1,1,59,0,0.0329148,"\int x^5 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^5*(a + b*ArcTanh[c*x]),x]","\frac{1}{6} x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b x^3}{18 c^3}+\frac{b x}{6 c^5}-\frac{b \tanh ^{-1}(c x)}{6 c^6}+\frac{b x^5}{30 c}","\frac{1}{6} x^6 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b x^3}{18 c^3}+\frac{b x}{6 c^5}-\frac{b \tanh ^{-1}(c x)}{6 c^6}+\frac{b x^5}{30 c}",1,"(b*x)/(6*c^5) + (b*x^3)/(18*c^3) + (b*x^5)/(30*c) - (b*ArcTanh[c*x])/(6*c^6) + (x^6*(a + b*ArcTanh[c*x]))/6","A",4,3,12,0.2500,1,"{5916, 302, 206}"
2,1,57,0,0.0426034,"\int x^4 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^4*(a + b*ArcTanh[c*x]),x]","\frac{1}{5} x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b x^2}{10 c^3}+\frac{b \log \left(1-c^2 x^2\right)}{10 c^5}+\frac{b x^4}{20 c}","\frac{1}{5} x^5 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b x^2}{10 c^3}+\frac{b \log \left(1-c^2 x^2\right)}{10 c^5}+\frac{b x^4}{20 c}",1,"(b*x^2)/(10*c^3) + (b*x^4)/(20*c) + (x^5*(a + b*ArcTanh[c*x]))/5 + (b*Log[1 - c^2*x^2])/(10*c^5)","A",4,3,12,0.2500,1,"{5916, 266, 43}"
3,1,48,0,0.0289794,"\int x^3 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^3*(a + b*ArcTanh[c*x]),x]","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b x}{4 c^3}-\frac{b \tanh ^{-1}(c x)}{4 c^4}+\frac{b x^3}{12 c}","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b x}{4 c^3}-\frac{b \tanh ^{-1}(c x)}{4 c^4}+\frac{b x^3}{12 c}",1,"(b*x)/(4*c^3) + (b*x^3)/(12*c) - (b*ArcTanh[c*x])/(4*c^4) + (x^4*(a + b*ArcTanh[c*x]))/4","A",4,3,12,0.2500,1,"{5916, 302, 206}"
4,1,46,0,0.03505,"\int x^2 \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x^2*(a + b*ArcTanh[c*x]),x]","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b \log \left(1-c^2 x^2\right)}{6 c^3}+\frac{b x^2}{6 c}","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}(c x)\right)+\frac{b \log \left(1-c^2 x^2\right)}{6 c^3}+\frac{b x^2}{6 c}",1,"(b*x^2)/(6*c) + (x^3*(a + b*ArcTanh[c*x]))/3 + (b*Log[1 - c^2*x^2])/(6*c^3)","A",4,3,12,0.2500,1,"{5916, 266, 43}"
5,1,37,0,0.0172118,"\int x \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[x*(a + b*ArcTanh[c*x]),x]","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{b \tanh ^{-1}(c x)}{2 c^2}+\frac{b x}{2 c}","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}(c x)\right)-\frac{b \tanh ^{-1}(c x)}{2 c^2}+\frac{b x}{2 c}",1,"(b*x)/(2*c) - (b*ArcTanh[c*x])/(2*c^2) + (x^2*(a + b*ArcTanh[c*x]))/2","A",3,3,10,0.3000,1,"{5916, 321, 206}"
6,1,30,0,0.0125908,"\int \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[a + b*ArcTanh[c*x],x]","a x+\frac{b \log \left(1-c^2 x^2\right)}{2 c}+b x \tanh ^{-1}(c x)","a x+\frac{b \log \left(1-c^2 x^2\right)}{2 c}+b x \tanh ^{-1}(c x)",1,"a*x + b*x*ArcTanh[c*x] + (b*Log[1 - c^2*x^2])/(2*c)","A",3,2,8,0.2500,1,"{5910, 260}"
7,1,26,0,0.0148648,"\int \frac{a+b \tanh ^{-1}(c x)}{x} \, dx","Int[(a + b*ArcTanh[c*x])/x,x]","-\frac{1}{2} b \text{PolyLog}(2,-c x)+\frac{1}{2} b \text{PolyLog}(2,c x)+a \log (x)","-\frac{1}{2} b \text{PolyLog}(2,-c x)+\frac{1}{2} b \text{PolyLog}(2,c x)+a \log (x)",1,"a*Log[x] - (b*PolyLog[2, -(c*x)])/2 + (b*PolyLog[2, c*x])/2","A",1,1,12,0.08333,1,"{5912}"
8,1,36,0,0.0262703,"\int \frac{a+b \tanh ^{-1}(c x)}{x^2} \, dx","Int[(a + b*ArcTanh[c*x])/x^2,x]","-\frac{a+b \tanh ^{-1}(c x)}{x}-\frac{1}{2} b c \log \left(1-c^2 x^2\right)+b c \log (x)","-\frac{a+b \tanh ^{-1}(c x)}{x}-\frac{1}{2} b c \log \left(1-c^2 x^2\right)+b c \log (x)",1,"-((a + b*ArcTanh[c*x])/x) + b*c*Log[x] - (b*c*Log[1 - c^2*x^2])/2","A",5,5,12,0.4167,1,"{5916, 266, 36, 29, 31}"
9,1,37,0,0.0216618,"\int \frac{a+b \tanh ^{-1}(c x)}{x^3} \, dx","Int[(a + b*ArcTanh[c*x])/x^3,x]","-\frac{a+b \tanh ^{-1}(c x)}{2 x^2}+\frac{1}{2} b c^2 \tanh ^{-1}(c x)-\frac{b c}{2 x}","-\frac{a+b \tanh ^{-1}(c x)}{2 x^2}+\frac{1}{2} b c^2 \tanh ^{-1}(c x)-\frac{b c}{2 x}",1,"-(b*c)/(2*x) + (b*c^2*ArcTanh[c*x])/2 - (a + b*ArcTanh[c*x])/(2*x^2)","A",3,3,12,0.2500,1,"{5916, 325, 206}"
10,1,54,0,0.0360336,"\int \frac{a+b \tanh ^{-1}(c x)}{x^4} \, dx","Int[(a + b*ArcTanh[c*x])/x^4,x]","-\frac{a+b \tanh ^{-1}(c x)}{3 x^3}-\frac{1}{6} b c^3 \log \left(1-c^2 x^2\right)+\frac{1}{3} b c^3 \log (x)-\frac{b c}{6 x^2}","-\frac{a+b \tanh ^{-1}(c x)}{3 x^3}-\frac{1}{6} b c^3 \log \left(1-c^2 x^2\right)+\frac{1}{3} b c^3 \log (x)-\frac{b c}{6 x^2}",1,"-(b*c)/(6*x^2) - (a + b*ArcTanh[c*x])/(3*x^3) + (b*c^3*Log[x])/3 - (b*c^3*Log[1 - c^2*x^2])/6","A",4,3,12,0.2500,1,"{5916, 266, 44}"
11,1,48,0,0.0266312,"\int \frac{a+b \tanh ^{-1}(c x)}{x^5} \, dx","Int[(a + b*ArcTanh[c*x])/x^5,x]","-\frac{a+b \tanh ^{-1}(c x)}{4 x^4}-\frac{b c^3}{4 x}+\frac{1}{4} b c^4 \tanh ^{-1}(c x)-\frac{b c}{12 x^3}","-\frac{a+b \tanh ^{-1}(c x)}{4 x^4}-\frac{b c^3}{4 x}+\frac{1}{4} b c^4 \tanh ^{-1}(c x)-\frac{b c}{12 x^3}",1,"-(b*c)/(12*x^3) - (b*c^3)/(4*x) + (b*c^4*ArcTanh[c*x])/4 - (a + b*ArcTanh[c*x])/(4*x^4)","A",4,3,12,0.2500,1,"{5916, 325, 206}"
12,1,65,0,0.0413205,"\int \frac{a+b \tanh ^{-1}(c x)}{x^6} \, dx","Int[(a + b*ArcTanh[c*x])/x^6,x]","-\frac{a+b \tanh ^{-1}(c x)}{5 x^5}-\frac{b c^3}{10 x^2}-\frac{1}{10} b c^5 \log \left(1-c^2 x^2\right)+\frac{1}{5} b c^5 \log (x)-\frac{b c}{20 x^4}","-\frac{a+b \tanh ^{-1}(c x)}{5 x^5}-\frac{b c^3}{10 x^2}-\frac{1}{10} b c^5 \log \left(1-c^2 x^2\right)+\frac{1}{5} b c^5 \log (x)-\frac{b c}{20 x^4}",1,"-(b*c)/(20*x^4) - (b*c^3)/(10*x^2) - (a + b*ArcTanh[c*x])/(5*x^5) + (b*c^5*Log[x])/5 - (b*c^5*Log[1 - c^2*x^2])/10","A",4,3,12,0.2500,1,"{5916, 266, 44}"
13,1,145,0,0.3268331,"\int x^5 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x^5*(a + b*ArcTanh[c*x])^2,x]","\frac{b x^3 \left(a+b \tanh ^{-1}(c x)\right)}{9 c^3}+\frac{a b x}{3 c^5}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{6 c^6}+\frac{1}{6} x^6 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{b x^5 \left(a+b \tanh ^{-1}(c x)\right)}{15 c}+\frac{b^2 x^4}{60 c^2}+\frac{4 b^2 x^2}{45 c^4}+\frac{23 b^2 \log \left(1-c^2 x^2\right)}{90 c^6}+\frac{b^2 x \tanh ^{-1}(c x)}{3 c^5}","\frac{b x^3 \left(a+b \tanh ^{-1}(c x)\right)}{9 c^3}+\frac{a b x}{3 c^5}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{6 c^6}+\frac{1}{6} x^6 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{b x^5 \left(a+b \tanh ^{-1}(c x)\right)}{15 c}+\frac{b^2 x^4}{60 c^2}+\frac{4 b^2 x^2}{45 c^4}+\frac{23 b^2 \log \left(1-c^2 x^2\right)}{90 c^6}+\frac{b^2 x \tanh ^{-1}(c x)}{3 c^5}",1,"(a*b*x)/(3*c^5) + (4*b^2*x^2)/(45*c^4) + (b^2*x^4)/(60*c^2) + (b^2*x*ArcTanh[c*x])/(3*c^5) + (b*x^3*(a + b*ArcTanh[c*x]))/(9*c^3) + (b*x^5*(a + b*ArcTanh[c*x]))/(15*c) - (a + b*ArcTanh[c*x])^2/(6*c^6) + (x^6*(a + b*ArcTanh[c*x])^2)/6 + (23*b^2*Log[1 - c^2*x^2])/(90*c^6)","A",16,7,14,0.5000,1,"{5916, 5980, 266, 43, 5910, 260, 5948}"
14,1,162,0,0.3022279,"\int x^4 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x^4*(a + b*ArcTanh[c*x])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{5 c^5}+\frac{b x^2 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{5 c^5}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{5 c^5}+\frac{1}{5} x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{b x^4 \left(a+b \tanh ^{-1}(c x)\right)}{10 c}+\frac{b^2 x^3}{30 c^2}+\frac{3 b^2 x}{10 c^4}-\frac{3 b^2 \tanh ^{-1}(c x)}{10 c^5}","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{5 c^5}+\frac{b x^2 \left(a+b \tanh ^{-1}(c x)\right)}{5 c^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{5 c^5}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{5 c^5}+\frac{1}{5} x^5 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{b x^4 \left(a+b \tanh ^{-1}(c x)\right)}{10 c}+\frac{b^2 x^3}{30 c^2}+\frac{3 b^2 x}{10 c^4}-\frac{3 b^2 \tanh ^{-1}(c x)}{10 c^5}",1,"(3*b^2*x)/(10*c^4) + (b^2*x^3)/(30*c^2) - (3*b^2*ArcTanh[c*x])/(10*c^5) + (b*x^2*(a + b*ArcTanh[c*x]))/(5*c^3) + (b*x^4*(a + b*ArcTanh[c*x]))/(10*c) + (a + b*ArcTanh[c*x])^2/(5*c^5) + (x^5*(a + b*ArcTanh[c*x])^2)/5 - (2*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(5*c^5) - (b^2*PolyLog[2, 1 - 2/(1 - c*x)])/(5*c^5)","A",14,9,14,0.6429,1,"{5916, 5980, 302, 206, 321, 5984, 5918, 2402, 2315}"
15,1,113,0,0.2225066,"\int x^3 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x^3*(a + b*ArcTanh[c*x])^2,x]","\frac{a b x}{2 c^3}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^4}+\frac{1}{4} x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{b x^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 c}+\frac{b^2 x^2}{12 c^2}+\frac{b^2 \log \left(1-c^2 x^2\right)}{3 c^4}+\frac{b^2 x \tanh ^{-1}(c x)}{2 c^3}","\frac{a b x}{2 c^3}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^4}+\frac{1}{4} x^4 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{b x^3 \left(a+b \tanh ^{-1}(c x)\right)}{6 c}+\frac{b^2 x^2}{12 c^2}+\frac{b^2 \log \left(1-c^2 x^2\right)}{3 c^4}+\frac{b^2 x \tanh ^{-1}(c x)}{2 c^3}",1,"(a*b*x)/(2*c^3) + (b^2*x^2)/(12*c^2) + (b^2*x*ArcTanh[c*x])/(2*c^3) + (b*x^3*(a + b*ArcTanh[c*x]))/(6*c) - (a + b*ArcTanh[c*x])^2/(4*c^4) + (x^4*(a + b*ArcTanh[c*x])^2)/4 + (b^2*Log[1 - c^2*x^2])/(3*c^4)","A",11,7,14,0.5000,1,"{5916, 5980, 266, 43, 5910, 260, 5948}"
16,1,130,0,0.2008162,"\int x^2 \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x^2*(a + b*ArcTanh[c*x])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{3 c^3}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{b x^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 c}+\frac{b^2 x}{3 c^2}-\frac{b^2 \tanh ^{-1}(c x)}{3 c^3}","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{3 c^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{3 c^3}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{b x^2 \left(a+b \tanh ^{-1}(c x)\right)}{3 c}+\frac{b^2 x}{3 c^2}-\frac{b^2 \tanh ^{-1}(c x)}{3 c^3}",1,"(b^2*x)/(3*c^2) - (b^2*ArcTanh[c*x])/(3*c^3) + (b*x^2*(a + b*ArcTanh[c*x]))/(3*c) + (a + b*ArcTanh[c*x])^2/(3*c^3) + (x^3*(a + b*ArcTanh[c*x])^2)/3 - (2*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(3*c^3) - (b^2*PolyLog[2, 1 - 2/(1 - c*x)])/(3*c^3)","A",9,8,14,0.5714,1,"{5916, 5980, 321, 206, 5984, 5918, 2402, 2315}"
17,1,75,0,0.1140091,"\int x \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[x*(a + b*ArcTanh[c*x])^2,x]","-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{a b x}{c}+\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^2}+\frac{b^2 x \tanh ^{-1}(c x)}{c}","-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{a b x}{c}+\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^2}+\frac{b^2 x \tanh ^{-1}(c x)}{c}",1,"(a*b*x)/c + (b^2*x*ArcTanh[c*x])/c - (a + b*ArcTanh[c*x])^2/(2*c^2) + (x^2*(a + b*ArcTanh[c*x])^2)/2 + (b^2*Log[1 - c^2*x^2])/(2*c^2)","A",6,5,12,0.4167,1,"{5916, 5980, 5910, 260, 5948}"
18,1,74,0,0.1011241,"\int \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[(a + b*ArcTanh[c*x])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c}+x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c}+x \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{c}-\frac{2 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c}",1,"(a + b*ArcTanh[c*x])^2/c + x*(a + b*ArcTanh[c*x])^2 - (2*b*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c - (b^2*PolyLog[2, 1 - 2/(1 - c*x)])/c","A",5,5,10,0.5000,1,"{5910, 5984, 5918, 2402, 2315}"
19,1,117,0,0.2636712,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x} \, dx","Int[(a + b*ArcTanh[c*x])^2/x,x]","-b \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2","-b \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)+b \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right)+2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2",1,"2*(a + b*ArcTanh[c*x])^2*ArcTanh[1 - 2/(1 - c*x)] - b*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)] + b*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 - c*x)] + (b^2*PolyLog[3, 1 - 2/(1 - c*x)])/2 - (b^2*PolyLog[3, -1 + 2/(1 - c*x)])/2","A",6,5,14,0.3571,1,"{5914, 6052, 5948, 6058, 6610}"
20,1,71,0,0.1452967,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[(a + b*ArcTanh[c*x])^2/x^2,x]","b^2 (-c) \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+c \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x}+2 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)","b^2 (-c) \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+c \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x}+2 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)",1,"c*(a + b*ArcTanh[c*x])^2 - (a + b*ArcTanh[c*x])^2/x + 2*b*c*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)] - b^2*c*PolyLog[2, -1 + 2/(1 + c*x)]","A",4,4,14,0.2857,1,"{5916, 5988, 5932, 2447}"
21,1,80,0,0.1330198,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[(a + b*ArcTanh[c*x])^2/x^3,x]","\frac{1}{2} c^2 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{1}{2} b^2 c^2 \log \left(1-c^2 x^2\right)+b^2 c^2 \log (x)","\frac{1}{2} c^2 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{x}-\frac{1}{2} b^2 c^2 \log \left(1-c^2 x^2\right)+b^2 c^2 \log (x)",1,"-((b*c*(a + b*ArcTanh[c*x]))/x) + (c^2*(a + b*ArcTanh[c*x])^2)/2 - (a + b*ArcTanh[c*x])^2/(2*x^2) + b^2*c^2*Log[x] - (b^2*c^2*Log[1 - c^2*x^2])/2","A",8,7,14,0.5000,1,"{5916, 5982, 266, 36, 29, 31, 5948}"
22,1,130,0,0.2308293,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[(a + b*ArcTanh[c*x])^2/x^4,x]","-\frac{1}{3} b^2 c^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{1}{3} c^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{2}{3} b c^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{3 x^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{3 x^3}-\frac{b^2 c^2}{3 x}+\frac{1}{3} b^2 c^3 \tanh ^{-1}(c x)","-\frac{1}{3} b^2 c^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+\frac{1}{3} c^3 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{2}{3} b c^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{3 x^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{3 x^3}-\frac{b^2 c^2}{3 x}+\frac{1}{3} b^2 c^3 \tanh ^{-1}(c x)",1,"-(b^2*c^2)/(3*x) + (b^2*c^3*ArcTanh[c*x])/3 - (b*c*(a + b*ArcTanh[c*x]))/(3*x^2) + (c^3*(a + b*ArcTanh[c*x])^2)/3 - (a + b*ArcTanh[c*x])^2/(3*x^3) + (2*b*c^3*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)])/3 - (b^2*c^3*PolyLog[2, -1 + 2/(1 + c*x)])/3","A",8,7,14,0.5000,1,"{5916, 5982, 325, 206, 5988, 5932, 2447}"
23,1,117,0,0.228329,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{x^5} \, dx","Int[(a + b*ArcTanh[c*x])^2/x^5,x]","\frac{1}{4} c^4 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{b c^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{6 x^3}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{4 x^4}-\frac{b^2 c^2}{12 x^2}-\frac{1}{3} b^2 c^4 \log \left(1-c^2 x^2\right)+\frac{2}{3} b^2 c^4 \log (x)","\frac{1}{4} c^4 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{b c^3 \left(a+b \tanh ^{-1}(c x)\right)}{2 x}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)}{6 x^3}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^2}{4 x^4}-\frac{b^2 c^2}{12 x^2}-\frac{1}{3} b^2 c^4 \log \left(1-c^2 x^2\right)+\frac{2}{3} b^2 c^4 \log (x)",1,"-(b^2*c^2)/(12*x^2) - (b*c*(a + b*ArcTanh[c*x]))/(6*x^3) - (b*c^3*(a + b*ArcTanh[c*x]))/(2*x) + (c^4*(a + b*ArcTanh[c*x])^2)/4 - (a + b*ArcTanh[c*x])^2/(4*x^4) + (2*b^2*c^4*Log[x])/3 - (b^2*c^4*Log[1 - c^2*x^2])/3","A",13,8,14,0.5714,1,"{5916, 5982, 266, 44, 36, 29, 31, 5948}"
24,1,247,0,0.9636076,"\int x^5 \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[x^5*(a + b*ArcTanh[c*x])^3,x]","-\frac{23 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{30 c^6}+\frac{b^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)}{20 c^2}+\frac{4 b^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{15 c^4}-\frac{23 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{15 c^6}+\frac{b x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{6 c^3}+\frac{b x \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^5}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{6 c^6}+\frac{23 b \left(a+b \tanh ^{-1}(c x)\right)^2}{30 c^6}+\frac{1}{6} x^6 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{b x^5 \left(a+b \tanh ^{-1}(c x)\right)^2}{10 c}+\frac{b^3 x^3}{60 c^3}+\frac{19 b^3 x}{60 c^5}-\frac{19 b^3 \tanh ^{-1}(c x)}{60 c^6}","-\frac{23 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{30 c^6}+\frac{b^2 x^4 \left(a+b \tanh ^{-1}(c x)\right)}{20 c^2}+\frac{4 b^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{15 c^4}-\frac{23 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{15 c^6}+\frac{b x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{6 c^3}+\frac{b x \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^5}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{6 c^6}+\frac{23 b \left(a+b \tanh ^{-1}(c x)\right)^2}{30 c^6}+\frac{1}{6} x^6 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{b x^5 \left(a+b \tanh ^{-1}(c x)\right)^2}{10 c}+\frac{b^3 x^3}{60 c^3}+\frac{19 b^3 x}{60 c^5}-\frac{19 b^3 \tanh ^{-1}(c x)}{60 c^6}",1,"(19*b^3*x)/(60*c^5) + (b^3*x^3)/(60*c^3) - (19*b^3*ArcTanh[c*x])/(60*c^6) + (4*b^2*x^2*(a + b*ArcTanh[c*x]))/(15*c^4) + (b^2*x^4*(a + b*ArcTanh[c*x]))/(20*c^2) + (23*b*(a + b*ArcTanh[c*x])^2)/(30*c^6) + (b*x*(a + b*ArcTanh[c*x])^2)/(2*c^5) + (b*x^3*(a + b*ArcTanh[c*x])^2)/(6*c^3) + (b*x^5*(a + b*ArcTanh[c*x])^2)/(10*c) - (a + b*ArcTanh[c*x])^3/(6*c^6) + (x^6*(a + b*ArcTanh[c*x])^3)/6 - (23*b^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/(15*c^6) - (23*b^3*PolyLog[2, 1 - 2/(1 - c*x)])/(30*c^6)","A",33,11,14,0.7857,1,"{5916, 5980, 302, 206, 321, 5984, 5918, 2402, 2315, 5910, 5948}"
25,1,262,0,0.7739535,"\int x^4 \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[x^4*(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)}{5 c^5}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{10 c^5}+\frac{b^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)}{10 c^2}+\frac{9 a b^2 x}{10 c^4}+\frac{3 b x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{10 c^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{5 c^5}-\frac{9 b \left(a+b \tanh ^{-1}(c x)\right)^2}{20 c^5}-\frac{3 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{5 c^5}+\frac{1}{5} x^5 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{3 b x^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{20 c}+\frac{b^3 x^2}{20 c^3}+\frac{b^3 \log \left(1-c^2 x^2\right)}{2 c^5}+\frac{9 b^3 x \tanh ^{-1}(c x)}{10 c^4}","-\frac{3 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{5 c^5}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{10 c^5}+\frac{b^2 x^3 \left(a+b \tanh ^{-1}(c x)\right)}{10 c^2}+\frac{9 a b^2 x}{10 c^4}+\frac{3 b x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{10 c^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{5 c^5}-\frac{9 b \left(a+b \tanh ^{-1}(c x)\right)^2}{20 c^5}-\frac{3 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{5 c^5}+\frac{1}{5} x^5 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{3 b x^4 \left(a+b \tanh ^{-1}(c x)\right)^2}{20 c}+\frac{b^3 x^2}{20 c^3}+\frac{b^3 \log \left(1-c^2 x^2\right)}{2 c^5}+\frac{9 b^3 x \tanh ^{-1}(c x)}{10 c^4}",1,"(9*a*b^2*x)/(10*c^4) + (b^3*x^2)/(20*c^3) + (9*b^3*x*ArcTanh[c*x])/(10*c^4) + (b^2*x^3*(a + b*ArcTanh[c*x]))/(10*c^2) - (9*b*(a + b*ArcTanh[c*x])^2)/(20*c^5) + (3*b*x^2*(a + b*ArcTanh[c*x])^2)/(10*c^3) + (3*b*x^4*(a + b*ArcTanh[c*x])^2)/(20*c) + (a + b*ArcTanh[c*x])^3/(5*c^5) + (x^5*(a + b*ArcTanh[c*x])^3)/5 - (3*b*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/(5*c^5) + (b^3*Log[1 - c^2*x^2])/(2*c^5) - (3*b^2*(a + b*ArcTanh[c*x])*PolyLog[2, 1 - 2/(1 - c*x)])/(5*c^5) + (3*b^3*PolyLog[3, 1 - 2/(1 - c*x)])/(10*c^5)","A",24,11,14,0.7857,1,"{5916, 5980, 266, 43, 5910, 260, 5948, 5984, 5918, 6058, 6610}"
26,1,185,0,0.5693908,"\int x^3 \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[x^3*(a + b*ArcTanh[c*x])^3,x]","-\frac{b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^4}+\frac{b^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2}-\frac{2 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4}+\frac{3 b x \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^3}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{4 c^4}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4}+\frac{1}{4} x^4 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{b x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c}+\frac{b^3 x}{4 c^3}-\frac{b^3 \tanh ^{-1}(c x)}{4 c^4}","-\frac{b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{c^4}+\frac{b^2 x^2 \left(a+b \tanh ^{-1}(c x)\right)}{4 c^2}-\frac{2 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^4}+\frac{3 b x \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c^3}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{4 c^4}+\frac{b \left(a+b \tanh ^{-1}(c x)\right)^2}{c^4}+\frac{1}{4} x^4 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{b x^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 c}+\frac{b^3 x}{4 c^3}-\frac{b^3 \tanh ^{-1}(c x)}{4 c^4}",1,"(b^3*x)/(4*c^3) - (b^3*ArcTanh[c*x])/(4*c^4) + (b^2*x^2*(a + b*ArcTanh[c*x]))/(4*c^2) + (b*(a + b*ArcTanh[c*x])^2)/c^4 + (3*b*x*(a + b*ArcTanh[c*x])^2)/(4*c^3) + (b*x^3*(a + b*ArcTanh[c*x])^2)/(4*c) - (a + b*ArcTanh[c*x])^3/(4*c^4) + (x^4*(a + b*ArcTanh[c*x])^3)/4 - (2*b^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c^4 - (b^3*PolyLog[2, 1 - 2/(1 - c*x)])/c^4","A",18,10,14,0.7143,1,"{5916, 5980, 321, 206, 5984, 5918, 2402, 2315, 5910, 5948}"
27,1,197,0,0.4490668,"\int x^2 \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[x^2*(a + b*ArcTanh[c*x])^3,x]","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3}+\frac{b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c^3}+\frac{a b^2 x}{c^2}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{3 c^3}-\frac{b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3}+\frac{b x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{1}{3} x^3 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{b^3 \log \left(1-c^2 x^2\right)}{2 c^3}+\frac{b^3 x \tanh ^{-1}(c x)}{c^2}","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^3}+\frac{b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right)}{2 c^3}+\frac{a b^2 x}{c^2}-\frac{b \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^3}+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{3 c^3}-\frac{b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c^3}+\frac{b x^2 \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}+\frac{1}{3} x^3 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{b^3 \log \left(1-c^2 x^2\right)}{2 c^3}+\frac{b^3 x \tanh ^{-1}(c x)}{c^2}",1,"(a*b^2*x)/c^2 + (b^3*x*ArcTanh[c*x])/c^2 - (b*(a + b*ArcTanh[c*x])^2)/(2*c^3) + (b*x^2*(a + b*ArcTanh[c*x])^2)/(2*c) + (a + b*ArcTanh[c*x])^3/(3*c^3) + (x^3*(a + b*ArcTanh[c*x])^3)/3 - (b*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/c^3 + (b^3*Log[1 - c^2*x^2])/(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^3)","A",12,9,14,0.6429,1,"{5916, 5980, 5910, 260, 5948, 5984, 5918, 6058, 6610}"
28,1,123,0,0.2503147,"\int x \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[x*(a + b*ArcTanh[c*x])^3,x]","-\frac{3 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{2 c^2}-\frac{3 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2}+\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{2 c^2}+\frac{1}{2} x^2 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{3 b x \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}","-\frac{3 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)}{2 c^2}-\frac{3 b^2 \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)}{c^2}+\frac{3 b \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{2 c^2}+\frac{1}{2} x^2 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{3 b x \left(a+b \tanh ^{-1}(c x)\right)^2}{2 c}",1,"(3*b*(a + b*ArcTanh[c*x])^2)/(2*c^2) + (3*b*x*(a + b*ArcTanh[c*x])^2)/(2*c) - (a + b*ArcTanh[c*x])^3/(2*c^2) + (x^2*(a + b*ArcTanh[c*x])^3)/2 - (3*b^2*(a + b*ArcTanh[c*x])*Log[2/(1 - c*x)])/c^2 - (3*b^3*PolyLog[2, 1 - 2/(1 - c*x)])/(2*c^2)","A",8,8,12,0.6667,1,"{5916, 5980, 5910, 5984, 5918, 2402, 2315, 5948}"
29,1,108,0,0.2172342,"\int \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[(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(3,1-\frac{2}{1-c x}\right)}{2 c}+x \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{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(3,1-\frac{2}{1-c x}\right)}{2 c}+x \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{c}-\frac{3 b \log \left(\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2}{c}",1,"(a + b*ArcTanh[c*x])^3/c + x*(a + b*ArcTanh[c*x])^3 - (3*b*(a + b*ArcTanh[c*x])^2*Log[2/(1 - c*x)])/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",5,6,10,0.6000,1,"{5910, 5984, 5918, 5948, 6058, 6610}"
30,1,184,0,0.4487177,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{x} \, dx","Int[(a + b*ArcTanh[c*x])^3/x,x]","\frac{3}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{3}{2} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{3}{2} b \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{2} b \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{3}{4} b^3 \text{PolyLog}\left(4,1-\frac{2}{1-c x}\right)+\frac{3}{4} b^3 \text{PolyLog}\left(4,\frac{2}{1-c x}-1\right)+2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^3","\frac{3}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{3}{2} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{3}{2} b \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{3}{2} b \text{PolyLog}\left(2,\frac{2}{1-c x}-1\right) \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{3}{4} b^3 \text{PolyLog}\left(4,1-\frac{2}{1-c x}\right)+\frac{3}{4} b^3 \text{PolyLog}\left(4,\frac{2}{1-c x}-1\right)+2 \tanh ^{-1}\left(1-\frac{2}{1-c x}\right) \left(a+b \tanh ^{-1}(c x)\right)^3",1,"2*(a + b*ArcTanh[c*x])^3*ArcTanh[1 - 2/(1 - c*x)] - (3*b*(a + b*ArcTanh[c*x])^2*PolyLog[2, 1 - 2/(1 - c*x)])/2 + (3*b*(a + b*ArcTanh[c*x])^2*PolyLog[2, -1 + 2/(1 - c*x)])/2 + (3*b^2*(a + b*ArcTanh[c*x])*PolyLog[3, 1 - 2/(1 - c*x)])/2 - (3*b^2*(a + b*ArcTanh[c*x])*PolyLog[3, -1 + 2/(1 - c*x)])/2 - (3*b^3*PolyLog[4, 1 - 2/(1 - c*x)])/4 + (3*b^3*PolyLog[4, -1 + 2/(1 - c*x)])/4","A",8,6,14,0.4286,1,"{5914, 6052, 5948, 6058, 6062, 6610}"
31,1,102,0,0.2683225,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{x^2} \, dx","Int[(a + b*ArcTanh[c*x])^3/x^2,x]","-3 b^2 c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{3}{2} b^3 c \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)+c \left(a+b \tanh ^{-1}(c x)\right)^3-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{x}+3 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2","-3 b^2 c \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{3}{2} b^3 c \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)+c \left(a+b \tanh ^{-1}(c x)\right)^3-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{x}+3 b c \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2",1,"c*(a + b*ArcTanh[c*x])^3 - (a + b*ArcTanh[c*x])^3/x + 3*b*c*(a + b*ArcTanh[c*x])^2*Log[2 - 2/(1 + c*x)] - 3*b^2*c*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 + c*x)] - (3*b^3*c*PolyLog[3, -1 + 2/(1 + c*x)])/2","A",5,6,14,0.4286,1,"{5916, 5988, 5932, 5948, 6056, 6610}"
32,1,123,0,0.2943552,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{x^3} \, dx","Int[(a + b*ArcTanh[c*x])^3/x^3,x]","-\frac{3}{2} b^3 c^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+3 b^2 c^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{2} b c^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{2} c^2 \left(a+b \tanh ^{-1}(c x)\right)^3-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{2 x^2}-\frac{3 b c \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x}","-\frac{3}{2} b^3 c^2 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)+3 b^2 c^2 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{3}{2} b c^2 \left(a+b \tanh ^{-1}(c x)\right)^2+\frac{1}{2} c^2 \left(a+b \tanh ^{-1}(c x)\right)^3-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{2 x^2}-\frac{3 b c \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x}",1,"(3*b*c^2*(a + b*ArcTanh[c*x])^2)/2 - (3*b*c*(a + b*ArcTanh[c*x])^2)/(2*x) + (c^2*(a + b*ArcTanh[c*x])^3)/2 - (a + b*ArcTanh[c*x])^3/(2*x^2) + 3*b^2*c^2*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)] - (3*b^3*c^2*PolyLog[2, -1 + 2/(1 + c*x)])/2","A",7,6,14,0.4286,1,"{5916, 5982, 5988, 5932, 2447, 5948}"
33,1,200,0,0.498341,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{x^4} \, dx","Int[(a + b*ArcTanh[c*x])^3/x^4,x]","-b^2 c^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{1}{2} b^3 c^3 \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)-\frac{b^2 c^2 \left(a+b \tanh ^{-1}(c x)\right)}{x}+\frac{1}{3} c^3 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{1}{2} b c^3 \left(a+b \tanh ^{-1}(c x)\right)^2+b c^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{3 x^3}-\frac{1}{2} b^3 c^3 \log \left(1-c^2 x^2\right)+b^3 c^3 \log (x)","-b^2 c^3 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right) \left(a+b \tanh ^{-1}(c x)\right)-\frac{1}{2} b^3 c^3 \text{PolyLog}\left(3,\frac{2}{c x+1}-1\right)-\frac{b^2 c^2 \left(a+b \tanh ^{-1}(c x)\right)}{x}+\frac{1}{3} c^3 \left(a+b \tanh ^{-1}(c x)\right)^3+\frac{1}{2} b c^3 \left(a+b \tanh ^{-1}(c x)\right)^2+b c^3 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)^2}{2 x^2}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{3 x^3}-\frac{1}{2} b^3 c^3 \log \left(1-c^2 x^2\right)+b^3 c^3 \log (x)",1,"-((b^2*c^2*(a + b*ArcTanh[c*x]))/x) + (b*c^3*(a + b*ArcTanh[c*x])^2)/2 - (b*c*(a + b*ArcTanh[c*x])^2)/(2*x^2) + (c^3*(a + b*ArcTanh[c*x])^3)/3 - (a + b*ArcTanh[c*x])^3/(3*x^3) + b^3*c^3*Log[x] - (b^3*c^3*Log[1 - c^2*x^2])/2 + b*c^3*(a + b*ArcTanh[c*x])^2*Log[2 - 2/(1 + c*x)] - b^2*c^3*(a + b*ArcTanh[c*x])*PolyLog[2, -1 + 2/(1 + c*x)] - (b^3*c^3*PolyLog[3, -1 + 2/(1 + c*x)])/2","A",14,11,14,0.7857,1,"{5916, 5982, 266, 36, 29, 31, 5948, 5988, 5932, 6056, 6610}"
34,1,187,0,0.6257898,"\int \frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{x^5} \, dx","Int[(a + b*ArcTanh[c*x])^3/x^5,x]","-b^3 c^4 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)-\frac{b^2 c^2 \left(a+b \tanh ^{-1}(c x)\right)}{4 x^2}+2 b^2 c^4 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} c^4 \left(a+b \tanh ^{-1}(c x)\right)^3+b c^4 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{3 b c^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 x}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)^2}{4 x^3}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{4 x^4}-\frac{b^3 c^3}{4 x}+\frac{1}{4} b^3 c^4 \tanh ^{-1}(c x)","-b^3 c^4 \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)-\frac{b^2 c^2 \left(a+b \tanh ^{-1}(c x)\right)}{4 x^2}+2 b^2 c^4 \log \left(2-\frac{2}{c x+1}\right) \left(a+b \tanh ^{-1}(c x)\right)+\frac{1}{4} c^4 \left(a+b \tanh ^{-1}(c x)\right)^3+b c^4 \left(a+b \tanh ^{-1}(c x)\right)^2-\frac{3 b c^3 \left(a+b \tanh ^{-1}(c x)\right)^2}{4 x}-\frac{b c \left(a+b \tanh ^{-1}(c x)\right)^2}{4 x^3}-\frac{\left(a+b \tanh ^{-1}(c x)\right)^3}{4 x^4}-\frac{b^3 c^3}{4 x}+\frac{1}{4} b^3 c^4 \tanh ^{-1}(c x)",1,"-(b^3*c^3)/(4*x) + (b^3*c^4*ArcTanh[c*x])/4 - (b^2*c^2*(a + b*ArcTanh[c*x]))/(4*x^2) + b*c^4*(a + b*ArcTanh[c*x])^2 - (b*c*(a + b*ArcTanh[c*x])^2)/(4*x^3) - (3*b*c^3*(a + b*ArcTanh[c*x])^2)/(4*x) + (c^4*(a + b*ArcTanh[c*x])^3)/4 - (a + b*ArcTanh[c*x])^3/(4*x^4) + 2*b^2*c^4*(a + b*ArcTanh[c*x])*Log[2 - 2/(1 + c*x)] - b^3*c^4*PolyLog[2, -1 + 2/(1 + c*x)]","A",16,8,14,0.5714,1,"{5916, 5982, 325, 206, 5988, 5932, 2447, 5948}"
35,1,124,0,0.0864655,"\int (d x)^{5/2} \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[(d*x)^(5/2)*(a + b*ArcTanh[c*x]),x]","\frac{2 (d x)^{7/2} \left(a+b \tanh ^{-1}(c x)\right)}{7 d}+\frac{4 b d^2 \sqrt{d x}}{7 c^3}-\frac{2 b d^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 c^{7/2}}-\frac{2 b d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 c^{7/2}}+\frac{4 b (d x)^{5/2}}{35 c}","\frac{2 (d x)^{7/2} \left(a+b \tanh ^{-1}(c x)\right)}{7 d}+\frac{4 b d^2 \sqrt{d x}}{7 c^3}-\frac{2 b d^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 c^{7/2}}-\frac{2 b d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 c^{7/2}}+\frac{4 b (d x)^{5/2}}{35 c}",1,"(4*b*d^2*Sqrt[d*x])/(7*c^3) + (4*b*(d*x)^(5/2))/(35*c) - (2*b*d^(5/2)*ArcTan[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(7*c^(7/2)) + (2*(d*x)^(7/2)*(a + b*ArcTanh[c*x]))/(7*d) - (2*b*d^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(7*c^(7/2))","A",7,6,16,0.3750,1,"{5916, 321, 329, 212, 208, 205}"
36,1,106,0,0.0672078,"\int (d x)^{3/2} \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[(d*x)^(3/2)*(a + b*ArcTanh[c*x]),x]","\frac{2 (d x)^{5/2} \left(a+b \tanh ^{-1}(c x)\right)}{5 d}+\frac{2 b d^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 c^{5/2}}-\frac{2 b d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 c^{5/2}}+\frac{4 b (d x)^{3/2}}{15 c}","\frac{2 (d x)^{5/2} \left(a+b \tanh ^{-1}(c x)\right)}{5 d}+\frac{2 b d^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 c^{5/2}}-\frac{2 b d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 c^{5/2}}+\frac{4 b (d x)^{3/2}}{15 c}",1,"(4*b*(d*x)^(3/2))/(15*c) + (2*b*d^(3/2)*ArcTan[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(5*c^(5/2)) + (2*(d*x)^(5/2)*(a + b*ArcTanh[c*x]))/(5*d) - (2*b*d^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(5*c^(5/2))","A",6,6,16,0.3750,1,"{5916, 321, 329, 298, 205, 208}"
37,1,106,0,0.0612043,"\int \sqrt{d x} \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[Sqrt[d*x]*(a + b*ArcTanh[c*x]),x]","\frac{2 (d x)^{3/2} \left(a+b \tanh ^{-1}(c x)\right)}{3 d}-\frac{2 b \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 c^{3/2}}-\frac{2 b \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 c^{3/2}}+\frac{4 b \sqrt{d x}}{3 c}","\frac{2 (d x)^{3/2} \left(a+b \tanh ^{-1}(c x)\right)}{3 d}-\frac{2 b \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 c^{3/2}}-\frac{2 b \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 c^{3/2}}+\frac{4 b \sqrt{d x}}{3 c}",1,"(4*b*Sqrt[d*x])/(3*c) - (2*b*Sqrt[d]*ArcTan[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(3*c^(3/2)) + (2*(d*x)^(3/2)*(a + b*ArcTanh[c*x]))/(3*d) - (2*b*Sqrt[d]*ArcTanh[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(3*c^(3/2))","A",6,6,16,0.3750,1,"{5916, 321, 329, 212, 208, 205}"
38,1,85,0,0.0515333,"\int \frac{a+b \tanh ^{-1}(c x)}{\sqrt{d x}} \, dx","Int[(a + b*ArcTanh[c*x])/Sqrt[d*x],x]","\frac{2 \sqrt{d x} \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{2 b \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt{c} \sqrt{d}}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt{c} \sqrt{d}}","\frac{2 \sqrt{d x} \left(a+b \tanh ^{-1}(c x)\right)}{d}+\frac{2 b \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt{c} \sqrt{d}}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt{c} \sqrt{d}}",1,"(2*b*ArcTan[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(Sqrt[c]*Sqrt[d]) + (2*Sqrt[d*x]*(a + b*ArcTanh[c*x]))/d - (2*b*ArcTanh[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(Sqrt[c]*Sqrt[d])","A",5,5,16,0.3125,1,"{5916, 329, 298, 205, 208}"
39,1,85,0,0.0546279,"\int \frac{a+b \tanh ^{-1}(c x)}{(d x)^{3/2}} \, dx","Int[(a + b*ArcTanh[c*x])/(d*x)^(3/2),x]","-\frac{2 \left(a+b \tanh ^{-1}(c x)\right)}{d \sqrt{d x}}+\frac{2 b \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{2 b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}","-\frac{2 \left(a+b \tanh ^{-1}(c x)\right)}{d \sqrt{d x}}+\frac{2 b \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{2 b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}",1,"(2*b*Sqrt[c]*ArcTan[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/d^(3/2) - (2*(a + b*ArcTanh[c*x]))/(d*Sqrt[d*x]) + (2*b*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/d^(3/2)","A",5,5,16,0.3125,1,"{5916, 329, 212, 208, 205}"
40,1,107,0,0.0633332,"\int \frac{a+b \tanh ^{-1}(c x)}{(d x)^{5/2}} \, dx","Int[(a + b*ArcTanh[c*x])/(d*x)^(5/2),x]","-\frac{2 \left(a+b \tanh ^{-1}(c x)\right)}{3 d (d x)^{3/2}}-\frac{2 b c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}+\frac{2 b c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{4 b c}{3 d^2 \sqrt{d x}}","-\frac{2 \left(a+b \tanh ^{-1}(c x)\right)}{3 d (d x)^{3/2}}-\frac{2 b c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}+\frac{2 b c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{4 b c}{3 d^2 \sqrt{d x}}",1,"(-4*b*c)/(3*d^2*Sqrt[d*x]) - (2*b*c^(3/2)*ArcTan[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(3*d^(5/2)) - (2*(a + b*ArcTanh[c*x]))/(3*d*(d*x)^(3/2)) + (2*b*c^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(3*d^(5/2))","A",6,6,16,0.3750,1,"{5916, 325, 329, 298, 205, 208}"
41,1,107,0,0.0662016,"\int \frac{a+b \tanh ^{-1}(c x)}{(d x)^{7/2}} \, dx","Int[(a + b*ArcTanh[c*x])/(d*x)^(7/2),x]","-\frac{2 \left(a+b \tanh ^{-1}(c x)\right)}{5 d (d x)^{5/2}}+\frac{2 b c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{2 b c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{4 b c}{15 d^2 (d x)^{3/2}}","-\frac{2 \left(a+b \tanh ^{-1}(c x)\right)}{5 d (d x)^{5/2}}+\frac{2 b c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{2 b c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{4 b c}{15 d^2 (d x)^{3/2}}",1,"(-4*b*c)/(15*d^2*(d*x)^(3/2)) + (2*b*c^(5/2)*ArcTan[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(5*d^(7/2)) - (2*(a + b*ArcTanh[c*x]))/(5*d*(d*x)^(5/2)) + (2*b*c^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(5*d^(7/2))","A",6,6,16,0.3750,1,"{5916, 325, 329, 212, 208, 205}"
42,1,125,0,0.078228,"\int \frac{a+b \tanh ^{-1}(c x)}{(d x)^{9/2}} \, dx","Int[(a + b*ArcTanh[c*x])/(d*x)^(9/2),x]","-\frac{2 \left(a+b \tanh ^{-1}(c x)\right)}{7 d (d x)^{7/2}}-\frac{4 b c^3}{7 d^4 \sqrt{d x}}-\frac{2 b c^{7/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 d^{9/2}}+\frac{2 b c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 d^{9/2}}-\frac{4 b c}{35 d^2 (d x)^{5/2}}","-\frac{2 \left(a+b \tanh ^{-1}(c x)\right)}{7 d (d x)^{7/2}}-\frac{4 b c^3}{7 d^4 \sqrt{d x}}-\frac{2 b c^{7/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 d^{9/2}}+\frac{2 b c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 d^{9/2}}-\frac{4 b c}{35 d^2 (d x)^{5/2}}",1,"(-4*b*c)/(35*d^2*(d*x)^(5/2)) - (4*b*c^3)/(7*d^4*Sqrt[d*x]) - (2*b*c^(7/2)*ArcTan[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(7*d^(9/2)) - (2*(a + b*ArcTanh[c*x]))/(7*d*(d*x)^(7/2)) + (2*b*c^(7/2)*ArcTanh[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]])/(7*d^(9/2))","A",7,6,16,0.3750,1,"{5916, 325, 329, 298, 205, 208}"
43,0,0,0,0.0244612,"\int (d x)^m \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x])^3,x]","\int (d x)^m \left(a+b \tanh ^{-1}(c x)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \tanh ^{-1}(c x)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTanh[c*x])^3, x]","A",0,0,0,0,-1,"{}"
44,0,0,0,0.0234099,"\int (d x)^m \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x])^2,x]","\int (d x)^m \left(a+b \tanh ^{-1}(c x)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \tanh ^{-1}(c x)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTanh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
45,1,72,0,0.032328,"\int (d x)^m \left(a+b \tanh ^{-1}(c x)\right) \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x]),x]","\frac{(d x)^{m+1} \left(a+b \tanh ^{-1}(c x)\right)}{d (m+1)}-\frac{b c (d x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{d^2 (m+1) (m+2)}","\frac{(d x)^{m+1} \left(a+b \tanh ^{-1}(c x)\right)}{d (m+1)}-\frac{b c (d x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{d^2 (m+1) (m+2)}",1,"((d*x)^(1 + m)*(a + b*ArcTanh[c*x]))/(d*(1 + m)) - (b*c*(d*x)^(2 + m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, c^2*x^2])/(d^2*(1 + m)*(2 + m))","A",2,2,14,0.1429,1,"{5916, 364}"
46,0,0,0,0.0271058,"\int \frac{(d x)^m}{a+b \tanh ^{-1}(c x)} \, dx","Int[(d*x)^m/(a + b*ArcTanh[c*x]),x]","\int \frac{(d x)^m}{a+b \tanh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \tanh ^{-1}(c x)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTanh[c*x]), x]","A",0,0,0,0,-1,"{}"
47,0,0,0,0.0263568,"\int \frac{(d x)^m}{\left(a+b \tanh ^{-1}(c x)\right)^2} \, dx","Int[(d*x)^m/(a + b*ArcTanh[c*x])^2,x]","\int \frac{(d x)^m}{\left(a+b \tanh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^m}{\left(a+b \tanh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTanh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
48,0,0,0,0.0053112,"\int \left(a+b \tanh ^{-1}(c x)\right)^p \, dx","Int[(a + b*ArcTanh[c*x])^p,x]","\int \left(a+b \tanh ^{-1}(c x)\right)^p \, dx","\text{Int}\left(\left(a+b \tanh ^{-1}(c x)\right)^p,x\right)",0,"Defer[Int][(a + b*ArcTanh[c*x])^p, x]","A",0,0,0,0,-1,"{}"
49,0,0,0,0.0236748,"\int (d x)^m \left(a+b \tanh ^{-1}(c x)\right)^p \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x])^p,x]","\int (d x)^m \left(a+b \tanh ^{-1}(c x)\right)^p \, dx","\text{Int}\left((d x)^m \left(a+b \tanh ^{-1}(c x)\right)^p,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTanh[c*x])^p, x]","A",0,0,0,0,-1,"{}"
50,1,54,0,0.03915,"\int x^7 \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[x^7*(a + b*ArcTanh[c*x^2]),x]","\frac{1}{8} x^8 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{b x^2}{8 c^3}-\frac{b \tanh ^{-1}\left(c x^2\right)}{8 c^4}+\frac{b x^6}{24 c}","\frac{1}{8} x^8 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{b x^2}{8 c^3}-\frac{b \tanh ^{-1}\left(c x^2\right)}{8 c^4}+\frac{b x^6}{24 c}",1,"(b*x^2)/(8*c^3) + (b*x^6)/(24*c) - (b*ArcTanh[c*x^2])/(8*c^4) + (x^8*(a + b*ArcTanh[c*x^2]))/8","A",5,4,14,0.2857,1,"{6097, 275, 302, 206}"
51,1,48,0,0.0347672,"\int x^5 \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[x^5*(a + b*ArcTanh[c*x^2]),x]","\frac{1}{6} x^6 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{b \log \left(1-c^2 x^4\right)}{12 c^3}+\frac{b x^4}{12 c}","\frac{1}{6} x^6 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{b \log \left(1-c^2 x^4\right)}{12 c^3}+\frac{b x^4}{12 c}",1,"(b*x^4)/(12*c) + (x^6*(a + b*ArcTanh[c*x^2]))/6 + (b*Log[1 - c^2*x^4])/(12*c^3)","A",4,3,14,0.2143,1,"{6097, 266, 43}"
52,1,43,0,0.0297085,"\int x^3 \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[x^3*(a + b*ArcTanh[c*x^2]),x]","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)-\frac{b \tanh ^{-1}\left(c x^2\right)}{4 c^2}+\frac{b x^2}{4 c}","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)-\frac{b \tanh ^{-1}\left(c x^2\right)}{4 c^2}+\frac{b x^2}{4 c}",1,"(b*x^2)/(4*c) - (b*ArcTanh[c*x^2])/(4*c^2) + (x^4*(a + b*ArcTanh[c*x^2]))/4","A",4,4,14,0.2857,1,"{6097, 275, 321, 206}"
53,1,37,0,0.0149314,"\int x \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[x*(a + b*ArcTanh[c*x^2]),x]","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{b \log \left(1-c^2 x^4\right)}{4 c}","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{b \log \left(1-c^2 x^4\right)}{4 c}",1,"(x^2*(a + b*ArcTanh[c*x^2]))/2 + (b*Log[1 - c^2*x^4])/(4*c)","A",2,2,12,0.1667,1,"{6097, 260}"
54,1,30,0,0.0331072,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{x} \, dx","Int[(a + b*ArcTanh[c*x^2])/x,x]","-\frac{1}{4} b \text{PolyLog}\left(2,-c x^2\right)+\frac{1}{4} b \text{PolyLog}\left(2,c x^2\right)+a \log (x)","-\frac{1}{4} b \text{PolyLog}\left(2,-c x^2\right)+\frac{1}{4} b \text{PolyLog}\left(2,c x^2\right)+a \log (x)",1,"a*Log[x] - (b*PolyLog[2, -(c*x^2)])/4 + (b*PolyLog[2, c*x^2])/4","A",2,2,14,0.1429,1,"{6095, 5912}"
55,1,40,0,0.0255877,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{x^3} \, dx","Int[(a + b*ArcTanh[c*x^2])/x^3,x]","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{2 x^2}-\frac{1}{4} b c \log \left(1-c^2 x^4\right)+b c \log (x)","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{2 x^2}-\frac{1}{4} b c \log \left(1-c^2 x^4\right)+b c \log (x)",1,"-(a + b*ArcTanh[c*x^2])/(2*x^2) + b*c*Log[x] - (b*c*Log[1 - c^2*x^4])/4","A",5,5,14,0.3571,1,"{6097, 266, 36, 29, 31}"
56,1,41,0,0.0266015,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{x^5} \, dx","Int[(a + b*ArcTanh[c*x^2])/x^5,x]","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{4 x^4}+\frac{1}{4} b c^2 \tanh ^{-1}\left(c x^2\right)-\frac{b c}{4 x^2}","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{4 x^4}+\frac{1}{4} b c^2 \tanh ^{-1}\left(c x^2\right)-\frac{b c}{4 x^2}",1,"-(b*c)/(4*x^2) + (b*c^2*ArcTanh[c*x^2])/4 - (a + b*ArcTanh[c*x^2])/(4*x^4)","A",4,4,14,0.2857,1,"{6097, 275, 325, 206}"
57,1,56,0,0.0340155,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{x^7} \, dx","Int[(a + b*ArcTanh[c*x^2])/x^7,x]","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{6 x^6}-\frac{1}{12} b c^3 \log \left(1-c^2 x^4\right)+\frac{1}{3} b c^3 \log (x)-\frac{b c}{12 x^4}","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{6 x^6}-\frac{1}{12} b c^3 \log \left(1-c^2 x^4\right)+\frac{1}{3} b c^3 \log (x)-\frac{b c}{12 x^4}",1,"-(b*c)/(12*x^4) - (a + b*ArcTanh[c*x^2])/(6*x^6) + (b*c^3*Log[x])/3 - (b*c^3*Log[1 - c^2*x^4])/12","A",4,3,14,0.2143,1,"{6097, 266, 44}"
58,1,65,0,0.0352452,"\int x^4 \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[x^4*(a + b*ArcTanh[c*x^2]),x]","\frac{1}{5} x^5 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{b \tan ^{-1}\left(\sqrt{c} x\right)}{5 c^{5/2}}-\frac{b \tanh ^{-1}\left(\sqrt{c} x\right)}{5 c^{5/2}}+\frac{2 b x^3}{15 c}","\frac{1}{5} x^5 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{b \tan ^{-1}\left(\sqrt{c} x\right)}{5 c^{5/2}}-\frac{b \tanh ^{-1}\left(\sqrt{c} x\right)}{5 c^{5/2}}+\frac{2 b x^3}{15 c}",1,"(2*b*x^3)/(15*c) + (b*ArcTan[Sqrt[c]*x])/(5*c^(5/2)) - (b*ArcTanh[Sqrt[c]*x])/(5*c^(5/2)) + (x^5*(a + b*ArcTanh[c*x^2]))/5","A",5,5,14,0.3571,1,"{6097, 321, 298, 203, 206}"
59,1,63,0,0.0330533,"\int x^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[x^2*(a + b*ArcTanh[c*x^2]),x]","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)-\frac{b \tan ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}-\frac{b \tanh ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}+\frac{2 b x}{3 c}","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)-\frac{b \tan ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}-\frac{b \tanh ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}+\frac{2 b x}{3 c}",1,"(2*b*x)/(3*c) - (b*ArcTan[Sqrt[c]*x])/(3*c^(3/2)) - (b*ArcTanh[Sqrt[c]*x])/(3*c^(3/2)) + (x^3*(a + b*ArcTanh[c*x^2]))/3","A",5,5,14,0.3571,1,"{6097, 321, 212, 206, 203}"
60,1,44,0,0.0244469,"\int \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[a + b*ArcTanh[c*x^2],x]","a x+b x \tanh ^{-1}\left(c x^2\right)+\frac{b \tan ^{-1}\left(\sqrt{c} x\right)}{\sqrt{c}}-\frac{b \tanh ^{-1}\left(\sqrt{c} x\right)}{\sqrt{c}}","a x+b x \tanh ^{-1}\left(c x^2\right)+\frac{b \tan ^{-1}\left(\sqrt{c} x\right)}{\sqrt{c}}-\frac{b \tanh ^{-1}\left(\sqrt{c} x\right)}{\sqrt{c}}",1,"a*x + (b*ArcTan[Sqrt[c]*x])/Sqrt[c] - (b*ArcTanh[Sqrt[c]*x])/Sqrt[c] + b*x*ArcTanh[c*x^2]","A",5,4,10,0.4000,1,"{6091, 298, 203, 206}"
61,1,46,0,0.0256217,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{x^2} \, dx","Int[(a + b*ArcTanh[c*x^2])/x^2,x]","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{x}+b \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right)+b \sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right)","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{x}+b \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right)+b \sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right)",1,"b*Sqrt[c]*ArcTan[Sqrt[c]*x] + b*Sqrt[c]*ArcTanh[Sqrt[c]*x] - (a + b*ArcTanh[c*x^2])/x","A",4,4,14,0.2857,1,"{6097, 212, 206, 203}"
62,1,63,0,0.0334463,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{x^4} \, dx","Int[(a + b*ArcTanh[c*x^2])/x^4,x]","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{3 x^3}-\frac{1}{3} b c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right)+\frac{1}{3} b c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right)-\frac{2 b c}{3 x}","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{3 x^3}-\frac{1}{3} b c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right)+\frac{1}{3} b c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right)-\frac{2 b c}{3 x}",1,"(-2*b*c)/(3*x) - (b*c^(3/2)*ArcTan[Sqrt[c]*x])/3 + (b*c^(3/2)*ArcTanh[Sqrt[c]*x])/3 - (a + b*ArcTanh[c*x^2])/(3*x^3)","A",5,5,14,0.3571,1,"{6097, 325, 298, 203, 206}"
63,1,63,0,0.0319471,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{x^6} \, dx","Int[(a + b*ArcTanh[c*x^2])/x^6,x]","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{5 x^5}+\frac{1}{5} b c^{5/2} \tan ^{-1}\left(\sqrt{c} x\right)+\frac{1}{5} b c^{5/2} \tanh ^{-1}\left(\sqrt{c} x\right)-\frac{2 b c}{15 x^3}","-\frac{a+b \tanh ^{-1}\left(c x^2\right)}{5 x^5}+\frac{1}{5} b c^{5/2} \tan ^{-1}\left(\sqrt{c} x\right)+\frac{1}{5} b c^{5/2} \tanh ^{-1}\left(\sqrt{c} x\right)-\frac{2 b c}{15 x^3}",1,"(-2*b*c)/(15*x^3) + (b*c^(5/2)*ArcTan[Sqrt[c]*x])/5 + (b*c^(5/2)*ArcTanh[Sqrt[c]*x])/5 - (a + b*ArcTanh[c*x^2])/(5*x^5)","A",5,5,14,0.3571,1,"{6097, 325, 212, 206, 203}"
64,1,636,0,1.5473129,"\int x^7 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[x^7*(a + b*ArcTanh[c*x^2])^2,x]","\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^2\right)\right)}{16 c^4}+\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^2+1\right)\right)}{16 c^4}+\frac{a b x^2}{8 c^3}-\frac{b x^4 \left(2 a-b \log \left(1-c x^2\right)\right)}{32 c^2}-\frac{1}{192} b \left(-\frac{3 \left(1-c x^2\right)^4}{c^4}+\frac{16 \left(1-c x^2\right)^3}{c^4}-\frac{36 \left(1-c x^2\right)^2}{c^4}+\frac{48 \left(1-c x^2\right)}{c^4}-\frac{12 \log \left(1-c x^2\right)}{c^4}\right) \left(2 a-b \log \left(1-c x^2\right)\right)-\frac{b \log \left(\frac{1}{2} \left(c x^2+1\right)\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{16 c^4}+\frac{1}{32} x^8 \left(2 a-b \log \left(1-c x^2\right)\right)^2-\frac{1}{64} b x^8 \left(2 a-b \log \left(1-c x^2\right)\right)+\frac{1}{16} b x^8 \log \left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)+\frac{b x^6 \left(2 a-b \log \left(1-c x^2\right)\right)}{48 c}+\frac{b^2 x^4}{128 c^2}+\frac{23 b^2 x^2}{192 c^3}+\frac{b^2 \left(1-c x^2\right)^4}{256 c^4}-\frac{b^2 \left(1-c x^2\right)^3}{36 c^4}+\frac{3 b^2 \left(1-c x^2\right)^2}{32 c^4}+\frac{b^2 \log ^2\left(1-c x^2\right)}{32 c^4}-\frac{b^2 \log ^2\left(c x^2+1\right)}{32 c^4}+\frac{b^2 \left(1-c x^2\right) \log \left(1-c x^2\right)}{16 c^4}-\frac{5 b^2 \log \left(1-c x^2\right)}{192 c^4}+\frac{b^2 \left(c x^2+1\right) \log \left(c x^2+1\right)}{8 c^4}+\frac{b^2 \log \left(\frac{1}{2} \left(1-c x^2\right)\right) \log \left(c x^2+1\right)}{16 c^4}+\frac{b^2 \log \left(c x^2+1\right)}{24 c^4}-\frac{7 b^2 x^6}{576 c}+\frac{1}{32} b^2 x^8 \log ^2\left(c x^2+1\right)+\frac{b^2 x^6 \log \left(c x^2+1\right)}{24 c}-\frac{1}{256} b^2 x^8","\frac{a b x^2}{4 c^3}-\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{8 c^4}+\frac{1}{8} x^8 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2+\frac{b x^6 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{12 c}+\frac{b^2 x^4}{24 c^2}+\frac{b^2 \log \left(1-c^2 x^4\right)}{6 c^4}+\frac{b^2 x^2 \tanh ^{-1}\left(c x^2\right)}{4 c^3}",1,"(a*b*x^2)/(8*c^3) + (23*b^2*x^2)/(192*c^3) + (b^2*x^4)/(128*c^2) - (7*b^2*x^6)/(576*c) - (b^2*x^8)/256 + (3*b^2*(1 - c*x^2)^2)/(32*c^4) - (b^2*(1 - c*x^2)^3)/(36*c^4) + (b^2*(1 - c*x^2)^4)/(256*c^4) - (5*b^2*Log[1 - c*x^2])/(192*c^4) + (b^2*(1 - c*x^2)*Log[1 - c*x^2])/(16*c^4) + (b^2*Log[1 - c*x^2]^2)/(32*c^4) - (b*x^4*(2*a - b*Log[1 - c*x^2]))/(32*c^2) + (b*x^6*(2*a - b*Log[1 - c*x^2]))/(48*c) - (b*x^8*(2*a - b*Log[1 - c*x^2]))/64 + (x^8*(2*a - b*Log[1 - c*x^2])^2)/32 - (b*(2*a - b*Log[1 - c*x^2])*((48*(1 - c*x^2))/c^4 - (36*(1 - c*x^2)^2)/c^4 + (16*(1 - c*x^2)^3)/c^4 - (3*(1 - c*x^2)^4)/c^4 - (12*Log[1 - c*x^2])/c^4))/192 - (b*(2*a - b*Log[1 - c*x^2])*Log[(1 + c*x^2)/2])/(16*c^4) + (b^2*Log[1 + c*x^2])/(24*c^4) + (b^2*x^6*Log[1 + c*x^2])/(24*c) + (b^2*(1 + c*x^2)*Log[1 + c*x^2])/(8*c^4) + (b^2*Log[(1 - c*x^2)/2]*Log[1 + c*x^2])/(16*c^4) + (b*x^8*(2*a - b*Log[1 - c*x^2])*Log[1 + c*x^2])/16 - (b^2*Log[1 + c*x^2]^2)/(32*c^4) + (b^2*x^8*Log[1 + c*x^2]^2)/32 + (b^2*PolyLog[2, (1 - c*x^2)/2])/(16*c^4) + (b^2*PolyLog[2, (1 + c*x^2)/2])/(16*c^4)","C",62,19,16,1.187,0,"{6099, 2454, 2398, 2411, 43, 2334, 12, 14, 2301, 2395, 2439, 2416, 2389, 2295, 2394, 2393, 2391, 2410, 2390}"
65,1,536,0,1.2960381,"\int x^5 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[x^5*(a + b*ArcTanh[c*x^2])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^2\right)\right)}{12 c^3}+\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^2+1\right)\right)}{12 c^3}-\frac{a b x^2}{6 c^2}-\frac{1}{72} b \left(\frac{2 \left(1-c x^2\right)^3}{c^3}-\frac{9 \left(1-c x^2\right)^2}{c^3}+\frac{18 \left(1-c x^2\right)}{c^3}-\frac{6 \log \left(1-c x^2\right)}{c^3}\right) \left(2 a-b \log \left(1-c x^2\right)\right)+\frac{b \log \left(\frac{1}{2} \left(c x^2+1\right)\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{12 c^3}+\frac{1}{24} x^6 \left(2 a-b \log \left(1-c x^2\right)\right)^2-\frac{1}{36} b x^6 \left(2 a-b \log \left(1-c x^2\right)\right)+\frac{1}{12} b x^6 \log \left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)+\frac{b x^4 \left(2 a-b \log \left(1-c x^2\right)\right)}{24 c}+\frac{19 b^2 x^2}{72 c^2}-\frac{b^2 \left(1-c x^2\right)^3}{108 c^3}+\frac{b^2 \left(1-c x^2\right)^2}{16 c^3}+\frac{b^2 \log ^2\left(1-c x^2\right)}{24 c^3}+\frac{b^2 \log ^2\left(c x^2+1\right)}{24 c^3}-\frac{b^2 \left(1-c x^2\right) \log \left(1-c x^2\right)}{12 c^3}+\frac{b^2 \log \left(1-c x^2\right)}{72 c^3}+\frac{b^2 \log \left(\frac{1}{2} \left(1-c x^2\right)\right) \log \left(c x^2+1\right)}{12 c^3}-\frac{b^2 \log \left(c x^2+1\right)}{12 c^3}-\frac{5 b^2 x^4}{144 c}+\frac{1}{24} b^2 x^6 \log ^2\left(c x^2+1\right)+\frac{b^2 x^4 \log \left(c x^2+1\right)}{12 c}-\frac{1}{108} b^2 x^6","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x^2}\right)}{6 c^3}+\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{6 c^3}-\frac{b \log \left(\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{3 c^3}+\frac{1}{6} x^6 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2+\frac{b x^4 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{6 c}+\frac{b^2 x^2}{6 c^2}-\frac{b^2 \tanh ^{-1}\left(c x^2\right)}{6 c^3}",1,"-(a*b*x^2)/(6*c^2) + (19*b^2*x^2)/(72*c^2) - (5*b^2*x^4)/(144*c) - (b^2*x^6)/108 + (b^2*(1 - c*x^2)^2)/(16*c^3) - (b^2*(1 - c*x^2)^3)/(108*c^3) + (b^2*Log[1 - c*x^2])/(72*c^3) - (b^2*(1 - c*x^2)*Log[1 - c*x^2])/(12*c^3) + (b^2*Log[1 - c*x^2]^2)/(24*c^3) + (b*x^4*(2*a - b*Log[1 - c*x^2]))/(24*c) - (b*x^6*(2*a - b*Log[1 - c*x^2]))/36 + (x^6*(2*a - b*Log[1 - c*x^2])^2)/24 - (b*(2*a - b*Log[1 - c*x^2])*((18*(1 - c*x^2))/c^3 - (9*(1 - c*x^2)^2)/c^3 + (2*(1 - c*x^2)^3)/c^3 - (6*Log[1 - c*x^2])/c^3))/72 + (b*(2*a - b*Log[1 - c*x^2])*Log[(1 + c*x^2)/2])/(12*c^3) - (b^2*Log[1 + c*x^2])/(12*c^3) + (b^2*x^4*Log[1 + c*x^2])/(12*c) + (b^2*Log[(1 - c*x^2)/2]*Log[1 + c*x^2])/(12*c^3) + (b*x^6*(2*a - b*Log[1 - c*x^2])*Log[1 + c*x^2])/12 + (b^2*Log[1 + c*x^2]^2)/(24*c^3) + (b^2*x^6*Log[1 + c*x^2]^2)/24 - (b^2*PolyLog[2, (1 - c*x^2)/2])/(12*c^3) + (b^2*PolyLog[2, (1 + c*x^2)/2])/(12*c^3)","B",53,19,16,1.187,0,"{6099, 2454, 2398, 2411, 43, 2334, 12, 14, 2301, 2395, 2439, 2416, 2389, 2295, 2394, 2393, 2391, 2410, 2390}"
66,1,524,0,0.9654895,"\int x^3 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[x^3*(a + b*ArcTanh[c*x^2])^2,x]","\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^2\right)\right)}{8 c^2}+\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^2+1\right)\right)}{8 c^2}+\frac{\left(1-c x^2\right)^2 \left(2 a-b \log \left(1-c x^2\right)\right)^2}{16 c^2}-\frac{\left(1-c x^2\right) \left(2 a-b \log \left(1-c x^2\right)\right)^2}{8 c^2}+\frac{b \left(1-c x^2\right)^2 \left(2 a-b \log \left(1-c x^2\right)\right)}{16 c^2}-\frac{b \log \left(\frac{1}{2} \left(c x^2+1\right)\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{8 c^2}+\frac{3 a b x^2}{4 c}-\frac{1}{16} b x^4 \left(2 a-b \log \left(1-c x^2\right)\right)+\frac{1}{8} b x^4 \log \left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)+\frac{b^2 \left(1-c x^2\right)^2}{32 c^2}+\frac{b^2 \left(c x^2+1\right)^2}{32 c^2}+\frac{b^2 \left(c x^2+1\right)^2 \log ^2\left(c x^2+1\right)}{16 c^2}-\frac{b^2 \left(c x^2+1\right) \log ^2\left(c x^2+1\right)}{8 c^2}+\frac{3 b^2 \left(1-c x^2\right) \log \left(1-c x^2\right)}{8 c^2}-\frac{b^2 \log \left(1-c x^2\right)}{16 c^2}-\frac{b^2 \left(c x^2+1\right)^2 \log \left(c x^2+1\right)}{16 c^2}+\frac{3 b^2 \left(c x^2+1\right) \log \left(c x^2+1\right)}{8 c^2}+\frac{b^2 \log \left(\frac{1}{2} \left(1-c x^2\right)\right) \log \left(c x^2+1\right)}{8 c^2}-\frac{b^2 \log \left(c x^2+1\right)}{16 c^2}+\frac{1}{16} b^2 x^4 \log \left(c x^2+1\right)-\frac{1}{16} b^2 x^4","-\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{4 c^2}+\frac{a b x^2}{2 c}+\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2+\frac{b^2 \log \left(1-c^2 x^4\right)}{4 c^2}+\frac{b^2 x^2 \tanh ^{-1}\left(c x^2\right)}{2 c}",1,"(3*a*b*x^2)/(4*c) - (b^2*x^4)/16 + (b^2*(1 - c*x^2)^2)/(32*c^2) + (b^2*(1 + c*x^2)^2)/(32*c^2) - (b^2*Log[1 - c*x^2])/(16*c^2) + (3*b^2*(1 - c*x^2)*Log[1 - c*x^2])/(8*c^2) - (b*x^4*(2*a - b*Log[1 - c*x^2]))/16 + (b*(1 - c*x^2)^2*(2*a - b*Log[1 - c*x^2]))/(16*c^2) - ((1 - c*x^2)*(2*a - b*Log[1 - c*x^2])^2)/(8*c^2) + ((1 - c*x^2)^2*(2*a - b*Log[1 - c*x^2])^2)/(16*c^2) - (b*(2*a - b*Log[1 - c*x^2])*Log[(1 + c*x^2)/2])/(8*c^2) - (b^2*Log[1 + c*x^2])/(16*c^2) + (b^2*x^4*Log[1 + c*x^2])/16 + (3*b^2*(1 + c*x^2)*Log[1 + c*x^2])/(8*c^2) - (b^2*(1 + c*x^2)^2*Log[1 + c*x^2])/(16*c^2) + (b^2*Log[(1 - c*x^2)/2]*Log[1 + c*x^2])/(8*c^2) + (b*x^4*(2*a - b*Log[1 - c*x^2])*Log[1 + c*x^2])/8 - (b^2*(1 + c*x^2)*Log[1 + c*x^2]^2)/(8*c^2) + (b^2*(1 + c*x^2)^2*Log[1 + c*x^2]^2)/(16*c^2) + (b^2*PolyLog[2, (1 - c*x^2)/2])/(8*c^2) + (b^2*PolyLog[2, (1 + c*x^2)/2])/(8*c^2)","C",44,16,16,1.000,0,"{6099, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2395, 43, 2439, 2416, 2394, 2393, 2391}"
67,1,207,0,0.5138985,"\int x \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[x*(a + b*ArcTanh[c*x^2])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^2\right)\right)}{4 c}+\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^2+1\right)\right)}{4 c}+\frac{b \log \left(\frac{1}{2} \left(c x^2+1\right)\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{4 c}+\frac{1}{4} b x^2 \log \left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)-\frac{\left(1-c x^2\right) \left(2 a-b \log \left(1-c x^2\right)\right)^2}{8 c}+\frac{b^2 \left(c x^2+1\right) \log ^2\left(c x^2+1\right)}{8 c}+\frac{b^2 \log \left(\frac{1}{2} \left(1-c x^2\right)\right) \log \left(c x^2+1\right)}{4 c}","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x^2}\right)}{2 c}+\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2+\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{2 c}-\frac{b \log \left(\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{c}",1,"-((1 - c*x^2)*(2*a - b*Log[1 - c*x^2])^2)/(8*c) + (b*(2*a - b*Log[1 - c*x^2])*Log[(1 + c*x^2)/2])/(4*c) + (b^2*Log[(1 - c*x^2)/2]*Log[1 + c*x^2])/(4*c) + (b*x^2*(2*a - b*Log[1 - c*x^2])*Log[1 + c*x^2])/4 + (b^2*(1 + c*x^2)*Log[1 + c*x^2]^2)/(8*c) - (b^2*PolyLog[2, (1 - c*x^2)/2])/(4*c) + (b^2*PolyLog[2, (1 + c*x^2)/2])/(4*c)","B",28,12,14,0.8571,0,"{6099, 2454, 2389, 2296, 2295, 6715, 2430, 43, 2416, 2394, 2393, 2391}"
68,1,137,0,0.3355391,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{x} \, dx","Int[(a + b*ArcTanh[c*x^2])^2/x,x]","-\frac{1}{2} b \text{PolyLog}\left(2,1-\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{1}{2} b \text{PolyLog}\left(2,\frac{2}{1-c x^2}-1\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{1}{4} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^2}\right)-\frac{1}{4} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^2}-1\right)+\tanh ^{-1}\left(1-\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2","-\frac{1}{2} b \text{PolyLog}\left(2,1-\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{1}{2} b \text{PolyLog}\left(2,\frac{2}{1-c x^2}-1\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{1}{4} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^2}\right)-\frac{1}{4} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^2}-1\right)+\tanh ^{-1}\left(1-\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2",1,"(a + b*ArcTanh[c*x^2])^2*ArcTanh[1 - 2/(1 - c*x^2)] - (b*(a + b*ArcTanh[c*x^2])*PolyLog[2, 1 - 2/(1 - c*x^2)])/2 + (b*(a + b*ArcTanh[c*x^2])*PolyLog[2, -1 + 2/(1 - c*x^2)])/2 + (b^2*PolyLog[3, 1 - 2/(1 - c*x^2)])/4 - (b^2*PolyLog[3, -1 + 2/(1 - c*x^2)])/4","A",7,6,16,0.3750,1,"{6095, 5914, 6052, 5948, 6058, 6610}"
69,1,237,0,0.6315902,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{x^3} \, dx","Int[(a + b*ArcTanh[c*x^2])^2/x^3,x]","-\frac{1}{2} b^2 c \text{PolyLog}\left(2,-c x^2\right)+\frac{1}{2} b^2 c \text{PolyLog}\left(2,c x^2\right)+\frac{1}{4} b^2 c \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^2\right)\right)-\frac{1}{4} b^2 c \text{PolyLog}\left(2,\frac{1}{2} \left(c x^2+1\right)\right)-\frac{1}{4} b c \log \left(\frac{1}{2} \left(c x^2+1\right)\right) \left(2 a-b \log \left(1-c x^2\right)\right)-\frac{b \log \left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{4 x^2}-\frac{\left(1-c x^2\right) \left(2 a-b \log \left(1-c x^2\right)\right)^2}{8 x^2}+2 a b c \log (x)-\frac{b^2 \left(c x^2+1\right) \log ^2\left(c x^2+1\right)}{8 x^2}-\frac{1}{4} b^2 c \log \left(\frac{1}{2} \left(1-c x^2\right)\right) \log \left(c x^2+1\right)","-\frac{1}{2} b^2 c \text{PolyLog}\left(2,\frac{2}{c x^2+1}-1\right)+\frac{1}{2} c \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2-\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{2 x^2}+b c \log \left(2-\frac{2}{c x^2+1}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)",1,"2*a*b*c*Log[x] - ((1 - c*x^2)*(2*a - b*Log[1 - c*x^2])^2)/(8*x^2) - (b*c*(2*a - b*Log[1 - c*x^2])*Log[(1 + c*x^2)/2])/4 - (b^2*c*Log[(1 - c*x^2)/2]*Log[1 + c*x^2])/4 - (b*(2*a - b*Log[1 - c*x^2])*Log[1 + c*x^2])/(4*x^2) - (b^2*(1 + c*x^2)*Log[1 + c*x^2]^2)/(8*x^2) - (b^2*c*PolyLog[2, -(c*x^2)])/2 + (b^2*c*PolyLog[2, c*x^2])/2 + (b^2*c*PolyLog[2, (1 - c*x^2)/2])/4 - (b^2*c*PolyLog[2, (1 + c*x^2)/2])/4","B",24,13,16,0.8125,0,"{6099, 2454, 2397, 2392, 2391, 2395, 36, 29, 31, 2439, 2416, 2394, 2393}"
70,1,360,0,1.0567167,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{x^5} \, dx","Int[(a + b*ArcTanh[c*x^2])^2/x^5,x]","-\frac{1}{8} b^2 c^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^2\right)\right)-\frac{1}{8} b^2 c^2 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^2+1\right)\right)+\frac{1}{8} b c^2 \log \left(\frac{1}{2} \left(c x^2+1\right)\right) \left(2 a-b \log \left(1-c x^2\right)\right)+\frac{1}{16} c^2 \left(2 a-b \log \left(1-c x^2\right)\right)^2-\frac{b c \left(1-c x^2\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{8 x^2}-\frac{b c \left(2 a-b \log \left(1-c x^2\right)\right)}{8 x^2}-\frac{b \log \left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{8 x^4}-\frac{\left(2 a-b \log \left(1-c x^2\right)\right)^2}{16 x^4}+\frac{1}{16} b^2 c^2 \log ^2\left(c x^2+1\right)-\frac{1}{8} b^2 c^2 \log \left(1-c x^2\right)-\frac{1}{4} b^2 c^2 \log \left(c x^2+1\right)-\frac{1}{8} b^2 c^2 \log \left(\frac{1}{2} \left(1-c x^2\right)\right) \log \left(c x^2+1\right)+b^2 c^2 \log (x)-\frac{b^2 \log ^2\left(c x^2+1\right)}{16 x^4}-\frac{b^2 c \log \left(c x^2+1\right)}{4 x^2}","\frac{1}{4} c^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2-\frac{b c \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{2 x^2}-\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{4 x^4}-\frac{1}{4} b^2 c^2 \log \left(1-c^2 x^4\right)+b^2 c^2 \log (x)",1,"b^2*c^2*Log[x] - (b^2*c^2*Log[1 - c*x^2])/8 - (b*c*(2*a - b*Log[1 - c*x^2]))/(8*x^2) - (b*c*(1 - c*x^2)*(2*a - b*Log[1 - c*x^2]))/(8*x^2) + (c^2*(2*a - b*Log[1 - c*x^2])^2)/16 - (2*a - b*Log[1 - c*x^2])^2/(16*x^4) + (b*c^2*(2*a - b*Log[1 - c*x^2])*Log[(1 + c*x^2)/2])/8 - (b^2*c^2*Log[1 + c*x^2])/4 - (b^2*c*Log[1 + c*x^2])/(4*x^2) - (b^2*c^2*Log[(1 - c*x^2)/2]*Log[1 + c*x^2])/8 - (b*(2*a - b*Log[1 - c*x^2])*Log[1 + c*x^2])/(8*x^4) + (b^2*c^2*Log[1 + c*x^2]^2)/16 - (b^2*Log[1 + c*x^2]^2)/(16*x^4) - (b^2*c^2*PolyLog[2, (1 - c*x^2)/2])/8 - (b^2*c^2*PolyLog[2, (1 + c*x^2)/2])/8","C",46,23,16,1.438,0,"{6099, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2395, 44, 2439, 2416, 36, 29, 2392, 2391, 2394, 2393, 2410, 2390}"
71,1,1173,0,2.3339413,"\int x^4 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[x^4*(a + b*ArcTanh[c*x^2])^2,x]","\frac{1}{20} \left(2 a-b \log \left(1-c x^2\right)\right)^2 x^5+\frac{1}{20} b^2 \log ^2\left(c x^2+1\right) x^5-\frac{2}{25} a b x^5+\frac{1}{25} b^2 \log \left(1-c x^2\right) x^5+\frac{1}{25} b \left(2 a-b \log \left(1-c x^2\right)\right) x^5+\frac{1}{5} a b \log \left(c x^2+1\right) x^5-\frac{1}{10} b^2 \log \left(1-c x^2\right) \log \left(c x^2+1\right) x^5-\frac{b^2 \log \left(1-c x^2\right) x^3}{15 c}+\frac{b \left(2 a-b \log \left(1-c x^2\right)\right) x^3}{15 c}+\frac{2 b^2 \log \left(c x^2+1\right) x^3}{15 c}+\frac{2 a b x^3}{15 c}+\frac{8 b^2 x}{15 c^2}+\frac{i b^2 \tan ^{-1}\left(\sqrt{c} x\right)^2}{5 c^{5/2}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right)^2}{5 c^{5/2}}-\frac{4 b^2 \tan ^{-1}\left(\sqrt{c} x\right)}{15 c^{5/2}}+\frac{2 a b \tan ^{-1}\left(\sqrt{c} x\right)}{5 c^{5/2}}-\frac{4 b^2 \tanh ^{-1}\left(\sqrt{c} x\right)}{15 c^{5/2}}+\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right)}{5 c^{5/2}}-\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right)}{5 c^{5/2}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{5 c^{5/2}}+\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right)}{5 c^{5/2}}-\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right)}{5 c^{5/2}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{5 c^{5/2}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{5 c^{5/2}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{5 c^{5/2}}-\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right)}{5 c^{5/2}}-\frac{b \tanh ^{-1}\left(\sqrt{c} x\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{5 c^{5/2}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{5 c^{5/2}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{5 c^{5/2}}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right)}{5 c^{5/2}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right)}{5 c^{5/2}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{10 c^{5/2}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right)}{5 c^{5/2}}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right)}{5 c^{5/2}}-\frac{b^2 \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right)}{10 c^{5/2}}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{10 c^{5/2}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{10 c^{5/2}}","\frac{1}{20} \left(2 a-b \log \left(1-c x^2\right)\right)^2 x^5+\frac{1}{20} b^2 \log ^2\left(c x^2+1\right) x^5-\frac{2}{25} a b x^5+\frac{1}{25} b^2 \log \left(1-c x^2\right) x^5+\frac{1}{25} b \left(2 a-b \log \left(1-c x^2\right)\right) x^5+\frac{1}{5} a b \log \left(c x^2+1\right) x^5-\frac{1}{10} b^2 \log \left(1-c x^2\right) \log \left(c x^2+1\right) x^5-\frac{b^2 \log \left(1-c x^2\right) x^3}{15 c}+\frac{b \left(2 a-b \log \left(1-c x^2\right)\right) x^3}{15 c}+\frac{2 b^2 \log \left(c x^2+1\right) x^3}{15 c}+\frac{2 a b x^3}{15 c}+\frac{8 b^2 x}{15 c^2}+\frac{i b^2 \tan ^{-1}\left(\sqrt{c} x\right)^2}{5 c^{5/2}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right)^2}{5 c^{5/2}}-\frac{4 b^2 \tan ^{-1}\left(\sqrt{c} x\right)}{15 c^{5/2}}+\frac{2 a b \tan ^{-1}\left(\sqrt{c} x\right)}{5 c^{5/2}}-\frac{4 b^2 \tanh ^{-1}\left(\sqrt{c} x\right)}{15 c^{5/2}}+\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right)}{5 c^{5/2}}-\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right)}{5 c^{5/2}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{5 c^{5/2}}+\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right)}{5 c^{5/2}}-\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right)}{5 c^{5/2}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{5 c^{5/2}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{5 c^{5/2}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{5 c^{5/2}}-\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right)}{5 c^{5/2}}-\frac{b \tanh ^{-1}\left(\sqrt{c} x\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{5 c^{5/2}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{5 c^{5/2}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{5 c^{5/2}}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right)}{5 c^{5/2}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right)}{5 c^{5/2}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{10 c^{5/2}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right)}{5 c^{5/2}}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right)}{5 c^{5/2}}-\frac{b^2 \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right)}{10 c^{5/2}}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{10 c^{5/2}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{10 c^{5/2}}",1,"(8*b^2*x)/(15*c^2) + (2*a*b*x^3)/(15*c) - (2*a*b*x^5)/25 + (2*a*b*ArcTan[Sqrt[c]*x])/(5*c^(5/2)) - (4*b^2*ArcTan[Sqrt[c]*x])/(15*c^(5/2)) + ((I/5)*b^2*ArcTan[Sqrt[c]*x]^2)/c^(5/2) - (4*b^2*ArcTanh[Sqrt[c]*x])/(15*c^(5/2)) - (b^2*ArcTanh[Sqrt[c]*x]^2)/(5*c^(5/2)) + (2*b^2*ArcTanh[Sqrt[c]*x]*Log[2/(1 - Sqrt[c]*x)])/(5*c^(5/2)) - (2*b^2*ArcTan[Sqrt[c]*x]*Log[2/(1 - I*Sqrt[c]*x)])/(5*c^(5/2)) + (b^2*ArcTan[Sqrt[c]*x]*Log[((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/(5*c^(5/2)) + (2*b^2*ArcTan[Sqrt[c]*x]*Log[2/(1 + I*Sqrt[c]*x)])/(5*c^(5/2)) - (2*b^2*ArcTanh[Sqrt[c]*x]*Log[2/(1 + Sqrt[c]*x)])/(5*c^(5/2)) + (b^2*ArcTanh[Sqrt[c]*x]*Log[(-2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/(5*c^(5/2)) + (b^2*ArcTanh[Sqrt[c]*x]*Log[(2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/(5*c^(5/2)) + (b^2*ArcTan[Sqrt[c]*x]*Log[((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/(5*c^(5/2)) - (b^2*x^3*Log[1 - c*x^2])/(15*c) + (b^2*x^5*Log[1 - c*x^2])/25 - (b^2*ArcTan[Sqrt[c]*x]*Log[1 - c*x^2])/(5*c^(5/2)) + (b*x^3*(2*a - b*Log[1 - c*x^2]))/(15*c) + (b*x^5*(2*a - b*Log[1 - c*x^2]))/25 - (b*ArcTanh[Sqrt[c]*x]*(2*a - b*Log[1 - c*x^2]))/(5*c^(5/2)) + (x^5*(2*a - b*Log[1 - c*x^2])^2)/20 + (2*b^2*x^3*Log[1 + c*x^2])/(15*c) + (a*b*x^5*Log[1 + c*x^2])/5 + (b^2*ArcTan[Sqrt[c]*x]*Log[1 + c*x^2])/(5*c^(5/2)) - (b^2*ArcTanh[Sqrt[c]*x]*Log[1 + c*x^2])/(5*c^(5/2)) - (b^2*x^5*Log[1 - c*x^2]*Log[1 + c*x^2])/10 + (b^2*x^5*Log[1 + c*x^2]^2)/20 + (b^2*PolyLog[2, 1 - 2/(1 - Sqrt[c]*x)])/(5*c^(5/2)) + ((I/5)*b^2*PolyLog[2, 1 - 2/(1 - I*Sqrt[c]*x)])/c^(5/2) - ((I/10)*b^2*PolyLog[2, 1 - ((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/c^(5/2) + ((I/5)*b^2*PolyLog[2, 1 - 2/(1 + I*Sqrt[c]*x)])/c^(5/2) + (b^2*PolyLog[2, 1 - 2/(1 + Sqrt[c]*x)])/(5*c^(5/2)) - (b^2*PolyLog[2, 1 + (2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/(10*c^(5/2)) - (b^2*PolyLog[2, 1 - (2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/(10*c^(5/2)) - ((I/10)*b^2*PolyLog[2, 1 - ((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/c^(5/2)","A",102,26,16,1.625,1,"{6099, 2457, 2476, 2448, 321, 206, 2455, 302, 2470, 12, 5984, 5918, 2402, 2315, 6742, 203, 30, 2557, 207, 5992, 5920, 2447, 4928, 4856, 4920, 4854}"
72,1,1129,0,2.0608061,"\int x^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[x^2*(a + b*ArcTanh[c*x^2])^2,x]","\frac{1}{12} \left(2 a-b \log \left(1-c x^2\right)\right)^2 x^3+\frac{1}{12} b^2 \log ^2\left(c x^2+1\right) x^3-\frac{2}{9} a b x^3+\frac{1}{9} b^2 \log \left(1-c x^2\right) x^3+\frac{1}{9} b \left(2 a-b \log \left(1-c x^2\right)\right) x^3+\frac{1}{3} a b \log \left(c x^2+1\right) x^3-\frac{1}{6} b^2 \log \left(1-c x^2\right) \log \left(c x^2+1\right) x^3-\frac{2 b^2 \log \left(1-c x^2\right) x}{3 c}+\frac{2 b^2 \log \left(c x^2+1\right) x}{3 c}+\frac{4 a b x}{3 c}-\frac{i b^2 \tan ^{-1}\left(\sqrt{c} x\right)^2}{3 c^{3/2}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right)^2}{3 c^{3/2}}+\frac{4 b^2 \tan ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}-\frac{2 a b \tan ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}-\frac{4 b^2 \tanh ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}+\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right)}{3 c^{3/2}}+\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right)}{3 c^{3/2}}-\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{3 c^{3/2}}-\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right)}{3 c^{3/2}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{3 c^{3/2}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{3 c^{3/2}}-\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{3 c^{3/2}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right)}{3 c^{3/2}}-\frac{b \tanh ^{-1}\left(\sqrt{c} x\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{3 c^{3/2}}-\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{3 c^{3/2}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{3 c^{3/2}}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right)}{3 c^{3/2}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right)}{3 c^{3/2}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{6 c^{3/2}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right)}{3 c^{3/2}}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{b^2 \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right)}{6 c^{3/2}}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{6 c^{3/2}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{6 c^{3/2}}","\frac{1}{12} \left(2 a-b \log \left(1-c x^2\right)\right)^2 x^3+\frac{1}{12} b^2 \log ^2\left(c x^2+1\right) x^3-\frac{2}{9} a b x^3+\frac{1}{9} b^2 \log \left(1-c x^2\right) x^3+\frac{1}{9} b \left(2 a-b \log \left(1-c x^2\right)\right) x^3+\frac{1}{3} a b \log \left(c x^2+1\right) x^3-\frac{1}{6} b^2 \log \left(1-c x^2\right) \log \left(c x^2+1\right) x^3-\frac{2 b^2 \log \left(1-c x^2\right) x}{3 c}+\frac{2 b^2 \log \left(c x^2+1\right) x}{3 c}+\frac{4 a b x}{3 c}-\frac{i b^2 \tan ^{-1}\left(\sqrt{c} x\right)^2}{3 c^{3/2}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right)^2}{3 c^{3/2}}+\frac{4 b^2 \tan ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}-\frac{2 a b \tan ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}-\frac{4 b^2 \tanh ^{-1}\left(\sqrt{c} x\right)}{3 c^{3/2}}+\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right)}{3 c^{3/2}}+\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right)}{3 c^{3/2}}-\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{3 c^{3/2}}-\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right)}{3 c^{3/2}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{3 c^{3/2}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{3 c^{3/2}}-\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{3 c^{3/2}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right)}{3 c^{3/2}}-\frac{b \tanh ^{-1}\left(\sqrt{c} x\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{3 c^{3/2}}-\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{3 c^{3/2}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{3 c^{3/2}}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right)}{3 c^{3/2}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right)}{3 c^{3/2}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{6 c^{3/2}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right)}{3 c^{3/2}}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{b^2 \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right)}{6 c^{3/2}}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{6 c^{3/2}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{6 c^{3/2}}",1,"(4*a*b*x)/(3*c) - (2*a*b*x^3)/9 - (2*a*b*ArcTan[Sqrt[c]*x])/(3*c^(3/2)) + (4*b^2*ArcTan[Sqrt[c]*x])/(3*c^(3/2)) - ((I/3)*b^2*ArcTan[Sqrt[c]*x]^2)/c^(3/2) - (4*b^2*ArcTanh[Sqrt[c]*x])/(3*c^(3/2)) - (b^2*ArcTanh[Sqrt[c]*x]^2)/(3*c^(3/2)) + (2*b^2*ArcTanh[Sqrt[c]*x]*Log[2/(1 - Sqrt[c]*x)])/(3*c^(3/2)) + (2*b^2*ArcTan[Sqrt[c]*x]*Log[2/(1 - I*Sqrt[c]*x)])/(3*c^(3/2)) - (b^2*ArcTan[Sqrt[c]*x]*Log[((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/(3*c^(3/2)) - (2*b^2*ArcTan[Sqrt[c]*x]*Log[2/(1 + I*Sqrt[c]*x)])/(3*c^(3/2)) - (2*b^2*ArcTanh[Sqrt[c]*x]*Log[2/(1 + Sqrt[c]*x)])/(3*c^(3/2)) + (b^2*ArcTanh[Sqrt[c]*x]*Log[(-2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/(3*c^(3/2)) + (b^2*ArcTanh[Sqrt[c]*x]*Log[(2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/(3*c^(3/2)) - (b^2*ArcTan[Sqrt[c]*x]*Log[((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/(3*c^(3/2)) - (2*b^2*x*Log[1 - c*x^2])/(3*c) + (b^2*x^3*Log[1 - c*x^2])/9 + (b^2*ArcTan[Sqrt[c]*x]*Log[1 - c*x^2])/(3*c^(3/2)) + (b*x^3*(2*a - b*Log[1 - c*x^2]))/9 - (b*ArcTanh[Sqrt[c]*x]*(2*a - b*Log[1 - c*x^2]))/(3*c^(3/2)) + (x^3*(2*a - b*Log[1 - c*x^2])^2)/12 + (2*b^2*x*Log[1 + c*x^2])/(3*c) + (a*b*x^3*Log[1 + c*x^2])/3 - (b^2*ArcTan[Sqrt[c]*x]*Log[1 + c*x^2])/(3*c^(3/2)) - (b^2*ArcTanh[Sqrt[c]*x]*Log[1 + c*x^2])/(3*c^(3/2)) - (b^2*x^3*Log[1 - c*x^2]*Log[1 + c*x^2])/6 + (b^2*x^3*Log[1 + c*x^2]^2)/12 + (b^2*PolyLog[2, 1 - 2/(1 - Sqrt[c]*x)])/(3*c^(3/2)) - ((I/3)*b^2*PolyLog[2, 1 - 2/(1 - I*Sqrt[c]*x)])/c^(3/2) + ((I/6)*b^2*PolyLog[2, 1 - ((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/c^(3/2) - ((I/3)*b^2*PolyLog[2, 1 - 2/(1 + I*Sqrt[c]*x)])/c^(3/2) + (b^2*PolyLog[2, 1 - 2/(1 + Sqrt[c]*x)])/(3*c^(3/2)) - (b^2*PolyLog[2, 1 + (2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/(6*c^(3/2)) - (b^2*PolyLog[2, 1 - (2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/(6*c^(3/2)) + ((I/6)*b^2*PolyLog[2, 1 - ((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/c^(3/2)","A",86,26,16,1.625,1,"{6099, 2457, 2476, 2448, 321, 206, 2455, 302, 2470, 12, 5984, 5918, 2402, 2315, 6742, 203, 30, 2557, 207, 5992, 5920, 2447, 4928, 4856, 4920, 4854}"
73,1,958,0,1.4681268,"\int \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[(a + b*ArcTanh[c*x^2])^2,x]","x a^2+\frac{2 b \tan ^{-1}\left(\sqrt{c} x\right) a}{\sqrt{c}}-\frac{2 b \tanh ^{-1}\left(\sqrt{c} x\right) a}{\sqrt{c}}-b x \log \left(1-c x^2\right) a+b x \log \left(c x^2+1\right) a+\frac{i b^2 \tan ^{-1}\left(\sqrt{c} x\right)^2}{\sqrt{c}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right)^2}{\sqrt{c}}+\frac{1}{4} b^2 x \log ^2\left(1-c x^2\right)+\frac{1}{4} b^2 x \log ^2\left(c x^2+1\right)+\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right)}{\sqrt{c}}-\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right)}{\sqrt{c}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{\sqrt{c}}+\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{\sqrt{c}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{\sqrt{c}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{\sqrt{c}}-\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right)}{\sqrt{c}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right)}{\sqrt{c}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{\sqrt{c}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{\sqrt{c}}-\frac{1}{2} b^2 x \log \left(1-c x^2\right) \log \left(c x^2+1\right)+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right)}{\sqrt{c}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right)}{\sqrt{c}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{2 \sqrt{c}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{b^2 \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right)}{2 \sqrt{c}}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{2 \sqrt{c}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{2 \sqrt{c}}","x a^2+\frac{2 b \tan ^{-1}\left(\sqrt{c} x\right) a}{\sqrt{c}}-\frac{2 b \tanh ^{-1}\left(\sqrt{c} x\right) a}{\sqrt{c}}-b x \log \left(1-c x^2\right) a+b x \log \left(c x^2+1\right) a+\frac{i b^2 \tan ^{-1}\left(\sqrt{c} x\right)^2}{\sqrt{c}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right)^2}{\sqrt{c}}+\frac{1}{4} b^2 x \log ^2\left(1-c x^2\right)+\frac{1}{4} b^2 x \log ^2\left(c x^2+1\right)+\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right)}{\sqrt{c}}-\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right)}{\sqrt{c}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{\sqrt{c}}+\frac{2 b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{2 b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{\sqrt{c}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{\sqrt{c}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{\sqrt{c}}-\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right)}{\sqrt{c}}+\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right)}{\sqrt{c}}+\frac{b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{\sqrt{c}}-\frac{b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right)}{\sqrt{c}}-\frac{1}{2} b^2 x \log \left(1-c x^2\right) \log \left(c x^2+1\right)+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right)}{\sqrt{c}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right)}{\sqrt{c}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right)}{2 \sqrt{c}}+\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{b^2 \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right)}{2 \sqrt{c}}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right)}{2 \sqrt{c}}-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right)}{2 \sqrt{c}}",1,"a^2*x + (2*a*b*ArcTan[Sqrt[c]*x])/Sqrt[c] + (I*b^2*ArcTan[Sqrt[c]*x]^2)/Sqrt[c] - (2*a*b*ArcTanh[Sqrt[c]*x])/Sqrt[c] - (b^2*ArcTanh[Sqrt[c]*x]^2)/Sqrt[c] + (2*b^2*ArcTanh[Sqrt[c]*x]*Log[2/(1 - Sqrt[c]*x)])/Sqrt[c] - (2*b^2*ArcTan[Sqrt[c]*x]*Log[2/(1 - I*Sqrt[c]*x)])/Sqrt[c] + (b^2*ArcTan[Sqrt[c]*x]*Log[((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/Sqrt[c] + (2*b^2*ArcTan[Sqrt[c]*x]*Log[2/(1 + I*Sqrt[c]*x)])/Sqrt[c] - (2*b^2*ArcTanh[Sqrt[c]*x]*Log[2/(1 + Sqrt[c]*x)])/Sqrt[c] + (b^2*ArcTanh[Sqrt[c]*x]*Log[(-2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/Sqrt[c] + (b^2*ArcTanh[Sqrt[c]*x]*Log[(2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/Sqrt[c] + (b^2*ArcTan[Sqrt[c]*x]*Log[((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/Sqrt[c] - a*b*x*Log[1 - c*x^2] - (b^2*ArcTan[Sqrt[c]*x]*Log[1 - c*x^2])/Sqrt[c] + (b^2*ArcTanh[Sqrt[c]*x]*Log[1 - c*x^2])/Sqrt[c] + (b^2*x*Log[1 - c*x^2]^2)/4 + a*b*x*Log[1 + c*x^2] + (b^2*ArcTan[Sqrt[c]*x]*Log[1 + c*x^2])/Sqrt[c] - (b^2*ArcTanh[Sqrt[c]*x]*Log[1 + c*x^2])/Sqrt[c] - (b^2*x*Log[1 - c*x^2]*Log[1 + c*x^2])/2 + (b^2*x*Log[1 + c*x^2]^2)/4 + (b^2*PolyLog[2, 1 - 2/(1 - Sqrt[c]*x)])/Sqrt[c] + (I*b^2*PolyLog[2, 1 - 2/(1 - I*Sqrt[c]*x)])/Sqrt[c] - ((I/2)*b^2*PolyLog[2, 1 - ((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/Sqrt[c] + (I*b^2*PolyLog[2, 1 - 2/(1 + I*Sqrt[c]*x)])/Sqrt[c] + (b^2*PolyLog[2, 1 - 2/(1 + Sqrt[c]*x)])/Sqrt[c] - (b^2*PolyLog[2, 1 + (2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/(2*Sqrt[c]) - (b^2*PolyLog[2, 1 - (2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/(2*Sqrt[c]) - ((I/2)*b^2*PolyLog[2, 1 - ((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/Sqrt[c]","A",69,21,12,1.750,1,"{6093, 2448, 321, 206, 2450, 2476, 2470, 12, 5984, 5918, 2402, 2315, 203, 2556, 5992, 5920, 2447, 4928, 4856, 4920, 4854}"
74,1,942,0,1.3350942,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{x^2} \, dx","Int[(a + b*ArcTanh[c*x^2])^2/x^2,x]","i \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right)^2 b^2+\sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right)^2 b^2-\frac{\log ^2\left(c x^2+1\right) b^2}{4 x}-2 \sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right) b^2-2 \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right) b^2+\sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) b^2+2 \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right) b^2+2 \sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right) b^2-\sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2-\sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2+\sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) b^2-\sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right) b^2+\sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) b^2+\sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) b^2+\frac{\log \left(1-c x^2\right) \log \left(c x^2+1\right) b^2}{2 x}-\sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right) b^2+i \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right) b^2-\frac{1}{2} i \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) b^2+i \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right) b^2-\sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right) b^2+\frac{1}{2} \sqrt{c} \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right) b^2+\frac{1}{2} \sqrt{c} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2-\frac{1}{2} i \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) b^2+2 a \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) b+\sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \left(2 a-b \log \left(1-c x^2\right)\right) b-\frac{a \log \left(c x^2+1\right) b}{x}-\frac{\left(2 a-b \log \left(1-c x^2\right)\right)^2}{4 x}","i \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right)^2 b^2+\sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right)^2 b^2-\frac{\log ^2\left(c x^2+1\right) b^2}{4 x}-2 \sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right) b^2-2 \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right) b^2+\sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) b^2+2 \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right) b^2+2 \sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right) b^2-\sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2-\sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2+\sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) b^2-\sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right) b^2+\sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) b^2+\sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) b^2+\frac{\log \left(1-c x^2\right) \log \left(c x^2+1\right) b^2}{2 x}-\sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right) b^2+i \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right) b^2-\frac{1}{2} i \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) b^2+i \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right) b^2-\sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right) b^2+\frac{1}{2} \sqrt{c} \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right) b^2+\frac{1}{2} \sqrt{c} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2-\frac{1}{2} i \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) b^2+2 a \sqrt{c} \tan ^{-1}\left(\sqrt{c} x\right) b+\sqrt{c} \tanh ^{-1}\left(\sqrt{c} x\right) \left(2 a-b \log \left(1-c x^2\right)\right) b-\frac{a \log \left(c x^2+1\right) b}{x}-\frac{\left(2 a-b \log \left(1-c x^2\right)\right)^2}{4 x}",1,"2*a*b*Sqrt[c]*ArcTan[Sqrt[c]*x] + I*b^2*Sqrt[c]*ArcTan[Sqrt[c]*x]^2 + b^2*Sqrt[c]*ArcTanh[Sqrt[c]*x]^2 - 2*b^2*Sqrt[c]*ArcTanh[Sqrt[c]*x]*Log[2/(1 - Sqrt[c]*x)] - 2*b^2*Sqrt[c]*ArcTan[Sqrt[c]*x]*Log[2/(1 - I*Sqrt[c]*x)] + b^2*Sqrt[c]*ArcTan[Sqrt[c]*x]*Log[((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)] + 2*b^2*Sqrt[c]*ArcTan[Sqrt[c]*x]*Log[2/(1 + I*Sqrt[c]*x)] + 2*b^2*Sqrt[c]*ArcTanh[Sqrt[c]*x]*Log[2/(1 + Sqrt[c]*x)] - b^2*Sqrt[c]*ArcTanh[Sqrt[c]*x]*Log[(-2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))] - b^2*Sqrt[c]*ArcTanh[Sqrt[c]*x]*Log[(2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))] + b^2*Sqrt[c]*ArcTan[Sqrt[c]*x]*Log[((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)] - b^2*Sqrt[c]*ArcTan[Sqrt[c]*x]*Log[1 - c*x^2] + b*Sqrt[c]*ArcTanh[Sqrt[c]*x]*(2*a - b*Log[1 - c*x^2]) - (2*a - b*Log[1 - c*x^2])^2/(4*x) - (a*b*Log[1 + c*x^2])/x + b^2*Sqrt[c]*ArcTan[Sqrt[c]*x]*Log[1 + c*x^2] + b^2*Sqrt[c]*ArcTanh[Sqrt[c]*x]*Log[1 + c*x^2] + (b^2*Log[1 - c*x^2]*Log[1 + c*x^2])/(2*x) - (b^2*Log[1 + c*x^2]^2)/(4*x) - b^2*Sqrt[c]*PolyLog[2, 1 - 2/(1 - Sqrt[c]*x)] + I*b^2*Sqrt[c]*PolyLog[2, 1 - 2/(1 - I*Sqrt[c]*x)] - (I/2)*b^2*Sqrt[c]*PolyLog[2, 1 - ((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)] + I*b^2*Sqrt[c]*PolyLog[2, 1 - 2/(1 + I*Sqrt[c]*x)] - b^2*Sqrt[c]*PolyLog[2, 1 - 2/(1 + Sqrt[c]*x)] + (b^2*Sqrt[c]*PolyLog[2, 1 + (2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/2 + (b^2*Sqrt[c]*PolyLog[2, 1 - (2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/2 - (I/2)*b^2*Sqrt[c]*PolyLog[2, 1 - ((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)]","A",47,21,16,1.313,1,"{6099, 2457, 206, 2470, 12, 5984, 5918, 2402, 2315, 2455, 6742, 203, 30, 2557, 5992, 5920, 2447, 4928, 4856, 4920, 4854}"
75,1,1102,0,1.8419441,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{x^4} \, dx","Int[(a + b*ArcTanh[c*x^2])^2/x^4,x]","-\frac{1}{3} i c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right)^2 b^2+\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right)^2 b^2-\frac{\log ^2\left(c x^2+1\right) b^2}{12 x^3}+\frac{4}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) b^2+\frac{4}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) b^2-\frac{2}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right) b^2+\frac{2}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right) b^2-\frac{1}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) b^2-\frac{2}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right) b^2+\frac{2}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right) b^2-\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2-\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2-\frac{1}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) b^2+\frac{1}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right) b^2+\frac{c \log \left(1-c x^2\right) b^2}{3 x}-\frac{1}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) b^2+\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) b^2+\frac{\log \left(1-c x^2\right) \log \left(c x^2+1\right) b^2}{6 x^3}-\frac{2 c \log \left(c x^2+1\right) b^2}{3 x}-\frac{1}{3} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right) b^2-\frac{1}{3} i c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right) b^2+\frac{1}{6} i c^{3/2} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) b^2-\frac{1}{3} i c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right) b^2-\frac{1}{3} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right) b^2+\frac{1}{6} c^{3/2} \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right) b^2+\frac{1}{6} c^{3/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2+\frac{1}{6} i c^{3/2} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) b^2-\frac{2}{3} a c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) b+\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \left(2 a-b \log \left(1-c x^2\right)\right) b-\frac{c \left(2 a-b \log \left(1-c x^2\right)\right) b}{3 x}-\frac{a \log \left(c x^2+1\right) b}{3 x^3}-\frac{2 a c b}{3 x}-\frac{\left(2 a-b \log \left(1-c x^2\right)\right)^2}{12 x^3}","-\frac{1}{3} i c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right)^2 b^2+\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right)^2 b^2-\frac{\log ^2\left(c x^2+1\right) b^2}{12 x^3}+\frac{4}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) b^2+\frac{4}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) b^2-\frac{2}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right) b^2+\frac{2}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right) b^2-\frac{1}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) b^2-\frac{2}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right) b^2+\frac{2}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right) b^2-\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2-\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2-\frac{1}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) b^2+\frac{1}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right) b^2+\frac{c \log \left(1-c x^2\right) b^2}{3 x}-\frac{1}{3} c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) b^2+\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) b^2+\frac{\log \left(1-c x^2\right) \log \left(c x^2+1\right) b^2}{6 x^3}-\frac{2 c \log \left(c x^2+1\right) b^2}{3 x}-\frac{1}{3} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right) b^2-\frac{1}{3} i c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right) b^2+\frac{1}{6} i c^{3/2} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) b^2-\frac{1}{3} i c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right) b^2-\frac{1}{3} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right) b^2+\frac{1}{6} c^{3/2} \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right) b^2+\frac{1}{6} c^{3/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) b^2+\frac{1}{6} i c^{3/2} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) b^2-\frac{2}{3} a c^{3/2} \tan ^{-1}\left(\sqrt{c} x\right) b+\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\sqrt{c} x\right) \left(2 a-b \log \left(1-c x^2\right)\right) b-\frac{c \left(2 a-b \log \left(1-c x^2\right)\right) b}{3 x}-\frac{a \log \left(c x^2+1\right) b}{3 x^3}-\frac{2 a c b}{3 x}-\frac{\left(2 a-b \log \left(1-c x^2\right)\right)^2}{12 x^3}",1,"(-2*a*b*c)/(3*x) - (2*a*b*c^(3/2)*ArcTan[Sqrt[c]*x])/3 + (4*b^2*c^(3/2)*ArcTan[Sqrt[c]*x])/3 - (I/3)*b^2*c^(3/2)*ArcTan[Sqrt[c]*x]^2 + (4*b^2*c^(3/2)*ArcTanh[Sqrt[c]*x])/3 + (b^2*c^(3/2)*ArcTanh[Sqrt[c]*x]^2)/3 - (2*b^2*c^(3/2)*ArcTanh[Sqrt[c]*x]*Log[2/(1 - Sqrt[c]*x)])/3 + (2*b^2*c^(3/2)*ArcTan[Sqrt[c]*x]*Log[2/(1 - I*Sqrt[c]*x)])/3 - (b^2*c^(3/2)*ArcTan[Sqrt[c]*x]*Log[((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/3 - (2*b^2*c^(3/2)*ArcTan[Sqrt[c]*x]*Log[2/(1 + I*Sqrt[c]*x)])/3 + (2*b^2*c^(3/2)*ArcTanh[Sqrt[c]*x]*Log[2/(1 + Sqrt[c]*x)])/3 - (b^2*c^(3/2)*ArcTanh[Sqrt[c]*x]*Log[(-2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/3 - (b^2*c^(3/2)*ArcTanh[Sqrt[c]*x]*Log[(2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/3 - (b^2*c^(3/2)*ArcTan[Sqrt[c]*x]*Log[((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/3 + (b^2*c*Log[1 - c*x^2])/(3*x) + (b^2*c^(3/2)*ArcTan[Sqrt[c]*x]*Log[1 - c*x^2])/3 - (b*c*(2*a - b*Log[1 - c*x^2]))/(3*x) + (b*c^(3/2)*ArcTanh[Sqrt[c]*x]*(2*a - b*Log[1 - c*x^2]))/3 - (2*a - b*Log[1 - c*x^2])^2/(12*x^3) - (a*b*Log[1 + c*x^2])/(3*x^3) - (2*b^2*c*Log[1 + c*x^2])/(3*x) - (b^2*c^(3/2)*ArcTan[Sqrt[c]*x]*Log[1 + c*x^2])/3 + (b^2*c^(3/2)*ArcTanh[Sqrt[c]*x]*Log[1 + c*x^2])/3 + (b^2*Log[1 - c*x^2]*Log[1 + c*x^2])/(6*x^3) - (b^2*Log[1 + c*x^2]^2)/(12*x^3) - (b^2*c^(3/2)*PolyLog[2, 1 - 2/(1 - Sqrt[c]*x)])/3 - (I/3)*b^2*c^(3/2)*PolyLog[2, 1 - 2/(1 - I*Sqrt[c]*x)] + (I/6)*b^2*c^(3/2)*PolyLog[2, 1 - ((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)] - (I/3)*b^2*c^(3/2)*PolyLog[2, 1 - 2/(1 + I*Sqrt[c]*x)] - (b^2*c^(3/2)*PolyLog[2, 1 - 2/(1 + Sqrt[c]*x)])/3 + (b^2*c^(3/2)*PolyLog[2, 1 + (2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/6 + (b^2*c^(3/2)*PolyLog[2, 1 - (2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/6 + (I/6)*b^2*c^(3/2)*PolyLog[2, 1 - ((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)]","A",64,24,16,1.500,1,"{6099, 2457, 2476, 2455, 206, 207, 2470, 12, 5984, 5918, 2402, 2315, 325, 6742, 203, 30, 2557, 5992, 5920, 2447, 4928, 4856, 4920, 4854}"
76,1,1176,0,1.9896637,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{x^6} \, dx","Int[(a + b*ArcTanh[c*x^2])^2/x^6,x]","\frac{1}{5} i b^2 \tan ^{-1}\left(\sqrt{c} x\right)^2 c^{5/2}+\frac{1}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right)^2 c^{5/2}-\frac{4}{15} b^2 \tan ^{-1}\left(\sqrt{c} x\right) c^{5/2}+\frac{2}{5} a b \tan ^{-1}\left(\sqrt{c} x\right) c^{5/2}+\frac{4}{15} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) c^{5/2}-\frac{2}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right) c^{5/2}-\frac{2}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right) c^{5/2}+\frac{1}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) c^{5/2}+\frac{2}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right) c^{5/2}+\frac{2}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right) c^{5/2}-\frac{1}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) c^{5/2}-\frac{1}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) c^{5/2}+\frac{1}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) c^{5/2}-\frac{1}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right) c^{5/2}+\frac{1}{5} b \tanh ^{-1}\left(\sqrt{c} x\right) \left(2 a-b \log \left(1-c x^2\right)\right) c^{5/2}+\frac{1}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) c^{5/2}+\frac{1}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) c^{5/2}-\frac{1}{5} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right) c^{5/2}+\frac{1}{5} i b^2 \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right) c^{5/2}-\frac{1}{10} i b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) c^{5/2}+\frac{1}{5} i b^2 \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right) c^{5/2}-\frac{1}{5} b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right) c^{5/2}+\frac{1}{10} b^2 \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right) c^{5/2}+\frac{1}{10} b^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) c^{5/2}-\frac{1}{10} i b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) c^{5/2}-\frac{b^2 \log \left(1-c x^2\right) c^2}{5 x}-\frac{b \left(2 a-b \log \left(1-c x^2\right)\right) c^2}{5 x}-\frac{8 b^2 c^2}{15 x}+\frac{2 a b c^2}{5 x}+\frac{b^2 \log \left(1-c x^2\right) c}{15 x^3}-\frac{b \left(2 a-b \log \left(1-c x^2\right)\right) c}{15 x^3}-\frac{2 b^2 \log \left(c x^2+1\right) c}{15 x^3}-\frac{2 a b c}{15 x^3}-\frac{\left(2 a-b \log \left(1-c x^2\right)\right)^2}{20 x^5}-\frac{b^2 \log ^2\left(c x^2+1\right)}{20 x^5}+\frac{b^2 \log \left(1-c x^2\right) \log \left(c x^2+1\right)}{10 x^5}-\frac{a b \log \left(c x^2+1\right)}{5 x^5}","\frac{1}{5} i b^2 \tan ^{-1}\left(\sqrt{c} x\right)^2 c^{5/2}+\frac{1}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right)^2 c^{5/2}-\frac{4}{15} b^2 \tan ^{-1}\left(\sqrt{c} x\right) c^{5/2}+\frac{2}{5} a b \tan ^{-1}\left(\sqrt{c} x\right) c^{5/2}+\frac{4}{15} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) c^{5/2}-\frac{2}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt{c} x}\right) c^{5/2}-\frac{2}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{1-i \sqrt{c} x}\right) c^{5/2}+\frac{1}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) c^{5/2}+\frac{2}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{i \sqrt{c} x+1}\right) c^{5/2}+\frac{2}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2}{\sqrt{c} x+1}\right) c^{5/2}-\frac{1}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(-\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) c^{5/2}-\frac{1}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) c^{5/2}+\frac{1}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) c^{5/2}-\frac{1}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(1-c x^2\right) c^{5/2}+\frac{1}{5} b \tanh ^{-1}\left(\sqrt{c} x\right) \left(2 a-b \log \left(1-c x^2\right)\right) c^{5/2}+\frac{1}{5} b^2 \tan ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) c^{5/2}+\frac{1}{5} b^2 \tanh ^{-1}\left(\sqrt{c} x\right) \log \left(c x^2+1\right) c^{5/2}-\frac{1}{5} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt{c} x}\right) c^{5/2}+\frac{1}{5} i b^2 \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt{c} x}\right) c^{5/2}-\frac{1}{10} i b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt{c} x\right)}{1-i \sqrt{c} x}\right) c^{5/2}+\frac{1}{5} i b^2 \text{PolyLog}\left(2,1-\frac{2}{i \sqrt{c} x+1}\right) c^{5/2}-\frac{1}{5} b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt{c} x+1}\right) c^{5/2}+\frac{1}{10} b^2 \text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\sqrt{-c} x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\sqrt{c} x+1\right)}+1\right) c^{5/2}+\frac{1}{10} b^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c} x+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\sqrt{c} x+1\right)}\right) c^{5/2}-\frac{1}{10} i b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt{c} x+1\right)}{1-i \sqrt{c} x}\right) c^{5/2}-\frac{b^2 \log \left(1-c x^2\right) c^2}{5 x}-\frac{b \left(2 a-b \log \left(1-c x^2\right)\right) c^2}{5 x}-\frac{8 b^2 c^2}{15 x}+\frac{2 a b c^2}{5 x}+\frac{b^2 \log \left(1-c x^2\right) c}{15 x^3}-\frac{b \left(2 a-b \log \left(1-c x^2\right)\right) c}{15 x^3}-\frac{2 b^2 \log \left(c x^2+1\right) c}{15 x^3}-\frac{2 a b c}{15 x^3}-\frac{\left(2 a-b \log \left(1-c x^2\right)\right)^2}{20 x^5}-\frac{b^2 \log ^2\left(c x^2+1\right)}{20 x^5}+\frac{b^2 \log \left(1-c x^2\right) \log \left(c x^2+1\right)}{10 x^5}-\frac{a b \log \left(c x^2+1\right)}{5 x^5}",1,"(-2*a*b*c)/(15*x^3) + (2*a*b*c^2)/(5*x) - (8*b^2*c^2)/(15*x) + (2*a*b*c^(5/2)*ArcTan[Sqrt[c]*x])/5 - (4*b^2*c^(5/2)*ArcTan[Sqrt[c]*x])/15 + (I/5)*b^2*c^(5/2)*ArcTan[Sqrt[c]*x]^2 + (4*b^2*c^(5/2)*ArcTanh[Sqrt[c]*x])/15 + (b^2*c^(5/2)*ArcTanh[Sqrt[c]*x]^2)/5 - (2*b^2*c^(5/2)*ArcTanh[Sqrt[c]*x]*Log[2/(1 - Sqrt[c]*x)])/5 - (2*b^2*c^(5/2)*ArcTan[Sqrt[c]*x]*Log[2/(1 - I*Sqrt[c]*x)])/5 + (b^2*c^(5/2)*ArcTan[Sqrt[c]*x]*Log[((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/5 + (2*b^2*c^(5/2)*ArcTan[Sqrt[c]*x]*Log[2/(1 + I*Sqrt[c]*x)])/5 + (2*b^2*c^(5/2)*ArcTanh[Sqrt[c]*x]*Log[2/(1 + Sqrt[c]*x)])/5 - (b^2*c^(5/2)*ArcTanh[Sqrt[c]*x]*Log[(-2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/5 - (b^2*c^(5/2)*ArcTanh[Sqrt[c]*x]*Log[(2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/5 + (b^2*c^(5/2)*ArcTan[Sqrt[c]*x]*Log[((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/5 + (b^2*c*Log[1 - c*x^2])/(15*x^3) - (b^2*c^2*Log[1 - c*x^2])/(5*x) - (b^2*c^(5/2)*ArcTan[Sqrt[c]*x]*Log[1 - c*x^2])/5 - (b*c*(2*a - b*Log[1 - c*x^2]))/(15*x^3) - (b*c^2*(2*a - b*Log[1 - c*x^2]))/(5*x) + (b*c^(5/2)*ArcTanh[Sqrt[c]*x]*(2*a - b*Log[1 - c*x^2]))/5 - (2*a - b*Log[1 - c*x^2])^2/(20*x^5) - (a*b*Log[1 + c*x^2])/(5*x^5) - (2*b^2*c*Log[1 + c*x^2])/(15*x^3) + (b^2*c^(5/2)*ArcTan[Sqrt[c]*x]*Log[1 + c*x^2])/5 + (b^2*c^(5/2)*ArcTanh[Sqrt[c]*x]*Log[1 + c*x^2])/5 + (b^2*Log[1 - c*x^2]*Log[1 + c*x^2])/(10*x^5) - (b^2*Log[1 + c*x^2]^2)/(20*x^5) - (b^2*c^(5/2)*PolyLog[2, 1 - 2/(1 - Sqrt[c]*x)])/5 + (I/5)*b^2*c^(5/2)*PolyLog[2, 1 - 2/(1 - I*Sqrt[c]*x)] - (I/10)*b^2*c^(5/2)*PolyLog[2, 1 - ((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)] + (I/5)*b^2*c^(5/2)*PolyLog[2, 1 - 2/(1 + I*Sqrt[c]*x)] - (b^2*c^(5/2)*PolyLog[2, 1 - 2/(1 + Sqrt[c]*x)])/5 + (b^2*c^(5/2)*PolyLog[2, 1 + (2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/10 + (b^2*c^(5/2)*PolyLog[2, 1 - (2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/10 - (I/10)*b^2*c^(5/2)*PolyLog[2, 1 - ((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)]","A",77,24,16,1.500,1,"{6099, 2457, 2476, 2455, 325, 206, 207, 2470, 12, 5984, 5918, 2402, 2315, 6742, 203, 30, 2557, 5992, 5920, 2447, 4928, 4856, 4920, 4854}"
77,1,479,0,4.2155191,"\int x^3 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3 \, dx","Int[x^3*(a + b*ArcTanh[c*x^2])^3,x]","-\frac{3 b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^2\right)\right)}{8 c^2}+\frac{3 b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^2+1\right)\right)}{8 c^2}-\frac{3 b^2 \log ^2\left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{32 c^2}+\frac{3 b^2 \log \left(\frac{1}{2} \left(c x^2+1\right)\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{8 c^2}+\frac{3}{32} b^2 x^4 \log ^2\left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)+\frac{3 b^2 x^2 \log \left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{8 c}+\frac{\left(1-c x^2\right)^2 \left(2 a-b \log \left(1-c x^2\right)\right)^3}{32 c^2}-\frac{\left(1-c x^2\right) \left(2 a-b \log \left(1-c x^2\right)\right)^3}{16 c^2}-\frac{3 b \left(1-c x^2\right) \left(2 a-b \log \left(1-c x^2\right)\right)^2}{16 c^2}-\frac{3 b \log \left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)^2}{32 c^2}+\frac{3}{32} b x^4 \log \left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)^2+\frac{b^3 \left(c x^2+1\right)^2 \log ^3\left(c x^2+1\right)}{32 c^2}-\frac{b^3 \left(c x^2+1\right) \log ^3\left(c x^2+1\right)}{16 c^2}+\frac{3 b^3 \left(c x^2+1\right) \log ^2\left(c x^2+1\right)}{16 c^2}+\frac{3 b^3 \log \left(\frac{1}{2} \left(1-c x^2\right)\right) \log \left(c x^2+1\right)}{8 c^2}","-\frac{3 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x^2}\right)}{4 c^2}-\frac{3 b^2 \log \left(\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{2 c^2}-\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3}{4 c^2}+\frac{3 b \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{4 c^2}+\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3+\frac{3 b x^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{4 c}",1,"(-3*b*(1 - c*x^2)*(2*a - b*Log[1 - c*x^2])^2)/(16*c^2) - ((1 - c*x^2)*(2*a - b*Log[1 - c*x^2])^3)/(16*c^2) + ((1 - c*x^2)^2*(2*a - b*Log[1 - c*x^2])^3)/(32*c^2) + (3*b^2*(2*a - b*Log[1 - c*x^2])*Log[(1 + c*x^2)/2])/(8*c^2) + (3*b^3*Log[(1 - c*x^2)/2]*Log[1 + c*x^2])/(8*c^2) + (3*b^2*x^2*(2*a - b*Log[1 - c*x^2])*Log[1 + c*x^2])/(8*c) - (3*b*(2*a - b*Log[1 - c*x^2])^2*Log[1 + c*x^2])/(32*c^2) + (3*b*x^4*(2*a - b*Log[1 - c*x^2])^2*Log[1 + c*x^2])/32 + (3*b^3*(1 + c*x^2)*Log[1 + c*x^2]^2)/(16*c^2) - (3*b^2*(2*a - b*Log[1 - c*x^2])*Log[1 + c*x^2]^2)/(32*c^2) + (3*b^2*x^4*(2*a - b*Log[1 - c*x^2])*Log[1 + c*x^2]^2)/32 - (b^3*(1 + c*x^2)*Log[1 + c*x^2]^3)/(16*c^2) + (b^3*(1 + c*x^2)^2*Log[1 + c*x^2]^3)/(32*c^2) - (3*b^3*PolyLog[2, (1 - c*x^2)/2])/(8*c^2) + (3*b^3*PolyLog[2, (1 + c*x^2)/2])/(8*c^2)","B",155,30,16,1.875,0,"{6099, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2439, 2416, 2396, 2433, 2374, 6589, 2411, 43, 2334, 12, 14, 2301, 6742, 2430, 2394, 2393, 2391, 2395, 2375, 2317, 2425}"
78,1,390,0,2.3231333,"\int x \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3 \, dx","Int[x*(a + b*ArcTanh[c*x^2])^3,x]","-\frac{3 b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^2\right)\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{4 c}-\frac{3 b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(1-c x^2\right)\right)}{4 c}-\frac{3 b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(c x^2+1\right)\right)}{4 c}+\frac{3 b^3 \log \left(c x^2+1\right) \text{PolyLog}\left(2,\frac{1}{2} \left(c x^2+1\right)\right)}{4 c}+\frac{3}{16} b^2 x^2 \log ^2\left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)+\frac{3 b^2 \log ^2\left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)}{16 c}+\frac{3 b \log \left(\frac{1}{2} \left(c x^2+1\right)\right) \left(2 a-b \log \left(1-c x^2\right)\right)^2}{8 c}+\frac{3}{16} b x^2 \log \left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)^2-\frac{3 b \log \left(c x^2+1\right) \left(2 a-b \log \left(1-c x^2\right)\right)^2}{16 c}-\frac{\left(1-c x^2\right) \left(2 a-b \log \left(1-c x^2\right)\right)^3}{16 c}+\frac{b^3 \left(c x^2+1\right) \log ^3\left(c x^2+1\right)}{16 c}+\frac{3 b^3 \log \left(\frac{1}{2} \left(1-c x^2\right)\right) \log ^2\left(c x^2+1\right)}{8 c}","-\frac{3 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{2 c}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x^2}\right)}{4 c}+\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3+\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3}{2 c}-\frac{3 b \log \left(\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{2 c}",1,"-((1 - c*x^2)*(2*a - b*Log[1 - c*x^2])^3)/(16*c) + (3*b*(2*a - b*Log[1 - c*x^2])^2*Log[(1 + c*x^2)/2])/(8*c) - (3*b*(2*a - b*Log[1 - c*x^2])^2*Log[1 + c*x^2])/(16*c) + (3*b*x^2*(2*a - b*Log[1 - c*x^2])^2*Log[1 + c*x^2])/16 + (3*b^3*Log[(1 - c*x^2)/2]*Log[1 + c*x^2]^2)/(8*c) + (3*b^2*(2*a - b*Log[1 - c*x^2])*Log[1 + c*x^2]^2)/(16*c) + (3*b^2*x^2*(2*a - b*Log[1 - c*x^2])*Log[1 + c*x^2]^2)/16 + (b^3*(1 + c*x^2)*Log[1 + c*x^2]^3)/(16*c) - (3*b^2*(2*a - b*Log[1 - c*x^2])*PolyLog[2, (1 - c*x^2)/2])/(4*c) + (3*b^3*Log[1 + c*x^2]*PolyLog[2, (1 + c*x^2)/2])/(4*c) - (3*b^3*PolyLog[3, (1 - c*x^2)/2])/(4*c) - (3*b^3*PolyLog[3, (1 + c*x^2)/2])/(4*c)","B",82,23,14,1.643,0,"{6099, 2454, 2389, 2296, 2295, 6715, 2430, 2416, 2396, 2433, 2374, 6589, 2411, 2346, 2301, 6742, 43, 2394, 2393, 2391, 2375, 2317, 2425}"
79,1,207,0,0.5597314,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3}{x} \, dx","Int[(a + b*ArcTanh[c*x^2])^3/x,x]","\frac{3}{4} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)-\frac{3}{4} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^2}-1\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)-\frac{3}{4} b \text{PolyLog}\left(2,1-\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2+\frac{3}{4} b \text{PolyLog}\left(2,\frac{2}{1-c x^2}-1\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2-\frac{3}{8} b^3 \text{PolyLog}\left(4,1-\frac{2}{1-c x^2}\right)+\frac{3}{8} b^3 \text{PolyLog}\left(4,\frac{2}{1-c x^2}-1\right)+\tanh ^{-1}\left(1-\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3","\frac{3}{4} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)-\frac{3}{4} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^2}-1\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)-\frac{3}{4} b \text{PolyLog}\left(2,1-\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2+\frac{3}{4} b \text{PolyLog}\left(2,\frac{2}{1-c x^2}-1\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2-\frac{3}{8} b^3 \text{PolyLog}\left(4,1-\frac{2}{1-c x^2}\right)+\frac{3}{8} b^3 \text{PolyLog}\left(4,\frac{2}{1-c x^2}-1\right)+\tanh ^{-1}\left(1-\frac{2}{1-c x^2}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3",1,"(a + b*ArcTanh[c*x^2])^3*ArcTanh[1 - 2/(1 - c*x^2)] - (3*b*(a + b*ArcTanh[c*x^2])^2*PolyLog[2, 1 - 2/(1 - c*x^2)])/4 + (3*b*(a + b*ArcTanh[c*x^2])^2*PolyLog[2, -1 + 2/(1 - c*x^2)])/4 + (3*b^2*(a + b*ArcTanh[c*x^2])*PolyLog[3, 1 - 2/(1 - c*x^2)])/4 - (3*b^2*(a + b*ArcTanh[c*x^2])*PolyLog[3, -1 + 2/(1 - c*x^2)])/4 - (3*b^3*PolyLog[4, 1 - 2/(1 - c*x^2)])/8 + (3*b^3*PolyLog[4, -1 + 2/(1 - c*x^2)])/8","A",9,7,16,0.4375,1,"{6095, 5914, 6052, 5948, 6058, 6062, 6610}"
80,0,0,0,0.7800713,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3}{x^3} \, dx","Int[(a + b*ArcTanh[c*x^2])^3/x^3,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3}{x^3} \, dx","-\frac{3}{2} b^2 c \text{PolyLog}\left(2,\frac{2}{c x^2+1}-1\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)-\frac{3}{4} b^3 c \text{PolyLog}\left(3,\frac{2}{c x^2+1}-1\right)+\frac{1}{2} c \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3-\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3}{2 x^2}+\frac{3}{2} b c \log \left(2-\frac{2}{c x^2+1}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2",1,"(3*b*c*Log[c*x^2]*(2*a - b*Log[1 - c*x^2])^2)/16 - ((1 - c*x^2)*(2*a - b*Log[1 - c*x^2])^3)/(16*x^2) + (3*b^3*c*Log[-(c*x^2)]*Log[1 + c*x^2]^2)/16 - (b^3*(1 + c*x^2)*Log[1 + c*x^2]^3)/(16*x^2) - (3*b^2*c*(2*a - b*Log[1 - c*x^2])*PolyLog[2, 1 - c*x^2])/8 + (3*b^3*c*Log[1 + c*x^2]*PolyLog[2, 1 + c*x^2])/8 - (3*b^3*c*PolyLog[3, 1 - c*x^2])/8 - (3*b^3*c*PolyLog[3, 1 + c*x^2])/8 + (3*b*Defer[Subst][Defer[Int][((-2*a + b*Log[1 - c*x])^2*Log[1 + c*x])/x^2, x], x, x^2])/16 - (3*b^2*Defer[Subst][Defer[Int][((-2*a + b*Log[1 - c*x])*Log[1 + c*x]^2)/x^2, x], x, x^2])/16","F",0,0,0,0,-1,"{}"
81,0,0,0,1.5579386,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3}{x^5} \, dx","Int[(a + b*ArcTanh[c*x^2])^3/x^5,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3}{x^5} \, dx","-\frac{3}{4} b^3 c^2 \text{PolyLog}\left(2,\frac{2}{c x^2+1}-1\right)+\frac{3}{2} b^2 c^2 \log \left(2-\frac{2}{c x^2+1}\right) \left(a+b \tanh ^{-1}\left(c x^2\right)\right)+\frac{3}{4} b c^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2+\frac{1}{4} c^2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3-\frac{3 b c \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{4 x^2}-\frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3}{4 x^4}",1,"(3*a*b^2*c^2*Log[x])/4 - (3*b*c*(1 - c*x^2)*(2*a - b*Log[1 - c*x^2])^2)/(32*x^2) + (3*b*c^2*Log[c*x^2]*(2*a - b*Log[1 - c*x^2])^2)/32 + (c^2*(2*a - b*Log[1 - c*x^2])^3)/32 - (2*a - b*Log[1 - c*x^2])^3/(32*x^4) - (3*b^3*c*(1 + c*x^2)*Log[1 + c*x^2]^2)/(32*x^2) - (3*b^3*c^2*Log[-(c*x^2)]*Log[1 + c*x^2]^2)/32 + (b^3*c^2*Log[1 + c*x^2]^3)/32 - (b^3*Log[1 + c*x^2]^3)/(32*x^4) - (3*b^3*c^2*PolyLog[2, -(c*x^2)])/16 + (3*b^3*c^2*PolyLog[2, c*x^2])/16 - (3*b^2*c^2*(2*a - b*Log[1 - c*x^2])*PolyLog[2, 1 - c*x^2])/16 - (3*b^3*c^2*Log[1 + c*x^2]*PolyLog[2, 1 + c*x^2])/16 - (3*b^3*c^2*PolyLog[3, 1 - c*x^2])/16 + (3*b^3*c^2*PolyLog[3, 1 + c*x^2])/16 + (3*b*Defer[Subst][Defer[Int][((-2*a + b*Log[1 - c*x])^2*Log[1 + c*x])/x^3, x], x, x^2])/16 - (3*b^2*Defer[Subst][Defer[Int][((-2*a + b*Log[1 - c*x])*Log[1 + c*x]^2)/x^3, x], x, x^2])/16","F",0,0,0,0,-1,"{}"
82,1,317,0,0.3343606,"\int (d x)^{5/2} \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[(d*x)^(5/2)*(a + b*ArcTanh[c*x^2]),x]","\frac{2 (d x)^{7/2} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{7 d}-\frac{b d^{5/2} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{7 \sqrt{2} c^{7/4}}+\frac{b d^{5/2} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{7 \sqrt{2} c^{7/4}}+\frac{2 b d^{5/2} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 c^{7/4}}+\frac{\sqrt{2} b d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 c^{7/4}}-\frac{\sqrt{2} b d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{7 c^{7/4}}-\frac{2 b d^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 c^{7/4}}+\frac{8 b d (d x)^{3/2}}{21 c}","\frac{2 (d x)^{7/2} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{7 d}-\frac{b d^{5/2} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{7 \sqrt{2} c^{7/4}}+\frac{b d^{5/2} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{7 \sqrt{2} c^{7/4}}+\frac{2 b d^{5/2} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 c^{7/4}}+\frac{\sqrt{2} b d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 c^{7/4}}-\frac{\sqrt{2} b d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{7 c^{7/4}}-\frac{2 b d^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 c^{7/4}}+\frac{8 b d (d x)^{3/2}}{21 c}",1,"(8*b*d*(d*x)^(3/2))/(21*c) + (2*b*d^(5/2)*ArcTan[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(7*c^(7/4)) + (Sqrt[2]*b*d^(5/2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(7*c^(7/4)) - (Sqrt[2]*b*d^(5/2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(7*c^(7/4)) + (2*(d*x)^(7/2)*(a + b*ArcTanh[c*x^2]))/(7*d) - (2*b*d^(5/2)*ArcTanh[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(7*c^(7/4)) - (b*d^(5/2)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x - Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(7*Sqrt[2]*c^(7/4)) + (b*d^(5/2)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x + Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(7*Sqrt[2]*c^(7/4))","A",17,14,18,0.7778,1,"{6097, 16, 321, 329, 300, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
83,1,317,0,0.299853,"\int (d x)^{3/2} \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[(d*x)^(3/2)*(a + b*ArcTanh[c*x^2]),x]","\frac{2 (d x)^{5/2} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{5 d}+\frac{b d^{3/2} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{5 \sqrt{2} c^{5/4}}-\frac{b d^{3/2} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{5 \sqrt{2} c^{5/4}}-\frac{2 b d^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 c^{5/4}}+\frac{\sqrt{2} b d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 c^{5/4}}-\frac{\sqrt{2} b d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{5 c^{5/4}}-\frac{2 b d^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 c^{5/4}}+\frac{8 b d \sqrt{d x}}{5 c}","\frac{2 (d x)^{5/2} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{5 d}+\frac{b d^{3/2} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{5 \sqrt{2} c^{5/4}}-\frac{b d^{3/2} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{5 \sqrt{2} c^{5/4}}-\frac{2 b d^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 c^{5/4}}+\frac{\sqrt{2} b d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 c^{5/4}}-\frac{\sqrt{2} b d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{5 c^{5/4}}-\frac{2 b d^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 c^{5/4}}+\frac{8 b d \sqrt{d x}}{5 c}",1,"(8*b*d*Sqrt[d*x])/(5*c) - (2*b*d^(3/2)*ArcTan[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(5*c^(5/4)) + (Sqrt[2]*b*d^(3/2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(5*c^(5/4)) - (Sqrt[2]*b*d^(3/2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(5*c^(5/4)) + (2*(d*x)^(5/2)*(a + b*ArcTanh[c*x^2]))/(5*d) - (2*b*d^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(5*c^(5/4)) + (b*d^(3/2)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x - Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(5*Sqrt[2]*c^(5/4)) - (b*d^(3/2)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x + Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(5*Sqrt[2]*c^(5/4))","A",17,14,18,0.7778,1,"{6097, 16, 321, 329, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
84,1,301,0,0.2508243,"\int \sqrt{d x} \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[Sqrt[d*x]*(a + b*ArcTanh[c*x^2]),x]","\frac{2 (d x)^{3/2} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{3 d}+\frac{b \sqrt{d} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{3 \sqrt{2} c^{3/4}}-\frac{b \sqrt{d} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{3 \sqrt{2} c^{3/4}}+\frac{2 b \sqrt{d} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 c^{3/4}}-\frac{\sqrt{2} b \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 c^{3/4}}+\frac{\sqrt{2} b \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{3 c^{3/4}}-\frac{2 b \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 c^{3/4}}","\frac{2 (d x)^{3/2} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{3 d}+\frac{b \sqrt{d} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{3 \sqrt{2} c^{3/4}}-\frac{b \sqrt{d} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{3 \sqrt{2} c^{3/4}}+\frac{2 b \sqrt{d} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 c^{3/4}}-\frac{\sqrt{2} b \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 c^{3/4}}+\frac{\sqrt{2} b \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{3 c^{3/4}}-\frac{2 b \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 c^{3/4}}",1,"(2*b*Sqrt[d]*ArcTan[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(3*c^(3/4)) - (Sqrt[2]*b*Sqrt[d]*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(3*c^(3/4)) + (Sqrt[2]*b*Sqrt[d]*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(3*c^(3/4)) + (2*(d*x)^(3/2)*(a + b*ArcTanh[c*x^2]))/(3*d) - (2*b*Sqrt[d]*ArcTanh[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(3*c^(3/4)) + (b*Sqrt[d]*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x - Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(3*Sqrt[2]*c^(3/4)) - (b*Sqrt[d]*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x + Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(3*Sqrt[2]*c^(3/4))","A",16,13,18,0.7222,1,"{6097, 16, 329, 301, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
85,1,285,0,0.2421397,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{\sqrt{d x}} \, dx","Int[(a + b*ArcTanh[c*x^2])/Sqrt[d*x],x]","\frac{2 \sqrt{d x} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{d}-\frac{b \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{\sqrt{2} \sqrt[4]{c} \sqrt{d}}+\frac{b \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{\sqrt{2} \sqrt[4]{c} \sqrt{d}}-\frac{2 b \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt[4]{c} \sqrt{d}}-\frac{\sqrt{2} b \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt[4]{c} \sqrt{d}}+\frac{\sqrt{2} b \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{\sqrt[4]{c} \sqrt{d}}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt[4]{c} \sqrt{d}}","\frac{2 \sqrt{d x} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{d}-\frac{b \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{\sqrt{2} \sqrt[4]{c} \sqrt{d}}+\frac{b \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{\sqrt{2} \sqrt[4]{c} \sqrt{d}}-\frac{2 b \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt[4]{c} \sqrt{d}}-\frac{\sqrt{2} b \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt[4]{c} \sqrt{d}}+\frac{\sqrt{2} b \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{\sqrt[4]{c} \sqrt{d}}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt[4]{c} \sqrt{d}}",1,"(-2*b*ArcTan[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(c^(1/4)*Sqrt[d]) - (Sqrt[2]*b*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(c^(1/4)*Sqrt[d]) + (Sqrt[2]*b*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(c^(1/4)*Sqrt[d]) + (2*Sqrt[d*x]*(a + b*ArcTanh[c*x^2]))/d - (2*b*ArcTanh[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(c^(1/4)*Sqrt[d]) - (b*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x - Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(Sqrt[2]*c^(1/4)*Sqrt[d]) + (b*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x + Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(Sqrt[2]*c^(1/4)*Sqrt[d])","A",16,13,18,0.7222,1,"{6097, 16, 329, 301, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
86,1,285,0,0.2484357,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{(d x)^{3/2}} \, dx","Int[(a + b*ArcTanh[c*x^2])/(d*x)^(3/2),x]","-\frac{2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{d \sqrt{d x}}+\frac{b \sqrt[4]{c} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{\sqrt{2} d^{3/2}}-\frac{b \sqrt[4]{c} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{\sqrt{2} d^{3/2}}-\frac{2 b \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{\sqrt{2} b \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{\sqrt{2} b \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{d^{3/2}}+\frac{2 b \sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}","-\frac{2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{d \sqrt{d x}}+\frac{b \sqrt[4]{c} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{\sqrt{2} d^{3/2}}-\frac{b \sqrt[4]{c} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{\sqrt{2} d^{3/2}}-\frac{2 b \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{\sqrt{2} b \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{\sqrt{2} b \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{d^{3/2}}+\frac{2 b \sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}",1,"(-2*b*c^(1/4)*ArcTan[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/d^(3/2) - (Sqrt[2]*b*c^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/d^(3/2) + (Sqrt[2]*b*c^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/d^(3/2) - (2*(a + b*ArcTanh[c*x^2]))/(d*Sqrt[d*x]) + (2*b*c^(1/4)*ArcTanh[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/d^(3/2) + (b*c^(1/4)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x - Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(Sqrt[2]*d^(3/2)) - (b*c^(1/4)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x + Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(Sqrt[2]*d^(3/2))","A",16,13,18,0.7222,1,"{6097, 16, 329, 300, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
87,1,301,0,0.2495113,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{(d x)^{5/2}} \, dx","Int[(a + b*ArcTanh[c*x^2])/(d*x)^(5/2),x]","-\frac{2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{3 d (d x)^{3/2}}-\frac{b c^{3/4} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{3 \sqrt{2} d^{5/2}}+\frac{b c^{3/4} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{3 \sqrt{2} d^{5/2}}+\frac{2 b c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{\sqrt{2} b c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}+\frac{\sqrt{2} b c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{3 d^{5/2}}+\frac{2 b c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}","-\frac{2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{3 d (d x)^{3/2}}-\frac{b c^{3/4} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{3 \sqrt{2} d^{5/2}}+\frac{b c^{3/4} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{3 \sqrt{2} d^{5/2}}+\frac{2 b c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{\sqrt{2} b c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}+\frac{\sqrt{2} b c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{3 d^{5/2}}+\frac{2 b c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}",1,"(2*b*c^(3/4)*ArcTan[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(3*d^(5/2)) - (Sqrt[2]*b*c^(3/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(3*d^(5/2)) + (Sqrt[2]*b*c^(3/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(3*d^(5/2)) - (2*(a + b*ArcTanh[c*x^2]))/(3*d*(d*x)^(3/2)) + (2*b*c^(3/4)*ArcTanh[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(3*d^(5/2)) - (b*c^(3/4)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x - Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(3*Sqrt[2]*d^(5/2)) + (b*c^(3/4)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x + Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(3*Sqrt[2]*d^(5/2))","A",16,13,18,0.7222,1,"{6097, 16, 329, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
88,1,317,0,0.2777616,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{(d x)^{7/2}} \, dx","Int[(a + b*ArcTanh[c*x^2])/(d*x)^(7/2),x]","-\frac{2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{5 d (d x)^{5/2}}-\frac{b c^{5/4} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{5 \sqrt{2} d^{7/2}}+\frac{b c^{5/4} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{5 \sqrt{2} d^{7/2}}-\frac{2 b c^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{\sqrt{2} b c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{\sqrt{2} b c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{5 d^{7/2}}+\frac{2 b c^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{8 b c}{5 d^3 \sqrt{d x}}","-\frac{2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{5 d (d x)^{5/2}}-\frac{b c^{5/4} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{5 \sqrt{2} d^{7/2}}+\frac{b c^{5/4} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{5 \sqrt{2} d^{7/2}}-\frac{2 b c^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{\sqrt{2} b c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{\sqrt{2} b c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{5 d^{7/2}}+\frac{2 b c^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{8 b c}{5 d^3 \sqrt{d x}}",1,"(-8*b*c)/(5*d^3*Sqrt[d*x]) - (2*b*c^(5/4)*ArcTan[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(5*d^(7/2)) + (Sqrt[2]*b*c^(5/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(5*d^(7/2)) - (Sqrt[2]*b*c^(5/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(5*d^(7/2)) - (2*(a + b*ArcTanh[c*x^2]))/(5*d*(d*x)^(5/2)) + (2*b*c^(5/4)*ArcTanh[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(5*d^(7/2)) - (b*c^(5/4)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x - Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(5*Sqrt[2]*d^(7/2)) + (b*c^(5/4)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x + Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(5*Sqrt[2]*d^(7/2))","A",17,14,18,0.7778,1,"{6097, 16, 325, 329, 301, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
89,1,317,0,0.2869339,"\int \frac{a+b \tanh ^{-1}\left(c x^2\right)}{(d x)^{9/2}} \, dx","Int[(a + b*ArcTanh[c*x^2])/(d*x)^(9/2),x]","-\frac{2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{7 d (d x)^{7/2}}+\frac{b c^{7/4} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{7 \sqrt{2} d^{9/2}}-\frac{b c^{7/4} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{7 \sqrt{2} d^{9/2}}+\frac{2 b c^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 d^{9/2}}+\frac{\sqrt{2} b c^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 d^{9/2}}-\frac{\sqrt{2} b c^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{7 d^{9/2}}+\frac{2 b c^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 d^{9/2}}-\frac{8 b c}{21 d^3 (d x)^{3/2}}","-\frac{2 \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{7 d (d x)^{7/2}}+\frac{b c^{7/4} \log \left(\sqrt{c} \sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{7 \sqrt{2} d^{9/2}}-\frac{b c^{7/4} \log \left(\sqrt{c} \sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt{d x}+\sqrt{d}\right)}{7 \sqrt{2} d^{9/2}}+\frac{2 b c^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 d^{9/2}}+\frac{\sqrt{2} b c^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 d^{9/2}}-\frac{\sqrt{2} b c^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}+1\right)}{7 d^{9/2}}+\frac{2 b c^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d x}}{\sqrt{d}}\right)}{7 d^{9/2}}-\frac{8 b c}{21 d^3 (d x)^{3/2}}",1,"(-8*b*c)/(21*d^3*(d*x)^(3/2)) + (2*b*c^(7/4)*ArcTan[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(7*d^(9/2)) + (Sqrt[2]*b*c^(7/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(7*d^(9/2)) - (Sqrt[2]*b*c^(7/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(7*d^(9/2)) - (2*(a + b*ArcTanh[c*x^2]))/(7*d*(d*x)^(7/2)) + (2*b*c^(7/4)*ArcTanh[(c^(1/4)*Sqrt[d*x])/Sqrt[d]])/(7*d^(9/2)) + (b*c^(7/4)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x - Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(7*Sqrt[2]*d^(9/2)) - (b*c^(7/4)*Log[Sqrt[d] + Sqrt[c]*Sqrt[d]*x + Sqrt[2]*c^(1/4)*Sqrt[d*x]])/(7*Sqrt[2]*d^(9/2))","A",17,14,18,0.7778,1,"{6097, 16, 325, 329, 301, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
90,0,0,0,0.0256037,"\int \sqrt{d x} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[Sqrt[d*x]*(a + b*ArcTanh[c*x^2])^2,x]","\int \sqrt{d x} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","-\frac{2 i \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right)^2 b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{2 i \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right)^2 b^2}{3 c^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right)^2 b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right)^2 b^2}{3 c^{3/4} \sqrt{x}}+\frac{1}{6} x \sqrt{d x} \log ^2\left(c x^2+1\right) b^2+\frac{4 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{1-\sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{4 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{(1+i) \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{4 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{i \sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{4 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{\sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{(1-i) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{4 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{1-\sqrt[4]{c} \sqrt{x}}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{4 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(i \sqrt[4]{-c}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(i \sqrt[4]{-c}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{(1+i) \left(1-\sqrt[4]{c} \sqrt{x}\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{4 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{i \sqrt[4]{c} \sqrt{x}+1}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{4 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{\sqrt[4]{c} \sqrt{x}+1}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{(1-i) \left(\sqrt[4]{c} \sqrt{x}+1\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(1-c x^2\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(1-c x^2\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{4}{9} x \sqrt{d x} \log \left(1-c x^2\right) b^2-\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{1}{3} x \sqrt{d x} \log \left(1-c x^2\right) \log \left(c x^2+1\right) b^2+\frac{2 \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{2 i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{i \sqrt{d x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}+1\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{2 i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{\sqrt{d x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}+1\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{\sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{\sqrt{d x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}+1\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{\sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{c} \sqrt{x}}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{\sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{2 i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{i \sqrt{d x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}+1\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{i \sqrt{d x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(i \sqrt[4]{-c}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}+1\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(i \sqrt[4]{-c}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt[4]{c} \sqrt{x}\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{2 i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt[4]{c} \sqrt{x}+1}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{c} \sqrt{x}+1}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{\sqrt{d x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{\sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{\sqrt{d x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{\sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{\sqrt{d x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{\sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 c^{3/4} \sqrt{x}}+\frac{i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{\sqrt{d x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 (-c)^{3/4} \sqrt{x}}-\frac{i \sqrt{d x} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt[4]{c} \sqrt{x}+1\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 c^{3/4} \sqrt{x}}-\frac{2 \sqrt{2} a \sqrt{d x} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{c} \sqrt{x}\right) b}{3 c^{3/4} \sqrt{x}}+\frac{2 \sqrt{2} a \sqrt{d x} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) b}{3 c^{3/4} \sqrt{x}}+\frac{\sqrt{2} a \sqrt{d x} \log \left(\sqrt{c} x-\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) b}{3 c^{3/4} \sqrt{x}}-\frac{\sqrt{2} a \sqrt{d x} \log \left(\sqrt{c} x+\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) b}{3 c^{3/4} \sqrt{x}}+\frac{2 \sqrt{d x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \left(2 a-b \log \left(1-c x^2\right)\right) b}{3 c^{3/4} \sqrt{x}}-\frac{2 \sqrt{d x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \left(2 a-b \log \left(1-c x^2\right)\right) b}{3 c^{3/4} \sqrt{x}}+\frac{4}{9} x \sqrt{d x} \left(2 a-b \log \left(1-c x^2\right)\right) b+\frac{2}{3} a x \sqrt{d x} \log \left(c x^2+1\right) b-\frac{8}{9} a x \sqrt{d x} b+\frac{1}{6} x \sqrt{d x} \left(2 a-b \log \left(1-c x^2\right)\right)^2",1,"Defer[Int][Sqrt[d*x]*(a + b*ArcTanh[c*x^2])^2, x]","F",0,0,0,0,-1,"{}"
91,0,0,0,0.025645,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{\sqrt{d x}} \, dx","Int[(a + b*ArcTanh[c*x^2])^2/Sqrt[d*x],x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{\sqrt{d x}} \, dx","\frac{2 x a^2}{\sqrt{d x}}-\frac{2 \sqrt{2} b \sqrt{x} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{c} \sqrt{x}\right) a}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 \sqrt{2} b \sqrt{x} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) a}{\sqrt[4]{c} \sqrt{d x}}-\frac{4 b \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) a}{\sqrt[4]{c} \sqrt{d x}}-\frac{4 b \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) a}{\sqrt[4]{c} \sqrt{d x}}-\frac{\sqrt{2} b \sqrt{x} \log \left(\sqrt{c} x-\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) a}{\sqrt[4]{c} \sqrt{d x}}+\frac{\sqrt{2} b \sqrt{x} \log \left(\sqrt{c} x+\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) a}{\sqrt[4]{c} \sqrt{d x}}-\frac{2 b x \log \left(1-c x^2\right) a}{\sqrt{d x}}+\frac{2 b x \log \left(c x^2+1\right) a}{\sqrt{d x}}+\frac{2 i b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right)^2}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 i b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right)^2}{\sqrt[4]{c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right)^2}{\sqrt[4]{-c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right)^2}{\sqrt[4]{c} \sqrt{d x}}+\frac{b^2 x \log ^2\left(1-c x^2\right)}{2 \sqrt{d x}}+\frac{b^2 x \log ^2\left(c x^2+1\right)}{2 \sqrt{d x}}+\frac{4 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{1-\sqrt[4]{-c} \sqrt{x}}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{4 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{1-i \sqrt[4]{-c} \sqrt{x}}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{(1+i) \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{4 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{i \sqrt[4]{-c} \sqrt{x}+1}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{4 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{\sqrt[4]{-c} \sqrt{x}+1}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{(1-i) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{4 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{1-\sqrt[4]{c} \sqrt{x}}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{4 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{1-i \sqrt[4]{c} \sqrt{x}}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(i \sqrt[4]{-c}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(i \sqrt[4]{-c}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{(1+i) \left(1-\sqrt[4]{c} \sqrt{x}\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{4 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{i \sqrt[4]{c} \sqrt{x}+1}\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{4 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{\sqrt[4]{c} \sqrt{x}+1}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{(1-i) \left(\sqrt[4]{c} \sqrt{x}+1\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(1-c x^2\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(1-c x^2\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(1-c x^2\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(1-c x^2\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(c x^2+1\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(c x^2+1\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(c x^2+1\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(c x^2+1\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{b^2 x \log \left(1-c x^2\right) \log \left(c x^2+1\right)}{\sqrt{d x}}+\frac{2 b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-c} \sqrt{x}}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt[4]{-c} \sqrt{x}}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}+1\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt[4]{-c} \sqrt{x}+1}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-c} \sqrt{x}+1}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}+1\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}+1\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{c} \sqrt{x}}\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{2 i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt[4]{c} \sqrt{x}}\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}+1\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(i \sqrt[4]{-c}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}+1\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(i \sqrt[4]{-c}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt[4]{c} \sqrt{x}\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt[4]{c} \sqrt{x}+1}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{2 b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{c} \sqrt{x}+1}\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right)}{\sqrt[4]{c} \sqrt{d x}}+\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{c} \sqrt{d x}}-\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}-\frac{b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right)}{\sqrt[4]{-c} \sqrt{d x}}+\frac{i b^2 \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt[4]{c} \sqrt{x}+1\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right)}{\sqrt[4]{c} \sqrt{d x}}",1,"Defer[Int][(a + b*ArcTanh[c*x^2])^2/Sqrt[d*x], x]","F",0,0,0,0,-1,"{}"
92,0,0,0,0.0292299,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{(d x)^{3/2}} \, dx","Int[(a + b*ArcTanh[c*x^2])^2/(d*x)^(3/2),x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{(d x)^{3/2}} \, dx","\frac{2 i \sqrt[4]{-c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right)^2 b^2}{d \sqrt{d x}}+\frac{2 i \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right)^2 b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{-c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right)^2 b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right)^2 b^2}{d \sqrt{d x}}-\frac{\log ^2\left(c x^2+1\right) b^2}{2 d \sqrt{d x}}-\frac{4 \sqrt[4]{-c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{1-\sqrt[4]{-c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}-\frac{4 \sqrt[4]{-c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{-c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{-c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{-c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{(1+i) \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}+\frac{4 \sqrt[4]{-c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{i \sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{d \sqrt{d x}}+\frac{4 \sqrt[4]{-c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{\sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{-c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{-c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{-c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{-c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{-c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{(1-i) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}-\frac{4 \sqrt[4]{c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{1-\sqrt[4]{c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{-c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{-c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}-\frac{4 \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(i \sqrt[4]{-c}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(i \sqrt[4]{-c}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{(1+i) \left(1-\sqrt[4]{c} \sqrt{x}\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}+\frac{4 \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{i \sqrt[4]{c} \sqrt{x}+1}\right) b^2}{d \sqrt{d x}}+\frac{4 \sqrt[4]{c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{\sqrt[4]{c} \sqrt{x}+1}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{-c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{-c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{(1-i) \left(\sqrt[4]{c} \sqrt{x}+1\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{-c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(1-c x^2\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{-c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(1-c x^2\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{-c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{-c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{d \sqrt{d x}}+\frac{2 \sqrt[4]{c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{d \sqrt{d x}}+\frac{\log \left(1-c x^2\right) \log \left(c x^2+1\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}+\frac{2 i \sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}-\frac{i \sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}+1\right) b^2}{d \sqrt{d x}}-\frac{i \sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}+\frac{i \sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}+\frac{2 i \sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{d \sqrt{d x}}-\frac{\sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}+1\right) b^2}{d \sqrt{d x}}-\frac{\sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}+\frac{\sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}+1\right) b^2}{d \sqrt{d x}}+\frac{\sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}+\frac{i \sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}-\frac{i \sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}+\frac{\sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}+\frac{2 i \sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}-\frac{i \sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}+1\right) b^2}{d \sqrt{d x}}-\frac{i \sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}-\frac{i \sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(i \sqrt[4]{-c}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}+1\right) b^2}{d \sqrt{d x}}-\frac{i \sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(i \sqrt[4]{-c}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}+\frac{i \sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt[4]{c} \sqrt{x}\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}+\frac{2 i \sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt[4]{c} \sqrt{x}+1}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{c} \sqrt{x}+1}\right) b^2}{d \sqrt{d x}}+\frac{\sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right) b^2}{d \sqrt{d x}}+\frac{\sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}-\frac{\sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right) b^2}{d \sqrt{d x}}-\frac{\sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}+\frac{\sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right) b^2}{d \sqrt{d x}}+\frac{\sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}-\frac{i \sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{d \sqrt{d x}}+\frac{\sqrt[4]{-c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{d \sqrt{d x}}+\frac{i \sqrt[4]{c} \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt[4]{c} \sqrt{x}+1\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{d \sqrt{d x}}-\frac{2 \sqrt{2} a \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{c} \sqrt{x}\right) b}{d \sqrt{d x}}+\frac{2 \sqrt{2} a \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) b}{d \sqrt{d x}}+\frac{\sqrt{2} a \sqrt[4]{c} \sqrt{x} \log \left(\sqrt{c} x-\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) b}{d \sqrt{d x}}-\frac{\sqrt{2} a \sqrt[4]{c} \sqrt{x} \log \left(\sqrt{c} x+\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) b}{d \sqrt{d x}}-\frac{2 \sqrt[4]{c} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \left(2 a-b \log \left(1-c x^2\right)\right) b}{d \sqrt{d x}}+\frac{2 \sqrt[4]{c} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \left(2 a-b \log \left(1-c x^2\right)\right) b}{d \sqrt{d x}}-\frac{2 a \log \left(c x^2+1\right) b}{d \sqrt{d x}}-\frac{\left(2 a-b \log \left(1-c x^2\right)\right)^2}{2 d \sqrt{d x}}",1,"Defer[Int][(a + b*ArcTanh[c*x^2])^2/(d*x)^(3/2), x]","F",0,0,0,0,-1,"{}"
93,0,0,0,0.030478,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{(d x)^{5/2}} \, dx","Int[(a + b*ArcTanh[c*x^2])^2/(d*x)^(5/2),x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2}{(d x)^{5/2}} \, dx","-\frac{2 i (-c)^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right)^2 b^2}{3 d^2 \sqrt{d x}}-\frac{2 i c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right)^2 b^2}{3 d^2 \sqrt{d x}}+\frac{2 (-c)^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right)^2 b^2}{3 d^2 \sqrt{d x}}+\frac{2 c^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right)^2 b^2}{3 d^2 \sqrt{d x}}-\frac{\log ^2\left(c x^2+1\right) b^2}{6 d^2 x \sqrt{d x}}-\frac{4 (-c)^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{1-\sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{4 (-c)^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 (-c)^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{(1+i) \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{4 (-c)^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{i \sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{4 (-c)^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2}{\sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 (-c)^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 (-c)^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 (-c)^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{(1-i) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{4 c^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{1-\sqrt[4]{c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{4 c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(i \sqrt[4]{-c}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(i \sqrt[4]{-c}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{(1+i) \left(1-\sqrt[4]{c} \sqrt{x}\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{4 c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{i \sqrt[4]{c} \sqrt{x}+1}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{4 c^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2}{\sqrt[4]{c} \sqrt{x}+1}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 c^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 c^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 c^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 c^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 c^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(-\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 c^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(\frac{(1-i) \left(\sqrt[4]{c} \sqrt{x}+1\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 (-c)^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(1-c x^2\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 (-c)^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(1-c x^2\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{-c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{3 d^2 \sqrt{d x}}+\frac{2 c^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \log \left(c x^2+1\right) b^2}{3 d^2 \sqrt{d x}}+\frac{\log \left(1-c x^2\right) \log \left(c x^2+1\right) b^2}{3 d^2 x \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 i (-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{i (-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}+1\right) b^2}{3 d^2 \sqrt{d x}}+\frac{i (-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{i (-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 i (-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 (-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-c} \sqrt{x}+1}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{(-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}+1\right) b^2}{3 d^2 \sqrt{d x}}-\frac{(-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{(-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{-c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}+1\right) b^2}{3 d^2 \sqrt{d x}}+\frac{(-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{-c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{i (-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{1-i \sqrt[4]{-c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 c^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{i (-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{(-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(1-\sqrt[4]{c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 i c^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{i c^{3/4} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(i \sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}+1\right) b^2}{3 d^2 \sqrt{d x}}+\frac{i c^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(i \sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{i c^{3/4} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(i \sqrt[4]{-c}-\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}+1\right) b^2}{3 d^2 \sqrt{d x}}+\frac{i c^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(i \sqrt[4]{-c}+\sqrt[4]{c}\right) \left(1-i \sqrt[4]{c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{i c^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\sqrt[4]{c} \sqrt{x}\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 i c^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{i \sqrt[4]{c} \sqrt{x}+1}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 c^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{c} \sqrt{x}+1}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{c^{3/4} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{-c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{-c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right) b^2}{3 d^2 \sqrt{d x}}+\frac{c^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{-c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{-c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{c^{3/4} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt{-\sqrt{c}} \sqrt{x}\right)}{\left(\sqrt{-\sqrt{c}}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right) b^2}{3 d^2 \sqrt{d x}}-\frac{c^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt{-\sqrt{c}} \sqrt{x}+1\right)}{\left(\sqrt{-\sqrt{c}}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{c^{3/4} \sqrt{x} \text{PolyLog}\left(2,\frac{2 \sqrt[4]{c} \left(1-\sqrt[4]{-c} \sqrt{x}\right)}{\left(\sqrt[4]{-c}-\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}+1\right) b^2}{3 d^2 \sqrt{d x}}+\frac{c^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{c} \left(\sqrt[4]{-c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{i (-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+i \sqrt[4]{c}\right) \left(1-i \sqrt[4]{-c} \sqrt{x}\right)}\right) b^2}{3 d^2 \sqrt{d x}}+\frac{(-c)^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{2 \sqrt[4]{-c} \left(\sqrt[4]{c} \sqrt{x}+1\right)}{\left(\sqrt[4]{-c}+\sqrt[4]{c}\right) \left(\sqrt[4]{-c} \sqrt{x}+1\right)}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{i c^{3/4} \sqrt{x} \text{PolyLog}\left(2,1-\frac{(1-i) \left(\sqrt[4]{c} \sqrt{x}+1\right)}{1-i \sqrt[4]{c} \sqrt{x}}\right) b^2}{3 d^2 \sqrt{d x}}-\frac{2 \sqrt{2} a c^{3/4} \sqrt{x} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{c} \sqrt{x}\right) b}{3 d^2 \sqrt{d x}}+\frac{2 \sqrt{2} a c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) b}{3 d^2 \sqrt{d x}}-\frac{\sqrt{2} a c^{3/4} \sqrt{x} \log \left(\sqrt{c} x-\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) b}{3 d^2 \sqrt{d x}}+\frac{\sqrt{2} a c^{3/4} \sqrt{x} \log \left(\sqrt{c} x+\sqrt{2} \sqrt[4]{c} \sqrt{x}+1\right) b}{3 d^2 \sqrt{d x}}+\frac{2 c^{3/4} \sqrt{x} \tan ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \left(2 a-b \log \left(1-c x^2\right)\right) b}{3 d^2 \sqrt{d x}}+\frac{2 c^{3/4} \sqrt{x} \tanh ^{-1}\left(\sqrt[4]{c} \sqrt{x}\right) \left(2 a-b \log \left(1-c x^2\right)\right) b}{3 d^2 \sqrt{d x}}-\frac{2 a \log \left(c x^2+1\right) b}{3 d^2 x \sqrt{d x}}-\frac{\left(2 a-b \log \left(1-c x^2\right)\right)^2}{6 d^2 x \sqrt{d x}}",1,"Defer[Int][(a + b*ArcTanh[c*x^2])^2/(d*x)^(5/2), x]","F",0,0,0,0,-1,"{}"
94,0,0,0,0.0239834,"\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x^2])^3,x]","\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTanh[c*x^2])^3, x]","A",0,0,0,0,-1,"{}"
95,0,0,0,0.0237911,"\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x^2])^2,x]","\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTanh[c*x^2])^2, x]","A",0,0,0,0,-1,"{}"
96,1,74,0,0.0397164,"\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^2\right)\right) \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x^2]),x]","\frac{(d x)^{m+1} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{d (m+1)}-\frac{2 b c (d x)^{m+3} \, _2F_1\left(1,\frac{m+3}{4};\frac{m+7}{4};c^2 x^4\right)}{d^3 (m+1) (m+3)}","\frac{(d x)^{m+1} \left(a+b \tanh ^{-1}\left(c x^2\right)\right)}{d (m+1)}-\frac{2 b c (d x)^{m+3} \, _2F_1\left(1,\frac{m+3}{4};\frac{m+7}{4};c^2 x^4\right)}{d^3 (m+1) (m+3)}",1,"((d*x)^(1 + m)*(a + b*ArcTanh[c*x^2]))/(d*(1 + m)) - (2*b*c*(d*x)^(3 + m)*Hypergeometric2F1[1, (3 + m)/4, (7 + m)/4, c^2*x^4])/(d^3*(1 + m)*(3 + m))","A",3,3,16,0.1875,1,"{6097, 16, 364}"
97,0,0,0,0.0287267,"\int \frac{(d x)^m}{a+b \tanh ^{-1}\left(c x^2\right)} \, dx","Int[(d*x)^m/(a + b*ArcTanh[c*x^2]),x]","\int \frac{(d x)^m}{a+b \tanh ^{-1}\left(c x^2\right)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \tanh ^{-1}\left(c x^2\right)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTanh[c*x^2]), x]","A",0,0,0,0,-1,"{}"
98,0,0,0,0.0271365,"\int \frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2} \, dx","Int[(d*x)^m/(a + b*ArcTanh[c*x^2])^2,x]","\int \frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(c x^2\right)\right)^2},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTanh[c*x^2])^2, x]","A",0,0,0,0,-1,"{}"
99,1,54,0,0.0382175,"\int x^{11} \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[x^11*(a + b*ArcTanh[c*x^3]),x]","\frac{1}{12} x^{12} \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b x^3}{12 c^3}-\frac{b \tanh ^{-1}\left(c x^3\right)}{12 c^4}+\frac{b x^9}{36 c}","\frac{1}{12} x^{12} \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b x^3}{12 c^3}-\frac{b \tanh ^{-1}\left(c x^3\right)}{12 c^4}+\frac{b x^9}{36 c}",1,"(b*x^3)/(12*c^3) + (b*x^9)/(36*c) - (b*ArcTanh[c*x^3])/(12*c^4) + (x^12*(a + b*ArcTanh[c*x^3]))/12","A",5,4,14,0.2857,1,"{6097, 275, 302, 206}"
100,1,48,0,0.0359128,"\int x^8 \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[x^8*(a + b*ArcTanh[c*x^3]),x]","\frac{1}{9} x^9 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(1-c^2 x^6\right)}{18 c^3}+\frac{b x^6}{18 c}","\frac{1}{9} x^9 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(1-c^2 x^6\right)}{18 c^3}+\frac{b x^6}{18 c}",1,"(b*x^6)/(18*c) + (x^9*(a + b*ArcTanh[c*x^3]))/9 + (b*Log[1 - c^2*x^6])/(18*c^3)","A",4,3,14,0.2143,1,"{6097, 266, 43}"
101,1,43,0,0.030026,"\int x^5 \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[x^5*(a + b*ArcTanh[c*x^3]),x]","\frac{1}{6} x^6 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)-\frac{b \tanh ^{-1}\left(c x^3\right)}{6 c^2}+\frac{b x^3}{6 c}","\frac{1}{6} x^6 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)-\frac{b \tanh ^{-1}\left(c x^3\right)}{6 c^2}+\frac{b x^3}{6 c}",1,"(b*x^3)/(6*c) - (b*ArcTanh[c*x^3])/(6*c^2) + (x^6*(a + b*ArcTanh[c*x^3]))/6","A",4,4,14,0.2857,1,"{6097, 275, 321, 206}"
102,1,37,0,0.020476,"\int x^2 \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[x^2*(a + b*ArcTanh[c*x^3]),x]","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(1-c^2 x^6\right)}{6 c}","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(1-c^2 x^6\right)}{6 c}",1,"(x^3*(a + b*ArcTanh[c*x^3]))/3 + (b*Log[1 - c^2*x^6])/(6*c)","A",2,2,14,0.1429,1,"{6097, 260}"
103,1,30,0,0.0337,"\int \frac{a+b \tanh ^{-1}\left(c x^3\right)}{x} \, dx","Int[(a + b*ArcTanh[c*x^3])/x,x]","-\frac{1}{6} b \text{PolyLog}\left(2,-c x^3\right)+\frac{1}{6} b \text{PolyLog}\left(2,c x^3\right)+a \log (x)","-\frac{1}{6} b \text{PolyLog}\left(2,-c x^3\right)+\frac{1}{6} b \text{PolyLog}\left(2,c x^3\right)+a \log (x)",1,"a*Log[x] - (b*PolyLog[2, -(c*x^3)])/6 + (b*PolyLog[2, c*x^3])/6","A",2,2,14,0.1429,1,"{6095, 5912}"
104,1,40,0,0.0270264,"\int \frac{a+b \tanh ^{-1}\left(c x^3\right)}{x^4} \, dx","Int[(a + b*ArcTanh[c*x^3])/x^4,x]","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{3 x^3}-\frac{1}{6} b c \log \left(1-c^2 x^6\right)+b c \log (x)","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{3 x^3}-\frac{1}{6} b c \log \left(1-c^2 x^6\right)+b c \log (x)",1,"-(a + b*ArcTanh[c*x^3])/(3*x^3) + b*c*Log[x] - (b*c*Log[1 - c^2*x^6])/6","A",5,5,14,0.3571,1,"{6097, 266, 36, 29, 31}"
105,1,41,0,0.0270646,"\int \frac{a+b \tanh ^{-1}\left(c x^3\right)}{x^7} \, dx","Int[(a + b*ArcTanh[c*x^3])/x^7,x]","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{6 x^6}+\frac{1}{6} b c^2 \tanh ^{-1}\left(c x^3\right)-\frac{b c}{6 x^3}","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{6 x^6}+\frac{1}{6} b c^2 \tanh ^{-1}\left(c x^3\right)-\frac{b c}{6 x^3}",1,"-(b*c)/(6*x^3) + (b*c^2*ArcTanh[c*x^3])/6 - (a + b*ArcTanh[c*x^3])/(6*x^6)","A",4,4,14,0.2857,1,"{6097, 275, 325, 206}"
106,1,56,0,0.0363813,"\int \frac{a+b \tanh ^{-1}\left(c x^3\right)}{x^{10}} \, dx","Int[(a + b*ArcTanh[c*x^3])/x^10,x]","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{9 x^9}-\frac{1}{18} b c^3 \log \left(1-c^2 x^6\right)+\frac{1}{3} b c^3 \log (x)-\frac{b c}{18 x^6}","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{9 x^9}-\frac{1}{18} b c^3 \log \left(1-c^2 x^6\right)+\frac{1}{3} b c^3 \log (x)-\frac{b c}{18 x^6}",1,"-(b*c)/(18*x^6) - (a + b*ArcTanh[c*x^3])/(9*x^9) + (b*c^3*Log[x])/3 - (b*c^3*Log[1 - c^2*x^6])/18","A",4,3,14,0.2143,1,"{6097, 266, 44}"
107,1,174,0,0.2197339,"\int x^3 \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[x^3*(a + b*ArcTanh[c*x^3]),x]","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{16 c^{4/3}}-\frac{b \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{16 c^{4/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{8 c^{4/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{8 c^{4/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} x\right)}{4 c^{4/3}}+\frac{3 b x}{4 c}","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{16 c^{4/3}}-\frac{b \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{16 c^{4/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{8 c^{4/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{8 c^{4/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} x\right)}{4 c^{4/3}}+\frac{3 b x}{4 c}",1,"(3*b*x)/(4*c) + (Sqrt[3]*b*ArcTan[1/Sqrt[3] - (2*c^(1/3)*x)/Sqrt[3]])/(8*c^(4/3)) - (Sqrt[3]*b*ArcTan[1/Sqrt[3] + (2*c^(1/3)*x)/Sqrt[3]])/(8*c^(4/3)) - (b*ArcTanh[c^(1/3)*x])/(4*c^(4/3)) + (x^4*(a + b*ArcTanh[c*x^3]))/4 + (b*Log[1 - c^(1/3)*x + c^(2/3)*x^2])/(16*c^(4/3)) - (b*Log[1 + c^(1/3)*x + c^(2/3)*x^2])/(16*c^(4/3))","A",12,8,14,0.5714,1,"{6097, 321, 210, 634, 618, 204, 628, 206}"
108,1,101,0,0.0966456,"\int \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[a + b*ArcTanh[c*x^3],x]","a x+\frac{b \log \left(1-c^{2/3} x^2\right)}{2 \sqrt[3]{c}}-\frac{b \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}+b x \tanh ^{-1}\left(c x^3\right)","a x+\frac{b \log \left(1-c^{2/3} x^2\right)}{2 \sqrt[3]{c}}-\frac{b \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}+b x \tanh ^{-1}\left(c x^3\right)",1,"a*x + (Sqrt[3]*b*ArcTan[(1 + 2*c^(2/3)*x^2)/Sqrt[3]])/(2*c^(1/3)) + b*x*ArcTanh[c*x^3] + (b*Log[1 - c^(2/3)*x^2])/(2*c^(1/3)) - (b*Log[1 + c^(2/3)*x^2 + c^(4/3)*x^4])/(4*c^(1/3))","A",9,8,10,0.8000,1,"{6091, 275, 292, 31, 634, 617, 204, 628}"
109,1,165,0,0.1974063,"\int \frac{a+b \tanh ^{-1}\left(c x^3\right)}{x^3} \, dx","Int[(a + b*ArcTanh[c*x^3])/x^3,x]","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{2 x^2}-\frac{1}{8} b c^{2/3} \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)+\frac{1}{8} b c^{2/3} \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)-\frac{1}{4} \sqrt{3} b c^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)+\frac{1}{4} \sqrt{3} b c^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)+\frac{1}{2} b c^{2/3} \tanh ^{-1}\left(\sqrt[3]{c} x\right)","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{2 x^2}-\frac{1}{8} b c^{2/3} \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)+\frac{1}{8} b c^{2/3} \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)-\frac{1}{4} \sqrt{3} b c^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)+\frac{1}{4} \sqrt{3} b c^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)+\frac{1}{2} b c^{2/3} \tanh ^{-1}\left(\sqrt[3]{c} x\right)",1,"-(Sqrt[3]*b*c^(2/3)*ArcTan[1/Sqrt[3] - (2*c^(1/3)*x)/Sqrt[3]])/4 + (Sqrt[3]*b*c^(2/3)*ArcTan[1/Sqrt[3] + (2*c^(1/3)*x)/Sqrt[3]])/4 + (b*c^(2/3)*ArcTanh[c^(1/3)*x])/2 - (a + b*ArcTanh[c*x^3])/(2*x^2) - (b*c^(2/3)*Log[1 - c^(1/3)*x + c^(2/3)*x^2])/8 + (b*c^(2/3)*Log[1 + c^(1/3)*x + c^(2/3)*x^2])/8","A",11,7,14,0.5000,1,"{6097, 210, 634, 618, 204, 628, 206}"
110,1,115,0,0.0945154,"\int \frac{a+b \tanh ^{-1}\left(c x^3\right)}{x^6} \, dx","Int[(a + b*ArcTanh[c*x^3])/x^6,x]","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{5 x^5}-\frac{1}{10} b c^{5/3} \log \left(1-c^{2/3} x^2\right)+\frac{1}{20} b c^{5/3} \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)-\frac{1}{10} \sqrt{3} b c^{5/3} \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)-\frac{3 b c}{10 x^2}","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{5 x^5}-\frac{1}{10} b c^{5/3} \log \left(1-c^{2/3} x^2\right)+\frac{1}{20} b c^{5/3} \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)-\frac{1}{10} \sqrt{3} b c^{5/3} \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)-\frac{3 b c}{10 x^2}",1,"(-3*b*c)/(10*x^2) - (Sqrt[3]*b*c^(5/3)*ArcTan[(1 + 2*c^(2/3)*x^2)/Sqrt[3]])/10 - (a + b*ArcTanh[c*x^3])/(5*x^5) - (b*c^(5/3)*Log[1 - c^(2/3)*x^2])/10 + (b*c^(5/3)*Log[1 + c^(2/3)*x^2 + c^(4/3)*x^4])/20","A",9,9,14,0.6429,1,"{6097, 275, 325, 292, 31, 634, 617, 204, 628}"
111,1,176,0,0.2837187,"\int x^7 \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[x^7*(a + b*ArcTanh[c*x^3]),x]","\frac{1}{8} x^8 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{32 c^{8/3}}-\frac{b \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{32 c^{8/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{16 c^{8/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{16 c^{8/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} x\right)}{8 c^{8/3}}+\frac{3 b x^5}{40 c}","\frac{1}{8} x^8 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{32 c^{8/3}}-\frac{b \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{32 c^{8/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{16 c^{8/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{16 c^{8/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} x\right)}{8 c^{8/3}}+\frac{3 b x^5}{40 c}",1,"(3*b*x^5)/(40*c) - (Sqrt[3]*b*ArcTan[1/Sqrt[3] - (2*c^(1/3)*x)/Sqrt[3]])/(16*c^(8/3)) + (Sqrt[3]*b*ArcTan[1/Sqrt[3] + (2*c^(1/3)*x)/Sqrt[3]])/(16*c^(8/3)) - (b*ArcTanh[c^(1/3)*x])/(8*c^(8/3)) + (x^8*(a + b*ArcTanh[c*x^3]))/8 + (b*Log[1 - c^(1/3)*x + c^(2/3)*x^2])/(32*c^(8/3)) - (b*Log[1 + c^(1/3)*x + c^(2/3)*x^2])/(32*c^(8/3))","A",12,8,14,0.5714,1,"{6097, 321, 296, 634, 618, 204, 628, 206}"
112,1,117,0,0.0972647,"\int x^4 \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[x^4*(a + b*ArcTanh[c*x^3]),x]","\frac{1}{5} x^5 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(1-c^{2/3} x^2\right)}{10 c^{5/3}}-\frac{b \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)}{20 c^{5/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)}{10 c^{5/3}}+\frac{3 b x^2}{10 c}","\frac{1}{5} x^5 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(1-c^{2/3} x^2\right)}{10 c^{5/3}}-\frac{b \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)}{20 c^{5/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)}{10 c^{5/3}}+\frac{3 b x^2}{10 c}",1,"(3*b*x^2)/(10*c) - (Sqrt[3]*b*ArcTan[(1 + 2*c^(2/3)*x^2)/Sqrt[3]])/(10*c^(5/3)) + (x^5*(a + b*ArcTanh[c*x^3]))/5 + (b*Log[1 - c^(2/3)*x^2])/(10*c^(5/3)) - (b*Log[1 + c^(2/3)*x^2 + c^(4/3)*x^4])/(20*c^(5/3))","A",9,9,14,0.6429,1,"{6097, 275, 321, 200, 31, 634, 617, 204, 628}"
113,1,165,0,0.2486062,"\int x \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[x*(a + b*ArcTanh[c*x^3]),x]","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{b \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{4 c^{2/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{4 c^{2/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} x\right)}{2 c^{2/3}}","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{b \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)}{4 c^{2/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{4 c^{2/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} x\right)}{2 c^{2/3}}",1,"-(Sqrt[3]*b*ArcTan[1/Sqrt[3] - (2*c^(1/3)*x)/Sqrt[3]])/(4*c^(2/3)) + (Sqrt[3]*b*ArcTan[1/Sqrt[3] + (2*c^(1/3)*x)/Sqrt[3]])/(4*c^(2/3)) - (b*ArcTanh[c^(1/3)*x])/(2*c^(2/3)) + (x^2*(a + b*ArcTanh[c*x^3]))/2 + (b*Log[1 - c^(1/3)*x + c^(2/3)*x^2])/(8*c^(2/3)) - (b*Log[1 + c^(1/3)*x + c^(2/3)*x^2])/(8*c^(2/3))","A",11,7,12,0.5833,1,"{6097, 296, 634, 618, 204, 628, 206}"
114,1,104,0,0.0827732,"\int \frac{a+b \tanh ^{-1}\left(c x^3\right)}{x^2} \, dx","Int[(a + b*ArcTanh[c*x^3])/x^2,x]","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{x}-\frac{1}{2} b \sqrt[3]{c} \log \left(1-c^{2/3} x^2\right)+\frac{1}{4} b \sqrt[3]{c} \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)+\frac{1}{2} \sqrt{3} b \sqrt[3]{c} \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{x}-\frac{1}{2} b \sqrt[3]{c} \log \left(1-c^{2/3} x^2\right)+\frac{1}{4} b \sqrt[3]{c} \log \left(c^{4/3} x^4+c^{2/3} x^2+1\right)+\frac{1}{2} \sqrt{3} b \sqrt[3]{c} \tan ^{-1}\left(\frac{2 c^{2/3} x^2+1}{\sqrt{3}}\right)",1,"(Sqrt[3]*b*c^(1/3)*ArcTan[(1 + 2*c^(2/3)*x^2)/Sqrt[3]])/2 - (a + b*ArcTanh[c*x^3])/x - (b*c^(1/3)*Log[1 - c^(2/3)*x^2])/2 + (b*c^(1/3)*Log[1 + c^(2/3)*x^2 + c^(4/3)*x^4])/4","A",8,8,14,0.5714,1,"{6097, 275, 200, 31, 634, 617, 204, 628}"
115,1,174,0,0.2671737,"\int \frac{a+b \tanh ^{-1}\left(c x^3\right)}{x^5} \, dx","Int[(a + b*ArcTanh[c*x^3])/x^5,x]","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{4 x^4}-\frac{1}{16} b c^{4/3} \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)+\frac{1}{16} b c^{4/3} \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)+\frac{1}{8} \sqrt{3} b c^{4/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)-\frac{1}{8} \sqrt{3} b c^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)+\frac{1}{4} b c^{4/3} \tanh ^{-1}\left(\sqrt[3]{c} x\right)-\frac{3 b c}{4 x}","-\frac{a+b \tanh ^{-1}\left(c x^3\right)}{4 x^4}-\frac{1}{16} b c^{4/3} \log \left(c^{2/3} x^2-\sqrt[3]{c} x+1\right)+\frac{1}{16} b c^{4/3} \log \left(c^{2/3} x^2+\sqrt[3]{c} x+1\right)+\frac{1}{8} \sqrt{3} b c^{4/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{c} x}{\sqrt{3}}\right)-\frac{1}{8} \sqrt{3} b c^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)+\frac{1}{4} b c^{4/3} \tanh ^{-1}\left(\sqrt[3]{c} x\right)-\frac{3 b c}{4 x}",1,"(-3*b*c)/(4*x) + (Sqrt[3]*b*c^(4/3)*ArcTan[1/Sqrt[3] - (2*c^(1/3)*x)/Sqrt[3]])/8 - (Sqrt[3]*b*c^(4/3)*ArcTan[1/Sqrt[3] + (2*c^(1/3)*x)/Sqrt[3]])/8 + (b*c^(4/3)*ArcTanh[c^(1/3)*x])/4 - (a + b*ArcTanh[c*x^3])/(4*x^4) - (b*c^(4/3)*Log[1 - c^(1/3)*x + c^(2/3)*x^2])/16 + (b*c^(4/3)*Log[1 + c^(1/3)*x + c^(2/3)*x^2])/16","A",12,8,14,0.5714,1,"{6097, 325, 296, 634, 618, 204, 628, 206}"
116,1,636,0,1.5458513,"\int x^{11} \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2 \, dx","Int[x^11*(a + b*ArcTanh[c*x^3])^2,x]","\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^3\right)\right)}{24 c^4}+\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^3+1\right)\right)}{24 c^4}+\frac{a b x^3}{12 c^3}-\frac{b x^6 \left(2 a-b \log \left(1-c x^3\right)\right)}{48 c^2}-\frac{1}{288} b \left(-\frac{3 \left(1-c x^3\right)^4}{c^4}+\frac{16 \left(1-c x^3\right)^3}{c^4}-\frac{36 \left(1-c x^3\right)^2}{c^4}+\frac{48 \left(1-c x^3\right)}{c^4}-\frac{12 \log \left(1-c x^3\right)}{c^4}\right) \left(2 a-b \log \left(1-c x^3\right)\right)-\frac{b \log \left(\frac{1}{2} \left(c x^3+1\right)\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{24 c^4}+\frac{1}{48} x^{12} \left(2 a-b \log \left(1-c x^3\right)\right)^2-\frac{1}{96} b x^{12} \left(2 a-b \log \left(1-c x^3\right)\right)+\frac{1}{24} b x^{12} \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)+\frac{b x^9 \left(2 a-b \log \left(1-c x^3\right)\right)}{72 c}+\frac{b^2 x^6}{192 c^2}+\frac{23 b^2 x^3}{288 c^3}+\frac{b^2 \left(1-c x^3\right)^4}{384 c^4}-\frac{b^2 \left(1-c x^3\right)^3}{54 c^4}+\frac{b^2 \left(1-c x^3\right)^2}{16 c^4}+\frac{b^2 \log ^2\left(1-c x^3\right)}{48 c^4}-\frac{b^2 \log ^2\left(c x^3+1\right)}{48 c^4}+\frac{b^2 \left(1-c x^3\right) \log \left(1-c x^3\right)}{24 c^4}-\frac{5 b^2 \log \left(1-c x^3\right)}{288 c^4}+\frac{b^2 \left(c x^3+1\right) \log \left(c x^3+1\right)}{12 c^4}+\frac{b^2 \log \left(\frac{1}{2} \left(1-c x^3\right)\right) \log \left(c x^3+1\right)}{24 c^4}+\frac{b^2 \log \left(c x^3+1\right)}{36 c^4}-\frac{7 b^2 x^9}{864 c}+\frac{1}{48} b^2 x^{12} \log ^2\left(c x^3+1\right)+\frac{b^2 x^9 \log \left(c x^3+1\right)}{36 c}-\frac{1}{384} b^2 x^{12}","\frac{a b x^3}{6 c^3}-\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{12 c^4}+\frac{1}{12} x^{12} \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2+\frac{b x^9 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{18 c}+\frac{b^2 x^6}{36 c^2}+\frac{b^2 \log \left(1-c^2 x^6\right)}{9 c^4}+\frac{b^2 x^3 \tanh ^{-1}\left(c x^3\right)}{6 c^3}",1,"(a*b*x^3)/(12*c^3) + (23*b^2*x^3)/(288*c^3) + (b^2*x^6)/(192*c^2) - (7*b^2*x^9)/(864*c) - (b^2*x^12)/384 + (b^2*(1 - c*x^3)^2)/(16*c^4) - (b^2*(1 - c*x^3)^3)/(54*c^4) + (b^2*(1 - c*x^3)^4)/(384*c^4) - (5*b^2*Log[1 - c*x^3])/(288*c^4) + (b^2*(1 - c*x^3)*Log[1 - c*x^3])/(24*c^4) + (b^2*Log[1 - c*x^3]^2)/(48*c^4) - (b*x^6*(2*a - b*Log[1 - c*x^3]))/(48*c^2) + (b*x^9*(2*a - b*Log[1 - c*x^3]))/(72*c) - (b*x^12*(2*a - b*Log[1 - c*x^3]))/96 + (x^12*(2*a - b*Log[1 - c*x^3])^2)/48 - (b*(2*a - b*Log[1 - c*x^3])*((48*(1 - c*x^3))/c^4 - (36*(1 - c*x^3)^2)/c^4 + (16*(1 - c*x^3)^3)/c^4 - (3*(1 - c*x^3)^4)/c^4 - (12*Log[1 - c*x^3])/c^4))/288 - (b*(2*a - b*Log[1 - c*x^3])*Log[(1 + c*x^3)/2])/(24*c^4) + (b^2*Log[1 + c*x^3])/(36*c^4) + (b^2*x^9*Log[1 + c*x^3])/(36*c) + (b^2*(1 + c*x^3)*Log[1 + c*x^3])/(12*c^4) + (b^2*Log[(1 - c*x^3)/2]*Log[1 + c*x^3])/(24*c^4) + (b*x^12*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3])/24 - (b^2*Log[1 + c*x^3]^2)/(48*c^4) + (b^2*x^12*Log[1 + c*x^3]^2)/48 + (b^2*PolyLog[2, (1 - c*x^3)/2])/(24*c^4) + (b^2*PolyLog[2, (1 + c*x^3)/2])/(24*c^4)","C",62,19,16,1.187,0,"{6099, 2454, 2398, 2411, 43, 2334, 12, 14, 2301, 2395, 2439, 2416, 2389, 2295, 2394, 2393, 2391, 2410, 2390}"
117,1,536,0,1.3093399,"\int x^8 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2 \, dx","Int[x^8*(a + b*ArcTanh[c*x^3])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^3\right)\right)}{18 c^3}+\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^3+1\right)\right)}{18 c^3}-\frac{a b x^3}{9 c^2}-\frac{1}{108} b \left(\frac{2 \left(1-c x^3\right)^3}{c^3}-\frac{9 \left(1-c x^3\right)^2}{c^3}+\frac{18 \left(1-c x^3\right)}{c^3}-\frac{6 \log \left(1-c x^3\right)}{c^3}\right) \left(2 a-b \log \left(1-c x^3\right)\right)+\frac{b \log \left(\frac{1}{2} \left(c x^3+1\right)\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{18 c^3}+\frac{1}{36} x^9 \left(2 a-b \log \left(1-c x^3\right)\right)^2-\frac{1}{54} b x^9 \left(2 a-b \log \left(1-c x^3\right)\right)+\frac{1}{18} b x^9 \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)+\frac{b x^6 \left(2 a-b \log \left(1-c x^3\right)\right)}{36 c}+\frac{19 b^2 x^3}{108 c^2}-\frac{b^2 \left(1-c x^3\right)^3}{162 c^3}+\frac{b^2 \left(1-c x^3\right)^2}{24 c^3}+\frac{b^2 \log ^2\left(1-c x^3\right)}{36 c^3}+\frac{b^2 \log ^2\left(c x^3+1\right)}{36 c^3}-\frac{b^2 \left(1-c x^3\right) \log \left(1-c x^3\right)}{18 c^3}+\frac{b^2 \log \left(1-c x^3\right)}{108 c^3}+\frac{b^2 \log \left(\frac{1}{2} \left(1-c x^3\right)\right) \log \left(c x^3+1\right)}{18 c^3}-\frac{b^2 \log \left(c x^3+1\right)}{18 c^3}-\frac{5 b^2 x^6}{216 c}+\frac{1}{36} b^2 x^9 \log ^2\left(c x^3+1\right)+\frac{b^2 x^6 \log \left(c x^3+1\right)}{18 c}-\frac{1}{162} b^2 x^9","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x^3}\right)}{9 c^3}+\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{9 c^3}-\frac{2 b \log \left(\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{9 c^3}+\frac{1}{9} x^9 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2+\frac{b x^6 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{9 c}+\frac{b^2 x^3}{9 c^2}-\frac{b^2 \tanh ^{-1}\left(c x^3\right)}{9 c^3}",1,"-(a*b*x^3)/(9*c^2) + (19*b^2*x^3)/(108*c^2) - (5*b^2*x^6)/(216*c) - (b^2*x^9)/162 + (b^2*(1 - c*x^3)^2)/(24*c^3) - (b^2*(1 - c*x^3)^3)/(162*c^3) + (b^2*Log[1 - c*x^3])/(108*c^3) - (b^2*(1 - c*x^3)*Log[1 - c*x^3])/(18*c^3) + (b^2*Log[1 - c*x^3]^2)/(36*c^3) + (b*x^6*(2*a - b*Log[1 - c*x^3]))/(36*c) - (b*x^9*(2*a - b*Log[1 - c*x^3]))/54 + (x^9*(2*a - b*Log[1 - c*x^3])^2)/36 - (b*(2*a - b*Log[1 - c*x^3])*((18*(1 - c*x^3))/c^3 - (9*(1 - c*x^3)^2)/c^3 + (2*(1 - c*x^3)^3)/c^3 - (6*Log[1 - c*x^3])/c^3))/108 + (b*(2*a - b*Log[1 - c*x^3])*Log[(1 + c*x^3)/2])/(18*c^3) - (b^2*Log[1 + c*x^3])/(18*c^3) + (b^2*x^6*Log[1 + c*x^3])/(18*c) + (b^2*Log[(1 - c*x^3)/2]*Log[1 + c*x^3])/(18*c^3) + (b*x^9*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3])/18 + (b^2*Log[1 + c*x^3]^2)/(36*c^3) + (b^2*x^9*Log[1 + c*x^3]^2)/36 - (b^2*PolyLog[2, (1 - c*x^3)/2])/(18*c^3) + (b^2*PolyLog[2, (1 + c*x^3)/2])/(18*c^3)","B",53,19,16,1.187,0,"{6099, 2454, 2398, 2411, 43, 2334, 12, 14, 2301, 2395, 2439, 2416, 2389, 2295, 2394, 2393, 2391, 2410, 2390}"
118,1,524,0,0.9854992,"\int x^5 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2 \, dx","Int[x^5*(a + b*ArcTanh[c*x^3])^2,x]","\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^3\right)\right)}{12 c^2}+\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^3+1\right)\right)}{12 c^2}+\frac{\left(1-c x^3\right)^2 \left(2 a-b \log \left(1-c x^3\right)\right)^2}{24 c^2}-\frac{\left(1-c x^3\right) \left(2 a-b \log \left(1-c x^3\right)\right)^2}{12 c^2}+\frac{b \left(1-c x^3\right)^2 \left(2 a-b \log \left(1-c x^3\right)\right)}{24 c^2}-\frac{b \log \left(\frac{1}{2} \left(c x^3+1\right)\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{12 c^2}+\frac{a b x^3}{2 c}-\frac{1}{24} b x^6 \left(2 a-b \log \left(1-c x^3\right)\right)+\frac{1}{12} b x^6 \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)+\frac{b^2 \left(1-c x^3\right)^2}{48 c^2}+\frac{b^2 \left(c x^3+1\right)^2}{48 c^2}+\frac{b^2 \left(c x^3+1\right)^2 \log ^2\left(c x^3+1\right)}{24 c^2}-\frac{b^2 \left(c x^3+1\right) \log ^2\left(c x^3+1\right)}{12 c^2}+\frac{b^2 \left(1-c x^3\right) \log \left(1-c x^3\right)}{4 c^2}-\frac{b^2 \log \left(1-c x^3\right)}{24 c^2}-\frac{b^2 \left(c x^3+1\right)^2 \log \left(c x^3+1\right)}{24 c^2}+\frac{b^2 \left(c x^3+1\right) \log \left(c x^3+1\right)}{4 c^2}+\frac{b^2 \log \left(\frac{1}{2} \left(1-c x^3\right)\right) \log \left(c x^3+1\right)}{12 c^2}-\frac{b^2 \log \left(c x^3+1\right)}{24 c^2}+\frac{1}{24} b^2 x^6 \log \left(c x^3+1\right)-\frac{1}{24} b^2 x^6","-\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{6 c^2}+\frac{a b x^3}{3 c}+\frac{1}{6} x^6 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2+\frac{b^2 \log \left(1-c^2 x^6\right)}{6 c^2}+\frac{b^2 x^3 \tanh ^{-1}\left(c x^3\right)}{3 c}",1,"(a*b*x^3)/(2*c) - (b^2*x^6)/24 + (b^2*(1 - c*x^3)^2)/(48*c^2) + (b^2*(1 + c*x^3)^2)/(48*c^2) - (b^2*Log[1 - c*x^3])/(24*c^2) + (b^2*(1 - c*x^3)*Log[1 - c*x^3])/(4*c^2) - (b*x^6*(2*a - b*Log[1 - c*x^3]))/24 + (b*(1 - c*x^3)^2*(2*a - b*Log[1 - c*x^3]))/(24*c^2) - ((1 - c*x^3)*(2*a - b*Log[1 - c*x^3])^2)/(12*c^2) + ((1 - c*x^3)^2*(2*a - b*Log[1 - c*x^3])^2)/(24*c^2) - (b*(2*a - b*Log[1 - c*x^3])*Log[(1 + c*x^3)/2])/(12*c^2) - (b^2*Log[1 + c*x^3])/(24*c^2) + (b^2*x^6*Log[1 + c*x^3])/24 + (b^2*(1 + c*x^3)*Log[1 + c*x^3])/(4*c^2) - (b^2*(1 + c*x^3)^2*Log[1 + c*x^3])/(24*c^2) + (b^2*Log[(1 - c*x^3)/2]*Log[1 + c*x^3])/(12*c^2) + (b*x^6*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3])/12 - (b^2*(1 + c*x^3)*Log[1 + c*x^3]^2)/(12*c^2) + (b^2*(1 + c*x^3)^2*Log[1 + c*x^3]^2)/(24*c^2) + (b^2*PolyLog[2, (1 - c*x^3)/2])/(12*c^2) + (b^2*PolyLog[2, (1 + c*x^3)/2])/(12*c^2)","C",44,16,16,1.000,0,"{6099, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2395, 43, 2439, 2416, 2394, 2393, 2391}"
119,1,207,0,0.591888,"\int x^2 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2 \, dx","Int[x^2*(a + b*ArcTanh[c*x^3])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^3\right)\right)}{6 c}+\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^3+1\right)\right)}{6 c}+\frac{1}{6} b x^3 \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)-\frac{\left(1-c x^3\right) \left(2 a-b \log \left(1-c x^3\right)\right)^2}{12 c}+\frac{b \log \left(\frac{1}{2} \left(c x^3+1\right)\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{6 c}+\frac{b^2 \left(c x^3+1\right) \log ^2\left(c x^3+1\right)}{12 c}+\frac{b^2 \log \left(\frac{1}{2} \left(1-c x^3\right)\right) \log \left(c x^3+1\right)}{6 c}","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x^3}\right)}{3 c}+\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2+\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{3 c}-\frac{2 b \log \left(\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{3 c}",1,"-((1 - c*x^3)*(2*a - b*Log[1 - c*x^3])^2)/(12*c) + (b*(2*a - b*Log[1 - c*x^3])*Log[(1 + c*x^3)/2])/(6*c) + (b^2*Log[(1 - c*x^3)/2]*Log[1 + c*x^3])/(6*c) + (b*x^3*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3])/6 + (b^2*(1 + c*x^3)*Log[1 + c*x^3]^2)/(12*c) - (b^2*PolyLog[2, (1 - c*x^3)/2])/(6*c) + (b^2*PolyLog[2, (1 + c*x^3)/2])/(6*c)","B",28,12,16,0.7500,0,"{6099, 2454, 2389, 2296, 2295, 6715, 2430, 43, 2416, 2394, 2393, 2391}"
120,1,140,0,0.334869,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{x} \, dx","Int[(a + b*ArcTanh[c*x^3])^2/x,x]","-\frac{1}{3} b \text{PolyLog}\left(2,1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{1}{3} b \text{PolyLog}\left(2,\frac{2}{1-c x^3}-1\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{1}{6} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^3}\right)-\frac{1}{6} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^3}-1\right)+\frac{2}{3} \tanh ^{-1}\left(1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2","-\frac{1}{3} b \text{PolyLog}\left(2,1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{1}{3} b \text{PolyLog}\left(2,\frac{2}{1-c x^3}-1\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{1}{6} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^3}\right)-\frac{1}{6} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^3}-1\right)+\frac{2}{3} \tanh ^{-1}\left(1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2",1,"(2*(a + b*ArcTanh[c*x^3])^2*ArcTanh[1 - 2/(1 - c*x^3)])/3 - (b*(a + b*ArcTanh[c*x^3])*PolyLog[2, 1 - 2/(1 - c*x^3)])/3 + (b*(a + b*ArcTanh[c*x^3])*PolyLog[2, -1 + 2/(1 - c*x^3)])/3 + (b^2*PolyLog[3, 1 - 2/(1 - c*x^3)])/6 - (b^2*PolyLog[3, -1 + 2/(1 - c*x^3)])/6","A",7,6,16,0.3750,1,"{6095, 5914, 6052, 5948, 6058, 6610}"
121,1,237,0,0.6191877,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{x^4} \, dx","Int[(a + b*ArcTanh[c*x^3])^2/x^4,x]","-\frac{1}{3} b^2 c \text{PolyLog}\left(2,-c x^3\right)+\frac{1}{3} b^2 c \text{PolyLog}\left(2,c x^3\right)+\frac{1}{6} b^2 c \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^3\right)\right)-\frac{1}{6} b^2 c \text{PolyLog}\left(2,\frac{1}{2} \left(c x^3+1\right)\right)-\frac{1}{6} b c \log \left(\frac{1}{2} \left(c x^3+1\right)\right) \left(2 a-b \log \left(1-c x^3\right)\right)-\frac{b \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{6 x^3}-\frac{\left(1-c x^3\right) \left(2 a-b \log \left(1-c x^3\right)\right)^2}{12 x^3}+2 a b c \log (x)-\frac{b^2 \left(c x^3+1\right) \log ^2\left(c x^3+1\right)}{12 x^3}-\frac{1}{6} b^2 c \log \left(\frac{1}{2} \left(1-c x^3\right)\right) \log \left(c x^3+1\right)","-\frac{1}{3} b^2 c \text{PolyLog}\left(2,\frac{2}{c x^3+1}-1\right)+\frac{1}{3} c \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2-\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{3 x^3}+\frac{2}{3} b c \log \left(2-\frac{2}{c x^3+1}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)",1,"2*a*b*c*Log[x] - ((1 - c*x^3)*(2*a - b*Log[1 - c*x^3])^2)/(12*x^3) - (b*c*(2*a - b*Log[1 - c*x^3])*Log[(1 + c*x^3)/2])/6 - (b^2*c*Log[(1 - c*x^3)/2]*Log[1 + c*x^3])/6 - (b*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3])/(6*x^3) - (b^2*(1 + c*x^3)*Log[1 + c*x^3]^2)/(12*x^3) - (b^2*c*PolyLog[2, -(c*x^3)])/3 + (b^2*c*PolyLog[2, c*x^3])/3 + (b^2*c*PolyLog[2, (1 - c*x^3)/2])/6 - (b^2*c*PolyLog[2, (1 + c*x^3)/2])/6","B",24,13,16,0.8125,0,"{6099, 2454, 2397, 2392, 2391, 2395, 36, 29, 31, 2439, 2416, 2394, 2393}"
122,1,360,0,1.0604276,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{x^7} \, dx","Int[(a + b*ArcTanh[c*x^3])^2/x^7,x]","-\frac{1}{12} b^2 c^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^3\right)\right)-\frac{1}{12} b^2 c^2 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^3+1\right)\right)+\frac{1}{12} b c^2 \log \left(\frac{1}{2} \left(c x^3+1\right)\right) \left(2 a-b \log \left(1-c x^3\right)\right)+\frac{1}{24} c^2 \left(2 a-b \log \left(1-c x^3\right)\right)^2-\frac{b c \left(1-c x^3\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{12 x^3}-\frac{b c \left(2 a-b \log \left(1-c x^3\right)\right)}{12 x^3}-\frac{b \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{12 x^6}-\frac{\left(2 a-b \log \left(1-c x^3\right)\right)^2}{24 x^6}+\frac{1}{24} b^2 c^2 \log ^2\left(c x^3+1\right)-\frac{1}{12} b^2 c^2 \log \left(1-c x^3\right)-\frac{1}{6} b^2 c^2 \log \left(c x^3+1\right)-\frac{1}{12} b^2 c^2 \log \left(\frac{1}{2} \left(1-c x^3\right)\right) \log \left(c x^3+1\right)+b^2 c^2 \log (x)-\frac{b^2 \log ^2\left(c x^3+1\right)}{24 x^6}-\frac{b^2 c \log \left(c x^3+1\right)}{6 x^3}","\frac{1}{6} c^2 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2-\frac{b c \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{3 x^3}-\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{6 x^6}-\frac{1}{6} b^2 c^2 \log \left(1-c^2 x^6\right)+b^2 c^2 \log (x)",1,"b^2*c^2*Log[x] - (b^2*c^2*Log[1 - c*x^3])/12 - (b*c*(2*a - b*Log[1 - c*x^3]))/(12*x^3) - (b*c*(1 - c*x^3)*(2*a - b*Log[1 - c*x^3]))/(12*x^3) + (c^2*(2*a - b*Log[1 - c*x^3])^2)/24 - (2*a - b*Log[1 - c*x^3])^2/(24*x^6) + (b*c^2*(2*a - b*Log[1 - c*x^3])*Log[(1 + c*x^3)/2])/12 - (b^2*c^2*Log[1 + c*x^3])/6 - (b^2*c*Log[1 + c*x^3])/(6*x^3) - (b^2*c^2*Log[(1 - c*x^3)/2]*Log[1 + c*x^3])/12 - (b*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3])/(12*x^6) + (b^2*c^2*Log[1 + c*x^3]^2)/24 - (b^2*Log[1 + c*x^3]^2)/(24*x^6) - (b^2*c^2*PolyLog[2, (1 - c*x^3)/2])/12 - (b^2*c^2*PolyLog[2, (1 + c*x^3)/2])/12","C",46,23,16,1.438,0,"{6099, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2395, 44, 2439, 2416, 36, 29, 2392, 2391, 2394, 2393, 2410, 2390}"
123,1,420,0,1.311316,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{x^{10}} \, dx","Int[(a + b*ArcTanh[c*x^3])^2/x^10,x]","-\frac{1}{9} b^2 c^3 \text{PolyLog}\left(2,-c x^3\right)+\frac{1}{9} b^2 c^3 \text{PolyLog}\left(2,c x^3\right)+\frac{1}{18} b^2 c^3 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^3\right)\right)-\frac{1}{18} b^2 c^3 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^3+1\right)\right)+\frac{1}{36} c^3 \left(2 a-b \log \left(1-c x^3\right)\right)^2-\frac{1}{18} b c^3 \log \left(\frac{1}{2} \left(c x^3+1\right)\right) \left(2 a-b \log \left(1-c x^3\right)\right)-\frac{b c^2 \left(1-c x^3\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{18 x^3}+\frac{b c^2 \left(2 a-b \log \left(1-c x^3\right)\right)}{18 x^3}+\frac{2}{3} a b c^3 \log (x)-\frac{b c \left(2 a-b \log \left(1-c x^3\right)\right)}{18 x^6}-\frac{\left(2 a-b \log \left(1-c x^3\right)\right)^2}{36 x^9}-\frac{b \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{18 x^9}-\frac{b^2 c^2}{9 x^3}-\frac{1}{36} b^2 c^3 \log ^2\left(c x^3+1\right)+\frac{1}{18} b^2 c^3 \log \left(c x^3+1\right)-\frac{1}{18} b^2 c^3 \log \left(\frac{1}{2} \left(1-c x^3\right)\right) \log \left(c x^3+1\right)-\frac{b^2 \log ^2\left(c x^3+1\right)}{36 x^9}-\frac{b^2 c \log \left(c x^3+1\right)}{18 x^6}","-\frac{1}{9} b^2 c^3 \text{PolyLog}\left(2,\frac{2}{c x^3+1}-1\right)+\frac{1}{9} c^3 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2+\frac{2}{9} b c^3 \log \left(2-\frac{2}{c x^3+1}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)-\frac{b c \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{9 x^6}-\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{9 x^9}-\frac{b^2 c^2}{9 x^3}+\frac{1}{9} b^2 c^3 \tanh ^{-1}\left(c x^3\right)",1,"-(b^2*c^2)/(9*x^3) + (2*a*b*c^3*Log[x])/3 - (b*c*(2*a - b*Log[1 - c*x^3]))/(18*x^6) + (b*c^2*(2*a - b*Log[1 - c*x^3]))/(18*x^3) - (b*c^2*(1 - c*x^3)*(2*a - b*Log[1 - c*x^3]))/(18*x^3) + (c^3*(2*a - b*Log[1 - c*x^3])^2)/36 - (2*a - b*Log[1 - c*x^3])^2/(36*x^9) - (b*c^3*(2*a - b*Log[1 - c*x^3])*Log[(1 + c*x^3)/2])/18 + (b^2*c^3*Log[1 + c*x^3])/18 - (b^2*c*Log[1 + c*x^3])/(18*x^6) - (b^2*c^3*Log[(1 - c*x^3)/2]*Log[1 + c*x^3])/18 - (b*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3])/(18*x^9) - (b^2*c^3*Log[1 + c*x^3]^2)/36 - (b^2*Log[1 + c*x^3]^2)/(36*x^9) - (b^2*c^3*PolyLog[2, -(c*x^3)])/9 + (b^2*c^3*PolyLog[2, c*x^3])/9 + (b^2*c^3*PolyLog[2, (1 - c*x^3)/2])/18 - (b^2*c^3*PolyLog[2, (1 + c*x^3)/2])/18","B",59,24,16,1.500,0,"{6099, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2319, 44, 2395, 2439, 2416, 36, 29, 2392, 2391, 2394, 2393, 2410, 2390}"
124,1,1421,0,6.3501716,"\int x^8 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3 \, dx","Int[x^8*(a + b*ArcTanh[c*x^3])^3,x]","\frac{b^3 x^9}{324}-\frac{1}{72} b \left(2 a-b \log \left(1-c x^3\right)\right)^2 x^9+\frac{1}{72} b^3 \log ^2\left(c x^3+1\right) x^9+\frac{1}{24} b^2 \left(2 a-b \log \left(1-c x^3\right)\right) \log ^2\left(c x^3+1\right) x^9-\frac{1}{108} b^3 \log \left(c x^3+1\right) x^9+\frac{1}{24} b \left(2 a-b \log \left(1-c x^3\right)\right)^2 \log \left(c x^3+1\right) x^9-\frac{b^2 \left(2 a-b \log \left(1-c x^3\right)\right) x^6}{24 c}+\frac{b^2 \left(2 a-b \log \left(1-c x^3\right)\right) \log \left(c x^3+1\right) x^6}{12 c}+\frac{b^3 \log \left(c x^3+1\right) x^6}{18 c}-\frac{23 b^3 x^6}{432 c}-\frac{7 b^3 x^3}{216 c^2}+\frac{2 a b^2 x^3}{3 c^2}-\frac{b^3 \left(c x^3+1\right)^3}{324 c^3}-\frac{\left(1-c x^3\right)^3 \left(2 a-b \log \left(1-c x^3\right)\right)^3}{72 c^3}+\frac{\left(1-c x^3\right)^2 \left(2 a-b \log \left(1-c x^3\right)\right)^3}{24 c^3}-\frac{\left(1-c x^3\right) \left(2 a-b \log \left(1-c x^3\right)\right)^3}{24 c^3}+\frac{b^3 \left(c x^3+1\right)^3 \log ^3\left(c x^3+1\right)}{72 c^3}-\frac{b^3 \left(c x^3+1\right)^2 \log ^3\left(c x^3+1\right)}{24 c^3}+\frac{b^3 \left(c x^3+1\right) \log ^3\left(c x^3+1\right)}{24 c^3}+\frac{b^3 \left(1-c x^3\right)^2}{48 c^3}+\frac{b^3 \left(c x^3+1\right)^2}{24 c^3}-\frac{b^3 \log ^2\left(1-c x^3\right)}{72 c^3}-\frac{b \left(1-c x^3\right)^3 \left(2 a-b \log \left(1-c x^3\right)\right)^2}{72 c^3}+\frac{b \left(1-c x^3\right)^2 \left(2 a-b \log \left(1-c x^3\right)\right)^2}{12 c^3}-\frac{b \left(1-c x^3\right) \left(2 a-b \log \left(1-c x^3\right)\right)^2}{8 c^3}-\frac{b^3 \left(c x^3+1\right)^3 \log ^2\left(c x^3+1\right)}{72 c^3}+\frac{b^3 \left(c x^3+1\right)^2 \log ^2\left(c x^3+1\right)}{12 c^3}-\frac{b^3 \left(c x^3+1\right) \log ^2\left(c x^3+1\right)}{8 c^3}+\frac{b^3 \log \left(\frac{1}{2} \left(1-c x^3\right)\right) \log ^2\left(c x^3+1\right)}{12 c^3}+\frac{b^2 \left(2 a-b \log \left(1-c x^3\right)\right) \log ^2\left(c x^3+1\right)}{24 c^3}+\frac{b^3 \log ^2\left(c x^3+1\right)}{72 c^3}+\frac{b^3 \left(1-c x^3\right) \log \left(1-c x^3\right)}{3 c^3}-\frac{b^3 \log \left(1-c x^3\right)}{24 c^3}-\frac{b^2 \left(1-c x^3\right)^3 \left(2 a-b \log \left(1-c x^3\right)\right)}{108 c^3}+\frac{b^2 \left(1-c x^3\right)^2 \left(2 a-b \log \left(1-c x^3\right)\right)}{12 c^3}+\frac{1}{216} b^2 \left(2 a-b \log \left(1-c x^3\right)\right) \left(\frac{2 \left(1-c x^3\right)^3}{c^3}-\frac{9 \left(1-c x^3\right)^2}{c^3}+\frac{18 \left(1-c x^3\right)}{c^3}-\frac{6 \log \left(1-c x^3\right)}{c^3}\right)+\frac{b \left(2 a-b \log \left(1-c x^3\right)\right)^2 \log \left(\frac{1}{2} \left(c x^3+1\right)\right)}{12 c^3}-\frac{b^2 \left(2 a-b \log \left(1-c x^3\right)\right) \log \left(\frac{1}{2} \left(c x^3+1\right)\right)}{12 c^3}+\frac{b^3 \left(c x^3+1\right)^3 \log \left(c x^3+1\right)}{108 c^3}-\frac{b^3 \left(c x^3+1\right)^2 \log \left(c x^3+1\right)}{12 c^3}-\frac{b \left(2 a-b \log \left(1-c x^3\right)\right)^2 \log \left(c x^3+1\right)}{24 c^3}+\frac{11 b^3 \left(c x^3+1\right) \log \left(c x^3+1\right)}{36 c^3}+\frac{b^3 \log \left(\frac{1}{2} \left(1-c x^3\right)\right) \log \left(c x^3+1\right)}{12 c^3}-\frac{7 b^3 \log \left(c x^3+1\right)}{108 c^3}-\frac{b^2 \left(2 a-b \log \left(1-c x^3\right)\right) \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^3\right)\right)}{6 c^3}+\frac{b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^3\right)\right)}{12 c^3}+\frac{b^3 \log \left(c x^3+1\right) \text{PolyLog}\left(2,\frac{1}{2} \left(c x^3+1\right)\right)}{6 c^3}+\frac{b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^3+1\right)\right)}{12 c^3}-\frac{b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(1-c x^3\right)\right)}{6 c^3}-\frac{b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(c x^3+1\right)\right)}{6 c^3}","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{3 c^3}+\frac{b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x^3}\right)}{6 c^3}+\frac{a b^2 x^3}{3 c^2}+\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3}{9 c^3}-\frac{b \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{6 c^3}-\frac{b \log \left(\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{3 c^3}+\frac{1}{9} x^9 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3+\frac{b x^6 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{6 c}+\frac{b^3 \log \left(1-c^2 x^6\right)}{6 c^3}+\frac{b^3 x^3 \tanh ^{-1}\left(c x^3\right)}{3 c^2}",1,"(2*a*b^2*x^3)/(3*c^2) - (7*b^3*x^3)/(216*c^2) - (23*b^3*x^6)/(432*c) + (b^3*x^9)/324 + (b^3*(1 - c*x^3)^2)/(48*c^3) + (b^3*(1 + c*x^3)^2)/(24*c^3) - (b^3*(1 + c*x^3)^3)/(324*c^3) - (b^3*Log[1 - c*x^3])/(24*c^3) + (b^3*(1 - c*x^3)*Log[1 - c*x^3])/(3*c^3) - (b^3*Log[1 - c*x^3]^2)/(72*c^3) - (b^2*x^6*(2*a - b*Log[1 - c*x^3]))/(24*c) + (b^2*(1 - c*x^3)^2*(2*a - b*Log[1 - c*x^3]))/(12*c^3) - (b^2*(1 - c*x^3)^3*(2*a - b*Log[1 - c*x^3]))/(108*c^3) - (b*x^9*(2*a - b*Log[1 - c*x^3])^2)/72 - (b*(1 - c*x^3)*(2*a - b*Log[1 - c*x^3])^2)/(8*c^3) + (b*(1 - c*x^3)^2*(2*a - b*Log[1 - c*x^3])^2)/(12*c^3) - (b*(1 - c*x^3)^3*(2*a - b*Log[1 - c*x^3])^2)/(72*c^3) - ((1 - c*x^3)*(2*a - b*Log[1 - c*x^3])^3)/(24*c^3) + ((1 - c*x^3)^2*(2*a - b*Log[1 - c*x^3])^3)/(24*c^3) - ((1 - c*x^3)^3*(2*a - b*Log[1 - c*x^3])^3)/(72*c^3) + (b^2*(2*a - b*Log[1 - c*x^3])*((18*(1 - c*x^3))/c^3 - (9*(1 - c*x^3)^2)/c^3 + (2*(1 - c*x^3)^3)/c^3 - (6*Log[1 - c*x^3])/c^3))/216 - (b^2*(2*a - b*Log[1 - c*x^3])*Log[(1 + c*x^3)/2])/(12*c^3) + (b*(2*a - b*Log[1 - c*x^3])^2*Log[(1 + c*x^3)/2])/(12*c^3) - (7*b^3*Log[1 + c*x^3])/(108*c^3) + (b^3*x^6*Log[1 + c*x^3])/(18*c) - (b^3*x^9*Log[1 + c*x^3])/108 + (11*b^3*(1 + c*x^3)*Log[1 + c*x^3])/(36*c^3) - (b^3*(1 + c*x^3)^2*Log[1 + c*x^3])/(12*c^3) + (b^3*(1 + c*x^3)^3*Log[1 + c*x^3])/(108*c^3) + (b^3*Log[(1 - c*x^3)/2]*Log[1 + c*x^3])/(12*c^3) + (b^2*x^6*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3])/(12*c) - (b*(2*a - b*Log[1 - c*x^3])^2*Log[1 + c*x^3])/(24*c^3) + (b*x^9*(2*a - b*Log[1 - c*x^3])^2*Log[1 + c*x^3])/24 + (b^3*Log[1 + c*x^3]^2)/(72*c^3) + (b^3*x^9*Log[1 + c*x^3]^2)/72 - (b^3*(1 + c*x^3)*Log[1 + c*x^3]^2)/(8*c^3) + (b^3*(1 + c*x^3)^2*Log[1 + c*x^3]^2)/(12*c^3) - (b^3*(1 + c*x^3)^3*Log[1 + c*x^3]^2)/(72*c^3) + (b^3*Log[(1 - c*x^3)/2]*Log[1 + c*x^3]^2)/(12*c^3) + (b^2*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3]^2)/(24*c^3) + (b^2*x^9*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3]^2)/24 + (b^3*(1 + c*x^3)*Log[1 + c*x^3]^3)/(24*c^3) - (b^3*(1 + c*x^3)^2*Log[1 + c*x^3]^3)/(24*c^3) + (b^3*(1 + c*x^3)^3*Log[1 + c*x^3]^3)/(72*c^3) + (b^3*PolyLog[2, (1 - c*x^3)/2])/(12*c^3) - (b^2*(2*a - b*Log[1 - c*x^3])*PolyLog[2, (1 - c*x^3)/2])/(6*c^3) + (b^3*PolyLog[2, (1 + c*x^3)/2])/(12*c^3) + (b^3*Log[1 + c*x^3]*PolyLog[2, (1 + c*x^3)/2])/(6*c^3) - (b^3*PolyLog[3, (1 - c*x^3)/2])/(6*c^3) - (b^3*PolyLog[3, (1 + c*x^3)/2])/(6*c^3)","B",239,32,16,2.000,0,"{6099, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2398, 2411, 43, 2334, 12, 14, 2301, 2439, 2416, 2396, 2433, 2374, 6589, 6742, 2430, 2394, 2393, 2391, 2395, 2375, 2317, 2410, 2425}"
125,1,479,0,4.2044948,"\int x^5 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3 \, dx","Int[x^5*(a + b*ArcTanh[c*x^3])^3,x]","-\frac{b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^3\right)\right)}{4 c^2}+\frac{b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(c x^3+1\right)\right)}{4 c^2}-\frac{b^2 \log ^2\left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{16 c^2}+\frac{b^2 \log \left(\frac{1}{2} \left(c x^3+1\right)\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{4 c^2}+\frac{1}{16} b^2 x^6 \log ^2\left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)+\frac{b^2 x^3 \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{4 c}+\frac{\left(1-c x^3\right)^2 \left(2 a-b \log \left(1-c x^3\right)\right)^3}{48 c^2}-\frac{\left(1-c x^3\right) \left(2 a-b \log \left(1-c x^3\right)\right)^3}{24 c^2}-\frac{b \left(1-c x^3\right) \left(2 a-b \log \left(1-c x^3\right)\right)^2}{8 c^2}-\frac{b \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)^2}{16 c^2}+\frac{1}{16} b x^6 \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)^2+\frac{b^3 \left(c x^3+1\right)^2 \log ^3\left(c x^3+1\right)}{48 c^2}-\frac{b^3 \left(c x^3+1\right) \log ^3\left(c x^3+1\right)}{24 c^2}+\frac{b^3 \left(c x^3+1\right) \log ^2\left(c x^3+1\right)}{8 c^2}+\frac{b^3 \log \left(\frac{1}{2} \left(1-c x^3\right)\right) \log \left(c x^3+1\right)}{4 c^2}","-\frac{b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c x^3}\right)}{2 c^2}-\frac{b^2 \log \left(\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{c^2}-\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3}{6 c^2}+\frac{b \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{2 c^2}+\frac{1}{6} x^6 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3+\frac{b x^3 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{2 c}",1,"-(b*(1 - c*x^3)*(2*a - b*Log[1 - c*x^3])^2)/(8*c^2) - ((1 - c*x^3)*(2*a - b*Log[1 - c*x^3])^3)/(24*c^2) + ((1 - c*x^3)^2*(2*a - b*Log[1 - c*x^3])^3)/(48*c^2) + (b^2*(2*a - b*Log[1 - c*x^3])*Log[(1 + c*x^3)/2])/(4*c^2) + (b^3*Log[(1 - c*x^3)/2]*Log[1 + c*x^3])/(4*c^2) + (b^2*x^3*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3])/(4*c) - (b*(2*a - b*Log[1 - c*x^3])^2*Log[1 + c*x^3])/(16*c^2) + (b*x^6*(2*a - b*Log[1 - c*x^3])^2*Log[1 + c*x^3])/16 + (b^3*(1 + c*x^3)*Log[1 + c*x^3]^2)/(8*c^2) - (b^2*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3]^2)/(16*c^2) + (b^2*x^6*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3]^2)/16 - (b^3*(1 + c*x^3)*Log[1 + c*x^3]^3)/(24*c^2) + (b^3*(1 + c*x^3)^2*Log[1 + c*x^3]^3)/(48*c^2) - (b^3*PolyLog[2, (1 - c*x^3)/2])/(4*c^2) + (b^3*PolyLog[2, (1 + c*x^3)/2])/(4*c^2)","B",155,30,16,1.875,0,"{6099, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2439, 2416, 2396, 2433, 2374, 6589, 2411, 43, 2334, 12, 14, 2301, 6742, 2430, 2394, 2393, 2391, 2395, 2375, 2317, 2425}"
126,1,390,0,2.4674545,"\int x^2 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3 \, dx","Int[x^2*(a + b*ArcTanh[c*x^3])^3,x]","-\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-c x^3\right)\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{2 c}-\frac{b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(1-c x^3\right)\right)}{2 c}-\frac{b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(c x^3+1\right)\right)}{2 c}+\frac{b^3 \log \left(c x^3+1\right) \text{PolyLog}\left(2,\frac{1}{2} \left(c x^3+1\right)\right)}{2 c}+\frac{1}{8} b^2 x^3 \log ^2\left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)+\frac{b^2 \log ^2\left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)}{8 c}+\frac{b \log \left(\frac{1}{2} \left(c x^3+1\right)\right) \left(2 a-b \log \left(1-c x^3\right)\right)^2}{4 c}+\frac{1}{8} b x^3 \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)^2-\frac{b \log \left(c x^3+1\right) \left(2 a-b \log \left(1-c x^3\right)\right)^2}{8 c}-\frac{\left(1-c x^3\right) \left(2 a-b \log \left(1-c x^3\right)\right)^3}{24 c}+\frac{b^3 \left(c x^3+1\right) \log ^3\left(c x^3+1\right)}{24 c}+\frac{b^3 \log \left(\frac{1}{2} \left(1-c x^3\right)\right) \log ^2\left(c x^3+1\right)}{4 c}","-\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{c}+\frac{b^3 \text{PolyLog}\left(3,1-\frac{2}{1-c x^3}\right)}{2 c}+\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3+\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3}{3 c}-\frac{b \log \left(\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{c}",1,"-((1 - c*x^3)*(2*a - b*Log[1 - c*x^3])^3)/(24*c) + (b*(2*a - b*Log[1 - c*x^3])^2*Log[(1 + c*x^3)/2])/(4*c) - (b*(2*a - b*Log[1 - c*x^3])^2*Log[1 + c*x^3])/(8*c) + (b*x^3*(2*a - b*Log[1 - c*x^3])^2*Log[1 + c*x^3])/8 + (b^3*Log[(1 - c*x^3)/2]*Log[1 + c*x^3]^2)/(4*c) + (b^2*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3]^2)/(8*c) + (b^2*x^3*(2*a - b*Log[1 - c*x^3])*Log[1 + c*x^3]^2)/8 + (b^3*(1 + c*x^3)*Log[1 + c*x^3]^3)/(24*c) - (b^2*(2*a - b*Log[1 - c*x^3])*PolyLog[2, (1 - c*x^3)/2])/(2*c) + (b^3*Log[1 + c*x^3]*PolyLog[2, (1 + c*x^3)/2])/(2*c) - (b^3*PolyLog[3, (1 - c*x^3)/2])/(2*c) - (b^3*PolyLog[3, (1 + c*x^3)/2])/(2*c)","B",82,23,16,1.438,0,"{6099, 2454, 2389, 2296, 2295, 6715, 2430, 2416, 2396, 2433, 2374, 6589, 2411, 2346, 2301, 6742, 43, 2394, 2393, 2391, 2375, 2317, 2425}"
127,1,210,0,0.5645683,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3}{x} \, dx","Int[(a + b*ArcTanh[c*x^3])^3/x,x]","\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^3}-1\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)-\frac{1}{2} b \text{PolyLog}\left(2,1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2+\frac{1}{2} b \text{PolyLog}\left(2,\frac{2}{1-c x^3}-1\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2-\frac{1}{4} b^3 \text{PolyLog}\left(4,1-\frac{2}{1-c x^3}\right)+\frac{1}{4} b^3 \text{PolyLog}\left(4,\frac{2}{1-c x^3}-1\right)+\frac{2}{3} \tanh ^{-1}\left(1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3","\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^3}-1\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)-\frac{1}{2} b \text{PolyLog}\left(2,1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2+\frac{1}{2} b \text{PolyLog}\left(2,\frac{2}{1-c x^3}-1\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2-\frac{1}{4} b^3 \text{PolyLog}\left(4,1-\frac{2}{1-c x^3}\right)+\frac{1}{4} b^3 \text{PolyLog}\left(4,\frac{2}{1-c x^3}-1\right)+\frac{2}{3} \tanh ^{-1}\left(1-\frac{2}{1-c x^3}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3",1,"(2*(a + b*ArcTanh[c*x^3])^3*ArcTanh[1 - 2/(1 - c*x^3)])/3 - (b*(a + b*ArcTanh[c*x^3])^2*PolyLog[2, 1 - 2/(1 - c*x^3)])/2 + (b*(a + b*ArcTanh[c*x^3])^2*PolyLog[2, -1 + 2/(1 - c*x^3)])/2 + (b^2*(a + b*ArcTanh[c*x^3])*PolyLog[3, 1 - 2/(1 - c*x^3)])/2 - (b^2*(a + b*ArcTanh[c*x^3])*PolyLog[3, -1 + 2/(1 - c*x^3)])/2 - (b^3*PolyLog[4, 1 - 2/(1 - c*x^3)])/4 + (b^3*PolyLog[4, -1 + 2/(1 - c*x^3)])/4","A",9,7,16,0.4375,1,"{6095, 5914, 6052, 5948, 6058, 6062, 6610}"
128,0,0,0,0.778839,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3}{x^4} \, dx","Int[(a + b*ArcTanh[c*x^3])^3/x^4,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3}{x^4} \, dx","-b^2 c \text{PolyLog}\left(2,\frac{2}{c x^3+1}-1\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)-\frac{1}{2} b^3 c \text{PolyLog}\left(3,\frac{2}{c x^3+1}-1\right)+\frac{1}{3} c \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3-\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3}{3 x^3}+b c \log \left(2-\frac{2}{c x^3+1}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2",1,"(b*c*Log[c*x^3]*(2*a - b*Log[1 - c*x^3])^2)/8 - ((1 - c*x^3)*(2*a - b*Log[1 - c*x^3])^3)/(24*x^3) + (b^3*c*Log[-(c*x^3)]*Log[1 + c*x^3]^2)/8 - (b^3*(1 + c*x^3)*Log[1 + c*x^3]^3)/(24*x^3) - (b^2*c*(2*a - b*Log[1 - c*x^3])*PolyLog[2, 1 - c*x^3])/4 + (b^3*c*Log[1 + c*x^3]*PolyLog[2, 1 + c*x^3])/4 - (b^3*c*PolyLog[3, 1 - c*x^3])/4 - (b^3*c*PolyLog[3, 1 + c*x^3])/4 + (b*Defer[Subst][Defer[Int][((-2*a + b*Log[1 - c*x])^2*Log[1 + c*x])/x^2, x], x, x^3])/8 - (b^2*Defer[Subst][Defer[Int][((-2*a + b*Log[1 - c*x])*Log[1 + c*x]^2)/x^2, x], x, x^3])/8","F",0,0,0,0,-1,"{}"
129,0,0,0,1.5749148,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3}{x^7} \, dx","Int[(a + b*ArcTanh[c*x^3])^3/x^7,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3}{x^7} \, dx","-\frac{1}{2} b^3 c^2 \text{PolyLog}\left(2,\frac{2}{c x^3+1}-1\right)+b^2 c^2 \log \left(2-\frac{2}{c x^3+1}\right) \left(a+b \tanh ^{-1}\left(c x^3\right)\right)+\frac{1}{2} b c^2 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2+\frac{1}{6} c^2 \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3-\frac{b c \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2}{2 x^3}-\frac{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3}{6 x^6}",1,"(3*a*b^2*c^2*Log[x])/4 - (b*c*(1 - c*x^3)*(2*a - b*Log[1 - c*x^3])^2)/(16*x^3) + (b*c^2*Log[c*x^3]*(2*a - b*Log[1 - c*x^3])^2)/16 + (c^2*(2*a - b*Log[1 - c*x^3])^3)/48 - (2*a - b*Log[1 - c*x^3])^3/(48*x^6) - (b^3*c*(1 + c*x^3)*Log[1 + c*x^3]^2)/(16*x^3) - (b^3*c^2*Log[-(c*x^3)]*Log[1 + c*x^3]^2)/16 + (b^3*c^2*Log[1 + c*x^3]^3)/48 - (b^3*Log[1 + c*x^3]^3)/(48*x^6) - (b^3*c^2*PolyLog[2, -(c*x^3)])/8 + (b^3*c^2*PolyLog[2, c*x^3])/8 - (b^2*c^2*(2*a - b*Log[1 - c*x^3])*PolyLog[2, 1 - c*x^3])/8 - (b^3*c^2*Log[1 + c*x^3]*PolyLog[2, 1 + c*x^3])/8 - (b^3*c^2*PolyLog[3, 1 - c*x^3])/8 + (b^3*c^2*PolyLog[3, 1 + c*x^3])/8 + (b*Defer[Subst][Defer[Int][((-2*a + b*Log[1 - c*x])^2*Log[1 + c*x])/x^3, x], x, x^3])/8 - (b^2*Defer[Subst][Defer[Int][((-2*a + b*Log[1 - c*x])*Log[1 + c*x]^2)/x^3, x], x, x^3])/8","F",0,0,0,0,-1,"{}"
130,0,0,0,0.0253039,"\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x^3])^3,x]","\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTanh[c*x^3])^3, x]","A",0,0,0,0,-1,"{}"
131,0,0,0,0.025162,"\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x^3])^2,x]","\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTanh[c*x^3])^2, x]","A",0,0,0,0,-1,"{}"
132,1,74,0,0.0431427,"\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^3\right)\right) \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x^3]),x]","\frac{(d x)^{m+1} \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{d (m+1)}-\frac{3 b c (d x)^{m+4} \, _2F_1\left(1,\frac{m+4}{6};\frac{m+10}{6};c^2 x^6\right)}{d^4 (m+1) (m+4)}","\frac{(d x)^{m+1} \left(a+b \tanh ^{-1}\left(c x^3\right)\right)}{d (m+1)}-\frac{3 b c (d x)^{m+4} \, _2F_1\left(1,\frac{m+4}{6};\frac{m+10}{6};c^2 x^6\right)}{d^4 (m+1) (m+4)}",1,"((d*x)^(1 + m)*(a + b*ArcTanh[c*x^3]))/(d*(1 + m)) - (3*b*c*(d*x)^(4 + m)*Hypergeometric2F1[1, (4 + m)/6, (10 + m)/6, c^2*x^6])/(d^4*(1 + m)*(4 + m))","A",3,3,16,0.1875,1,"{6097, 16, 364}"
133,0,0,0,0.0280181,"\int \frac{(d x)^m}{a+b \tanh ^{-1}\left(c x^3\right)} \, dx","Int[(d*x)^m/(a + b*ArcTanh[c*x^3]),x]","\int \frac{(d x)^m}{a+b \tanh ^{-1}\left(c x^3\right)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \tanh ^{-1}\left(c x^3\right)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTanh[c*x^3]), x]","A",0,0,0,0,-1,"{}"
134,0,0,0,0.0274606,"\int \frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2} \, dx","Int[(d*x)^m/(a + b*ArcTanh[c*x^3])^2,x]","\int \frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(c x^3\right)\right)^2},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTanh[c*x^3])^2, x]","A",0,0,0,0,-1,"{}"
135,1,50,0,0.0319407,"\int x^3 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[x^3*(a + b*ArcTanh[c/x]),x]","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)+\frac{1}{4} b c^3 x-\frac{1}{4} b c^4 \tanh ^{-1}\left(\frac{x}{c}\right)+\frac{1}{12} b c x^3","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)+\frac{1}{4} b c^3 x-\frac{1}{4} b c^4 \tanh ^{-1}\left(\frac{x}{c}\right)+\frac{1}{12} b c x^3",1,"(b*c^3*x)/4 + (b*c*x^3)/12 + (x^4*(a + b*ArcTanh[c/x]))/4 - (b*c^4*ArcTanh[x/c])/4","A",5,4,14,0.2857,1,"{6097, 263, 302, 207}"
136,1,45,0,0.0327064,"\int x^2 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[x^2*(a + b*ArcTanh[c/x]),x]","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)+\frac{1}{6} b c^3 \log \left(c^2-x^2\right)+\frac{1}{6} b c x^2","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)+\frac{1}{6} b c^3 \log \left(c^2-x^2\right)+\frac{1}{6} b c x^2",1,"(b*c*x^2)/6 + (x^3*(a + b*ArcTanh[c/x]))/3 + (b*c^3*Log[c^2 - x^2])/6","A",5,4,14,0.2857,1,"{6097, 263, 266, 43}"
137,1,39,0,0.0202438,"\int x \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[x*(a + b*ArcTanh[c/x]),x]","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)-\frac{1}{2} b c^2 \tanh ^{-1}\left(\frac{x}{c}\right)+\frac{b c x}{2}","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)-\frac{1}{2} b c^2 \tanh ^{-1}\left(\frac{x}{c}\right)+\frac{b c x}{2}",1,"(b*c*x)/2 + (x^2*(a + b*ArcTanh[c/x]))/2 - (b*c^2*ArcTanh[x/c])/2","A",4,4,12,0.3333,1,"{6097, 193, 321, 207}"
138,1,29,0,0.0133345,"\int \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[a + b*ArcTanh[c/x],x]","a x+\frac{1}{2} b c \log \left(c^2-x^2\right)+b x \tanh ^{-1}\left(\frac{c}{x}\right)","a x+\frac{1}{2} b c \log \left(c^2-x^2\right)+b x \tanh ^{-1}\left(\frac{c}{x}\right)",1,"a*x + b*x*ArcTanh[c/x] + (b*c*Log[c^2 - x^2])/2","A",4,3,10,0.3000,1,"{6091, 263, 260}"
139,1,30,0,0.031678,"\int \frac{a+b \tanh ^{-1}\left(\frac{c}{x}\right)}{x} \, dx","Int[(a + b*ArcTanh[c/x])/x,x]","\frac{1}{2} b \text{PolyLog}\left(2,-\frac{c}{x}\right)-\frac{1}{2} b \text{PolyLog}\left(2,\frac{c}{x}\right)+a \log (x)","\frac{1}{2} b \text{PolyLog}\left(2,-\frac{c}{x}\right)-\frac{1}{2} b \text{PolyLog}\left(2,\frac{c}{x}\right)+a \log (x)",1,"a*Log[x] + (b*PolyLog[2, -(c/x)])/2 - (b*PolyLog[2, c/x])/2","A",2,2,14,0.1429,1,"{6095, 5912}"
140,1,35,0,0.0208549,"\int \frac{a+b \tanh ^{-1}\left(\frac{c}{x}\right)}{x^2} \, dx","Int[(a + b*ArcTanh[c/x])/x^2,x]","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x}\right)}{x}-\frac{b \log \left(1-\frac{c^2}{x^2}\right)}{2 c}","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x}\right)}{x}-\frac{b \log \left(1-\frac{c^2}{x^2}\right)}{2 c}",1,"-((a + b*ArcTanh[c/x])/x) - (b*Log[1 - c^2/x^2])/(2*c)","A",2,2,14,0.1429,1,"{6097, 260}"
141,1,43,0,0.0266653,"\int \frac{a+b \tanh ^{-1}\left(\frac{c}{x}\right)}{x^3} \, dx","Int[(a + b*ArcTanh[c/x])/x^3,x]","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x}\right)}{2 x^2}+\frac{b \tanh ^{-1}\left(\frac{x}{c}\right)}{2 c^2}-\frac{b}{2 c x}","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x}\right)}{2 x^2}+\frac{b \tanh ^{-1}\left(\frac{x}{c}\right)}{2 c^2}-\frac{b}{2 c x}",1,"-b/(2*c*x) - (a + b*ArcTanh[c/x])/(2*x^2) + (b*ArcTanh[x/c])/(2*c^2)","A",4,4,14,0.2857,1,"{6097, 263, 325, 207}"
142,1,57,0,0.0407439,"\int \frac{a+b \tanh ^{-1}\left(\frac{c}{x}\right)}{x^4} \, dx","Int[(a + b*ArcTanh[c/x])/x^4,x]","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x}\right)}{3 x^3}-\frac{b \log \left(c^2-x^2\right)}{6 c^3}+\frac{b \log (x)}{3 c^3}-\frac{b}{6 c x^2}","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x}\right)}{3 x^3}-\frac{b \log \left(c^2-x^2\right)}{6 c^3}+\frac{b \log (x)}{3 c^3}-\frac{b}{6 c x^2}",1,"-b/(6*c*x^2) - (a + b*ArcTanh[c/x])/(3*x^3) + (b*Log[x])/(3*c^3) - (b*Log[c^2 - x^2])/(6*c^3)","A",5,4,14,0.2857,1,"{6097, 263, 266, 44}"
143,1,812,0,1.703131,"\int x^3 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^2 \, dx","Int[x^3*(a + b*ArcTanh[c/x])^2,x]","-\frac{1}{16} \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2 c^4-\frac{1}{16} b^2 \log ^2\left(\frac{c+x}{x}\right) c^4+\frac{5}{48} b^2 \log \left(1-\frac{c}{x}\right) c^4+\frac{5}{48} b^2 \log (c-x) c^4+\frac{1}{8} b^2 \log \left(\frac{c}{x}+1\right) \log (c-x) c^4+\frac{11}{24} b^2 \log (x) c^4+\frac{1}{4} a b \log (x) c^4+\frac{1}{8} b^2 \log (c-x) \log \left(\frac{x}{c}\right) c^4+\frac{5}{48} b^2 \log (c+x) c^4-\frac{1}{4} a b \log (c+x) c^4+\frac{1}{8} b^2 \log \left(1-\frac{c}{x}\right) \log (c+x) c^4-\frac{1}{8} b^2 \log \left(\frac{c-x}{2 c}\right) \log (c+x) c^4+\frac{1}{8} b^2 \log \left(-\frac{x}{c}\right) \log (c+x) c^4-\frac{1}{8} b^2 \log (c-x) \log \left(\frac{c+x}{2 c}\right) c^4+\frac{11}{48} b^2 \log \left(\frac{c+x}{x}\right) c^4-\frac{1}{8} b^2 \text{PolyLog}\left(2,\frac{c-x}{2 c}\right) c^4-\frac{1}{8} b^2 \text{PolyLog}\left(2,-\frac{c}{x}\right) c^4-\frac{1}{8} b^2 \text{PolyLog}\left(2,\frac{c}{x}\right) c^4-\frac{1}{8} b^2 \text{PolyLog}\left(2,\frac{c+x}{2 c}\right) c^4+\frac{1}{8} b^2 \text{PolyLog}\left(2,1-\frac{x}{c}\right) c^4+\frac{1}{8} b^2 \text{PolyLog}\left(2,\frac{x}{c}+1\right) c^4+\frac{1}{4} a b x c^3-\frac{1}{8} b^2 x \log \left(1-\frac{c}{x}\right) c^3+\frac{1}{8} b \left(1-\frac{c}{x}\right) x \left(2 a-b \log \left(1-\frac{c}{x}\right)\right) c^3+\frac{1}{8} b^2 x \log \left(\frac{c}{x}+1\right) c^3+\frac{1}{8} b^2 x \log \left(\frac{c+x}{x}\right) c^3+\frac{1}{12} b^2 x^2 c^2-\frac{1}{8} a b x^2 c^2+\frac{1}{16} b^2 x^2 \log \left(1-\frac{c}{x}\right) c^2+\frac{1}{16} b x^2 \left(2 a-b \log \left(1-\frac{c}{x}\right)\right) c^2+\frac{1}{16} b^2 x^2 \log \left(\frac{c}{x}+1\right) c^2-\frac{1}{16} b^2 x^2 \log \left(\frac{c+x}{x}\right) c^2+\frac{1}{12} a b x^3 c-\frac{1}{24} b^2 x^3 \log \left(1-\frac{c}{x}\right) c+\frac{1}{24} b x^3 \left(2 a-b \log \left(1-\frac{c}{x}\right)\right) c+\frac{1}{24} b^2 x^3 \log \left(\frac{c}{x}+1\right) c+\frac{1}{24} b^2 x^3 \log \left(\frac{c+x}{x}\right) c+\frac{1}{16} x^4 \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2+\frac{1}{16} b^2 x^4 \log ^2\left(\frac{c+x}{x}\right)+\frac{1}{4} a b x^4 \log \left(\frac{c}{x}+1\right)-\frac{1}{8} b^2 x^4 \log \left(1-\frac{c}{x}\right) \log \left(\frac{c}{x}+1\right)","-\frac{1}{4} c^4 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{2} b c^3 x \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{6} b c x^3 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{4} x^4 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{12} b^2 c^2 x^2+\frac{1}{3} b^2 c^4 \log \left(1-\frac{c^2}{x^2}\right)+\frac{2}{3} b^2 c^4 \log (x)",1,"(a*b*c^3*x)/4 - (a*b*c^2*x^2)/8 + (b^2*c^2*x^2)/12 + (a*b*c*x^3)/12 + (5*b^2*c^4*Log[1 - c/x])/48 - (b^2*c^3*x*Log[1 - c/x])/8 + (b^2*c^2*x^2*Log[1 - c/x])/16 - (b^2*c*x^3*Log[1 - c/x])/24 + (b*c^3*(1 - c/x)*x*(2*a - b*Log[1 - c/x]))/8 + (b*c^2*x^2*(2*a - b*Log[1 - c/x]))/16 + (b*c*x^3*(2*a - b*Log[1 - c/x]))/24 - (c^4*(2*a - b*Log[1 - c/x])^2)/16 + (x^4*(2*a - b*Log[1 - c/x])^2)/16 + (b^2*c^3*x*Log[1 + c/x])/8 + (b^2*c^2*x^2*Log[1 + c/x])/16 + (b^2*c*x^3*Log[1 + c/x])/24 + (a*b*x^4*Log[1 + c/x])/4 - (b^2*x^4*Log[1 - c/x]*Log[1 + c/x])/8 + (5*b^2*c^4*Log[c - x])/48 + (b^2*c^4*Log[1 + c/x]*Log[c - x])/8 + (a*b*c^4*Log[x])/4 + (11*b^2*c^4*Log[x])/24 + (b^2*c^4*Log[c - x]*Log[x/c])/8 - (a*b*c^4*Log[c + x])/4 + (5*b^2*c^4*Log[c + x])/48 + (b^2*c^4*Log[1 - c/x]*Log[c + x])/8 - (b^2*c^4*Log[(c - x)/(2*c)]*Log[c + x])/8 + (b^2*c^4*Log[-(x/c)]*Log[c + x])/8 - (b^2*c^4*Log[c - x]*Log[(c + x)/(2*c)])/8 + (11*b^2*c^4*Log[(c + x)/x])/48 + (b^2*c^3*x*Log[(c + x)/x])/8 - (b^2*c^2*x^2*Log[(c + x)/x])/16 + (b^2*c*x^3*Log[(c + x)/x])/24 - (b^2*c^4*Log[(c + x)/x]^2)/16 + (b^2*x^4*Log[(c + x)/x]^2)/16 - (b^2*c^4*PolyLog[2, (c - x)/(2*c)])/8 - (b^2*c^4*PolyLog[2, -(c/x)])/8 - (b^2*c^4*PolyLog[2, c/x])/8 - (b^2*c^4*PolyLog[2, (c + x)/(2*c)])/8 + (b^2*c^4*PolyLog[2, 1 - x/c])/8 + (b^2*c^4*PolyLog[2, 1 + x/c])/8","C",88,34,16,2.125,0,"{6099, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2319, 44, 2455, 263, 43, 6742, 30, 2557, 12, 2466, 2448, 2462, 260, 2416, 2394, 2393, 2391, 193, 2410, 2395, 36, 29, 2390}"
144,1,695,0,1.3892428,"\int x^2 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^2 \, dx","Int[x^2*(a + b*ArcTanh[c/x])^2,x]","-\frac{1}{6} b^2 c^3 \text{PolyLog}\left(2,\frac{c-x}{2 c}\right)+\frac{1}{6} b^2 c^3 \text{PolyLog}\left(2,-\frac{c}{x}\right)-\frac{1}{6} b^2 c^3 \text{PolyLog}\left(2,\frac{c}{x}\right)+\frac{1}{6} b^2 c^3 \text{PolyLog}\left(2,\frac{c+x}{2 c}\right)+\frac{1}{6} b^2 c^3 \text{PolyLog}\left(2,1-\frac{x}{c}\right)-\frac{1}{6} b^2 c^3 \text{PolyLog}\left(2,\frac{x}{c}+1\right)-\frac{1}{3} a b c^2 x-\frac{1}{12} c^3 \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2+\frac{1}{3} a b c^3 \log (x)+\frac{1}{3} a b c^3 \log (c+x)+\frac{1}{6} b c^2 x \left(1-\frac{c}{x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)+\frac{1}{6} a b c x^2+\frac{1}{12} b c x^2 \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)+\frac{1}{12} x^3 \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2+\frac{1}{3} a b x^3 \log \left(\frac{c}{x}+1\right)+\frac{1}{3} b^2 c^2 x+\frac{1}{12} b^2 c^3 \log ^2\left(\frac{c+x}{x}\right)+\frac{1}{12} b^2 c^3 \log \left(1-\frac{c}{x}\right)-\frac{1}{12} b^2 c^3 \log (c-x)+\frac{1}{6} b^2 c^3 \log \left(\frac{c}{x}+1\right) \log (c-x)+\frac{1}{6} b^2 c^3 \log (c-x) \log \left(\frac{x}{c}\right)+\frac{1}{12} b^2 c^3 \log (c+x)-\frac{1}{6} b^2 c^3 \log \left(1-\frac{c}{x}\right) \log (c+x)+\frac{1}{6} b^2 c^3 \log \left(\frac{c-x}{2 c}\right) \log (c+x)-\frac{1}{6} b^2 c^3 \log \left(-\frac{x}{c}\right) \log (c+x)-\frac{1}{6} b^2 c^3 \log (c-x) \log \left(\frac{c+x}{2 c}\right)-\frac{1}{4} b^2 c^3 \log \left(\frac{c+x}{x}\right)+\frac{1}{6} b^2 c^2 x \log \left(1-\frac{c}{x}\right)+\frac{1}{6} b^2 c^2 x \log \left(\frac{c}{x}+1\right)-\frac{1}{6} b^2 c^2 x \log \left(\frac{c+x}{x}\right)+\frac{1}{12} b^2 x^3 \log ^2\left(\frac{c+x}{x}\right)-\frac{1}{12} b^2 c x^2 \log \left(1-\frac{c}{x}\right)+\frac{1}{12} b^2 c x^2 \log \left(\frac{c}{x}+1\right)+\frac{1}{12} b^2 c x^2 \log \left(\frac{c+x}{x}\right)-\frac{1}{6} b^2 x^3 \log \left(1-\frac{c}{x}\right) \log \left(\frac{c}{x}+1\right)","\frac{1}{3} b^2 c^3 \text{PolyLog}\left(2,\frac{2}{\frac{c}{x}+1}-1\right)-\frac{1}{3} c^3 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2-\frac{2}{3} b c^3 \log \left(2-\frac{2}{\frac{c}{x}+1}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{3} b c x^2 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{3} x^3 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{3} b^2 c^2 x-\frac{1}{3} b^2 c^3 \coth ^{-1}\left(\frac{x}{c}\right)",1,"-(a*b*c^2*x)/3 + (b^2*c^2*x)/3 + (a*b*c*x^2)/6 + (b^2*c^3*Log[1 - c/x])/12 + (b^2*c^2*x*Log[1 - c/x])/6 - (b^2*c*x^2*Log[1 - c/x])/12 + (b*c^2*(1 - c/x)*x*(2*a - b*Log[1 - c/x]))/6 + (b*c*x^2*(2*a - b*Log[1 - c/x]))/12 - (c^3*(2*a - b*Log[1 - c/x])^2)/12 + (x^3*(2*a - b*Log[1 - c/x])^2)/12 + (b^2*c^2*x*Log[1 + c/x])/6 + (b^2*c*x^2*Log[1 + c/x])/12 + (a*b*x^3*Log[1 + c/x])/3 - (b^2*x^3*Log[1 - c/x]*Log[1 + c/x])/6 - (b^2*c^3*Log[c - x])/12 + (b^2*c^3*Log[1 + c/x]*Log[c - x])/6 + (a*b*c^3*Log[x])/3 + (b^2*c^3*Log[c - x]*Log[x/c])/6 + (a*b*c^3*Log[c + x])/3 + (b^2*c^3*Log[c + x])/12 - (b^2*c^3*Log[1 - c/x]*Log[c + x])/6 + (b^2*c^3*Log[(c - x)/(2*c)]*Log[c + x])/6 - (b^2*c^3*Log[-(x/c)]*Log[c + x])/6 - (b^2*c^3*Log[c - x]*Log[(c + x)/(2*c)])/6 - (b^2*c^3*Log[(c + x)/x])/4 - (b^2*c^2*x*Log[(c + x)/x])/6 + (b^2*c*x^2*Log[(c + x)/x])/12 + (b^2*c^3*Log[(c + x)/x]^2)/12 + (b^2*x^3*Log[(c + x)/x]^2)/12 - (b^2*c^3*PolyLog[2, (c - x)/(2*c)])/6 + (b^2*c^3*PolyLog[2, -(c/x)])/6 - (b^2*c^3*PolyLog[2, c/x])/6 + (b^2*c^3*PolyLog[2, (c + x)/(2*c)])/6 + (b^2*c^3*PolyLog[2, 1 - x/c])/6 - (b^2*c^3*PolyLog[2, 1 + x/c])/6","B",73,34,16,2.125,0,"{6099, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2319, 44, 2455, 263, 43, 6742, 30, 2557, 12, 2466, 2448, 2462, 260, 2416, 2394, 2393, 2391, 193, 2410, 2395, 36, 29, 2390}"
145,1,574,0,1.0409938,"\int x \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^2 \, dx","Int[x*(a + b*ArcTanh[c/x])^2,x]","-\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,\frac{c-x}{2 c}\right)-\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,-\frac{c}{x}\right)-\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,\frac{c}{x}\right)-\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,\frac{c+x}{2 c}\right)+\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,1-\frac{x}{c}\right)+\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,\frac{x}{c}+1\right)+\frac{1}{2} a b c^2 \log (x)-\frac{1}{2} a b c^2 \log (c+x)-\frac{1}{8} c^2 \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2+\frac{1}{2} a b x^2 \log \left(\frac{c}{x}+1\right)+\frac{1}{8} x^2 \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2+\frac{1}{2} a b c x+\frac{1}{4} b c x \left(1-\frac{c}{x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)-\frac{1}{8} b^2 c^2 \log ^2\left(\frac{c+x}{x}\right)+\frac{1}{4} b^2 c^2 \log (c-x)+\frac{1}{4} b^2 c^2 \log \left(\frac{c}{x}+1\right) \log (c-x)+\frac{1}{2} b^2 c^2 \log (x)+\frac{1}{4} b^2 c^2 \log (c-x) \log \left(\frac{x}{c}\right)+\frac{1}{4} b^2 c^2 \log (c+x)+\frac{1}{4} b^2 c^2 \log \left(1-\frac{c}{x}\right) \log (c+x)-\frac{1}{4} b^2 c^2 \log \left(\frac{c-x}{2 c}\right) \log (c+x)+\frac{1}{4} b^2 c^2 \log \left(-\frac{x}{c}\right) \log (c+x)-\frac{1}{4} b^2 c^2 \log (c-x) \log \left(\frac{c+x}{2 c}\right)+\frac{1}{4} b^2 c^2 \log \left(\frac{c+x}{x}\right)+\frac{1}{8} b^2 x^2 \log ^2\left(\frac{c+x}{x}\right)-\frac{1}{4} b^2 x^2 \log \left(1-\frac{c}{x}\right) \log \left(\frac{c}{x}+1\right)-\frac{1}{4} b^2 c x \log \left(1-\frac{c}{x}\right)+\frac{1}{4} b^2 c x \log \left(\frac{c}{x}+1\right)+\frac{1}{4} b^2 c x \log \left(\frac{c+x}{x}\right)","-\frac{1}{2} c^2 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{2} x^2 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+b c x \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{2} b^2 c^2 \log \left(1-\frac{c^2}{x^2}\right)+b^2 c^2 \log (x)",1,"(a*b*c*x)/2 - (b^2*c*x*Log[1 - c/x])/4 + (b*c*(1 - c/x)*x*(2*a - b*Log[1 - c/x]))/4 - (c^2*(2*a - b*Log[1 - c/x])^2)/8 + (x^2*(2*a - b*Log[1 - c/x])^2)/8 + (b^2*c*x*Log[1 + c/x])/4 + (a*b*x^2*Log[1 + c/x])/2 - (b^2*x^2*Log[1 - c/x]*Log[1 + c/x])/4 + (b^2*c^2*Log[c - x])/4 + (b^2*c^2*Log[1 + c/x]*Log[c - x])/4 + (a*b*c^2*Log[x])/2 + (b^2*c^2*Log[x])/2 + (b^2*c^2*Log[c - x]*Log[x/c])/4 - (a*b*c^2*Log[c + x])/2 + (b^2*c^2*Log[c + x])/4 + (b^2*c^2*Log[1 - c/x]*Log[c + x])/4 - (b^2*c^2*Log[(c - x)/(2*c)]*Log[c + x])/4 + (b^2*c^2*Log[-(x/c)]*Log[c + x])/4 - (b^2*c^2*Log[c - x]*Log[(c + x)/(2*c)])/4 + (b^2*c^2*Log[(c + x)/x])/4 + (b^2*c*x*Log[(c + x)/x])/4 - (b^2*c^2*Log[(c + x)/x]^2)/8 + (b^2*x^2*Log[(c + x)/x]^2)/8 - (b^2*c^2*PolyLog[2, (c - x)/(2*c)])/4 - (b^2*c^2*PolyLog[2, -(c/x)])/4 - (b^2*c^2*PolyLog[2, c/x])/4 - (b^2*c^2*PolyLog[2, (c + x)/(2*c)])/4 + (b^2*c^2*PolyLog[2, 1 - x/c])/4 + (b^2*c^2*PolyLog[2, 1 + x/c])/4","C",58,32,14,2.286,0,"{6099, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2455, 193, 43, 6742, 30, 2557, 12, 2466, 2448, 263, 2462, 260, 2416, 2394, 2393, 2391, 2410, 2395, 36, 29, 2390}"
146,1,370,0,0.4020786,"\int \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^2 \, dx","Int[(a + b*ArcTanh[c/x])^2,x]","-\frac{1}{2} b^2 c \text{PolyLog}\left(2,\frac{c-x}{2 c}\right)+\frac{1}{2} b^2 c \text{PolyLog}\left(2,-\frac{c}{x}\right)-\frac{1}{2} b^2 c \text{PolyLog}\left(2,\frac{c}{x}\right)+\frac{1}{2} b^2 c \text{PolyLog}\left(2,\frac{c+x}{2 c}\right)+\frac{1}{2} b^2 c \text{PolyLog}\left(2,1-\frac{x}{c}\right)-\frac{1}{2} b^2 c \text{PolyLog}\left(2,\frac{x}{c}+1\right)+a^2 x-a b x \log \left(1-\frac{c}{x}\right)+a b x \log \left(\frac{c}{x}+1\right)+a b c \log (c-x)+a b c \log (c+x)-\frac{1}{4} b^2 (c-x) \log ^2\left(1-\frac{c}{x}\right)+\frac{1}{4} b^2 (c+x) \log ^2\left(\frac{c}{x}+1\right)-\frac{1}{2} b^2 x \log \left(1-\frac{c}{x}\right) \log \left(\frac{c}{x}+1\right)-\frac{1}{2} b^2 c \log \left(1-\frac{c}{x}\right) \log (-c-x)+\frac{1}{2} b^2 c \log (-c-x) \log \left(\frac{c-x}{2 c}\right)-\frac{1}{2} b^2 c \log (-c-x) \log \left(-\frac{x}{c}\right)+\frac{1}{2} b^2 c \log \left(\frac{c}{x}+1\right) \log (x-c)+\frac{1}{2} b^2 c \log \left(\frac{x}{c}\right) \log (x-c)-\frac{1}{2} b^2 c \log (x-c) \log \left(\frac{c+x}{2 c}\right)","b^2 (-c) \text{PolyLog}\left(2,-\frac{c+x}{c-x}\right)+c \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+x \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2-2 b c \log \left(\frac{2 c}{c-x}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)",1,"a^2*x - a*b*x*Log[1 - c/x] - (b^2*(c - x)*Log[1 - c/x]^2)/4 + a*b*x*Log[1 + c/x] - (b^2*x*Log[1 - c/x]*Log[1 + c/x])/2 + (b^2*(c + x)*Log[1 + c/x]^2)/4 - (b^2*c*Log[1 - c/x]*Log[-c - x])/2 + a*b*c*Log[c - x] + (b^2*c*Log[-c - x]*Log[(c - x)/(2*c)])/2 - (b^2*c*Log[-c - x]*Log[-(x/c)])/2 + (b^2*c*Log[1 + c/x]*Log[-c + x])/2 + (b^2*c*Log[x/c]*Log[-c + x])/2 + a*b*c*Log[c + x] - (b^2*c*Log[-c + x]*Log[(c + x)/(2*c)])/2 - (b^2*c*PolyLog[2, (c - x)/(2*c)])/2 + (b^2*c*PolyLog[2, -(c/x)])/2 - (b^2*c*PolyLog[2, c/x])/2 + (b^2*c*PolyLog[2, (c + x)/(2*c)])/2 + (b^2*c*PolyLog[2, 1 - x/c])/2 - (b^2*c*PolyLog[2, 1 + x/c])/2","B",31,14,12,1.167,0,"{6093, 2448, 263, 31, 2449, 2391, 2556, 12, 2462, 260, 2416, 2394, 2315, 2393}"
147,1,133,0,0.3144729,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^2}{x} \, dx","Int[(a + b*ArcTanh[c/x])^2/x,x]","b \text{PolyLog}\left(2,1-\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)-b \text{PolyLog}\left(2,\frac{2}{1-\frac{c}{x}}-1\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-\frac{c}{x}}\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,\frac{2}{1-\frac{c}{x}}-1\right)-2 \tanh ^{-1}\left(1-\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2","b \text{PolyLog}\left(2,1-\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)-b \text{PolyLog}\left(2,\frac{2}{1-\frac{c}{x}}-1\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-\frac{c}{x}}\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,\frac{2}{1-\frac{c}{x}}-1\right)-2 \tanh ^{-1}\left(1-\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2",1,"-2*(a + b*ArcCoth[x/c])^2*ArcTanh[1 - 2/(1 - c/x)] + b*(a + b*ArcCoth[x/c])*PolyLog[2, 1 - 2/(1 - c/x)] - b*(a + b*ArcCoth[x/c])*PolyLog[2, -1 + 2/(1 - c/x)] - (b^2*PolyLog[3, 1 - 2/(1 - c/x)])/2 + (b^2*PolyLog[3, -1 + 2/(1 - c/x)])/2","A",7,6,16,0.3750,1,"{6095, 5914, 6052, 5948, 6058, 6610}"
148,1,205,0,0.5068386,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^2}{x^2} \, dx","Int[(a + b*ArcTanh[c/x])^2/x^2,x]","\frac{b^2 \text{PolyLog}\left(2,-\frac{c-x}{2 x}\right)}{2 c}-\frac{b^2 \text{PolyLog}\left(2,\frac{c+x}{2 x}\right)}{2 c}-\frac{b \log \left(\frac{c+x}{2 x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)}{2 c}-\frac{b \log \left(\frac{c+x}{x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)}{2 x}+\frac{\left(1-\frac{c}{x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2}{4 c}-\frac{b^2 \left(\frac{c}{x}+1\right) \log ^2\left(\frac{c+x}{x}\right)}{4 c}-\frac{b^2 \log \left(-\frac{c-x}{2 x}\right) \log \left(\frac{c+x}{x}\right)}{2 c}","\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{c}{x}}\right)}{c}-\frac{\left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2}{c}-\frac{\left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2}{x}+\frac{2 b \log \left(\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)}{c}",1,"((1 - c/x)*(2*a - b*Log[1 - c/x])^2)/(4*c) - (b*(2*a - b*Log[1 - c/x])*Log[(c + x)/(2*x)])/(2*c) - (b*(2*a - b*Log[1 - c/x])*Log[(c + x)/x])/(2*x) - (b^2*Log[-(c - x)/(2*x)]*Log[(c + x)/x])/(2*c) - (b^2*(1 + c/x)*Log[(c + x)/x]^2)/(4*c) + (b^2*PolyLog[2, -(c - x)/(2*x)])/(2*c) - (b^2*PolyLog[2, (c + x)/(2*x)])/(2*c)","B",28,12,16,0.7500,0,"{6099, 2454, 2389, 2296, 2295, 6715, 2430, 43, 2416, 2394, 2393, 2391}"
149,1,707,0,1.2469811,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^2}{x^3} \, dx","Int[(a + b*ArcTanh[c/x])^2/x^3,x]","\frac{b^2 \text{PolyLog}\left(2,\frac{c-x}{2 c}\right)}{4 c^2}+\frac{b^2 \text{PolyLog}\left(2,-\frac{c}{x}\right)}{4 c^2}+\frac{b^2 \text{PolyLog}\left(2,\frac{c}{x}\right)}{4 c^2}+\frac{b^2 \text{PolyLog}\left(2,\frac{c+x}{2 c}\right)}{4 c^2}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{x}{c}\right)}{4 c^2}-\frac{b^2 \text{PolyLog}\left(2,\frac{x}{c}+1\right)}{4 c^2}-\frac{b \left(1-\frac{c}{x}\right)^2 \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)}{8 c^2}+\frac{a b \log \left(\frac{c+x}{x}\right)}{2 c^2}-\frac{\left(1-\frac{c}{x}\right)^2 \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2}{8 c^2}+\frac{\left(1-\frac{c}{x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2}{4 c^2}-\frac{a b \log \left(\frac{c+x}{x}\right)}{2 x^2}-\frac{3 a b}{2 c x}+\frac{a b}{4 x^2}-\frac{b^2 \left(1-\frac{c}{x}\right)^2}{16 c^2}-\frac{b^2 \left(\frac{c}{x}+1\right)^2}{16 c^2}-\frac{b^2 \left(\frac{c}{x}+1\right)^2 \log ^2\left(\frac{c+x}{x}\right)}{8 c^2}+\frac{b^2 \left(\frac{c}{x}+1\right) \log ^2\left(\frac{c+x}{x}\right)}{4 c^2}-\frac{3 b^2 \left(1-\frac{c}{x}\right) \log \left(1-\frac{c}{x}\right)}{4 c^2}+\frac{b^2 \log \left(1-\frac{c}{x}\right)}{8 c^2}-\frac{b^2 \log \left(\frac{c}{x}+1\right) \log (c-x)}{4 c^2}-\frac{b^2 \log (c-x) \log \left(\frac{x}{c}\right)}{4 c^2}-\frac{b^2 \log \left(1-\frac{c}{x}\right) \log (c+x)}{4 c^2}+\frac{b^2 \log \left(\frac{c-x}{2 c}\right) \log (c+x)}{4 c^2}-\frac{b^2 \log \left(-\frac{x}{c}\right) \log (c+x)}{4 c^2}+\frac{b^2 \log (c-x) \log \left(\frac{c+x}{2 c}\right)}{4 c^2}+\frac{b^2 \left(\frac{c}{x}+1\right)^2 \log \left(\frac{c+x}{x}\right)}{8 c^2}-\frac{3 b^2 \left(\frac{c}{x}+1\right) \log \left(\frac{c+x}{x}\right)}{4 c^2}+\frac{b^2 \log \left(\frac{c+x}{x}\right)}{8 c^2}-\frac{b^2 \log \left(1-\frac{c}{x}\right)}{8 x^2}+\frac{b^2 \log \left(1-\frac{c}{x}\right) \log \left(\frac{c}{x}+1\right)}{4 x^2}-\frac{b^2 \log \left(\frac{c+x}{x}\right)}{8 x^2}+\frac{b^2}{8 x^2}","\frac{\left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2}{2 c^2}-\frac{\left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2}{2 x^2}-\frac{a b}{c x}-\frac{b^2 \log \left(1-\frac{c^2}{x^2}\right)}{2 c^2}-\frac{b^2 \coth ^{-1}\left(\frac{x}{c}\right)}{c x}",1,"-(b^2*(1 - c/x)^2)/(16*c^2) - (b^2*(1 + c/x)^2)/(16*c^2) + (a*b)/(4*x^2) + b^2/(8*x^2) - (3*a*b)/(2*c*x) + (b^2*Log[1 - c/x])/(8*c^2) - (3*b^2*(1 - c/x)*Log[1 - c/x])/(4*c^2) - (b^2*Log[1 - c/x])/(8*x^2) - (b*(1 - c/x)^2*(2*a - b*Log[1 - c/x]))/(8*c^2) + ((1 - c/x)*(2*a - b*Log[1 - c/x])^2)/(4*c^2) - ((1 - c/x)^2*(2*a - b*Log[1 - c/x])^2)/(8*c^2) + (b^2*Log[1 - c/x]*Log[1 + c/x])/(4*x^2) - (b^2*Log[1 + c/x]*Log[c - x])/(4*c^2) - (b^2*Log[c - x]*Log[x/c])/(4*c^2) - (b^2*Log[1 - c/x]*Log[c + x])/(4*c^2) + (b^2*Log[(c - x)/(2*c)]*Log[c + x])/(4*c^2) - (b^2*Log[-(x/c)]*Log[c + x])/(4*c^2) + (b^2*Log[c - x]*Log[(c + x)/(2*c)])/(4*c^2) + (a*b*Log[(c + x)/x])/(2*c^2) + (b^2*Log[(c + x)/x])/(8*c^2) - (3*b^2*(1 + c/x)*Log[(c + x)/x])/(4*c^2) + (b^2*(1 + c/x)^2*Log[(c + x)/x])/(8*c^2) - (a*b*Log[(c + x)/x])/(2*x^2) - (b^2*Log[(c + x)/x])/(8*x^2) + (b^2*(1 + c/x)*Log[(c + x)/x]^2)/(4*c^2) - (b^2*(1 + c/x)^2*Log[(c + x)/x]^2)/(8*c^2) + (b^2*PolyLog[2, (c - x)/(2*c)])/(4*c^2) + (b^2*PolyLog[2, -(c/x)])/(4*c^2) + (b^2*PolyLog[2, c/x])/(4*c^2) + (b^2*PolyLog[2, (c + x)/(2*c)])/(4*c^2) - (b^2*PolyLog[2, 1 - x/c])/(4*c^2) - (b^2*PolyLog[2, 1 + x/c])/(4*c^2)","C",66,23,16,1.438,0,"{6099, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2395, 43, 6742, 30, 2557, 12, 2466, 2462, 260, 2416, 2394, 2315, 2393, 2391}"
150,0,0,0,4.3903641,"\int x^3 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","Int[x^3*(a + b*ArcTanh[c/x])^3,x]","\int x^3 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","b^3 c^4 \text{PolyLog}\left(2,\frac{2}{\frac{c}{x}+1}-1\right)+\frac{1}{4} b^2 c^2 x^2 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)-2 b^2 c^4 \log \left(2-\frac{2}{\frac{c}{x}+1}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)-\frac{1}{4} c^4 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3-b c^4 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{3}{4} b c^3 x \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{4} b c x^3 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{4} x^4 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3+\frac{1}{4} b^3 c^3 x-\frac{1}{4} b^3 c^4 \coth ^{-1}\left(\frac{x}{c}\right)",1,"(3*a^2*b*c^3*x)/8 - (5*a*b^2*c^3*x)/16 + (b^3*c^3*x)/16 - (3*a^2*b*c^2*x^2)/16 + (3*a*b^2*c^2*x^2)/16 + (a^2*b*c*x^3)/8 + (b^3*c^4*Log[1 - c/x])/32 - (3*a*b^2*c^3*x*Log[1 - c/x])/8 + (3*a*b^2*c^2*x^2*Log[1 - c/x])/16 - (a*b^2*c*x^3*Log[1 - c/x])/8 + (5*b^2*c^3*(1 - c/x)*x*(2*a - b*Log[1 - c/x]))/32 + (b^2*c^2*x^2*(2*a - b*Log[1 - c/x]))/32 - (5*b*c^4*(2*a - b*Log[1 - c/x])^2)/64 + (3*b*c^3*(1 - c/x)*x*(2*a - b*Log[1 - c/x])^2)/32 + (3*b*c^2*x^2*(2*a - b*Log[1 - c/x])^2)/64 + (b*c*x^3*(2*a - b*Log[1 - c/x])^2)/32 - (c^4*(2*a - b*Log[1 - c/x])^3)/32 + (x^4*(2*a - b*Log[1 - c/x])^3)/32 + (3*a*b^2*c^3*x*Log[1 + c/x])/8 + (3*a*b^2*c^2*x^2*Log[1 + c/x])/16 + (a*b^2*c*x^3*Log[1 + c/x])/8 + (3*a^2*b*x^4*Log[1 + c/x])/8 - (3*a*b^2*x^4*Log[1 - c/x]*Log[1 + c/x])/8 + (5*a*b^2*c^4*Log[c - x])/16 + (3*a*b^2*c^4*Log[1 + c/x]*Log[c - x])/8 - (3*b*c^4*(2*a - b*Log[1 - c/x])^2*Log[c/x])/32 + (11*a*b^2*c^4*Log[x])/8 + (3*a*b^2*c^4*Log[c - x]*Log[x/c])/8 - (3*a^2*b*c^4*Log[c + x])/8 + (5*a*b^2*c^4*Log[c + x])/16 + (3*a*b^2*c^4*Log[1 - c/x]*Log[c + x])/8 - (3*a*b^2*c^4*Log[(c - x)/(2*c)]*Log[c + x])/8 + (3*a*b^2*c^4*Log[-(x/c)]*Log[c + x])/8 - (3*a*b^2*c^4*Log[c - x]*Log[(c + x)/(2*c)])/8 + (11*a*b^2*c^4*Log[(c + x)/x])/16 - (b^3*c^4*Log[(c + x)/x])/32 + (3*a*b^2*c^3*x*Log[(c + x)/x])/8 - (5*b^3*c^3*(1 + c/x)*x*Log[(c + x)/x])/32 - (3*a*b^2*c^2*x^2*Log[(c + x)/x])/16 + (b^3*c^2*x^2*Log[(c + x)/x])/32 + (a*b^2*c*x^3*Log[(c + x)/x])/8 - (3*a*b^2*c^4*Log[(c + x)/x]^2)/16 + (5*b^3*c^4*Log[(c + x)/x]^2)/64 + (3*b^3*c^3*(1 + c/x)*x*Log[(c + x)/x]^2)/32 - (3*b^3*c^2*x^2*Log[(c + x)/x]^2)/64 + (b^3*c*x^3*Log[(c + x)/x]^2)/32 + (3*a*b^2*x^4*Log[(c + x)/x]^2)/16 + (3*b^3*c^4*Log[-(c/x)]*Log[(c + x)/x]^2)/32 - (b^3*c^4*Log[(c + x)/x]^3)/32 + (b^3*x^4*Log[(c + x)/x]^3)/32 + (3*b^2*c^4*(2*a - b*Log[1 - c/x])*PolyLog[2, 1 - c/x])/16 - (3*a*b^2*c^4*PolyLog[2, (c - x)/(2*c)])/8 - (3*a*b^2*c^4*PolyLog[2, -(c/x)])/8 + (11*b^3*c^4*PolyLog[2, -(c/x)])/32 - (11*b^3*c^4*PolyLog[2, c/x])/32 - (3*a*b^2*c^4*PolyLog[2, (c + x)/(2*c)])/8 + (3*b^3*c^4*Log[(c + x)/x]*PolyLog[2, (c + x)/x])/16 + (3*a*b^2*c^4*PolyLog[2, 1 - x/c])/8 + (3*a*b^2*c^4*PolyLog[2, 1 + x/c])/8 + (3*b^3*c^4*PolyLog[3, 1 - c/x])/16 - (3*b^3*c^4*PolyLog[3, (c + x)/x])/16 + (3*b^3*Defer[Int][x^3*Log[1 - c/x]^2*Log[1 + c/x], x])/8 - (3*b^3*Defer[Int][x^3*Log[1 - c/x]*Log[1 + c/x]^2, x])/8","F",0,0,0,0,-1,"{}"
151,0,0,0,3.3015595,"\int x^2 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","Int[x^2*(a + b*ArcTanh[c/x])^3,x]","\int x^2 \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","b^2 c^3 \text{PolyLog}\left(2,\frac{2}{\frac{c}{x}+1}-1\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{2} b^3 c^3 \text{PolyLog}\left(3,\frac{2}{\frac{c}{x}+1}-1\right)+b^2 c^2 x \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)-\frac{1}{3} c^3 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3-\frac{1}{2} b c^3 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2-b c^3 \log \left(2-\frac{2}{\frac{c}{x}+1}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{2} b c x^2 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{3} x^3 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3+\frac{1}{2} b^3 c^3 \log \left(1-\frac{c^2}{x^2}\right)+b^3 c^3 \log (x)",1,"-(a^2*b*c^2*x)/2 + (3*a*b^2*c^2*x)/4 + (a^2*b*c*x^2)/4 + (a*b^2*c^2*x*Log[1 - c/x])/2 - (a*b^2*c*x^2*Log[1 - c/x])/4 + (b^2*c^2*(1 - c/x)*x*(2*a - b*Log[1 - c/x]))/8 - (b*c^3*(2*a - b*Log[1 - c/x])^2)/16 + (b*c^2*(1 - c/x)*x*(2*a - b*Log[1 - c/x])^2)/8 + (b*c*x^2*(2*a - b*Log[1 - c/x])^2)/16 - (c^3*(2*a - b*Log[1 - c/x])^3)/24 + (x^3*(2*a - b*Log[1 - c/x])^3)/24 + (a*b^2*c^2*x*Log[1 + c/x])/2 + (a*b^2*c*x^2*Log[1 + c/x])/4 + (a^2*b*x^3*Log[1 + c/x])/2 - (a*b^2*x^3*Log[1 - c/x]*Log[1 + c/x])/2 - (a*b^2*c^3*Log[c - x])/4 + (a*b^2*c^3*Log[1 + c/x]*Log[c - x])/2 - (b*c^3*(2*a - b*Log[1 - c/x])^2*Log[c/x])/8 + (b^3*c^3*Log[x])/4 + (a*b^2*c^3*Log[c - x]*Log[x/c])/2 + (a^2*b*c^3*Log[c + x])/2 + (a*b^2*c^3*Log[c + x])/4 - (a*b^2*c^3*Log[1 - c/x]*Log[c + x])/2 + (a*b^2*c^3*Log[(c - x)/(2*c)]*Log[c + x])/2 - (a*b^2*c^3*Log[-(x/c)]*Log[c + x])/2 - (a*b^2*c^3*Log[c - x]*Log[(c + x)/(2*c)])/2 - (3*a*b^2*c^3*Log[(c + x)/x])/4 - (a*b^2*c^2*x*Log[(c + x)/x])/2 + (b^3*c^2*(1 + c/x)*x*Log[(c + x)/x])/8 + (a*b^2*c*x^2*Log[(c + x)/x])/4 + (a*b^2*c^3*Log[(c + x)/x]^2)/4 - (b^3*c^3*Log[(c + x)/x]^2)/16 - (b^3*c^2*(1 + c/x)*x*Log[(c + x)/x]^2)/8 + (b^3*c*x^2*Log[(c + x)/x]^2)/16 + (a*b^2*x^3*Log[(c + x)/x]^2)/4 - (b^3*c^3*Log[-(c/x)]*Log[(c + x)/x]^2)/8 + (b^3*c^3*Log[(c + x)/x]^3)/24 + (b^3*x^3*Log[(c + x)/x]^3)/24 + (b^2*c^3*(2*a - b*Log[1 - c/x])*PolyLog[2, 1 - c/x])/4 - (a*b^2*c^3*PolyLog[2, (c - x)/(2*c)])/2 + (a*b^2*c^3*PolyLog[2, -(c/x)])/2 - (3*b^3*c^3*PolyLog[2, -(c/x)])/8 - (3*b^3*c^3*PolyLog[2, c/x])/8 + (a*b^2*c^3*PolyLog[2, (c + x)/(2*c)])/2 - (b^3*c^3*Log[(c + x)/x]*PolyLog[2, (c + x)/x])/4 + (a*b^2*c^3*PolyLog[2, 1 - x/c])/2 - (a*b^2*c^3*PolyLog[2, 1 + x/c])/2 + (b^3*c^3*PolyLog[3, 1 - c/x])/4 + (b^3*c^3*PolyLog[3, (c + x)/x])/4 + (3*b^3*Defer[Int][x^2*Log[1 - c/x]^2*Log[1 + c/x], x])/8 - (3*b^3*Defer[Int][x^2*Log[1 - c/x]*Log[1 + c/x]^2, x])/8","F",0,0,0,0,-1,"{}"
152,0,0,0,2.2448198,"\int x \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","Int[x*(a + b*ArcTanh[c/x])^3,x]","\int x \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","\frac{3}{2} b^3 c^2 \text{PolyLog}\left(2,\frac{2}{\frac{c}{x}+1}-1\right)-3 b^2 c^2 \log \left(2-\frac{2}{\frac{c}{x}+1}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)-\frac{3}{2} b c^2 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2-\frac{1}{2} c^2 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3+\frac{1}{2} x^2 \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3+\frac{3}{2} b c x \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2",1,"(3*a^2*b*c*x)/4 - (3*a*b^2*c*x*Log[1 - c/x])/4 + (3*b*c*(1 - c/x)*x*(2*a - b*Log[1 - c/x])^2)/16 - (c^2*(2*a - b*Log[1 - c/x])^3)/16 + (x^2*(2*a - b*Log[1 - c/x])^3)/16 + (3*a*b^2*c*x*Log[1 + c/x])/4 + (3*a^2*b*x^2*Log[1 + c/x])/4 - (3*a*b^2*x^2*Log[1 - c/x]*Log[1 + c/x])/4 + (3*a*b^2*c^2*Log[c - x])/4 + (3*a*b^2*c^2*Log[1 + c/x]*Log[c - x])/4 - (3*b*c^2*(2*a - b*Log[1 - c/x])^2*Log[c/x])/16 + (3*a*b^2*c^2*Log[x])/2 + (3*a*b^2*c^2*Log[c - x]*Log[x/c])/4 - (3*a^2*b*c^2*Log[c + x])/4 + (3*a*b^2*c^2*Log[c + x])/4 + (3*a*b^2*c^2*Log[1 - c/x]*Log[c + x])/4 - (3*a*b^2*c^2*Log[(c - x)/(2*c)]*Log[c + x])/4 + (3*a*b^2*c^2*Log[-(x/c)]*Log[c + x])/4 - (3*a*b^2*c^2*Log[c - x]*Log[(c + x)/(2*c)])/4 + (3*a*b^2*c^2*Log[(c + x)/x])/4 + (3*a*b^2*c*x*Log[(c + x)/x])/4 - (3*a*b^2*c^2*Log[(c + x)/x]^2)/8 + (3*b^3*c*(1 + c/x)*x*Log[(c + x)/x]^2)/16 + (3*a*b^2*x^2*Log[(c + x)/x]^2)/8 + (3*b^3*c^2*Log[-(c/x)]*Log[(c + x)/x]^2)/16 - (b^3*c^2*Log[(c + x)/x]^3)/16 + (b^3*x^2*Log[(c + x)/x]^3)/16 + (3*b^2*c^2*(2*a - b*Log[1 - c/x])*PolyLog[2, 1 - c/x])/8 - (3*a*b^2*c^2*PolyLog[2, (c - x)/(2*c)])/4 - (3*a*b^2*c^2*PolyLog[2, -(c/x)])/4 + (3*b^3*c^2*PolyLog[2, -(c/x)])/8 - (3*b^3*c^2*PolyLog[2, c/x])/8 - (3*a*b^2*c^2*PolyLog[2, (c + x)/(2*c)])/4 + (3*b^3*c^2*Log[(c + x)/x]*PolyLog[2, (c + x)/x])/8 + (3*a*b^2*c^2*PolyLog[2, 1 - x/c])/4 + (3*a*b^2*c^2*PolyLog[2, 1 + x/c])/4 + (3*b^3*c^2*PolyLog[3, 1 - c/x])/8 - (3*b^3*c^2*PolyLog[3, (c + x)/x])/8 + (3*b^3*Defer[Int][x*Log[1 - c/x]^2*Log[1 + c/x], x])/8 - (3*b^3*Defer[Int][x*Log[1 - c/x]*Log[1 + c/x]^2, x])/8","F",0,0,0,0,-1,"{}"
153,0,0,0,0.700751,"\int \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","Int[(a + b*ArcTanh[c/x])^3,x]","\int \left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","-3 b^2 c \text{PolyLog}\left(2,1-\frac{2 c}{c-x}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)+\frac{3}{2} b^3 c \text{PolyLog}\left(3,1-\frac{2 c}{c-x}\right)+c \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3+x \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3-3 b c \log \left(\frac{2 c}{c-x}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2",1,"a^3*x - (3*a^2*b*x*Log[1 - c/x])/2 - (3*a*b^2*(c - x)*Log[1 - c/x]^2)/4 + (b^3*(c - x)*Log[1 - c/x]^3)/8 + (3*a^2*b*x*Log[1 + c/x])/2 - (3*a*b^2*x*Log[1 - c/x]*Log[1 + c/x])/2 + (3*a*b^2*(c + x)*Log[1 + c/x]^2)/4 + (b^3*(c + x)*Log[1 + c/x]^3)/8 - (3*a*b^2*c*Log[1 - c/x]*Log[-c - x])/2 + (3*a^2*b*c*Log[c - x])/2 + (3*a*b^2*c*Log[-c - x]*Log[(c - x)/(2*c)])/2 - (3*b^3*c*Log[1 - c/x]^2*Log[c/x])/8 - (3*a*b^2*c*Log[-c - x]*Log[-(x/c)])/2 + (3*a*b^2*c*Log[1 + c/x]*Log[-c + x])/2 + (3*a*b^2*c*Log[x/c]*Log[-c + x])/2 + (3*a^2*b*c*Log[c + x])/2 - (3*a*b^2*c*Log[-c + x]*Log[(c + x)/(2*c)])/2 - (3*b^3*c*Log[-(c/x)]*Log[(c + x)/x]^2)/8 - (3*b^3*c*Log[1 - c/x]*PolyLog[2, 1 - c/x])/4 - (3*a*b^2*c*PolyLog[2, (c - x)/(2*c)])/2 + (3*a*b^2*c*PolyLog[2, -(c/x)])/2 - (3*a*b^2*c*PolyLog[2, c/x])/2 + (3*a*b^2*c*PolyLog[2, (c + x)/(2*c)])/2 - (3*b^3*c*Log[(c + x)/x]*PolyLog[2, (c + x)/x])/4 + (3*a*b^2*c*PolyLog[2, 1 - x/c])/2 - (3*a*b^2*c*PolyLog[2, 1 + x/c])/2 + (3*b^3*c*PolyLog[3, 1 - c/x])/4 + (3*b^3*c*PolyLog[3, (c + x)/x])/4 + (3*b^3*Defer[Int][Log[1 - c/x]^2*Log[1 + c/x], x])/8 - (3*b^3*Defer[Int][Log[1 - c/x]*Log[1 + c/x]^2, x])/8","F",0,0,0,0,-1,"{}"
154,1,208,0,0.5086054,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3}{x} \, dx","Int[(a + b*ArcTanh[c/x])^3/x,x]","-\frac{3}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)+\frac{3}{2} b^2 \text{PolyLog}\left(3,\frac{2}{1-\frac{c}{x}}-1\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)+\frac{3}{2} b \text{PolyLog}\left(2,1-\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2-\frac{3}{2} b \text{PolyLog}\left(2,\frac{2}{1-\frac{c}{x}}-1\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{3}{4} b^3 \text{PolyLog}\left(4,1-\frac{2}{1-\frac{c}{x}}\right)-\frac{3}{4} b^3 \text{PolyLog}\left(4,\frac{2}{1-\frac{c}{x}}-1\right)-2 \tanh ^{-1}\left(1-\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3","-\frac{3}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)+\frac{3}{2} b^2 \text{PolyLog}\left(3,\frac{2}{1-\frac{c}{x}}-1\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)+\frac{3}{2} b \text{PolyLog}\left(2,1-\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2-\frac{3}{2} b \text{PolyLog}\left(2,\frac{2}{1-\frac{c}{x}}-1\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{3}{4} b^3 \text{PolyLog}\left(4,1-\frac{2}{1-\frac{c}{x}}\right)-\frac{3}{4} b^3 \text{PolyLog}\left(4,\frac{2}{1-\frac{c}{x}}-1\right)-2 \tanh ^{-1}\left(1-\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3",1,"-2*(a + b*ArcCoth[x/c])^3*ArcTanh[1 - 2/(1 - c/x)] + (3*b*(a + b*ArcCoth[x/c])^2*PolyLog[2, 1 - 2/(1 - c/x)])/2 - (3*b*(a + b*ArcCoth[x/c])^2*PolyLog[2, -1 + 2/(1 - c/x)])/2 - (3*b^2*(a + b*ArcCoth[x/c])*PolyLog[3, 1 - 2/(1 - c/x)])/2 + (3*b^2*(a + b*ArcCoth[x/c])*PolyLog[3, -1 + 2/(1 - c/x)])/2 + (3*b^3*PolyLog[4, 1 - 2/(1 - c/x)])/4 - (3*b^3*PolyLog[4, -1 + 2/(1 - c/x)])/4","A",9,7,16,0.4375,1,"{6095, 5914, 6052, 5948, 6058, 6062, 6610}"
155,1,387,0,2.2369115,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3}{x^2} \, dx","Int[(a + b*ArcTanh[c/x])^3/x^2,x]","\frac{3 b^2 \text{PolyLog}\left(2,-\frac{c-x}{2 x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)}{2 c}+\frac{3 b^3 \text{PolyLog}\left(3,-\frac{c-x}{2 x}\right)}{2 c}+\frac{3 b^3 \text{PolyLog}\left(3,\frac{c+x}{2 x}\right)}{2 c}-\frac{3 b^3 \log \left(\frac{c+x}{x}\right) \text{PolyLog}\left(2,\frac{c+x}{2 x}\right)}{2 c}-\frac{3 b^2 \log ^2\left(\frac{c+x}{x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)}{8 c}-\frac{3 b^2 \log ^2\left(\frac{c+x}{x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)}{8 x}-\frac{3 b \log \left(\frac{c+x}{2 x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2}{4 c}+\frac{3 b \log \left(\frac{c+x}{x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2}{8 c}-\frac{3 b \log \left(\frac{c+x}{x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^2}{8 x}+\frac{\left(1-\frac{c}{x}\right) \left(2 a-b \log \left(1-\frac{c}{x}\right)\right)^3}{8 c}-\frac{b^3 \left(\frac{c}{x}+1\right) \log ^3\left(\frac{c+x}{x}\right)}{8 c}-\frac{3 b^3 \log \left(-\frac{c-x}{2 x}\right) \log ^2\left(\frac{c+x}{x}\right)}{4 c}","\frac{3 b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)}{c}-\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1-\frac{c}{x}}\right)}{2 c}-\frac{\left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3}{c}-\frac{\left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3}{x}+\frac{3 b \log \left(\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2}{c}",1,"((1 - c/x)*(2*a - b*Log[1 - c/x])^3)/(8*c) - (3*b*(2*a - b*Log[1 - c/x])^2*Log[(c + x)/(2*x)])/(4*c) + (3*b*(2*a - b*Log[1 - c/x])^2*Log[(c + x)/x])/(8*c) - (3*b*(2*a - b*Log[1 - c/x])^2*Log[(c + x)/x])/(8*x) - (3*b^2*(2*a - b*Log[1 - c/x])*Log[(c + x)/x]^2)/(8*c) - (3*b^2*(2*a - b*Log[1 - c/x])*Log[(c + x)/x]^2)/(8*x) - (3*b^3*Log[-(c - x)/(2*x)]*Log[(c + x)/x]^2)/(4*c) - (b^3*(1 + c/x)*Log[(c + x)/x]^3)/(8*c) + (3*b^2*(2*a - b*Log[1 - c/x])*PolyLog[2, -(c - x)/(2*x)])/(2*c) - (3*b^3*Log[(c + x)/x]*PolyLog[2, (c + x)/(2*x)])/(2*c) + (3*b^3*PolyLog[3, -(c - x)/(2*x)])/(2*c) + (3*b^3*PolyLog[3, (c + x)/(2*x)])/(2*c)","B",82,23,16,1.438,0,"{6099, 2454, 2389, 2296, 2295, 6715, 2430, 2416, 2396, 2433, 2374, 6589, 2411, 2346, 2301, 6742, 43, 2394, 2393, 2391, 2375, 2317, 2425}"
156,0,0,0,2.1021411,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3}{x^3} \, dx","Int[(a + b*ArcTanh[c/x])^3/x^3,x]","\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x}\right)\right)^3}{x^3} \, dx","\frac{3 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{c}{x}}\right)}{2 c^2}+\frac{3 b^2 \log \left(\frac{2}{1-\frac{c}{x}}\right) \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)}{c^2}-\frac{3 b \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2}{2 c^2}+\frac{\left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3}{2 c^2}-\frac{\left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^3}{2 x^2}-\frac{3 b \left(a+b \coth ^{-1}\left(\frac{x}{c}\right)\right)^2}{2 c x}",1,"(-3*b^3*(1 - c/x)^2)/(64*c^2) - (3*a*b^2*(1 + c/x)^2)/(16*c^2) + (3*b^3*(1 + c/x)^2)/(64*c^2) + (3*a^2*b)/(8*x^2) + (3*a*b^2)/(8*x^2) - (3*a^2*b)/(4*c*x) - (3*b^3)/(2*c*x) + (3*a*b^2*Log[1 - c/x])/(8*c^2) - (3*a*b^2*(1 - c/x)*Log[1 - c/x])/(4*c^2) - (3*b^3*(1 - c/x)*Log[1 - c/x])/(4*c^2) - (3*a*b^2*Log[1 - c/x])/(8*x^2) - (3*b^2*(1 - c/x)^2*(2*a - b*Log[1 - c/x]))/(32*c^2) + (3*b*(1 - c/x)*(2*a - b*Log[1 - c/x])^2)/(8*c^2) - (3*b*(1 - c/x)^2*(2*a - b*Log[1 - c/x])^2)/(32*c^2) + ((1 - c/x)*(2*a - b*Log[1 - c/x])^3)/(8*c^2) - ((1 - c/x)^2*(2*a - b*Log[1 - c/x])^3)/(16*c^2) + (3*a*b^2*Log[1 - c/x]*Log[1 + c/x])/(4*x^2) - (3*a*b^2*Log[1 + c/x]*Log[c - x])/(4*c^2) - (3*a*b^2*Log[c - x]*Log[x/c])/(4*c^2) - (3*a*b^2*Log[1 - c/x]*Log[c + x])/(4*c^2) + (3*a*b^2*Log[(c - x)/(2*c)]*Log[c + x])/(4*c^2) - (3*a*b^2*Log[-(x/c)]*Log[c + x])/(4*c^2) + (3*a*b^2*Log[c - x]*Log[(c + x)/(2*c)])/(4*c^2) + (3*a^2*b*Log[(c + x)/x])/(4*c^2) + (3*a*b^2*Log[(c + x)/x])/(8*c^2) - (9*a*b^2*(1 + c/x)*Log[(c + x)/x])/(4*c^2) + (3*b^3*(1 + c/x)*Log[(c + x)/x])/(4*c^2) + (3*a*b^2*(1 + c/x)^2*Log[(c + x)/x])/(8*c^2) - (3*b^3*(1 + c/x)^2*Log[(c + x)/x])/(32*c^2) - (3*a^2*b*Log[(c + x)/x])/(4*x^2) - (3*a*b^2*Log[(c + x)/x])/(8*x^2) + (3*a*b^2*(1 + c/x)*Log[(c + x)/x]^2)/(4*c^2) - (3*b^3*(1 + c/x)*Log[(c + x)/x]^2)/(8*c^2) - (3*a*b^2*(1 + c/x)^2*Log[(c + x)/x]^2)/(8*c^2) + (3*b^3*(1 + c/x)^2*Log[(c + x)/x]^2)/(32*c^2) + (b^3*(1 + c/x)*Log[(c + x)/x]^3)/(8*c^2) - (b^3*(1 + c/x)^2*Log[(c + x)/x]^3)/(16*c^2) + (3*a*b^2*PolyLog[2, (c - x)/(2*c)])/(4*c^2) + (3*a*b^2*PolyLog[2, -(c/x)])/(4*c^2) + (3*a*b^2*PolyLog[2, c/x])/(4*c^2) + (3*a*b^2*PolyLog[2, (c + x)/(2*c)])/(4*c^2) - (3*a*b^2*PolyLog[2, 1 - x/c])/(4*c^2) - (3*a*b^2*PolyLog[2, 1 + x/c])/(4*c^2) + (3*b^3*Defer[Int][(Log[1 - c/x]^2*Log[1 + c/x])/x^3, x])/8 - (3*b^3*Defer[Int][(Log[1 - c/x]*Log[1 + c/x]^2)/x^3, x])/8","F",0,0,0,0,-1,"{}"
157,1,54,0,0.0417084,"\int x^7 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right) \, dx","Int[x^7*(a + b*ArcTanh[c/x^2]),x]","\frac{1}{8} x^8 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)+\frac{1}{8} b c^3 x^2-\frac{1}{8} b c^4 \tanh ^{-1}\left(\frac{x^2}{c}\right)+\frac{1}{24} b c x^6","\frac{1}{8} x^8 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)+\frac{1}{8} b c^3 x^2-\frac{1}{8} b c^4 \tanh ^{-1}\left(\frac{x^2}{c}\right)+\frac{1}{24} b c x^6",1,"(b*c^3*x^2)/8 + (b*c*x^6)/24 + (x^8*(a + b*ArcTanh[c/x^2]))/8 - (b*c^4*ArcTanh[x^2/c])/8","A",6,5,14,0.3571,1,"{6097, 263, 275, 302, 207}"
158,1,45,0,0.0329161,"\int x^5 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right) \, dx","Int[x^5*(a + b*ArcTanh[c/x^2]),x]","\frac{1}{6} x^6 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)+\frac{1}{12} b c^3 \log \left(c^2-x^4\right)+\frac{1}{12} b c x^4","\frac{1}{6} x^6 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)+\frac{1}{12} b c^3 \log \left(c^2-x^4\right)+\frac{1}{12} b c x^4",1,"(b*c*x^4)/12 + (x^6*(a + b*ArcTanh[c/x^2]))/6 + (b*c^3*Log[c^2 - x^4])/12","A",5,4,14,0.2857,1,"{6097, 263, 266, 43}"
159,1,43,0,0.0297014,"\int x^3 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right) \, dx","Int[x^3*(a + b*ArcTanh[c/x^2]),x]","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)-\frac{1}{4} b c^2 \tanh ^{-1}\left(\frac{x^2}{c}\right)+\frac{1}{4} b c x^2","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)-\frac{1}{4} b c^2 \tanh ^{-1}\left(\frac{x^2}{c}\right)+\frac{1}{4} b c x^2",1,"(b*c*x^2)/4 + (x^4*(a + b*ArcTanh[c/x^2]))/4 - (b*c^2*ArcTanh[x^2/c])/4","A",5,5,14,0.3571,1,"{6097, 263, 275, 321, 207}"
160,1,34,0,0.0180373,"\int x \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right) \, dx","Int[x*(a + b*ArcTanh[c/x^2]),x]","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)+\frac{1}{4} b c \log \left(c^2-x^4\right)","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)+\frac{1}{4} b c \log \left(c^2-x^4\right)",1,"(x^2*(a + b*ArcTanh[c/x^2]))/2 + (b*c*Log[c^2 - x^4])/4","A",3,3,12,0.2500,1,"{6097, 263, 260}"
161,1,30,0,0.0327894,"\int \frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{x} \, dx","Int[(a + b*ArcTanh[c/x^2])/x,x]","\frac{1}{4} b \text{PolyLog}\left(2,-\frac{c}{x^2}\right)-\frac{1}{4} b \text{PolyLog}\left(2,\frac{c}{x^2}\right)+a \log (x)","\frac{1}{4} b \text{PolyLog}\left(2,-\frac{c}{x^2}\right)-\frac{1}{4} b \text{PolyLog}\left(2,\frac{c}{x^2}\right)+a \log (x)",1,"a*Log[x] + (b*PolyLog[2, -(c/x^2)])/4 - (b*PolyLog[2, c/x^2])/4","A",2,2,14,0.1429,1,"{6095, 5912}"
162,1,37,0,0.0202372,"\int \frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{x^3} \, dx","Int[(a + b*ArcTanh[c/x^2])/x^3,x]","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{2 x^2}-\frac{b \log \left(1-\frac{c^2}{x^4}\right)}{4 c}","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{2 x^2}-\frac{b \log \left(1-\frac{c^2}{x^4}\right)}{4 c}",1,"-(a + b*ArcTanh[c/x^2])/(2*x^2) - (b*Log[1 - c^2/x^4])/(4*c)","A",2,2,14,0.1429,1,"{6097, 260}"
163,1,45,0,0.0320788,"\int \frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{x^5} \, dx","Int[(a + b*ArcTanh[c/x^2])/x^5,x]","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{4 x^4}+\frac{b \tanh ^{-1}\left(\frac{x^2}{c}\right)}{4 c^2}-\frac{b}{4 c x^2}","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{4 x^4}+\frac{b \tanh ^{-1}\left(\frac{x^2}{c}\right)}{4 c^2}-\frac{b}{4 c x^2}",1,"-b/(4*c*x^2) - (a + b*ArcTanh[c/x^2])/(4*x^4) + (b*ArcTanh[x^2/c])/(4*c^2)","A",5,5,14,0.3571,1,"{6097, 263, 275, 325, 207}"
164,1,57,0,0.0400527,"\int \frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{x^7} \, dx","Int[(a + b*ArcTanh[c/x^2])/x^7,x]","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{6 x^6}-\frac{b \log \left(c^2-x^4\right)}{12 c^3}+\frac{b \log (x)}{3 c^3}-\frac{b}{12 c x^4}","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{6 x^6}-\frac{b \log \left(c^2-x^4\right)}{12 c^3}+\frac{b \log (x)}{3 c^3}-\frac{b}{12 c x^4}",1,"-b/(12*c*x^4) - (a + b*ArcTanh[c/x^2])/(6*x^6) + (b*Log[x])/(3*c^3) - (b*Log[c^2 - x^4])/(12*c^3)","A",5,4,14,0.2857,1,"{6097, 263, 266, 44}"
165,1,63,0,0.0347141,"\int x^4 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right) \, dx","Int[x^4*(a + b*ArcTanh[c/x^2]),x]","\frac{1}{5} x^5 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)+\frac{1}{5} b c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{1}{5} b c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)+\frac{2}{15} b c x^3","\frac{1}{5} x^5 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)+\frac{1}{5} b c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{1}{5} b c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)+\frac{2}{15} b c x^3",1,"(2*b*c*x^3)/15 + (b*c^(5/2)*ArcTan[x/Sqrt[c]])/5 + (x^5*(a + b*ArcTanh[c/x^2]))/5 - (b*c^(5/2)*ArcTanh[x/Sqrt[c]])/5","A",6,6,14,0.4286,1,"{6097, 263, 321, 298, 203, 206}"
166,1,61,0,0.0331548,"\int x^2 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right) \, dx","Int[x^2*(a + b*ArcTanh[c/x^2]),x]","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)-\frac{1}{3} b c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{1}{3} b c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)+\frac{2 b c x}{3}","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)-\frac{1}{3} b c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{1}{3} b c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)+\frac{2 b c x}{3}",1,"(2*b*c*x)/3 - (b*c^(3/2)*ArcTan[x/Sqrt[c]])/3 + (x^3*(a + b*ArcTanh[c/x^2]))/3 - (b*c^(3/2)*ArcTanh[x/Sqrt[c]])/3","A",6,6,14,0.4286,1,"{6097, 193, 321, 212, 206, 203}"
167,1,44,0,0.0244142,"\int \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right) \, dx","Int[a + b*ArcTanh[c/x^2],x]","a x+b x \tanh ^{-1}\left(\frac{c}{x^2}\right)+b \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-b \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)","a x+b x \tanh ^{-1}\left(\frac{c}{x^2}\right)+b \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-b \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)",1,"a*x + b*Sqrt[c]*ArcTan[x/Sqrt[c]] + b*x*ArcTanh[c/x^2] - b*Sqrt[c]*ArcTanh[x/Sqrt[c]]","A",6,5,10,0.5000,1,"{6091, 263, 298, 203, 206}"
168,1,46,0,0.0309239,"\int \frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{x^2} \, dx","Int[(a + b*ArcTanh[c/x^2])/x^2,x]","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{x}+\frac{b \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{\sqrt{c}}+\frac{b \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{\sqrt{c}}","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{x}+\frac{b \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{\sqrt{c}}+\frac{b \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{\sqrt{c}}",1,"(b*ArcTan[x/Sqrt[c]])/Sqrt[c] - (a + b*ArcTanh[c/x^2])/x + (b*ArcTanh[x/Sqrt[c]])/Sqrt[c]","A",5,5,14,0.3571,1,"{6097, 263, 212, 206, 203}"
169,1,65,0,0.0371315,"\int \frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{x^4} \, dx","Int[(a + b*ArcTanh[c/x^2])/x^4,x]","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{3 x^3}-\frac{b \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{3 c^{3/2}}+\frac{b \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{3 c^{3/2}}-\frac{2 b}{3 c x}","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{3 x^3}-\frac{b \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{3 c^{3/2}}+\frac{b \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{3 c^{3/2}}-\frac{2 b}{3 c x}",1,"(-2*b)/(3*c*x) - (b*ArcTan[x/Sqrt[c]])/(3*c^(3/2)) - (a + b*ArcTanh[c/x^2])/(3*x^3) + (b*ArcTanh[x/Sqrt[c]])/(3*c^(3/2))","A",6,6,14,0.4286,1,"{6097, 263, 325, 298, 203, 206}"
170,1,65,0,0.0375865,"\int \frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{x^6} \, dx","Int[(a + b*ArcTanh[c/x^2])/x^6,x]","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{5 x^5}+\frac{b \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{5 c^{5/2}}+\frac{b \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{5 c^{5/2}}-\frac{2 b}{15 c x^3}","-\frac{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)}{5 x^5}+\frac{b \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{5 c^{5/2}}+\frac{b \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)}{5 c^{5/2}}-\frac{2 b}{15 c x^3}",1,"(-2*b)/(15*c*x^3) + (b*ArcTan[x/Sqrt[c]])/(5*c^(5/2)) - (a + b*ArcTanh[c/x^2])/(5*x^5) + (b*ArcTanh[x/Sqrt[c]])/(5*c^(5/2))","A",6,6,14,0.4286,1,"{6097, 263, 325, 212, 206, 203}"
171,1,599,0,1.2957362,"\int x^3 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2 \, dx","Int[x^3*(a + b*ArcTanh[c/x^2])^2,x]","-\frac{1}{8} b^2 c^2 \text{PolyLog}\left(2,-\frac{c}{x^2}\right)-\frac{1}{8} b^2 c^2 \text{PolyLog}\left(2,\frac{c}{x^2}\right)-\frac{1}{8} b^2 c^2 \text{PolyLog}\left(2,\frac{c-x^2}{2 c}\right)-\frac{1}{8} b^2 c^2 \text{PolyLog}\left(2,\frac{c+x^2}{2 c}\right)+\frac{1}{8} b^2 c^2 \text{PolyLog}\left(2,\frac{c+x^2}{c}\right)+\frac{1}{8} b^2 c^2 \text{PolyLog}\left(2,1-\frac{x^2}{c}\right)-\frac{1}{16} c^2 \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2-\frac{1}{4} a b c^2 \log \left(c+x^2\right)+\frac{1}{2} a b c^2 \log (x)+\frac{1}{4} a b c x^2+\frac{1}{16} x^4 \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2+\frac{1}{4} a b x^4 \log \left(\frac{c}{x^2}+1\right)+\frac{1}{8} b c x^2 \left(1-\frac{c}{x^2}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)-\frac{1}{16} b^2 c^2 \log ^2\left(\frac{c}{x^2}+1\right)+\frac{1}{8} b^2 c^2 \log \left(\frac{c}{x^2}+1\right)+\frac{1}{8} b^2 c^2 \log \left(c-x^2\right)+\frac{1}{8} b^2 c^2 \log \left(\frac{c}{x^2}+1\right) \log \left(c-x^2\right)+\frac{1}{8} b^2 c^2 \log \left(\frac{x^2}{c}\right) \log \left(c-x^2\right)+\frac{1}{8} b^2 c^2 \log \left(c+x^2\right)+\frac{1}{8} b^2 c^2 \log \left(1-\frac{c}{x^2}\right) \log \left(c+x^2\right)+\frac{1}{8} b^2 c^2 \log \left(-\frac{x^2}{c}\right) \log \left(c+x^2\right)-\frac{1}{8} b^2 c^2 \log \left(\frac{c-x^2}{2 c}\right) \log \left(c+x^2\right)-\frac{1}{8} b^2 c^2 \log \left(c-x^2\right) \log \left(\frac{c+x^2}{2 c}\right)+\frac{1}{2} b^2 c^2 \log (x)+\frac{1}{16} b^2 x^4 \log ^2\left(\frac{c}{x^2}+1\right)-\frac{1}{8} b^2 x^4 \log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{1}{8} b^2 c x^2 \log \left(1-\frac{c}{x^2}\right)+\frac{1}{4} b^2 c x^2 \log \left(\frac{c}{x^2}+1\right)","-\frac{1}{4} c^2 \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)^2+\frac{1}{4} x^4 \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)^2+\frac{1}{2} b c x^2 \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)+\frac{1}{4} b^2 c^2 \log \left(1-\frac{c^2}{x^4}\right)+b^2 c^2 \log (x)",1,"(a*b*c*x^2)/4 - (b^2*c*x^2*Log[1 - c/x^2])/8 + (b*c*(1 - c/x^2)*x^2*(2*a - b*Log[1 - c/x^2]))/8 - (c^2*(2*a - b*Log[1 - c/x^2])^2)/16 + (x^4*(2*a - b*Log[1 - c/x^2])^2)/16 + (b^2*c^2*Log[1 + c/x^2])/8 + (b^2*c*x^2*Log[1 + c/x^2])/4 + (a*b*x^4*Log[1 + c/x^2])/4 - (b^2*x^4*Log[1 - c/x^2]*Log[1 + c/x^2])/8 - (b^2*c^2*Log[1 + c/x^2]^2)/16 + (b^2*x^4*Log[1 + c/x^2]^2)/16 + (a*b*c^2*Log[x])/2 + (b^2*c^2*Log[x])/2 + (b^2*c^2*Log[c - x^2])/8 + (b^2*c^2*Log[1 + c/x^2]*Log[c - x^2])/8 + (b^2*c^2*Log[x^2/c]*Log[c - x^2])/8 - (a*b*c^2*Log[c + x^2])/4 + (b^2*c^2*Log[c + x^2])/8 + (b^2*c^2*Log[1 - c/x^2]*Log[c + x^2])/8 + (b^2*c^2*Log[-(x^2/c)]*Log[c + x^2])/8 - (b^2*c^2*Log[(c - x^2)/(2*c)]*Log[c + x^2])/8 - (b^2*c^2*Log[c - x^2]*Log[(c + x^2)/(2*c)])/8 - (b^2*c^2*PolyLog[2, -(c/x^2)])/8 - (b^2*c^2*PolyLog[2, c/x^2])/8 - (b^2*c^2*PolyLog[2, (c - x^2)/(2*c)])/8 - (b^2*c^2*PolyLog[2, (c + x^2)/(2*c)])/8 + (b^2*c^2*PolyLog[2, (c + x^2)/c])/8 + (b^2*c^2*PolyLog[2, 1 - x^2/c])/8","C",59,33,16,2.063,0,"{6099, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2455, 263, 266, 43, 193, 6742, 30, 2557, 12, 2466, 2448, 2462, 260, 2416, 2394, 2393, 2391, 2410, 2395, 36, 29, 2390}"
172,1,404,0,0.6962463,"\int x \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2 \, dx","Int[x*(a + b*ArcTanh[c/x^2])^2,x]","\frac{1}{4} b^2 c \text{PolyLog}\left(2,-\frac{c}{x^2}\right)-\frac{1}{4} b^2 c \text{PolyLog}\left(2,\frac{c}{x^2}\right)-\frac{1}{4} b^2 c \text{PolyLog}\left(2,\frac{c-x^2}{2 c}\right)+\frac{1}{4} b^2 c \text{PolyLog}\left(2,\frac{c+x^2}{2 c}\right)-\frac{1}{4} b^2 c \text{PolyLog}\left(2,\frac{c+x^2}{c}\right)+\frac{1}{4} b^2 c \text{PolyLog}\left(2,1-\frac{x^2}{c}\right)+\frac{1}{2} a b x^2 \log \left(\frac{c}{x^2}+1\right)+\frac{1}{2} a b c \log \left(c+x^2\right)+\frac{1}{8} x^2 \left(1-\frac{c}{x^2}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2+a b c \log (x)+\frac{1}{8} b^2 x^2 \left(\frac{c}{x^2}+1\right) \log ^2\left(\frac{c}{x^2}+1\right)-\frac{1}{4} b^2 x^2 \log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{1}{4} b^2 c \log \left(1-\frac{c}{x^2}\right) \log \left(-c-x^2\right)-\frac{1}{4} b^2 c \log \left(-\frac{x^2}{c}\right) \log \left(-c-x^2\right)+\frac{1}{4} b^2 c \log \left(-c-x^2\right) \log \left(\frac{c-x^2}{2 c}\right)+\frac{1}{4} b^2 c \log \left(\frac{c}{x^2}+1\right) \log \left(x^2-c\right)+\frac{1}{4} b^2 c \log \left(\frac{x^2}{c}\right) \log \left(x^2-c\right)-\frac{1}{4} b^2 c \log \left(x^2-c\right) \log \left(\frac{c+x^2}{2 c}\right)","\frac{1}{2} b^2 c \text{PolyLog}\left(2,\frac{2}{\frac{c}{x^2}+1}-1\right)+\frac{1}{2} x^2 \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)^2-\frac{1}{2} c \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)^2-b c \log \left(2-\frac{2}{\frac{c}{x^2}+1}\right) \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)",1,"((1 - c/x^2)*x^2*(2*a - b*Log[1 - c/x^2])^2)/8 + (a*b*x^2*Log[1 + c/x^2])/2 - (b^2*x^2*Log[1 - c/x^2]*Log[1 + c/x^2])/4 + (b^2*(1 + c/x^2)*x^2*Log[1 + c/x^2]^2)/8 + a*b*c*Log[x] - (b^2*c*Log[1 - c/x^2]*Log[-c - x^2])/4 - (b^2*c*Log[-(x^2/c)]*Log[-c - x^2])/4 + (b^2*c*Log[-c - x^2]*Log[(c - x^2)/(2*c)])/4 + (b^2*c*Log[1 + c/x^2]*Log[-c + x^2])/4 + (b^2*c*Log[x^2/c]*Log[-c + x^2])/4 + (a*b*c*Log[c + x^2])/2 - (b^2*c*Log[-c + x^2]*Log[(c + x^2)/(2*c)])/4 + (b^2*c*PolyLog[2, -(c/x^2)])/4 - (b^2*c*PolyLog[2, c/x^2])/4 - (b^2*c*PolyLog[2, (c - x^2)/(2*c)])/4 + (b^2*c*PolyLog[2, (c + x^2)/(2*c)])/4 - (b^2*c*PolyLog[2, (c + x^2)/c])/4 + (b^2*c*PolyLog[2, 1 - x^2/c])/4","B",34,19,14,1.357,0,"{6099, 2454, 2397, 2392, 2391, 2455, 263, 260, 6715, 2448, 31, 6742, 2556, 12, 2462, 2416, 2394, 2315, 2393}"
173,1,144,0,0.3242796,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2}{x} \, dx","Int[(a + b*ArcTanh[c/x^2])^2/x,x]","\frac{1}{2} b \text{PolyLog}\left(2,1-\frac{2}{1-\frac{c}{x^2}}\right) \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)-\frac{1}{2} b \text{PolyLog}\left(2,\frac{2}{1-\frac{c}{x^2}}-1\right) \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)-\frac{1}{4} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-\frac{c}{x^2}}\right)+\frac{1}{4} b^2 \text{PolyLog}\left(3,\frac{2}{1-\frac{c}{x^2}}-1\right)-\tanh ^{-1}\left(1-\frac{2}{1-\frac{c}{x^2}}\right) \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)^2","\frac{1}{2} b \text{PolyLog}\left(2,1-\frac{2}{1-\frac{c}{x^2}}\right) \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)-\frac{1}{2} b \text{PolyLog}\left(2,\frac{2}{1-\frac{c}{x^2}}-1\right) \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)-\frac{1}{4} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-\frac{c}{x^2}}\right)+\frac{1}{4} b^2 \text{PolyLog}\left(3,\frac{2}{1-\frac{c}{x^2}}-1\right)-\tanh ^{-1}\left(1-\frac{2}{1-\frac{c}{x^2}}\right) \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)^2",1,"-((a + b*ArcCoth[x^2/c])^2*ArcTanh[1 - 2/(1 - c/x^2)]) + (b*(a + b*ArcCoth[x^2/c])*PolyLog[2, 1 - 2/(1 - c/x^2)])/2 - (b*(a + b*ArcCoth[x^2/c])*PolyLog[2, -1 + 2/(1 - c/x^2)])/2 - (b^2*PolyLog[3, 1 - 2/(1 - c/x^2)])/4 + (b^2*PolyLog[3, -1 + 2/(1 - c/x^2)])/4","A",7,6,16,0.3750,1,"{6095, 5914, 6052, 5948, 6058, 6610}"
174,1,207,0,0.5289567,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2}{x^3} \, dx","Int[(a + b*ArcTanh[c/x^2])^2/x^3,x]","\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-\frac{c}{x^2}\right)\right)}{4 c}-\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(\frac{c}{x^2}+1\right)\right)}{4 c}-\frac{b \log \left(\frac{1}{2} \left(\frac{c}{x^2}+1\right)\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)}{4 c}-\frac{b \log \left(\frac{c}{x^2}+1\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)}{4 x^2}+\frac{\left(1-\frac{c}{x^2}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2}{8 c}-\frac{b^2 \left(\frac{c}{x^2}+1\right) \log ^2\left(\frac{c}{x^2}+1\right)}{8 c}-\frac{b^2 \log \left(\frac{1}{2} \left(1-\frac{c}{x^2}\right)\right) \log \left(\frac{c}{x^2}+1\right)}{4 c}","\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\frac{c}{x^2}}\right)}{2 c}-\frac{\left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)^2}{2 c}-\frac{\left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)^2}{2 x^2}+\frac{b \log \left(\frac{2}{1-\frac{c}{x^2}}\right) \left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)}{c}",1,"((1 - c/x^2)*(2*a - b*Log[1 - c/x^2])^2)/(8*c) - (b*(2*a - b*Log[1 - c/x^2])*Log[(1 + c/x^2)/2])/(4*c) - (b^2*Log[(1 - c/x^2)/2]*Log[1 + c/x^2])/(4*c) - (b*(2*a - b*Log[1 - c/x^2])*Log[1 + c/x^2])/(4*x^2) - (b^2*(1 + c/x^2)*Log[1 + c/x^2]^2)/(8*c) + (b^2*PolyLog[2, (1 - c/x^2)/2])/(4*c) - (b^2*PolyLog[2, (1 + c/x^2)/2])/(4*c)","B",28,12,16,0.7500,0,"{6099, 2454, 2389, 2296, 2295, 6715, 2430, 43, 2416, 2394, 2393, 2391}"
175,1,770,0,1.5301034,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2}{x^5} \, dx","Int[(a + b*ArcTanh[c/x^2])^2/x^5,x]","\frac{b^2 \text{PolyLog}\left(2,-\frac{c}{x^2}\right)}{8 c^2}+\frac{b^2 \text{PolyLog}\left(2,\frac{c}{x^2}\right)}{8 c^2}+\frac{b^2 \text{PolyLog}\left(2,\frac{c-x^2}{2 c}\right)}{8 c^2}+\frac{b^2 \text{PolyLog}\left(2,\frac{c+x^2}{2 c}\right)}{8 c^2}-\frac{b^2 \text{PolyLog}\left(2,\frac{c+x^2}{c}\right)}{8 c^2}-\frac{b^2 \text{PolyLog}\left(2,1-\frac{x^2}{c}\right)}{8 c^2}-\frac{b \left(1-\frac{c}{x^2}\right)^2 \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)}{16 c^2}+\frac{a b \log \left(\frac{c+x^2}{x^2}\right)}{4 c^2}-\frac{\left(1-\frac{c}{x^2}\right)^2 \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2}{16 c^2}+\frac{\left(1-\frac{c}{x^2}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2}{8 c^2}-\frac{3 a b}{4 c x^2}-\frac{a b \log \left(\frac{c+x^2}{x^2}\right)}{4 x^4}+\frac{a b}{8 x^4}-\frac{b^2 \left(1-\frac{c}{x^2}\right)^2}{32 c^2}-\frac{b^2 \left(\frac{c}{x^2}+1\right)^2}{32 c^2}-\frac{b^2 \left(\frac{c}{x^2}+1\right)^2 \log ^2\left(\frac{c}{x^2}+1\right)}{16 c^2}+\frac{b^2 \left(\frac{c}{x^2}+1\right) \log ^2\left(\frac{c}{x^2}+1\right)}{8 c^2}-\frac{3 b^2 \left(1-\frac{c}{x^2}\right) \log \left(1-\frac{c}{x^2}\right)}{8 c^2}+\frac{b^2 \log \left(1-\frac{c}{x^2}\right)}{16 c^2}+\frac{b^2 \left(\frac{c}{x^2}+1\right)^2 \log \left(\frac{c}{x^2}+1\right)}{16 c^2}-\frac{b^2 \left(\frac{c}{x^2}+1\right) \log \left(\frac{c}{x^2}+1\right)}{4 c^2}-\frac{b^2 \log \left(\frac{c}{x^2}+1\right) \log \left(c-x^2\right)}{8 c^2}-\frac{b^2 \log \left(\frac{x^2}{c}\right) \log \left(c-x^2\right)}{8 c^2}-\frac{b^2 \log \left(1-\frac{c}{x^2}\right) \log \left(c+x^2\right)}{8 c^2}-\frac{b^2 \log \left(-\frac{x^2}{c}\right) \log \left(c+x^2\right)}{8 c^2}+\frac{b^2 \log \left(\frac{c-x^2}{2 c}\right) \log \left(c+x^2\right)}{8 c^2}+\frac{b^2 \log \left(c-x^2\right) \log \left(\frac{c+x^2}{2 c}\right)}{8 c^2}-\frac{b^2 \left(\frac{c}{x^2}+1\right) \log \left(\frac{c+x^2}{x^2}\right)}{8 c^2}+\frac{b^2 \log \left(\frac{c+x^2}{x^2}\right)}{16 c^2}-\frac{b^2 \log \left(1-\frac{c}{x^2}\right)}{16 x^4}+\frac{b^2 \log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right)}{8 x^4}-\frac{b^2 \log \left(\frac{c+x^2}{x^2}\right)}{16 x^4}+\frac{b^2}{16 x^4}","\frac{\left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)^2}{4 c^2}-\frac{a b}{2 c x^2}-\frac{\left(a+b \coth ^{-1}\left(\frac{x^2}{c}\right)\right)^2}{4 x^4}-\frac{b^2 \log \left(1-\frac{c^2}{x^4}\right)}{4 c^2}-\frac{b^2 \coth ^{-1}\left(\frac{x^2}{c}\right)}{2 c x^2}",1,"-(b^2*(1 - c/x^2)^2)/(32*c^2) - (b^2*(1 + c/x^2)^2)/(32*c^2) + (a*b)/(8*x^4) + b^2/(16*x^4) - (3*a*b)/(4*c*x^2) + (b^2*Log[1 - c/x^2])/(16*c^2) - (3*b^2*(1 - c/x^2)*Log[1 - c/x^2])/(8*c^2) - (b^2*Log[1 - c/x^2])/(16*x^4) - (b*(1 - c/x^2)^2*(2*a - b*Log[1 - c/x^2]))/(16*c^2) + ((1 - c/x^2)*(2*a - b*Log[1 - c/x^2])^2)/(8*c^2) - ((1 - c/x^2)^2*(2*a - b*Log[1 - c/x^2])^2)/(16*c^2) - (b^2*(1 + c/x^2)*Log[1 + c/x^2])/(4*c^2) + (b^2*(1 + c/x^2)^2*Log[1 + c/x^2])/(16*c^2) + (b^2*Log[1 - c/x^2]*Log[1 + c/x^2])/(8*x^4) + (b^2*(1 + c/x^2)*Log[1 + c/x^2]^2)/(8*c^2) - (b^2*(1 + c/x^2)^2*Log[1 + c/x^2]^2)/(16*c^2) - (b^2*Log[1 + c/x^2]*Log[c - x^2])/(8*c^2) - (b^2*Log[x^2/c]*Log[c - x^2])/(8*c^2) - (b^2*Log[1 - c/x^2]*Log[c + x^2])/(8*c^2) - (b^2*Log[-(x^2/c)]*Log[c + x^2])/(8*c^2) + (b^2*Log[(c - x^2)/(2*c)]*Log[c + x^2])/(8*c^2) + (b^2*Log[c - x^2]*Log[(c + x^2)/(2*c)])/(8*c^2) + (a*b*Log[(c + x^2)/x^2])/(4*c^2) + (b^2*Log[(c + x^2)/x^2])/(16*c^2) - (b^2*(1 + c/x^2)*Log[(c + x^2)/x^2])/(8*c^2) - (a*b*Log[(c + x^2)/x^2])/(4*x^4) - (b^2*Log[(c + x^2)/x^2])/(16*x^4) + (b^2*PolyLog[2, -(c/x^2)])/(8*c^2) + (b^2*PolyLog[2, c/x^2])/(8*c^2) + (b^2*PolyLog[2, (c - x^2)/(2*c)])/(8*c^2) + (b^2*PolyLog[2, (c + x^2)/(2*c)])/(8*c^2) - (b^2*PolyLog[2, (c + x^2)/c])/(8*c^2) - (b^2*PolyLog[2, 1 - x^2/c])/(8*c^2)","C",67,23,16,1.438,0,"{6099, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2395, 43, 6742, 30, 2557, 12, 2466, 2462, 260, 2416, 2394, 2315, 2393, 2391}"
176,1,1214,0,2.7123428,"\int x^4 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2 \, dx","Int[x^4*(a + b*ArcTanh[c/x^2])^2,x]","\frac{1}{20} \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2 x^5+\frac{1}{20} b^2 \log ^2\left(\frac{c}{x^2}+1\right) x^5+\frac{1}{5} a b \log \left(\frac{c}{x^2}+1\right) x^5-\frac{1}{10} b^2 \log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right) x^5+\frac{2}{15} a b c x^3-\frac{1}{15} b^2 c \log \left(1-\frac{c}{x^2}\right) x^3+\frac{1}{15} b c \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) x^3+\frac{2}{15} b^2 c \log \left(\frac{c}{x^2}+1\right) x^3+\frac{8}{15} b^2 c^2 x-\frac{1}{5} i b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2+\frac{1}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2-\frac{4}{15} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)+\frac{2}{5} a b c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{4}{15} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)+\frac{2}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)-\frac{1}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right)-\frac{1}{5} b c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)+\frac{1}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{1}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{2}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)+\frac{1}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)-\frac{2}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)+\frac{1}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+\frac{1}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+\frac{1}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)+\frac{2}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)+\frac{1}{5} i b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)-\frac{1}{5} i b^2 c^{5/2} \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{\sqrt{c}-i x}-1\right)-\frac{1}{10} i b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)+\frac{1}{5} b^2 c^{5/2} \text{PolyLog}\left(2,-\frac{x}{\sqrt{c}}\right)-\frac{1}{5} i b^2 c^{5/2} \text{PolyLog}\left(2,-\frac{i x}{\sqrt{c}}\right)+\frac{1}{5} i b^2 c^{5/2} \text{PolyLog}\left(2,\frac{i x}{\sqrt{c}}\right)-\frac{1}{5} b^2 c^{5/2} \text{PolyLog}\left(2,\frac{x}{\sqrt{c}}\right)+\frac{1}{5} b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)-\frac{1}{5} b^2 c^{5/2} \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{x+\sqrt{c}}-1\right)-\frac{1}{10} b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{10} b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{10} i b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)","\frac{1}{20} \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2 x^5+\frac{1}{20} b^2 \log ^2\left(\frac{c}{x^2}+1\right) x^5+\frac{1}{5} a b \log \left(\frac{c}{x^2}+1\right) x^5-\frac{1}{10} b^2 \log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right) x^5+\frac{2}{15} a b c x^3-\frac{1}{15} b^2 c \log \left(1-\frac{c}{x^2}\right) x^3+\frac{1}{15} b c \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) x^3+\frac{2}{15} b^2 c \log \left(\frac{c}{x^2}+1\right) x^3+\frac{8}{15} b^2 c^2 x-\frac{1}{5} i b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2+\frac{1}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2-\frac{4}{15} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)+\frac{2}{5} a b c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{4}{15} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)+\frac{2}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)-\frac{1}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right)-\frac{1}{5} b c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)+\frac{1}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{1}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{2}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)+\frac{1}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)-\frac{2}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)+\frac{1}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+\frac{1}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+\frac{1}{5} b^2 c^{5/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)+\frac{2}{5} b^2 c^{5/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)+\frac{1}{5} i b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)-\frac{1}{5} i b^2 c^{5/2} \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{\sqrt{c}-i x}-1\right)-\frac{1}{10} i b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)+\frac{1}{5} b^2 c^{5/2} \text{PolyLog}\left(2,-\frac{x}{\sqrt{c}}\right)-\frac{1}{5} i b^2 c^{5/2} \text{PolyLog}\left(2,-\frac{i x}{\sqrt{c}}\right)+\frac{1}{5} i b^2 c^{5/2} \text{PolyLog}\left(2,\frac{i x}{\sqrt{c}}\right)-\frac{1}{5} b^2 c^{5/2} \text{PolyLog}\left(2,\frac{x}{\sqrt{c}}\right)+\frac{1}{5} b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)-\frac{1}{5} b^2 c^{5/2} \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{x+\sqrt{c}}-1\right)-\frac{1}{10} b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{10} b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{10} i b^2 c^{5/2} \text{PolyLog}\left(2,1-\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)",1,"(8*b^2*c^2*x)/15 + (2*a*b*c*x^3)/15 + (2*a*b*c^(5/2)*ArcTan[x/Sqrt[c]])/5 - (4*b^2*c^(5/2)*ArcTan[x/Sqrt[c]])/15 - (I/5)*b^2*c^(5/2)*ArcTan[x/Sqrt[c]]^2 - (4*b^2*c^(5/2)*ArcTanh[x/Sqrt[c]])/15 + (b^2*c^(5/2)*ArcTanh[x/Sqrt[c]]^2)/5 + (2*b^2*c^(5/2)*ArcTan[x/Sqrt[c]]*Log[2 - (2*Sqrt[c])/(Sqrt[c] - I*x)])/5 - (b^2*c*x^3*Log[1 - c/x^2])/15 - (b^2*c^(5/2)*ArcTan[x/Sqrt[c]]*Log[1 - c/x^2])/5 + (b*c*x^3*(2*a - b*Log[1 - c/x^2]))/15 - (b*c^(5/2)*ArcTanh[x/Sqrt[c]]*(2*a - b*Log[1 - c/x^2]))/5 + (x^5*(2*a - b*Log[1 - c/x^2])^2)/20 + (2*b^2*c*x^3*Log[1 + c/x^2])/15 + (a*b*x^5*Log[1 + c/x^2])/5 + (b^2*c^(5/2)*ArcTan[x/Sqrt[c]]*Log[1 + c/x^2])/5 - (b^2*c^(5/2)*ArcTanh[x/Sqrt[c]]*Log[1 + c/x^2])/5 - (b^2*x^5*Log[1 - c/x^2]*Log[1 + c/x^2])/10 + (b^2*x^5*Log[1 + c/x^2]^2)/20 - (2*b^2*c^(5/2)*ArcTan[x/Sqrt[c]]*Log[(2*Sqrt[c])/(Sqrt[c] - I*x)])/5 + (b^2*c^(5/2)*ArcTan[x/Sqrt[c]]*Log[((1 + I)*(Sqrt[c] - x))/(Sqrt[c] - I*x)])/5 - (2*b^2*c^(5/2)*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c])/(Sqrt[c] + x)])/5 + (b^2*c^(5/2)*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c]*(Sqrt[-c] - x))/((Sqrt[-c] - Sqrt[c])*(Sqrt[c] + x))])/5 + (b^2*c^(5/2)*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c]*(Sqrt[-c] + x))/((Sqrt[-c] + Sqrt[c])*(Sqrt[c] + x))])/5 + (b^2*c^(5/2)*ArcTan[x/Sqrt[c]]*Log[((1 - I)*(Sqrt[c] + x))/(Sqrt[c] - I*x)])/5 + (2*b^2*c^(5/2)*ArcTanh[x/Sqrt[c]]*Log[2 - (2*Sqrt[c])/(Sqrt[c] + x)])/5 + (I/5)*b^2*c^(5/2)*PolyLog[2, 1 - (2*Sqrt[c])/(Sqrt[c] - I*x)] - (I/5)*b^2*c^(5/2)*PolyLog[2, -1 + (2*Sqrt[c])/(Sqrt[c] - I*x)] - (I/10)*b^2*c^(5/2)*PolyLog[2, 1 - ((1 + I)*(Sqrt[c] - x))/(Sqrt[c] - I*x)] + (b^2*c^(5/2)*PolyLog[2, -(x/Sqrt[c])])/5 - (I/5)*b^2*c^(5/2)*PolyLog[2, ((-I)*x)/Sqrt[c]] + (I/5)*b^2*c^(5/2)*PolyLog[2, (I*x)/Sqrt[c]] - (b^2*c^(5/2)*PolyLog[2, x/Sqrt[c]])/5 + (b^2*c^(5/2)*PolyLog[2, 1 - (2*Sqrt[c])/(Sqrt[c] + x)])/5 - (b^2*c^(5/2)*PolyLog[2, -1 + (2*Sqrt[c])/(Sqrt[c] + x)])/5 - (b^2*c^(5/2)*PolyLog[2, 1 - (2*Sqrt[c]*(Sqrt[-c] - x))/((Sqrt[-c] - Sqrt[c])*(Sqrt[c] + x))])/10 - (b^2*c^(5/2)*PolyLog[2, 1 - (2*Sqrt[c]*(Sqrt[-c] + x))/((Sqrt[-c] + Sqrt[c])*(Sqrt[c] + x))])/10 - (I/10)*b^2*c^(5/2)*PolyLog[2, 1 - ((1 - I)*(Sqrt[c] + x))/(Sqrt[c] - I*x)]","A",97,33,16,2.063,1,"{6099, 2457, 2476, 2448, 263, 207, 2455, 193, 321, 2470, 12, 260, 6688, 5988, 5932, 2447, 302, 6742, 203, 30, 2557, 5992, 5912, 5920, 2402, 2315, 204, 4928, 4848, 2391, 4856, 4924, 4868}"
177,1,1172,0,2.2079568,"\int x^2 \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2 \, dx","Int[x^2*(a + b*ArcTanh[c/x^2])^2,x]","\frac{1}{12} \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2 x^3+\frac{1}{12} b^2 \log ^2\left(\frac{c}{x^2}+1\right) x^3+\frac{1}{3} a b \log \left(\frac{c}{x^2}+1\right) x^3-\frac{1}{6} b^2 \log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right) x^3+\frac{4}{3} a b c x-\frac{2}{3} b^2 c \log \left(1-\frac{c}{x^2}\right) x+\frac{2}{3} b^2 c \log \left(\frac{c}{x^2}+1\right) x+\frac{1}{3} i b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2+\frac{1}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2+\frac{4}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{2}{3} a b c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{4}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{2}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)+\frac{1}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right)-\frac{1}{3} b c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)-\frac{1}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{1}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right)+\frac{2}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)-\frac{1}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)-\frac{2}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)+\frac{1}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+\frac{1}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)+\frac{2}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)-\frac{1}{3} i b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)+\frac{1}{3} i b^2 c^{3/2} \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{\sqrt{c}-i x}-1\right)+\frac{1}{6} i b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)+\frac{1}{3} b^2 c^{3/2} \text{PolyLog}\left(2,-\frac{x}{\sqrt{c}}\right)+\frac{1}{3} i b^2 c^{3/2} \text{PolyLog}\left(2,-\frac{i x}{\sqrt{c}}\right)-\frac{1}{3} i b^2 c^{3/2} \text{PolyLog}\left(2,\frac{i x}{\sqrt{c}}\right)-\frac{1}{3} b^2 c^{3/2} \text{PolyLog}\left(2,\frac{x}{\sqrt{c}}\right)+\frac{1}{3} b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)-\frac{1}{3} b^2 c^{3/2} \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{x+\sqrt{c}}-1\right)-\frac{1}{6} b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{6} b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+\frac{1}{6} i b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)","\frac{1}{12} \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2 x^3+\frac{1}{12} b^2 \log ^2\left(\frac{c}{x^2}+1\right) x^3+\frac{1}{3} a b \log \left(\frac{c}{x^2}+1\right) x^3-\frac{1}{6} b^2 \log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right) x^3+\frac{4}{3} a b c x-\frac{2}{3} b^2 c \log \left(1-\frac{c}{x^2}\right) x+\frac{2}{3} b^2 c \log \left(\frac{c}{x^2}+1\right) x+\frac{1}{3} i b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2+\frac{1}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2+\frac{4}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{2}{3} a b c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{4}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)-\frac{2}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)+\frac{1}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right)-\frac{1}{3} b c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)-\frac{1}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{1}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right)+\frac{2}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)-\frac{1}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)-\frac{2}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)+\frac{1}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+\frac{1}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{3} b^2 c^{3/2} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)+\frac{2}{3} b^2 c^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)-\frac{1}{3} i b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)+\frac{1}{3} i b^2 c^{3/2} \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{\sqrt{c}-i x}-1\right)+\frac{1}{6} i b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)+\frac{1}{3} b^2 c^{3/2} \text{PolyLog}\left(2,-\frac{x}{\sqrt{c}}\right)+\frac{1}{3} i b^2 c^{3/2} \text{PolyLog}\left(2,-\frac{i x}{\sqrt{c}}\right)-\frac{1}{3} i b^2 c^{3/2} \text{PolyLog}\left(2,\frac{i x}{\sqrt{c}}\right)-\frac{1}{3} b^2 c^{3/2} \text{PolyLog}\left(2,\frac{x}{\sqrt{c}}\right)+\frac{1}{3} b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)-\frac{1}{3} b^2 c^{3/2} \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{x+\sqrt{c}}-1\right)-\frac{1}{6} b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{6} b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+\frac{1}{6} i b^2 c^{3/2} \text{PolyLog}\left(2,1-\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)",1,"(4*a*b*c*x)/3 - (2*a*b*c^(3/2)*ArcTan[x/Sqrt[c]])/3 + (4*b^2*c^(3/2)*ArcTan[x/Sqrt[c]])/3 + (I/3)*b^2*c^(3/2)*ArcTan[x/Sqrt[c]]^2 - (4*b^2*c^(3/2)*ArcTanh[x/Sqrt[c]])/3 + (b^2*c^(3/2)*ArcTanh[x/Sqrt[c]]^2)/3 - (2*b^2*c^(3/2)*ArcTan[x/Sqrt[c]]*Log[2 - (2*Sqrt[c])/(Sqrt[c] - I*x)])/3 - (2*b^2*c*x*Log[1 - c/x^2])/3 + (b^2*c^(3/2)*ArcTan[x/Sqrt[c]]*Log[1 - c/x^2])/3 - (b*c^(3/2)*ArcTanh[x/Sqrt[c]]*(2*a - b*Log[1 - c/x^2]))/3 + (x^3*(2*a - b*Log[1 - c/x^2])^2)/12 + (2*b^2*c*x*Log[1 + c/x^2])/3 + (a*b*x^3*Log[1 + c/x^2])/3 - (b^2*c^(3/2)*ArcTan[x/Sqrt[c]]*Log[1 + c/x^2])/3 - (b^2*c^(3/2)*ArcTanh[x/Sqrt[c]]*Log[1 + c/x^2])/3 - (b^2*x^3*Log[1 - c/x^2]*Log[1 + c/x^2])/6 + (b^2*x^3*Log[1 + c/x^2]^2)/12 + (2*b^2*c^(3/2)*ArcTan[x/Sqrt[c]]*Log[(2*Sqrt[c])/(Sqrt[c] - I*x)])/3 - (b^2*c^(3/2)*ArcTan[x/Sqrt[c]]*Log[((1 + I)*(Sqrt[c] - x))/(Sqrt[c] - I*x)])/3 - (2*b^2*c^(3/2)*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c])/(Sqrt[c] + x)])/3 + (b^2*c^(3/2)*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c]*(Sqrt[-c] - x))/((Sqrt[-c] - Sqrt[c])*(Sqrt[c] + x))])/3 + (b^2*c^(3/2)*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c]*(Sqrt[-c] + x))/((Sqrt[-c] + Sqrt[c])*(Sqrt[c] + x))])/3 - (b^2*c^(3/2)*ArcTan[x/Sqrt[c]]*Log[((1 - I)*(Sqrt[c] + x))/(Sqrt[c] - I*x)])/3 + (2*b^2*c^(3/2)*ArcTanh[x/Sqrt[c]]*Log[2 - (2*Sqrt[c])/(Sqrt[c] + x)])/3 - (I/3)*b^2*c^(3/2)*PolyLog[2, 1 - (2*Sqrt[c])/(Sqrt[c] - I*x)] + (I/3)*b^2*c^(3/2)*PolyLog[2, -1 + (2*Sqrt[c])/(Sqrt[c] - I*x)] + (I/6)*b^2*c^(3/2)*PolyLog[2, 1 - ((1 + I)*(Sqrt[c] - x))/(Sqrt[c] - I*x)] + (b^2*c^(3/2)*PolyLog[2, -(x/Sqrt[c])])/3 + (I/3)*b^2*c^(3/2)*PolyLog[2, ((-I)*x)/Sqrt[c]] - (I/3)*b^2*c^(3/2)*PolyLog[2, (I*x)/Sqrt[c]] - (b^2*c^(3/2)*PolyLog[2, x/Sqrt[c]])/3 + (b^2*c^(3/2)*PolyLog[2, 1 - (2*Sqrt[c])/(Sqrt[c] + x)])/3 - (b^2*c^(3/2)*PolyLog[2, -1 + (2*Sqrt[c])/(Sqrt[c] + x)])/3 - (b^2*c^(3/2)*PolyLog[2, 1 - (2*Sqrt[c]*(Sqrt[-c] - x))/((Sqrt[-c] - Sqrt[c])*(Sqrt[c] + x))])/6 - (b^2*c^(3/2)*PolyLog[2, 1 - (2*Sqrt[c]*(Sqrt[-c] + x))/((Sqrt[-c] + Sqrt[c])*(Sqrt[c] + x))])/6 + (I/6)*b^2*c^(3/2)*PolyLog[2, 1 - ((1 - I)*(Sqrt[c] + x))/(Sqrt[c] - I*x)]","A",79,33,16,2.063,1,"{6099, 2457, 2471, 2448, 263, 207, 2470, 12, 260, 6688, 5988, 5932, 2447, 2455, 193, 321, 6742, 203, 30, 2557, 5992, 5912, 5920, 2402, 2315, 2476, 204, 4928, 4848, 2391, 4856, 4924, 4868}"
178,1,1549,0,2.2489071,"\int \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2 \, dx","Int[(a + b*ArcTanh[c/x^2])^2,x]","x a^2+2 b \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) a-2 b \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) a-b x \log \left(1-\frac{c}{x^2}\right) a+b x \log \left(\frac{c}{x^2}+1\right) a+\frac{1}{4} b^2 x \log ^2\left(1-\frac{c}{x^2}\right)+\frac{1}{4} b^2 x \log ^2\left(\frac{c}{x^2}+1\right)+\frac{1}{4} b^2 \sqrt{-c} \log ^2\left(\sqrt{-c}-x\right)+\frac{1}{4} b^2 \sqrt{c} \log ^2\left(\sqrt{c}-x\right)-\frac{1}{4} b^2 \sqrt{-c} \log ^2\left(x+\sqrt{-c}\right)-\frac{1}{4} b^2 \sqrt{c} \log ^2\left(x+\sqrt{c}\right)-b^2 \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right)-b^2 \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{1}{2} b^2 x \log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{1}{2} b^2 \sqrt{-c} \log \left(\frac{c}{x^2}+1\right) \log \left(\sqrt{-c}-x\right)-\frac{1}{2} b^2 \sqrt{c} \log \left(1-\frac{c}{x^2}\right) \log \left(\sqrt{c}-x\right)-2 b^2 \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)+b^2 \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)-b^2 \sqrt{-c} \log \left(\sqrt{-c}-x\right) \log \left(\frac{x}{\sqrt{-c}}\right)-b^2 \sqrt{c} \log \left(\sqrt{c}-x\right) \log \left(\frac{x}{\sqrt{c}}\right)+\frac{1}{2} b^2 \sqrt{-c} \log \left(\frac{c}{x^2}+1\right) \log \left(x+\sqrt{-c}\right)-\frac{1}{2} b^2 \sqrt{-c} \log \left(\frac{\sqrt{-c}-x}{2 \sqrt{-c}}\right) \log \left(x+\sqrt{-c}\right)+b^2 \sqrt{-c} \log \left(-\frac{x}{\sqrt{-c}}\right) \log \left(x+\sqrt{-c}\right)+\frac{1}{2} b^2 \sqrt{-c} \log \left(\sqrt{-c}-x\right) \log \left(\frac{x+\sqrt{-c}}{2 \sqrt{-c}}\right)-2 b^2 \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)+b^2 \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+b^2 \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+\frac{1}{2} b^2 \sqrt{c} \log \left(1-\frac{c}{x^2}\right) \log \left(x+\sqrt{c}\right)-\frac{1}{2} b^2 \sqrt{c} \log \left(\frac{\sqrt{c}-x}{2 \sqrt{c}}\right) \log \left(x+\sqrt{c}\right)+b^2 \sqrt{c} \log \left(-\frac{x}{\sqrt{c}}\right) \log \left(x+\sqrt{c}\right)+\frac{1}{2} b^2 \sqrt{c} \log \left(\sqrt{c}-x\right) \log \left(\frac{x+\sqrt{c}}{2 \sqrt{c}}\right)+b^2 \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)+i b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)-\frac{1}{2} i b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)+b^2 \sqrt{c} \text{PolyLog}\left(2,-\frac{x}{\sqrt{c}}\right)-i b^2 \sqrt{c} \text{PolyLog}\left(2,-\frac{i x}{\sqrt{c}}\right)+i b^2 \sqrt{c} \text{PolyLog}\left(2,\frac{i x}{\sqrt{c}}\right)-b^2 \sqrt{c} \text{PolyLog}\left(2,\frac{x}{\sqrt{c}}\right)-\frac{1}{2} b^2 \sqrt{c} \text{PolyLog}\left(2,\frac{x+\sqrt{c}}{2 \sqrt{c}}\right)+\frac{1}{2} b^2 \sqrt{-c} \text{PolyLog}\left(2,\frac{1}{2} \left(1-\frac{x}{\sqrt{-c}}\right)\right)-b^2 \sqrt{-c} \text{PolyLog}\left(2,1-\frac{x}{\sqrt{-c}}\right)+b^2 \sqrt{-c} \text{PolyLog}\left(2,\frac{x}{\sqrt{-c}}+1\right)-\frac{1}{2} b^2 \sqrt{-c} \text{PolyLog}\left(2,\frac{c-\sqrt{-c} x}{2 c}\right)-b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{x}{\sqrt{c}}\right)+\frac{1}{2} b^2 \sqrt{c} \text{PolyLog}\left(2,\frac{1}{2}-\frac{x}{2 \sqrt{c}}\right)+b^2 \sqrt{c} \text{PolyLog}\left(2,\frac{x}{\sqrt{c}}+1\right)+b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)-\frac{1}{2} b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{2} b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{2} i b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)","x a^2+2 b \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) a-2 b \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) a-b x \log \left(1-\frac{c}{x^2}\right) a+b x \log \left(\frac{c}{x^2}+1\right) a+\frac{1}{4} b^2 x \log ^2\left(1-\frac{c}{x^2}\right)+\frac{1}{4} b^2 x \log ^2\left(\frac{c}{x^2}+1\right)+\frac{1}{4} b^2 \sqrt{-c} \log ^2\left(\sqrt{-c}-x\right)+\frac{1}{4} b^2 \sqrt{c} \log ^2\left(\sqrt{c}-x\right)-\frac{1}{4} b^2 \sqrt{-c} \log ^2\left(x+\sqrt{-c}\right)-\frac{1}{4} b^2 \sqrt{c} \log ^2\left(x+\sqrt{c}\right)-b^2 \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right)-b^2 \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{1}{2} b^2 x \log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right)-\frac{1}{2} b^2 \sqrt{-c} \log \left(\frac{c}{x^2}+1\right) \log \left(\sqrt{-c}-x\right)-\frac{1}{2} b^2 \sqrt{c} \log \left(1-\frac{c}{x^2}\right) \log \left(\sqrt{c}-x\right)-2 b^2 \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)+b^2 \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)-b^2 \sqrt{-c} \log \left(\sqrt{-c}-x\right) \log \left(\frac{x}{\sqrt{-c}}\right)-b^2 \sqrt{c} \log \left(\sqrt{c}-x\right) \log \left(\frac{x}{\sqrt{c}}\right)+\frac{1}{2} b^2 \sqrt{-c} \log \left(\frac{c}{x^2}+1\right) \log \left(x+\sqrt{-c}\right)-\frac{1}{2} b^2 \sqrt{-c} \log \left(\frac{\sqrt{-c}-x}{2 \sqrt{-c}}\right) \log \left(x+\sqrt{-c}\right)+b^2 \sqrt{-c} \log \left(-\frac{x}{\sqrt{-c}}\right) \log \left(x+\sqrt{-c}\right)+\frac{1}{2} b^2 \sqrt{-c} \log \left(\sqrt{-c}-x\right) \log \left(\frac{x+\sqrt{-c}}{2 \sqrt{-c}}\right)-2 b^2 \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)+b^2 \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+b^2 \sqrt{c} \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)+\frac{1}{2} b^2 \sqrt{c} \log \left(1-\frac{c}{x^2}\right) \log \left(x+\sqrt{c}\right)-\frac{1}{2} b^2 \sqrt{c} \log \left(\frac{\sqrt{c}-x}{2 \sqrt{c}}\right) \log \left(x+\sqrt{c}\right)+b^2 \sqrt{c} \log \left(-\frac{x}{\sqrt{c}}\right) \log \left(x+\sqrt{c}\right)+\frac{1}{2} b^2 \sqrt{c} \log \left(\sqrt{c}-x\right) \log \left(\frac{x+\sqrt{c}}{2 \sqrt{c}}\right)+b^2 \sqrt{c} \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)+i b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right)-\frac{1}{2} i b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right)+b^2 \sqrt{c} \text{PolyLog}\left(2,-\frac{x}{\sqrt{c}}\right)-i b^2 \sqrt{c} \text{PolyLog}\left(2,-\frac{i x}{\sqrt{c}}\right)+i b^2 \sqrt{c} \text{PolyLog}\left(2,\frac{i x}{\sqrt{c}}\right)-b^2 \sqrt{c} \text{PolyLog}\left(2,\frac{x}{\sqrt{c}}\right)-\frac{1}{2} b^2 \sqrt{c} \text{PolyLog}\left(2,\frac{x+\sqrt{c}}{2 \sqrt{c}}\right)+\frac{1}{2} b^2 \sqrt{-c} \text{PolyLog}\left(2,\frac{1}{2} \left(1-\frac{x}{\sqrt{-c}}\right)\right)-b^2 \sqrt{-c} \text{PolyLog}\left(2,1-\frac{x}{\sqrt{-c}}\right)+b^2 \sqrt{-c} \text{PolyLog}\left(2,\frac{x}{\sqrt{-c}}+1\right)-\frac{1}{2} b^2 \sqrt{-c} \text{PolyLog}\left(2,\frac{c-\sqrt{-c} x}{2 c}\right)-b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{x}{\sqrt{c}}\right)+\frac{1}{2} b^2 \sqrt{c} \text{PolyLog}\left(2,\frac{1}{2}-\frac{x}{2 \sqrt{c}}\right)+b^2 \sqrt{c} \text{PolyLog}\left(2,\frac{x}{\sqrt{c}}+1\right)+b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right)-\frac{1}{2} b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{2} b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right)-\frac{1}{2} i b^2 \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right)",1,"a^2*x + 2*a*b*Sqrt[c]*ArcTan[x/Sqrt[c]] - 2*a*b*Sqrt[c]*ArcTanh[x/Sqrt[c]] - a*b*x*Log[1 - c/x^2] - b^2*Sqrt[c]*ArcTan[x/Sqrt[c]]*Log[1 - c/x^2] + (b^2*x*Log[1 - c/x^2]^2)/4 + a*b*x*Log[1 + c/x^2] - b^2*Sqrt[c]*ArcTanh[x/Sqrt[c]]*Log[1 + c/x^2] - (b^2*x*Log[1 - c/x^2]*Log[1 + c/x^2])/2 + (b^2*x*Log[1 + c/x^2]^2)/4 - (b^2*Sqrt[-c]*Log[1 + c/x^2]*Log[Sqrt[-c] - x])/2 + (b^2*Sqrt[-c]*Log[Sqrt[-c] - x]^2)/4 - (b^2*Sqrt[c]*Log[1 - c/x^2]*Log[Sqrt[c] - x])/2 + (b^2*Sqrt[c]*Log[Sqrt[c] - x]^2)/4 - 2*b^2*Sqrt[c]*ArcTan[x/Sqrt[c]]*Log[(2*Sqrt[c])/(Sqrt[c] - I*x)] + b^2*Sqrt[c]*ArcTan[x/Sqrt[c]]*Log[((1 + I)*(Sqrt[c] - x))/(Sqrt[c] - I*x)] - b^2*Sqrt[-c]*Log[Sqrt[-c] - x]*Log[x/Sqrt[-c]] - b^2*Sqrt[c]*Log[Sqrt[c] - x]*Log[x/Sqrt[c]] + (b^2*Sqrt[-c]*Log[1 + c/x^2]*Log[Sqrt[-c] + x])/2 - (b^2*Sqrt[-c]*Log[(Sqrt[-c] - x)/(2*Sqrt[-c])]*Log[Sqrt[-c] + x])/2 + b^2*Sqrt[-c]*Log[-(x/Sqrt[-c])]*Log[Sqrt[-c] + x] - (b^2*Sqrt[-c]*Log[Sqrt[-c] + x]^2)/4 + (b^2*Sqrt[-c]*Log[Sqrt[-c] - x]*Log[(Sqrt[-c] + x)/(2*Sqrt[-c])])/2 - 2*b^2*Sqrt[c]*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c])/(Sqrt[c] + x)] + b^2*Sqrt[c]*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c]*(Sqrt[-c] - x))/((Sqrt[-c] - Sqrt[c])*(Sqrt[c] + x))] + b^2*Sqrt[c]*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c]*(Sqrt[-c] + x))/((Sqrt[-c] + Sqrt[c])*(Sqrt[c] + x))] + (b^2*Sqrt[c]*Log[1 - c/x^2]*Log[Sqrt[c] + x])/2 - (b^2*Sqrt[c]*Log[(Sqrt[c] - x)/(2*Sqrt[c])]*Log[Sqrt[c] + x])/2 + b^2*Sqrt[c]*Log[-(x/Sqrt[c])]*Log[Sqrt[c] + x] - (b^2*Sqrt[c]*Log[Sqrt[c] + x]^2)/4 + (b^2*Sqrt[c]*Log[Sqrt[c] - x]*Log[(Sqrt[c] + x)/(2*Sqrt[c])])/2 + b^2*Sqrt[c]*ArcTan[x/Sqrt[c]]*Log[((1 - I)*(Sqrt[c] + x))/(Sqrt[c] - I*x)] + I*b^2*Sqrt[c]*PolyLog[2, 1 - (2*Sqrt[c])/(Sqrt[c] - I*x)] - (I/2)*b^2*Sqrt[c]*PolyLog[2, 1 - ((1 + I)*(Sqrt[c] - x))/(Sqrt[c] - I*x)] + b^2*Sqrt[c]*PolyLog[2, -(x/Sqrt[c])] - I*b^2*Sqrt[c]*PolyLog[2, ((-I)*x)/Sqrt[c]] + I*b^2*Sqrt[c]*PolyLog[2, (I*x)/Sqrt[c]] - b^2*Sqrt[c]*PolyLog[2, x/Sqrt[c]] - (b^2*Sqrt[c]*PolyLog[2, (Sqrt[c] + x)/(2*Sqrt[c])])/2 + (b^2*Sqrt[-c]*PolyLog[2, (1 - x/Sqrt[-c])/2])/2 - b^2*Sqrt[-c]*PolyLog[2, 1 - x/Sqrt[-c]] + b^2*Sqrt[-c]*PolyLog[2, 1 + x/Sqrt[-c]] - (b^2*Sqrt[-c]*PolyLog[2, (c - Sqrt[-c]*x)/(2*c)])/2 - b^2*Sqrt[c]*PolyLog[2, 1 - x/Sqrt[c]] + (b^2*Sqrt[c]*PolyLog[2, 1/2 - x/(2*Sqrt[c])])/2 + b^2*Sqrt[c]*PolyLog[2, 1 + x/Sqrt[c]] + b^2*Sqrt[c]*PolyLog[2, 1 - (2*Sqrt[c])/(Sqrt[c] + x)] - (b^2*Sqrt[c]*PolyLog[2, 1 - (2*Sqrt[c]*(Sqrt[-c] - x))/((Sqrt[-c] - Sqrt[c])*(Sqrt[c] + x))])/2 - (b^2*Sqrt[c]*PolyLog[2, 1 - (2*Sqrt[c]*(Sqrt[-c] + x))/((Sqrt[-c] + Sqrt[c])*(Sqrt[c] + x))])/2 - (I/2)*b^2*Sqrt[c]*PolyLog[2, 1 - ((1 - I)*(Sqrt[c] + x))/(Sqrt[c] - I*x)]","A",99,29,12,2.417,1,"{6093, 2448, 263, 207, 2450, 2476, 2462, 260, 2416, 2394, 2315, 2390, 2301, 2393, 2391, 203, 2556, 12, 2470, 6688, 5992, 5912, 5920, 2402, 2447, 204, 4928, 4848, 4856}"
179,1,1117,0,2.1503706,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2}{x^2} \, dx","Int[(a + b*ArcTanh[c/x^2])^2/x^2,x]","-\frac{i \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{\sqrt{c}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{\sqrt{c}}-\frac{\log ^2\left(\frac{c}{x^2}+1\right) b^2}{4 x}-\frac{2 \cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{\sqrt{c}}-\frac{2 \coth ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{\sqrt{c}}-\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{\sqrt{c}}+\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{\sqrt{c}}+\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{\sqrt{c}}+\frac{\cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right) b^2}{\sqrt{c}}-\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{x}+\frac{\coth ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{\sqrt{c}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{\sqrt{c}}+\frac{\log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{2 x}+\frac{2 \cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{\sqrt{c}}-\frac{\cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(1-\frac{\sqrt{c}}{x}\right)}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{\sqrt{c}}+\frac{2 \coth ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2}{\frac{\sqrt{c}}{x}+1}\right) b^2}{\sqrt{c}}-\frac{\coth ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(-\frac{2 \sqrt{c} \left(1-\frac{\sqrt{-c}}{x}\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\frac{\sqrt{c}}{x}+1\right)}\right) b^2}{\sqrt{c}}-\frac{\coth ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\frac{\sqrt{-c}}{x}+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\frac{\sqrt{c}}{x}+1\right)}\right) b^2}{\sqrt{c}}-\frac{\cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(\frac{\sqrt{c}}{x}+1\right)}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{\sqrt{c}}-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{\sqrt{c}}-\frac{i \text{PolyLog}\left(2,1-\frac{2}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{\sqrt{c}}+\frac{i \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\frac{\sqrt{c}}{x}\right)}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{2 \sqrt{c}}-\frac{\text{PolyLog}\left(2,1-\frac{2}{\frac{\sqrt{c}}{x}+1}\right) b^2}{\sqrt{c}}+\frac{\text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\frac{\sqrt{-c}}{x}\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\frac{\sqrt{c}}{x}+1\right)}+1\right) b^2}{2 \sqrt{c}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\frac{\sqrt{-c}}{x}+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\frac{\sqrt{c}}{x}+1\right)}\right) b^2}{2 \sqrt{c}}+\frac{i \text{PolyLog}\left(2,1-\frac{(1-i) \left(\frac{\sqrt{c}}{x}+1\right)}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{2 \sqrt{c}}-\frac{i \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{\sqrt{c}-i x}-1\right) b^2}{\sqrt{c}}+\frac{\text{PolyLog}\left(2,\frac{2 \sqrt{c}}{x+\sqrt{c}}-1\right) b^2}{\sqrt{c}}-\frac{2 a \cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) b}{\sqrt{c}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{\sqrt{c}}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{x}-\frac{a \log \left(\frac{c}{x^2}+1\right) b}{x}+\frac{2 a b}{x}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2}{4 x}","-\frac{i \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{\sqrt{c}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{\sqrt{c}}-\frac{\log ^2\left(\frac{c}{x^2}+1\right) b^2}{4 x}-\frac{2 \cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{\sqrt{c}}-\frac{2 \coth ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{\sqrt{c}}-\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{\sqrt{c}}+\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{\sqrt{c}}+\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{\sqrt{c}}+\frac{\cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right) b^2}{\sqrt{c}}-\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{x}+\frac{\coth ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{\sqrt{c}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{\sqrt{c}}+\frac{\log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{2 x}+\frac{2 \cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{\sqrt{c}}-\frac{\cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(1-\frac{\sqrt{c}}{x}\right)}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{\sqrt{c}}+\frac{2 \coth ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2}{\frac{\sqrt{c}}{x}+1}\right) b^2}{\sqrt{c}}-\frac{\coth ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(-\frac{2 \sqrt{c} \left(1-\frac{\sqrt{-c}}{x}\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\frac{\sqrt{c}}{x}+1\right)}\right) b^2}{\sqrt{c}}-\frac{\coth ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\frac{\sqrt{-c}}{x}+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\frac{\sqrt{c}}{x}+1\right)}\right) b^2}{\sqrt{c}}-\frac{\cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(\frac{\sqrt{c}}{x}+1\right)}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{\sqrt{c}}-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{\sqrt{c}}-\frac{i \text{PolyLog}\left(2,1-\frac{2}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{\sqrt{c}}+\frac{i \text{PolyLog}\left(2,1-\frac{(1+i) \left(1-\frac{\sqrt{c}}{x}\right)}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{2 \sqrt{c}}-\frac{\text{PolyLog}\left(2,1-\frac{2}{\frac{\sqrt{c}}{x}+1}\right) b^2}{\sqrt{c}}+\frac{\text{PolyLog}\left(2,\frac{2 \sqrt{c} \left(1-\frac{\sqrt{-c}}{x}\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(\frac{\sqrt{c}}{x}+1\right)}+1\right) b^2}{2 \sqrt{c}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\frac{\sqrt{-c}}{x}+1\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(\frac{\sqrt{c}}{x}+1\right)}\right) b^2}{2 \sqrt{c}}+\frac{i \text{PolyLog}\left(2,1-\frac{(1-i) \left(\frac{\sqrt{c}}{x}+1\right)}{1-\frac{i \sqrt{c}}{x}}\right) b^2}{2 \sqrt{c}}-\frac{i \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{\sqrt{c}-i x}-1\right) b^2}{\sqrt{c}}+\frac{\text{PolyLog}\left(2,\frac{2 \sqrt{c}}{x+\sqrt{c}}-1\right) b^2}{\sqrt{c}}-\frac{2 a \cot ^{-1}\left(\frac{x}{\sqrt{c}}\right) b}{\sqrt{c}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{\sqrt{c}}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{x}-\frac{a \log \left(\frac{c}{x^2}+1\right) b}{x}+\frac{2 a b}{x}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2}{4 x}",1,"(2*a*b)/x - (2*a*b*ArcCot[x/Sqrt[c]])/Sqrt[c] - (2*b^2*ArcCot[x/Sqrt[c]])/Sqrt[c] - (2*b^2*ArcCoth[x/Sqrt[c]])/Sqrt[c] - (2*b^2*ArcTan[x/Sqrt[c]])/Sqrt[c] - (I*b^2*ArcTan[x/Sqrt[c]]^2)/Sqrt[c] + (2*b^2*ArcTanh[x/Sqrt[c]])/Sqrt[c] - (b^2*ArcTanh[x/Sqrt[c]]^2)/Sqrt[c] + (2*b^2*ArcTan[x/Sqrt[c]]*Log[2 - (2*Sqrt[c])/(Sqrt[c] - I*x)])/Sqrt[c] - (b^2*Log[1 - c/x^2])/x + (b^2*ArcCot[x/Sqrt[c]]*Log[1 - c/x^2])/Sqrt[c] - (b*(2*a - b*Log[1 - c/x^2]))/x + (b*ArcTanh[x/Sqrt[c]]*(2*a - b*Log[1 - c/x^2]))/Sqrt[c] - (2*a - b*Log[1 - c/x^2])^2/(4*x) - (a*b*Log[1 + c/x^2])/x + (b^2*ArcCoth[x/Sqrt[c]]*Log[1 + c/x^2])/Sqrt[c] + (b^2*ArcTan[x/Sqrt[c]]*Log[1 + c/x^2])/Sqrt[c] + (b^2*Log[1 - c/x^2]*Log[1 + c/x^2])/(2*x) - (b^2*Log[1 + c/x^2]^2)/(4*x) + (2*b^2*ArcCot[x/Sqrt[c]]*Log[2/(1 - (I*Sqrt[c])/x)])/Sqrt[c] - (b^2*ArcCot[x/Sqrt[c]]*Log[((1 + I)*(1 - Sqrt[c]/x))/(1 - (I*Sqrt[c])/x)])/Sqrt[c] + (2*b^2*ArcCoth[x/Sqrt[c]]*Log[2/(1 + Sqrt[c]/x)])/Sqrt[c] - (b^2*ArcCoth[x/Sqrt[c]]*Log[(-2*Sqrt[c]*(1 - Sqrt[-c]/x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]/x))])/Sqrt[c] - (b^2*ArcCoth[x/Sqrt[c]]*Log[(2*Sqrt[c]*(1 + Sqrt[-c]/x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]/x))])/Sqrt[c] - (b^2*ArcCot[x/Sqrt[c]]*Log[((1 - I)*(1 + Sqrt[c]/x))/(1 - (I*Sqrt[c])/x)])/Sqrt[c] - (2*b^2*ArcTanh[x/Sqrt[c]]*Log[2 - (2*Sqrt[c])/(Sqrt[c] + x)])/Sqrt[c] - (I*b^2*PolyLog[2, 1 - 2/(1 - (I*Sqrt[c])/x)])/Sqrt[c] + ((I/2)*b^2*PolyLog[2, 1 - ((1 + I)*(1 - Sqrt[c]/x))/(1 - (I*Sqrt[c])/x)])/Sqrt[c] - (b^2*PolyLog[2, 1 - 2/(1 + Sqrt[c]/x)])/Sqrt[c] + (b^2*PolyLog[2, 1 + (2*Sqrt[c]*(1 - Sqrt[-c]/x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]/x))])/(2*Sqrt[c]) + (b^2*PolyLog[2, 1 - (2*Sqrt[c]*(1 + Sqrt[-c]/x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]/x))])/(2*Sqrt[c]) + ((I/2)*b^2*PolyLog[2, 1 - ((1 - I)*(1 + Sqrt[c]/x))/(1 - (I*Sqrt[c])/x)])/Sqrt[c] - (I*b^2*PolyLog[2, -1 + (2*Sqrt[c])/(Sqrt[c] - I*x)])/Sqrt[c] + (b^2*PolyLog[2, -1 + (2*Sqrt[c])/(Sqrt[c] + x)])/Sqrt[c]","A",71,29,16,1.812,1,"{6099, 2457, 2476, 2455, 263, 325, 207, 206, 2470, 12, 260, 6688, 5988, 5932, 2447, 6715, 2448, 321, 6742, 203, 2556, 5992, 5920, 2402, 2315, 4928, 4856, 4924, 4868}"
180,1,1263,0,2.5847634,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2}{x^4} \, dx","Int[(a + b*ArcTanh[c/x^2])^2/x^4,x]","\frac{i \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{3 c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{3 c^{3/2}}-\frac{\log ^2\left(\frac{c}{x^2}+1\right) b^2}{12 x^3}+\frac{4 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}+\frac{4 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}-\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{3 c^{3/2}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right) b^2}{3 c^{3/2}}+\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{3 c x}-\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{9 x^3}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{3 c^{3/2}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{3 c^{3/2}}+\frac{\log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{6 x^3}-\frac{2 \log \left(\frac{c}{x^2}+1\right) b^2}{3 c x}+\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{3 c^{3/2}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right) b^2}{3 c^{3/2}}+\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{3 c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{3 c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{3 c^{3/2}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right) b^2}{3 c^{3/2}}-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{3 c^{3/2}}-\frac{i \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{3 c^{3/2}}+\frac{i \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{\sqrt{c}-i x}-1\right) b^2}{3 c^{3/2}}+\frac{i \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right) b^2}{6 c^{3/2}}-\frac{\text{PolyLog}\left(2,-\frac{x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}+\frac{i \text{PolyLog}\left(2,-\frac{i x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}-\frac{i \text{PolyLog}\left(2,\frac{i x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}+\frac{\text{PolyLog}\left(2,\frac{x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}-\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{3 c^{3/2}}+\frac{\text{PolyLog}\left(2,\frac{2 \sqrt{c}}{x+\sqrt{c}}-1\right) b^2}{3 c^{3/2}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{6 c^{3/2}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{6 c^{3/2}}+\frac{i \text{PolyLog}\left(2,1-\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right) b^2}{6 c^{3/2}}-\frac{2 a \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) b}{3 c^{3/2}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{3 c^{3/2}}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{3 c x}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{9 x^3}-\frac{a \log \left(\frac{c}{x^2}+1\right) b}{3 x^3}-\frac{2 a b}{3 c x}+\frac{2 a b}{9 x^3}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2}{12 x^3}","\frac{i \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{3 c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{3 c^{3/2}}-\frac{\log ^2\left(\frac{c}{x^2}+1\right) b^2}{12 x^3}+\frac{4 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}+\frac{4 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}-\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{3 c^{3/2}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right) b^2}{3 c^{3/2}}+\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{3 c x}-\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{9 x^3}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{3 c^{3/2}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{3 c^{3/2}}+\frac{\log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{6 x^3}-\frac{2 \log \left(\frac{c}{x^2}+1\right) b^2}{3 c x}+\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{3 c^{3/2}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right) b^2}{3 c^{3/2}}+\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{3 c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{3 c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{3 c^{3/2}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right) b^2}{3 c^{3/2}}-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{3 c^{3/2}}-\frac{i \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{3 c^{3/2}}+\frac{i \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{\sqrt{c}-i x}-1\right) b^2}{3 c^{3/2}}+\frac{i \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right) b^2}{6 c^{3/2}}-\frac{\text{PolyLog}\left(2,-\frac{x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}+\frac{i \text{PolyLog}\left(2,-\frac{i x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}-\frac{i \text{PolyLog}\left(2,\frac{i x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}+\frac{\text{PolyLog}\left(2,\frac{x}{\sqrt{c}}\right) b^2}{3 c^{3/2}}-\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{3 c^{3/2}}+\frac{\text{PolyLog}\left(2,\frac{2 \sqrt{c}}{x+\sqrt{c}}-1\right) b^2}{3 c^{3/2}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{6 c^{3/2}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{6 c^{3/2}}+\frac{i \text{PolyLog}\left(2,1-\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right) b^2}{6 c^{3/2}}-\frac{2 a \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) b}{3 c^{3/2}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{3 c^{3/2}}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{3 c x}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{9 x^3}-\frac{a \log \left(\frac{c}{x^2}+1\right) b}{3 x^3}-\frac{2 a b}{3 c x}+\frac{2 a b}{9 x^3}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2}{12 x^3}",1,"(2*a*b)/(9*x^3) - (2*a*b)/(3*c*x) - (2*a*b*ArcTan[x/Sqrt[c]])/(3*c^(3/2)) + (4*b^2*ArcTan[x/Sqrt[c]])/(3*c^(3/2)) + ((I/3)*b^2*ArcTan[x/Sqrt[c]]^2)/c^(3/2) + (4*b^2*ArcTanh[x/Sqrt[c]])/(3*c^(3/2)) - (b^2*ArcTanh[x/Sqrt[c]]^2)/(3*c^(3/2)) - (2*b^2*ArcTan[x/Sqrt[c]]*Log[2 - (2*Sqrt[c])/(Sqrt[c] - I*x)])/(3*c^(3/2)) - (b^2*Log[1 - c/x^2])/(9*x^3) + (b^2*Log[1 - c/x^2])/(3*c*x) + (b^2*ArcTan[x/Sqrt[c]]*Log[1 - c/x^2])/(3*c^(3/2)) - (b*(2*a - b*Log[1 - c/x^2]))/(9*x^3) - (b*(2*a - b*Log[1 - c/x^2]))/(3*c*x) + (b*ArcTanh[x/Sqrt[c]]*(2*a - b*Log[1 - c/x^2]))/(3*c^(3/2)) - (2*a - b*Log[1 - c/x^2])^2/(12*x^3) - (a*b*Log[1 + c/x^2])/(3*x^3) - (2*b^2*Log[1 + c/x^2])/(3*c*x) - (b^2*ArcTan[x/Sqrt[c]]*Log[1 + c/x^2])/(3*c^(3/2)) + (b^2*ArcTanh[x/Sqrt[c]]*Log[1 + c/x^2])/(3*c^(3/2)) + (b^2*Log[1 - c/x^2]*Log[1 + c/x^2])/(6*x^3) - (b^2*Log[1 + c/x^2]^2)/(12*x^3) + (2*b^2*ArcTan[x/Sqrt[c]]*Log[(2*Sqrt[c])/(Sqrt[c] - I*x)])/(3*c^(3/2)) - (b^2*ArcTan[x/Sqrt[c]]*Log[((1 + I)*(Sqrt[c] - x))/(Sqrt[c] - I*x)])/(3*c^(3/2)) + (2*b^2*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c])/(Sqrt[c] + x)])/(3*c^(3/2)) - (b^2*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c]*(Sqrt[-c] - x))/((Sqrt[-c] - Sqrt[c])*(Sqrt[c] + x))])/(3*c^(3/2)) - (b^2*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c]*(Sqrt[-c] + x))/((Sqrt[-c] + Sqrt[c])*(Sqrt[c] + x))])/(3*c^(3/2)) - (b^2*ArcTan[x/Sqrt[c]]*Log[((1 - I)*(Sqrt[c] + x))/(Sqrt[c] - I*x)])/(3*c^(3/2)) - (2*b^2*ArcTanh[x/Sqrt[c]]*Log[2 - (2*Sqrt[c])/(Sqrt[c] + x)])/(3*c^(3/2)) - ((I/3)*b^2*PolyLog[2, 1 - (2*Sqrt[c])/(Sqrt[c] - I*x)])/c^(3/2) + ((I/3)*b^2*PolyLog[2, -1 + (2*Sqrt[c])/(Sqrt[c] - I*x)])/c^(3/2) + ((I/6)*b^2*PolyLog[2, 1 - ((1 + I)*(Sqrt[c] - x))/(Sqrt[c] - I*x)])/c^(3/2) - (b^2*PolyLog[2, -(x/Sqrt[c])])/(3*c^(3/2)) + ((I/3)*b^2*PolyLog[2, ((-I)*x)/Sqrt[c]])/c^(3/2) - ((I/3)*b^2*PolyLog[2, (I*x)/Sqrt[c]])/c^(3/2) + (b^2*PolyLog[2, x/Sqrt[c]])/(3*c^(3/2)) - (b^2*PolyLog[2, 1 - (2*Sqrt[c])/(Sqrt[c] + x)])/(3*c^(3/2)) + (b^2*PolyLog[2, -1 + (2*Sqrt[c])/(Sqrt[c] + x)])/(3*c^(3/2)) + (b^2*PolyLog[2, 1 - (2*Sqrt[c]*(Sqrt[-c] - x))/((Sqrt[-c] - Sqrt[c])*(Sqrt[c] + x))])/(6*c^(3/2)) + (b^2*PolyLog[2, 1 - (2*Sqrt[c]*(Sqrt[-c] + x))/((Sqrt[-c] + Sqrt[c])*(Sqrt[c] + x))])/(6*c^(3/2)) + ((I/6)*b^2*PolyLog[2, 1 - ((1 - I)*(Sqrt[c] + x))/(Sqrt[c] - I*x)])/c^(3/2)","A",104,30,16,1.875,1,"{6099, 2457, 2476, 2455, 263, 325, 207, 206, 2470, 12, 260, 6688, 5988, 5932, 2447, 6742, 203, 30, 2557, 5992, 5912, 5920, 2402, 2315, 4928, 4848, 2391, 4856, 4924, 4868}"
181,1,1337,0,2.7899186,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2}{x^6} \, dx","Int[(a + b*ArcTanh[c/x^2])^2/x^6,x]","-\frac{i \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{5 c^{5/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{5 c^{5/2}}-\frac{\log ^2\left(\frac{c}{x^2}+1\right) b^2}{20 x^5}-\frac{4 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{15 c^{5/2}}+\frac{4 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{15 c^{5/2}}+\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{5 c^{5/2}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right) b^2}{5 c^{5/2}}-\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{5 c^2 x}+\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{15 c x^3}-\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{25 x^5}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{5 c^{5/2}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{5 c^{5/2}}+\frac{\log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{10 x^5}-\frac{2 \log \left(\frac{c}{x^2}+1\right) b^2}{15 c x^3}-\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{5 c^{5/2}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right) b^2}{5 c^{5/2}}+\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{5 c^{5/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{5 c^{5/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{5 c^{5/2}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right) b^2}{5 c^{5/2}}-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{5 c^{5/2}}+\frac{i \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{5 c^{5/2}}-\frac{i \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{\sqrt{c}-i x}-1\right) b^2}{5 c^{5/2}}-\frac{i \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right) b^2}{10 c^{5/2}}-\frac{\text{PolyLog}\left(2,-\frac{x}{\sqrt{c}}\right) b^2}{5 c^{5/2}}-\frac{i \text{PolyLog}\left(2,-\frac{i x}{\sqrt{c}}\right) b^2}{5 c^{5/2}}+\frac{i \text{PolyLog}\left(2,\frac{i x}{\sqrt{c}}\right) b^2}{5 c^{5/2}}+\frac{\text{PolyLog}\left(2,\frac{x}{\sqrt{c}}\right) b^2}{5 c^{5/2}}-\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{5 c^{5/2}}+\frac{\text{PolyLog}\left(2,\frac{2 \sqrt{c}}{x+\sqrt{c}}-1\right) b^2}{5 c^{5/2}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{10 c^{5/2}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{10 c^{5/2}}-\frac{i \text{PolyLog}\left(2,1-\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right) b^2}{10 c^{5/2}}-\frac{8 b^2}{15 c^2 x}+\frac{2 a \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) b}{5 c^{5/2}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{5 c^{5/2}}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{5 c^2 x}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{15 c x^3}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{25 x^5}-\frac{a \log \left(\frac{c}{x^2}+1\right) b}{5 x^5}+\frac{2 a b}{5 c^2 x}-\frac{2 a b}{15 c x^3}+\frac{2 a b}{25 x^5}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2}{20 x^5}","-\frac{i \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{5 c^{5/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right)^2 b^2}{5 c^{5/2}}-\frac{\log ^2\left(\frac{c}{x^2}+1\right) b^2}{20 x^5}-\frac{4 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{15 c^{5/2}}+\frac{4 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) b^2}{15 c^{5/2}}+\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{5 c^{5/2}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(1-\frac{c}{x^2}\right) b^2}{5 c^{5/2}}-\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{5 c^2 x}+\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{15 c x^3}-\frac{\log \left(1-\frac{c}{x^2}\right) b^2}{25 x^5}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{5 c^{5/2}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{5 c^{5/2}}+\frac{\log \left(1-\frac{c}{x^2}\right) \log \left(\frac{c}{x^2}+1\right) b^2}{10 x^5}-\frac{2 \log \left(\frac{c}{x^2}+1\right) b^2}{15 c x^3}-\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{5 c^{5/2}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right) b^2}{5 c^{5/2}}+\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{5 c^{5/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{5 c^{5/2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{5 c^{5/2}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right) b^2}{5 c^{5/2}}-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \log \left(2-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{5 c^{5/2}}+\frac{i \text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{\sqrt{c}-i x}\right) b^2}{5 c^{5/2}}-\frac{i \text{PolyLog}\left(2,\frac{2 \sqrt{c}}{\sqrt{c}-i x}-1\right) b^2}{5 c^{5/2}}-\frac{i \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt{c}-x\right)}{\sqrt{c}-i x}\right) b^2}{10 c^{5/2}}-\frac{\text{PolyLog}\left(2,-\frac{x}{\sqrt{c}}\right) b^2}{5 c^{5/2}}-\frac{i \text{PolyLog}\left(2,-\frac{i x}{\sqrt{c}}\right) b^2}{5 c^{5/2}}+\frac{i \text{PolyLog}\left(2,\frac{i x}{\sqrt{c}}\right) b^2}{5 c^{5/2}}+\frac{\text{PolyLog}\left(2,\frac{x}{\sqrt{c}}\right) b^2}{5 c^{5/2}}-\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c}}{x+\sqrt{c}}\right) b^2}{5 c^{5/2}}+\frac{\text{PolyLog}\left(2,\frac{2 \sqrt{c}}{x+\sqrt{c}}-1\right) b^2}{5 c^{5/2}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(\sqrt{-c}-x\right)}{\left(\sqrt{-c}-\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{10 c^{5/2}}+\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \left(x+\sqrt{-c}\right)}{\left(\sqrt{-c}+\sqrt{c}\right) \left(x+\sqrt{c}\right)}\right) b^2}{10 c^{5/2}}-\frac{i \text{PolyLog}\left(2,1-\frac{(1-i) \left(x+\sqrt{c}\right)}{\sqrt{c}-i x}\right) b^2}{10 c^{5/2}}-\frac{8 b^2}{15 c^2 x}+\frac{2 a \tan ^{-1}\left(\frac{x}{\sqrt{c}}\right) b}{5 c^{5/2}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{c}}\right) \left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{5 c^{5/2}}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{5 c^2 x}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{15 c x^3}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right) b}{25 x^5}-\frac{a \log \left(\frac{c}{x^2}+1\right) b}{5 x^5}+\frac{2 a b}{5 c^2 x}-\frac{2 a b}{15 c x^3}+\frac{2 a b}{25 x^5}-\frac{\left(2 a-b \log \left(1-\frac{c}{x^2}\right)\right)^2}{20 x^5}",1,"(2*a*b)/(25*x^5) - (2*a*b)/(15*c*x^3) + (2*a*b)/(5*c^2*x) - (8*b^2)/(15*c^2*x) + (2*a*b*ArcTan[x/Sqrt[c]])/(5*c^(5/2)) - (4*b^2*ArcTan[x/Sqrt[c]])/(15*c^(5/2)) - ((I/5)*b^2*ArcTan[x/Sqrt[c]]^2)/c^(5/2) + (4*b^2*ArcTanh[x/Sqrt[c]])/(15*c^(5/2)) - (b^2*ArcTanh[x/Sqrt[c]]^2)/(5*c^(5/2)) + (2*b^2*ArcTan[x/Sqrt[c]]*Log[2 - (2*Sqrt[c])/(Sqrt[c] - I*x)])/(5*c^(5/2)) - (b^2*Log[1 - c/x^2])/(25*x^5) + (b^2*Log[1 - c/x^2])/(15*c*x^3) - (b^2*Log[1 - c/x^2])/(5*c^2*x) - (b^2*ArcTan[x/Sqrt[c]]*Log[1 - c/x^2])/(5*c^(5/2)) - (b*(2*a - b*Log[1 - c/x^2]))/(25*x^5) - (b*(2*a - b*Log[1 - c/x^2]))/(15*c*x^3) - (b*(2*a - b*Log[1 - c/x^2]))/(5*c^2*x) + (b*ArcTanh[x/Sqrt[c]]*(2*a - b*Log[1 - c/x^2]))/(5*c^(5/2)) - (2*a - b*Log[1 - c/x^2])^2/(20*x^5) - (a*b*Log[1 + c/x^2])/(5*x^5) - (2*b^2*Log[1 + c/x^2])/(15*c*x^3) + (b^2*ArcTan[x/Sqrt[c]]*Log[1 + c/x^2])/(5*c^(5/2)) + (b^2*ArcTanh[x/Sqrt[c]]*Log[1 + c/x^2])/(5*c^(5/2)) + (b^2*Log[1 - c/x^2]*Log[1 + c/x^2])/(10*x^5) - (b^2*Log[1 + c/x^2]^2)/(20*x^5) - (2*b^2*ArcTan[x/Sqrt[c]]*Log[(2*Sqrt[c])/(Sqrt[c] - I*x)])/(5*c^(5/2)) + (b^2*ArcTan[x/Sqrt[c]]*Log[((1 + I)*(Sqrt[c] - x))/(Sqrt[c] - I*x)])/(5*c^(5/2)) + (2*b^2*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c])/(Sqrt[c] + x)])/(5*c^(5/2)) - (b^2*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c]*(Sqrt[-c] - x))/((Sqrt[-c] - Sqrt[c])*(Sqrt[c] + x))])/(5*c^(5/2)) - (b^2*ArcTanh[x/Sqrt[c]]*Log[(2*Sqrt[c]*(Sqrt[-c] + x))/((Sqrt[-c] + Sqrt[c])*(Sqrt[c] + x))])/(5*c^(5/2)) + (b^2*ArcTan[x/Sqrt[c]]*Log[((1 - I)*(Sqrt[c] + x))/(Sqrt[c] - I*x)])/(5*c^(5/2)) - (2*b^2*ArcTanh[x/Sqrt[c]]*Log[2 - (2*Sqrt[c])/(Sqrt[c] + x)])/(5*c^(5/2)) + ((I/5)*b^2*PolyLog[2, 1 - (2*Sqrt[c])/(Sqrt[c] - I*x)])/c^(5/2) - ((I/5)*b^2*PolyLog[2, -1 + (2*Sqrt[c])/(Sqrt[c] - I*x)])/c^(5/2) - ((I/10)*b^2*PolyLog[2, 1 - ((1 + I)*(Sqrt[c] - x))/(Sqrt[c] - I*x)])/c^(5/2) - (b^2*PolyLog[2, -(x/Sqrt[c])])/(5*c^(5/2)) - ((I/5)*b^2*PolyLog[2, ((-I)*x)/Sqrt[c]])/c^(5/2) + ((I/5)*b^2*PolyLog[2, (I*x)/Sqrt[c]])/c^(5/2) + (b^2*PolyLog[2, x/Sqrt[c]])/(5*c^(5/2)) - (b^2*PolyLog[2, 1 - (2*Sqrt[c])/(Sqrt[c] + x)])/(5*c^(5/2)) + (b^2*PolyLog[2, -1 + (2*Sqrt[c])/(Sqrt[c] + x)])/(5*c^(5/2)) + (b^2*PolyLog[2, 1 - (2*Sqrt[c]*(Sqrt[-c] - x))/((Sqrt[-c] - Sqrt[c])*(Sqrt[c] + x))])/(10*c^(5/2)) + (b^2*PolyLog[2, 1 - (2*Sqrt[c]*(Sqrt[-c] + x))/((Sqrt[-c] + Sqrt[c])*(Sqrt[c] + x))])/(10*c^(5/2)) - ((I/10)*b^2*PolyLog[2, 1 - ((1 - I)*(Sqrt[c] + x))/(Sqrt[c] - I*x)])/c^(5/2)","A",129,30,16,1.875,1,"{6099, 2457, 2476, 2455, 263, 325, 207, 206, 2470, 12, 260, 6688, 5988, 5932, 2447, 6742, 203, 30, 2557, 5992, 5912, 5920, 2402, 2315, 4928, 4848, 2391, 4856, 4924, 4868}"
182,0,0,0,0.0248424,"\int (d x)^m \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcTanh[c/x^2])^3,x]","\int (d x)^m \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTanh[c/x^2])^3, x]","A",0,0,0,0,-1,"{}"
183,0,0,0,0.0247062,"\int (d x)^m \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcTanh[c/x^2])^2,x]","\int (d x)^m \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTanh[c/x^2])^2, x]","A",0,0,0,0,-1,"{}"
184,1,75,0,0.0557798,"\int (d x)^m \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right) \, dx","Int[(d*x)^m*(a + b*ArcTanh[c/x^2]),x]","\frac{(d x)^{m+1} \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)}{d (m+1)}-\frac{2 b c d (d x)^{m-1} \, _2F_1\left(1,\frac{1-m}{4};\frac{5-m}{4};\frac{c^2}{x^4}\right)}{1-m^2}","\frac{(d x)^{m+1} \left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)}{d (m+1)}-\frac{2 b c d (d x)^{m-1} \, _2F_1\left(1,\frac{1-m}{4};\frac{5-m}{4};\frac{c^2}{x^4}\right)}{1-m^2}",1,"((d*x)^(1 + m)*(a + b*ArcTanh[c/x^2]))/(d*(1 + m)) - (2*b*c*d*(d*x)^(-1 + m)*Hypergeometric2F1[1, (1 - m)/4, (5 - m)/4, c^2/x^4])/(1 - m^2)","A",4,4,16,0.2500,1,"{6097, 16, 339, 364}"
185,0,0,0,0.027983,"\int \frac{(d x)^m}{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)} \, dx","Int[(d*x)^m/(a + b*ArcTanh[c/x^2]),x]","\int \frac{(d x)^m}{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTanh[c/x^2]), x]","A",0,0,0,0,-1,"{}"
186,0,0,0,0.0263933,"\int \frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2} \, dx","Int[(d*x)^m/(a + b*ArcTanh[c/x^2])^2,x]","\int \frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(\frac{c}{x^2}\right)\right)^2},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTanh[c/x^2])^2, x]","A",0,0,0,0,-1,"{}"
187,1,88,0,0.0415064,"\int x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \, dx","Int[x^3*(a + b*ArcTanh[c*Sqrt[x]]),x]","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+\frac{b x^{5/2}}{20 c^3}+\frac{b x^{3/2}}{12 c^5}+\frac{b \sqrt{x}}{4 c^7}-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{4 c^8}+\frac{b x^{7/2}}{28 c}","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+\frac{b x^{5/2}}{20 c^3}+\frac{b x^{3/2}}{12 c^5}+\frac{b \sqrt{x}}{4 c^7}-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{4 c^8}+\frac{b x^{7/2}}{28 c}",1,"(b*Sqrt[x])/(4*c^7) + (b*x^(3/2))/(12*c^5) + (b*x^(5/2))/(20*c^3) + (b*x^(7/2))/(28*c) - (b*ArcTanh[c*Sqrt[x]])/(4*c^8) + (x^4*(a + b*ArcTanh[c*Sqrt[x]]))/4","A",7,4,16,0.2500,1,"{6097, 50, 63, 206}"
188,1,75,0,0.0345661,"\int x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \, dx","Int[x^2*(a + b*ArcTanh[c*Sqrt[x]]),x]","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+\frac{b x^{3/2}}{9 c^3}+\frac{b \sqrt{x}}{3 c^5}-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{3 c^6}+\frac{b x^{5/2}}{15 c}","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+\frac{b x^{3/2}}{9 c^3}+\frac{b \sqrt{x}}{3 c^5}-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{3 c^6}+\frac{b x^{5/2}}{15 c}",1,"(b*Sqrt[x])/(3*c^5) + (b*x^(3/2))/(9*c^3) + (b*x^(5/2))/(15*c) - (b*ArcTanh[c*Sqrt[x]])/(3*c^6) + (x^3*(a + b*ArcTanh[c*Sqrt[x]]))/3","A",6,4,16,0.2500,1,"{6097, 50, 63, 206}"
189,1,62,0,0.0238849,"\int x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \, dx","Int[x*(a + b*ArcTanh[c*Sqrt[x]]),x]","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+\frac{b \sqrt{x}}{2 c^3}-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 c^4}+\frac{b x^{3/2}}{6 c}","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+\frac{b \sqrt{x}}{2 c^3}-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 c^4}+\frac{b x^{3/2}}{6 c}",1,"(b*Sqrt[x])/(2*c^3) + (b*x^(3/2))/(6*c) - (b*ArcTanh[c*Sqrt[x]])/(2*c^4) + (x^2*(a + b*ArcTanh[c*Sqrt[x]]))/2","A",5,4,14,0.2857,1,"{6097, 50, 63, 206}"
190,1,39,0,0.0204042,"\int \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right) \, dx","Int[a + b*ArcTanh[c*Sqrt[x]],x]","a x-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{c^2}+\frac{b \sqrt{x}}{c}+b x \tanh ^{-1}\left(c \sqrt{x}\right)","a x-\frac{b \tanh ^{-1}\left(c \sqrt{x}\right)}{c^2}+\frac{b \sqrt{x}}{c}+b x \tanh ^{-1}\left(c \sqrt{x}\right)",1,"(b*Sqrt[x])/c + a*x - (b*ArcTanh[c*Sqrt[x]])/c^2 + b*x*ArcTanh[c*Sqrt[x]]","A",5,4,12,0.3333,1,"{6091, 50, 63, 206}"
191,1,29,0,0.0315208,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/x,x]","-b \text{PolyLog}\left(2,-c \sqrt{x}\right)+b \text{PolyLog}\left(2,c \sqrt{x}\right)+a \log (x)","-b \text{PolyLog}\left(2,-c \sqrt{x}\right)+b \text{PolyLog}\left(2,c \sqrt{x}\right)+a \log (x)",1,"a*Log[x] - b*PolyLog[2, -(c*Sqrt[x])] + b*PolyLog[2, c*Sqrt[x]]","A",2,2,16,0.1250,1,"{6095, 5912}"
192,1,40,0,0.0229893,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x^2} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/x^2,x]","-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x}+b c^2 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{\sqrt{x}}","-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x}+b c^2 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{\sqrt{x}}",1,"-((b*c)/Sqrt[x]) + b*c^2*ArcTanh[c*Sqrt[x]] - (a + b*ArcTanh[c*Sqrt[x]])/x","A",4,4,16,0.2500,1,"{6097, 51, 63, 206}"
193,1,60,0,0.0263707,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x^3} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/x^3,x]","-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 x^2}-\frac{b c^3}{2 \sqrt{x}}+\frac{1}{2} b c^4 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{6 x^{3/2}}","-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{2 x^2}-\frac{b c^3}{2 \sqrt{x}}+\frac{1}{2} b c^4 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{6 x^{3/2}}",1,"-(b*c)/(6*x^(3/2)) - (b*c^3)/(2*Sqrt[x]) + (b*c^4*ArcTanh[c*Sqrt[x]])/2 - (a + b*ArcTanh[c*Sqrt[x]])/(2*x^2)","A",5,4,16,0.2500,1,"{6097, 51, 63, 206}"
194,1,73,0,0.0335061,"\int \frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{x^4} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])/x^4,x]","-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{3 x^3}-\frac{b c^3}{9 x^{3/2}}-\frac{b c^5}{3 \sqrt{x}}+\frac{1}{3} b c^6 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{15 x^{5/2}}","-\frac{a+b \tanh ^{-1}\left(c \sqrt{x}\right)}{3 x^3}-\frac{b c^3}{9 x^{3/2}}-\frac{b c^5}{3 \sqrt{x}}+\frac{1}{3} b c^6 \tanh ^{-1}\left(c \sqrt{x}\right)-\frac{b c}{15 x^{5/2}}",1,"-(b*c)/(15*x^(5/2)) - (b*c^3)/(9*x^(3/2)) - (b*c^5)/(3*Sqrt[x]) + (b*c^6*ArcTanh[c*Sqrt[x]])/3 - (a + b*ArcTanh[c*Sqrt[x]])/(3*x^3)","A",6,4,16,0.2500,1,"{6097, 51, 63, 206}"
195,0,0,0,0.0251889,"\int x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2 \, dx","Int[x^3*(a + b*ArcTanh[c*Sqrt[x]])^2,x]","\int x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2 \, dx","\frac{b x^{5/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{10 c^3}+\frac{b x^{3/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{6 c^5}+\frac{a b \sqrt{x}}{2 c^7}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{4 c^8}+\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2+\frac{b x^{7/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{14 c}+\frac{b^2 x^3}{84 c^2}+\frac{3 b^2 x^2}{70 c^4}+\frac{71 b^2 x}{420 c^6}+\frac{44 b^2 \log \left(1-c^2 x\right)}{105 c^8}+\frac{b^2 \sqrt{x} \tanh ^{-1}\left(c \sqrt{x}\right)}{2 c^7}",1,"Defer[Int][x^3*(a + b*ArcTanh[c*Sqrt[x]])^2, x]","F",0,0,0,0,-1,"{}"
196,0,0,0,0.023916,"\int x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2 \, dx","Int[x^2*(a + b*ArcTanh[c*Sqrt[x]])^2,x]","\int x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2 \, dx","\frac{2 b x^{3/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{9 c^3}+\frac{2 a b \sqrt{x}}{3 c^5}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{3 c^6}+\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2+\frac{2 b x^{5/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{15 c}+\frac{b^2 x^2}{30 c^2}+\frac{8 b^2 x}{45 c^4}+\frac{23 b^2 \log \left(1-c^2 x\right)}{45 c^6}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(c \sqrt{x}\right)}{3 c^5}",1,"Defer[Int][x^2*(a + b*ArcTanh[c*Sqrt[x]])^2, x]","F",0,0,0,0,-1,"{}"
197,0,0,0,0.013963,"\int x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2 \, dx","Int[x*(a + b*ArcTanh[c*Sqrt[x]])^2,x]","\int x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2 \, dx","\frac{a b \sqrt{x}}{c^3}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{2 c^4}+\frac{b x^{3/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{3 c}+\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2+\frac{b^2 x}{6 c^2}+\frac{2 b^2 \log \left(1-c^2 x\right)}{3 c^4}+\frac{b^2 \sqrt{x} \tanh ^{-1}\left(c \sqrt{x}\right)}{c^3}",1,"Defer[Int][x*(a + b*ArcTanh[c*Sqrt[x]])^2, x]","F",0,0,0,0,-1,"{}"
198,0,0,0,0.0063505,"\int \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2 \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])^2,x]","\int \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2 \, dx","-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{c^2}+\frac{2 a b \sqrt{x}}{c}+x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2+\frac{b^2 \log \left(1-c^2 x\right)}{c^2}+\frac{2 b^2 \sqrt{x} \tanh ^{-1}\left(c \sqrt{x}\right)}{c}",1,"Defer[Int][(a + b*ArcTanh[c*Sqrt[x]])^2, x]","F",0,0,0,0,-1,"{}"
199,1,145,0,0.3173119,"\int \frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{x} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])^2/x,x]","-2 b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+2 b \text{PolyLog}\left(2,\frac{2}{1-c \sqrt{x}}-1\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c \sqrt{x}}\right)-b^2 \text{PolyLog}\left(3,\frac{2}{1-c \sqrt{x}}-1\right)+4 \tanh ^{-1}\left(1-\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2","-2 b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+2 b \text{PolyLog}\left(2,\frac{2}{1-c \sqrt{x}}-1\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c \sqrt{x}}\right)-b^2 \text{PolyLog}\left(3,\frac{2}{1-c \sqrt{x}}-1\right)+4 \tanh ^{-1}\left(1-\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2",1,"4*ArcTanh[1 - 2/(1 - c*Sqrt[x])]*(a + b*ArcTanh[c*Sqrt[x]])^2 - 2*b*(a + b*ArcTanh[c*Sqrt[x]])*PolyLog[2, 1 - 2/(1 - c*Sqrt[x])] + 2*b*(a + b*ArcTanh[c*Sqrt[x]])*PolyLog[2, -1 + 2/(1 - c*Sqrt[x])] + b^2*PolyLog[3, 1 - 2/(1 - c*Sqrt[x])] - b^2*PolyLog[3, -1 + 2/(1 - c*Sqrt[x])]","A",7,6,18,0.3333,1,"{6095, 5914, 6052, 5948, 6058, 6610}"
200,0,0,0,0.0238263,"\int \frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{x^2} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])^2/x^2,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{x^2} \, dx","c^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2-\frac{2 b c \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{\sqrt{x}}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{x}+b^2 c^2 \log (x)-b^2 c^2 \log \left(1-c^2 x\right)",1,"Defer[Int][(a + b*ArcTanh[c*Sqrt[x]])^2/x^2, x]","F",0,0,0,0,-1,"{}"
201,0,0,0,0.0240127,"\int \frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{x^3} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])^2/x^3,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{x^3} \, dx","\frac{1}{2} c^4 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2-\frac{b c^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{\sqrt{x}}-\frac{b c \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{3 x^{3/2}}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{2 x^2}-\frac{b^2 c^2}{6 x}+\frac{2}{3} b^2 c^4 \log (x)-\frac{2}{3} b^2 c^4 \log \left(1-c^2 x\right)",1,"Defer[Int][(a + b*ArcTanh[c*Sqrt[x]])^2/x^3, x]","F",0,0,0,0,-1,"{}"
202,0,0,0,0.0233636,"\int x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3 \, dx","Int[x^3*(a + b*ArcTanh[c*Sqrt[x]])^3,x]","\int x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3 \, dx","-\frac{44 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{35 c^8}+\frac{b^2 x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{28 c^2}+\frac{9 b^2 x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{70 c^4}+\frac{71 b^2 x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{140 c^6}-\frac{88 b^2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{35 c^8}+\frac{3 b x^{5/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{20 c^3}+\frac{b x^{3/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{4 c^5}+\frac{3 b \sqrt{x} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{4 c^7}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3}{4 c^8}+\frac{44 b \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{35 c^8}+\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3+\frac{3 b x^{7/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{28 c}+\frac{b^3 x^{5/2}}{140 c^3}+\frac{23 b^3 x^{3/2}}{420 c^5}+\frac{47 b^3 \sqrt{x}}{70 c^7}-\frac{47 b^3 \tanh ^{-1}\left(c \sqrt{x}\right)}{70 c^8}",1,"Defer[Int][x^3*(a + b*ArcTanh[c*Sqrt[x]])^3, x]","F",0,0,0,0,-1,"{}"
203,0,0,0,0.0237346,"\int x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3 \, dx","Int[x^2*(a + b*ArcTanh[c*Sqrt[x]])^3,x]","\int x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3 \, dx","-\frac{23 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{15 c^6}+\frac{b^2 x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{10 c^2}+\frac{8 b^2 x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{15 c^4}-\frac{46 b^2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{15 c^6}+\frac{b x^{3/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{3 c^3}+\frac{b \sqrt{x} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{c^5}+\frac{23 b \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{15 c^6}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3}{3 c^6}+\frac{b x^{5/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{5 c}+\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3+\frac{b^3 x^{3/2}}{30 c^3}+\frac{19 b^3 \sqrt{x}}{30 c^5}-\frac{19 b^3 \tanh ^{-1}\left(c \sqrt{x}\right)}{30 c^6}",1,"Defer[Int][x^2*(a + b*ArcTanh[c*Sqrt[x]])^3, x]","F",0,0,0,0,-1,"{}"
204,0,0,0,0.0142464,"\int x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3 \, dx","Int[x*(a + b*ArcTanh[c*Sqrt[x]])^3,x]","\int x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3 \, dx","-\frac{2 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{c^4}+\frac{b^2 x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{2 c^2}-\frac{4 b^2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^4}+\frac{3 b \sqrt{x} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{2 c^3}+\frac{2 b \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{c^4}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3}{2 c^4}+\frac{b x^{3/2} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{2 c}+\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3+\frac{b^3 \sqrt{x}}{2 c^3}-\frac{b^3 \tanh ^{-1}\left(c \sqrt{x}\right)}{2 c^4}",1,"Defer[Int][x*(a + b*ArcTanh[c*Sqrt[x]])^3, x]","F",0,0,0,0,-1,"{}"
205,0,0,0,0.0063135,"\int \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3 \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])^3,x]","\int \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3 \, dx","-\frac{3 b^3 \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right)}{c^2}-\frac{6 b^2 \log \left(\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{c^2}+\frac{3 b \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{c^2}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3}{c^2}+\frac{3 b \sqrt{x} \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{c}+x \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3",1,"Defer[Int][(a + b*ArcTanh[c*Sqrt[x]])^3, x]","F",0,0,0,0,-1,"{}"
206,1,224,0,0.5115269,"\int \frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3}{x} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])^3/x,x]","3 b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)-3 b^2 \text{PolyLog}\left(3,\frac{2}{1-c \sqrt{x}}-1\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)-3 b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2+3 b \text{PolyLog}\left(2,\frac{2}{1-c \sqrt{x}}-1\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2-\frac{3}{2} b^3 \text{PolyLog}\left(4,1-\frac{2}{1-c \sqrt{x}}\right)+\frac{3}{2} b^3 \text{PolyLog}\left(4,\frac{2}{1-c \sqrt{x}}-1\right)+4 \tanh ^{-1}\left(1-\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3","3 b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)-3 b^2 \text{PolyLog}\left(3,\frac{2}{1-c \sqrt{x}}-1\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)-3 b \text{PolyLog}\left(2,1-\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2+3 b \text{PolyLog}\left(2,\frac{2}{1-c \sqrt{x}}-1\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2-\frac{3}{2} b^3 \text{PolyLog}\left(4,1-\frac{2}{1-c \sqrt{x}}\right)+\frac{3}{2} b^3 \text{PolyLog}\left(4,\frac{2}{1-c \sqrt{x}}-1\right)+4 \tanh ^{-1}\left(1-\frac{2}{1-c \sqrt{x}}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3",1,"4*ArcTanh[1 - 2/(1 - c*Sqrt[x])]*(a + b*ArcTanh[c*Sqrt[x]])^3 - 3*b*(a + b*ArcTanh[c*Sqrt[x]])^2*PolyLog[2, 1 - 2/(1 - c*Sqrt[x])] + 3*b*(a + b*ArcTanh[c*Sqrt[x]])^2*PolyLog[2, -1 + 2/(1 - c*Sqrt[x])] + 3*b^2*(a + b*ArcTanh[c*Sqrt[x]])*PolyLog[3, 1 - 2/(1 - c*Sqrt[x])] - 3*b^2*(a + b*ArcTanh[c*Sqrt[x]])*PolyLog[3, -1 + 2/(1 - c*Sqrt[x])] - (3*b^3*PolyLog[4, 1 - 2/(1 - c*Sqrt[x])])/2 + (3*b^3*PolyLog[4, -1 + 2/(1 - c*Sqrt[x])])/2","A",9,7,18,0.3889,1,"{6095, 5914, 6052, 5948, 6058, 6062, 6610}"
207,0,0,0,0.0222653,"\int \frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3}{x^2} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])^3/x^2,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3}{x^2} \, dx","-3 b^3 c^2 \text{PolyLog}\left(2,\frac{2}{c \sqrt{x}+1}-1\right)+6 b^2 c^2 \log \left(2-\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+3 b c^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2+c^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3-\frac{3 b c \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{\sqrt{x}}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3}{x}",1,"Defer[Int][(a + b*ArcTanh[c*Sqrt[x]])^3/x^2, x]","F",0,0,0,0,-1,"{}"
208,0,0,0,0.0232819,"\int \frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3}{x^3} \, dx","Int[(a + b*ArcTanh[c*Sqrt[x]])^3/x^3,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3}{x^3} \, dx","-2 b^3 c^4 \text{PolyLog}\left(2,\frac{2}{c \sqrt{x}+1}-1\right)-\frac{b^2 c^2 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)}{2 x}+4 b^2 c^4 \log \left(2-\frac{2}{c \sqrt{x}+1}\right) \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)+\frac{1}{2} c^4 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3+2 b c^4 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2-\frac{3 b c^3 \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{2 \sqrt{x}}-\frac{b c \left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^2}{2 x^{3/2}}-\frac{\left(a+b \tanh ^{-1}\left(c \sqrt{x}\right)\right)^3}{2 x^2}-\frac{b^3 c^3}{2 \sqrt{x}}+\frac{1}{2} b^3 c^4 \tanh ^{-1}\left(c \sqrt{x}\right)",1,"Defer[Int][(a + b*ArcTanh[c*Sqrt[x]])^3/x^3, x]","F",0,0,0,0,-1,"{}"
209,1,38,0,0.0162326,"\int x^{3/2} \tanh ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^(3/2)*ArcTanh[Sqrt[x]],x]","\frac{x^2}{10}+\frac{2}{5} x^{5/2} \tanh ^{-1}\left(\sqrt{x}\right)+\frac{x}{5}+\frac{1}{5} \log (1-x)","\frac{x^2}{10}+\frac{2}{5} x^{5/2} \tanh ^{-1}\left(\sqrt{x}\right)+\frac{x}{5}+\frac{1}{5} \log (1-x)",1,"x/5 + x^2/10 + (2*x^(5/2)*ArcTanh[Sqrt[x]])/5 + Log[1 - x]/5","A",3,2,12,0.1667,1,"{6097, 43}"
210,1,31,0,0.0129167,"\int \sqrt{x} \tanh ^{-1}\left(\sqrt{x}\right) \, dx","Int[Sqrt[x]*ArcTanh[Sqrt[x]],x]","\frac{2}{3} x^{3/2} \tanh ^{-1}\left(\sqrt{x}\right)+\frac{x}{3}+\frac{1}{3} \log (1-x)","\frac{2}{3} x^{3/2} \tanh ^{-1}\left(\sqrt{x}\right)+\frac{x}{3}+\frac{1}{3} \log (1-x)",1,"x/3 + (2*x^(3/2)*ArcTanh[Sqrt[x]])/3 + Log[1 - x]/3","A",3,2,12,0.1667,1,"{6097, 43}"
211,1,20,0,0.0091329,"\int \frac{\tanh ^{-1}\left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Int[ArcTanh[Sqrt[x]]/Sqrt[x],x]","\log (1-x)+2 \sqrt{x} \tanh ^{-1}\left(\sqrt{x}\right)","\log (1-x)+2 \sqrt{x} \tanh ^{-1}\left(\sqrt{x}\right)",1,"2*Sqrt[x]*ArcTanh[Sqrt[x]] + Log[1 - x]","A",2,2,12,0.1667,1,"{6097, 31}"
212,1,24,0,0.0102569,"\int \frac{\tanh ^{-1}\left(\sqrt{x}\right)}{x^{3/2}} \, dx","Int[ArcTanh[Sqrt[x]]/x^(3/2),x]","-\log (1-x)+\log (x)-\frac{2 \tanh ^{-1}\left(\sqrt{x}\right)}{\sqrt{x}}","-\log (1-x)+\log (x)-\frac{2 \tanh ^{-1}\left(\sqrt{x}\right)}{\sqrt{x}}",1,"(-2*ArcTanh[Sqrt[x]])/Sqrt[x] - Log[1 - x] + Log[x]","A",4,4,12,0.3333,1,"{6097, 36, 31, 29}"
213,1,190,0,0.3005856,"\int x^3 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right) \, dx","Int[x^3*(a + b*ArcTanh[c*x^(3/2)]),x]","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)+\frac{b \log \left(c^{2/3} x-\sqrt[3]{c} \sqrt{x}+1\right)}{16 c^{8/3}}-\frac{b \log \left(c^{2/3} x+\sqrt[3]{c} \sqrt{x}+1\right)}{16 c^{8/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} \sqrt{x}}{\sqrt{3}}\right)}{8 c^{8/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} \sqrt{x}+1}{\sqrt{3}}\right)}{8 c^{8/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} \sqrt{x}\right)}{4 c^{8/3}}+\frac{3 b x^{5/2}}{20 c}","\frac{1}{4} x^4 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)+\frac{b \log \left(c^{2/3} x-\sqrt[3]{c} \sqrt{x}+1\right)}{16 c^{8/3}}-\frac{b \log \left(c^{2/3} x+\sqrt[3]{c} \sqrt{x}+1\right)}{16 c^{8/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} \sqrt{x}}{\sqrt{3}}\right)}{8 c^{8/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} \sqrt{x}+1}{\sqrt{3}}\right)}{8 c^{8/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} \sqrt{x}\right)}{4 c^{8/3}}+\frac{3 b x^{5/2}}{20 c}",1,"(3*b*x^(5/2))/(20*c) - (Sqrt[3]*b*ArcTan[(1 - 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(8*c^(8/3)) + (Sqrt[3]*b*ArcTan[(1 + 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(8*c^(8/3)) - (b*ArcTanh[c^(1/3)*Sqrt[x]])/(4*c^(8/3)) + (x^4*(a + b*ArcTanh[c*x^(3/2)]))/4 + (b*Log[1 - c^(1/3)*Sqrt[x] + c^(2/3)*x])/(16*c^(8/3)) - (b*Log[1 + c^(1/3)*Sqrt[x] + c^(2/3)*x])/(16*c^(8/3))","A",13,9,16,0.5625,1,"{6097, 321, 329, 296, 634, 618, 204, 628, 206}"
214,1,49,0,0.0337865,"\int x^2 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right) \, dx","Int[x^2*(a + b*ArcTanh[c*x^(3/2)]),x]","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)-\frac{b \tanh ^{-1}\left(c x^{3/2}\right)}{3 c^2}+\frac{b x^{3/2}}{3 c}","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)-\frac{b \tanh ^{-1}\left(c x^{3/2}\right)}{3 c^2}+\frac{b x^{3/2}}{3 c}",1,"(b*x^(3/2))/(3*c) - (b*ArcTanh[c*x^(3/2)])/(3*c^2) + (x^3*(a + b*ArcTanh[c*x^(3/2)]))/3","A",5,5,16,0.3125,1,"{6097, 321, 329, 275, 206}"
215,1,190,0,0.2382178,"\int x \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right) \, dx","Int[x*(a + b*ArcTanh[c*x^(3/2)]),x]","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)+\frac{b \log \left(c^{2/3} x-\sqrt[3]{c} \sqrt{x}+1\right)}{8 c^{4/3}}-\frac{b \log \left(c^{2/3} x+\sqrt[3]{c} \sqrt{x}+1\right)}{8 c^{4/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} \sqrt{x}}{\sqrt{3}}\right)}{4 c^{4/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} \sqrt{x}+1}{\sqrt{3}}\right)}{4 c^{4/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} \sqrt{x}\right)}{2 c^{4/3}}+\frac{3 b \sqrt{x}}{2 c}","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)+\frac{b \log \left(c^{2/3} x-\sqrt[3]{c} \sqrt{x}+1\right)}{8 c^{4/3}}-\frac{b \log \left(c^{2/3} x+\sqrt[3]{c} \sqrt{x}+1\right)}{8 c^{4/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} \sqrt{x}}{\sqrt{3}}\right)}{4 c^{4/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} \sqrt{x}+1}{\sqrt{3}}\right)}{4 c^{4/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} \sqrt{x}\right)}{2 c^{4/3}}+\frac{3 b \sqrt{x}}{2 c}",1,"(3*b*Sqrt[x])/(2*c) + (Sqrt[3]*b*ArcTan[(1 - 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(4*c^(4/3)) - (Sqrt[3]*b*ArcTan[(1 + 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(4*c^(4/3)) - (b*ArcTanh[c^(1/3)*Sqrt[x]])/(2*c^(4/3)) + (x^2*(a + b*ArcTanh[c*x^(3/2)]))/2 + (b*Log[1 - c^(1/3)*Sqrt[x] + c^(2/3)*x])/(8*c^(4/3)) - (b*Log[1 + c^(1/3)*Sqrt[x] + c^(2/3)*x])/(8*c^(4/3))","A",13,9,14,0.6429,1,"{6097, 321, 329, 210, 634, 618, 204, 628, 206}"
216,1,170,0,0.2870178,"\int \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right) \, dx","Int[a + b*ArcTanh[c*x^(3/2)],x]","a x+\frac{b \log \left(c^{2/3} x-\sqrt[3]{c} \sqrt{x}+1\right)}{4 c^{2/3}}-\frac{b \log \left(c^{2/3} x+\sqrt[3]{c} \sqrt{x}+1\right)}{4 c^{2/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} \sqrt{x}}{\sqrt{3}}\right)}{2 c^{2/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} \sqrt{x}+1}{\sqrt{3}}\right)}{2 c^{2/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} \sqrt{x}\right)}{c^{2/3}}+b x \tanh ^{-1}\left(c x^{3/2}\right)","a x+\frac{b \log \left(c^{2/3} x-\sqrt[3]{c} \sqrt{x}+1\right)}{4 c^{2/3}}-\frac{b \log \left(c^{2/3} x+\sqrt[3]{c} \sqrt{x}+1\right)}{4 c^{2/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} \sqrt{x}}{\sqrt{3}}\right)}{2 c^{2/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{c} \sqrt{x}+1}{\sqrt{3}}\right)}{2 c^{2/3}}-\frac{b \tanh ^{-1}\left(\sqrt[3]{c} \sqrt{x}\right)}{c^{2/3}}+b x \tanh ^{-1}\left(c x^{3/2}\right)",1,"a*x - (Sqrt[3]*b*ArcTan[(1 - 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(2*c^(2/3)) + (Sqrt[3]*b*ArcTan[(1 + 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(2*c^(2/3)) - (b*ArcTanh[c^(1/3)*Sqrt[x]])/c^(2/3) + b*x*ArcTanh[c*x^(3/2)] + (b*Log[1 - c^(1/3)*Sqrt[x] + c^(2/3)*x])/(4*c^(2/3)) - (b*Log[1 + c^(1/3)*Sqrt[x] + c^(2/3)*x])/(4*c^(2/3))","A",13,8,12,0.6667,1,"{6091, 329, 296, 634, 618, 204, 628, 206}"
217,1,34,0,0.033444,"\int \frac{a+b \tanh ^{-1}\left(c x^{3/2}\right)}{x} \, dx","Int[(a + b*ArcTanh[c*x^(3/2)])/x,x]","-\frac{1}{3} b \text{PolyLog}\left(2,-c x^{3/2}\right)+\frac{1}{3} b \text{PolyLog}\left(2,c x^{3/2}\right)+a \log (x)","-\frac{1}{3} b \text{PolyLog}\left(2,-c x^{3/2}\right)+\frac{1}{3} b \text{PolyLog}\left(2,c x^{3/2}\right)+a \log (x)",1,"a*Log[x] - (b*PolyLog[2, -(c*x^(3/2))])/3 + (b*PolyLog[2, c*x^(3/2)])/3","A",2,2,16,0.1250,1,"{6095, 5912}"
218,1,172,0,0.2208778,"\int \frac{a+b \tanh ^{-1}\left(c x^{3/2}\right)}{x^2} \, dx","Int[(a + b*ArcTanh[c*x^(3/2)])/x^2,x]","-\frac{a+b \tanh ^{-1}\left(c x^{3/2}\right)}{x}-\frac{1}{4} b c^{2/3} \log \left(c^{2/3} x-\sqrt[3]{c} \sqrt{x}+1\right)+\frac{1}{4} b c^{2/3} \log \left(c^{2/3} x+\sqrt[3]{c} \sqrt{x}+1\right)-\frac{1}{2} \sqrt{3} b c^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} \sqrt{x}}{\sqrt{3}}\right)+\frac{1}{2} \sqrt{3} b c^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c} \sqrt{x}+1}{\sqrt{3}}\right)+b c^{2/3} \tanh ^{-1}\left(\sqrt[3]{c} \sqrt{x}\right)","-\frac{a+b \tanh ^{-1}\left(c x^{3/2}\right)}{x}-\frac{1}{4} b c^{2/3} \log \left(c^{2/3} x-\sqrt[3]{c} \sqrt{x}+1\right)+\frac{1}{4} b c^{2/3} \log \left(c^{2/3} x+\sqrt[3]{c} \sqrt{x}+1\right)-\frac{1}{2} \sqrt{3} b c^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} \sqrt{x}}{\sqrt{3}}\right)+\frac{1}{2} \sqrt{3} b c^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c} \sqrt{x}+1}{\sqrt{3}}\right)+b c^{2/3} \tanh ^{-1}\left(\sqrt[3]{c} \sqrt{x}\right)",1,"-(Sqrt[3]*b*c^(2/3)*ArcTan[(1 - 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/2 + (Sqrt[3]*b*c^(2/3)*ArcTan[(1 + 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/2 + b*c^(2/3)*ArcTanh[c^(1/3)*Sqrt[x]] - (a + b*ArcTanh[c*x^(3/2)])/x - (b*c^(2/3)*Log[1 - c^(1/3)*Sqrt[x] + c^(2/3)*x])/4 + (b*c^(2/3)*Log[1 + c^(1/3)*Sqrt[x] + c^(2/3)*x])/4","A",12,8,16,0.5000,1,"{6097, 329, 210, 634, 618, 204, 628, 206}"
219,1,188,0,0.2865807,"\int \frac{a+b \tanh ^{-1}\left(c x^{3/2}\right)}{x^3} \, dx","Int[(a + b*ArcTanh[c*x^(3/2)])/x^3,x]","-\frac{a+b \tanh ^{-1}\left(c x^{3/2}\right)}{2 x^2}-\frac{1}{8} b c^{4/3} \log \left(c^{2/3} x-\sqrt[3]{c} \sqrt{x}+1\right)+\frac{1}{8} b c^{4/3} \log \left(c^{2/3} x+\sqrt[3]{c} \sqrt{x}+1\right)+\frac{1}{4} \sqrt{3} b c^{4/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} \sqrt{x}}{\sqrt{3}}\right)-\frac{1}{4} \sqrt{3} b c^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c} \sqrt{x}+1}{\sqrt{3}}\right)+\frac{1}{2} b c^{4/3} \tanh ^{-1}\left(\sqrt[3]{c} \sqrt{x}\right)-\frac{3 b c}{2 \sqrt{x}}","-\frac{a+b \tanh ^{-1}\left(c x^{3/2}\right)}{2 x^2}-\frac{1}{8} b c^{4/3} \log \left(c^{2/3} x-\sqrt[3]{c} \sqrt{x}+1\right)+\frac{1}{8} b c^{4/3} \log \left(c^{2/3} x+\sqrt[3]{c} \sqrt{x}+1\right)+\frac{1}{4} \sqrt{3} b c^{4/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{c} \sqrt{x}}{\sqrt{3}}\right)-\frac{1}{4} \sqrt{3} b c^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c} \sqrt{x}+1}{\sqrt{3}}\right)+\frac{1}{2} b c^{4/3} \tanh ^{-1}\left(\sqrt[3]{c} \sqrt{x}\right)-\frac{3 b c}{2 \sqrt{x}}",1,"(-3*b*c)/(2*Sqrt[x]) + (Sqrt[3]*b*c^(4/3)*ArcTan[(1 - 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/4 - (Sqrt[3]*b*c^(4/3)*ArcTan[(1 + 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/4 + (b*c^(4/3)*ArcTanh[c^(1/3)*Sqrt[x]])/2 - (a + b*ArcTanh[c*x^(3/2)])/(2*x^2) - (b*c^(4/3)*Log[1 - c^(1/3)*Sqrt[x] + c^(2/3)*x])/8 + (b*c^(4/3)*Log[1 + c^(1/3)*Sqrt[x] + c^(2/3)*x])/8","A",13,9,16,0.5625,1,"{6097, 325, 329, 296, 634, 618, 204, 628, 206}"
220,1,47,0,0.0322121,"\int \frac{a+b \tanh ^{-1}\left(c x^{3/2}\right)}{x^4} \, dx","Int[(a + b*ArcTanh[c*x^(3/2)])/x^4,x]","-\frac{a+b \tanh ^{-1}\left(c x^{3/2}\right)}{3 x^3}+\frac{1}{3} b c^2 \tanh ^{-1}\left(c x^{3/2}\right)-\frac{b c}{3 x^{3/2}}","-\frac{a+b \tanh ^{-1}\left(c x^{3/2}\right)}{3 x^3}+\frac{1}{3} b c^2 \tanh ^{-1}\left(c x^{3/2}\right)-\frac{b c}{3 x^{3/2}}",1,"-(b*c)/(3*x^(3/2)) + (b*c^2*ArcTanh[c*x^(3/2)])/3 - (a + b*ArcTanh[c*x^(3/2)])/(3*x^3)","A",5,5,16,0.3125,1,"{6097, 325, 329, 275, 206}"
221,0,0,0,0.0244631,"\int x^2 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)^2 \, dx","Int[x^2*(a + b*ArcTanh[c*x^(3/2)])^2,x]","\int x^2 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)^2 \, dx","-\frac{\left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)^2}{3 c^2}+\frac{2 a b x^{3/2}}{3 c}+\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)^2+\frac{b^2 \log \left(1-c^2 x^3\right)}{3 c^2}+\frac{2 b^2 x^{3/2} \tanh ^{-1}\left(c x^{3/2}\right)}{3 c}",1,"Defer[Int][x^2*(a + b*ArcTanh[c*x^(3/2)])^2, x]","F",0,0,0,0,-1,"{}"
222,1,156,0,0.319783,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)^2}{x} \, dx","Int[(a + b*ArcTanh[c*x^(3/2)])^2/x,x]","-\frac{2}{3} b \text{PolyLog}\left(2,1-\frac{2}{1-c x^{3/2}}\right) \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)+\frac{2}{3} b \text{PolyLog}\left(2,\frac{2}{1-c x^{3/2}}-1\right) \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)+\frac{1}{3} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^{3/2}}\right)-\frac{1}{3} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^{3/2}}-1\right)+\frac{4}{3} \tanh ^{-1}\left(1-\frac{2}{1-c x^{3/2}}\right) \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)^2","-\frac{2}{3} b \text{PolyLog}\left(2,1-\frac{2}{1-c x^{3/2}}\right) \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)+\frac{2}{3} b \text{PolyLog}\left(2,\frac{2}{1-c x^{3/2}}-1\right) \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)+\frac{1}{3} b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^{3/2}}\right)-\frac{1}{3} b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^{3/2}}-1\right)+\frac{4}{3} \tanh ^{-1}\left(1-\frac{2}{1-c x^{3/2}}\right) \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)^2",1,"(4*(a + b*ArcTanh[c*x^(3/2)])^2*ArcTanh[1 - 2/(1 - c*x^(3/2))])/3 - (2*b*(a + b*ArcTanh[c*x^(3/2)])*PolyLog[2, 1 - 2/(1 - c*x^(3/2))])/3 + (2*b*(a + b*ArcTanh[c*x^(3/2)])*PolyLog[2, -1 + 2/(1 - c*x^(3/2))])/3 + (b^2*PolyLog[3, 1 - 2/(1 - c*x^(3/2))])/3 - (b^2*PolyLog[3, -1 + 2/(1 - c*x^(3/2))])/3","A",7,6,18,0.3333,1,"{6095, 5914, 6052, 5948, 6058, 6610}"
223,0,0,0,0.0237288,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)^2}{x^4} \, dx","Int[(a + b*ArcTanh[c*x^(3/2)])^2/x^4,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)^2}{x^4} \, dx","\frac{1}{3} c^2 \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)^2-\frac{2 b c \left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)}{3 x^{3/2}}-\frac{\left(a+b \tanh ^{-1}\left(c x^{3/2}\right)\right)^2}{3 x^3}-\frac{1}{3} b^2 c^2 \log \left(1-c^2 x^3\right)+b^2 c^2 \log (x)",1,"Defer[Int][(a + b*ArcTanh[c*x^(3/2)])^2/x^4, x]","F",0,0,0,0,-1,"{}"
224,1,66,0,0.0305945,"\int x^2 \left(a+b \tanh ^{-1}\left(c x^n\right)\right) \, dx","Int[x^2*(a + b*ArcTanh[c*x^n]),x]","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c x^n\right)\right)-\frac{b c n x^{n+3} \, _2F_1\left(1,\frac{n+3}{2 n};\frac{3 (n+1)}{2 n};c^2 x^{2 n}\right)}{3 (n+3)}","\frac{1}{3} x^3 \left(a+b \tanh ^{-1}\left(c x^n\right)\right)-\frac{b c n x^{n+3} \, _2F_1\left(1,\frac{n+3}{2 n};\frac{3 (n+1)}{2 n};c^2 x^{2 n}\right)}{3 (n+3)}",1,"(x^3*(a + b*ArcTanh[c*x^n]))/3 - (b*c*n*x^(3 + n)*Hypergeometric2F1[1, (3 + n)/(2*n), (3*(1 + n))/(2*n), c^2*x^(2*n)])/(3*(3 + n))","A",2,2,14,0.1429,1,"{6097, 364}"
225,1,67,0,0.0243278,"\int x \left(a+b \tanh ^{-1}\left(c x^n\right)\right) \, dx","Int[x*(a + b*ArcTanh[c*x^n]),x]","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c x^n\right)\right)-\frac{b c n x^{n+2} \, _2F_1\left(1,\frac{n+2}{2 n};\frac{1}{2} \left(3+\frac{2}{n}\right);c^2 x^{2 n}\right)}{2 (n+2)}","\frac{1}{2} x^2 \left(a+b \tanh ^{-1}\left(c x^n\right)\right)-\frac{b c n x^{n+2} \, _2F_1\left(1,\frac{n+2}{2 n};\frac{1}{2} \left(3+\frac{2}{n}\right);c^2 x^{2 n}\right)}{2 (n+2)}",1,"(x^2*(a + b*ArcTanh[c*x^n]))/2 - (b*c*n*x^(2 + n)*Hypergeometric2F1[1, (2 + n)/(2*n), (3 + 2/n)/2, c^2*x^(2*n)])/(2*(2 + n))","A",2,2,12,0.1667,1,"{6097, 364}"
226,1,58,0,0.0279346,"\int \left(a+b \tanh ^{-1}\left(c x^n\right)\right) \, dx","Int[a + b*ArcTanh[c*x^n],x]","a x-\frac{b c n x^{n+1} \, _2F_1\left(1,\frac{n+1}{2 n};\frac{1}{2} \left(3+\frac{1}{n}\right);c^2 x^{2 n}\right)}{n+1}+b x \tanh ^{-1}\left(c x^n\right)","a x-\frac{b c n x^{n+1} \, _2F_1\left(1,\frac{n+1}{2 n};\frac{1}{2} \left(3+\frac{1}{n}\right);c^2 x^{2 n}\right)}{n+1}+b x \tanh ^{-1}\left(c x^n\right)",1,"a*x + b*x*ArcTanh[c*x^n] - (b*c*n*x^(1 + n)*Hypergeometric2F1[1, (1 + n)/(2*n), (3 + n^(-1))/2, c^2*x^(2*n)])/(1 + n)","A",3,2,10,0.2000,1,"{6091, 364}"
227,1,36,0,0.0350596,"\int \frac{a+b \tanh ^{-1}\left(c x^n\right)}{x} \, dx","Int[(a + b*ArcTanh[c*x^n])/x,x]","-\frac{b \text{PolyLog}\left(2,-c x^n\right)}{2 n}+\frac{b \text{PolyLog}\left(2,c x^n\right)}{2 n}+a \log (x)","-\frac{b \text{PolyLog}\left(2,-c x^n\right)}{2 n}+\frac{b \text{PolyLog}\left(2,c x^n\right)}{2 n}+a \log (x)",1,"a*Log[x] - (b*PolyLog[2, -(c*x^n)])/(2*n) + (b*PolyLog[2, c*x^n])/(2*n)","A",2,2,14,0.1429,1,"{6095, 5912}"
228,1,67,0,0.032358,"\int \frac{a+b \tanh ^{-1}\left(c x^n\right)}{x^2} \, dx","Int[(a + b*ArcTanh[c*x^n])/x^2,x]","-\frac{a+b \tanh ^{-1}\left(c x^n\right)}{x}-\frac{b c n x^{n-1} \, _2F_1\left(1,-\frac{1-n}{2 n};\frac{1}{2} \left(3-\frac{1}{n}\right);c^2 x^{2 n}\right)}{1-n}","-\frac{a+b \tanh ^{-1}\left(c x^n\right)}{x}-\frac{b c n x^{n-1} \, _2F_1\left(1,-\frac{1-n}{2 n};\frac{1}{2} \left(3-\frac{1}{n}\right);c^2 x^{2 n}\right)}{1-n}",1,"-((a + b*ArcTanh[c*x^n])/x) - (b*c*n*x^(-1 + n)*Hypergeometric2F1[1, -(1 - n)/(2*n), (3 - n^(-1))/2, c^2*x^(2*n)])/(1 - n)","A",2,2,14,0.1429,1,"{6097, 364}"
229,1,70,0,0.0311192,"\int \frac{a+b \tanh ^{-1}\left(c x^n\right)}{x^3} \, dx","Int[(a + b*ArcTanh[c*x^n])/x^3,x]","-\frac{a+b \tanh ^{-1}\left(c x^n\right)}{2 x^2}-\frac{b c n x^{n-2} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{2}{n}\right);\frac{1}{2} \left(3-\frac{2}{n}\right);c^2 x^{2 n}\right)}{2 (2-n)}","-\frac{a+b \tanh ^{-1}\left(c x^n\right)}{2 x^2}-\frac{b c n x^{n-2} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{2}{n}\right);\frac{1}{2} \left(3-\frac{2}{n}\right);c^2 x^{2 n}\right)}{2 (2-n)}",1,"-(a + b*ArcTanh[c*x^n])/(2*x^2) - (b*c*n*x^(-2 + n)*Hypergeometric2F1[1, (1 - 2/n)/2, (3 - 2/n)/2, c^2*x^(2*n)])/(2*(2 - n))","A",2,2,14,0.1429,1,"{6097, 364}"
230,1,72,0,0.0342286,"\int \frac{a+b \tanh ^{-1}\left(c x^n\right)}{x^4} \, dx","Int[(a + b*ArcTanh[c*x^n])/x^4,x]","-\frac{a+b \tanh ^{-1}\left(c x^n\right)}{3 x^3}-\frac{b c n x^{n-3} \, _2F_1\left(1,-\frac{3-n}{2 n};-\frac{3 (1-n)}{2 n};c^2 x^{2 n}\right)}{3 (3-n)}","-\frac{a+b \tanh ^{-1}\left(c x^n\right)}{3 x^3}-\frac{b c n x^{n-3} \, _2F_1\left(1,-\frac{3-n}{2 n};-\frac{3 (1-n)}{2 n};c^2 x^{2 n}\right)}{3 (3-n)}",1,"-(a + b*ArcTanh[c*x^n])/(3*x^3) - (b*c*n*x^(-3 + n)*Hypergeometric2F1[1, -(3 - n)/(2*n), (-3*(1 - n))/(2*n), c^2*x^(2*n)])/(3*(3 - n))","A",2,2,14,0.1429,1,"{6097, 364}"
231,0,0,0,0.0149523,"\int x \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2 \, dx","Int[x*(a + b*ArcTanh[c*x^n])^2,x]","\int x \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2 \, dx","\text{Int}\left(x \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2,x\right)",0,"Defer[Int][x*(a + b*ArcTanh[c*x^n])^2, x]","A",0,0,0,0,-1,"{}"
232,0,0,0,0.0063323,"\int \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2 \, dx","Int[(a + b*ArcTanh[c*x^n])^2,x]","\int \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2 \, dx","\text{Int}\left(\left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2,x\right)",0,"Defer[Int][(a + b*ArcTanh[c*x^n])^2, x]","A",0,0,0,0,-1,"{}"
233,1,148,0,0.3134628,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2}{x} \, dx","Int[(a + b*ArcTanh[c*x^n])^2/x,x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c x^n}\right) \left(a+b \tanh ^{-1}\left(c x^n\right)\right)}{n}+\frac{b \text{PolyLog}\left(2,\frac{2}{1-c x^n}-1\right) \left(a+b \tanh ^{-1}\left(c x^n\right)\right)}{n}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^n}\right)}{2 n}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^n}-1\right)}{2 n}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-c x^n}\right) \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2}{n}","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-c x^n}\right) \left(a+b \tanh ^{-1}\left(c x^n\right)\right)}{n}+\frac{b \text{PolyLog}\left(2,\frac{2}{1-c x^n}-1\right) \left(a+b \tanh ^{-1}\left(c x^n\right)\right)}{n}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1-c x^n}\right)}{2 n}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{1-c x^n}-1\right)}{2 n}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-c x^n}\right) \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2}{n}",1,"(2*(a + b*ArcTanh[c*x^n])^2*ArcTanh[1 - 2/(1 - c*x^n)])/n - (b*(a + b*ArcTanh[c*x^n])*PolyLog[2, 1 - 2/(1 - c*x^n)])/n + (b*(a + b*ArcTanh[c*x^n])*PolyLog[2, -1 + 2/(1 - c*x^n)])/n + (b^2*PolyLog[3, 1 - 2/(1 - c*x^n)])/(2*n) - (b^2*PolyLog[3, -1 + 2/(1 - c*x^n)])/(2*n)","A",7,6,16,0.3750,1,"{6095, 5914, 6052, 5948, 6058, 6610}"
234,0,0,0,0.02298,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2}{x^2} \, dx","Int[(a + b*ArcTanh[c*x^n])^2/x^2,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2}{x^2},x\right)",0,"Defer[Int][(a + b*ArcTanh[c*x^n])^2/x^2, x]","A",0,0,0,0,-1,"{}"
235,0,0,0,0.0233473,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2}{x^3} \, dx","Int[(a + b*ArcTanh[c*x^n])^2/x^3,x]","\int \frac{\left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2}{x^3} \, dx","\text{Int}\left(\frac{\left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2}{x^3},x\right)",0,"Defer[Int][(a + b*ArcTanh[c*x^n])^2/x^3, x]","A",0,0,0,0,-1,"{}"
236,1,30,0,0.0213019,"\int \frac{\tanh ^{-1}\left(a x^n\right)}{x} \, dx","Int[ArcTanh[a*x^n]/x,x]","\frac{\text{PolyLog}\left(2,a x^n\right)}{2 n}-\frac{\text{PolyLog}\left(2,-a x^n\right)}{2 n}","\frac{\text{PolyLog}\left(2,a x^n\right)}{2 n}-\frac{\text{PolyLog}\left(2,-a x^n\right)}{2 n}",1,"-PolyLog[2, -(a*x^n)]/(2*n) + PolyLog[2, a*x^n]/(2*n)","A",2,2,10,0.2000,1,"{6095, 5912}"
237,1,24,0,0.0212865,"\int \frac{\tanh ^{-1}\left(a x^5\right)}{x} \, dx","Int[ArcTanh[a*x^5]/x,x]","\frac{1}{10} \text{PolyLog}\left(2,a x^5\right)-\frac{1}{10} \text{PolyLog}\left(2,-a x^5\right)","\frac{1}{10} \text{PolyLog}\left(2,a x^5\right)-\frac{1}{10} \text{PolyLog}\left(2,-a x^5\right)",1,"-PolyLog[2, -(a*x^5)]/10 + PolyLog[2, a*x^5]/10","A",2,2,10,0.2000,1,"{6095, 5912}"
238,1,19,0,0.006243,"\int \tanh ^{-1}\left(\frac{1}{x}\right) \, dx","Int[ArcTanh[x^(-1)],x]","\frac{1}{2} \log \left(1-x^2\right)+x \tanh ^{-1}\left(\frac{1}{x}\right)","\frac{1}{2} \log \left(1-x^2\right)+x \tanh ^{-1}\left(\frac{1}{x}\right)",1,"x*ArcTanh[x^(-1)] + Log[1 - x^2]/2","A",3,3,4,0.7500,1,"{6091, 263, 260}"
239,0,0,0,0.0235968,"\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x^n])^3,x]","\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTanh[c*x^n])^3, x]","A",0,0,0,0,-1,"{}"
240,0,0,0,0.0241501,"\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x^n])^2,x]","\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTanh[c*x^n])^2, x]","A",0,0,0,0,-1,"{}"
241,1,88,0,0.0441134,"\int (d x)^m \left(a+b \tanh ^{-1}\left(c x^n\right)\right) \, dx","Int[(d*x)^m*(a + b*ArcTanh[c*x^n]),x]","\frac{(d x)^{m+1} \left(a+b \tanh ^{-1}\left(c x^n\right)\right)}{d (m+1)}-\frac{b c n x^{n+1} (d x)^m \, _2F_1\left(1,\frac{m+n+1}{2 n};\frac{m+3 n+1}{2 n};c^2 x^{2 n}\right)}{(m+1) (m+n+1)}","\frac{x (d x)^m \left(a+b \tanh ^{-1}\left(c x^n\right)\right)}{m+1}-\frac{b c n x^{n+1} (d x)^m \, _2F_1\left(1,\frac{m+n+1}{2 n};\frac{m+3 n+1}{2 n};c^2 x^{2 n}\right)}{(m+1) (m+n+1)}",1,"((d*x)^(1 + m)*(a + b*ArcTanh[c*x^n]))/(d*(1 + m)) - (b*c*n*x^(1 + n)*(d*x)^m*Hypergeometric2F1[1, (1 + m + n)/(2*n), (1 + m + 3*n)/(2*n), c^2*x^(2*n)])/((1 + m)*(1 + m + n))","A",3,3,16,0.1875,1,"{6097, 20, 364}"
242,0,0,0,0.0269594,"\int \frac{(d x)^m}{a+b \tanh ^{-1}\left(c x^n\right)} \, dx","Int[(d*x)^m/(a + b*ArcTanh[c*x^n]),x]","\int \frac{(d x)^m}{a+b \tanh ^{-1}\left(c x^n\right)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \tanh ^{-1}\left(c x^n\right)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTanh[c*x^n]), x]","A",0,0,0,0,-1,"{}"
243,0,0,0,0.0264206,"\int \frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2} \, dx","Int[(d*x)^m/(a + b*ArcTanh[c*x^n])^2,x]","\int \frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^m}{\left(a+b \tanh ^{-1}\left(c x^n\right)\right)^2},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTanh[c*x^n])^2, x]","A",0,0,0,0,-1,"{}"