] - 3*a^2*ArcTanh[a*x]*PolyLog[3, E^ArcTanh[a*x]] - 3*a^2*PolyLog[4, -E^ArcTanh[a*x]] + 3*a^2*PolyLog[4, E^ArcTanh[a*x]]","A",13,9,24,0.3750,1,"{6026, 6008, 6018, 6020, 4182, 2531, 6609, 2282, 6589}"
387,0,0,0,0.0763378,"\int \frac{x^m \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x^m*ArcTanh[a*x])/(1 - a^2*x^2)^(3/2),x]","\int \frac{x^m \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^m \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^m*ArcTanh[a*x])/(1 - a^2*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
388,1,74,0,0.1699428,"\int \frac{x^3 \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x^3*ArcTanh[a*x])/(1 - a^2*x^2)^(3/2),x]","-\frac{x}{a^3 \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a^4}+\frac{\tanh ^{-1}(a x)}{a^4 \sqrt{1-a^2 x^2}}-\frac{\sin ^{-1}(a x)}{a^4}","-\frac{x}{a^3 \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a^4}+\frac{\tanh ^{-1}(a x)}{a^4 \sqrt{1-a^2 x^2}}-\frac{\sin ^{-1}(a x)}{a^4}",1,"-(x/(a^3*Sqrt[1 - a^2*x^2])) - ArcSin[a*x]/a^4 + ArcTanh[a*x]/(a^4*Sqrt[1 - a^2*x^2]) + (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/a^4","A",5,4,22,0.1818,1,"{6028, 5994, 216, 191}"
389,1,137,0,0.1053531,"\int \frac{x^2 \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x^2*ArcTanh[a*x])/(1 - a^2*x^2)^(3/2),x]","\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^3}-\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^3}-\frac{1}{a^3 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)}{a^2 \sqrt{1-a^2 x^2}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a^3}","\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^3}-\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^3}-\frac{1}{a^3 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)}{a^2 \sqrt{1-a^2 x^2}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a^3}",1,"-(1/(a^3*Sqrt[1 - a^2*x^2])) + (x*ArcTanh[a*x])/(a^2*Sqrt[1 - a^2*x^2]) + (2*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/a^3 + (I*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^3 - (I*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^3","A",2,2,22,0.09091,1,"{5998, 5950}"
390,1,43,0,0.0506343,"\int \frac{x \tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x*ArcTanh[a*x])/(1 - a^2*x^2)^(3/2),x]","\frac{\tanh ^{-1}(a x)}{a^2 \sqrt{1-a^2 x^2}}-\frac{x}{a \sqrt{1-a^2 x^2}}","\frac{\tanh ^{-1}(a x)}{a^2 \sqrt{1-a^2 x^2}}-\frac{x}{a \sqrt{1-a^2 x^2}}",1,"-(x/(a*Sqrt[1 - a^2*x^2])) + ArcTanh[a*x]/(a^2*Sqrt[1 - a^2*x^2])","A",2,2,20,0.1000,1,"{5994, 191}"
391,1,40,0,0.0252848,"\int \frac{\tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]/(1 - a^2*x^2)^(3/2),x]","\frac{x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-\frac{1}{a \sqrt{1-a^2 x^2}}","\frac{x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-\frac{1}{a \sqrt{1-a^2 x^2}}",1,"-(1/(a*Sqrt[1 - a^2*x^2])) + (x*ArcTanh[a*x])/Sqrt[1 - a^2*x^2]","A",1,1,19,0.05263,1,"{5958}"
392,1,112,0,0.1859607,"\int \frac{\tanh ^{-1}(a x)}{x \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]/(x*(1 - a^2*x^2)^(3/2)),x]","\text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a x}{\sqrt{1-a^2 x^2}}+\frac{\tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","\text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a x}{\sqrt{1-a^2 x^2}}+\frac{\tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-((a*x)/Sqrt[1 - a^2*x^2]) + ArcTanh[a*x]/Sqrt[1 - a^2*x^2] - 2*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] + PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])] - PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]]","A",4,4,22,0.1818,1,"{6030, 6018, 5994, 191}"
393,1,82,0,0.170999,"\int \frac{\tanh ^{-1}(a x)}{x^2 \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]/(x^2*(1 - a^2*x^2)^(3/2)),x]","-\frac{a}{\sqrt{1-a^2 x^2}}+\frac{a^2 x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}","-\frac{a}{\sqrt{1-a^2 x^2}}+\frac{a^2 x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}",1,"-(a/Sqrt[1 - a^2*x^2]) + (a^2*x*ArcTanh[a*x])/Sqrt[1 - a^2*x^2] - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x - a*ArcTanh[Sqrt[1 - a^2*x^2]]","A",6,6,22,0.2727,1,"{6030, 6008, 266, 63, 208, 5958}"
394,1,179,0,0.4022112,"\int \frac{\tanh ^{-1}(a x)}{x^3 \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]/(x^3*(1 - a^2*x^2)^(3/2)),x]","\frac{3}{2} a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{3}{2} a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a^3 x}{\sqrt{1-a^2 x^2}}-\frac{a \sqrt{1-a^2 x^2}}{2 x}+\frac{a^2 \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 x^2}-3 a^2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","\frac{3}{2} a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{3}{2} a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a^3 x}{\sqrt{1-a^2 x^2}}-\frac{a \sqrt{1-a^2 x^2}}{2 x}+\frac{a^2 \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 x^2}-3 a^2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-((a^3*x)/Sqrt[1 - a^2*x^2]) - (a*Sqrt[1 - a^2*x^2])/(2*x) + (a^2*ArcTanh[a*x])/Sqrt[1 - a^2*x^2] - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(2*x^2) - 3*a^2*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] + (3*a^2*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])])/2 - (3*a^2*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]])/2","A",8,6,22,0.2727,1,"{6030, 6026, 264, 6018, 5994, 191}"
395,0,0,0,0.1019197,"\int \frac{x^m \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x^m*ArcTanh[a*x]^2)/(1 - a^2*x^2)^(3/2),x]","\int \frac{x^m \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^m \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^m*ArcTanh[a*x]^2)/(1 - a^2*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
396,1,186,0,0.3103885,"\int \frac{x^3 \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x^3*ArcTanh[a*x]^2)/(1 - a^2*x^2)^(3/2),x]","\frac{2 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^4}-\frac{2 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^4}+\frac{2}{a^4 \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{a^4}+\frac{\tanh ^{-1}(a x)^2}{a^4 \sqrt{1-a^2 x^2}}-\frac{2 x \tanh ^{-1}(a x)}{a^3 \sqrt{1-a^2 x^2}}+\frac{4 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a^4}","\frac{2 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^4}-\frac{2 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a^4}+\frac{2}{a^4 \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{a^4}+\frac{\tanh ^{-1}(a x)^2}{a^4 \sqrt{1-a^2 x^2}}-\frac{2 x \tanh ^{-1}(a x)}{a^3 \sqrt{1-a^2 x^2}}+\frac{4 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a^4}",1,"2/(a^4*Sqrt[1 - a^2*x^2]) - (2*x*ArcTanh[a*x])/(a^3*Sqrt[1 - a^2*x^2]) + (4*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/a^4 + ArcTanh[a*x]^2/(a^4*Sqrt[1 - a^2*x^2]) + (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/a^4 + ((2*I)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^4 - ((2*I)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^4","A",5,4,24,0.1667,1,"{6028, 5994, 5950, 5958}"
397,1,171,0,0.2517507,"\int \frac{x^2 \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x^2*ArcTanh[a*x]^2)/(1 - a^2*x^2)^(3/2),x]","\frac{2 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{2 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{2 i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{2 i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{2 x}{a^2 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^2}{a^2 \sqrt{1-a^2 x^2}}-\frac{2 \tanh ^{-1}(a x)}{a^3 \sqrt{1-a^2 x^2}}-\frac{2 \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^3}","\frac{2 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{2 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{2 i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{2 i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{2 x}{a^2 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^2}{a^2 \sqrt{1-a^2 x^2}}-\frac{2 \tanh ^{-1}(a x)}{a^3 \sqrt{1-a^2 x^2}}-\frac{2 \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^3}",1,"(2*x)/(a^2*Sqrt[1 - a^2*x^2]) - (2*ArcTanh[a*x])/(a^3*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x]^2)/(a^2*Sqrt[1 - a^2*x^2]) - (2*ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^2)/a^3 + ((2*I)*ArcTanh[a*x]*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a^3 - ((2*I)*ArcTanh[a*x]*PolyLog[2, I*E^ArcTanh[a*x]])/a^3 - ((2*I)*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a^3 + ((2*I)*PolyLog[3, I*E^ArcTanh[a*x]])/a^3","A",11,8,24,0.3333,1,"{6028, 5952, 4180, 2531, 2282, 6589, 5962, 191}"
398,1,68,0,0.0983558,"\int \frac{x \tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x*ArcTanh[a*x]^2)/(1 - a^2*x^2)^(3/2),x]","\frac{2}{a^2 \sqrt{1-a^2 x^2}}+\frac{\tanh ^{-1}(a x)^2}{a^2 \sqrt{1-a^2 x^2}}-\frac{2 x \tanh ^{-1}(a x)}{a \sqrt{1-a^2 x^2}}","\frac{2}{a^2 \sqrt{1-a^2 x^2}}+\frac{\tanh ^{-1}(a x)^2}{a^2 \sqrt{1-a^2 x^2}}-\frac{2 x \tanh ^{-1}(a x)}{a \sqrt{1-a^2 x^2}}",1,"2/(a^2*Sqrt[1 - a^2*x^2]) - (2*x*ArcTanh[a*x])/(a*Sqrt[1 - a^2*x^2]) + ArcTanh[a*x]^2/(a^2*Sqrt[1 - a^2*x^2])","A",2,2,22,0.09091,1,"{5994, 5958}"
399,1,63,0,0.0396381,"\int \frac{\tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]^2/(1 - a^2*x^2)^(3/2),x]","\frac{2 x}{\sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}-\frac{2 \tanh ^{-1}(a x)}{a \sqrt{1-a^2 x^2}}","\frac{2 x}{\sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}-\frac{2 \tanh ^{-1}(a x)}{a \sqrt{1-a^2 x^2}}",1,"(2*x)/Sqrt[1 - a^2*x^2] - (2*ArcTanh[a*x])/(a*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x]^2)/Sqrt[1 - a^2*x^2]","A",2,2,21,0.09524,1,"{5962, 191}"
400,1,127,0,0.3412266,"\int \frac{\tanh ^{-1}(a x)^2}{x \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]^2/(x*(1 - a^2*x^2)^(3/2)),x]","-2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)+\frac{2}{\sqrt{1-a^2 x^2}}+\frac{\tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}-\frac{2 a x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2","-2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)+\frac{2}{\sqrt{1-a^2 x^2}}+\frac{\tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}-\frac{2 a x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2",1,"2/Sqrt[1 - a^2*x^2] - (2*a*x*ArcTanh[a*x])/Sqrt[1 - a^2*x^2] + ArcTanh[a*x]^2/Sqrt[1 - a^2*x^2] - 2*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^2 - 2*ArcTanh[a*x]*PolyLog[2, -E^ArcTanh[a*x]] + 2*ArcTanh[a*x]*PolyLog[2, E^ArcTanh[a*x]] + 2*PolyLog[3, -E^ArcTanh[a*x]] - 2*PolyLog[3, E^ArcTanh[a*x]]","A",11,8,24,0.3333,1,"{6030, 6020, 4182, 2531, 2282, 6589, 5994, 5958}"
401,1,171,0,0.312958,"\int \frac{\tanh ^{-1}(a x)^2}{x^2 \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]^2/(x^2*(1 - a^2*x^2)^(3/2)),x]","2 a \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 a \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{2 a^2 x}{\sqrt{1-a^2 x^2}}+\frac{a^2 x \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}-\frac{2 a \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{x}-4 a \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","2 a \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 a \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{2 a^2 x}{\sqrt{1-a^2 x^2}}+\frac{a^2 x \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}-\frac{2 a \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{x}-4 a \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"(2*a^2*x)/Sqrt[1 - a^2*x^2] - (2*a*ArcTanh[a*x])/Sqrt[1 - a^2*x^2] + (a^2*x*ArcTanh[a*x]^2)/Sqrt[1 - a^2*x^2] - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/x - 4*a*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] + 2*a*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])] - 2*a*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]]","A",5,5,24,0.2083,1,"{6030, 6008, 6018, 5962, 191}"
402,1,221,0,0.7763237,"\int \frac{\tanh ^{-1}(a x)^2}{x^3 \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]^2/(x^3*(1 - a^2*x^2)^(3/2)),x]","-3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-3 a^2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)+\frac{2 a^2}{\sqrt{1-a^2 x^2}}-\frac{2 a^3 x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}+\frac{a^2 \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}-a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 x^2}-3 a^2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2","-3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+3 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-3 a^2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)+\frac{2 a^2}{\sqrt{1-a^2 x^2}}-\frac{2 a^3 x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}+\frac{a^2 \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}-a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 x^2}-3 a^2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2",1,"(2*a^2)/Sqrt[1 - a^2*x^2] - (2*a^3*x*ArcTanh[a*x])/Sqrt[1 - a^2*x^2] - (a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x + (a^2*ArcTanh[a*x]^2)/Sqrt[1 - a^2*x^2] - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(2*x^2) - 3*a^2*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^2 - a^2*ArcTanh[Sqrt[1 - a^2*x^2]] - 3*a^2*ArcTanh[a*x]*PolyLog[2, -E^ArcTanh[a*x]] + 3*a^2*ArcTanh[a*x]*PolyLog[2, E^ArcTanh[a*x]] + 3*a^2*PolyLog[3, -E^ArcTanh[a*x]] - 3*a^2*PolyLog[3, E^ArcTanh[a*x]]","A",25,13,24,0.5417,1,"{6030, 6026, 6008, 266, 63, 208, 6020, 4182, 2531, 2282, 6589, 5994, 5958}"
403,0,0,0,0.1002647,"\int \frac{x^m \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x^m*ArcTanh[a*x]^3)/(1 - a^2*x^2)^(3/2),x]","\int \frac{x^m \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^m \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^m*ArcTanh[a*x]^3)/(1 - a^2*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
404,1,220,0,0.4054681,"\int \frac{x^3 \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x^3*ArcTanh[a*x]^3)/(1 - a^2*x^2)^(3/2),x]","\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^4}-\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^4}-\frac{6 i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^4}+\frac{6 i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^4}-\frac{6 x}{a^3 \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{a^4}+\frac{\tanh ^{-1}(a x)^3}{a^4 \sqrt{1-a^2 x^2}}-\frac{3 x \tanh ^{-1}(a x)^2}{a^3 \sqrt{1-a^2 x^2}}+\frac{6 \tanh ^{-1}(a x)}{a^4 \sqrt{1-a^2 x^2}}-\frac{6 \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^4}","\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^4}-\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^4}-\frac{6 i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^4}+\frac{6 i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^4}-\frac{6 x}{a^3 \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{a^4}+\frac{\tanh ^{-1}(a x)^3}{a^4 \sqrt{1-a^2 x^2}}-\frac{3 x \tanh ^{-1}(a x)^2}{a^3 \sqrt{1-a^2 x^2}}+\frac{6 \tanh ^{-1}(a x)}{a^4 \sqrt{1-a^2 x^2}}-\frac{6 \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^4}",1,"(-6*x)/(a^3*Sqrt[1 - a^2*x^2]) + (6*ArcTanh[a*x])/(a^4*Sqrt[1 - a^2*x^2]) - (3*x*ArcTanh[a*x]^2)/(a^3*Sqrt[1 - a^2*x^2]) - (6*ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^2)/a^4 + ArcTanh[a*x]^3/(a^4*Sqrt[1 - a^2*x^2]) + (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3)/a^4 + ((6*I)*ArcTanh[a*x]*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a^4 - ((6*I)*ArcTanh[a*x]*PolyLog[2, I*E^ArcTanh[a*x]])/a^4 - ((6*I)*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a^4 + ((6*I)*PolyLog[3, I*E^ArcTanh[a*x]])/a^4","A",13,9,24,0.3750,1,"{6028, 5994, 5952, 4180, 2531, 2282, 6589, 5962, 191}"
405,1,246,0,0.3174753,"\int \frac{x^2 \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x^2*ArcTanh[a*x]^3)/(1 - a^2*x^2)^(3/2),x]","\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{6 i \text{PolyLog}\left(4,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{6 i \text{PolyLog}\left(4,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{6}{a^3 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^3}{a^2 \sqrt{1-a^2 x^2}}-\frac{3 \tanh ^{-1}(a x)^2}{a^3 \sqrt{1-a^2 x^2}}+\frac{6 x \tanh ^{-1}(a x)}{a^2 \sqrt{1-a^2 x^2}}-\frac{2 \tanh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^3}","\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{6 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a^3}+\frac{6 i \text{PolyLog}\left(4,-i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{6 i \text{PolyLog}\left(4,i e^{\tanh ^{-1}(a x)}\right)}{a^3}-\frac{6}{a^3 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^3}{a^2 \sqrt{1-a^2 x^2}}-\frac{3 \tanh ^{-1}(a x)^2}{a^3 \sqrt{1-a^2 x^2}}+\frac{6 x \tanh ^{-1}(a x)}{a^2 \sqrt{1-a^2 x^2}}-\frac{2 \tanh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a^3}",1,"-6/(a^3*Sqrt[1 - a^2*x^2]) + (6*x*ArcTanh[a*x])/(a^2*Sqrt[1 - a^2*x^2]) - (3*ArcTanh[a*x]^2)/(a^3*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x]^3)/(a^2*Sqrt[1 - a^2*x^2]) - (2*ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^3)/a^3 + ((3*I)*ArcTanh[a*x]^2*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a^3 - ((3*I)*ArcTanh[a*x]^2*PolyLog[2, I*E^ArcTanh[a*x]])/a^3 - ((6*I)*ArcTanh[a*x]*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a^3 + ((6*I)*ArcTanh[a*x]*PolyLog[3, I*E^ArcTanh[a*x]])/a^3 + ((6*I)*PolyLog[4, (-I)*E^ArcTanh[a*x]])/a^3 - ((6*I)*PolyLog[4, I*E^ArcTanh[a*x]])/a^3","A",13,9,24,0.3750,1,"{6028, 5952, 4180, 2531, 6609, 2282, 6589, 5962, 5958}"
406,1,94,0,0.1245346,"\int \frac{x \tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x*ArcTanh[a*x]^3)/(1 - a^2*x^2)^(3/2),x]","-\frac{6 x}{a \sqrt{1-a^2 x^2}}+\frac{\tanh ^{-1}(a x)^3}{a^2 \sqrt{1-a^2 x^2}}-\frac{3 x \tanh ^{-1}(a x)^2}{a \sqrt{1-a^2 x^2}}+\frac{6 \tanh ^{-1}(a x)}{a^2 \sqrt{1-a^2 x^2}}","-\frac{6 x}{a \sqrt{1-a^2 x^2}}+\frac{\tanh ^{-1}(a x)^3}{a^2 \sqrt{1-a^2 x^2}}-\frac{3 x \tanh ^{-1}(a x)^2}{a \sqrt{1-a^2 x^2}}+\frac{6 \tanh ^{-1}(a x)}{a^2 \sqrt{1-a^2 x^2}}",1,"(-6*x)/(a*Sqrt[1 - a^2*x^2]) + (6*ArcTanh[a*x])/(a^2*Sqrt[1 - a^2*x^2]) - (3*x*ArcTanh[a*x]^2)/(a*Sqrt[1 - a^2*x^2]) + ArcTanh[a*x]^3/(a^2*Sqrt[1 - a^2*x^2])","A",3,3,22,0.1364,1,"{5994, 5962, 191}"
407,1,88,0,0.0707551,"\int \frac{\tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]^3/(1 - a^2*x^2)^(3/2),x]","-\frac{6}{a \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}}-\frac{3 \tanh ^{-1}(a x)^2}{a \sqrt{1-a^2 x^2}}+\frac{6 x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}","-\frac{6}{a \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}}-\frac{3 \tanh ^{-1}(a x)^2}{a \sqrt{1-a^2 x^2}}+\frac{6 x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}",1,"-6/(a*Sqrt[1 - a^2*x^2]) + (6*x*ArcTanh[a*x])/Sqrt[1 - a^2*x^2] - (3*ArcTanh[a*x]^2)/(a*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x]^3)/Sqrt[1 - a^2*x^2]","A",2,2,21,0.09524,1,"{5962, 5958}"
408,1,185,0,0.4094204,"\int \frac{\tanh ^{-1}(a x)^3}{x \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]^3/(x*(1 - a^2*x^2)^(3/2)),x]","-3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-6 \text{PolyLog}\left(4,-e^{\tanh ^{-1}(a x)}\right)+6 \text{PolyLog}\left(4,e^{\tanh ^{-1}(a x)}\right)-\frac{6 a x}{\sqrt{1-a^2 x^2}}+\frac{\tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}}-\frac{3 a x \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}+\frac{6 \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^3","-3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+3 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-6 \tanh ^{-1}(a x) \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-6 \text{PolyLog}\left(4,-e^{\tanh ^{-1}(a x)}\right)+6 \text{PolyLog}\left(4,e^{\tanh ^{-1}(a x)}\right)-\frac{6 a x}{\sqrt{1-a^2 x^2}}+\frac{\tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}}-\frac{3 a x \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}+\frac{6 \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^3",1,"(-6*a*x)/Sqrt[1 - a^2*x^2] + (6*ArcTanh[a*x])/Sqrt[1 - a^2*x^2] - (3*a*x*ArcTanh[a*x]^2)/Sqrt[1 - a^2*x^2] + ArcTanh[a*x]^3/Sqrt[1 - a^2*x^2] - 2*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^3 - 3*ArcTanh[a*x]^2*PolyLog[2, -E^ArcTanh[a*x]] + 3*ArcTanh[a*x]^2*PolyLog[2, E^ArcTanh[a*x]] + 6*ArcTanh[a*x]*PolyLog[3, -E^ArcTanh[a*x]] - 6*ArcTanh[a*x]*PolyLog[3, E^ArcTanh[a*x]] - 6*PolyLog[4, -E^ArcTanh[a*x]] + 6*PolyLog[4, E^ArcTanh[a*x]]","A",14,10,24,0.4167,1,"{6030, 6020, 4182, 2531, 6609, 2282, 6589, 5994, 5962, 191}"
409,1,187,0,0.424716,"\int \frac{\tanh ^{-1}(a x)^3}{x^2 \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]^3/(x^2*(1 - a^2*x^2)^(3/2)),x]","-6 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+6 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+6 a \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-6 a \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-\frac{6 a}{\sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{x}+\frac{a^2 x \tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}}-\frac{3 a \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}+\frac{6 a^2 x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-6 a \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2","-6 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+6 a \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+6 a \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-6 a \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-\frac{6 a}{\sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{x}+\frac{a^2 x \tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}}-\frac{3 a \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}+\frac{6 a^2 x \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-6 a \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2",1,"(-6*a)/Sqrt[1 - a^2*x^2] + (6*a^2*x*ArcTanh[a*x])/Sqrt[1 - a^2*x^2] - (3*a*ArcTanh[a*x]^2)/Sqrt[1 - a^2*x^2] - 6*a*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^2 + (a^2*x*ArcTanh[a*x]^3)/Sqrt[1 - a^2*x^2] - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3)/x - 6*a*ArcTanh[a*x]*PolyLog[2, -E^ArcTanh[a*x]] + 6*a*ArcTanh[a*x]*PolyLog[2, E^ArcTanh[a*x]] + 6*a*PolyLog[3, -E^ArcTanh[a*x]] - 6*a*PolyLog[3, E^ArcTanh[a*x]]","A",12,9,24,0.3750,1,"{6030, 6008, 6020, 4182, 2531, 2282, 6589, 5962, 5958}"
410,1,360,0,0.9823835,"\int \frac{\tanh ^{-1}(a x)^3}{x^3 \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]^3/(x^3*(1 - a^2*x^2)^(3/2)),x]","3 a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-3 a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{9}{2} a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+\frac{9}{2} a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+9 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-9 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-9 a^2 \text{PolyLog}\left(4,-e^{\tanh ^{-1}(a x)}\right)+9 a^2 \text{PolyLog}\left(4,e^{\tanh ^{-1}(a x)}\right)-\frac{6 a^3 x}{\sqrt{1-a^2 x^2}}-\frac{3 a^3 x \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}+\frac{a^2 \tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}}+\frac{6 a^2 \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-\frac{3 a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{2 x^2}-3 a^2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^3-6 a^2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","3 a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-3 a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{9}{2} a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+\frac{9}{2} a^2 \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+9 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-9 a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-9 a^2 \text{PolyLog}\left(4,-e^{\tanh ^{-1}(a x)}\right)+9 a^2 \text{PolyLog}\left(4,e^{\tanh ^{-1}(a x)}\right)-\frac{6 a^3 x}{\sqrt{1-a^2 x^2}}-\frac{3 a^3 x \tanh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}+\frac{a^2 \tanh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}}+\frac{6 a^2 \tanh ^{-1}(a x)}{\sqrt{1-a^2 x^2}}-\frac{3 a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3}{2 x^2}-3 a^2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^3-6 a^2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"(-6*a^3*x)/Sqrt[1 - a^2*x^2] + (6*a^2*ArcTanh[a*x])/Sqrt[1 - a^2*x^2] - (3*a^3*x*ArcTanh[a*x]^2)/Sqrt[1 - a^2*x^2] - (3*a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(2*x) + (a^2*ArcTanh[a*x]^3)/Sqrt[1 - a^2*x^2] - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3)/(2*x^2) - 3*a^2*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^3 - 6*a^2*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] - (9*a^2*ArcTanh[a*x]^2*PolyLog[2, -E^ArcTanh[a*x]])/2 + (9*a^2*ArcTanh[a*x]^2*PolyLog[2, E^ArcTanh[a*x]])/2 + 3*a^2*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])] - 3*a^2*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]] + 9*a^2*ArcTanh[a*x]*PolyLog[3, -E^ArcTanh[a*x]] - 9*a^2*ArcTanh[a*x]*PolyLog[3, E^ArcTanh[a*x]] - 9*a^2*PolyLog[4, -E^ArcTanh[a*x]] + 9*a^2*PolyLog[4, E^ArcTanh[a*x]]","A",28,13,24,0.5417,1,"{6030, 6026, 6008, 6018, 6020, 4182, 2531, 6609, 2282, 6589, 5994, 5962, 191}"
411,0,0,0,0.1235015,"\int \frac{x^m}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)} \, dx","Int[x^m/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]),x]","\int \frac{x^m}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x^m}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][x^m/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
412,0,0,0,0.1324706,"\int \frac{x^2}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)} \, dx","Int[x^2/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]),x]","\int \frac{x^2}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x^2}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][x^2/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
413,1,9,0,0.1036551,"\int \frac{x}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)} \, dx","Int[x/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]),x]","\frac{\text{Shi}\left(\tanh ^{-1}(a x)\right)}{a^2}","\frac{\text{Shi}\left(\tanh ^{-1}(a x)\right)}{a^2}",1,"SinhIntegral[ArcTanh[a*x]]/a^2","A",2,2,22,0.09091,1,"{6034, 3298}"
414,1,9,0,0.0622549,"\int \frac{1}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)} \, dx","Int[1/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]),x]","\frac{\text{Chi}\left(\tanh ^{-1}(a x)\right)}{a}","\frac{\text{Chi}\left(\tanh ^{-1}(a x)\right)}{a}",1,"CoshIntegral[ArcTanh[a*x]]/a","A",2,2,21,0.09524,1,"{5968, 3301}"
415,0,0,0,0.1184745,"\int \frac{1}{x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)} \, dx","Int[1/(x*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x]),x]","\int \frac{1}{x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
416,0,0,0,0.1090016,"\int \frac{x^m}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2} \, dx","Int[x^m/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^2),x]","\int \frac{x^m}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{x^m}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][x^m/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^2), x]","A",0,0,0,0,-1,"{}"
417,0,0,0,0.2663094,"\int \frac{x^2}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2} \, dx","Int[x^2/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^2),x]","\int \frac{x^2}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2} \, dx","-\frac{\text{Int}\left(\frac{1}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2},x\right)}{a^2}+\frac{\text{Shi}\left(\tanh ^{-1}(a x)\right)}{a^3}-\frac{1}{a^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}",0,"-(1/(a^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])) + SinhIntegral[ArcTanh[a*x]]/a^3 - Defer[Int][1/(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2), x]/a^2","A",0,0,0,0,-1,"{}"
418,1,36,0,0.121882,"\int \frac{x}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2} \, dx","Int[x/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^2),x]","\frac{\text{Chi}\left(\tanh ^{-1}(a x)\right)}{a^2}-\frac{x}{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}","\frac{\text{Chi}\left(\tanh ^{-1}(a x)\right)}{a^2}-\frac{x}{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}",1,"-(x/(a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])) + CoshIntegral[ArcTanh[a*x]]/a^2","A",3,3,22,0.1364,1,"{6006, 5968, 3301}"
419,1,35,0,0.1258337,"\int \frac{1}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2} \, dx","Int[1/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^2),x]","\frac{\text{Shi}\left(\tanh ^{-1}(a x)\right)}{a}-\frac{1}{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}","\frac{\text{Shi}\left(\tanh ^{-1}(a x)\right)}{a}-\frac{1}{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}",1,"-(1/(a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])) + SinhIntegral[ArcTanh[a*x]]/a","A",3,3,21,0.1429,1,"{5966, 6034, 3298}"
420,0,0,0,0.4173181,"\int \frac{1}{x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2} \, dx","Int[1/(x*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^2),x]","\int \frac{1}{x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)},x\right)}{a}-\frac{a x}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}-\frac{\sqrt{1-a^2 x^2}}{a x \tanh ^{-1}(a x)}+\text{Chi}\left(\tanh ^{-1}(a x)\right)",0,"-((a*x)/(Sqrt[1 - a^2*x^2]*ArcTanh[a*x])) - Sqrt[1 - a^2*x^2]/(a*x*ArcTanh[a*x]) + CoshIntegral[ArcTanh[a*x]] - Defer[Int][1/(x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]), x]/a","A",0,0,0,0,-1,"{}"
421,0,0,0,0.1068306,"\int \frac{x^m}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^3} \, dx","Int[x^m/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^3),x]","\int \frac{x^m}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{x^m}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^3},x\right)",0,"Defer[Int][x^m/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^3), x]","A",0,0,0,0,-1,"{}"
422,0,0,0,0.303998,"\int \frac{x^2}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^3} \, dx","Int[x^2/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^3),x]","\int \frac{x^2}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^3} \, dx","-\frac{\text{Int}\left(\frac{1}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3},x\right)}{a^2}+\frac{\text{Chi}\left(\tanh ^{-1}(a x)\right)}{2 a^3}-\frac{x}{2 a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}-\frac{1}{2 a^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}",0,"-1/(2*a^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2) - x/(2*a^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]) + CoshIntegral[ArcTanh[a*x]]/(2*a^3) - Defer[Int][1/(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3), x]/a^2","A",0,0,0,0,-1,"{}"
423,1,68,0,0.1959596,"\int \frac{x}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^3} \, dx","Int[x/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^3),x]","\frac{\text{Shi}\left(\tanh ^{-1}(a x)\right)}{2 a^2}-\frac{x}{2 a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}-\frac{1}{2 a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}","\frac{\text{Shi}\left(\tanh ^{-1}(a x)\right)}{2 a^2}-\frac{x}{2 a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}-\frac{1}{2 a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}",1,"-x/(2*a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2) - 1/(2*a^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]) + SinhIntegral[ArcTanh[a*x]]/(2*a^2)","A",4,4,22,0.1818,1,"{6006, 5966, 6034, 3298}"
424,1,65,0,0.1630919,"\int \frac{1}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^3} \, dx","Int[1/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^3),x]","-\frac{x}{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}-\frac{1}{2 a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}+\frac{\text{Chi}\left(\tanh ^{-1}(a x)\right)}{2 a}","-\frac{x}{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}-\frac{1}{2 a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}+\frac{\text{Chi}\left(\tanh ^{-1}(a x)\right)}{2 a}",1,"-1/(2*a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2) - x/(2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]) + CoshIntegral[ArcTanh[a*x]]/(2*a)","A",4,4,21,0.1905,1,"{5966, 6006, 5968, 3301}"
425,0,0,0,0.4848254,"\int \frac{1}{x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^3} \, dx","Int[1/(x*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^3),x]","\int \frac{1}{x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^3} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2},x\right)}{2 a}-\frac{a x}{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}-\frac{1}{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}-\frac{\sqrt{1-a^2 x^2}}{2 a x \tanh ^{-1}(a x)^2}+\frac{1}{2} \text{Shi}\left(\tanh ^{-1}(a x)\right)",0,"-(a*x)/(2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2) - Sqrt[1 - a^2*x^2]/(2*a*x*ArcTanh[a*x]^2) - 1/(2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]) + SinhIntegral[ArcTanh[a*x]]/2 - Defer[Int][1/(x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2), x]/(2*a)","A",0,0,0,0,-1,"{}"
426,1,243,0,0.3078259,"\int x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x) \, dx","Int[x^4*Sqrt[1 - a^2*x^2]*ArcTanh[a*x],x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a^5}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a^5}+\frac{\left(1-a^2 x^2\right)^{5/2}}{30 a^5}-\frac{7 \left(1-a^2 x^2\right)^{3/2}}{72 a^5}+\frac{\sqrt{1-a^2 x^2}}{16 a^5}+\frac{1}{6} x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{24 a^2}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{16 a^4}-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{8 a^5}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a^5}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a^5}+\frac{\left(1-a^2 x^2\right)^{5/2}}{30 a^5}-\frac{7 \left(1-a^2 x^2\right)^{3/2}}{72 a^5}+\frac{\sqrt{1-a^2 x^2}}{16 a^5}+\frac{1}{6} x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{24 a^2}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{16 a^4}-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{8 a^5}",1,"Sqrt[1 - a^2*x^2]/(16*a^5) - (7*(1 - a^2*x^2)^(3/2))/(72*a^5) + (1 - a^2*x^2)^(5/2)/(30*a^5) - (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(16*a^4) - (x^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(24*a^2) + (x^5*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/6 - (ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(8*a^5) - ((I/16)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^5 + ((I/16)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^5","A",11,6,22,0.2727,1,"{6010, 6016, 266, 43, 261, 5950}"
427,1,136,0,0.2032944,"\int x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x) \, dx","Int[x^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x],x]","\frac{x^3 \sqrt{1-a^2 x^2}}{20 a}+\frac{x \sqrt{1-a^2 x^2}}{24 a^3}+\frac{1}{5} x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 a^2}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 a^4}+\frac{11 \sin ^{-1}(a x)}{120 a^4}","\frac{x^3 \sqrt{1-a^2 x^2}}{20 a}+\frac{x \sqrt{1-a^2 x^2}}{24 a^3}+\frac{1}{5} x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 a^2}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 a^4}+\frac{11 \sin ^{-1}(a x)}{120 a^4}",1,"(x*Sqrt[1 - a^2*x^2])/(24*a^3) + (x^3*Sqrt[1 - a^2*x^2])/(20*a) + (11*ArcSin[a*x])/(120*a^4) - (2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(15*a^4) - (x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(15*a^2) + (x^4*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/5","A",9,5,22,0.2273,1,"{6010, 6016, 321, 216, 5994}"
428,1,194,0,0.193429,"\int x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x) \, dx","Int[x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x],x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a^3}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a^3}-\frac{\left(1-a^2 x^2\right)^{3/2}}{12 a^3}+\frac{\sqrt{1-a^2 x^2}}{8 a^3}+\frac{1}{4} x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 a^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a^3}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a^3}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a^3}-\frac{\left(1-a^2 x^2\right)^{3/2}}{12 a^3}+\frac{\sqrt{1-a^2 x^2}}{8 a^3}+\frac{1}{4} x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 a^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a^3}",1,"Sqrt[1 - a^2*x^2]/(8*a^3) - (1 - a^2*x^2)^(3/2)/(12*a^3) - (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(8*a^2) + (x^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/4 - (ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(4*a^3) - ((I/8)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^3 + ((I/8)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^3","A",7,6,22,0.2727,1,"{6010, 6016, 261, 5950, 266, 43}"
429,1,59,0,0.0485783,"\int x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x) \, dx","Int[x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x],x]","\frac{x \sqrt{1-a^2 x^2}}{6 a}-\frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{3 a^2}+\frac{\sin ^{-1}(a x)}{6 a^2}","\frac{x \sqrt{1-a^2 x^2}}{6 a}-\frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{3 a^2}+\frac{\sin ^{-1}(a x)}{6 a^2}",1,"(x*Sqrt[1 - a^2*x^2])/(6*a) + ArcSin[a*x]/(6*a^2) - ((1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/(3*a^2)","A",3,3,20,0.1500,1,"{5994, 195, 216}"
430,1,143,0,0.0554435,"\int \sqrt{1-a^2 x^2} \tanh ^{-1}(a x) \, dx","Int[Sqrt[1 - a^2*x^2]*ArcTanh[a*x],x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}+\frac{\sqrt{1-a^2 x^2}}{2 a}+\frac{1}{2} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}+\frac{\sqrt{1-a^2 x^2}}{2 a}+\frac{1}{2} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a}",1,"Sqrt[1 - a^2*x^2]/(2*a) + (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/2 - (ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/a - ((I/2)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a + ((I/2)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a","A",2,2,19,0.1053,1,"{5942, 5950}"
431,1,100,0,0.1260758,"\int \frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x} \, dx","Int[(Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x,x]","\text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\sin ^{-1}(a x)-2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","\text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\sin ^{-1}(a x)-2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-ArcSin[a*x] + Sqrt[1 - a^2*x^2]*ArcTanh[a*x] - 2*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] + PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])] - PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]]","A",3,3,22,0.1364,1,"{6010, 6018, 216}"
432,1,130,0,0.1629523,"\int \frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x^2} \, dx","Int[(Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x^2,x]","i a \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-i a \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+2 a \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)","i a \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-i a \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+2 a \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)",1,"-((Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x) + 2*a*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x] - a*ArcTanh[Sqrt[1 - a^2*x^2]] + I*a*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]] - I*a*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]]","A",6,6,22,0.2727,1,"{6014, 6008, 266, 63, 208, 5950}"
433,1,136,0,0.1981668,"\int \frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x^3} \, dx","Int[(Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x^3,x]","-\frac{1}{2} a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{1}{2} a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a \sqrt{1-a^2 x^2}}{2 x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 x^2}+a^2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","-\frac{1}{2} a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{1}{2} a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a \sqrt{1-a^2 x^2}}{2 x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 x^2}+a^2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-(a*Sqrt[1 - a^2*x^2])/(2*x) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(2*x^2) + a^2*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] - (a^2*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])])/2 + (a^2*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]])/2","A",5,4,22,0.1818,1,"{6010, 6026, 264, 6018}"
434,1,70,0,0.0816485,"\int \frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x^4} \, dx","Int[(Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x^4,x]","-\frac{a \sqrt{1-a^2 x^2}}{6 x^2}+\frac{1}{6} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{3 x^3}","-\frac{a \sqrt{1-a^2 x^2}}{6 x^2}+\frac{1}{6} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{3 x^3}",1,"-(a*Sqrt[1 - a^2*x^2])/(6*x^2) - ((1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/(3*x^3) + (a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/6","A",5,5,22,0.2273,1,"{6008, 266, 47, 63, 208}"
435,1,191,0,0.2999655,"\int \frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x^5} \, dx","Int[(Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x^5,x]","-\frac{1}{8} a^4 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{1}{8} a^4 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a^3 \sqrt{1-a^2 x^2}}{24 x}-\frac{a \sqrt{1-a^2 x^2}}{12 x^3}+\frac{a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 x^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{4 x^4}+\frac{1}{4} a^4 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","-\frac{1}{8} a^4 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{1}{8} a^4 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a^3 \sqrt{1-a^2 x^2}}{24 x}-\frac{a \sqrt{1-a^2 x^2}}{12 x^3}+\frac{a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 x^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{4 x^4}+\frac{1}{4} a^4 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-(a*Sqrt[1 - a^2*x^2])/(12*x^3) - (a^3*Sqrt[1 - a^2*x^2])/(24*x) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(4*x^4) + (a^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(8*x^2) + (a^4*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]])/4 - (a^4*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])])/8 + (a^4*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]])/8","A",9,5,22,0.2273,1,"{6010, 6026, 271, 264, 6018}"
436,1,150,0,0.3731095,"\int \frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x^6} \, dx","Int[(Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x^6,x]","-\frac{a^3 \sqrt{1-a^2 x^2}}{24 x^2}-\frac{a \sqrt{1-a^2 x^2}}{20 x^4}+\frac{11}{120} a^5 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{2 a^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 x}+\frac{a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 x^3}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{5 x^5}","-\frac{a^3 \sqrt{1-a^2 x^2}}{24 x^2}-\frac{a \sqrt{1-a^2 x^2}}{20 x^4}+\frac{11}{120} a^5 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{2 a^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 x}+\frac{a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 x^3}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{5 x^5}",1,"-(a*Sqrt[1 - a^2*x^2])/(20*x^4) - (a^3*Sqrt[1 - a^2*x^2])/(24*x^2) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(5*x^5) + (a^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(15*x^3) + (2*a^4*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(15*x) + (11*a^5*ArcTanh[Sqrt[1 - a^2*x^2]])/120","A",21,7,22,0.3182,1,"{6010, 6026, 266, 51, 63, 208, 6008}"
437,1,243,0,0.4127566,"\int \frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x^7} \, dx","Int[(Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x^7,x]","-\frac{1}{16} a^6 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{1}{16} a^6 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{a^5 \sqrt{1-a^2 x^2}}{720 x}-\frac{11 a^3 \sqrt{1-a^2 x^2}}{360 x^3}-\frac{a \sqrt{1-a^2 x^2}}{30 x^5}+\frac{a^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{16 x^2}+\frac{a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{24 x^4}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{6 x^6}+\frac{1}{8} a^6 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","-\frac{1}{16} a^6 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{1}{16} a^6 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{a^5 \sqrt{1-a^2 x^2}}{720 x}-\frac{11 a^3 \sqrt{1-a^2 x^2}}{360 x^3}-\frac{a \sqrt{1-a^2 x^2}}{30 x^5}+\frac{a^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{16 x^2}+\frac{a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{24 x^4}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{6 x^6}+\frac{1}{8} a^6 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-(a*Sqrt[1 - a^2*x^2])/(30*x^5) - (11*a^3*Sqrt[1 - a^2*x^2])/(360*x^3) + (a^5*Sqrt[1 - a^2*x^2])/(720*x) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(6*x^6) + (a^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(24*x^4) + (a^4*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(16*x^2) + (a^6*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]])/8 - (a^6*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])])/16 + (a^6*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]])/16","A",14,5,22,0.2273,1,"{6010, 6026, 271, 264, 6018}"
438,1,336,0,1.4027251,"\int x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2 \, dx","Int[x^4*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2,x]","-\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{8 a^5}+\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{8 a^5}+\frac{i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{8 a^5}-\frac{i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{8 a^5}+\frac{x^3 \sqrt{1-a^2 x^2}}{60 a^2}+\frac{x \sqrt{1-a^2 x^2}}{18 a^4}+\frac{1}{6} x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2+\frac{x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 a}-\frac{x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{24 a^2}+\frac{11 x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{180 a^3}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{16 a^4}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{360 a^5}-\frac{19 \sin ^{-1}(a x)}{360 a^5}+\frac{\tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{8 a^5}","-\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{8 a^5}+\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{8 a^5}+\frac{i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{8 a^5}-\frac{i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{8 a^5}+\frac{x^3 \sqrt{1-a^2 x^2}}{60 a^2}+\frac{x \sqrt{1-a^2 x^2}}{18 a^4}+\frac{1}{6} x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2+\frac{x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{15 a}-\frac{x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{24 a^2}+\frac{11 x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{180 a^3}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{16 a^4}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{360 a^5}-\frac{19 \sin ^{-1}(a x)}{360 a^5}+\frac{\tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{8 a^5}",1,"(x*Sqrt[1 - a^2*x^2])/(18*a^4) + (x^3*Sqrt[1 - a^2*x^2])/(60*a^2) - (19*ArcSin[a*x])/(360*a^5) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(360*a^5) + (11*x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(180*a^3) + (x^4*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(15*a) - (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(16*a^4) - (x^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(24*a^2) + (x^5*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/6 + (ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^2)/(8*a^5) - ((I/8)*ArcTanh[a*x]*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a^5 + ((I/8)*ArcTanh[a*x]*PolyLog[2, I*E^ArcTanh[a*x]])/a^5 + ((I/8)*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a^5 - ((I/8)*PolyLog[3, I*E^ArcTanh[a*x]])/a^5","A",45,10,24,0.4167,1,"{6014, 6016, 321, 216, 5994, 5952, 4180, 2531, 2282, 6589}"
439,1,281,0,1.0730707,"\int x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2 \, dx","Int[x^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2,x]","-\frac{11 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{60 a^4}+\frac{11 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{60 a^4}-\frac{\left(1-a^2 x^2\right)^{3/2}}{30 a^4}+\frac{11 \sqrt{1-a^2 x^2}}{60 a^4}+\frac{1}{5} x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2+\frac{x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{10 a}-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{15 a^2}+\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{12 a^3}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{15 a^4}-\frac{11 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{30 a^4}","-\frac{11 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{60 a^4}+\frac{11 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{60 a^4}-\frac{\left(1-a^2 x^2\right)^{3/2}}{30 a^4}+\frac{11 \sqrt{1-a^2 x^2}}{60 a^4}+\frac{1}{5} x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2+\frac{x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{10 a}-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{15 a^2}+\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{12 a^3}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{15 a^4}-\frac{11 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{30 a^4}",1,"(11*Sqrt[1 - a^2*x^2])/(60*a^4) - (1 - a^2*x^2)^(3/2)/(30*a^4) + (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(12*a^3) + (x^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(10*a) - (11*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(30*a^4) - (2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(15*a^4) - (x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(15*a^2) + (x^4*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/5 - (((11*I)/60)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^4 + (((11*I)/60)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^4","A",21,7,24,0.2917,1,"{6014, 6016, 261, 5950, 5994, 266, 43}"
440,1,254,0,0.8527065,"\int x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2 \, dx","Int[x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2,x]","-\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{4 a^3}+\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{4 a^3}+\frac{i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{4 a^3}-\frac{i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{4 a^3}+\frac{x \sqrt{1-a^2 x^2}}{12 a^2}+\frac{1}{4} x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2+\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{6 a}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{8 a^2}+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{12 a^3}-\frac{\sin ^{-1}(a x)}{6 a^3}+\frac{\tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{4 a^3}","-\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{4 a^3}+\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{4 a^3}+\frac{i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{4 a^3}-\frac{i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{4 a^3}+\frac{x \sqrt{1-a^2 x^2}}{12 a^2}+\frac{1}{4} x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2+\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{6 a}-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{8 a^2}+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{12 a^3}-\frac{\sin ^{-1}(a x)}{6 a^3}+\frac{\tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{4 a^3}",1,"(x*Sqrt[1 - a^2*x^2])/(12*a^2) - ArcSin[a*x]/(6*a^3) + (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(12*a^3) + (x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(6*a) - (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(8*a^2) + (x^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/4 + (ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^2)/(4*a^3) - ((I/4)*ArcTanh[a*x]*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a^3 + ((I/4)*ArcTanh[a*x]*PolyLog[2, I*E^ArcTanh[a*x]])/a^3 + ((I/4)*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a^3 - ((I/4)*PolyLog[3, I*E^ArcTanh[a*x]])/a^3","A",29,10,24,0.4167,1,"{6014, 6016, 5994, 216, 5952, 4180, 2531, 2282, 6589, 321}"
441,1,175,0,0.1245852,"\int x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2 \, dx","Int[x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2,x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{3 a^2}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{3 a^2}+\frac{\sqrt{1-a^2 x^2}}{3 a^2}-\frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2}{3 a^2}+\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{3 a}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{3 a^2}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{3 a^2}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{3 a^2}+\frac{\sqrt{1-a^2 x^2}}{3 a^2}-\frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2}{3 a^2}+\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{3 a}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{3 a^2}",1,"Sqrt[1 - a^2*x^2]/(3*a^2) + (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(3*a) - (2*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(3*a^2) - ((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^2)/(3*a^2) - ((I/3)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^2 + ((I/3)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^2","A",3,3,22,0.1364,1,"{5994, 5942, 5950}"
442,1,158,0,0.1461997,"\int \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2 \, dx","Int[Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2,x]","-\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{1}{2} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a}-\frac{\sin ^{-1}(a x)}{a}+\frac{\tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a}","-\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{1}{2} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a}-\frac{\sin ^{-1}(a x)}{a}+\frac{\tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a}",1,"-(ArcSin[a*x]/a) + (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/a + (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/2 + (ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^2)/a - (I*ArcTanh[a*x]*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a + (I*ArcTanh[a*x]*PolyLog[2, I*E^ArcTanh[a*x]])/a + (I*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a - (I*PolyLog[3, I*E^ArcTanh[a*x]])/a","A",10,7,21,0.3333,1,"{5944, 5952, 4180, 2531, 2282, 6589, 216}"
443,1,174,0,0.3931518,"\int \frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{x} \, dx","Int[(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/x,x]","2 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)+\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2-2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2+4 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)","2 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)+2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)+2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)-2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)+\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2-2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2+4 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)",1,"4*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x] + Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2 - 2*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^2 - 2*ArcTanh[a*x]*PolyLog[2, -E^ArcTanh[a*x]] + 2*ArcTanh[a*x]*PolyLog[2, E^ArcTanh[a*x]] + (2*I)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]] - (2*I)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]] + 2*PolyLog[3, -E^ArcTanh[a*x]] - 2*PolyLog[3, E^ArcTanh[a*x]]","A",11,8,24,0.3333,1,"{6014, 6020, 4182, 2531, 2282, 6589, 5994, 5950}"
444,1,197,0,0.3825176,"\int \frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{x^2} \, dx","Int[(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/x^2,x]","2 a \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 a \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+2 i a \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)-2 i a \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)-2 i a \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)+2 i a \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{x}-4 a \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)-2 a \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)","2 a \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-2 a \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+2 i a \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)-2 i a \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)-2 i a \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)+2 i a \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{x}-4 a \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)-2 a \tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)",1,"-((Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/x) - 2*a*ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^2 - 4*a*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] + (2*I)*a*ArcTanh[a*x]*PolyLog[2, (-I)*E^ArcTanh[a*x]] - (2*I)*a*ArcTanh[a*x]*PolyLog[2, I*E^ArcTanh[a*x]] + 2*a*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])] - 2*a*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]] - (2*I)*a*PolyLog[3, (-I)*E^ArcTanh[a*x]] + (2*I)*a*PolyLog[3, I*E^ArcTanh[a*x]]","A",11,8,24,0.3333,1,"{6014, 6008, 6018, 5952, 4180, 2531, 2282, 6589}"
445,1,151,0,0.5444672,"\int \frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{x^3} \, dx","Int[(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/x^3,x]","a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)-a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)-a^2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)+a^2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 x^2}+a^2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2","a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\tanh ^{-1}(a x)}\right)-a^2 \tanh ^{-1}(a x) \text{PolyLog}\left(2,e^{\tanh ^{-1}(a x)}\right)-a^2 \text{PolyLog}\left(3,-e^{\tanh ^{-1}(a x)}\right)+a^2 \text{PolyLog}\left(3,e^{\tanh ^{-1}(a x)}\right)-a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 x^2}+a^2 \tanh ^{-1}\left(e^{\tanh ^{-1}(a x)}\right) \tanh ^{-1}(a x)^2",1,"-((a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(2*x^2) + a^2*ArcTanh[E^ArcTanh[a*x]]*ArcTanh[a*x]^2 - a^2*ArcTanh[Sqrt[1 - a^2*x^2]] + a^2*ArcTanh[a*x]*PolyLog[2, -E^ArcTanh[a*x]] - a^2*ArcTanh[a*x]*PolyLog[2, E^ArcTanh[a*x]] - a^2*PolyLog[3, -E^ArcTanh[a*x]] + a^2*PolyLog[3, E^ArcTanh[a*x]]","A",22,11,24,0.4583,1,"{6014, 6026, 6008, 266, 63, 208, 6020, 4182, 2531, 2282, 6589}"
446,1,169,0,0.2974623,"\int \frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{x^4} \, dx","Int[(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/x^4,x]","-\frac{1}{3} a^3 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{1}{3} a^3 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a^2 \sqrt{1-a^2 x^2}}{3 x}-\frac{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{3 x^2}-\frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2}{3 x^3}+\frac{2}{3} a^3 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","-\frac{1}{3} a^3 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{1}{3} a^3 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a^2 \sqrt{1-a^2 x^2}}{3 x}-\frac{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{3 x^2}-\frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2}{3 x^3}+\frac{2}{3} a^3 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-(a^2*Sqrt[1 - a^2*x^2])/(3*x) - (a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(3*x^2) - ((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^2)/(3*x^3) + (2*a^3*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]])/3 - (a^3*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])])/3 + (a^3*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]])/3","A",6,5,24,0.2083,1,"{6008, 6010, 6026, 264, 6018}"
447,1,292,0,0.8175376,"\int x^4 \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x) \, dx","Int[x^4*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x],x]","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{128 a^5}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{128 a^5}+\frac{\left(1-a^2 x^2\right)^{7/2}}{56 a^5}-\frac{3 \left(1-a^2 x^2\right)^{5/2}}{80 a^5}+\frac{\left(1-a^2 x^2\right)^{3/2}}{192 a^5}+\frac{3 \sqrt{1-a^2 x^2}}{128 a^5}-\frac{1}{8} a^2 x^7 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)+\frac{3}{16} x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{64 a^2}-\frac{3 x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{128 a^4}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{64 a^5}","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{128 a^5}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{128 a^5}+\frac{\left(1-a^2 x^2\right)^{7/2}}{56 a^5}-\frac{3 \left(1-a^2 x^2\right)^{5/2}}{80 a^5}+\frac{\left(1-a^2 x^2\right)^{3/2}}{192 a^5}+\frac{3 \sqrt{1-a^2 x^2}}{128 a^5}-\frac{1}{8} a^2 x^7 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)+\frac{3}{16} x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{64 a^2}-\frac{3 x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{128 a^4}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{64 a^5}",1,"(3*Sqrt[1 - a^2*x^2])/(128*a^5) + (1 - a^2*x^2)^(3/2)/(192*a^5) - (3*(1 - a^2*x^2)^(5/2))/(80*a^5) + (1 - a^2*x^2)^(7/2)/(56*a^5) - (3*x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(128*a^4) - (x^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(64*a^2) + (3*x^5*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/16 - (a^2*x^7*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/8 - (3*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(64*a^5) - (((3*I)/128)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^5 + (((3*I)/128)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^5","A",27,7,22,0.3182,1,"{6014, 6010, 6016, 266, 43, 261, 5950}"
448,1,186,0,0.5707372,"\int x^3 \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x) \, dx","Int[x^3*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x],x]","-\frac{1}{42} a x^5 \sqrt{1-a^2 x^2}+\frac{23 x^3 \sqrt{1-a^2 x^2}}{840 a}+\frac{3 x \sqrt{1-a^2 x^2}}{112 a^3}-\frac{1}{7} a^2 x^6 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)+\frac{8}{35} x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{35 a^2}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{35 a^4}+\frac{17 \sin ^{-1}(a x)}{560 a^4}","-\frac{1}{42} a x^5 \sqrt{1-a^2 x^2}+\frac{23 x^3 \sqrt{1-a^2 x^2}}{840 a}+\frac{3 x \sqrt{1-a^2 x^2}}{112 a^3}-\frac{1}{7} a^2 x^6 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)+\frac{8}{35} x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{35 a^2}-\frac{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{35 a^4}+\frac{17 \sin ^{-1}(a x)}{560 a^4}",1,"(3*x*Sqrt[1 - a^2*x^2])/(112*a^3) + (23*x^3*Sqrt[1 - a^2*x^2])/(840*a) - (a*x^5*Sqrt[1 - a^2*x^2])/42 + (17*ArcSin[a*x])/(560*a^4) - (2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(35*a^4) - (x^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(35*a^2) + (8*x^4*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/35 - (a^2*x^6*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/7","A",24,6,22,0.2727,1,"{6014, 6010, 6016, 321, 216, 5994}"
449,1,243,0,0.5722966,"\int x^2 \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x) \, dx","Int[x^2*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x],x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a^3}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a^3}-\frac{\left(1-a^2 x^2\right)^{5/2}}{30 a^3}+\frac{\left(1-a^2 x^2\right)^{3/2}}{72 a^3}+\frac{\sqrt{1-a^2 x^2}}{16 a^3}-\frac{1}{6} a^2 x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)+\frac{7}{24} x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{16 a^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{8 a^3}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a^3}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a^3}-\frac{\left(1-a^2 x^2\right)^{5/2}}{30 a^3}+\frac{\left(1-a^2 x^2\right)^{3/2}}{72 a^3}+\frac{\sqrt{1-a^2 x^2}}{16 a^3}-\frac{1}{6} a^2 x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)+\frac{7}{24} x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{16 a^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{8 a^3}",1,"Sqrt[1 - a^2*x^2]/(16*a^3) + (1 - a^2*x^2)^(3/2)/(72*a^3) - (1 - a^2*x^2)^(5/2)/(30*a^3) - (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(16*a^2) + (7*x^3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/24 - (a^2*x^5*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/6 - (ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(8*a^3) - ((I/16)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^3 + ((I/16)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a^3","A",19,7,22,0.3182,1,"{6014, 6010, 6016, 261, 5950, 266, 43}"
450,1,81,0,0.0575997,"\int x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x) \, dx","Int[x*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x],x]","\frac{x \left(1-a^2 x^2\right)^{3/2}}{20 a}+\frac{3 x \sqrt{1-a^2 x^2}}{40 a}-\frac{\left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)}{5 a^2}+\frac{3 \sin ^{-1}(a x)}{40 a^2}","\frac{x \left(1-a^2 x^2\right)^{3/2}}{20 a}+\frac{3 x \sqrt{1-a^2 x^2}}{40 a}-\frac{\left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)}{5 a^2}+\frac{3 \sin ^{-1}(a x)}{40 a^2}",1,"(3*x*Sqrt[1 - a^2*x^2])/(40*a) + (x*(1 - a^2*x^2)^(3/2))/(20*a) + (3*ArcSin[a*x])/(40*a^2) - ((1 - a^2*x^2)^(5/2)*ArcTanh[a*x])/(5*a^2)","A",4,3,20,0.1500,1,"{5994, 195, 216}"
451,1,189,0,0.0859679,"\int \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x) \, dx","Int[(1 - a^2*x^2)^(3/2)*ArcTanh[a*x],x]","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a}+\frac{\left(1-a^2 x^2\right)^{3/2}}{12 a}+\frac{3 \sqrt{1-a^2 x^2}}{8 a}+\frac{1}{4} x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)+\frac{3}{8} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{3 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a}","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a}+\frac{\left(1-a^2 x^2\right)^{3/2}}{12 a}+\frac{3 \sqrt{1-a^2 x^2}}{8 a}+\frac{1}{4} x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)+\frac{3}{8} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{3 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a}",1,"(3*Sqrt[1 - a^2*x^2])/(8*a) + (1 - a^2*x^2)^(3/2)/(12*a) + (3*x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/8 + (x*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/4 - (3*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(4*a) - (((3*I)/8)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a + (((3*I)/8)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a","A",3,2,19,0.1053,1,"{5942, 5950}"
452,1,144,0,0.2315502,"\int \frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{x} \, dx","Int[((1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/x,x]","\text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{1}{6} a x \sqrt{1-a^2 x^2}+\frac{1}{3} \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)+\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{7}{6} \sin ^{-1}(a x)-2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","\text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{1}{6} a x \sqrt{1-a^2 x^2}+\frac{1}{3} \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)+\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{7}{6} \sin ^{-1}(a x)-2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-(a*x*Sqrt[1 - a^2*x^2])/6 - (7*ArcSin[a*x])/6 + Sqrt[1 - a^2*x^2]*ArcTanh[a*x] + ((1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/3 - 2*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] + PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])] - PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]]","A",7,6,22,0.2727,1,"{6014, 6010, 6018, 216, 5994, 195}"
453,1,179,0,0.2844875,"\int \frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{x^2} \, dx","Int[((1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/x^2,x]","\frac{3}{2} i a \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{3}{2} i a \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{1}{2} a \sqrt{1-a^2 x^2}-\frac{1}{2} a^2 x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}+3 a \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)","\frac{3}{2} i a \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{3}{2} i a \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{1}{2} a \sqrt{1-a^2 x^2}-\frac{1}{2} a^2 x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}+3 a \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)",1,"-(a*Sqrt[1 - a^2*x^2])/2 - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x - (a^2*x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/2 + 3*a*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x] - a*ArcTanh[Sqrt[1 - a^2*x^2]] + ((3*I)/2)*a*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]] - ((3*I)/2)*a*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]]","A",9,7,22,0.3182,1,"{6014, 6008, 266, 63, 208, 5950, 5942}"
454,1,168,0,0.3873387,"\int \frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{x^3} \, dx","Int[((1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/x^3,x]","-\frac{3}{2} a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{3}{2} a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a \sqrt{1-a^2 x^2}}{2 x}-a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 x^2}+a^2 \sin ^{-1}(a x)+3 a^2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","-\frac{3}{2} a^2 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{3}{2} a^2 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a \sqrt{1-a^2 x^2}}{2 x}-a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 x^2}+a^2 \sin ^{-1}(a x)+3 a^2 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-(a*Sqrt[1 - a^2*x^2])/(2*x) + a^2*ArcSin[a*x] - a^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x] - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(2*x^2) + 3*a^2*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]] - (3*a^2*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])])/2 + (3*a^2*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]])/2","A",9,6,22,0.2727,1,"{6014, 6010, 6026, 264, 6018, 216}"
455,1,189,0,0.3122699,"\int \frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{x^4} \, dx","Int[((1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/x^4,x]","-i a^3 \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)+i a^3 \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a \sqrt{1-a^2 x^2}}{6 x^2}+\frac{7}{6} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-\frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{3 x^3}-2 a^3 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)","-i a^3 \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)+i a^3 \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{a \sqrt{1-a^2 x^2}}{6 x^2}+\frac{7}{6} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{x}-\frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{3 x^3}-2 a^3 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)",1,"-(a*Sqrt[1 - a^2*x^2])/(6*x^2) + (a^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/x - ((1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/(3*x^3) - 2*a^3*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x] + (7*a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/6 - I*a^3*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]] + I*a^3*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]]","A",12,7,22,0.3182,1,"{6014, 6008, 266, 47, 63, 208, 5950}"
456,1,191,0,0.56626,"\int \frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{x^5} \, dx","Int[((1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/x^5,x]","\frac{3}{8} a^4 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{3}{8} a^4 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{11 a^3 \sqrt{1-a^2 x^2}}{24 x}-\frac{a \sqrt{1-a^2 x^2}}{12 x^3}+\frac{5 a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 x^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{4 x^4}-\frac{3}{4} a^4 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","\frac{3}{8} a^4 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{3}{8} a^4 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{11 a^3 \sqrt{1-a^2 x^2}}{24 x}-\frac{a \sqrt{1-a^2 x^2}}{12 x^3}+\frac{5 a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 x^2}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{4 x^4}-\frac{3}{4} a^4 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-(a*Sqrt[1 - a^2*x^2])/(12*x^3) + (11*a^3*Sqrt[1 - a^2*x^2])/(24*x) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(4*x^4) + (5*a^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(8*x^2) - (3*a^4*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]])/4 + (3*a^4*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])])/8 - (3*a^4*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]])/8","A",15,6,22,0.2727,1,"{6014, 6010, 6026, 271, 264, 6018}"
457,1,94,0,0.1008637,"\int \frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{x^6} \, dx","Int[((1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/x^6,x]","\frac{3 a^3 \sqrt{1-a^2 x^2}}{40 x^2}-\frac{a \left(1-a^2 x^2\right)^{3/2}}{20 x^4}-\frac{3}{40} a^5 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)}{5 x^5}","\frac{3 a^3 \sqrt{1-a^2 x^2}}{40 x^2}-\frac{a \left(1-a^2 x^2\right)^{3/2}}{20 x^4}-\frac{3}{40} a^5 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)}{5 x^5}",1,"(3*a^3*Sqrt[1 - a^2*x^2])/(40*x^2) - (a*(1 - a^2*x^2)^(3/2))/(20*x^4) - ((1 - a^2*x^2)^(5/2)*ArcTanh[a*x])/(5*x^5) - (3*a^5*ArcTanh[Sqrt[1 - a^2*x^2]])/40","A",6,5,22,0.2273,1,"{6008, 266, 47, 63, 208}"
458,1,243,0,0.7729838,"\int \frac{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}{x^7} \, dx","Int[((1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/x^7,x]","\frac{1}{16} a^6 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{1}{16} a^6 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{31 a^5 \sqrt{1-a^2 x^2}}{720 x}+\frac{19 a^3 \sqrt{1-a^2 x^2}}{360 x^3}-\frac{a \sqrt{1-a^2 x^2}}{30 x^5}-\frac{a^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{16 x^2}+\frac{7 a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{24 x^4}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{6 x^6}-\frac{1}{8} a^6 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)","\frac{1}{16} a^6 \text{PolyLog}\left(2,-\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\frac{1}{16} a^6 \text{PolyLog}\left(2,\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)+\frac{31 a^5 \sqrt{1-a^2 x^2}}{720 x}+\frac{19 a^3 \sqrt{1-a^2 x^2}}{360 x^3}-\frac{a \sqrt{1-a^2 x^2}}{30 x^5}-\frac{a^4 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{16 x^2}+\frac{7 a^2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{24 x^4}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{6 x^6}-\frac{1}{8} a^6 \tanh ^{-1}(a x) \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)",1,"-(a*Sqrt[1 - a^2*x^2])/(30*x^5) + (19*a^3*Sqrt[1 - a^2*x^2])/(360*x^3) + (31*a^5*Sqrt[1 - a^2*x^2])/(720*x) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(6*x^6) + (7*a^2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(24*x^4) - (a^4*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(16*x^2) - (a^6*ArcTanh[a*x]*ArcTanh[Sqrt[1 - a*x]/Sqrt[1 + a*x]])/8 + (a^6*PolyLog[2, -(Sqrt[1 - a*x]/Sqrt[1 + a*x])])/16 - (a^6*PolyLog[2, Sqrt[1 - a*x]/Sqrt[1 + a*x]])/16","A",24,6,22,0.2727,1,"{6014, 6010, 6026, 271, 264, 6018}"
459,1,233,0,0.1210502,"\int \left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x) \, dx","Int[(1 - a^2*x^2)^(5/2)*ArcTanh[a*x],x]","-\frac{5 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a}+\frac{5 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a}+\frac{\left(1-a^2 x^2\right)^{5/2}}{30 a}+\frac{5 \left(1-a^2 x^2\right)^{3/2}}{72 a}+\frac{5 \sqrt{1-a^2 x^2}}{16 a}+\frac{1}{6} x \left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)+\frac{5}{24} x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)+\frac{5}{16} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{5 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{8 a}","-\frac{5 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a}+\frac{5 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{16 a}+\frac{\left(1-a^2 x^2\right)^{5/2}}{30 a}+\frac{5 \left(1-a^2 x^2\right)^{3/2}}{72 a}+\frac{5 \sqrt{1-a^2 x^2}}{16 a}+\frac{1}{6} x \left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)+\frac{5}{24} x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)+\frac{5}{16} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{5 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{8 a}",1,"(5*Sqrt[1 - a^2*x^2])/(16*a) + (5*(1 - a^2*x^2)^(3/2))/(72*a) + (1 - a^2*x^2)^(5/2)/(30*a) + (5*x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/16 + (5*x*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/24 + (x*(1 - a^2*x^2)^(5/2)*ArcTanh[a*x])/6 - (5*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(8*a) - (((5*I)/16)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a + (((5*I)/16)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a","A",4,2,19,0.1053,1,"{5942, 5950}"
460,1,189,0,0.0890607,"\int \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x) \, dx","Int[(1 - a^2*x^2)^(3/2)*ArcTanh[a*x],x]","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a}+\frac{\left(1-a^2 x^2\right)^{3/2}}{12 a}+\frac{3 \sqrt{1-a^2 x^2}}{8 a}+\frac{1}{4} x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)+\frac{3}{8} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{3 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a}","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a}+\frac{\left(1-a^2 x^2\right)^{3/2}}{12 a}+\frac{3 \sqrt{1-a^2 x^2}}{8 a}+\frac{1}{4} x \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)+\frac{3}{8} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{3 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a}",1,"(3*Sqrt[1 - a^2*x^2])/(8*a) + (1 - a^2*x^2)^(3/2)/(12*a) + (3*x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/8 + (x*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x])/4 - (3*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(4*a) - (((3*I)/8)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a + (((3*I)/8)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a","A",3,2,19,0.1053,1,"{5942, 5950}"
461,1,143,0,0.0540413,"\int \sqrt{1-a^2 x^2} \tanh ^{-1}(a x) \, dx","Int[Sqrt[1 - a^2*x^2]*ArcTanh[a*x],x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}+\frac{\sqrt{1-a^2 x^2}}{2 a}+\frac{1}{2} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}+\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}+\frac{\sqrt{1-a^2 x^2}}{2 a}+\frac{1}{2} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)-\frac{\tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a}",1,"Sqrt[1 - a^2*x^2]/(2*a) + (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/2 - (ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/a - ((I/2)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a + ((I/2)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a","A",2,2,19,0.1053,1,"{5942, 5950}"
462,1,89,0,0.0513439,"\int \frac{\tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[ArcTanh[a*x]/(1 - a^2*x^2)^(5/2),x]","-\frac{2}{3 a \sqrt{1-a^2 x^2}}-\frac{1}{9 a \left(1-a^2 x^2\right)^{3/2}}+\frac{2 x \tanh ^{-1}(a x)}{3 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)}{3 \left(1-a^2 x^2\right)^{3/2}}","-\frac{2}{3 a \sqrt{1-a^2 x^2}}-\frac{1}{9 a \left(1-a^2 x^2\right)^{3/2}}+\frac{2 x \tanh ^{-1}(a x)}{3 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)}{3 \left(1-a^2 x^2\right)^{3/2}}",1,"-1/(9*a*(1 - a^2*x^2)^(3/2)) - 2/(3*a*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x])/(3*(1 - a^2*x^2)^(3/2)) + (2*x*ArcTanh[a*x])/(3*Sqrt[1 - a^2*x^2])","A",2,2,19,0.1053,1,"{5960, 5958}"
463,1,133,0,0.0806322,"\int \frac{\tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^{7/2}} \, dx","Int[ArcTanh[a*x]/(1 - a^2*x^2)^(7/2),x]","-\frac{8}{15 a \sqrt{1-a^2 x^2}}-\frac{4}{45 a \left(1-a^2 x^2\right)^{3/2}}-\frac{1}{25 a \left(1-a^2 x^2\right)^{5/2}}+\frac{8 x \tanh ^{-1}(a x)}{15 \sqrt{1-a^2 x^2}}+\frac{4 x \tanh ^{-1}(a x)}{15 \left(1-a^2 x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(a x)}{5 \left(1-a^2 x^2\right)^{5/2}}","-\frac{8}{15 a \sqrt{1-a^2 x^2}}-\frac{4}{45 a \left(1-a^2 x^2\right)^{3/2}}-\frac{1}{25 a \left(1-a^2 x^2\right)^{5/2}}+\frac{8 x \tanh ^{-1}(a x)}{15 \sqrt{1-a^2 x^2}}+\frac{4 x \tanh ^{-1}(a x)}{15 \left(1-a^2 x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(a x)}{5 \left(1-a^2 x^2\right)^{5/2}}",1,"-1/(25*a*(1 - a^2*x^2)^(5/2)) - 4/(45*a*(1 - a^2*x^2)^(3/2)) - 8/(15*a*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x])/(5*(1 - a^2*x^2)^(5/2)) + (4*x*ArcTanh[a*x])/(15*(1 - a^2*x^2)^(3/2)) + (8*x*ArcTanh[a*x])/(15*Sqrt[1 - a^2*x^2])","A",3,2,19,0.1053,1,"{5960, 5958}"
464,1,177,0,0.1131128,"\int \frac{\tanh ^{-1}(a x)}{\left(1-a^2 x^2\right)^{9/2}} \, dx","Int[ArcTanh[a*x]/(1 - a^2*x^2)^(9/2),x]","-\frac{16}{35 a \sqrt{1-a^2 x^2}}-\frac{8}{105 a \left(1-a^2 x^2\right)^{3/2}}-\frac{6}{175 a \left(1-a^2 x^2\right)^{5/2}}-\frac{1}{49 a \left(1-a^2 x^2\right)^{7/2}}+\frac{16 x \tanh ^{-1}(a x)}{35 \sqrt{1-a^2 x^2}}+\frac{8 x \tanh ^{-1}(a x)}{35 \left(1-a^2 x^2\right)^{3/2}}+\frac{6 x \tanh ^{-1}(a x)}{35 \left(1-a^2 x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(a x)}{7 \left(1-a^2 x^2\right)^{7/2}}","-\frac{16}{35 a \sqrt{1-a^2 x^2}}-\frac{8}{105 a \left(1-a^2 x^2\right)^{3/2}}-\frac{6}{175 a \left(1-a^2 x^2\right)^{5/2}}-\frac{1}{49 a \left(1-a^2 x^2\right)^{7/2}}+\frac{16 x \tanh ^{-1}(a x)}{35 \sqrt{1-a^2 x^2}}+\frac{8 x \tanh ^{-1}(a x)}{35 \left(1-a^2 x^2\right)^{3/2}}+\frac{6 x \tanh ^{-1}(a x)}{35 \left(1-a^2 x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(a x)}{7 \left(1-a^2 x^2\right)^{7/2}}",1,"-1/(49*a*(1 - a^2*x^2)^(7/2)) - 6/(175*a*(1 - a^2*x^2)^(5/2)) - 8/(105*a*(1 - a^2*x^2)^(3/2)) - 16/(35*a*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x])/(7*(1 - a^2*x^2)^(7/2)) + (6*x*ArcTanh[a*x])/(35*(1 - a^2*x^2)^(5/2)) + (8*x*ArcTanh[a*x])/(35*(1 - a^2*x^2)^(3/2)) + (16*x*ArcTanh[a*x])/(35*Sqrt[1 - a^2*x^2])","A",4,2,19,0.1053,1,"{5960, 5958}"
465,1,291,0,0.1496353,"\int \left(c-a^2 c x^2\right)^{3/2} \tanh ^{-1}(a x) \, dx","Int[(c - a^2*c*x^2)^(3/2)*ArcTanh[a*x],x]","-\frac{3 i c^2 \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a \sqrt{c-a^2 c x^2}}+\frac{3 i c^2 \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a \sqrt{c-a^2 c x^2}}-\frac{3 c^2 \sqrt{1-a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a \sqrt{c-a^2 c x^2}}+\frac{3 c \sqrt{c-a^2 c x^2}}{8 a}+\frac{\left(c-a^2 c x^2\right)^{3/2}}{12 a}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \tanh ^{-1}(a x)+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \tanh ^{-1}(a x)","-\frac{3 i c^2 \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a \sqrt{c-a^2 c x^2}}+\frac{3 i c^2 \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{8 a \sqrt{c-a^2 c x^2}}-\frac{3 c^2 \sqrt{1-a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{4 a \sqrt{c-a^2 c x^2}}+\frac{3 c \sqrt{c-a^2 c x^2}}{8 a}+\frac{\left(c-a^2 c x^2\right)^{3/2}}{12 a}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \tanh ^{-1}(a x)+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \tanh ^{-1}(a x)",1,"(3*c*Sqrt[c - a^2*c*x^2])/(8*a) + (c - a^2*c*x^2)^(3/2)/(12*a) + (3*c*x*Sqrt[c - a^2*c*x^2]*ArcTanh[a*x])/8 + (x*(c - a^2*c*x^2)^(3/2)*ArcTanh[a*x])/4 - (3*c^2*Sqrt[1 - a^2*x^2]*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(4*a*Sqrt[c - a^2*c*x^2]) - (((3*I)/8)*c^2*Sqrt[1 - a^2*x^2]*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/(a*Sqrt[c - a^2*c*x^2]) + (((3*I)/8)*c^2*Sqrt[1 - a^2*x^2]*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/(a*Sqrt[c - a^2*c*x^2])","A",4,3,20,0.1500,1,"{5942, 5954, 5950}"
466,1,235,0,0.1019532,"\int \sqrt{c-a^2 c x^2} \tanh ^{-1}(a x) \, dx","Int[Sqrt[c - a^2*c*x^2]*ArcTanh[a*x],x]","-\frac{i c \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a \sqrt{c-a^2 c x^2}}+\frac{i c \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a \sqrt{c-a^2 c x^2}}+\frac{\sqrt{c-a^2 c x^2}}{2 a}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \tanh ^{-1}(a x)-\frac{c \sqrt{1-a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a \sqrt{c-a^2 c x^2}}","-\frac{i c \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a \sqrt{c-a^2 c x^2}}+\frac{i c \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a \sqrt{c-a^2 c x^2}}+\frac{\sqrt{c-a^2 c x^2}}{2 a}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \tanh ^{-1}(a x)-\frac{c \sqrt{1-a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a \sqrt{c-a^2 c x^2}}",1,"Sqrt[c - a^2*c*x^2]/(2*a) + (x*Sqrt[c - a^2*c*x^2]*ArcTanh[a*x])/2 - (c*Sqrt[1 - a^2*x^2]*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(a*Sqrt[c - a^2*c*x^2]) - ((I/2)*c*Sqrt[1 - a^2*x^2]*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/(a*Sqrt[c - a^2*c*x^2]) + ((I/2)*c*Sqrt[1 - a^2*x^2]*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/(a*Sqrt[c - a^2*c*x^2])","A",3,3,20,0.1500,1,"{5942, 5954, 5950}"
467,1,182,0,0.0622075,"\int \frac{\tanh ^{-1}(a x)}{\sqrt{c-a^2 c x^2}} \, dx","Int[ArcTanh[a*x]/Sqrt[c - a^2*c*x^2],x]","-\frac{i \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a \sqrt{c-a^2 c x^2}}+\frac{i \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{1-a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a \sqrt{c-a^2 c x^2}}","-\frac{i \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a \sqrt{c-a^2 c x^2}}+\frac{i \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{1-a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a \sqrt{c-a^2 c x^2}}",1,"(-2*Sqrt[1 - a^2*x^2]*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/(a*Sqrt[c - a^2*c*x^2]) - (I*Sqrt[1 - a^2*x^2]*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/(a*Sqrt[c - a^2*c*x^2]) + (I*Sqrt[1 - a^2*x^2]*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/(a*Sqrt[c - a^2*c*x^2])","A",2,2,20,0.1000,1,"{5954, 5950}"
468,1,48,0,0.0289554,"\int \frac{\tanh ^{-1}(a x)}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]/(c - a^2*c*x^2)^(3/2),x]","\frac{x \tanh ^{-1}(a x)}{c \sqrt{c-a^2 c x^2}}-\frac{1}{a c \sqrt{c-a^2 c x^2}}","\frac{x \tanh ^{-1}(a x)}{c \sqrt{c-a^2 c x^2}}-\frac{1}{a c \sqrt{c-a^2 c x^2}}",1,"-(1/(a*c*Sqrt[c - a^2*c*x^2])) + (x*ArcTanh[a*x])/(c*Sqrt[c - a^2*c*x^2])","A",1,1,20,0.05000,1,"{5958}"
469,1,105,0,0.0656546,"\int \frac{\tanh ^{-1}(a x)}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[ArcTanh[a*x]/(c - a^2*c*x^2)^(5/2),x]","-\frac{2}{3 a c^2 \sqrt{c-a^2 c x^2}}+\frac{2 x \tanh ^{-1}(a x)}{3 c^2 \sqrt{c-a^2 c x^2}}-\frac{1}{9 a c \left(c-a^2 c x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(a x)}{3 c \left(c-a^2 c x^2\right)^{3/2}}","-\frac{2}{3 a c^2 \sqrt{c-a^2 c x^2}}+\frac{2 x \tanh ^{-1}(a x)}{3 c^2 \sqrt{c-a^2 c x^2}}-\frac{1}{9 a c \left(c-a^2 c x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(a x)}{3 c \left(c-a^2 c x^2\right)^{3/2}}",1,"-1/(9*a*c*(c - a^2*c*x^2)^(3/2)) - 2/(3*a*c^2*Sqrt[c - a^2*c*x^2]) + (x*ArcTanh[a*x])/(3*c*(c - a^2*c*x^2)^(3/2)) + (2*x*ArcTanh[a*x])/(3*c^2*Sqrt[c - a^2*c*x^2])","A",2,2,20,0.1000,1,"{5960, 5958}"
470,1,157,0,0.1014783,"\int \frac{\tanh ^{-1}(a x)}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[ArcTanh[a*x]/(c - a^2*c*x^2)^(7/2),x]","-\frac{8}{15 a c^3 \sqrt{c-a^2 c x^2}}-\frac{4}{45 a c^2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{8 x \tanh ^{-1}(a x)}{15 c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \tanh ^{-1}(a x)}{15 c^2 \left(c-a^2 c x^2\right)^{3/2}}-\frac{1}{25 a c \left(c-a^2 c x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(a x)}{5 c \left(c-a^2 c x^2\right)^{5/2}}","-\frac{8}{15 a c^3 \sqrt{c-a^2 c x^2}}-\frac{4}{45 a c^2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{8 x \tanh ^{-1}(a x)}{15 c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \tanh ^{-1}(a x)}{15 c^2 \left(c-a^2 c x^2\right)^{3/2}}-\frac{1}{25 a c \left(c-a^2 c x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(a x)}{5 c \left(c-a^2 c x^2\right)^{5/2}}",1,"-1/(25*a*c*(c - a^2*c*x^2)^(5/2)) - 4/(45*a*c^2*(c - a^2*c*x^2)^(3/2)) - 8/(15*a*c^3*Sqrt[c - a^2*c*x^2]) + (x*ArcTanh[a*x])/(5*c*(c - a^2*c*x^2)^(5/2)) + (4*x*ArcTanh[a*x])/(15*c^2*(c - a^2*c*x^2)^(3/2)) + (8*x*ArcTanh[a*x])/(15*c^3*Sqrt[c - a^2*c*x^2])","A",3,2,20,0.1000,1,"{5960, 5958}"
471,1,158,0,0.1430489,"\int \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2 \, dx","Int[Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2,x]","-\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{1}{2} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a}-\frac{\sin ^{-1}(a x)}{a}+\frac{\tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a}","-\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{i \tanh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{i \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{i \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{1}{2} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{a}-\frac{\sin ^{-1}(a x)}{a}+\frac{\tanh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a}",1,"-(ArcSin[a*x]/a) + (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/a + (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/2 + (ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^2)/a - (I*ArcTanh[a*x]*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a + (I*ArcTanh[a*x]*PolyLog[2, I*E^ArcTanh[a*x]])/a + (I*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a - (I*PolyLog[3, I*E^ArcTanh[a*x]])/a","A",10,7,21,0.3333,1,"{5944, 5952, 4180, 2531, 2282, 6589, 216}"
472,1,139,0,0.0928308,"\int \frac{\tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[ArcTanh[a*x]^2/(1 - a^2*x^2)^(5/2),x]","\frac{40 x}{27 \sqrt{1-a^2 x^2}}+\frac{2 x}{27 \left(1-a^2 x^2\right)^{3/2}}+\frac{2 x \tanh ^{-1}(a x)^2}{3 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^2}{3 \left(1-a^2 x^2\right)^{3/2}}-\frac{4 \tanh ^{-1}(a x)}{3 a \sqrt{1-a^2 x^2}}-\frac{2 \tanh ^{-1}(a x)}{9 a \left(1-a^2 x^2\right)^{3/2}}","\frac{40 x}{27 \sqrt{1-a^2 x^2}}+\frac{2 x}{27 \left(1-a^2 x^2\right)^{3/2}}+\frac{2 x \tanh ^{-1}(a x)^2}{3 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^2}{3 \left(1-a^2 x^2\right)^{3/2}}-\frac{4 \tanh ^{-1}(a x)}{3 a \sqrt{1-a^2 x^2}}-\frac{2 \tanh ^{-1}(a x)}{9 a \left(1-a^2 x^2\right)^{3/2}}",1,"(2*x)/(27*(1 - a^2*x^2)^(3/2)) + (40*x)/(27*Sqrt[1 - a^2*x^2]) - (2*ArcTanh[a*x])/(9*a*(1 - a^2*x^2)^(3/2)) - (4*ArcTanh[a*x])/(3*a*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x]^2)/(3*(1 - a^2*x^2)^(3/2)) + (2*x*ArcTanh[a*x]^2)/(3*Sqrt[1 - a^2*x^2])","A",5,4,21,0.1905,1,"{5964, 5962, 191, 192}"
473,1,208,0,0.152059,"\int \frac{\tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^{7/2}} \, dx","Int[ArcTanh[a*x]^2/(1 - a^2*x^2)^(7/2),x]","\frac{4144 x}{3375 \sqrt{1-a^2 x^2}}+\frac{272 x}{3375 \left(1-a^2 x^2\right)^{3/2}}+\frac{2 x}{125 \left(1-a^2 x^2\right)^{5/2}}+\frac{8 x \tanh ^{-1}(a x)^2}{15 \sqrt{1-a^2 x^2}}+\frac{4 x \tanh ^{-1}(a x)^2}{15 \left(1-a^2 x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(a x)^2}{5 \left(1-a^2 x^2\right)^{5/2}}-\frac{16 \tanh ^{-1}(a x)}{15 a \sqrt{1-a^2 x^2}}-\frac{8 \tanh ^{-1}(a x)}{45 a \left(1-a^2 x^2\right)^{3/2}}-\frac{2 \tanh ^{-1}(a x)}{25 a \left(1-a^2 x^2\right)^{5/2}}","\frac{4144 x}{3375 \sqrt{1-a^2 x^2}}+\frac{272 x}{3375 \left(1-a^2 x^2\right)^{3/2}}+\frac{2 x}{125 \left(1-a^2 x^2\right)^{5/2}}+\frac{8 x \tanh ^{-1}(a x)^2}{15 \sqrt{1-a^2 x^2}}+\frac{4 x \tanh ^{-1}(a x)^2}{15 \left(1-a^2 x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(a x)^2}{5 \left(1-a^2 x^2\right)^{5/2}}-\frac{16 \tanh ^{-1}(a x)}{15 a \sqrt{1-a^2 x^2}}-\frac{8 \tanh ^{-1}(a x)}{45 a \left(1-a^2 x^2\right)^{3/2}}-\frac{2 \tanh ^{-1}(a x)}{25 a \left(1-a^2 x^2\right)^{5/2}}",1,"(2*x)/(125*(1 - a^2*x^2)^(5/2)) + (272*x)/(3375*(1 - a^2*x^2)^(3/2)) + (4144*x)/(3375*Sqrt[1 - a^2*x^2]) - (2*ArcTanh[a*x])/(25*a*(1 - a^2*x^2)^(5/2)) - (8*ArcTanh[a*x])/(45*a*(1 - a^2*x^2)^(3/2)) - (16*ArcTanh[a*x])/(15*a*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x]^2)/(5*(1 - a^2*x^2)^(5/2)) + (4*x*ArcTanh[a*x]^2)/(15*(1 - a^2*x^2)^(3/2)) + (8*x*ArcTanh[a*x]^2)/(15*Sqrt[1 - a^2*x^2])","A",9,4,21,0.1905,1,"{5964, 5962, 191, 192}"
474,1,277,0,0.2283883,"\int \frac{\tanh ^{-1}(a x)^2}{\left(1-a^2 x^2\right)^{9/2}} \, dx","Int[ArcTanh[a*x]^2/(1 - a^2*x^2)^(9/2),x]","\frac{413312 x}{385875 \sqrt{1-a^2 x^2}}+\frac{30256 x}{385875 \left(1-a^2 x^2\right)^{3/2}}+\frac{888 x}{42875 \left(1-a^2 x^2\right)^{5/2}}+\frac{2 x}{343 \left(1-a^2 x^2\right)^{7/2}}+\frac{16 x \tanh ^{-1}(a x)^2}{35 \sqrt{1-a^2 x^2}}+\frac{8 x \tanh ^{-1}(a x)^2}{35 \left(1-a^2 x^2\right)^{3/2}}+\frac{6 x \tanh ^{-1}(a x)^2}{35 \left(1-a^2 x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(a x)^2}{7 \left(1-a^2 x^2\right)^{7/2}}-\frac{32 \tanh ^{-1}(a x)}{35 a \sqrt{1-a^2 x^2}}-\frac{16 \tanh ^{-1}(a x)}{105 a \left(1-a^2 x^2\right)^{3/2}}-\frac{12 \tanh ^{-1}(a x)}{175 a \left(1-a^2 x^2\right)^{5/2}}-\frac{2 \tanh ^{-1}(a x)}{49 a \left(1-a^2 x^2\right)^{7/2}}","\frac{413312 x}{385875 \sqrt{1-a^2 x^2}}+\frac{30256 x}{385875 \left(1-a^2 x^2\right)^{3/2}}+\frac{888 x}{42875 \left(1-a^2 x^2\right)^{5/2}}+\frac{2 x}{343 \left(1-a^2 x^2\right)^{7/2}}+\frac{16 x \tanh ^{-1}(a x)^2}{35 \sqrt{1-a^2 x^2}}+\frac{8 x \tanh ^{-1}(a x)^2}{35 \left(1-a^2 x^2\right)^{3/2}}+\frac{6 x \tanh ^{-1}(a x)^2}{35 \left(1-a^2 x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(a x)^2}{7 \left(1-a^2 x^2\right)^{7/2}}-\frac{32 \tanh ^{-1}(a x)}{35 a \sqrt{1-a^2 x^2}}-\frac{16 \tanh ^{-1}(a x)}{105 a \left(1-a^2 x^2\right)^{3/2}}-\frac{12 \tanh ^{-1}(a x)}{175 a \left(1-a^2 x^2\right)^{5/2}}-\frac{2 \tanh ^{-1}(a x)}{49 a \left(1-a^2 x^2\right)^{7/2}}",1,"(2*x)/(343*(1 - a^2*x^2)^(7/2)) + (888*x)/(42875*(1 - a^2*x^2)^(5/2)) + (30256*x)/(385875*(1 - a^2*x^2)^(3/2)) + (413312*x)/(385875*Sqrt[1 - a^2*x^2]) - (2*ArcTanh[a*x])/(49*a*(1 - a^2*x^2)^(7/2)) - (12*ArcTanh[a*x])/(175*a*(1 - a^2*x^2)^(5/2)) - (16*ArcTanh[a*x])/(105*a*(1 - a^2*x^2)^(3/2)) - (32*ArcTanh[a*x])/(35*a*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x]^2)/(7*(1 - a^2*x^2)^(7/2)) + (6*x*ArcTanh[a*x]^2)/(35*(1 - a^2*x^2)^(5/2)) + (8*x*ArcTanh[a*x]^2)/(35*(1 - a^2*x^2)^(3/2)) + (16*x*ArcTanh[a*x]^2)/(35*Sqrt[1 - a^2*x^2])","A",14,4,21,0.1905,1,"{5964, 5962, 191, 192}"
475,1,302,0,0.1973458,"\int \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3 \, dx","Int[Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3,x]","\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}-\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}-\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{2 a}+\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{2 a}+\frac{3 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{3 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{3 i \text{PolyLog}\left(4,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{3 i \text{PolyLog}\left(4,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{1}{2} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3+\frac{3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 a}+\frac{\tanh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{6 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a}","\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}-\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}-\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\tanh ^{-1}(a x)}\right)}{2 a}+\frac{3 i \tanh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\tanh ^{-1}(a x)}\right)}{2 a}+\frac{3 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{3 i \tanh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\tanh ^{-1}(a x)}\right)}{a}-\frac{3 i \text{PolyLog}\left(4,-i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{3 i \text{PolyLog}\left(4,i e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{1}{2} x \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3+\frac{3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}{2 a}+\frac{\tanh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\tanh ^{-1}(a x)}\right)}{a}+\frac{6 \tan ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right) \tanh ^{-1}(a x)}{a}",1,"(6*ArcTan[Sqrt[1 - a*x]/Sqrt[1 + a*x]]*ArcTanh[a*x])/a + (3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2)/(2*a) + (x*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3)/2 + (ArcTan[E^ArcTanh[a*x]]*ArcTanh[a*x]^3)/a - (((3*I)/2)*ArcTanh[a*x]^2*PolyLog[2, (-I)*E^ArcTanh[a*x]])/a + (((3*I)/2)*ArcTanh[a*x]^2*PolyLog[2, I*E^ArcTanh[a*x]])/a + ((3*I)*PolyLog[2, ((-I)*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a - ((3*I)*PolyLog[2, (I*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/a + ((3*I)*ArcTanh[a*x]*PolyLog[3, (-I)*E^ArcTanh[a*x]])/a - ((3*I)*ArcTanh[a*x]*PolyLog[3, I*E^ArcTanh[a*x]])/a - ((3*I)*PolyLog[4, (-I)*E^ArcTanh[a*x]])/a + ((3*I)*PolyLog[4, I*E^ArcTanh[a*x]])/a","A",12,8,21,0.3810,1,"{5944, 5952, 4180, 2531, 6609, 2282, 6589, 5950}"
476,1,191,0,0.1648476,"\int \frac{\tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[ArcTanh[a*x]^3/(1 - a^2*x^2)^(5/2),x]","-\frac{40}{9 a \sqrt{1-a^2 x^2}}-\frac{2}{27 a \left(1-a^2 x^2\right)^{3/2}}+\frac{2 x \tanh ^{-1}(a x)^3}{3 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^3}{3 \left(1-a^2 x^2\right)^{3/2}}-\frac{2 \tanh ^{-1}(a x)^2}{a \sqrt{1-a^2 x^2}}-\frac{\tanh ^{-1}(a x)^2}{3 a \left(1-a^2 x^2\right)^{3/2}}+\frac{40 x \tanh ^{-1}(a x)}{9 \sqrt{1-a^2 x^2}}+\frac{2 x \tanh ^{-1}(a x)}{9 \left(1-a^2 x^2\right)^{3/2}}","-\frac{40}{9 a \sqrt{1-a^2 x^2}}-\frac{2}{27 a \left(1-a^2 x^2\right)^{3/2}}+\frac{2 x \tanh ^{-1}(a x)^3}{3 \sqrt{1-a^2 x^2}}+\frac{x \tanh ^{-1}(a x)^3}{3 \left(1-a^2 x^2\right)^{3/2}}-\frac{2 \tanh ^{-1}(a x)^2}{a \sqrt{1-a^2 x^2}}-\frac{\tanh ^{-1}(a x)^2}{3 a \left(1-a^2 x^2\right)^{3/2}}+\frac{40 x \tanh ^{-1}(a x)}{9 \sqrt{1-a^2 x^2}}+\frac{2 x \tanh ^{-1}(a x)}{9 \left(1-a^2 x^2\right)^{3/2}}",1,"-2/(27*a*(1 - a^2*x^2)^(3/2)) - 40/(9*a*Sqrt[1 - a^2*x^2]) + (2*x*ArcTanh[a*x])/(9*(1 - a^2*x^2)^(3/2)) + (40*x*ArcTanh[a*x])/(9*Sqrt[1 - a^2*x^2]) - ArcTanh[a*x]^2/(3*a*(1 - a^2*x^2)^(3/2)) - (2*ArcTanh[a*x]^2)/(a*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x]^3)/(3*(1 - a^2*x^2)^(3/2)) + (2*x*ArcTanh[a*x]^3)/(3*Sqrt[1 - a^2*x^2])","A",5,4,21,0.1905,1,"{5964, 5962, 5958, 5960}"
477,1,289,0,0.3042523,"\int \frac{\tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^{7/2}} \, dx","Int[ArcTanh[a*x]^3/(1 - a^2*x^2)^(7/2),x]","-\frac{4144}{1125 a \sqrt{1-a^2 x^2}}-\frac{272}{3375 a \left(1-a^2 x^2\right)^{3/2}}-\frac{6}{625 a \left(1-a^2 x^2\right)^{5/2}}+\frac{8 x \tanh ^{-1}(a x)^3}{15 \sqrt{1-a^2 x^2}}+\frac{4 x \tanh ^{-1}(a x)^3}{15 \left(1-a^2 x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(a x)^3}{5 \left(1-a^2 x^2\right)^{5/2}}-\frac{8 \tanh ^{-1}(a x)^2}{5 a \sqrt{1-a^2 x^2}}-\frac{4 \tanh ^{-1}(a x)^2}{15 a \left(1-a^2 x^2\right)^{3/2}}-\frac{3 \tanh ^{-1}(a x)^2}{25 a \left(1-a^2 x^2\right)^{5/2}}+\frac{4144 x \tanh ^{-1}(a x)}{1125 \sqrt{1-a^2 x^2}}+\frac{272 x \tanh ^{-1}(a x)}{1125 \left(1-a^2 x^2\right)^{3/2}}+\frac{6 x \tanh ^{-1}(a x)}{125 \left(1-a^2 x^2\right)^{5/2}}","-\frac{4144}{1125 a \sqrt{1-a^2 x^2}}-\frac{272}{3375 a \left(1-a^2 x^2\right)^{3/2}}-\frac{6}{625 a \left(1-a^2 x^2\right)^{5/2}}+\frac{8 x \tanh ^{-1}(a x)^3}{15 \sqrt{1-a^2 x^2}}+\frac{4 x \tanh ^{-1}(a x)^3}{15 \left(1-a^2 x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(a x)^3}{5 \left(1-a^2 x^2\right)^{5/2}}-\frac{8 \tanh ^{-1}(a x)^2}{5 a \sqrt{1-a^2 x^2}}-\frac{4 \tanh ^{-1}(a x)^2}{15 a \left(1-a^2 x^2\right)^{3/2}}-\frac{3 \tanh ^{-1}(a x)^2}{25 a \left(1-a^2 x^2\right)^{5/2}}+\frac{4144 x \tanh ^{-1}(a x)}{1125 \sqrt{1-a^2 x^2}}+\frac{272 x \tanh ^{-1}(a x)}{1125 \left(1-a^2 x^2\right)^{3/2}}+\frac{6 x \tanh ^{-1}(a x)}{125 \left(1-a^2 x^2\right)^{5/2}}",1,"-6/(625*a*(1 - a^2*x^2)^(5/2)) - 272/(3375*a*(1 - a^2*x^2)^(3/2)) - 4144/(1125*a*Sqrt[1 - a^2*x^2]) + (6*x*ArcTanh[a*x])/(125*(1 - a^2*x^2)^(5/2)) + (272*x*ArcTanh[a*x])/(1125*(1 - a^2*x^2)^(3/2)) + (4144*x*ArcTanh[a*x])/(1125*Sqrt[1 - a^2*x^2]) - (3*ArcTanh[a*x]^2)/(25*a*(1 - a^2*x^2)^(5/2)) - (4*ArcTanh[a*x]^2)/(15*a*(1 - a^2*x^2)^(3/2)) - (8*ArcTanh[a*x]^2)/(5*a*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x]^3)/(5*(1 - a^2*x^2)^(5/2)) + (4*x*ArcTanh[a*x]^3)/(15*(1 - a^2*x^2)^(3/2)) + (8*x*ArcTanh[a*x]^3)/(15*Sqrt[1 - a^2*x^2])","A",9,4,21,0.1905,1,"{5964, 5962, 5958, 5960}"
478,1,385,0,0.4838679,"\int \frac{\tanh ^{-1}(a x)^3}{\left(1-a^2 x^2\right)^{9/2}} \, dx","Int[ArcTanh[a*x]^3/(1 - a^2*x^2)^(9/2),x]","-\frac{413312}{128625 a \sqrt{1-a^2 x^2}}-\frac{30256}{385875 a \left(1-a^2 x^2\right)^{3/2}}-\frac{2664}{214375 a \left(1-a^2 x^2\right)^{5/2}}-\frac{6}{2401 a \left(1-a^2 x^2\right)^{7/2}}+\frac{16 x \tanh ^{-1}(a x)^3}{35 \sqrt{1-a^2 x^2}}+\frac{8 x \tanh ^{-1}(a x)^3}{35 \left(1-a^2 x^2\right)^{3/2}}+\frac{6 x \tanh ^{-1}(a x)^3}{35 \left(1-a^2 x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(a x)^3}{7 \left(1-a^2 x^2\right)^{7/2}}-\frac{48 \tanh ^{-1}(a x)^2}{35 a \sqrt{1-a^2 x^2}}-\frac{8 \tanh ^{-1}(a x)^2}{35 a \left(1-a^2 x^2\right)^{3/2}}-\frac{18 \tanh ^{-1}(a x)^2}{175 a \left(1-a^2 x^2\right)^{5/2}}-\frac{3 \tanh ^{-1}(a x)^2}{49 a \left(1-a^2 x^2\right)^{7/2}}+\frac{413312 x \tanh ^{-1}(a x)}{128625 \sqrt{1-a^2 x^2}}+\frac{30256 x \tanh ^{-1}(a x)}{128625 \left(1-a^2 x^2\right)^{3/2}}+\frac{2664 x \tanh ^{-1}(a x)}{42875 \left(1-a^2 x^2\right)^{5/2}}+\frac{6 x \tanh ^{-1}(a x)}{343 \left(1-a^2 x^2\right)^{7/2}}","-\frac{413312}{128625 a \sqrt{1-a^2 x^2}}-\frac{30256}{385875 a \left(1-a^2 x^2\right)^{3/2}}-\frac{2664}{214375 a \left(1-a^2 x^2\right)^{5/2}}-\frac{6}{2401 a \left(1-a^2 x^2\right)^{7/2}}+\frac{16 x \tanh ^{-1}(a x)^3}{35 \sqrt{1-a^2 x^2}}+\frac{8 x \tanh ^{-1}(a x)^3}{35 \left(1-a^2 x^2\right)^{3/2}}+\frac{6 x \tanh ^{-1}(a x)^3}{35 \left(1-a^2 x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(a x)^3}{7 \left(1-a^2 x^2\right)^{7/2}}-\frac{48 \tanh ^{-1}(a x)^2}{35 a \sqrt{1-a^2 x^2}}-\frac{8 \tanh ^{-1}(a x)^2}{35 a \left(1-a^2 x^2\right)^{3/2}}-\frac{18 \tanh ^{-1}(a x)^2}{175 a \left(1-a^2 x^2\right)^{5/2}}-\frac{3 \tanh ^{-1}(a x)^2}{49 a \left(1-a^2 x^2\right)^{7/2}}+\frac{413312 x \tanh ^{-1}(a x)}{128625 \sqrt{1-a^2 x^2}}+\frac{30256 x \tanh ^{-1}(a x)}{128625 \left(1-a^2 x^2\right)^{3/2}}+\frac{2664 x \tanh ^{-1}(a x)}{42875 \left(1-a^2 x^2\right)^{5/2}}+\frac{6 x \tanh ^{-1}(a x)}{343 \left(1-a^2 x^2\right)^{7/2}}",1,"-6/(2401*a*(1 - a^2*x^2)^(7/2)) - 2664/(214375*a*(1 - a^2*x^2)^(5/2)) - 30256/(385875*a*(1 - a^2*x^2)^(3/2)) - 413312/(128625*a*Sqrt[1 - a^2*x^2]) + (6*x*ArcTanh[a*x])/(343*(1 - a^2*x^2)^(7/2)) + (2664*x*ArcTanh[a*x])/(42875*(1 - a^2*x^2)^(5/2)) + (30256*x*ArcTanh[a*x])/(128625*(1 - a^2*x^2)^(3/2)) + (413312*x*ArcTanh[a*x])/(128625*Sqrt[1 - a^2*x^2]) - (3*ArcTanh[a*x]^2)/(49*a*(1 - a^2*x^2)^(7/2)) - (18*ArcTanh[a*x]^2)/(175*a*(1 - a^2*x^2)^(5/2)) - (8*ArcTanh[a*x]^2)/(35*a*(1 - a^2*x^2)^(3/2)) - (48*ArcTanh[a*x]^2)/(35*a*Sqrt[1 - a^2*x^2]) + (x*ArcTanh[a*x]^3)/(7*(1 - a^2*x^2)^(7/2)) + (6*x*ArcTanh[a*x]^3)/(35*(1 - a^2*x^2)^(5/2)) + (8*x*ArcTanh[a*x]^3)/(35*(1 - a^2*x^2)^(3/2)) + (16*x*ArcTanh[a*x]^3)/(35*Sqrt[1 - a^2*x^2])","A",14,4,21,0.1905,1,"{5964, 5962, 5958, 5960}"
479,0,0,0,0.0343793,"\int \frac{\sqrt{1-a^2 x^2}}{\tanh ^{-1}(a x)} \, dx","Int[Sqrt[1 - a^2*x^2]/ArcTanh[a*x],x]","\int \frac{\sqrt{1-a^2 x^2}}{\tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{\sqrt{1-a^2 x^2}}{\tanh ^{-1}(a x)},x\right)",0,"Defer[Int][Sqrt[1 - a^2*x^2]/ArcTanh[a*x], x]","A",0,0,0,0,-1,"{}"
480,0,0,0,0.0345926,"\int \frac{1}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)} \, dx","Int[1/(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]),x]","\int \frac{1}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]), x]","A",0,0,0,0,-1,"{}"
481,1,9,0,0.0529276,"\int \frac{1}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)} \, dx","Int[1/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]),x]","\frac{\text{Chi}\left(\tanh ^{-1}(a x)\right)}{a}","\frac{\text{Chi}\left(\tanh ^{-1}(a x)\right)}{a}",1,"CoshIntegral[ArcTanh[a*x]]/a","A",2,2,21,0.09524,1,"{5968, 3301}"
482,1,27,0,0.0930111,"\int \frac{1}{\left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)} \, dx","Int[1/((1 - a^2*x^2)^(5/2)*ArcTanh[a*x]),x]","\frac{3 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{4 a}+\frac{\text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{4 a}","\frac{3 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{4 a}+\frac{\text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{4 a}",1,"(3*CoshIntegral[ArcTanh[a*x]])/(4*a) + CoshIntegral[3*ArcTanh[a*x]]/(4*a)","A",5,3,21,0.1429,1,"{5968, 3312, 3301}"
483,1,41,0,0.1088344,"\int \frac{1}{\left(1-a^2 x^2\right)^{7/2} \tanh ^{-1}(a x)} \, dx","Int[1/((1 - a^2*x^2)^(7/2)*ArcTanh[a*x]),x]","\frac{5 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{8 a}+\frac{5 \text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{16 a}+\frac{\text{Chi}\left(5 \tanh ^{-1}(a x)\right)}{16 a}","\frac{5 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{8 a}+\frac{5 \text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{16 a}+\frac{\text{Chi}\left(5 \tanh ^{-1}(a x)\right)}{16 a}",1,"(5*CoshIntegral[ArcTanh[a*x]])/(8*a) + (5*CoshIntegral[3*ArcTanh[a*x]])/(16*a) + CoshIntegral[5*ArcTanh[a*x]]/(16*a)","A",6,3,21,0.1429,1,"{5968, 3312, 3301}"
484,1,55,0,0.1229954,"\int \frac{1}{\left(1-a^2 x^2\right)^{9/2} \tanh ^{-1}(a x)} \, dx","Int[1/((1 - a^2*x^2)^(9/2)*ArcTanh[a*x]),x]","\frac{35 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{64 a}+\frac{21 \text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{64 a}+\frac{7 \text{Chi}\left(5 \tanh ^{-1}(a x)\right)}{64 a}+\frac{\text{Chi}\left(7 \tanh ^{-1}(a x)\right)}{64 a}","\frac{35 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{64 a}+\frac{21 \text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{64 a}+\frac{7 \text{Chi}\left(5 \tanh ^{-1}(a x)\right)}{64 a}+\frac{\text{Chi}\left(7 \tanh ^{-1}(a x)\right)}{64 a}",1,"(35*CoshIntegral[ArcTanh[a*x]])/(64*a) + (21*CoshIntegral[3*ArcTanh[a*x]])/(64*a) + (7*CoshIntegral[5*ArcTanh[a*x]])/(64*a) + CoshIntegral[7*ArcTanh[a*x]]/(64*a)","A",7,3,21,0.1429,1,"{5968, 3312, 3301}"
485,0,0,0,0.0302258,"\int \frac{\sqrt{1-a^2 x^2}}{\tanh ^{-1}(a x)^2} \, dx","Int[Sqrt[1 - a^2*x^2]/ArcTanh[a*x]^2,x]","\int \frac{\sqrt{1-a^2 x^2}}{\tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{\sqrt{1-a^2 x^2}}{\tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][Sqrt[1 - a^2*x^2]/ArcTanh[a*x]^2, x]","A",0,0,0,0,-1,"{}"
486,0,0,0,0.0332581,"\int \frac{1}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2} \, dx","Int[1/(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2),x]","\int \frac{1}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2},x\right)",0,"Defer[Int][1/(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2), x]","A",0,0,0,0,-1,"{}"
487,1,35,0,0.1230951,"\int \frac{1}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2} \, dx","Int[1/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^2),x]","\frac{\text{Shi}\left(\tanh ^{-1}(a x)\right)}{a}-\frac{1}{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}","\frac{\text{Shi}\left(\tanh ^{-1}(a x)\right)}{a}-\frac{1}{a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}",1,"-(1/(a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])) + SinhIntegral[ArcTanh[a*x]]/a","A",3,3,21,0.1429,1,"{5966, 6034, 3298}"
488,1,52,0,0.1598928,"\int \frac{1}{\left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)^2} \, dx","Int[1/((1 - a^2*x^2)^(5/2)*ArcTanh[a*x]^2),x]","-\frac{1}{a \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}+\frac{3 \text{Shi}\left(\tanh ^{-1}(a x)\right)}{4 a}+\frac{3 \text{Shi}\left(3 \tanh ^{-1}(a x)\right)}{4 a}","-\frac{1}{a \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}+\frac{3 \text{Shi}\left(\tanh ^{-1}(a x)\right)}{4 a}+\frac{3 \text{Shi}\left(3 \tanh ^{-1}(a x)\right)}{4 a}",1,"-(1/(a*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x])) + (3*SinhIntegral[ArcTanh[a*x]])/(4*a) + (3*SinhIntegral[3*ArcTanh[a*x]])/(4*a)","A",6,4,21,0.1905,1,"{5966, 6034, 5448, 3298}"
489,1,66,0,0.1769864,"\int \frac{1}{\left(1-a^2 x^2\right)^{7/2} \tanh ^{-1}(a x)^2} \, dx","Int[1/((1 - a^2*x^2)^(7/2)*ArcTanh[a*x]^2),x]","-\frac{1}{a \left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)}+\frac{5 \text{Shi}\left(\tanh ^{-1}(a x)\right)}{8 a}+\frac{15 \text{Shi}\left(3 \tanh ^{-1}(a x)\right)}{16 a}+\frac{5 \text{Shi}\left(5 \tanh ^{-1}(a x)\right)}{16 a}","-\frac{1}{a \left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)}+\frac{5 \text{Shi}\left(\tanh ^{-1}(a x)\right)}{8 a}+\frac{15 \text{Shi}\left(3 \tanh ^{-1}(a x)\right)}{16 a}+\frac{5 \text{Shi}\left(5 \tanh ^{-1}(a x)\right)}{16 a}",1,"-(1/(a*(1 - a^2*x^2)^(5/2)*ArcTanh[a*x])) + (5*SinhIntegral[ArcTanh[a*x]])/(8*a) + (15*SinhIntegral[3*ArcTanh[a*x]])/(16*a) + (5*SinhIntegral[5*ArcTanh[a*x]])/(16*a)","A",7,4,21,0.1905,1,"{5966, 6034, 5448, 3298}"
490,1,80,0,0.1905093,"\int \frac{1}{\left(1-a^2 x^2\right)^{9/2} \tanh ^{-1}(a x)^2} \, dx","Int[1/((1 - a^2*x^2)^(9/2)*ArcTanh[a*x]^2),x]","-\frac{1}{a \left(1-a^2 x^2\right)^{7/2} \tanh ^{-1}(a x)}+\frac{35 \text{Shi}\left(\tanh ^{-1}(a x)\right)}{64 a}+\frac{63 \text{Shi}\left(3 \tanh ^{-1}(a x)\right)}{64 a}+\frac{35 \text{Shi}\left(5 \tanh ^{-1}(a x)\right)}{64 a}+\frac{7 \text{Shi}\left(7 \tanh ^{-1}(a x)\right)}{64 a}","-\frac{1}{a \left(1-a^2 x^2\right)^{7/2} \tanh ^{-1}(a x)}+\frac{35 \text{Shi}\left(\tanh ^{-1}(a x)\right)}{64 a}+\frac{63 \text{Shi}\left(3 \tanh ^{-1}(a x)\right)}{64 a}+\frac{35 \text{Shi}\left(5 \tanh ^{-1}(a x)\right)}{64 a}+\frac{7 \text{Shi}\left(7 \tanh ^{-1}(a x)\right)}{64 a}",1,"-(1/(a*(1 - a^2*x^2)^(7/2)*ArcTanh[a*x])) + (35*SinhIntegral[ArcTanh[a*x]])/(64*a) + (63*SinhIntegral[3*ArcTanh[a*x]])/(64*a) + (35*SinhIntegral[5*ArcTanh[a*x]])/(64*a) + (7*SinhIntegral[7*ArcTanh[a*x]])/(64*a)","A",8,4,21,0.1905,1,"{5966, 6034, 5448, 3298}"
491,0,0,0,0.0311558,"\int \frac{\sqrt{1-a^2 x^2}}{\tanh ^{-1}(a x)^3} \, dx","Int[Sqrt[1 - a^2*x^2]/ArcTanh[a*x]^3,x]","\int \frac{\sqrt{1-a^2 x^2}}{\tanh ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{\sqrt{1-a^2 x^2}}{\tanh ^{-1}(a x)^3},x\right)",0,"Defer[Int][Sqrt[1 - a^2*x^2]/ArcTanh[a*x]^3, x]","A",0,0,0,0,-1,"{}"
492,0,0,0,0.03318,"\int \frac{1}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3} \, dx","Int[1/(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3),x]","\int \frac{1}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{1}{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^3},x\right)",0,"Defer[Int][1/(Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^3), x]","A",0,0,0,0,-1,"{}"
493,1,65,0,0.1670219,"\int \frac{1}{\left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^3} \, dx","Int[1/((1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^3),x]","-\frac{x}{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}-\frac{1}{2 a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}+\frac{\text{Chi}\left(\tanh ^{-1}(a x)\right)}{2 a}","-\frac{x}{2 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}-\frac{1}{2 a \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)^2}+\frac{\text{Chi}\left(\tanh ^{-1}(a x)\right)}{2 a}",1,"-1/(2*a*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]^2) - x/(2*Sqrt[1 - a^2*x^2]*ArcTanh[a*x]) + CoshIntegral[ArcTanh[a*x]]/(2*a)","A",4,4,21,0.1905,1,"{5966, 6006, 5968, 3301}"
494,1,79,0,0.3619847,"\int \frac{1}{\left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)^3} \, dx","Int[1/((1 - a^2*x^2)^(5/2)*ArcTanh[a*x]^3),x]","-\frac{3 x}{2 \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2}+\frac{3 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{8 a}+\frac{9 \text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{8 a}","-\frac{3 x}{2 \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right)^{3/2} \tanh ^{-1}(a x)^2}+\frac{3 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{8 a}+\frac{9 \text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{8 a}",1,"-1/(2*a*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x]^2) - (3*x)/(2*(1 - a^2*x^2)^(3/2)*ArcTanh[a*x]) + (3*CoshIntegral[ArcTanh[a*x]])/(8*a) + (9*CoshIntegral[3*ArcTanh[a*x]])/(8*a)","A",12,7,21,0.3333,1,"{5966, 6032, 6034, 5448, 3301, 5968, 3312}"
495,1,93,0,0.4046967,"\int \frac{1}{\left(1-a^2 x^2\right)^{7/2} \tanh ^{-1}(a x)^3} \, dx","Int[1/((1 - a^2*x^2)^(7/2)*ArcTanh[a*x]^3),x]","-\frac{5 x}{2 \left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)^2}+\frac{5 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{16 a}+\frac{45 \text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{32 a}+\frac{25 \text{Chi}\left(5 \tanh ^{-1}(a x)\right)}{32 a}","-\frac{5 x}{2 \left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right)^{5/2} \tanh ^{-1}(a x)^2}+\frac{5 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{16 a}+\frac{45 \text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{32 a}+\frac{25 \text{Chi}\left(5 \tanh ^{-1}(a x)\right)}{32 a}",1,"-1/(2*a*(1 - a^2*x^2)^(5/2)*ArcTanh[a*x]^2) - (5*x)/(2*(1 - a^2*x^2)^(5/2)*ArcTanh[a*x]) + (5*CoshIntegral[ArcTanh[a*x]])/(16*a) + (45*CoshIntegral[3*ArcTanh[a*x]])/(32*a) + (25*CoshIntegral[5*ArcTanh[a*x]])/(32*a)","A",14,7,21,0.3333,1,"{5966, 6032, 6034, 5448, 3301, 5968, 3312}"
496,1,107,0,0.4391899,"\int \frac{1}{\left(1-a^2 x^2\right)^{9/2} \tanh ^{-1}(a x)^3} \, dx","Int[1/((1 - a^2*x^2)^(9/2)*ArcTanh[a*x]^3),x]","-\frac{7 x}{2 \left(1-a^2 x^2\right)^{7/2} \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right)^{7/2} \tanh ^{-1}(a x)^2}+\frac{35 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{128 a}+\frac{189 \text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{128 a}+\frac{175 \text{Chi}\left(5 \tanh ^{-1}(a x)\right)}{128 a}+\frac{49 \text{Chi}\left(7 \tanh ^{-1}(a x)\right)}{128 a}","-\frac{7 x}{2 \left(1-a^2 x^2\right)^{7/2} \tanh ^{-1}(a x)}-\frac{1}{2 a \left(1-a^2 x^2\right)^{7/2} \tanh ^{-1}(a x)^2}+\frac{35 \text{Chi}\left(\tanh ^{-1}(a x)\right)}{128 a}+\frac{189 \text{Chi}\left(3 \tanh ^{-1}(a x)\right)}{128 a}+\frac{175 \text{Chi}\left(5 \tanh ^{-1}(a x)\right)}{128 a}+\frac{49 \text{Chi}\left(7 \tanh ^{-1}(a x)\right)}{128 a}",1,"-1/(2*a*(1 - a^2*x^2)^(7/2)*ArcTanh[a*x]^2) - (7*x)/(2*(1 - a^2*x^2)^(7/2)*ArcTanh[a*x]) + (35*CoshIntegral[ArcTanh[a*x]])/(128*a) + (189*CoshIntegral[3*ArcTanh[a*x]])/(128*a) + (175*CoshIntegral[5*ArcTanh[a*x]])/(128*a) + (49*CoshIntegral[7*ArcTanh[a*x]])/(128*a)","A",16,7,21,0.3333,1,"{5966, 6032, 6034, 5448, 3301, 5968, 3312}"
497,1,122,0,0.3184119,"\int \frac{(d+e x) \left(a+b \tanh ^{-1}(c x)\right)^2}{1-c^2 x^2} \, dx","Int[((d + e*x)*(a + b*ArcTanh[c*x])^2)/(1 - c^2*x^2),x]","\frac{b e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2}-\frac{b^2 e \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c^2}-\frac{e \left(a+b \tanh ^{-1}(c x)\right)^3}{3 b c^2}+\frac{e \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2}+\frac{d \left(a+b \tanh ^{-1}(c x)\right)^3}{3 b c}","\frac{b e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2}-\frac{b^2 e \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c^2}-\frac{e \left(a+b \tanh ^{-1}(c x)\right)^3}{3 b c^2}+\frac{e \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^2}+\frac{d \left(a+b \tanh ^{-1}(c x)\right)^3}{3 b c}",1,"(d*(a + b*ArcTanh[c*x])^3)/(3*b*c) - (e*(a + b*ArcTanh[c*x])^3)/(3*b*c^2) + (e*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/c^2 + (b*e*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/c^2 - (b^2*e*PolyLog[3, 1 - 2/(1 - c*x)])/(2*c^2)","A",7,6,28,0.2143,1,"{6048, 5948, 5984, 5918, 6058, 6610}"
498,1,245,0,0.1798771,"\int \left(c+d x^2\right)^4 \tanh ^{-1}(a x) \, dx","Int[(c + d*x^2)^4*ArcTanh[a*x],x]","\frac{d^2 x^4 \left(378 a^4 c^2+180 a^2 c d+35 d^2\right)}{1260 a^5}+\frac{d x^2 \left(378 a^4 c^2 d+420 a^6 c^3+180 a^2 c d^2+35 d^3\right)}{630 a^7}+\frac{\left(378 a^4 c^2 d^2+420 a^6 c^3 d+315 a^8 c^4+180 a^2 c d^3+35 d^4\right) \log \left(1-a^2 x^2\right)}{630 a^9}+\frac{d^3 x^6 \left(36 a^2 c+7 d\right)}{378 a^3}+\frac{6}{5} c^2 d^2 x^5 \tanh ^{-1}(a x)+\frac{4}{3} c^3 d x^3 \tanh ^{-1}(a x)+c^4 x \tanh ^{-1}(a x)+\frac{4}{7} c d^3 x^7 \tanh ^{-1}(a x)+\frac{d^4 x^8}{72 a}+\frac{1}{9} d^4 x^9 \tanh ^{-1}(a x)","\frac{d^2 x^4 \left(378 a^4 c^2+180 a^2 c d+35 d^2\right)}{1260 a^5}+\frac{d x^2 \left(378 a^4 c^2 d+420 a^6 c^3+180 a^2 c d^2+35 d^3\right)}{630 a^7}+\frac{\left(378 a^4 c^2 d^2+420 a^6 c^3 d+315 a^8 c^4+180 a^2 c d^3+35 d^4\right) \log \left(1-a^2 x^2\right)}{630 a^9}+\frac{d^3 x^6 \left(36 a^2 c+7 d\right)}{378 a^3}+\frac{6}{5} c^2 d^2 x^5 \tanh ^{-1}(a x)+\frac{4}{3} c^3 d x^3 \tanh ^{-1}(a x)+c^4 x \tanh ^{-1}(a x)+\frac{4}{7} c d^3 x^7 \tanh ^{-1}(a x)+\frac{d^4 x^8}{72 a}+\frac{1}{9} d^4 x^9 \tanh ^{-1}(a x)",1,"(d*(420*a^6*c^3 + 378*a^4*c^2*d + 180*a^2*c*d^2 + 35*d^3)*x^2)/(630*a^7) + (d^2*(378*a^4*c^2 + 180*a^2*c*d + 35*d^2)*x^4)/(1260*a^5) + (d^3*(36*a^2*c + 7*d)*x^6)/(378*a^3) + (d^4*x^8)/(72*a) + c^4*x*ArcTanh[a*x] + (4*c^3*d*x^3*ArcTanh[a*x])/3 + (6*c^2*d^2*x^5*ArcTanh[a*x])/5 + (4*c*d^3*x^7*ArcTanh[a*x])/7 + (d^4*x^9*ArcTanh[a*x])/9 + ((315*a^8*c^4 + 420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*Log[1 - a^2*x^2])/(630*a^9)","A",4,4,14,0.2857,1,"{194, 5976, 1810, 260}"
499,1,169,0,0.129409,"\int \left(c+d x^2\right)^3 \tanh ^{-1}(a x) \, dx","Int[(c + d*x^2)^3*ArcTanh[a*x],x]","\frac{d x^2 \left(35 a^4 c^2+21 a^2 c d+5 d^2\right)}{70 a^5}+\frac{\left(35 a^4 c^2 d+35 a^6 c^3+21 a^2 c d^2+5 d^3\right) \log \left(1-a^2 x^2\right)}{70 a^7}+\frac{d^2 x^4 \left(21 a^2 c+5 d\right)}{140 a^3}+c^2 d x^3 \tanh ^{-1}(a x)+c^3 x \tanh ^{-1}(a x)+\frac{3}{5} c d^2 x^5 \tanh ^{-1}(a x)+\frac{d^3 x^6}{42 a}+\frac{1}{7} d^3 x^7 \tanh ^{-1}(a x)","\frac{d x^2 \left(35 a^4 c^2+21 a^2 c d+5 d^2\right)}{70 a^5}+\frac{\left(35 a^4 c^2 d+35 a^6 c^3+21 a^2 c d^2+5 d^3\right) \log \left(1-a^2 x^2\right)}{70 a^7}+\frac{d^2 x^4 \left(21 a^2 c+5 d\right)}{140 a^3}+c^2 d x^3 \tanh ^{-1}(a x)+c^3 x \tanh ^{-1}(a x)+\frac{3}{5} c d^2 x^5 \tanh ^{-1}(a x)+\frac{d^3 x^6}{42 a}+\frac{1}{7} d^3 x^7 \tanh ^{-1}(a x)",1,"(d*(35*a^4*c^2 + 21*a^2*c*d + 5*d^2)*x^2)/(70*a^5) + (d^2*(21*a^2*c + 5*d)*x^4)/(140*a^3) + (d^3*x^6)/(42*a) + c^3*x*ArcTanh[a*x] + c^2*d*x^3*ArcTanh[a*x] + (3*c*d^2*x^5*ArcTanh[a*x])/5 + (d^3*x^7*ArcTanh[a*x])/7 + ((35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*Log[1 - a^2*x^2])/(70*a^7)","A",4,4,14,0.2857,1,"{194, 5976, 1810, 260}"
500,1,110,0,0.1351948,"\int \left(c+d x^2\right)^2 \tanh ^{-1}(a x) \, dx","Int[(c + d*x^2)^2*ArcTanh[a*x],x]","\frac{\left(15 a^4 c^2+10 a^2 c d+3 d^2\right) \log \left(1-a^2 x^2\right)}{30 a^5}+\frac{d x^2 \left(10 a^2 c+3 d\right)}{30 a^3}+c^2 x \tanh ^{-1}(a x)+\frac{2}{3} c d x^3 \tanh ^{-1}(a x)+\frac{d^2 x^4}{20 a}+\frac{1}{5} d^2 x^5 \tanh ^{-1}(a x)","\frac{\left(15 a^4 c^2+10 a^2 c d+3 d^2\right) \log \left(1-a^2 x^2\right)}{30 a^5}+\frac{d x^2 \left(10 a^2 c+3 d\right)}{30 a^3}+c^2 x \tanh ^{-1}(a x)+\frac{2}{3} c d x^3 \tanh ^{-1}(a x)+\frac{d^2 x^4}{20 a}+\frac{1}{5} d^2 x^5 \tanh ^{-1}(a x)",1,"(d*(10*a^2*c + 3*d)*x^2)/(30*a^3) + (d^2*x^4)/(20*a) + c^2*x*ArcTanh[a*x] + (2*c*d*x^3*ArcTanh[a*x])/3 + (d^2*x^5*ArcTanh[a*x])/5 + ((15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*Log[1 - a^2*x^2])/(30*a^5)","A",5,5,14,0.3571,1,"{194, 5976, 1594, 1247, 698}"
501,1,57,0,0.066788,"\int \left(c+d x^2\right) \tanh ^{-1}(a x) \, dx","Int[(c + d*x^2)*ArcTanh[a*x],x]","\frac{\left(3 a^2 c+d\right) \log \left(1-a^2 x^2\right)}{6 a^3}+c x \tanh ^{-1}(a x)+\frac{d x^2}{6 a}+\frac{1}{3} d x^3 \tanh ^{-1}(a x)","\frac{\left(3 a^2 c+d\right) \log \left(1-a^2 x^2\right)}{6 a^3}+c x \tanh ^{-1}(a x)+\frac{d x^2}{6 a}+\frac{1}{3} d x^3 \tanh ^{-1}(a x)",1,"(d*x^2)/(6*a) + c*x*ArcTanh[a*x] + (d*x^3*ArcTanh[a*x])/3 + ((3*a^2*c + d)*Log[1 - a^2*x^2])/(6*a^3)","A",5,4,12,0.3333,1,"{5976, 1593, 444, 43}"
502,1,429,0,0.4417113,"\int \frac{\tanh ^{-1}(a x)}{c+d x^2} \, dx","Int[ArcTanh[a*x]/(c + d*x^2),x]","-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} (1-a x)}{a \sqrt{-c}-\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} (1-a x)}{a \sqrt{-c}+\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} (a x+1)}{a \sqrt{-c}-\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} (a x+1)}{a \sqrt{-c}+\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log (1-a x) \log \left(\frac{a \left(\sqrt{-c}-\sqrt{d} x\right)}{a \sqrt{-c}-\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log (a x+1) \log \left(\frac{a \left(\sqrt{-c}-\sqrt{d} x\right)}{a \sqrt{-c}+\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log (a x+1) \log \left(\frac{a \left(\sqrt{-c}+\sqrt{d} x\right)}{a \sqrt{-c}-\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log (1-a x) \log \left(\frac{a \left(\sqrt{-c}+\sqrt{d} x\right)}{a \sqrt{-c}+\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}","-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} (1-a x)}{a \sqrt{-c}-\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} (1-a x)}{a \sqrt{-c}+\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} (a x+1)}{a \sqrt{-c}-\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} (a x+1)}{a \sqrt{-c}+\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log (1-a x) \log \left(\frac{a \left(\sqrt{-c}-\sqrt{d} x\right)}{a \sqrt{-c}-\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log (a x+1) \log \left(\frac{a \left(\sqrt{-c}-\sqrt{d} x\right)}{a \sqrt{-c}+\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log (a x+1) \log \left(\frac{a \left(\sqrt{-c}+\sqrt{d} x\right)}{a \sqrt{-c}-\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log (1-a x) \log \left(\frac{a \left(\sqrt{-c}+\sqrt{d} x\right)}{a \sqrt{-c}+\sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}",1,"-(Log[1 - a*x]*Log[(a*(Sqrt[-c] - Sqrt[d]*x))/(a*Sqrt[-c] - Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) + (Log[1 + a*x]*Log[(a*(Sqrt[-c] - Sqrt[d]*x))/(a*Sqrt[-c] + Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) - (Log[1 + a*x]*Log[(a*(Sqrt[-c] + Sqrt[d]*x))/(a*Sqrt[-c] - Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) + (Log[1 - a*x]*Log[(a*(Sqrt[-c] + Sqrt[d]*x))/(a*Sqrt[-c] + Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) - PolyLog[2, -((Sqrt[d]*(1 - a*x))/(a*Sqrt[-c] - Sqrt[d]))]/(4*Sqrt[-c]*Sqrt[d]) + PolyLog[2, (Sqrt[d]*(1 - a*x))/(a*Sqrt[-c] + Sqrt[d])]/(4*Sqrt[-c]*Sqrt[d]) - PolyLog[2, -((Sqrt[d]*(1 + a*x))/(a*Sqrt[-c] - Sqrt[d]))]/(4*Sqrt[-c]*Sqrt[d]) + PolyLog[2, (Sqrt[d]*(1 + a*x))/(a*Sqrt[-c] + Sqrt[d])]/(4*Sqrt[-c]*Sqrt[d])","A",17,5,14,0.3571,1,"{5972, 2409, 2394, 2393, 2391}"
503,1,590,0,0.9104645,"\int \frac{\tanh ^{-1}(a x)}{\left(c+d x^2\right)^2} \, dx","Int[ArcTanh[a*x]/(c + d*x^2)^2,x]","\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{a \log \left(1-a^2 x^2\right)}{4 c \left(a^2 c+d\right)}-\frac{a \log \left(c+d x^2\right)}{4 c \left(a^2 c+d\right)}+\frac{i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (1-a x)}{\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (a x+1)}{-\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (1-a x)}{-\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (a x+1)}{\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{\tanh ^{-1}(a x) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{3/2} \sqrt{d}}+\frac{x \tanh ^{-1}(a x)}{2 c \left(c+d x^2\right)}","\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{a \log \left(1-a^2 x^2\right)}{4 c \left(a^2 c+d\right)}-\frac{a \log \left(c+d x^2\right)}{4 c \left(a^2 c+d\right)}+\frac{i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (1-a x)}{\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (a x+1)}{-\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (1-a x)}{-\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (a x+1)}{\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{\tanh ^{-1}(a x) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{3/2} \sqrt{d}}+\frac{x \tanh ^{-1}(a x)}{2 c \left(c+d x^2\right)}",1,"(x*ArcTanh[a*x])/(2*c*(c + d*x^2)) + (ArcTan[(Sqrt[d]*x)/Sqrt[c]]*ArcTanh[a*x])/(2*c^(3/2)*Sqrt[d]) + ((I/8)*Log[(Sqrt[d]*(1 - a*x))/(I*a*Sqrt[c] + Sqrt[d])]*Log[1 - (I*Sqrt[d]*x)/Sqrt[c]])/(c^(3/2)*Sqrt[d]) - ((I/8)*Log[-((Sqrt[d]*(1 + a*x))/(I*a*Sqrt[c] - Sqrt[d]))]*Log[1 - (I*Sqrt[d]*x)/Sqrt[c]])/(c^(3/2)*Sqrt[d]) - ((I/8)*Log[-((Sqrt[d]*(1 - a*x))/(I*a*Sqrt[c] - Sqrt[d]))]*Log[1 + (I*Sqrt[d]*x)/Sqrt[c]])/(c^(3/2)*Sqrt[d]) + ((I/8)*Log[(Sqrt[d]*(1 + a*x))/(I*a*Sqrt[c] + Sqrt[d])]*Log[1 + (I*Sqrt[d]*x)/Sqrt[c]])/(c^(3/2)*Sqrt[d]) + (a*Log[1 - a^2*x^2])/(4*c*(a^2*c + d)) - (a*Log[c + d*x^2])/(4*c*(a^2*c + d)) + ((I/8)*PolyLog[2, (a*(Sqrt[c] - I*Sqrt[d]*x))/(a*Sqrt[c] - I*Sqrt[d])])/(c^(3/2)*Sqrt[d]) - ((I/8)*PolyLog[2, (a*(Sqrt[c] - I*Sqrt[d]*x))/(a*Sqrt[c] + I*Sqrt[d])])/(c^(3/2)*Sqrt[d]) + ((I/8)*PolyLog[2, (a*(Sqrt[c] + I*Sqrt[d]*x))/(a*Sqrt[c] - I*Sqrt[d])])/(c^(3/2)*Sqrt[d]) - ((I/8)*PolyLog[2, (a*(Sqrt[c] + I*Sqrt[d]*x))/(a*Sqrt[c] + I*Sqrt[d])])/(c^(3/2)*Sqrt[d])","A",25,13,14,0.9286,1,"{199, 205, 5976, 6725, 517, 444, 36, 31, 4908, 2409, 2394, 2393, 2391}"
504,1,657,0,0.9662957,"\int \frac{\tanh ^{-1}(a x)}{\left(c+d x^2\right)^3} \, dx","Int[ArcTanh[a*x]/(c + d*x^2)^3,x]","\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{a \left(5 a^2 c+3 d\right) \log \left(1-a^2 x^2\right)}{16 c^2 \left(a^2 c+d\right)^2}-\frac{a \left(5 a^2 c+3 d\right) \log \left(c+d x^2\right)}{16 c^2 \left(a^2 c+d\right)^2}+\frac{a}{8 c \left(a^2 c+d\right) \left(c+d x^2\right)}+\frac{3 x \tanh ^{-1}(a x)}{8 c^2 \left(c+d x^2\right)}+\frac{3 i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (1-a x)}{\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (a x+1)}{-\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (1-a x)}{-\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (a x+1)}{\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 \tanh ^{-1}(a x) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{5/2} \sqrt{d}}+\frac{x \tanh ^{-1}(a x)}{4 c \left(c+d x^2\right)^2}","\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{a \left(5 a^2 c+3 d\right) \log \left(1-a^2 x^2\right)}{16 c^2 \left(a^2 c+d\right)^2}-\frac{a \left(5 a^2 c+3 d\right) \log \left(c+d x^2\right)}{16 c^2 \left(a^2 c+d\right)^2}+\frac{a}{8 c \left(a^2 c+d\right) \left(c+d x^2\right)}+\frac{3 x \tanh ^{-1}(a x)}{8 c^2 \left(c+d x^2\right)}+\frac{3 i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (1-a x)}{\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (a x+1)}{-\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (1-a x)}{-\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (a x+1)}{\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 \tanh ^{-1}(a x) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{5/2} \sqrt{d}}+\frac{x \tanh ^{-1}(a x)}{4 c \left(c+d x^2\right)^2}",1,"a/(8*c*(a^2*c + d)*(c + d*x^2)) + (x*ArcTanh[a*x])/(4*c*(c + d*x^2)^2) + (3*x*ArcTanh[a*x])/(8*c^2*(c + d*x^2)) + (3*ArcTan[(Sqrt[d]*x)/Sqrt[c]]*ArcTanh[a*x])/(8*c^(5/2)*Sqrt[d]) + (((3*I)/32)*Log[(Sqrt[d]*(1 - a*x))/(I*a*Sqrt[c] + Sqrt[d])]*Log[1 - (I*Sqrt[d]*x)/Sqrt[c]])/(c^(5/2)*Sqrt[d]) - (((3*I)/32)*Log[-((Sqrt[d]*(1 + a*x))/(I*a*Sqrt[c] - Sqrt[d]))]*Log[1 - (I*Sqrt[d]*x)/Sqrt[c]])/(c^(5/2)*Sqrt[d]) - (((3*I)/32)*Log[-((Sqrt[d]*(1 - a*x))/(I*a*Sqrt[c] - Sqrt[d]))]*Log[1 + (I*Sqrt[d]*x)/Sqrt[c]])/(c^(5/2)*Sqrt[d]) + (((3*I)/32)*Log[(Sqrt[d]*(1 + a*x))/(I*a*Sqrt[c] + Sqrt[d])]*Log[1 + (I*Sqrt[d]*x)/Sqrt[c]])/(c^(5/2)*Sqrt[d]) + (a*(5*a^2*c + 3*d)*Log[1 - a^2*x^2])/(16*c^2*(a^2*c + d)^2) - (a*(5*a^2*c + 3*d)*Log[c + d*x^2])/(16*c^2*(a^2*c + d)^2) + (((3*I)/32)*PolyLog[2, (a*(Sqrt[c] - I*Sqrt[d]*x))/(a*Sqrt[c] - I*Sqrt[d])])/(c^(5/2)*Sqrt[d]) - (((3*I)/32)*PolyLog[2, (a*(Sqrt[c] - I*Sqrt[d]*x))/(a*Sqrt[c] + I*Sqrt[d])])/(c^(5/2)*Sqrt[d]) + (((3*I)/32)*PolyLog[2, (a*(Sqrt[c] + I*Sqrt[d]*x))/(a*Sqrt[c] - I*Sqrt[d])])/(c^(5/2)*Sqrt[d]) - (((3*I)/32)*PolyLog[2, (a*(Sqrt[c] + I*Sqrt[d]*x))/(a*Sqrt[c] + I*Sqrt[d])])/(c^(5/2)*Sqrt[d])","A",23,11,14,0.7857,1,"{199, 205, 5976, 6725, 571, 77, 4908, 2409, 2394, 2393, 2391}"
505,1,17,0,0.0444294,"\int \frac{1}{\left(a-a x^2\right) \left(b-2 b \tanh ^{-1}(x)\right)} \, dx","Int[1/((a - a*x^2)*(b - 2*b*ArcTanh[x])),x]","-\frac{\log \left(1-2 \tanh ^{-1}(x)\right)}{2 a b}","-\frac{\log \left(1-2 \tanh ^{-1}(x)\right)}{2 a b}",1,"-Log[1 - 2*ArcTanh[x]]/(2*a*b)","A",1,1,20,0.05000,1,"{5946}"
506,1,171,0,0.2401175,"\int \frac{\tanh ^{-1}(b x)}{1-x^2} \, dx","Int[ArcTanh[b*x]/(1 - x^2),x]","\frac{1}{4} \text{PolyLog}\left(2,\frac{1-b x}{1-b}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{1-b x}{b+1}\right)+\frac{1}{4} \text{PolyLog}\left(2,\frac{b x+1}{1-b}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{b x+1}{b+1}\right)+\frac{1}{4} \log \left(-\frac{b (1-x)}{1-b}\right) \log (1-b x)-\frac{1}{4} \log \left(\frac{b (x+1)}{b+1}\right) \log (1-b x)-\frac{1}{4} \log \left(\frac{b (1-x)}{b+1}\right) \log (b x+1)+\frac{1}{4} \log \left(-\frac{b (x+1)}{1-b}\right) \log (b x+1)","\frac{1}{4} \text{PolyLog}\left(2,\frac{1-b x}{1-b}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{1-b x}{b+1}\right)+\frac{1}{4} \text{PolyLog}\left(2,\frac{b x+1}{1-b}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{b x+1}{b+1}\right)+\frac{1}{4} \log \left(-\frac{b (1-x)}{1-b}\right) \log (1-b x)-\frac{1}{4} \log \left(\frac{b (x+1)}{b+1}\right) \log (1-b x)-\frac{1}{4} \log \left(\frac{b (1-x)}{b+1}\right) \log (b x+1)+\frac{1}{4} \log \left(-\frac{b (x+1)}{1-b}\right) \log (b x+1)",1,"(Log[-((b*(1 - x))/(1 - b))]*Log[1 - b*x])/4 - (Log[(b*(1 + x))/(1 + b)]*Log[1 - b*x])/4 - (Log[(b*(1 - x))/(1 + b)]*Log[1 + b*x])/4 + (Log[-((b*(1 + x))/(1 - b))]*Log[1 + b*x])/4 + PolyLog[2, (1 - b*x)/(1 - b)]/4 - PolyLog[2, (1 - b*x)/(1 + b)]/4 + PolyLog[2, (1 + b*x)/(1 - b)]/4 - PolyLog[2, (1 + b*x)/(1 + b)]/4","A",17,5,14,0.3571,1,"{5972, 2409, 2394, 2393, 2391}"
507,1,203,0,0.2577963,"\int \frac{\tanh ^{-1}(a+b x)}{1-x^2} \, dx","Int[ArcTanh[a + b*x]/(1 - x^2),x]","\frac{1}{4} \text{PolyLog}\left(2,\frac{-a-b x+1}{-a-b+1}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{-a-b x+1}{-a+b+1}\right)+\frac{1}{4} \text{PolyLog}\left(2,\frac{a+b x+1}{a-b+1}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{a+b x+1}{a+b+1}\right)+\frac{1}{4} \log \left(-\frac{b (1-x)}{-a-b+1}\right) \log (-a-b x+1)-\frac{1}{4} \log \left(\frac{b (x+1)}{-a+b+1}\right) \log (-a-b x+1)-\frac{1}{4} \log \left(\frac{b (1-x)}{a+b+1}\right) \log (a+b x+1)+\frac{1}{4} \log \left(-\frac{b (x+1)}{a-b+1}\right) \log (a+b x+1)","\frac{1}{4} \text{PolyLog}\left(2,\frac{-a-b x+1}{-a-b+1}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{-a-b x+1}{-a+b+1}\right)+\frac{1}{4} \text{PolyLog}\left(2,\frac{a+b x+1}{a-b+1}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{a+b x+1}{a+b+1}\right)+\frac{1}{4} \log \left(-\frac{b (1-x)}{-a-b+1}\right) \log (-a-b x+1)-\frac{1}{4} \log \left(\frac{b (x+1)}{-a+b+1}\right) \log (-a-b x+1)-\frac{1}{4} \log \left(\frac{b (1-x)}{a+b+1}\right) \log (a+b x+1)+\frac{1}{4} \log \left(-\frac{b (x+1)}{a-b+1}\right) \log (a+b x+1)",1,"(Log[-((b*(1 - x))/(1 - a - b))]*Log[1 - a - b*x])/4 - (Log[(b*(1 + x))/(1 - a + b)]*Log[1 - a - b*x])/4 - (Log[(b*(1 - x))/(1 + a + b)]*Log[1 + a + b*x])/4 + (Log[-((b*(1 + x))/(1 + a - b))]*Log[1 + a + b*x])/4 + PolyLog[2, (1 - a - b*x)/(1 - a - b)]/4 - PolyLog[2, (1 - a - b*x)/(1 - a + b)]/4 + PolyLog[2, (1 + a + b*x)/(1 + a - b)]/4 - PolyLog[2, (1 + a + b*x)/(1 + a + b)]/4","A",17,5,16,0.3125,1,"{6115, 2409, 2394, 2393, 2391}"
508,1,86,0,0.0608797,"\int \frac{\tanh ^{-1}(x)}{a+b x} \, dx","Int[ArcTanh[x]/(a + b*x),x]","-\frac{\text{PolyLog}\left(2,1-\frac{2 (a+b x)}{(x+1) (a+b)}\right)}{2 b}+\frac{\text{PolyLog}\left(2,1-\frac{2}{x+1}\right)}{2 b}+\frac{\tanh ^{-1}(x) \log \left(\frac{2 (a+b x)}{(x+1) (a+b)}\right)}{b}-\frac{\log \left(\frac{2}{x+1}\right) \tanh ^{-1}(x)}{b}","-\frac{\text{PolyLog}\left(2,1-\frac{2 (a+b x)}{(x+1) (a+b)}\right)}{2 b}+\frac{\text{PolyLog}\left(2,1-\frac{2}{x+1}\right)}{2 b}+\frac{\tanh ^{-1}(x) \log \left(\frac{2 (a+b x)}{(x+1) (a+b)}\right)}{b}-\frac{\log \left(\frac{2}{x+1}\right) \tanh ^{-1}(x)}{b}",1,"-((ArcTanh[x]*Log[2/(1 + x)])/b) + (ArcTanh[x]*Log[(2*(a + b*x))/((a + b)*(1 + x))])/b + PolyLog[2, 1 - 2/(1 + x)]/(2*b) - PolyLog[2, 1 - (2*(a + b*x))/((a + b)*(1 + x))]/(2*b)","A",4,4,10,0.4000,1,"{5920, 2402, 2315, 2447}"
509,1,397,0,0.3720738,"\int \frac{\tanh ^{-1}(x)}{a+b x^2} \, dx","Int[ArcTanh[x]/(a + b*x^2),x]","-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{b} (1-x)}{\sqrt{-a}-\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{b} (1-x)}{\sqrt{-a}+\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{b} (x+1)}{\sqrt{-a}-\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{b} (x+1)}{\sqrt{-a}+\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\log (1-x) \log \left(\frac{\sqrt{-a}-\sqrt{b} x}{\sqrt{-a}-\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\log (x+1) \log \left(\frac{\sqrt{-a}-\sqrt{b} x}{\sqrt{-a}+\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\log (x+1) \log \left(\frac{\sqrt{-a}+\sqrt{b} x}{\sqrt{-a}-\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\log (1-x) \log \left(\frac{\sqrt{-a}+\sqrt{b} x}{\sqrt{-a}+\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}","-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{b} (1-x)}{\sqrt{-a}-\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{b} (1-x)}{\sqrt{-a}+\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{b} (x+1)}{\sqrt{-a}-\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{b} (x+1)}{\sqrt{-a}+\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\log (1-x) \log \left(\frac{\sqrt{-a}-\sqrt{b} x}{\sqrt{-a}-\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\log (x+1) \log \left(\frac{\sqrt{-a}-\sqrt{b} x}{\sqrt{-a}+\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}-\frac{\log (x+1) \log \left(\frac{\sqrt{-a}+\sqrt{b} x}{\sqrt{-a}-\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}+\frac{\log (1-x) \log \left(\frac{\sqrt{-a}+\sqrt{b} x}{\sqrt{-a}+\sqrt{b}}\right)}{4 \sqrt{-a} \sqrt{b}}",1,"-(Log[1 - x]*Log[(Sqrt[-a] - Sqrt[b]*x)/(Sqrt[-a] - Sqrt[b])])/(4*Sqrt[-a]*Sqrt[b]) + (Log[1 + x]*Log[(Sqrt[-a] - Sqrt[b]*x)/(Sqrt[-a] + Sqrt[b])])/(4*Sqrt[-a]*Sqrt[b]) - (Log[1 + x]*Log[(Sqrt[-a] + Sqrt[b]*x)/(Sqrt[-a] - Sqrt[b])])/(4*Sqrt[-a]*Sqrt[b]) + (Log[1 - x]*Log[(Sqrt[-a] + Sqrt[b]*x)/(Sqrt[-a] + Sqrt[b])])/(4*Sqrt[-a]*Sqrt[b]) - PolyLog[2, -((Sqrt[b]*(1 - x))/(Sqrt[-a] - Sqrt[b]))]/(4*Sqrt[-a]*Sqrt[b]) + PolyLog[2, (Sqrt[b]*(1 - x))/(Sqrt[-a] + Sqrt[b])]/(4*Sqrt[-a]*Sqrt[b]) - PolyLog[2, -((Sqrt[b]*(1 + x))/(Sqrt[-a] - Sqrt[b]))]/(4*Sqrt[-a]*Sqrt[b]) + PolyLog[2, (Sqrt[b]*(1 + x))/(Sqrt[-a] + Sqrt[b])]/(4*Sqrt[-a]*Sqrt[b])","A",17,5,12,0.4167,1,"{5972, 2409, 2394, 2393, 2391}"
510,1,258,0,0.3280026,"\int \frac{\tanh ^{-1}(x)}{a+b x+c x^2} \, dx","Int[ArcTanh[x]/(a + b*x + c*x^2),x]","-\frac{\text{PolyLog}\left(2,1-\frac{2 \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{(x+1) \left(-\sqrt{b^2-4 a c}+b+2 c\right)}\right)}{2 \sqrt{b^2-4 a c}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{(x+1) \left(\sqrt{b^2-4 a c}+b+2 c\right)}\right)}{2 \sqrt{b^2-4 a c}}+\frac{\tanh ^{-1}(x) \log \left(\frac{2 \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{(x+1) \left(-\sqrt{b^2-4 a c}+b+2 c\right)}\right)}{\sqrt{b^2-4 a c}}-\frac{\tanh ^{-1}(x) \log \left(\frac{2 \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{(x+1) \left(\sqrt{b^2-4 a c}+b+2 c\right)}\right)}{\sqrt{b^2-4 a c}}","-\frac{\text{PolyLog}\left(2,1-\frac{2 \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{(x+1) \left(-\sqrt{b^2-4 a c}+b+2 c\right)}\right)}{2 \sqrt{b^2-4 a c}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{(x+1) \left(\sqrt{b^2-4 a c}+b+2 c\right)}\right)}{2 \sqrt{b^2-4 a c}}+\frac{\tanh ^{-1}(x) \log \left(\frac{2 \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{(x+1) \left(-\sqrt{b^2-4 a c}+b+2 c\right)}\right)}{\sqrt{b^2-4 a c}}-\frac{\tanh ^{-1}(x) \log \left(\frac{2 \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{(x+1) \left(\sqrt{b^2-4 a c}+b+2 c\right)}\right)}{\sqrt{b^2-4 a c}}",1,"(ArcTanh[x]*Log[(2*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/((b + 2*c - Sqrt[b^2 - 4*a*c])*(1 + x))])/Sqrt[b^2 - 4*a*c] - (ArcTanh[x]*Log[(2*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((b + 2*c + Sqrt[b^2 - 4*a*c])*(1 + x))])/Sqrt[b^2 - 4*a*c] - PolyLog[2, 1 - (2*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/((b + 2*c - Sqrt[b^2 - 4*a*c])*(1 + x))]/(2*Sqrt[b^2 - 4*a*c]) + PolyLog[2, 1 - (2*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((b + 2*c + Sqrt[b^2 - 4*a*c])*(1 + x))]/(2*Sqrt[b^2 - 4*a*c])","A",10,7,15,0.4667,1,"{618, 206, 6728, 5920, 2402, 2315, 2447}"
511,0,0,0,0.0218606,"\int \sqrt{c+d x^2} \tanh ^{-1}(a x) \, dx","Int[Sqrt[c + d*x^2]*ArcTanh[a*x],x]","\int \sqrt{c+d x^2} \tanh ^{-1}(a x) \, dx","\text{Int}\left(\tanh ^{-1}(a x) \sqrt{c+d x^2},x\right)",0,"Defer[Int][Sqrt[c + d*x^2]*ArcTanh[a*x], x]","A",0,0,0,0,-1,"{}"
512,0,0,0,0.0239079,"\int \frac{\tanh ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx","Int[ArcTanh[a*x]/Sqrt[c + d*x^2],x]","\int \frac{\tanh ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(a x)}{\sqrt{c+d x^2}},x\right)",0,"Defer[Int][ArcTanh[a*x]/Sqrt[c + d*x^2], x]","A",0,0,0,0,-1,"{}"
513,1,62,0,0.121636,"\int \frac{\tanh ^{-1}(a x)}{\left(c+d x^2\right)^{3/2}} \, dx","Int[ArcTanh[a*x]/(c + d*x^2)^(3/2),x]","\frac{x \tanh ^{-1}(a x)}{c \sqrt{c+d x^2}}-\frac{\tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{c \sqrt{a^2 c+d}}","\frac{x \tanh ^{-1}(a x)}{c \sqrt{c+d x^2}}-\frac{\tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{c \sqrt{a^2 c+d}}",1,"(x*ArcTanh[a*x])/(c*Sqrt[c + d*x^2]) - ArcTanh[(a*Sqrt[c + d*x^2])/Sqrt[a^2*c + d]]/(c*Sqrt[a^2*c + d])","A",5,6,16,0.3750,1,"{191, 5976, 12, 444, 63, 208}"
514,1,128,0,0.3749718,"\int \frac{\tanh ^{-1}(a x)}{\left(c+d x^2\right)^{5/2}} \, dx","Int[ArcTanh[a*x]/(c + d*x^2)^(5/2),x]","-\frac{\left(3 a^2 c+2 d\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{3 c^2 \left(a^2 c+d\right)^{3/2}}+\frac{a}{3 c \left(a^2 c+d\right) \sqrt{c+d x^2}}+\frac{2 x \tanh ^{-1}(a x)}{3 c^2 \sqrt{c+d x^2}}+\frac{x \tanh ^{-1}(a x)}{3 c \left(c+d x^2\right)^{3/2}}","-\frac{\left(3 a^2 c+2 d\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{3 c^2 \left(a^2 c+d\right)^{3/2}}+\frac{a}{3 c \left(a^2 c+d\right) \sqrt{c+d x^2}}+\frac{2 x \tanh ^{-1}(a x)}{3 c^2 \sqrt{c+d x^2}}+\frac{x \tanh ^{-1}(a x)}{3 c \left(c+d x^2\right)^{3/2}}",1,"a/(3*c*(a^2*c + d)*Sqrt[c + d*x^2]) + (x*ArcTanh[a*x])/(3*c*(c + d*x^2)^(3/2)) + (2*x*ArcTanh[a*x])/(3*c^2*Sqrt[c + d*x^2]) - ((3*a^2*c + 2*d)*ArcTanh[(a*Sqrt[c + d*x^2])/Sqrt[a^2*c + d]])/(3*c^2*(a^2*c + d)^(3/2))","A",7,9,16,0.5625,1,"{192, 191, 5976, 6688, 12, 571, 78, 63, 208}"
515,1,200,0,1.081567,"\int \frac{\tanh ^{-1}(a x)}{\left(c+d x^2\right)^{7/2}} \, dx","Int[ArcTanh[a*x]/(c + d*x^2)^(7/2),x]","-\frac{\left(15 a^4 c^2+20 a^2 c d+8 d^2\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{15 c^3 \left(a^2 c+d\right)^{5/2}}+\frac{a \left(7 a^2 c+4 d\right)}{15 c^2 \left(a^2 c+d\right)^2 \sqrt{c+d x^2}}+\frac{a}{15 c \left(a^2 c+d\right) \left(c+d x^2\right)^{3/2}}+\frac{8 x \tanh ^{-1}(a x)}{15 c^3 \sqrt{c+d x^2}}+\frac{4 x \tanh ^{-1}(a x)}{15 c^2 \left(c+d x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(a x)}{5 c \left(c+d x^2\right)^{5/2}}","-\frac{\left(15 a^4 c^2+20 a^2 c d+8 d^2\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{15 c^3 \left(a^2 c+d\right)^{5/2}}+\frac{a \left(7 a^2 c+4 d\right)}{15 c^2 \left(a^2 c+d\right)^2 \sqrt{c+d x^2}}+\frac{a}{15 c \left(a^2 c+d\right) \left(c+d x^2\right)^{3/2}}+\frac{8 x \tanh ^{-1}(a x)}{15 c^3 \sqrt{c+d x^2}}+\frac{4 x \tanh ^{-1}(a x)}{15 c^2 \left(c+d x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(a x)}{5 c \left(c+d x^2\right)^{5/2}}",1,"a/(15*c*(a^2*c + d)*(c + d*x^2)^(3/2)) + (a*(7*a^2*c + 4*d))/(15*c^2*(a^2*c + d)^2*Sqrt[c + d*x^2]) + (x*ArcTanh[a*x])/(5*c*(c + d*x^2)^(5/2)) + (4*x*ArcTanh[a*x])/(15*c^2*(c + d*x^2)^(3/2)) + (8*x*ArcTanh[a*x])/(15*c^3*Sqrt[c + d*x^2]) - ((15*a^4*c^2 + 20*a^2*c*d + 8*d^2)*ArcTanh[(a*Sqrt[c + d*x^2])/Sqrt[a^2*c + d]])/(15*c^3*(a^2*c + d)^(5/2))","A",8,9,16,0.5625,1,"{192, 191, 5976, 6688, 12, 6715, 897, 1261, 208}"
516,1,283,0,1.5110969,"\int \frac{\tanh ^{-1}(a x)}{\left(c+d x^2\right)^{9/2}} \, dx","Int[ArcTanh[a*x]/(c + d*x^2)^(9/2),x]","\frac{a \left(19 a^4 c^2+22 a^2 c d+8 d^2\right)}{35 c^3 \left(a^2 c+d\right)^3 \sqrt{c+d x^2}}-\frac{\left(70 a^4 c^2 d+35 a^6 c^3+56 a^2 c d^2+16 d^3\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{35 c^4 \left(a^2 c+d\right)^{7/2}}+\frac{a \left(11 a^2 c+6 d\right)}{105 c^2 \left(a^2 c+d\right)^2 \left(c+d x^2\right)^{3/2}}+\frac{a}{35 c \left(a^2 c+d\right) \left(c+d x^2\right)^{5/2}}+\frac{16 x \tanh ^{-1}(a x)}{35 c^4 \sqrt{c+d x^2}}+\frac{8 x \tanh ^{-1}(a x)}{35 c^3 \left(c+d x^2\right)^{3/2}}+\frac{6 x \tanh ^{-1}(a x)}{35 c^2 \left(c+d x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(a x)}{7 c \left(c+d x^2\right)^{7/2}}","\frac{a \left(19 a^4 c^2+22 a^2 c d+8 d^2\right)}{35 c^3 \left(a^2 c+d\right)^3 \sqrt{c+d x^2}}-\frac{\left(70 a^4 c^2 d+35 a^6 c^3+56 a^2 c d^2+16 d^3\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{35 c^4 \left(a^2 c+d\right)^{7/2}}+\frac{a \left(11 a^2 c+6 d\right)}{105 c^2 \left(a^2 c+d\right)^2 \left(c+d x^2\right)^{3/2}}+\frac{a}{35 c \left(a^2 c+d\right) \left(c+d x^2\right)^{5/2}}+\frac{16 x \tanh ^{-1}(a x)}{35 c^4 \sqrt{c+d x^2}}+\frac{8 x \tanh ^{-1}(a x)}{35 c^3 \left(c+d x^2\right)^{3/2}}+\frac{6 x \tanh ^{-1}(a x)}{35 c^2 \left(c+d x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(a x)}{7 c \left(c+d x^2\right)^{7/2}}",1,"a/(35*c*(a^2*c + d)*(c + d*x^2)^(5/2)) + (a*(11*a^2*c + 6*d))/(105*c^2*(a^2*c + d)^2*(c + d*x^2)^(3/2)) + (a*(19*a^4*c^2 + 22*a^2*c*d + 8*d^2))/(35*c^3*(a^2*c + d)^3*Sqrt[c + d*x^2]) + (x*ArcTanh[a*x])/(7*c*(c + d*x^2)^(7/2)) + (6*x*ArcTanh[a*x])/(35*c^2*(c + d*x^2)^(5/2)) + (8*x*ArcTanh[a*x])/(35*c^3*(c + d*x^2)^(3/2)) + (16*x*ArcTanh[a*x])/(35*c^4*Sqrt[c + d*x^2]) - ((35*a^6*c^3 + 70*a^4*c^2*d + 56*a^2*c*d^2 + 16*d^3)*ArcTanh[(a*Sqrt[c + d*x^2])/Sqrt[a^2*c + d]])/(35*c^4*(a^2*c + d)^(7/2))","A",8,9,16,0.5625,1,"{192, 191, 5976, 6688, 12, 6715, 1619, 63, 208}"
517,1,186,0,0.0880305,"\int \sqrt{a-a x^2} \tanh ^{-1}(x) \, dx","Int[Sqrt[a - a*x^2]*ArcTanh[x],x]","-\frac{i a \sqrt{1-x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{2 \sqrt{a-a x^2}}+\frac{i a \sqrt{1-x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{2 \sqrt{a-a x^2}}+\frac{1}{2} \sqrt{a-a x^2}+\frac{1}{2} x \sqrt{a-a x^2} \tanh ^{-1}(x)-\frac{a \sqrt{1-x^2} \tan ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{x+1}}\right) \tanh ^{-1}(x)}{\sqrt{a-a x^2}}","-\frac{i a \sqrt{1-x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{2 \sqrt{a-a x^2}}+\frac{i a \sqrt{1-x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{2 \sqrt{a-a x^2}}+\frac{1}{2} \sqrt{a-a x^2}+\frac{1}{2} x \sqrt{a-a x^2} \tanh ^{-1}(x)-\frac{a \sqrt{1-x^2} \tan ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{x+1}}\right) \tanh ^{-1}(x)}{\sqrt{a-a x^2}}",1,"Sqrt[a - a*x^2]/2 + (x*Sqrt[a - a*x^2]*ArcTanh[x])/2 - (a*Sqrt[1 - x^2]*ArcTan[Sqrt[1 - x]/Sqrt[1 + x]]*ArcTanh[x])/Sqrt[a - a*x^2] - ((I/2)*a*Sqrt[1 - x^2]*PolyLog[2, ((-I)*Sqrt[1 - x])/Sqrt[1 + x]])/Sqrt[a - a*x^2] + ((I/2)*a*Sqrt[1 - x^2]*PolyLog[2, (I*Sqrt[1 - x])/Sqrt[1 + x]])/Sqrt[a - a*x^2]","A",3,3,15,0.2000,1,"{5942, 5954, 5950}"
518,1,144,0,0.0543704,"\int \frac{\tanh ^{-1}(x)}{\sqrt{a-a x^2}} \, dx","Int[ArcTanh[x]/Sqrt[a - a*x^2],x]","-\frac{i \sqrt{1-x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{\sqrt{a-a x^2}}+\frac{i \sqrt{1-x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{\sqrt{a-a x^2}}-\frac{2 \sqrt{1-x^2} \tan ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{x+1}}\right) \tanh ^{-1}(x)}{\sqrt{a-a x^2}}","-\frac{i \sqrt{1-x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{\sqrt{a-a x^2}}+\frac{i \sqrt{1-x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{\sqrt{a-a x^2}}-\frac{2 \sqrt{1-x^2} \tan ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{x+1}}\right) \tanh ^{-1}(x)}{\sqrt{a-a x^2}}",1,"(-2*Sqrt[1 - x^2]*ArcTan[Sqrt[1 - x]/Sqrt[1 + x]]*ArcTanh[x])/Sqrt[a - a*x^2] - (I*Sqrt[1 - x^2]*PolyLog[2, ((-I)*Sqrt[1 - x])/Sqrt[1 + x]])/Sqrt[a - a*x^2] + (I*Sqrt[1 - x^2]*PolyLog[2, (I*Sqrt[1 - x])/Sqrt[1 + x]])/Sqrt[a - a*x^2]","A",2,2,15,0.1333,1,"{5954, 5950}"
519,1,37,0,0.0245407,"\int \frac{\tanh ^{-1}(x)}{\left(a-a x^2\right)^{3/2}} \, dx","Int[ArcTanh[x]/(a - a*x^2)^(3/2),x]","\frac{x \tanh ^{-1}(x)}{a \sqrt{a-a x^2}}-\frac{1}{a \sqrt{a-a x^2}}","\frac{x \tanh ^{-1}(x)}{a \sqrt{a-a x^2}}-\frac{1}{a \sqrt{a-a x^2}}",1,"-(1/(a*Sqrt[a - a*x^2])) + (x*ArcTanh[x])/(a*Sqrt[a - a*x^2])","A",1,1,15,0.06667,1,"{5958}"
520,1,83,0,0.0526752,"\int \frac{\tanh ^{-1}(x)}{\left(a-a x^2\right)^{5/2}} \, dx","Int[ArcTanh[x]/(a - a*x^2)^(5/2),x]","-\frac{2}{3 a^2 \sqrt{a-a x^2}}+\frac{2 x \tanh ^{-1}(x)}{3 a^2 \sqrt{a-a x^2}}-\frac{1}{9 a \left(a-a x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(x)}{3 a \left(a-a x^2\right)^{3/2}}","-\frac{2}{3 a^2 \sqrt{a-a x^2}}+\frac{2 x \tanh ^{-1}(x)}{3 a^2 \sqrt{a-a x^2}}-\frac{1}{9 a \left(a-a x^2\right)^{3/2}}+\frac{x \tanh ^{-1}(x)}{3 a \left(a-a x^2\right)^{3/2}}",1,"-1/(9*a*(a - a*x^2)^(3/2)) - 2/(3*a^2*Sqrt[a - a*x^2]) + (x*ArcTanh[x])/(3*a*(a - a*x^2)^(3/2)) + (2*x*ArcTanh[x])/(3*a^2*Sqrt[a - a*x^2])","A",2,2,15,0.1333,1,"{5960, 5958}"
521,1,124,0,0.0816819,"\int \frac{\tanh ^{-1}(x)}{\left(a-a x^2\right)^{7/2}} \, dx","Int[ArcTanh[x]/(a - a*x^2)^(7/2),x]","-\frac{8}{15 a^3 \sqrt{a-a x^2}}-\frac{4}{45 a^2 \left(a-a x^2\right)^{3/2}}+\frac{8 x \tanh ^{-1}(x)}{15 a^3 \sqrt{a-a x^2}}+\frac{4 x \tanh ^{-1}(x)}{15 a^2 \left(a-a x^2\right)^{3/2}}-\frac{1}{25 a \left(a-a x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(x)}{5 a \left(a-a x^2\right)^{5/2}}","-\frac{8}{15 a^3 \sqrt{a-a x^2}}-\frac{4}{45 a^2 \left(a-a x^2\right)^{3/2}}+\frac{8 x \tanh ^{-1}(x)}{15 a^3 \sqrt{a-a x^2}}+\frac{4 x \tanh ^{-1}(x)}{15 a^2 \left(a-a x^2\right)^{3/2}}-\frac{1}{25 a \left(a-a x^2\right)^{5/2}}+\frac{x \tanh ^{-1}(x)}{5 a \left(a-a x^2\right)^{5/2}}",1,"-1/(25*a*(a - a*x^2)^(5/2)) - 4/(45*a^2*(a - a*x^2)^(3/2)) - 8/(15*a^3*Sqrt[a - a*x^2]) + (x*ArcTanh[x])/(5*a*(a - a*x^2)^(5/2)) + (4*x*ArcTanh[x])/(15*a^2*(a - a*x^2)^(3/2)) + (8*x*ArcTanh[x])/(15*a^3*Sqrt[a - a*x^2])","A",3,2,15,0.1333,1,"{5960, 5958}"
522,1,315,0,0.7761199,"\int x^4 \left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right) \, dx","Int[x^4*(a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]),x]","\frac{1}{5} x^5 \left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e (4 a+3 b) \log (1-c x)}{20 c^5}+\frac{e (4 a-3 b) \log (c x+1)}{20 c^5}-\frac{2 a e x^3}{15 c^2}-\frac{2 a e x}{5 c^4}-\frac{2}{25} a e x^5+\frac{b x^4 \left(e \log \left(1-c^2 x^2\right)+d\right)}{20 c}+\frac{b x^2 \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 c^3}+\frac{b \log \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 c^5}-\frac{77 b e x^2}{300 c^3}-\frac{b e \log ^2\left(1-c^2 x^2\right)}{20 c^5}-\frac{23 b e \log \left(1-c^2 x^2\right)}{75 c^5}-\frac{2 b e x^3 \tanh ^{-1}(c x)}{15 c^2}-\frac{2 b e x \tanh ^{-1}(c x)}{5 c^4}+\frac{b e \tanh ^{-1}(c x)^2}{5 c^5}-\frac{9 b e x^4}{200 c}-\frac{2}{25} b e x^5 \tanh ^{-1}(c x)","\frac{1}{5} x^5 \left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e (4 a+3 b) \log (1-c x)}{20 c^5}+\frac{e (4 a-3 b) \log (c x+1)}{20 c^5}-\frac{2 a e x^3}{15 c^2}-\frac{2 a e x}{5 c^4}-\frac{2}{25} a e x^5+\frac{b x^4 \left(e \log \left(1-c^2 x^2\right)+d\right)}{20 c}+\frac{b x^2 \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 c^3}+\frac{b \log \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 c^5}-\frac{77 b e x^2}{300 c^3}-\frac{b e \log ^2\left(1-c^2 x^2\right)}{20 c^5}-\frac{23 b e \log \left(1-c^2 x^2\right)}{75 c^5}-\frac{2 b e x^3 \tanh ^{-1}(c x)}{15 c^2}-\frac{2 b e x \tanh ^{-1}(c x)}{5 c^4}+\frac{b e \tanh ^{-1}(c x)^2}{5 c^5}-\frac{9 b e x^4}{200 c}-\frac{2}{25} b e x^5 \tanh ^{-1}(c x)",1,"(-2*a*e*x)/(5*c^4) - (77*b*e*x^2)/(300*c^3) - (2*a*e*x^3)/(15*c^2) - (9*b*e*x^4)/(200*c) - (2*a*e*x^5)/25 - (2*b*e*x*ArcTanh[c*x])/(5*c^4) - (2*b*e*x^3*ArcTanh[c*x])/(15*c^2) - (2*b*e*x^5*ArcTanh[c*x])/25 + (b*e*ArcTanh[c*x]^2)/(5*c^5) - ((4*a + 3*b)*e*Log[1 - c*x])/(20*c^5) + ((4*a - 3*b)*e*Log[1 + c*x])/(20*c^5) - (23*b*e*Log[1 - c^2*x^2])/(75*c^5) - (b*e*Log[1 - c^2*x^2]^2)/(20*c^5) + (b*x^2*(d + e*Log[1 - c^2*x^2]))/(10*c^3) + (b*x^4*(d + e*Log[1 - c^2*x^2]))/(20*c) + (x^5*(a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/5 + (b*Log[1 - c^2*x^2]*(d + e*Log[1 - c^2*x^2]))/(10*c^5)","A",26,15,27,0.5556,1,"{5916, 266, 43, 6085, 6725, 1802, 633, 31, 5980, 5910, 260, 5948, 2475, 2390, 2301}"
523,1,225,0,0.2693206,"\int x^3 \left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right) \, dx","Int[x^3*(a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]),x]","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e x^2 \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2}-\frac{e \log \left(1-c^2 x^2\right) \left(a+b \tanh ^{-1}(c x)\right)}{4 c^4}-\frac{1}{8} e x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b x (2 d-3 e)}{8 c^3}-\frac{b (2 d-3 e) \tanh ^{-1}(c x)}{8 c^4}+\frac{b e x^3 \log \left(1-c^2 x^2\right)}{12 c}+\frac{b e x \log \left(1-c^2 x^2\right)}{4 c^3}-\frac{2 b e x}{3 c^3}+\frac{2 b e \tanh ^{-1}(c x)}{3 c^4}+\frac{b x^3 (2 d-e)}{24 c}-\frac{b e x^3}{18 c}","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e x^2 \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2}-\frac{e \log \left(1-c^2 x^2\right) \left(a+b \tanh ^{-1}(c x)\right)}{4 c^4}-\frac{1}{8} e x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b x (2 d-3 e)}{8 c^3}-\frac{b (2 d-3 e) \tanh ^{-1}(c x)}{8 c^4}+\frac{b e x^3 \log \left(1-c^2 x^2\right)}{12 c}+\frac{b e x \log \left(1-c^2 x^2\right)}{4 c^3}-\frac{2 b e x}{3 c^3}+\frac{2 b e \tanh ^{-1}(c x)}{3 c^4}+\frac{b x^3 (2 d-e)}{24 c}-\frac{b e x^3}{18 c}",1,"(b*(2*d - 3*e)*x)/(8*c^3) - (2*b*e*x)/(3*c^3) + (b*(2*d - e)*x^3)/(24*c) - (b*e*x^3)/(18*c) - (b*(2*d - 3*e)*ArcTanh[c*x])/(8*c^4) + (2*b*e*ArcTanh[c*x])/(3*c^4) - (e*x^2*(a + b*ArcTanh[c*x]))/(4*c^2) - (e*x^4*(a + b*ArcTanh[c*x]))/8 + (b*e*x*Log[1 - c^2*x^2])/(4*c^3) + (b*e*x^3*Log[1 - c^2*x^2])/(12*c) - (e*(a + b*ArcTanh[c*x])*Log[1 - c^2*x^2])/(4*c^4) + (x^4*(a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/4","A",14,11,27,0.4074,1,"{2454, 2395, 43, 6083, 459, 321, 206, 2471, 2448, 2455, 302}"
524,1,247,0,0.6335441,"\int x^2 \left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right) \, dx","Int[x^2*(a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]),x]","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e (2 a+b) \log (1-c x)}{6 c^3}+\frac{e (2 a-b) \log (c x+1)}{6 c^3}-\frac{2 a e x}{3 c^2}-\frac{2}{9} a e x^3+\frac{b x^2 \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 c}+\frac{b \log \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 c^3}-\frac{b e \log ^2\left(1-c^2 x^2\right)}{12 c^3}-\frac{4 b e \log \left(1-c^2 x^2\right)}{9 c^3}-\frac{2 b e x \tanh ^{-1}(c x)}{3 c^2}+\frac{b e \tanh ^{-1}(c x)^2}{3 c^3}-\frac{5 b e x^2}{18 c}-\frac{2}{9} b e x^3 \tanh ^{-1}(c x)","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e (2 a+b) \log (1-c x)}{6 c^3}+\frac{e (2 a-b) \log (c x+1)}{6 c^3}-\frac{2 a e x}{3 c^2}-\frac{2}{9} a e x^3+\frac{b x^2 \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 c}+\frac{b \log \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 c^3}-\frac{b e \log ^2\left(1-c^2 x^2\right)}{12 c^3}-\frac{4 b e \log \left(1-c^2 x^2\right)}{9 c^3}-\frac{2 b e x \tanh ^{-1}(c x)}{3 c^2}+\frac{b e \tanh ^{-1}(c x)^2}{3 c^3}-\frac{5 b e x^2}{18 c}-\frac{2}{9} b e x^3 \tanh ^{-1}(c x)",1,"(-2*a*e*x)/(3*c^2) - (5*b*e*x^2)/(18*c) - (2*a*e*x^3)/9 - (2*b*e*x*ArcTanh[c*x])/(3*c^2) - (2*b*e*x^3*ArcTanh[c*x])/9 + (b*e*ArcTanh[c*x]^2)/(3*c^3) - ((2*a + b)*e*Log[1 - c*x])/(6*c^3) + ((2*a - b)*e*Log[1 + c*x])/(6*c^3) - (4*b*e*Log[1 - c^2*x^2])/(9*c^3) - (b*e*Log[1 - c^2*x^2]^2)/(12*c^3) + (b*x^2*(d + e*Log[1 - c^2*x^2]))/(6*c) + (x^3*(a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/3 + (b*Log[1 - c^2*x^2]*(d + e*Log[1 - c^2*x^2]))/(6*c^3)","A",21,15,27,0.5556,1,"{5916, 266, 43, 6085, 6725, 801, 633, 31, 5980, 5910, 260, 5948, 2475, 2390, 2301}"
525,1,140,0,0.1188216,"\int x \left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right) \, dx","Int[x*(a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]),x]","-\frac{e \left(1-c^2 x^2\right) \log \left(1-c^2 x^2\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 c^2}+\frac{1}{2} d x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{1}{2} e x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{b (d-e) \tanh ^{-1}(c x)}{2 c^2}+\frac{b e x \log \left(1-c^2 x^2\right)}{2 c}+\frac{b e \tanh ^{-1}(c x)}{c^2}+\frac{b x (d-e)}{2 c}-\frac{b e x}{c}","-\frac{e \left(1-c^2 x^2\right) \log \left(1-c^2 x^2\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 c^2}+\frac{1}{2} d x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{1}{2} e x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{b (d-e) \tanh ^{-1}(c x)}{2 c^2}+\frac{b e x \log \left(1-c^2 x^2\right)}{2 c}+\frac{b e \tanh ^{-1}(c x)}{c^2}+\frac{b x (d-e)}{2 c}-\frac{b e x}{c}",1,"(b*(d - e)*x)/(2*c) - (b*e*x)/c - (b*(d - e)*ArcTanh[c*x])/(2*c^2) + (b*e*ArcTanh[c*x])/c^2 + (d*x^2*(a + b*ArcTanh[c*x]))/2 - (e*x^2*(a + b*ArcTanh[c*x]))/2 + (b*e*x*Log[1 - c^2*x^2])/(2*c) - (e*(1 - c^2*x^2)*(a + b*ArcTanh[c*x])*Log[1 - c^2*x^2])/(2*c^2)","A",7,8,25,0.3200,1,"{2454, 2389, 2295, 6083, 321, 207, 2448, 206}"
526,1,104,0,0.1950377,"\int \left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right) \, dx","Int[(a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]),x]","x \left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)+\frac{e \left(a+b \tanh ^{-1}(c x)\right)^2}{b c}-2 a e x+\frac{b \left(e \log \left(1-c^2 x^2\right)+d\right)^2}{4 c e}-\frac{b e \log \left(1-c^2 x^2\right)}{c}-2 b e x \tanh ^{-1}(c x)","x \left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)+\frac{e \left(a+b \tanh ^{-1}(c x)\right)^2}{b c}-2 a e x+\frac{b \left(e \log \left(1-c^2 x^2\right)+d\right)^2}{4 c e}-\frac{b e \log \left(1-c^2 x^2\right)}{c}-2 b e x \tanh ^{-1}(c x)",1,"-2*a*e*x - 2*b*e*x*ArcTanh[c*x] + (e*(a + b*ArcTanh[c*x])^2)/(b*c) - (b*e*Log[1 - c^2*x^2])/c + x*(a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]) + (b*(d + e*Log[1 - c^2*x^2])^2)/(4*c*e)","A",9,8,24,0.3333,1,"{6073, 2475, 2390, 2301, 5980, 5910, 260, 5948}"
527,1,216,0,0.2801805,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x} \, dx","Int[((a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/x,x]","-\frac{1}{2} a e \text{PolyLog}\left(2,c^2 x^2\right)+\frac{1}{2} b e \left(-\log \left(1-c^2 x^2\right)+\log (1-c x)+\log (c x+1)\right) \text{PolyLog}(2,-c x)-\frac{1}{2} b e \left(-\log \left(1-c^2 x^2\right)+\log (1-c x)+\log (c x+1)\right) \text{PolyLog}(2,c x)-\frac{1}{2} b d \text{PolyLog}(2,-c x)+\frac{1}{2} b d \text{PolyLog}(2,c x)+b e \text{PolyLog}(3,1-c x)-b e \text{PolyLog}(3,c x+1)-b e \log (1-c x) \text{PolyLog}(2,1-c x)+b e \log (c x+1) \text{PolyLog}(2,c x+1)+a d \log (x)-\frac{1}{2} b e \log (c x) \log ^2(1-c x)+\frac{1}{2} b e \log (-c x) \log ^2(c x+1)","-\frac{1}{2} a e \text{PolyLog}\left(2,c^2 x^2\right)+\frac{1}{2} b e \left(-\log \left(1-c^2 x^2\right)+\log (1-c x)+\log (c x+1)\right) \text{PolyLog}(2,-c x)-\frac{1}{2} b e \left(-\log \left(1-c^2 x^2\right)+\log (1-c x)+\log (c x+1)\right) \text{PolyLog}(2,c x)-\frac{1}{2} b d \text{PolyLog}(2,-c x)+\frac{1}{2} b d \text{PolyLog}(2,c x)+b e \text{PolyLog}(3,1-c x)-b e \text{PolyLog}(3,c x+1)-b e \log (1-c x) \text{PolyLog}(2,1-c x)+b e \log (c x+1) \text{PolyLog}(2,c x+1)+a d \log (x)-\frac{1}{2} b e \log (c x) \log ^2(1-c x)+\frac{1}{2} b e \log (-c x) \log ^2(c x+1)",1,"a*d*Log[x] - (b*e*Log[c*x]*Log[1 - c*x]^2)/2 + (b*e*Log[-(c*x)]*Log[1 + c*x]^2)/2 - (b*d*PolyLog[2, -(c*x)])/2 + (b*e*(Log[1 - c*x] + Log[1 + c*x] - Log[1 - c^2*x^2])*PolyLog[2, -(c*x)])/2 + (b*d*PolyLog[2, c*x])/2 - (b*e*(Log[1 - c*x] + Log[1 + c*x] - Log[1 - c^2*x^2])*PolyLog[2, c*x])/2 - (a*e*PolyLog[2, c^2*x^2])/2 - b*e*Log[1 - c*x]*PolyLog[2, 1 - c*x] + b*e*Log[1 + c*x]*PolyLog[2, 1 + c*x] + b*e*PolyLog[3, 1 - c*x] - b*e*PolyLog[3, 1 + c*x]","A",14,9,27,0.3333,1,"{6079, 5912, 6077, 2391, 6075, 2396, 2433, 2374, 6589}"
528,1,94,0,0.2559076,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x^2} \, dx","Int[((a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/x^2,x]","-\frac{1}{2} b c e \text{PolyLog}\left(2,c^2 x^2\right)-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{x}-\frac{c e \left(a+b \tanh ^{-1}(c x)\right)^2}{b}-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)^2}{4 e}+b c d \log (x)","-\frac{1}{2} b c e \text{PolyLog}\left(2,\frac{1}{1-c^2 x^2}\right)-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{x}-\frac{c e \left(a+b \tanh ^{-1}(c x)\right)^2}{b}+\frac{1}{2} b c \log \left(1-\frac{1}{1-c^2 x^2}\right) \left(e \log \left(1-c^2 x^2\right)+d\right)",1,"-((c*e*(a + b*ArcTanh[c*x])^2)/b) + b*c*d*Log[x] - ((a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/x - (b*c*(d + e*Log[1 - c^2*x^2])^2)/(4*e) - (b*c*e*PolyLog[2, c^2*x^2])/2","A",8,8,27,0.2963,1,"{6081, 2475, 2411, 2344, 2301, 2316, 2315, 5948}"
529,1,157,0,0.1402021,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x^3} \, dx","Int[((a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/x^3,x]","\frac{1}{2} b c^2 e \text{PolyLog}(2,-c x)-\frac{1}{2} b c^2 e \text{PolyLog}(2,c x)-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{2 x^2}+\frac{1}{2} c^2 e (a+b) \log (1-c x)+\frac{1}{2} c^2 e (a-b) \log (c x+1)-a c^2 e \log (x)-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{2 x}+\frac{1}{2} b c^2 \tanh ^{-1}(c x) \left(e \log \left(1-c^2 x^2\right)+d\right)","\frac{1}{2} b c^2 e \text{PolyLog}(2,-c x)-\frac{1}{2} b c^2 e \text{PolyLog}(2,c x)-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{2 x^2}+\frac{1}{2} c^2 e (a+b) \log (1-c x)+\frac{1}{2} c^2 e (a-b) \log (c x+1)-a c^2 e \log (x)-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{2 x}+\frac{1}{2} b c^2 \tanh ^{-1}(c x) \left(e \log \left(1-c^2 x^2\right)+d\right)",1,"-(a*c^2*e*Log[x]) + ((a + b)*c^2*e*Log[1 - c*x])/2 + ((a - b)*c^2*e*Log[1 + c*x])/2 - (b*c*(d + e*Log[1 - c^2*x^2]))/(2*x) + (b*c^2*ArcTanh[c*x]*(d + e*Log[1 - c^2*x^2]))/2 - ((a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/(2*x^2) + (b*c^2*e*PolyLog[2, -(c*x)])/2 - (b*c^2*e*PolyLog[2, c*x])/2","A",5,6,27,0.2222,1,"{5916, 325, 206, 6085, 801, 5912}"
530,1,191,0,0.4646096,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x^4} \, dx","Int[((a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/x^4,x]","-\frac{1}{6} b c^3 e \text{PolyLog}\left(2,c^2 x^2\right)-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{3 x^3}-\frac{c^3 e \left(a+b \tanh ^{-1}(c x)\right)^2}{3 b}+\frac{2 c^2 e \left(a+b \tanh ^{-1}(c x)\right)}{3 x}-\frac{b c^3 \left(e \log \left(1-c^2 x^2\right)+d\right)^2}{12 e}-\frac{b c \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 x^2}+\frac{1}{3} b c^3 d \log (x)+\frac{1}{3} b c^3 e \log \left(1-c^2 x^2\right)-b c^3 e \log (x)","-\frac{1}{6} b c^3 e \text{PolyLog}\left(2,\frac{1}{1-c^2 x^2}\right)-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{3 x^3}-\frac{c^3 e \left(a+b \tanh ^{-1}(c x)\right)^2}{3 b}+\frac{2 c^2 e \left(a+b \tanh ^{-1}(c x)\right)}{3 x}+\frac{1}{6} b c^3 \log \left(1-\frac{1}{1-c^2 x^2}\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{b c \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 x^2}+\frac{1}{3} b c^3 e \log \left(1-c^2 x^2\right)-b c^3 e \log (x)",1,"(2*c^2*e*(a + b*ArcTanh[c*x]))/(3*x) - (c^3*e*(a + b*ArcTanh[c*x])^2)/(3*b) + (b*c^3*d*Log[x])/3 - b*c^3*e*Log[x] + (b*c^3*e*Log[1 - c^2*x^2])/3 - (b*c*(1 - c^2*x^2)*(d + e*Log[1 - c^2*x^2]))/(6*x^2) - ((a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/(3*x^3) - (b*c^3*(d + e*Log[1 - c^2*x^2])^2)/(12*e) - (b*c^3*e*PolyLog[2, c^2*x^2])/6","A",17,16,27,0.5926,1,"{6081, 2475, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 5982, 5916, 266, 36, 29, 5948}"
531,1,244,0,0.2605074,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x^5} \, dx","Int[((a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/x^5,x]","\frac{1}{4} b c^4 e \text{PolyLog}(2,-c x)-\frac{1}{4} b c^4 e \text{PolyLog}(2,c x)-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{4 x^4}+\frac{1}{12} c^4 e (3 a+4 b) \log (1-c x)+\frac{1}{12} c^4 e (3 a-4 b) \log (c x+1)+\frac{a c^2 e}{4 x^2}-\frac{1}{2} a c^4 e \log (x)-\frac{b c^3 \left(e \log \left(1-c^2 x^2\right)+d\right)}{4 x}-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{12 x^3}+\frac{1}{4} b c^4 \tanh ^{-1}(c x) \left(e \log \left(1-c^2 x^2\right)+d\right)+\frac{b c^2 e \tanh ^{-1}(c x)}{4 x^2}+\frac{5 b c^3 e}{12 x}-\frac{1}{4} b c^4 e \tanh ^{-1}(c x)","\frac{1}{4} b c^4 e \text{PolyLog}(2,-c x)-\frac{1}{4} b c^4 e \text{PolyLog}(2,c x)-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{4 x^4}+\frac{1}{12} c^4 e (3 a+4 b) \log (1-c x)+\frac{1}{12} c^4 e (3 a-4 b) \log (c x+1)+\frac{a c^2 e}{4 x^2}-\frac{1}{2} a c^4 e \log (x)-\frac{b c^3 \left(e \log \left(1-c^2 x^2\right)+d\right)}{4 x}-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{12 x^3}+\frac{1}{4} b c^4 \tanh ^{-1}(c x) \left(e \log \left(1-c^2 x^2\right)+d\right)+\frac{b c^2 e \tanh ^{-1}(c x)}{4 x^2}+\frac{5 b c^3 e}{12 x}-\frac{1}{4} b c^4 e \tanh ^{-1}(c x)",1,"(a*c^2*e)/(4*x^2) + (5*b*c^3*e)/(12*x) - (b*c^4*e*ArcTanh[c*x])/4 + (b*c^2*e*ArcTanh[c*x])/(4*x^2) - (a*c^4*e*Log[x])/2 + ((3*a + 4*b)*c^4*e*Log[1 - c*x])/12 + ((3*a - 4*b)*c^4*e*Log[1 + c*x])/12 - (b*c*(d + e*Log[1 - c^2*x^2]))/(12*x^3) - (b*c^3*(d + e*Log[1 - c^2*x^2]))/(4*x) + (b*c^4*ArcTanh[c*x]*(d + e*Log[1 - c^2*x^2]))/4 - ((a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/(4*x^4) + (b*c^4*e*PolyLog[2, -(c*x)])/4 - (b*c^4*e*PolyLog[2, c*x])/4","A",10,7,27,0.2593,1,"{5916, 325, 206, 6085, 1802, 6044, 5912}"
532,1,250,0,0.6644239,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x^6} \, dx","Int[((a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/x^6,x]","-\frac{1}{10} b c^5 e \text{PolyLog}\left(2,c^2 x^2\right)-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{5 x^5}+\frac{2 c^2 e \left(a+b \tanh ^{-1}(c x)\right)}{15 x^3}-\frac{c^5 e \left(a+b \tanh ^{-1}(c x)\right)^2}{5 b}+\frac{2 c^4 e \left(a+b \tanh ^{-1}(c x)\right)}{5 x}-\frac{b c^5 \left(e \log \left(1-c^2 x^2\right)+d\right)^2}{20 e}-\frac{b c^3 \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 x^2}-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{20 x^4}+\frac{1}{5} b c^5 d \log (x)+\frac{7 b c^3 e}{60 x^2}+\frac{19}{60} b c^5 e \log \left(1-c^2 x^2\right)-\frac{5}{6} b c^5 e \log (x)","-\frac{1}{10} b c^5 e \text{PolyLog}\left(2,\frac{1}{1-c^2 x^2}\right)-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{5 x^5}+\frac{2 c^2 e \left(a+b \tanh ^{-1}(c x)\right)}{15 x^3}-\frac{c^5 e \left(a+b \tanh ^{-1}(c x)\right)^2}{5 b}+\frac{2 c^4 e \left(a+b \tanh ^{-1}(c x)\right)}{5 x}+\frac{1}{10} b c^5 \log \left(1-\frac{1}{1-c^2 x^2}\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{b c^3 \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 x^2}-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{20 x^4}+\frac{7 b c^3 e}{60 x^2}+\frac{19}{60} b c^5 e \log \left(1-c^2 x^2\right)-\frac{5}{6} b c^5 e \log (x)",1,"(7*b*c^3*e)/(60*x^2) + (2*c^2*e*(a + b*ArcTanh[c*x]))/(15*x^3) + (2*c^4*e*(a + b*ArcTanh[c*x]))/(5*x) - (c^5*e*(a + b*ArcTanh[c*x])^2)/(5*b) + (b*c^5*d*Log[x])/5 - (5*b*c^5*e*Log[x])/6 + (19*b*c^5*e*Log[1 - c^2*x^2])/60 - (b*c*(d + e*Log[1 - c^2*x^2]))/(20*x^4) - (b*c^3*(1 - c^2*x^2)*(d + e*Log[1 - c^2*x^2]))/(10*x^2) - ((a + b*ArcTanh[c*x])*(d + e*Log[1 - c^2*x^2]))/(5*x^5) - (b*c^5*(d + e*Log[1 - c^2*x^2])^2)/(20*e) - (b*c^5*e*PolyLog[2, c^2*x^2])/10","A",26,18,27,0.6667,1,"{6081, 2475, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2319, 44, 5982, 5916, 266, 36, 29, 5948}"
533,1,512,0,0.7627148,"\int x \left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right) \, dx","Int[x*(a + b*ArcTanh[c*x])*(d + e*Log[f + g*x^2]),x]","\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^2 g}-\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{4 c^2 g}-\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{4 c^2 g}+\frac{1}{2} d x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{e \left(f+g x^2\right) \log \left(f+g x^2\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 g}-\frac{1}{2} e x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{b (d-e) \tanh ^{-1}(c x)}{2 c^2}-\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(f+g x^2\right)}{2 c^2 g}-\frac{b e \left(c^2 f+g\right) \log \left(\frac{2}{c x+1}\right) \tanh ^{-1}(c x)}{c^2 g}+\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{2 c^2 g}+\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{2 c^2 g}+\frac{b x (d-e)}{2 c}+\frac{b e x \log \left(f+g x^2\right)}{2 c}+\frac{b e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{c \sqrt{g}}-\frac{b e x}{c}","\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^2 g}-\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{4 c^2 g}-\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{4 c^2 g}+\frac{1}{2} d x^2 \left(a+b \tanh ^{-1}(c x)\right)+\frac{e \left(f+g x^2\right) \log \left(f+g x^2\right) \left(a+b \tanh ^{-1}(c x)\right)}{2 g}-\frac{1}{2} e x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{b (d-e) \tanh ^{-1}(c x)}{2 c^2}-\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(f+g x^2\right)}{2 c^2 g}-\frac{b e \left(c^2 f+g\right) \log \left(\frac{2}{c x+1}\right) \tanh ^{-1}(c x)}{c^2 g}+\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{2 c^2 g}+\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{2 c^2 g}+\frac{b x (d-e)}{2 c}+\frac{b e x \log \left(f+g x^2\right)}{2 c}+\frac{b e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{c \sqrt{g}}-\frac{b e x}{c}",1,"(b*(d - e)*x)/(2*c) - (b*e*x)/c + (b*e*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/(c*Sqrt[g]) - (b*(d - e)*ArcTanh[c*x])/(2*c^2) + (d*x^2*(a + b*ArcTanh[c*x]))/2 - (e*x^2*(a + b*ArcTanh[c*x]))/2 - (b*e*(c^2*f + g)*ArcTanh[c*x]*Log[2/(1 + c*x)])/(c^2*g) + (b*e*(c^2*f + g)*ArcTanh[c*x]*Log[(2*c*(Sqrt[-f] - Sqrt[g]*x))/((c*Sqrt[-f] - Sqrt[g])*(1 + c*x))])/(2*c^2*g) + (b*e*(c^2*f + g)*ArcTanh[c*x]*Log[(2*c*(Sqrt[-f] + Sqrt[g]*x))/((c*Sqrt[-f] + Sqrt[g])*(1 + c*x))])/(2*c^2*g) + (b*e*x*Log[f + g*x^2])/(2*c) - (b*e*(c^2*f + g)*ArcTanh[c*x]*Log[f + g*x^2])/(2*c^2*g) + (e*(f + g*x^2)*(a + b*ArcTanh[c*x])*Log[f + g*x^2])/(2*g) + (b*e*(c^2*f + g)*PolyLog[2, 1 - 2/(1 + c*x)])/(2*c^2*g) - (b*e*(c^2*f + g)*PolyLog[2, 1 - (2*c*(Sqrt[-f] - Sqrt[g]*x))/((c*Sqrt[-f] - Sqrt[g])*(1 + c*x))])/(4*c^2*g) - (b*e*(c^2*f + g)*PolyLog[2, 1 - (2*c*(Sqrt[-f] + Sqrt[g]*x))/((c*Sqrt[-f] + Sqrt[g])*(1 + c*x))])/(4*c^2*g)","A",22,17,22,0.7727,1,"{2454, 2389, 2295, 6083, 321, 207, 517, 2528, 2448, 205, 2470, 12, 5992, 5920, 2402, 2315, 2447}"
534,1,599,0,0.7973108,"\int \left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right) \, dx","Int[(a + b*ArcTanh[c*x])*(d + e*Log[f + g*x^2]),x]","\frac{b e \text{PolyLog}\left(2,\frac{c^2 \left(f+g x^2\right)}{c^2 f+g}\right)}{2 c}+\frac{b e \sqrt{-f} \text{PolyLog}\left(2,-\frac{\sqrt{g} (1-c x)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{g}}-\frac{b e \sqrt{-f} \text{PolyLog}\left(2,\frac{\sqrt{g} (1-c x)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{g}}+\frac{b e \sqrt{-f} \text{PolyLog}\left(2,-\frac{\sqrt{g} (c x+1)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{g}}-\frac{b e \sqrt{-f} \text{PolyLog}\left(2,\frac{\sqrt{g} (c x+1)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{g}}+x \left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)+\frac{2 a e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{g}}-2 a e x+\frac{b \log \left(\frac{g \left(1-c^2 x^2\right)}{c^2 f+g}\right) \left(d+e \log \left(f+g x^2\right)\right)}{2 c}-\frac{b e \log \left(1-c^2 x^2\right)}{c}+\frac{b e \sqrt{-f} \log (1-c x) \log \left(\frac{c \left(\sqrt{-f}-\sqrt{g} x\right)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{g}}-\frac{b e \sqrt{-f} \log (c x+1) \log \left(\frac{c \left(\sqrt{-f}-\sqrt{g} x\right)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{g}}+\frac{b e \sqrt{-f} \log (c x+1) \log \left(\frac{c \left(\sqrt{-f}+\sqrt{g} x\right)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{g}}-\frac{b e \sqrt{-f} \log (1-c x) \log \left(\frac{c \left(\sqrt{-f}+\sqrt{g} x\right)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{g}}-2 b e x \tanh ^{-1}(c x)","\frac{b e \text{PolyLog}\left(2,\frac{c^2 \left(f+g x^2\right)}{c^2 f+g}\right)}{2 c}+\frac{b e \sqrt{-f} \text{PolyLog}\left(2,-\frac{\sqrt{g} (1-c x)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{g}}-\frac{b e \sqrt{-f} \text{PolyLog}\left(2,\frac{\sqrt{g} (1-c x)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{g}}+\frac{b e \sqrt{-f} \text{PolyLog}\left(2,-\frac{\sqrt{g} (c x+1)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{g}}-\frac{b e \sqrt{-f} \text{PolyLog}\left(2,\frac{\sqrt{g} (c x+1)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{g}}+x \left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)+\frac{2 a e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{g}}-2 a e x+\frac{b \log \left(\frac{g \left(1-c^2 x^2\right)}{c^2 f+g}\right) \left(d+e \log \left(f+g x^2\right)\right)}{2 c}-\frac{b e \log \left(1-c^2 x^2\right)}{c}+\frac{b e \sqrt{-f} \log (1-c x) \log \left(\frac{c \left(\sqrt{-f}-\sqrt{g} x\right)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{g}}-\frac{b e \sqrt{-f} \log (c x+1) \log \left(\frac{c \left(\sqrt{-f}-\sqrt{g} x\right)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{g}}+\frac{b e \sqrt{-f} \log (c x+1) \log \left(\frac{c \left(\sqrt{-f}+\sqrt{g} x\right)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{g}}-\frac{b e \sqrt{-f} \log (1-c x) \log \left(\frac{c \left(\sqrt{-f}+\sqrt{g} x\right)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{g}}-2 b e x \tanh ^{-1}(c x)",1,"-2*a*e*x + (2*a*e*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/Sqrt[g] - 2*b*e*x*ArcTanh[c*x] + (b*e*Sqrt[-f]*Log[1 - c*x]*Log[(c*(Sqrt[-f] - Sqrt[g]*x))/(c*Sqrt[-f] - Sqrt[g])])/(2*Sqrt[g]) - (b*e*Sqrt[-f]*Log[1 + c*x]*Log[(c*(Sqrt[-f] - Sqrt[g]*x))/(c*Sqrt[-f] + Sqrt[g])])/(2*Sqrt[g]) + (b*e*Sqrt[-f]*Log[1 + c*x]*Log[(c*(Sqrt[-f] + Sqrt[g]*x))/(c*Sqrt[-f] - Sqrt[g])])/(2*Sqrt[g]) - (b*e*Sqrt[-f]*Log[1 - c*x]*Log[(c*(Sqrt[-f] + Sqrt[g]*x))/(c*Sqrt[-f] + Sqrt[g])])/(2*Sqrt[g]) - (b*e*Log[1 - c^2*x^2])/c + x*(a + b*ArcTanh[c*x])*(d + e*Log[f + g*x^2]) + (b*Log[(g*(1 - c^2*x^2))/(c^2*f + g)]*(d + e*Log[f + g*x^2]))/(2*c) + (b*e*Sqrt[-f]*PolyLog[2, -((Sqrt[g]*(1 - c*x))/(c*Sqrt[-f] - Sqrt[g]))])/(2*Sqrt[g]) - (b*e*Sqrt[-f]*PolyLog[2, (Sqrt[g]*(1 - c*x))/(c*Sqrt[-f] + Sqrt[g])])/(2*Sqrt[g]) + (b*e*Sqrt[-f]*PolyLog[2, -((Sqrt[g]*(1 + c*x))/(c*Sqrt[-f] - Sqrt[g]))])/(2*Sqrt[g]) - (b*e*Sqrt[-f]*PolyLog[2, (Sqrt[g]*(1 + c*x))/(c*Sqrt[-f] + Sqrt[g])])/(2*Sqrt[g]) + (b*e*PolyLog[2, (c^2*(f + g*x^2))/(c^2*f + g)])/(2*c)","A",28,12,21,0.5714,1,"{6073, 2475, 2394, 2393, 2391, 5980, 5910, 260, 5974, 205, 5972, 2409}"
535,0,0,0,0.2523871,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x} \, dx","Int[((a + b*ArcTanh[c*x])*(d + e*Log[f + g*x^2]))/x,x]","\int \frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x} \, dx","\frac{1}{2} a e \text{PolyLog}\left(2,\frac{g x^2}{f}+1\right)-\frac{1}{2} b d \text{PolyLog}(2,-c x)+\frac{1}{2} b d \text{PolyLog}(2,c x)+b e \text{Int}\left(\frac{\tanh ^{-1}(c x) \log \left(f+g x^2\right)}{x},x\right)+a d \log (x)+\frac{1}{2} a e \log \left(-\frac{g x^2}{f}\right) \log \left(f+g x^2\right)",0,"a*d*Log[x] + (a*e*Log[-((g*x^2)/f)]*Log[f + g*x^2])/2 - (b*d*PolyLog[2, -(c*x)])/2 + (b*d*PolyLog[2, c*x])/2 + (a*e*PolyLog[2, 1 + (g*x^2)/f])/2 + b*e*Defer[Int][(ArcTanh[c*x]*Log[f + g*x^2])/x, x]","A",0,0,0,0,-1,"{}"
536,1,613,0,0.7387557,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x^2} \, dx","Int[((a + b*ArcTanh[c*x])*(d + e*Log[f + g*x^2]))/x^2,x]","-\frac{1}{2} b c e \text{PolyLog}\left(2,\frac{c^2 \left(f+g x^2\right)}{c^2 f+g}\right)+\frac{1}{2} b c e \text{PolyLog}\left(2,\frac{g x^2}{f}+1\right)-\frac{b e \sqrt{g} \text{PolyLog}\left(2,-\frac{\sqrt{g} (1-c x)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{-f}}+\frac{b e \sqrt{g} \text{PolyLog}\left(2,\frac{\sqrt{g} (1-c x)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{-f}}-\frac{b e \sqrt{g} \text{PolyLog}\left(2,-\frac{\sqrt{g} (c x+1)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{-f}}+\frac{b e \sqrt{g} \text{PolyLog}\left(2,\frac{\sqrt{g} (c x+1)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{-f}}-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x}+\frac{2 a e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}-\frac{1}{2} b c \log \left(\frac{g \left(1-c^2 x^2\right)}{c^2 f+g}\right) \left(d+e \log \left(f+g x^2\right)\right)+\frac{1}{2} b c \log \left(-\frac{g x^2}{f}\right) \left(d+e \log \left(f+g x^2\right)\right)-\frac{b e \sqrt{g} \log (1-c x) \log \left(\frac{c \left(\sqrt{-f}-\sqrt{g} x\right)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{-f}}+\frac{b e \sqrt{g} \log (c x+1) \log \left(\frac{c \left(\sqrt{-f}-\sqrt{g} x\right)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{-f}}-\frac{b e \sqrt{g} \log (c x+1) \log \left(\frac{c \left(\sqrt{-f}+\sqrt{g} x\right)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{-f}}+\frac{b e \sqrt{g} \log (1-c x) \log \left(\frac{c \left(\sqrt{-f}+\sqrt{g} x\right)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{-f}}","-\frac{1}{2} b c e \text{PolyLog}\left(2,\frac{c^2 \left(f+g x^2\right)}{c^2 f+g}\right)+\frac{1}{2} b c e \text{PolyLog}\left(2,\frac{g x^2}{f}+1\right)-\frac{b e \sqrt{g} \text{PolyLog}\left(2,-\frac{\sqrt{g} (1-c x)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{-f}}+\frac{b e \sqrt{g} \text{PolyLog}\left(2,\frac{\sqrt{g} (1-c x)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{-f}}-\frac{b e \sqrt{g} \text{PolyLog}\left(2,-\frac{\sqrt{g} (c x+1)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{-f}}+\frac{b e \sqrt{g} \text{PolyLog}\left(2,\frac{\sqrt{g} (c x+1)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{-f}}-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x}+\frac{2 a e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}-\frac{1}{2} b c \log \left(\frac{g \left(1-c^2 x^2\right)}{c^2 f+g}\right) \left(d+e \log \left(f+g x^2\right)\right)+\frac{1}{2} b c \log \left(-\frac{g x^2}{f}\right) \left(d+e \log \left(f+g x^2\right)\right)-\frac{b e \sqrt{g} \log (1-c x) \log \left(\frac{c \left(\sqrt{-f}-\sqrt{g} x\right)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{-f}}+\frac{b e \sqrt{g} \log (c x+1) \log \left(\frac{c \left(\sqrt{-f}-\sqrt{g} x\right)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{-f}}-\frac{b e \sqrt{g} \log (c x+1) \log \left(\frac{c \left(\sqrt{-f}+\sqrt{g} x\right)}{c \sqrt{-f}-\sqrt{g}}\right)}{2 \sqrt{-f}}+\frac{b e \sqrt{g} \log (1-c x) \log \left(\frac{c \left(\sqrt{-f}+\sqrt{g} x\right)}{c \sqrt{-f}+\sqrt{g}}\right)}{2 \sqrt{-f}}",1,"(2*a*e*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/Sqrt[f] - (b*e*Sqrt[g]*Log[1 - c*x]*Log[(c*(Sqrt[-f] - Sqrt[g]*x))/(c*Sqrt[-f] - Sqrt[g])])/(2*Sqrt[-f]) + (b*e*Sqrt[g]*Log[1 + c*x]*Log[(c*(Sqrt[-f] - Sqrt[g]*x))/(c*Sqrt[-f] + Sqrt[g])])/(2*Sqrt[-f]) - (b*e*Sqrt[g]*Log[1 + c*x]*Log[(c*(Sqrt[-f] + Sqrt[g]*x))/(c*Sqrt[-f] - Sqrt[g])])/(2*Sqrt[-f]) + (b*e*Sqrt[g]*Log[1 - c*x]*Log[(c*(Sqrt[-f] + Sqrt[g]*x))/(c*Sqrt[-f] + Sqrt[g])])/(2*Sqrt[-f]) - ((a + b*ArcTanh[c*x])*(d + e*Log[f + g*x^2]))/x + (b*c*Log[-((g*x^2)/f)]*(d + e*Log[f + g*x^2]))/2 - (b*c*Log[(g*(1 - c^2*x^2))/(c^2*f + g)]*(d + e*Log[f + g*x^2]))/2 - (b*e*Sqrt[g]*PolyLog[2, -((Sqrt[g]*(1 - c*x))/(c*Sqrt[-f] - Sqrt[g]))])/(2*Sqrt[-f]) + (b*e*Sqrt[g]*PolyLog[2, (Sqrt[g]*(1 - c*x))/(c*Sqrt[-f] + Sqrt[g])])/(2*Sqrt[-f]) - (b*e*Sqrt[g]*PolyLog[2, -((Sqrt[g]*(1 + c*x))/(c*Sqrt[-f] - Sqrt[g]))])/(2*Sqrt[-f]) + (b*e*Sqrt[g]*PolyLog[2, (Sqrt[g]*(1 + c*x))/(c*Sqrt[-f] + Sqrt[g])])/(2*Sqrt[-f]) - (b*c*e*PolyLog[2, (c^2*(f + g*x^2))/(c^2*f + g)])/2 + (b*c*e*PolyLog[2, 1 + (g*x^2)/f])/2","A",28,14,24,0.5833,1,"{6081, 2475, 36, 29, 31, 2416, 2394, 2315, 2393, 2391, 5974, 205, 5972, 2409}"
537,1,470,0,0.7461348,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x^3} \, dx","Int[((a + b*ArcTanh[c*x])*(d + e*Log[f + g*x^2]))/x^3,x]","-\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 f}+\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{4 f}+\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{4 f}-\frac{b e g \text{PolyLog}(2,-c x)}{2 f}+\frac{b e g \text{PolyLog}(2,c x)}{2 f}-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{2 x^2}-\frac{a e g \log \left(f+g x^2\right)}{2 f}+\frac{a e g \log (x)}{f}+\frac{1}{2} b c^2 \tanh ^{-1}(c x) \left(d+e \log \left(f+g x^2\right)\right)+\frac{b e \left(c^2 f+g\right) \log \left(\frac{2}{c x+1}\right) \tanh ^{-1}(c x)}{f}-\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{2 f}-\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{2 f}-\frac{b c \left(d+e \log \left(f+g x^2\right)\right)}{2 x}+\frac{b c e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}","-\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 f}+\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{4 f}+\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{4 f}-\frac{b e g \text{PolyLog}(2,-c x)}{2 f}+\frac{b e g \text{PolyLog}(2,c x)}{2 f}-\frac{\left(a+b \tanh ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{2 x^2}-\frac{a e g \log \left(f+g x^2\right)}{2 f}+\frac{a e g \log (x)}{f}+\frac{1}{2} b c^2 \tanh ^{-1}(c x) \left(d+e \log \left(f+g x^2\right)\right)+\frac{b e \left(c^2 f+g\right) \log \left(\frac{2}{c x+1}\right) \tanh ^{-1}(c x)}{f}-\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{2 f}-\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{2 f}-\frac{b c \left(d+e \log \left(f+g x^2\right)\right)}{2 x}+\frac{b c e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}",1,"(b*c*e*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/Sqrt[f] + (a*e*g*Log[x])/f + (b*e*(c^2*f + g)*ArcTanh[c*x]*Log[2/(1 + c*x)])/f - (b*e*(c^2*f + g)*ArcTanh[c*x]*Log[(2*c*(Sqrt[-f] - Sqrt[g]*x))/((c*Sqrt[-f] - Sqrt[g])*(1 + c*x))])/(2*f) - (b*e*(c^2*f + g)*ArcTanh[c*x]*Log[(2*c*(Sqrt[-f] + Sqrt[g]*x))/((c*Sqrt[-f] + Sqrt[g])*(1 + c*x))])/(2*f) - (a*e*g*Log[f + g*x^2])/(2*f) - (b*c*(d + e*Log[f + g*x^2]))/(2*x) + (b*c^2*ArcTanh[c*x]*(d + e*Log[f + g*x^2]))/2 - ((a + b*ArcTanh[c*x])*(d + e*Log[f + g*x^2]))/(2*x^2) - (b*e*g*PolyLog[2, -(c*x)])/(2*f) + (b*e*g*PolyLog[2, c*x])/(2*f) - (b*e*(c^2*f + g)*PolyLog[2, 1 - 2/(1 + c*x)])/(2*f) + (b*e*(c^2*f + g)*PolyLog[2, 1 - (2*c*(Sqrt[-f] - Sqrt[g]*x))/((c*Sqrt[-f] - Sqrt[g])*(1 + c*x))])/(4*f) + (b*e*(c^2*f + g)*PolyLog[2, 1 - (2*c*(Sqrt[-f] + Sqrt[g]*x))/((c*Sqrt[-f] + Sqrt[g])*(1 + c*x))])/(4*f)","A",20,17,24,0.7083,1,"{5916, 325, 206, 6085, 801, 635, 205, 260, 446, 72, 6725, 5912, 5992, 5920, 2402, 2315, 2447}"
538,1,122,0,0.2932579,"\int \frac{\tanh ^{-1}(c x) \left(a+b \tanh ^{-1}(c x)\right)}{(1+c x)^2} \, dx","Int[(ArcTanh[c*x]*(a + b*ArcTanh[c*x]))/(1 + c*x)^2,x]","-\frac{a}{2 c (c x+1)}+\frac{a \tanh ^{-1}(c x)}{2 c}-\frac{a \tanh ^{-1}(c x)}{c (c x+1)}-\frac{b}{2 c (c x+1)}+\frac{b \tanh ^{-1}(c x)^2}{2 c}-\frac{b \tanh ^{-1}(c x)^2}{c (c x+1)}+\frac{b \tanh ^{-1}(c x)}{2 c}-\frac{b \tanh ^{-1}(c x)}{c (c x+1)}","-\frac{a+b}{2 c (c x+1)}+\frac{(a+b) \tanh ^{-1}(c x)}{2 c}-\frac{(a+b) \tanh ^{-1}(c x)}{c (c x+1)}-\frac{b (1-c x) \tanh ^{-1}(c x)^2}{2 c (c x+1)}",1,"-a/(2*c*(1 + c*x)) - b/(2*c*(1 + c*x)) + (a*ArcTanh[c*x])/(2*c) + (b*ArcTanh[c*x])/(2*c) - (a*ArcTanh[c*x])/(c*(1 + c*x)) - (b*ArcTanh[c*x])/(c*(1 + c*x)) + (b*ArcTanh[c*x]^2)/(2*c) - (b*ArcTanh[c*x]^2)/(c*(1 + c*x))","A",16,7,20,0.3500,1,"{5926, 627, 44, 207, 6742, 5928, 5948}"