1,1,263,0,0.3387513,"\int x^3 \tanh ^{-1}(a+b x)^2 \, dx","Int[x^3*ArcTanh[a + b*x]^2,x]","\frac{a \left(a^2+1\right) \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b^4}+\frac{\left(6 a^2+1\right) \log \left(1-(a+b x)^2\right)}{4 b^4}-\frac{a \left(a^2+1\right) \tanh ^{-1}(a+b x)^2}{b^4}-\frac{\left(a^4+6 a^2+1\right) \tanh ^{-1}(a+b x)^2}{4 b^4}+\frac{\left(6 a^2+1\right) (a+b x) \tanh ^{-1}(a+b x)}{2 b^4}+\frac{2 a \left(a^2+1\right) \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{b^4}-\frac{a x}{b^3}+\frac{(a+b x)^2}{12 b^4}+\frac{\log \left(1-(a+b x)^2\right)}{12 b^4}+\frac{(a+b x)^3 \tanh ^{-1}(a+b x)}{6 b^4}-\frac{a (a+b x)^2 \tanh ^{-1}(a+b x)}{b^4}+\frac{a \tanh ^{-1}(a+b x)}{b^4}+\frac{1}{4} x^4 \tanh ^{-1}(a+b x)^2","\frac{a \left(a^2+1\right) \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b^4}+\frac{\left(6 a^2+1\right) \log \left(1-(a+b x)^2\right)}{4 b^4}-\frac{a \left(a^2+1\right) \tanh ^{-1}(a+b x)^2}{b^4}-\frac{\left(a^4+6 a^2+1\right) \tanh ^{-1}(a+b x)^2}{4 b^4}+\frac{\left(6 a^2+1\right) (a+b x) \tanh ^{-1}(a+b x)}{2 b^4}+\frac{2 a \left(a^2+1\right) \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{b^4}-\frac{a x}{b^3}+\frac{(a+b x)^2}{12 b^4}+\frac{\log \left(1-(a+b x)^2\right)}{12 b^4}+\frac{(a+b x)^3 \tanh ^{-1}(a+b x)}{6 b^4}-\frac{a (a+b x)^2 \tanh ^{-1}(a+b x)}{b^4}+\frac{a \tanh ^{-1}(a+b x)}{b^4}+\frac{1}{4} x^4 \tanh ^{-1}(a+b x)^2",1,"-((a*x)/b^3) + (a + b*x)^2/(12*b^4) + (a*ArcTanh[a + b*x])/b^4 + ((1 + 6*a^2)*(a + b*x)*ArcTanh[a + b*x])/(2*b^4) - (a*(a + b*x)^2*ArcTanh[a + b*x])/b^4 + ((a + b*x)^3*ArcTanh[a + b*x])/(6*b^4) - (a*(1 + a^2)*ArcTanh[a + b*x]^2)/b^4 - ((1 + 6*a^2 + a^4)*ArcTanh[a + b*x]^2)/(4*b^4) + (x^4*ArcTanh[a + b*x]^2)/4 + (2*a*(1 + a^2)*ArcTanh[a + b*x]*Log[2/(1 - a - b*x)])/b^4 + Log[1 - (a + b*x)^2]/(12*b^4) + ((1 + 6*a^2)*Log[1 - (a + b*x)^2])/(4*b^4) + (a*(1 + a^2)*PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))])/b^4","A",19,15,12,1.250,1,"{6111, 5928, 5910, 260, 5916, 321, 206, 266, 43, 6048, 5948, 5984, 5918, 2402, 2315}"
2,1,204,0,0.2685699,"\int x^2 \tanh ^{-1}(a+b x)^2 \, dx","Int[x^2*ArcTanh[a + b*x]^2,x]","-\frac{\left(3 a^2+1\right) \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{3 b^3}+\frac{a \left(a^2+3\right) \tanh ^{-1}(a+b x)^2}{3 b^3}+\frac{\left(3 a^2+1\right) \tanh ^{-1}(a+b x)^2}{3 b^3}-\frac{2 \left(3 a^2+1\right) \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{3 b^3}-\frac{a \log \left(1-(a+b x)^2\right)}{b^3}+\frac{(a+b x)^2 \tanh ^{-1}(a+b x)}{3 b^3}-\frac{2 a (a+b x) \tanh ^{-1}(a+b x)}{b^3}-\frac{\tanh ^{-1}(a+b x)}{3 b^3}+\frac{1}{3} x^3 \tanh ^{-1}(a+b x)^2+\frac{x}{3 b^2}","-\frac{\left(3 a^2+1\right) \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{3 b^3}+\frac{a \left(a^2+3\right) \tanh ^{-1}(a+b x)^2}{3 b^3}+\frac{\left(3 a^2+1\right) \tanh ^{-1}(a+b x)^2}{3 b^3}-\frac{2 \left(3 a^2+1\right) \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{3 b^3}-\frac{a \log \left(1-(a+b x)^2\right)}{b^3}+\frac{(a+b x)^2 \tanh ^{-1}(a+b x)}{3 b^3}-\frac{2 a (a+b x) \tanh ^{-1}(a+b x)}{b^3}-\frac{\tanh ^{-1}(a+b x)}{3 b^3}+\frac{1}{3} x^3 \tanh ^{-1}(a+b x)^2+\frac{x}{3 b^2}",1,"x/(3*b^2) - ArcTanh[a + b*x]/(3*b^3) - (2*a*(a + b*x)*ArcTanh[a + b*x])/b^3 + ((a + b*x)^2*ArcTanh[a + b*x])/(3*b^3) + (a*(3 + a^2)*ArcTanh[a + b*x]^2)/(3*b^3) + ((1 + 3*a^2)*ArcTanh[a + b*x]^2)/(3*b^3) + (x^3*ArcTanh[a + b*x]^2)/3 - (2*(1 + 3*a^2)*ArcTanh[a + b*x]*Log[2/(1 - a - b*x)])/(3*b^3) - (a*Log[1 - (a + b*x)^2])/b^3 - ((1 + 3*a^2)*PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))])/(3*b^3)","A",15,13,12,1.083,1,"{6111, 5928, 5910, 260, 5916, 321, 206, 6048, 5948, 5984, 5918, 2402, 2315}"
3,1,136,0,0.2002183,"\int x \tanh ^{-1}(a+b x)^2 \, dx","Int[x*ArcTanh[a + b*x]^2,x]","\frac{a \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b^2}-\frac{\left(a^2+1\right) \tanh ^{-1}(a+b x)^2}{2 b^2}+\frac{\log \left(1-(a+b x)^2\right)}{2 b^2}-\frac{a \tanh ^{-1}(a+b x)^2}{b^2}+\frac{(a+b x) \tanh ^{-1}(a+b x)}{b^2}+\frac{2 a \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{b^2}+\frac{1}{2} x^2 \tanh ^{-1}(a+b x)^2","\frac{a \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b^2}-\frac{\left(a^2+1\right) \tanh ^{-1}(a+b x)^2}{2 b^2}+\frac{\log \left(1-(a+b x)^2\right)}{2 b^2}-\frac{a \tanh ^{-1}(a+b x)^2}{b^2}+\frac{(a+b x) \tanh ^{-1}(a+b x)}{b^2}+\frac{2 a \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{b^2}+\frac{1}{2} x^2 \tanh ^{-1}(a+b x)^2",1,"((a + b*x)*ArcTanh[a + b*x])/b^2 - (a*ArcTanh[a + b*x]^2)/b^2 - ((1 + a^2)*ArcTanh[a + b*x]^2)/(2*b^2) + (x^2*ArcTanh[a + b*x]^2)/2 + (2*a*ArcTanh[a + b*x]*Log[2/(1 - a - b*x)])/b^2 + Log[1 - (a + b*x)^2]/(2*b^2) + (a*PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))])/b^2","A",12,10,10,1.000,1,"{6111, 5928, 5910, 260, 6048, 5948, 5984, 5918, 2402, 2315}"
4,1,81,0,0.086324,"\int \tanh ^{-1}(a+b x)^2 \, dx","Int[ArcTanh[a + b*x]^2,x]","-\frac{\text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b}+\frac{(a+b x) \tanh ^{-1}(a+b x)^2}{b}+\frac{\tanh ^{-1}(a+b x)^2}{b}-\frac{2 \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{b}","-\frac{\text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b}+\frac{(a+b x) \tanh ^{-1}(a+b x)^2}{b}+\frac{\tanh ^{-1}(a+b x)^2}{b}-\frac{2 \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{b}",1,"ArcTanh[a + b*x]^2/b + ((a + b*x)*ArcTanh[a + b*x]^2)/b - (2*ArcTanh[a + b*x]*Log[2/(1 - a - b*x)])/b - PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))]/b","A",6,6,8,0.7500,1,"{6103, 5910, 5984, 5918, 2402, 2315}"
5,1,148,0,0.0901863,"\int \frac{\tanh ^{-1}(a+b x)^2}{x} \, dx","Int[ArcTanh[a + b*x]^2/x,x]","\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2}{a+b x+1}\right)-\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)+\tanh ^{-1}(a+b x) \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)-\tanh ^{-1}(a+b x) \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)-\log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)^2+\log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \tanh ^{-1}(a+b x)^2","\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2}{a+b x+1}\right)-\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)+\tanh ^{-1}(a+b x) \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)-\tanh ^{-1}(a+b x) \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)-\log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)^2+\log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \tanh ^{-1}(a+b x)^2",1,"-(ArcTanh[a + b*x]^2*Log[2/(1 + a + b*x)]) + ArcTanh[a + b*x]^2*Log[(2*b*x)/((1 - a)*(1 + a + b*x))] + ArcTanh[a + b*x]*PolyLog[2, 1 - 2/(1 + a + b*x)] - ArcTanh[a + b*x]*PolyLog[2, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))] + PolyLog[3, 1 - 2/(1 + a + b*x)]/2 - PolyLog[3, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))]/2","A",2,2,12,0.1667,1,"{6111, 5922}"
6,1,251,0,0.6990523,"\int \frac{\tanh ^{-1}(a+b x)^2}{x^2} \, dx","Int[ArcTanh[a + b*x]^2/x^2,x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{1-a^2}-\frac{b \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)}{1-a^2}+\frac{b \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{2 (1-a)}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{2 (a+1)}-\frac{2 b \log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)}{1-a^2}+\frac{2 b \log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \tanh ^{-1}(a+b x)}{1-a^2}-\frac{\tanh ^{-1}(a+b x)^2}{x}+\frac{b \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{1-a}+\frac{b \log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)}{a+1}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{1-a^2}-\frac{b \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)}{1-a^2}+\frac{b \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{2 (1-a)}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{2 (a+1)}-\frac{2 b \log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)}{1-a^2}+\frac{2 b \log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \tanh ^{-1}(a+b x)}{1-a^2}-\frac{\tanh ^{-1}(a+b x)^2}{x}+\frac{b \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{1-a}+\frac{b \log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)}{a+1}",1,"-(ArcTanh[a + b*x]^2/x) + (b*ArcTanh[a + b*x]*Log[2/(1 - a - b*x)])/(1 - a) + (b*ArcTanh[a + b*x]*Log[2/(1 + a + b*x)])/(1 + a) - (2*b*ArcTanh[a + b*x]*Log[2/(1 + a + b*x)])/(1 - a^2) + (2*b*ArcTanh[a + b*x]*Log[(2*b*x)/((1 - a)*(1 + a + b*x))])/(1 - a^2) + (b*PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))])/(2*(1 - a)) - (b*PolyLog[2, 1 - 2/(1 + a + b*x)])/(2*(1 + a)) + (b*PolyLog[2, 1 - 2/(1 + a + b*x)])/(1 - a^2) - (b*PolyLog[2, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))])/(1 - a^2)","A",17,15,12,1.250,1,"{6109, 371, 706, 31, 633, 6741, 6121, 6688, 12, 6725, 5920, 2402, 2315, 2447, 5918}"
7,1,370,0,0.8009444,"\int \frac{\tanh ^{-1}(a+b x)^2}{x^3} \, dx","Int[ArcTanh[a + b*x]^2/x^3,x]","\frac{a b^2 \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{\left(1-a^2\right)^2}-\frac{a b^2 \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)}{\left(1-a^2\right)^2}+\frac{b^2 \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{4 (1-a)^2}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{4 (a+1)^2}+\frac{b^2 \log (x)}{\left(1-a^2\right)^2}-\frac{2 a b^2 \log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)}{\left(1-a^2\right)^2}+\frac{2 a b^2 \log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \tanh ^{-1}(a+b x)}{\left(1-a^2\right)^2}-\frac{b \tanh ^{-1}(a+b x)}{\left(1-a^2\right) x}-\frac{b^2 \log (-a-b x+1)}{2 (1-a)^2 (a+1)}-\frac{b^2 \log (a+b x+1)}{2 (1-a) (a+1)^2}+\frac{b^2 \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{2 (1-a)^2}-\frac{b^2 \log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)}{2 (a+1)^2}-\frac{\tanh ^{-1}(a+b x)^2}{2 x^2}","\frac{a b^2 \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{\left(1-a^2\right)^2}-\frac{a b^2 \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)}{\left(1-a^2\right)^2}+\frac{b^2 \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{4 (1-a)^2}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{4 (a+1)^2}+\frac{b^2 \log (x)}{\left(1-a^2\right)^2}-\frac{2 a b^2 \log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)}{\left(1-a^2\right)^2}+\frac{2 a b^2 \log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \tanh ^{-1}(a+b x)}{\left(1-a^2\right)^2}-\frac{b \tanh ^{-1}(a+b x)}{\left(1-a^2\right) x}-\frac{b^2 \log (-a-b x+1)}{2 (1-a)^2 (a+1)}-\frac{b^2 \log (a+b x+1)}{2 (1-a) (a+1)^2}+\frac{b^2 \log \left(\frac{2}{-a-b x+1}\right) \tanh ^{-1}(a+b x)}{2 (1-a)^2}-\frac{b^2 \log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)}{2 (a+1)^2}-\frac{\tanh ^{-1}(a+b x)^2}{2 x^2}",1,"-((b*ArcTanh[a + b*x])/((1 - a^2)*x)) - ArcTanh[a + b*x]^2/(2*x^2) + (b^2*Log[x])/(1 - a^2)^2 + (b^2*ArcTanh[a + b*x]*Log[2/(1 - a - b*x)])/(2*(1 - a)^2) - (b^2*Log[1 - a - b*x])/(2*(1 - a)^2*(1 + a)) - (b^2*ArcTanh[a + b*x]*Log[2/(1 + a + b*x)])/(2*(1 + a)^2) - (2*a*b^2*ArcTanh[a + b*x]*Log[2/(1 + a + b*x)])/(1 - a^2)^2 + (2*a*b^2*ArcTanh[a + b*x]*Log[(2*b*x)/((1 - a)*(1 + a + b*x))])/(1 - a^2)^2 - (b^2*Log[1 + a + b*x])/(2*(1 - a)*(1 + a)^2) + (b^2*PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))])/(4*(1 - a)^2) + (b^2*PolyLog[2, 1 - 2/(1 + a + b*x)])/(4*(1 + a)^2) + (a*b^2*PolyLog[2, 1 - 2/(1 + a + b*x)])/(1 - a^2)^2 - (a*b^2*PolyLog[2, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))])/(1 - a^2)^2","A",21,16,12,1.333,1,"{6109, 371, 710, 801, 6741, 6121, 6725, 5926, 706, 31, 633, 5920, 2402, 2315, 2447, 5918}"
8,1,56,0,0.1279955,"\int \frac{\tanh ^{-1}(1+b x)^2}{x} \, dx","Int[ArcTanh[1 + b*x]^2/x,x]","\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{b x}+1\right)-\tanh ^{-1}(b x+1) \text{PolyLog}\left(2,\frac{2}{b x}+1\right)-\log \left(-\frac{2}{b x}\right) \tanh ^{-1}(b x+1)^2","\frac{1}{2} \text{PolyLog}\left(3,\frac{2}{b x}+1\right)-\tanh ^{-1}(b x+1) \text{PolyLog}\left(2,\frac{2}{b x}+1\right)-\log \left(-\frac{2}{b x}\right) \tanh ^{-1}(b x+1)^2",1,"-(ArcTanh[1 + b*x]^2*Log[-2/(b*x)]) - ArcTanh[1 + b*x]*PolyLog[2, 1 + 2/(b*x)] + PolyLog[3, 1 + 2/(b*x)]/2","A",4,5,12,0.4167,1,"{6111, 5918, 5948, 6058, 6610}"
9,1,72,0,0.0666851,"\int (c e+d e x)^3 \left(a+b \tanh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcTanh[c + d*x]),x]","\frac{e^3 (c+d x)^4 \left(a+b \tanh ^{-1}(c+d x)\right)}{4 d}+\frac{b e^3 (c+d x)^3}{12 d}-\frac{b e^3 \tanh ^{-1}(c+d x)}{4 d}+\frac{1}{4} b e^3 x","\frac{e^3 (c+d x)^4 \left(a+b \tanh ^{-1}(c+d x)\right)}{4 d}+\frac{b e^3 (c+d x)^3}{12 d}-\frac{b e^3 \tanh ^{-1}(c+d x)}{4 d}+\frac{1}{4} b e^3 x",1,"(b*e^3*x)/4 + (b*e^3*(c + d*x)^3)/(12*d) - (b*e^3*ArcTanh[c + d*x])/(4*d) + (e^3*(c + d*x)^4*(a + b*ArcTanh[c + d*x]))/(4*d)","A",6,5,21,0.2381,1,"{6107, 12, 5916, 302, 206}"
10,1,69,0,0.0651115,"\int (c e+d e x)^2 \left(a+b \tanh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcTanh[c + d*x]),x]","\frac{e^2 (c+d x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d}+\frac{b e^2 (c+d x)^2}{6 d}+\frac{b e^2 \log \left(1-(c+d x)^2\right)}{6 d}","\frac{e^2 (c+d x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d}+\frac{b e^2 (c+d x)^2}{6 d}+\frac{b e^2 \log \left(1-(c+d x)^2\right)}{6 d}",1,"(b*e^2*(c + d*x)^2)/(6*d) + (e^2*(c + d*x)^3*(a + b*ArcTanh[c + d*x]))/(3*d) + (b*e^2*Log[1 - (c + d*x)^2])/(6*d)","A",6,5,21,0.2381,1,"{6107, 12, 5916, 266, 43}"
11,1,48,0,0.0344056,"\int (c e+d e x) \left(a+b \tanh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)*(a + b*ArcTanh[c + d*x]),x]","\frac{e (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)}{2 d}-\frac{b e \tanh ^{-1}(c+d x)}{2 d}+\frac{b e x}{2}","\frac{e (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)}{2 d}-\frac{b e \tanh ^{-1}(c+d x)}{2 d}+\frac{b e x}{2}",1,"(b*e*x)/2 - (b*e*ArcTanh[c + d*x])/(2*d) + (e*(c + d*x)^2*(a + b*ArcTanh[c + d*x]))/(2*d)","A",5,5,19,0.2632,1,"{6107, 12, 5916, 321, 206}"
12,1,54,0,0.0447492,"\int \frac{a+b \tanh ^{-1}(c+d x)}{c e+d e x} \, dx","Int[(a + b*ArcTanh[c + d*x])/(c*e + d*e*x),x]","-\frac{b \text{PolyLog}(2,-c-d x)}{2 d e}+\frac{b \text{PolyLog}(2,c+d x)}{2 d e}+\frac{a \log (c+d x)}{d e}","-\frac{b \text{PolyLog}(2,-c-d x)}{2 d e}+\frac{b \text{PolyLog}(2,c+d x)}{2 d e}+\frac{a \log (c+d x)}{d e}",1,"(a*Log[c + d*x])/(d*e) - (b*PolyLog[2, -c - d*x])/(2*d*e) + (b*PolyLog[2, c + d*x])/(2*d*e)","A",3,3,21,0.1429,1,"{6107, 12, 5912}"
13,1,63,0,0.0585116,"\int \frac{a+b \tanh ^{-1}(c+d x)}{(c e+d e x)^2} \, dx","Int[(a + b*ArcTanh[c + d*x])/(c*e + d*e*x)^2,x]","-\frac{a+b \tanh ^{-1}(c+d x)}{d e^2 (c+d x)}+\frac{b \log (c+d x)}{d e^2}-\frac{b \log \left(1-(c+d x)^2\right)}{2 d e^2}","-\frac{a+b \tanh ^{-1}(c+d x)}{d e^2 (c+d x)}+\frac{b \log (c+d x)}{d e^2}-\frac{b \log \left(1-(c+d x)^2\right)}{2 d e^2}",1,"-((a + b*ArcTanh[c + d*x])/(d*e^2*(c + d*x))) + (b*Log[c + d*x])/(d*e^2) - (b*Log[1 - (c + d*x)^2])/(2*d*e^2)","A",7,7,21,0.3333,1,"{6107, 12, 5916, 266, 36, 31, 29}"
14,1,63,0,0.048815,"\int \frac{a+b \tanh ^{-1}(c+d x)}{(c e+d e x)^3} \, dx","Int[(a + b*ArcTanh[c + d*x])/(c*e + d*e*x)^3,x]","-\frac{a+b \tanh ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}-\frac{b}{2 d e^3 (c+d x)}+\frac{b \tanh ^{-1}(c+d x)}{2 d e^3}","-\frac{a+b \tanh ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}-\frac{b}{2 d e^3 (c+d x)}+\frac{b \tanh ^{-1}(c+d x)}{2 d e^3}",1,"-b/(2*d*e^3*(c + d*x)) + (b*ArcTanh[c + d*x])/(2*d*e^3) - (a + b*ArcTanh[c + d*x])/(2*d*e^3*(c + d*x)^2)","A",5,5,21,0.2381,1,"{6107, 12, 5916, 325, 206}"
15,1,159,0,0.2475472,"\int (c e+d e x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcTanh[c + d*x])^2,x]","\frac{e^3 (c+d x)^4 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 d}+\frac{b e^3 (c+d x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)}{6 d}-\frac{e^3 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 d}+\frac{1}{2} a b e^3 x+\frac{b^2 e^3 (c+d x)^2}{12 d}+\frac{b^2 e^3 \log \left(1-(c+d x)^2\right)}{3 d}+\frac{b^2 e^3 (c+d x) \tanh ^{-1}(c+d x)}{2 d}","\frac{e^3 (c+d x)^4 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 d}+\frac{b e^3 (c+d x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)}{6 d}-\frac{e^3 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 d}+\frac{1}{2} a b e^3 x+\frac{b^2 e^3 (c+d x)^2}{12 d}+\frac{b^2 e^3 \log \left(1-(c+d x)^2\right)}{3 d}+\frac{b^2 e^3 (c+d x) \tanh ^{-1}(c+d x)}{2 d}",1,"(a*b*e^3*x)/2 + (b^2*e^3*(c + d*x)^2)/(12*d) + (b^2*e^3*(c + d*x)*ArcTanh[c + d*x])/(2*d) + (b*e^3*(c + d*x)^3*(a + b*ArcTanh[c + d*x]))/(6*d) - (e^3*(a + b*ArcTanh[c + d*x])^2)/(4*d) + (e^3*(c + d*x)^4*(a + b*ArcTanh[c + d*x])^2)/(4*d) + (b^2*e^3*Log[1 - (c + d*x)^2])/(3*d)","A",13,9,23,0.3913,1,"{6107, 12, 5916, 5980, 266, 43, 5910, 260, 5948}"
16,1,179,0,0.2372244,"\int (c e+d e x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcTanh[c + d*x])^2,x]","-\frac{b^2 e^2 \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{3 d}+\frac{e^2 (c+d x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d}+\frac{b e^2 (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d}+\frac{e^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d}-\frac{b^2 e^2 \tanh ^{-1}(c+d x)}{3 d}+\frac{1}{3} b^2 e^2 x","-\frac{b^2 e^2 \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{3 d}+\frac{e^2 (c+d x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d}+\frac{b e^2 (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d}+\frac{e^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d}-\frac{b^2 e^2 \tanh ^{-1}(c+d x)}{3 d}+\frac{1}{3} b^2 e^2 x",1,"(b^2*e^2*x)/3 - (b^2*e^2*ArcTanh[c + d*x])/(3*d) + (b*e^2*(c + d*x)^2*(a + b*ArcTanh[c + d*x]))/(3*d) + (e^2*(a + b*ArcTanh[c + d*x])^2)/(3*d) + (e^2*(c + d*x)^3*(a + b*ArcTanh[c + d*x])^2)/(3*d) - (2*b*e^2*(a + b*ArcTanh[c + d*x])*Log[2/(1 - c - d*x)])/(3*d) - (b^2*e^2*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(3*d)","A",11,10,23,0.4348,1,"{6107, 12, 5916, 5980, 321, 206, 5984, 5918, 2402, 2315}"
17,1,95,0,0.135102,"\int (c e+d e x) \left(a+b \tanh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)*(a + b*ArcTanh[c + d*x])^2,x]","\frac{e (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}-\frac{e \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}+a b e x+\frac{b^2 e \log \left(1-(c+d x)^2\right)}{2 d}+\frac{b^2 e (c+d x) \tanh ^{-1}(c+d x)}{d}","\frac{e (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}-\frac{e \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}+a b e x+\frac{b^2 e \log \left(1-(c+d x)^2\right)}{2 d}+\frac{b^2 e (c+d x) \tanh ^{-1}(c+d x)}{d}",1,"a*b*e*x + (b^2*e*(c + d*x)*ArcTanh[c + d*x])/d - (e*(a + b*ArcTanh[c + d*x])^2)/(2*d) + (e*(c + d*x)^2*(a + b*ArcTanh[c + d*x])^2)/(2*d) + (b^2*e*Log[1 - (c + d*x)^2])/(2*d)","A",8,7,21,0.3333,1,"{6107, 12, 5916, 5980, 5910, 260, 5948}"
18,1,168,0,0.3027443,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{c e+d e x} \, dx","Int[(a + b*ArcTanh[c + d*x])^2/(c*e + d*e*x),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e}+\frac{b \text{PolyLog}\left(2,\frac{2}{-c-d x+1}-1\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d e}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{-c-d x+1}-1\right)}{2 d e}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d e}","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e}+\frac{b \text{PolyLog}\left(2,\frac{2}{-c-d x+1}-1\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d e}-\frac{b^2 \text{PolyLog}\left(3,\frac{2}{-c-d x+1}-1\right)}{2 d e}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d e}",1,"(2*(a + b*ArcTanh[c + d*x])^2*ArcTanh[1 - 2/(1 - c - d*x)])/(d*e) - (b*(a + b*ArcTanh[c + d*x])*PolyLog[2, 1 - 2/(1 - c - d*x)])/(d*e) + (b*(a + b*ArcTanh[c + d*x])*PolyLog[2, -1 + 2/(1 - c - d*x)])/(d*e) + (b^2*PolyLog[3, 1 - 2/(1 - c - d*x)])/(2*d*e) - (b^2*PolyLog[3, -1 + 2/(1 - c - d*x)])/(2*d*e)","A",8,7,23,0.3043,1,"{6107, 12, 5914, 6052, 5948, 6058, 6610}"
19,1,104,0,0.1806617,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{(c e+d e x)^2} \, dx","Int[(a + b*ArcTanh[c + d*x])^2/(c*e + d*e*x)^2,x]","-\frac{b^2 \text{PolyLog}\left(2,\frac{2}{c+d x+1}-1\right)}{d e^2}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{d e^2 (c+d x)}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{d e^2}+\frac{2 b \log \left(2-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^2}","-\frac{b^2 \text{PolyLog}\left(2,\frac{2}{c+d x+1}-1\right)}{d e^2}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{d e^2 (c+d x)}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{d e^2}+\frac{2 b \log \left(2-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^2}",1,"(a + b*ArcTanh[c + d*x])^2/(d*e^2) - (a + b*ArcTanh[c + d*x])^2/(d*e^2*(c + d*x)) + (2*b*(a + b*ArcTanh[c + d*x])*Log[2 - 2/(1 + c + d*x)])/(d*e^2) - (b^2*PolyLog[2, -1 + 2/(1 + c + d*x)])/(d*e^2)","A",6,6,23,0.2609,1,"{6107, 12, 5916, 5988, 5932, 2447}"
20,1,119,0,0.1741762,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{(c e+d e x)^3} \, dx","Int[(a + b*ArcTanh[c + d*x])^2/(c*e + d*e*x)^3,x]","-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^3 (c+d x)}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)^2}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^3}+\frac{b^2 \log (c+d x)}{d e^3}-\frac{b^2 \log \left(1-(c+d x)^2\right)}{2 d e^3}","-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^3 (c+d x)}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)^2}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^3}+\frac{b^2 \log (c+d x)}{d e^3}-\frac{b^2 \log \left(1-(c+d x)^2\right)}{2 d e^3}",1,"-((b*(a + b*ArcTanh[c + d*x]))/(d*e^3*(c + d*x))) + (a + b*ArcTanh[c + d*x])^2/(2*d*e^3) - (a + b*ArcTanh[c + d*x])^2/(2*d*e^3*(c + d*x)^2) + (b^2*Log[c + d*x])/(d*e^3) - (b^2*Log[1 - (c + d*x)^2])/(2*d*e^3)","A",10,9,23,0.3913,1,"{6107, 12, 5916, 5982, 266, 36, 31, 29, 5948}"
21,1,180,0,0.2701269,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{(c e+d e x)^4} \, dx","Int[(a + b*ArcTanh[c + d*x])^2/(c*e + d*e*x)^4,x]","-\frac{b^2 \text{PolyLog}\left(2,\frac{2}{c+d x+1}-1\right)}{3 d e^4}-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d e^4 (c+d x)^3}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d e^4}+\frac{2 b \log \left(2-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d e^4}-\frac{b^2}{3 d e^4 (c+d x)}+\frac{b^2 \tanh ^{-1}(c+d x)}{3 d e^4}","-\frac{b^2 \text{PolyLog}\left(2,\frac{2}{c+d x+1}-1\right)}{3 d e^4}-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d e^4 (c+d x)^3}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d e^4}+\frac{2 b \log \left(2-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d e^4}-\frac{b^2}{3 d e^4 (c+d x)}+\frac{b^2 \tanh ^{-1}(c+d x)}{3 d e^4}",1,"-b^2/(3*d*e^4*(c + d*x)) + (b^2*ArcTanh[c + d*x])/(3*d*e^4) - (b*(a + b*ArcTanh[c + d*x]))/(3*d*e^4*(c + d*x)^2) + (a + b*ArcTanh[c + d*x])^2/(3*d*e^4) - (a + b*ArcTanh[c + d*x])^2/(3*d*e^4*(c + d*x)^3) + (2*b*(a + b*ArcTanh[c + d*x])*Log[2 - 2/(1 + c + d*x)])/(3*d*e^4) - (b^2*PolyLog[2, -1 + 2/(1 + c + d*x)])/(3*d*e^4)","A",10,9,23,0.3913,1,"{6107, 12, 5916, 5982, 325, 206, 5988, 5932, 2447}"
22,1,172,0,0.2624468,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{(c e+d e x)^5} \, dx","Int[(a + b*ArcTanh[c + d*x])^2/(c*e + d*e*x)^5,x]","-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)}{2 d e^5 (c+d x)}-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)}{6 d e^5 (c+d x)^3}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 d e^5 (c+d x)^4}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 d e^5}-\frac{b^2}{12 d e^5 (c+d x)^2}+\frac{2 b^2 \log (c+d x)}{3 d e^5}-\frac{b^2 \log \left(1-(c+d x)^2\right)}{3 d e^5}","-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)}{2 d e^5 (c+d x)}-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)}{6 d e^5 (c+d x)^3}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 d e^5 (c+d x)^4}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 d e^5}-\frac{b^2}{12 d e^5 (c+d x)^2}+\frac{2 b^2 \log (c+d x)}{3 d e^5}-\frac{b^2 \log \left(1-(c+d x)^2\right)}{3 d e^5}",1,"-b^2/(12*d*e^5*(c + d*x)^2) - (b*(a + b*ArcTanh[c + d*x]))/(6*d*e^5*(c + d*x)^3) - (b*(a + b*ArcTanh[c + d*x]))/(2*d*e^5*(c + d*x)) + (a + b*ArcTanh[c + d*x])^2/(4*d*e^5) - (a + b*ArcTanh[c + d*x])^2/(4*d*e^5*(c + d*x)^4) + (2*b^2*Log[c + d*x])/(3*d*e^5) - (b^2*Log[1 - (c + d*x)^2])/(3*d*e^5)","A",15,10,23,0.4348,1,"{6107, 12, 5916, 5982, 266, 44, 36, 31, 29, 5948}"
23,1,263,0,0.4668797,"\int (c e+d e x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcTanh[c + d*x])^3,x]","-\frac{b^2 e^2 \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d}+\frac{b^3 e^2 \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d}+a b^2 e^2 x-\frac{b e^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}+\frac{b e^2 (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}+\frac{e^2 (c+d x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d}+\frac{e^2 \left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d}-\frac{b e^2 \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d}+\frac{b^3 e^2 \log \left(1-(c+d x)^2\right)}{2 d}+\frac{b^3 e^2 (c+d x) \tanh ^{-1}(c+d x)}{d}","-\frac{b^2 e^2 \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d}+\frac{b^3 e^2 \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d}+a b^2 e^2 x-\frac{b e^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}+\frac{b e^2 (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}+\frac{e^2 (c+d x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d}+\frac{e^2 \left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d}-\frac{b e^2 \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d}+\frac{b^3 e^2 \log \left(1-(c+d x)^2\right)}{2 d}+\frac{b^3 e^2 (c+d x) \tanh ^{-1}(c+d x)}{d}",1,"a*b^2*e^2*x + (b^3*e^2*(c + d*x)*ArcTanh[c + d*x])/d - (b*e^2*(a + b*ArcTanh[c + d*x])^2)/(2*d) + (b*e^2*(c + d*x)^2*(a + b*ArcTanh[c + d*x])^2)/(2*d) + (e^2*(a + b*ArcTanh[c + d*x])^3)/(3*d) + (e^2*(c + d*x)^3*(a + b*ArcTanh[c + d*x])^3)/(3*d) - (b*e^2*(a + b*ArcTanh[c + d*x])^2*Log[2/(1 - c - d*x)])/d + (b^3*e^2*Log[1 - (c + d*x)^2])/(2*d) - (b^2*e^2*(a + b*ArcTanh[c + d*x])*PolyLog[2, 1 - 2/(1 - c - d*x)])/d + (b^3*e^2*PolyLog[3, 1 - 2/(1 - c - d*x)])/(2*d)","A",14,11,23,0.4783,1,"{6107, 12, 5916, 5980, 5910, 260, 5948, 5984, 5918, 6058, 6610}"
24,1,160,0,0.262531,"\int (c e+d e x) \left(a+b \tanh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)*(a + b*ArcTanh[c + d*x])^3,x]","-\frac{3 b^3 e \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 d}-\frac{3 b^2 e \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d}+\frac{3 b e \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}+\frac{3 b e (c+d x) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}+\frac{e (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 d}-\frac{e \left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 d}","-\frac{3 b^3 e \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 d}-\frac{3 b^2 e \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d}+\frac{3 b e \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}+\frac{3 b e (c+d x) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}+\frac{e (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 d}-\frac{e \left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 d}",1,"(3*b*e*(a + b*ArcTanh[c + d*x])^2)/(2*d) + (3*b*e*(c + d*x)*(a + b*ArcTanh[c + d*x])^2)/(2*d) - (e*(a + b*ArcTanh[c + d*x])^3)/(2*d) + (e*(c + d*x)^2*(a + b*ArcTanh[c + d*x])^3)/(2*d) - (3*b^2*e*(a + b*ArcTanh[c + d*x])*Log[2/(1 - c - d*x)])/d - (3*b^3*e*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(2*d)","A",10,10,21,0.4762,1,"{6107, 12, 5916, 5980, 5910, 5984, 5918, 2402, 2315, 5948}"
25,1,257,0,0.4917678,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{c e+d e x} \, dx","Int[(a + b*ArcTanh[c + d*x])^3/(c*e + d*e*x),x]","\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{2 d e}-\frac{3 b^2 \text{PolyLog}\left(3,\frac{2}{-c-d x+1}-1\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{2 d e}-\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e}+\frac{3 b \text{PolyLog}\left(2,\frac{2}{-c-d x+1}-1\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e}-\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{-c-d x+1}\right)}{4 d e}+\frac{3 b^3 \text{PolyLog}\left(4,\frac{2}{-c-d x+1}-1\right)}{4 d e}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{d e}","\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{2 d e}-\frac{3 b^2 \text{PolyLog}\left(3,\frac{2}{-c-d x+1}-1\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{2 d e}-\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e}+\frac{3 b \text{PolyLog}\left(2,\frac{2}{-c-d x+1}-1\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e}-\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{-c-d x+1}\right)}{4 d e}+\frac{3 b^3 \text{PolyLog}\left(4,\frac{2}{-c-d x+1}-1\right)}{4 d e}+\frac{2 \tanh ^{-1}\left(1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{d e}",1,"(2*(a + b*ArcTanh[c + d*x])^3*ArcTanh[1 - 2/(1 - c - d*x)])/(d*e) - (3*b*(a + b*ArcTanh[c + d*x])^2*PolyLog[2, 1 - 2/(1 - c - d*x)])/(2*d*e) + (3*b*(a + b*ArcTanh[c + d*x])^2*PolyLog[2, -1 + 2/(1 - c - d*x)])/(2*d*e) + (3*b^2*(a + b*ArcTanh[c + d*x])*PolyLog[3, 1 - 2/(1 - c - d*x)])/(2*d*e) - (3*b^2*(a + b*ArcTanh[c + d*x])*PolyLog[3, -1 + 2/(1 - c - d*x)])/(2*d*e) - (3*b^3*PolyLog[4, 1 - 2/(1 - c - d*x)])/(4*d*e) + (3*b^3*PolyLog[4, -1 + 2/(1 - c - d*x)])/(4*d*e)","A",10,8,23,0.3478,1,"{6107, 12, 5914, 6052, 5948, 6058, 6062, 6610}"
26,1,143,0,0.3042308,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{(c e+d e x)^2} \, dx","Int[(a + b*ArcTanh[c + d*x])^3/(c*e + d*e*x)^2,x]","-\frac{3 b^2 \text{PolyLog}\left(2,\frac{2}{c+d x+1}-1\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^2}-\frac{3 b^3 \text{PolyLog}\left(3,\frac{2}{c+d x+1}-1\right)}{2 d e^2}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{d e^2 (c+d x)}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{d e^2}+\frac{3 b \log \left(2-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d e^2}","-\frac{3 b^2 \text{PolyLog}\left(2,\frac{2}{c+d x+1}-1\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^2}-\frac{3 b^3 \text{PolyLog}\left(3,\frac{2}{c+d x+1}-1\right)}{2 d e^2}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{d e^2 (c+d x)}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{d e^2}+\frac{3 b \log \left(2-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d e^2}",1,"(a + b*ArcTanh[c + d*x])^3/(d*e^2) - (a + b*ArcTanh[c + d*x])^3/(d*e^2*(c + d*x)) + (3*b*(a + b*ArcTanh[c + d*x])^2*Log[2 - 2/(1 + c + d*x)])/(d*e^2) - (3*b^2*(a + b*ArcTanh[c + d*x])*PolyLog[2, -1 + 2/(1 + c + d*x)])/(d*e^2) - (3*b^3*PolyLog[3, -1 + 2/(1 + c + d*x)])/(2*d*e^2)","A",7,8,23,0.3478,1,"{6107, 12, 5916, 5988, 5932, 5948, 6056, 6610}"
27,1,166,0,0.3350195,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{(c e+d e x)^3} \, dx","Int[(a + b*ArcTanh[c + d*x])^3/(c*e + d*e*x)^3,x]","-\frac{3 b^3 \text{PolyLog}\left(2,\frac{2}{c+d x+1}-1\right)}{2 d e^3}+\frac{3 b^2 \log \left(2-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^3}-\frac{3 b \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)}+\frac{3 b \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^3}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 d e^3 (c+d x)^2}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 d e^3}","-\frac{3 b^3 \text{PolyLog}\left(2,\frac{2}{c+d x+1}-1\right)}{2 d e^3}+\frac{3 b^2 \log \left(2-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^3}-\frac{3 b \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)}+\frac{3 b \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^3}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 d e^3 (c+d x)^2}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 d e^3}",1,"(3*b*(a + b*ArcTanh[c + d*x])^2)/(2*d*e^3) - (3*b*(a + b*ArcTanh[c + d*x])^2)/(2*d*e^3*(c + d*x)) + (a + b*ArcTanh[c + d*x])^3/(2*d*e^3) - (a + b*ArcTanh[c + d*x])^3/(2*d*e^3*(c + d*x)^2) + (3*b^2*(a + b*ArcTanh[c + d*x])*Log[2 - 2/(1 + c + d*x)])/(d*e^3) - (3*b^3*PolyLog[2, -1 + 2/(1 + c + d*x)])/(2*d*e^3)","A",9,8,23,0.3478,1,"{6107, 12, 5916, 5982, 5988, 5932, 2447, 5948}"
28,1,269,0,0.5136236,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{(c e+d e x)^4} \, dx","Int[(a + b*ArcTanh[c + d*x])^3/(c*e + d*e*x)^4,x]","-\frac{b^2 \text{PolyLog}\left(2,\frac{2}{c+d x+1}-1\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^4}-\frac{b^3 \text{PolyLog}\left(3,\frac{2}{c+d x+1}-1\right)}{2 d e^4}-\frac{b^2 \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^4 (c+d x)}-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^4 (c+d x)^2}+\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^4}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^3}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d e^4}+\frac{b \log \left(2-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d e^4}+\frac{b^3 \log (c+d x)}{d e^4}-\frac{b^3 \log \left(1-(c+d x)^2\right)}{2 d e^4}","-\frac{b^2 \text{PolyLog}\left(2,\frac{2}{c+d x+1}-1\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^4}-\frac{b^3 \text{PolyLog}\left(3,\frac{2}{c+d x+1}-1\right)}{2 d e^4}-\frac{b^2 \left(a+b \tanh ^{-1}(c+d x)\right)}{d e^4 (c+d x)}-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^4 (c+d x)^2}+\frac{b \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d e^4}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^3}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d e^4}+\frac{b \log \left(2-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d e^4}+\frac{b^3 \log (c+d x)}{d e^4}-\frac{b^3 \log \left(1-(c+d x)^2\right)}{2 d e^4}",1,"-((b^2*(a + b*ArcTanh[c + d*x]))/(d*e^4*(c + d*x))) + (b*(a + b*ArcTanh[c + d*x])^2)/(2*d*e^4) - (b*(a + b*ArcTanh[c + d*x])^2)/(2*d*e^4*(c + d*x)^2) + (a + b*ArcTanh[c + d*x])^3/(3*d*e^4) - (a + b*ArcTanh[c + d*x])^3/(3*d*e^4*(c + d*x)^3) + (b^3*Log[c + d*x])/(d*e^4) - (b^3*Log[1 - (c + d*x)^2])/(2*d*e^4) + (b*(a + b*ArcTanh[c + d*x])^2*Log[2 - 2/(1 + c + d*x)])/(d*e^4) - (b^2*(a + b*ArcTanh[c + d*x])*PolyLog[2, -1 + 2/(1 + c + d*x)])/(d*e^4) - (b^3*PolyLog[3, -1 + 2/(1 + c + d*x)])/(2*d*e^4)","A",16,13,23,0.5652,1,"{6107, 12, 5916, 5982, 266, 36, 31, 29, 5948, 5988, 5932, 6056, 6610}"
29,1,21,0,0.022476,"\int \frac{\tanh ^{-1}(1+x)}{2+2 x} \, dx","Int[ArcTanh[1 + x]/(2 + 2*x),x]","\frac{1}{4} \text{PolyLog}(2,x+1)-\frac{1}{4} \text{PolyLog}(2,-x-1)","\frac{1}{4} \text{PolyLog}(2,x+1)-\frac{1}{4} \text{PolyLog}(2,-x-1)",1,"-PolyLog[2, -1 - x]/4 + PolyLog[2, 1 + x]/4","A",3,3,12,0.2500,1,"{6107, 12, 5912}"
30,1,32,0,0.0310902,"\int \frac{\tanh ^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Int[ArcTanh[a + b*x]/((a*d)/b + d*x),x]","\frac{\text{PolyLog}(2,a+b x)}{2 d}-\frac{\text{PolyLog}(2,-a-b x)}{2 d}","\frac{\text{PolyLog}(2,a+b x)}{2 d}-\frac{\text{PolyLog}(2,-a-b x)}{2 d}",1,"-PolyLog[2, -a - b*x]/(2*d) + PolyLog[2, a + b*x]/(2*d)","A",3,3,19,0.1579,1,"{6107, 12, 5912}"
31,1,168,0,0.3309428,"\int (e+f x)^3 \left(a+b \tanh ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)^3*(a + b*ArcTanh[c + d*x]),x]","\frac{(e+f x)^4 \left(a+b \tanh ^{-1}(c+d x)\right)}{4 f}+\frac{b f x \left(\left(6 c^2+1\right) f^2-12 c d e f+6 d^2 e^2\right)}{4 d^3}+\frac{b f^2 (c+d x)^2 (d e-c f)}{2 d^4}-\frac{b (-c f+d e-f)^4 \log (c+d x+1)}{8 d^4 f}+\frac{b (-c f+d e+f)^4 \log (-c-d x+1)}{8 d^4 f}+\frac{b f^3 (c+d x)^3}{12 d^4}","\frac{(e+f x)^4 \left(a+b \tanh ^{-1}(c+d x)\right)}{4 f}+\frac{b f x \left(\left(6 c^2+1\right) f^2-12 c d e f+6 d^2 e^2\right)}{4 d^3}+\frac{b f^2 (c+d x)^2 (d e-c f)}{2 d^4}-\frac{b (-c f+d e-f)^4 \log (c+d x+1)}{8 d^4 f}+\frac{b (-c f+d e+f)^4 \log (-c-d x+1)}{8 d^4 f}+\frac{b f^3 (c+d x)^3}{12 d^4}",1,"(b*f*(6*d^2*e^2 - 12*c*d*e*f + (1 + 6*c^2)*f^2)*x)/(4*d^3) + (b*f^2*(d*e - c*f)*(c + d*x)^2)/(2*d^4) + (b*f^3*(c + d*x)^3)/(12*d^4) + ((e + f*x)^4*(a + b*ArcTanh[c + d*x]))/(4*f) + (b*(d*e + f - c*f)^4*Log[1 - c - d*x])/(8*d^4*f) - (b*(d*e - f - c*f)^4*Log[1 + c + d*x])/(8*d^4*f)","A",7,5,18,0.2778,1,"{6111, 5926, 702, 633, 31}"
32,1,120,0,0.2035328,"\int (e+f x)^2 \left(a+b \tanh ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)^2*(a + b*ArcTanh[c + d*x]),x]","\frac{(e+f x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)}{3 f}+\frac{b f x (d e-c f)}{d^2}+\frac{b (-c f+d e+f)^3 \log (-c-d x+1)}{6 d^3 f}-\frac{b (d e-(c+1) f)^3 \log (c+d x+1)}{6 d^3 f}+\frac{b f^2 (c+d x)^2}{6 d^3}","\frac{(e+f x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)}{3 f}+\frac{b f x (d e-c f)}{d^2}+\frac{b (-c f+d e+f)^3 \log (-c-d x+1)}{6 d^3 f}-\frac{b (d e-(c+1) f)^3 \log (c+d x+1)}{6 d^3 f}+\frac{b f^2 (c+d x)^2}{6 d^3}",1,"(b*f*(d*e - c*f)*x)/d^2 + (b*f^2*(c + d*x)^2)/(6*d^3) + ((e + f*x)^3*(a + b*ArcTanh[c + d*x]))/(3*f) + (b*(d*e + f - c*f)^3*Log[1 - c - d*x])/(6*d^3*f) - (b*(d*e - (1 + c)*f)^3*Log[1 + c + d*x])/(6*d^3*f)","A",7,5,18,0.2778,1,"{6111, 5926, 702, 633, 31}"
33,1,97,0,0.1690682,"\int (e+f x) \left(a+b \tanh ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)*(a + b*ArcTanh[c + d*x]),x]","\frac{(e+f x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)}{2 f}+\frac{b (-c f+d e+f)^2 \log (-c-d x+1)}{4 d^2 f}-\frac{b (d e-(c+1) f)^2 \log (c+d x+1)}{4 d^2 f}+\frac{b f x}{2 d}","\frac{(e+f x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)}{2 f}+\frac{b (-c f+d e+f)^2 \log (-c-d x+1)}{4 d^2 f}-\frac{b (d e-(c+1) f)^2 \log (c+d x+1)}{4 d^2 f}+\frac{b f x}{2 d}",1,"(b*f*x)/(2*d) + ((e + f*x)^2*(a + b*ArcTanh[c + d*x]))/(2*f) + (b*(d*e + f - c*f)^2*Log[1 - c - d*x])/(4*d^2*f) - (b*(d*e - (1 + c)*f)^2*Log[1 + c + d*x])/(4*d^2*f)","A",7,5,16,0.3125,1,"{6111, 5926, 702, 633, 31}"
34,1,40,0,0.023844,"\int \left(a+b \tanh ^{-1}(c+d x)\right) \, dx","Int[a + b*ArcTanh[c + d*x],x]","a x+\frac{b \log \left(1-(c+d x)^2\right)}{2 d}+\frac{b (c+d x) \tanh ^{-1}(c+d x)}{d}","a x+\frac{b \log \left(1-(c+d x)^2\right)}{2 d}+\frac{b (c+d x) \tanh ^{-1}(c+d x)}{d}",1,"a*x + (b*(c + d*x)*ArcTanh[c + d*x])/d + (b*Log[1 - (c + d*x)^2])/(2*d)","A",4,3,10,0.3000,1,"{6103, 5910, 260}"
35,1,130,0,0.1362522,"\int \frac{a+b \tanh ^{-1}(c+d x)}{e+f x} \, dx","Int[(a + b*ArcTanh[c + d*x])/(e + f*x),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{2 f}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right) \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{f}","-\frac{b \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{2 f}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right) \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{f}",1,"-(((a + b*ArcTanh[c + d*x])*Log[2/(1 + c + d*x)])/f) + ((a + b*ArcTanh[c + d*x])*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/f + (b*PolyLog[2, 1 - 2/(1 + c + d*x)])/(2*f) - (b*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(2*f)","A",5,5,18,0.2778,1,"{6111, 5920, 2402, 2315, 2447}"
36,1,115,0,0.1694853,"\int \frac{a+b \tanh ^{-1}(c+d x)}{(e+f x)^2} \, dx","Int[(a + b*ArcTanh[c + d*x])/(e + f*x)^2,x]","-\frac{a+b \tanh ^{-1}(c+d x)}{f (e+f x)}-\frac{b d \log (-c-d x+1)}{2 f (-c f+d e+f)}+\frac{b d \log (c+d x+1)}{2 f (-c f+d e-f)}-\frac{b d \log (e+f x)}{(-c f+d e+f) (d e-(c+1) f)}","-\frac{a+b \tanh ^{-1}(c+d x)}{f (e+f x)}-\frac{b d \log (-c-d x+1)}{2 f (-c f+d e+f)}+\frac{b d \log (c+d x+1)}{2 f (-c f+d e-f)}-\frac{b d \log (e+f x)}{(-c f+d e+f) (d e-(c+1) f)}",1,"-((a + b*ArcTanh[c + d*x])/(f*(e + f*x))) - (b*d*Log[1 - c - d*x])/(2*f*(d*e + f - c*f)) + (b*d*Log[1 + c + d*x])/(2*f*(d*e - f - c*f)) - (b*d*Log[e + f*x])/((d*e + f - c*f)*(d*e - (1 + c)*f))","A",7,5,18,0.2778,1,"{6109, 1982, 705, 31, 632}"
37,1,167,0,0.2539323,"\int \frac{a+b \tanh ^{-1}(c+d x)}{(e+f x)^3} \, dx","Int[(a + b*ArcTanh[c + d*x])/(e + f*x)^3,x]","-\frac{a+b \tanh ^{-1}(c+d x)}{2 f (e+f x)^2}-\frac{b d^2 \log (-c-d x+1)}{4 f (-c f+d e+f)^2}+\frac{b d^2 \log (c+d x+1)}{4 f (-c f+d e-f)^2}-\frac{b d^2 (d e-c f) \log (e+f x)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}+\frac{b d}{2 (e+f x) (-c f+d e+f) (d e-(c+1) f)}","-\frac{a+b \tanh ^{-1}(c+d x)}{2 f (e+f x)^2}-\frac{b d^2 \log (-c-d x+1)}{4 f (-c f+d e+f)^2}+\frac{b d^2 \log (c+d x+1)}{4 f (-c f+d e-f)^2}-\frac{b d^2 (d e-c f) \log (e+f x)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}+\frac{b d}{2 (e+f x) (-c f+d e+f) (d e-(c+1) f)}",1,"(b*d)/(2*(d*e + f - c*f)*(d*e - (1 + c)*f)*(e + f*x)) - (a + b*ArcTanh[c + d*x])/(2*f*(e + f*x)^2) - (b*d^2*Log[1 - c - d*x])/(4*f*(d*e + f - c*f)^2) + (b*d^2*Log[1 + c + d*x])/(4*f*(d*e - f - c*f)^2) - (b*d^2*(d*e - c*f)*Log[e + f*x])/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2)","A",5,4,18,0.2222,1,"{6109, 1982, 709, 800}"
38,1,562,0,1.0412848,"\int (e+f x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)^3*(a + b*ArcTanh[c + d*x])^2,x]","-\frac{b^2 (d e-c f) \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d^4}+\frac{a b f x \left(\left(6 c^2+1\right) f^2-12 c d e f+6 d^2 e^2\right)}{2 d^3}+\frac{(d e-c f) \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^4}-\frac{\left(6 \left(c^2+1\right) d^2 e^2 f^2-4 c \left(c^2+3\right) d e f^3+\left(c^4+6 c^2+1\right) f^4-4 c d^3 e^3 f+d^4 e^4\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 d^4 f}-\frac{2 b (d e-c f) \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^4}+\frac{b f^2 (c+d x)^2 (d e-c f) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^4}+\frac{b f^3 (c+d x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)}{6 d^4}+\frac{(e+f x)^4 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 f}+\frac{b^2 f \left(\left(6 c^2+1\right) f^2-12 c d e f+6 d^2 e^2\right) \log \left(1-(c+d x)^2\right)}{4 d^4}+\frac{b^2 f (c+d x) \left(\left(6 c^2+1\right) f^2-12 c d e f+6 d^2 e^2\right) \tanh ^{-1}(c+d x)}{2 d^4}+\frac{b^2 f^2 x (d e-c f)}{d^3}-\frac{b^2 f^2 (d e-c f) \tanh ^{-1}(c+d x)}{d^4}+\frac{b^2 f^3 (c+d x)^2}{12 d^4}+\frac{b^2 f^3 \log \left(1-(c+d x)^2\right)}{12 d^4}","-\frac{b^2 (d e-c f) \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d^4}+\frac{a b f x \left(\left(6 c^2+1\right) f^2-12 c d e f+6 d^2 e^2\right)}{2 d^3}+\frac{(d e-c f) \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^4}-\frac{\left(6 \left(c^2+1\right) d^2 e^2 f^2-4 c \left(c^2+3\right) d e f^3+\left(c^4+6 c^2+1\right) f^4-4 c d^3 e^3 f+d^4 e^4\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 d^4 f}-\frac{2 b (d e-c f) \left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^4}+\frac{b f^2 (c+d x)^2 (d e-c f) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^4}+\frac{b f^3 (c+d x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)}{6 d^4}+\frac{(e+f x)^4 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{4 f}+\frac{b^2 f \left(\left(6 c^2+1\right) f^2-12 c d e f+6 d^2 e^2\right) \log \left(1-(c+d x)^2\right)}{4 d^4}+\frac{b^2 f (c+d x) \left(\left(6 c^2+1\right) f^2-12 c d e f+6 d^2 e^2\right) \tanh ^{-1}(c+d x)}{2 d^4}+\frac{b^2 f^2 x (d e-c f)}{d^3}-\frac{b^2 f^2 (d e-c f) \tanh ^{-1}(c+d x)}{d^4}+\frac{b^2 f^3 (c+d x)^2}{12 d^4}+\frac{b^2 f^3 \log \left(1-(c+d x)^2\right)}{12 d^4}",1,"(b^2*f^2*(d*e - c*f)*x)/d^3 + (a*b*f*(6*d^2*e^2 - 12*c*d*e*f + (1 + 6*c^2)*f^2)*x)/(2*d^3) + (b^2*f^3*(c + d*x)^2)/(12*d^4) - (b^2*f^2*(d*e - c*f)*ArcTanh[c + d*x])/d^4 + (b^2*f*(6*d^2*e^2 - 12*c*d*e*f + (1 + 6*c^2)*f^2)*(c + d*x)*ArcTanh[c + d*x])/(2*d^4) + (b*f^2*(d*e - c*f)*(c + d*x)^2*(a + b*ArcTanh[c + d*x]))/d^4 + (b*f^3*(c + d*x)^3*(a + b*ArcTanh[c + d*x]))/(6*d^4) + ((d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)*(a + b*ArcTanh[c + d*x])^2)/d^4 - ((d^4*e^4 - 4*c*d^3*e^3*f + 6*(1 + c^2)*d^2*e^2*f^2 - 4*c*(3 + c^2)*d*e*f^3 + (1 + 6*c^2 + c^4)*f^4)*(a + b*ArcTanh[c + d*x])^2)/(4*d^4*f) + ((e + f*x)^4*(a + b*ArcTanh[c + d*x])^2)/(4*f) - (2*b*(d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)*(a + b*ArcTanh[c + d*x])*Log[2/(1 - c - d*x)])/d^4 + (b^2*f^3*Log[1 - (c + d*x)^2])/(12*d^4) + (b^2*f*(6*d^2*e^2 - 12*c*d*e*f + (1 + 6*c^2)*f^2)*Log[1 - (c + d*x)^2])/(4*d^4) - (b^2*(d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/d^4","A",20,15,20,0.7500,1,"{6111, 5928, 5910, 260, 5916, 321, 206, 266, 43, 6048, 5948, 5984, 5918, 2402, 2315}"
39,1,374,0,0.6395864,"\int (e+f x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)^2*(a + b*ArcTanh[c + d*x])^2,x]","-\frac{b^2 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{3 d^3}-\frac{(d e-c f) \left(\left(c^2+3\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d^3 f}+\frac{\left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d^3}-\frac{2 b \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d^3}+\frac{2 a b f x (d e-c f)}{d^2}+\frac{b f^2 (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d^3}+\frac{(e+f x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 f}+\frac{b^2 f (d e-c f) \log \left(1-(c+d x)^2\right)}{d^3}+\frac{2 b^2 f (c+d x) (d e-c f) \tanh ^{-1}(c+d x)}{d^3}-\frac{b^2 f^2 \tanh ^{-1}(c+d x)}{3 d^3}+\frac{b^2 f^2 x}{3 d^2}","-\frac{b^2 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{3 d^3}-\frac{(d e-c f) \left(\left(c^2+3\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d^3 f}+\frac{\left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 d^3}-\frac{2 b \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d^3}+\frac{2 a b f x (d e-c f)}{d^2}+\frac{b f^2 (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)}{3 d^3}+\frac{(e+f x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{3 f}+\frac{b^2 f (d e-c f) \log \left(1-(c+d x)^2\right)}{d^3}+\frac{2 b^2 f (c+d x) (d e-c f) \tanh ^{-1}(c+d x)}{d^3}-\frac{b^2 f^2 \tanh ^{-1}(c+d x)}{3 d^3}+\frac{b^2 f^2 x}{3 d^2}",1,"(b^2*f^2*x)/(3*d^2) + (2*a*b*f*(d*e - c*f)*x)/d^2 - (b^2*f^2*ArcTanh[c + d*x])/(3*d^3) + (2*b^2*f*(d*e - c*f)*(c + d*x)*ArcTanh[c + d*x])/d^3 + (b*f^2*(c + d*x)^2*(a + b*ArcTanh[c + d*x]))/(3*d^3) - ((d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (3 + c^2)*f^2)*(a + b*ArcTanh[c + d*x])^2)/(3*d^3*f) + ((3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*ArcTanh[c + d*x])^2)/(3*d^3) + ((e + f*x)^3*(a + b*ArcTanh[c + d*x])^2)/(3*f) - (2*b*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*ArcTanh[c + d*x])*Log[2/(1 - c - d*x)])/(3*d^3) + (b^2*f*(d*e - c*f)*Log[1 - (c + d*x)^2])/d^3 - (b^2*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(3*d^3)","A",16,13,20,0.6500,1,"{6111, 5928, 5910, 260, 5916, 321, 206, 6048, 5948, 5984, 5918, 2402, 2315}"
40,1,220,0,0.4622049,"\int (e+f x) \left(a+b \tanh ^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)*(a + b*ArcTanh[c + d*x])^2,x]","-\frac{b^2 (d e-c f) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d^2}+\frac{\left(-\frac{\left(c^2+1\right) f}{d}+2 c e-\frac{d e^2}{f}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d}+\frac{(d e-c f) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^2}-\frac{2 b (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^2}+\frac{(e+f x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 f}+\frac{a b f x}{d}+\frac{b^2 f \log \left(1-(c+d x)^2\right)}{2 d^2}+\frac{b^2 f (c+d x) \tanh ^{-1}(c+d x)}{d^2}","-\frac{b^2 (d e-c f) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d^2}-\frac{\left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d^2 f}+\frac{(d e-c f) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^2}-\frac{2 b (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^2}+\frac{(e+f x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 f}+\frac{a b f x}{d}+\frac{b^2 f \log \left(1-(c+d x)^2\right)}{2 d^2}+\frac{b^2 f (c+d x) \tanh ^{-1}(c+d x)}{d^2}",1,"(a*b*f*x)/d + (b^2*f*(c + d*x)*ArcTanh[c + d*x])/d^2 + ((d*e - c*f)*(a + b*ArcTanh[c + d*x])^2)/d^2 + ((2*c*e - (d*e^2)/f - ((1 + c^2)*f)/d)*(a + b*ArcTanh[c + d*x])^2)/(2*d) + ((e + f*x)^2*(a + b*ArcTanh[c + d*x])^2)/(2*f) - (2*b*(d*e - c*f)*(a + b*ArcTanh[c + d*x])*Log[2/(1 - c - d*x)])/d^2 + (b^2*f*Log[1 - (c + d*x)^2])/(2*d^2) - (b^2*(d*e - c*f)*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/d^2","A",13,10,18,0.5556,1,"{6111, 5928, 5910, 260, 6048, 5948, 5984, 5918, 2402, 2315}"
41,1,97,0,0.1210882,"\int \left(a+b \tanh ^{-1}(c+d x)\right)^2 \, dx","Int[(a + b*ArcTanh[c + d*x])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d}+\frac{(c+d x) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{d}-\frac{2 b \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d}","-\frac{b^2 \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d}+\frac{(c+d x) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{d}-\frac{2 b \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d}",1,"(a + b*ArcTanh[c + d*x])^2/d + ((c + d*x)*(a + b*ArcTanh[c + d*x])^2)/d - (2*b*(a + b*ArcTanh[c + d*x])*Log[2/(1 - c - d*x)])/d - (b^2*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/d","A",6,6,12,0.5000,1,"{6103, 5910, 5984, 5918, 2402, 2315}"
42,1,214,0,0.1542437,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{e+f x} \, dx","Int[(a + b*ArcTanh[c + d*x])^2/(e + f*x),x]","-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{f}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right)}{2 f}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2 \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{f}","-\frac{b \left(a+b \tanh ^{-1}(c+d x)\right) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{f}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right)}{2 f}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2 \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{f}",1,"-(((a + b*ArcTanh[c + d*x])^2*Log[2/(1 + c + d*x)])/f) + ((a + b*ArcTanh[c + d*x])^2*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/f + (b*(a + b*ArcTanh[c + d*x])*PolyLog[2, 1 - 2/(1 + c + d*x)])/f - (b*(a + b*ArcTanh[c + d*x])*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/f + (b^2*PolyLog[3, 1 - 2/(1 + c + d*x)])/(2*f) - (b^2*PolyLog[3, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(2*f)","A",2,2,20,0.1000,1,"{6111, 5922}"
43,1,485,0,1.7129619,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{(e+f x)^2} \, dx","Int[(a + b*ArcTanh[c + d*x])^2/(e + f*x)^2,x]","\frac{b^2 d \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 f (-c f+d e+f)}+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{2 f (-c f+d e-f)}-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{(-c f+d e+f) (d e-(c+1) f)}+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f) (d e-(c+1) f)}-\frac{a b d \log (-c-d x+1)}{f (-c f+d e+f)}+\frac{a b d \log (c+d x+1)}{f (-c f+d e-f)}-\frac{2 a b d \log (e+f x)}{(-c f+d e+f) (d e-(c+1) f)}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{f (e+f x)}+\frac{b^2 d \log \left(\frac{2}{-c-d x+1}\right) \tanh ^{-1}(c+d x)}{f (-c f+d e+f)}-\frac{b^2 d \log \left(\frac{2}{c+d x+1}\right) \tanh ^{-1}(c+d x)}{f (-c f+d e-f)}+\frac{2 b^2 d \log \left(\frac{2}{c+d x+1}\right) \tanh ^{-1}(c+d x)}{(-c f+d e+f) (d e-(c+1) f)}-\frac{2 b^2 d \tanh ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f) (d e-(c+1) f)}","\frac{b^2 d \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 f (-c f+d e+f)}+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{2 f (-c f+d e-f)}-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{(-c f+d e+f) (d e-(c+1) f)}+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f) (d e-(c+1) f)}+\frac{2 a b d \log (e+f x)}{f^2-(d e-c f)^2}-\frac{a b d \log (-c-d x+1)}{f (-c f+d e+f)}+\frac{a b d \log (c+d x+1)}{f (-c f+d e-f)}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{f (e+f x)}+\frac{b^2 d \log \left(\frac{2}{-c-d x+1}\right) \tanh ^{-1}(c+d x)}{f (-c f+d e+f)}-\frac{b^2 d \log \left(\frac{2}{c+d x+1}\right) \tanh ^{-1}(c+d x)}{f (-c f+d e-f)}+\frac{2 b^2 d \log \left(\frac{2}{c+d x+1}\right) \tanh ^{-1}(c+d x)}{(-c f+d e+f) (d e-(c+1) f)}-\frac{2 b^2 d \tanh ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f) (d e-(c+1) f)}",1,"-((a + b*ArcTanh[c + d*x])^2/(f*(e + f*x))) + (b^2*d*ArcTanh[c + d*x]*Log[2/(1 - c - d*x)])/(f*(d*e + f - c*f)) - (a*b*d*Log[1 - c - d*x])/(f*(d*e + f - c*f)) - (b^2*d*ArcTanh[c + d*x]*Log[2/(1 + c + d*x)])/(f*(d*e - f - c*f)) + (2*b^2*d*ArcTanh[c + d*x]*Log[2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (a*b*d*Log[1 + c + d*x])/(f*(d*e - f - c*f)) - (2*a*b*d*Log[e + f*x])/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (2*b^2*d*ArcTanh[c + d*x]*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (b^2*d*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(2*f*(d*e + f - c*f)) + (b^2*d*PolyLog[2, 1 - 2/(1 + c + d*x)])/(2*f*(d*e - f - c*f)) - (b^2*d*PolyLog[2, 1 - 2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (b^2*d*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f))","A",21,19,20,0.9500,1,"{6109, 1982, 705, 31, 632, 6741, 6121, 706, 633, 6688, 12, 6725, 72, 6742, 5918, 2402, 2315, 5920, 2447}"
44,1,750,0,2.1256677,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{(e+f x)^3} \, dx","Int[(a + b*ArcTanh[c + d*x])^2/(e + f*x)^3,x]","\frac{b^2 d^2 \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{4 f (-c f+d e+f)^2}+\frac{b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{4 f (-c f+d e-f)^2}-\frac{b^2 d^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}+\frac{b^2 d^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}-\frac{a b d^2 \log (-c-d x+1)}{2 f (-c f+d e+f)^2}+\frac{a b d^2 \log (c+d x+1)}{2 f (-c f+d e-f)^2}-\frac{2 a b d^2 (d e-c f) \log (e+f x)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}-\frac{a b d}{(e+f x) \left(f^2-(d e-c f)^2\right)}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 f (e+f x)^2}+\frac{b^2 d^2 \log (-c-d x+1)}{2 (-c f+d e+f)^2 (d e-(c+1) f)}-\frac{b^2 d^2 \log (c+d x+1)}{2 (-c f+d e+f) (d e-(c+1) f)^2}+\frac{b^2 d^2 f \log (e+f x)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}+\frac{b^2 d^2 \log \left(\frac{2}{-c-d x+1}\right) \tanh ^{-1}(c+d x)}{2 f (-c f+d e+f)^2}-\frac{b^2 d^2 \log \left(\frac{2}{c+d x+1}\right) \tanh ^{-1}(c+d x)}{2 f (-c f+d e-f)^2}+\frac{2 b^2 d^2 (d e-c f) \log \left(\frac{2}{c+d x+1}\right) \tanh ^{-1}(c+d x)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}-\frac{2 b^2 d^2 (d e-c f) \tanh ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}+\frac{b^2 d \tanh ^{-1}(c+d x)}{(e+f x) (-c f+d e+f) (d e-(c+1) f)}","\frac{b^2 d^2 \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{4 f (-c f+d e+f)^2}+\frac{b^2 d^2 \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{4 f (-c f+d e-f)^2}-\frac{b^2 d^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}+\frac{b^2 d^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}-\frac{a b d^2 \log (-c-d x+1)}{2 f (-c f+d e+f)^2}+\frac{a b d^2 \log (c+d x+1)}{2 f (-c f+d e-f)^2}-\frac{2 a b d^2 (d e-c f) \log (e+f x)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}-\frac{a b d}{(e+f x) \left(f^2-(d e-c f)^2\right)}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 f (e+f x)^2}+\frac{b^2 d^2 \log (-c-d x+1)}{2 (-c f+d e+f)^2 (d e-(c+1) f)}-\frac{b^2 d^2 \log (c+d x+1)}{2 (-c f+d e+f) (d e-(c+1) f)^2}+\frac{b^2 d^2 f \log (e+f x)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}+\frac{b^2 d^2 \log \left(\frac{2}{-c-d x+1}\right) \tanh ^{-1}(c+d x)}{2 f (-c f+d e+f)^2}-\frac{b^2 d^2 \log \left(\frac{2}{c+d x+1}\right) \tanh ^{-1}(c+d x)}{2 f (-c f+d e-f)^2}+\frac{2 b^2 d^2 (d e-c f) \log \left(\frac{2}{c+d x+1}\right) \tanh ^{-1}(c+d x)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}-\frac{2 b^2 d^2 (d e-c f) \tanh ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}+\frac{b^2 d \tanh ^{-1}(c+d x)}{(e+f x) (-c f+d e+f) (d e-(c+1) f)}",1,"-((a*b*d)/((f^2 - (d*e - c*f)^2)*(e + f*x))) + (b^2*d*ArcTanh[c + d*x])/((d*e + f - c*f)*(d*e - (1 + c)*f)*(e + f*x)) - (a + b*ArcTanh[c + d*x])^2/(2*f*(e + f*x)^2) + (b^2*d^2*ArcTanh[c + d*x]*Log[2/(1 - c - d*x)])/(2*f*(d*e + f - c*f)^2) - (a*b*d^2*Log[1 - c - d*x])/(2*f*(d*e + f - c*f)^2) + (b^2*d^2*Log[1 - c - d*x])/(2*(d*e + f - c*f)^2*(d*e - (1 + c)*f)) - (b^2*d^2*ArcTanh[c + d*x]*Log[2/(1 + c + d*x)])/(2*f*(d*e - f - c*f)^2) + (2*b^2*d^2*(d*e - c*f)*ArcTanh[c + d*x]*Log[2/(1 + c + d*x)])/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) + (a*b*d^2*Log[1 + c + d*x])/(2*f*(d*e - f - c*f)^2) - (b^2*d^2*Log[1 + c + d*x])/(2*(d*e + f - c*f)*(d*e - (1 + c)*f)^2) + (b^2*d^2*f*Log[e + f*x])/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) - (2*a*b*d^2*(d*e - c*f)*Log[e + f*x])/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) - (2*b^2*d^2*(d*e - c*f)*ArcTanh[c + d*x]*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) + (b^2*d^2*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(4*f*(d*e + f - c*f)^2) + (b^2*d^2*PolyLog[2, 1 - 2/(1 + c + d*x)])/(4*f*(d*e - f - c*f)^2) - (b^2*d^2*(d*e - c*f)*PolyLog[2, 1 - 2/(1 + c + d*x)])/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) + (b^2*d^2*(d*e - c*f)*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2)","A",26,18,20,0.9000,1,"{6109, 1982, 709, 800, 6741, 6121, 710, 801, 6725, 5918, 2402, 2315, 5926, 706, 31, 633, 5920, 2447}"
45,1,546,0,1.0464617,"\int (e+f x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^3 \, dx","Int[(e + f*x)^2*(a + b*ArcTanh[c + d*x])^3,x]","-\frac{b^2 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^3}+\frac{b^3 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d^3}-\frac{3 b^3 f (d e-c f) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d^3}-\frac{6 b^2 f (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^3}+\frac{a b^2 f^2 x}{d^2}-\frac{(d e-c f) \left(\left(c^2+3\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d^3 f}+\frac{\left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d^3}-\frac{b \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^3}+\frac{3 b f (d e-c f) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^3}+\frac{3 b f (c+d x) (d e-c f) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^3}-\frac{b f^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d^3}+\frac{b f^2 (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d^3}+\frac{(e+f x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 f}+\frac{b^3 f^2 \log \left(1-(c+d x)^2\right)}{2 d^3}+\frac{b^3 f^2 (c+d x) \tanh ^{-1}(c+d x)}{d^3}","-\frac{b^2 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^3}+\frac{b^3 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d^3}-\frac{3 b^3 f (d e-c f) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d^3}-\frac{6 b^2 f (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^3}+\frac{a b^2 f^2 x}{d^2}-\frac{(d e-c f) \left(\left(c^2+3\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d^3 f}+\frac{\left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 d^3}-\frac{b \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^3}+\frac{3 b f (d e-c f) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^3}+\frac{3 b f (c+d x) (d e-c f) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^3}-\frac{b f^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d^3}+\frac{b f^2 (c+d x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d^3}+\frac{(e+f x)^3 \left(a+b \tanh ^{-1}(c+d x)\right)^3}{3 f}+\frac{b^3 f^2 \log \left(1-(c+d x)^2\right)}{2 d^3}+\frac{b^3 f^2 (c+d x) \tanh ^{-1}(c+d x)}{d^3}",1,"(a*b^2*f^2*x)/d^2 + (b^3*f^2*(c + d*x)*ArcTanh[c + d*x])/d^3 - (b*f^2*(a + b*ArcTanh[c + d*x])^2)/(2*d^3) + (3*b*f*(d*e - c*f)*(a + b*ArcTanh[c + d*x])^2)/d^3 + (3*b*f*(d*e - c*f)*(c + d*x)*(a + b*ArcTanh[c + d*x])^2)/d^3 + (b*f^2*(c + d*x)^2*(a + b*ArcTanh[c + d*x])^2)/(2*d^3) - ((d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (3 + c^2)*f^2)*(a + b*ArcTanh[c + d*x])^3)/(3*d^3*f) + ((3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*ArcTanh[c + d*x])^3)/(3*d^3) + ((e + f*x)^3*(a + b*ArcTanh[c + d*x])^3)/(3*f) - (6*b^2*f*(d*e - c*f)*(a + b*ArcTanh[c + d*x])*Log[2/(1 - c - d*x)])/d^3 - (b*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*ArcTanh[c + d*x])^2*Log[2/(1 - c - d*x)])/d^3 + (b^3*f^2*Log[1 - (c + d*x)^2])/(2*d^3) - (3*b^3*f*(d*e - c*f)*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/d^3 - (b^2*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*ArcTanh[c + d*x])*PolyLog[2, 1 - 2/(1 - c - d*x)])/d^3 + (b^3*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*PolyLog[3, 1 - 2/(1 - c - d*x)])/(2*d^3)","A",21,14,20,0.7000,1,"{6111, 5928, 5910, 5984, 5918, 2402, 2315, 5916, 5980, 260, 5948, 6048, 6058, 6610}"
46,1,325,0,0.7259446,"\int (e+f x) \left(a+b \tanh ^{-1}(c+d x)\right)^3 \, dx","Int[(e + f*x)*(a + b*ArcTanh[c + d*x])^3,x]","-\frac{3 b^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^2}+\frac{3 b^3 (d e-c f) \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d^2}-\frac{3 b^3 f \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 d^2}-\frac{3 b^2 f \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^2}+\frac{\left(-\frac{\left(c^2+1\right) f}{d}+2 c e-\frac{d e^2}{f}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 d}+\frac{(d e-c f) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{d^2}-\frac{3 b (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^2}+\frac{3 b f \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d^2}+\frac{3 b f (c+d x) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d^2}+\frac{(e+f x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 f}","-\frac{3 b^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^2}+\frac{3 b^3 (d e-c f) \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d^2}-\frac{3 b^3 f \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 d^2}-\frac{3 b^2 f \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d^2}-\frac{\left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 d^2 f}+\frac{(d e-c f) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{d^2}-\frac{3 b (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d^2}+\frac{3 b f \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d^2}+\frac{3 b f (c+d x) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 d^2}+\frac{(e+f x)^2 \left(a+b \tanh ^{-1}(c+d x)\right)^3}{2 f}",1,"(3*b*f*(a + b*ArcTanh[c + d*x])^2)/(2*d^2) + (3*b*f*(c + d*x)*(a + b*ArcTanh[c + d*x])^2)/(2*d^2) + ((d*e - c*f)*(a + b*ArcTanh[c + d*x])^3)/d^2 + ((2*c*e - (d*e^2)/f - ((1 + c^2)*f)/d)*(a + b*ArcTanh[c + d*x])^3)/(2*d) + ((e + f*x)^2*(a + b*ArcTanh[c + d*x])^3)/(2*f) - (3*b^2*f*(a + b*ArcTanh[c + d*x])*Log[2/(1 - c - d*x)])/d^2 - (3*b*(d*e - c*f)*(a + b*ArcTanh[c + d*x])^2*Log[2/(1 - c - d*x)])/d^2 - (3*b^3*f*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(2*d^2) - (3*b^2*(d*e - c*f)*(a + b*ArcTanh[c + d*x])*PolyLog[2, 1 - 2/(1 - c - d*x)])/d^2 + (3*b^3*(d*e - c*f)*PolyLog[3, 1 - 2/(1 - c - d*x)])/(2*d^2)","A",15,11,18,0.6111,1,"{6111, 5928, 5910, 5984, 5918, 2402, 2315, 6048, 5948, 6058, 6610}"
47,1,132,0,0.2296022,"\int \left(a+b \tanh ^{-1}(c+d x)\right)^3 \, dx","Int[(a + b*ArcTanh[c + d*x])^3,x]","-\frac{3 b^2 \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d}+\frac{(c+d x) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{d}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{d}-\frac{3 b \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d}","-\frac{3 b^2 \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d}+\frac{(c+d x) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{d}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{d}-\frac{3 b \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{d}",1,"(a + b*ArcTanh[c + d*x])^3/d + ((c + d*x)*(a + b*ArcTanh[c + d*x])^3)/d - (3*b*(a + b*ArcTanh[c + d*x])^2*Log[2/(1 - c - d*x)])/d - (3*b^2*(a + b*ArcTanh[c + d*x])*PolyLog[2, 1 - 2/(1 - c - d*x)])/d + (3*b^3*PolyLog[3, 1 - 2/(1 - c - d*x)])/(2*d)","A",6,7,12,0.5833,1,"{6103, 5910, 5984, 5918, 5948, 6058, 6610}"
48,1,308,0,0.1929883,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{e+f x} \, dx","Int[(a + b*ArcTanh[c + d*x])^3/(e + f*x),x]","-\frac{3 b^2 \left(a+b \tanh ^{-1}(c+d x)\right) \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{2 f}-\frac{3 b \left(a+b \tanh ^{-1}(c+d x)\right)^2 \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 f}-\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{4 f}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{c+d x+1}\right)}{4 f}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3 \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{f}","-\frac{3 b^2 \left(a+b \tanh ^{-1}(c+d x)\right) \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{2 f}-\frac{3 b \left(a+b \tanh ^{-1}(c+d x)\right)^2 \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 f}-\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{4 f}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{c+d x+1}\right)}{4 f}+\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3 \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)^3}{f}",1,"-(((a + b*ArcTanh[c + d*x])^3*Log[2/(1 + c + d*x)])/f) + ((a + b*ArcTanh[c + d*x])^3*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/f + (3*b*(a + b*ArcTanh[c + d*x])^2*PolyLog[2, 1 - 2/(1 + c + d*x)])/(2*f) - (3*b*(a + b*ArcTanh[c + d*x])^2*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(2*f) + (3*b^2*(a + b*ArcTanh[c + d*x])*PolyLog[3, 1 - 2/(1 + c + d*x)])/(2*f) - (3*b^2*(a + b*ArcTanh[c + d*x])*PolyLog[3, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(2*f) + (3*b^3*PolyLog[4, 1 - 2/(1 + c + d*x)])/(4*f) - (3*b^3*PolyLog[4, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(4*f)","A",2,2,20,0.1000,1,"{6111, 5924}"
49,1,1094,0,2.8271782,"\int \frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{(e+f x)^2} \, dx","Int[(a + b*ArcTanh[c + d*x])^3/(e + f*x)^2,x]","\frac{3 d \tanh ^{-1}(c+d x)^2 \log \left(\frac{2}{-c-d x+1}\right) b^3}{2 f (d e-c f+f)}-\frac{3 d \tanh ^{-1}(c+d x)^2 \log \left(\frac{2}{c+d x+1}\right) b^3}{2 f (d e-c f-f)}+\frac{3 d \tanh ^{-1}(c+d x)^2 \log \left(\frac{2}{c+d x+1}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 d \tanh ^{-1}(c+d x)^2 \log \left(\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 d \tanh ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) b^3}{2 f (d e-c f+f)}+\frac{3 d \tanh ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^3}{2 f (d e-c f-f)}-\frac{3 d \tanh ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 d \tanh ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right) b^3}{4 f (d e-c f+f)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) b^3}{4 f (d e-c f-f)}-\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) b^3}{2 (d e-c f+f) (d e-(c+1) f)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{2 (d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \tanh ^{-1}(c+d x) \log \left(\frac{2}{-c-d x+1}\right) b^2}{f (d e-c f+f)}-\frac{3 a d \tanh ^{-1}(c+d x) \log \left(\frac{2}{c+d x+1}\right) b^2}{f (d e-c f-f)}+\frac{6 a d \tanh ^{-1}(c+d x) \log \left(\frac{2}{c+d x+1}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}-\frac{6 a d \tanh ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right) b^2}{2 f (d e-c f+f)}+\frac{3 a d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^2}{2 f (d e-c f-f)}-\frac{3 a d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 a^2 d \log (-c-d x+1) b}{2 f (d e-c f+f)}+\frac{3 a^2 d \log (c+d x+1) b}{2 f (d e-c f-f)}-\frac{3 a^2 d \log (e+f x) b}{(d e-c f+f) (d e-(c+1) f)}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{f (e+f x)}","\frac{3 d \tanh ^{-1}(c+d x)^2 \log \left(\frac{2}{-c-d x+1}\right) b^3}{2 f (d e-c f+f)}-\frac{3 d \tanh ^{-1}(c+d x)^2 \log \left(\frac{2}{c+d x+1}\right) b^3}{2 f (d e-c f-f)}+\frac{3 d \tanh ^{-1}(c+d x)^2 \log \left(\frac{2}{c+d x+1}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 d \tanh ^{-1}(c+d x)^2 \log \left(\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 d \tanh ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) b^3}{2 f (d e-c f+f)}+\frac{3 d \tanh ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^3}{2 f (d e-c f-f)}-\frac{3 d \tanh ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 d \tanh ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right) b^3}{4 f (d e-c f+f)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) b^3}{4 f (d e-c f-f)}-\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) b^3}{2 (d e-c f+f) (d e-(c+1) f)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{2 (d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \tanh ^{-1}(c+d x) \log \left(\frac{2}{-c-d x+1}\right) b^2}{f (d e-c f+f)}-\frac{3 a d \tanh ^{-1}(c+d x) \log \left(\frac{2}{c+d x+1}\right) b^2}{f (d e-c f-f)}+\frac{6 a d \tanh ^{-1}(c+d x) \log \left(\frac{2}{c+d x+1}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}-\frac{6 a d \tanh ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right) b^2}{2 f (d e-c f+f)}+\frac{3 a d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^2}{2 f (d e-c f-f)}-\frac{3 a d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 a^2 d \log (-c-d x+1) b}{2 f (d e-c f+f)}+\frac{3 a^2 d \log (c+d x+1) b}{2 f (d e-c f-f)}+\frac{3 a^2 d \log (e+f x) b}{f^2-(d e-c f)^2}-\frac{\left(a+b \tanh ^{-1}(c+d x)\right)^3}{f (e+f x)}",1,"-((a + b*ArcTanh[c + d*x])^3/(f*(e + f*x))) + (3*a*b^2*d*ArcTanh[c + d*x]*Log[2/(1 - c - d*x)])/(f*(d*e + f - c*f)) + (3*b^3*d*ArcTanh[c + d*x]^2*Log[2/(1 - c - d*x)])/(2*f*(d*e + f - c*f)) - (3*a^2*b*d*Log[1 - c - d*x])/(2*f*(d*e + f - c*f)) - (3*a*b^2*d*ArcTanh[c + d*x]*Log[2/(1 + c + d*x)])/(f*(d*e - f - c*f)) + (6*a*b^2*d*ArcTanh[c + d*x]*Log[2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (3*b^3*d*ArcTanh[c + d*x]^2*Log[2/(1 + c + d*x)])/(2*f*(d*e - f - c*f)) + (3*b^3*d*ArcTanh[c + d*x]^2*Log[2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*a^2*b*d*Log[1 + c + d*x])/(2*f*(d*e - f - c*f)) - (3*a^2*b*d*Log[e + f*x])/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (6*a*b^2*d*ArcTanh[c + d*x]*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (3*b^3*d*ArcTanh[c + d*x]^2*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*a*b^2*d*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(2*f*(d*e + f - c*f)) + (3*b^3*d*ArcTanh[c + d*x]*PolyLog[2, 1 - 2/(1 - c - d*x)])/(2*f*(d*e + f - c*f)) + (3*a*b^2*d*PolyLog[2, 1 - 2/(1 + c + d*x)])/(2*f*(d*e - f - c*f)) - (3*a*b^2*d*PolyLog[2, 1 - 2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*b^3*d*ArcTanh[c + d*x]*PolyLog[2, 1 - 2/(1 + c + d*x)])/(2*f*(d*e - f - c*f)) - (3*b^3*d*ArcTanh[c + d*x]*PolyLog[2, 1 - 2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*a*b^2*d*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*b^3*d*ArcTanh[c + d*x]*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (3*b^3*d*PolyLog[3, 1 - 2/(1 - c - d*x)])/(4*f*(d*e + f - c*f)) + (3*b^3*d*PolyLog[3, 1 - 2/(1 + c + d*x)])/(4*f*(d*e - f - c*f)) - (3*b^3*d*PolyLog[3, 1 - 2/(1 + c + d*x)])/(2*(d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*b^3*d*PolyLog[3, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(2*(d*e + f - c*f)*(d*e - (1 + c)*f))","A",30,18,20,0.9000,1,"{6109, 6741, 6121, 6688, 12, 6725, 72, 6742, 5918, 2402, 2315, 5920, 2447, 5948, 6058, 6610, 6056, 5922}"
50,0,0,0,0.0681645,"\int (e+f x)^m \left(a+b \tanh ^{-1}(c+d x)\right)^3 \, dx","Int[(e + f*x)^m*(a + b*ArcTanh[c + d*x])^3,x]","\int (e+f x)^m \left(a+b \tanh ^{-1}(c+d x)\right)^3 \, dx","\text{Int}\left((e+f x)^m \left(a+b \tanh ^{-1}(c+d x)\right)^3,x\right)",0,"Defer[Subst][Defer[Int][((d*e - c*f)/d + (f*x)/d)^m*(a + b*ArcTanh[x])^3, x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
51,0,0,0,0.0690405,"\int (e+f x)^m \left(a+b \tanh ^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)^m*(a + b*ArcTanh[c + d*x])^2,x]","\int (e+f x)^m \left(a+b \tanh ^{-1}(c+d x)\right)^2 \, dx","\text{Int}\left((e+f x)^m \left(a+b \tanh ^{-1}(c+d x)\right)^2,x\right)",0,"Defer[Subst][Defer[Int][((d*e - c*f)/d + (f*x)/d)^m*(a + b*ArcTanh[x])^2, x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
52,1,162,0,0.2570523,"\int (e+f x)^m \left(a+b \tanh ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)^m*(a + b*ArcTanh[c + d*x]),x]","\frac{(e+f x)^{m+1} \left(a+b \tanh ^{-1}(c+d x)\right)}{f (m+1)}+\frac{b d (e+f x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{d (e+f x)}{d e-c f-f}\right)}{2 f (m+1) (m+2) (d e-(c+1) f)}-\frac{b d (e+f x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{d (e+f x)}{d e-c f+f}\right)}{2 f (m+1) (m+2) (-c f+d e+f)}","\frac{(e+f x)^{m+1} \left(a+b \tanh ^{-1}(c+d x)\right)}{f (m+1)}+\frac{b d (e+f x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{d (e+f x)}{d e-c f-f}\right)}{2 f (m+1) (m+2) (d e-(c+1) f)}-\frac{b d (e+f x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{d (e+f x)}{d e-c f+f}\right)}{2 f (m+1) (m+2) (-c f+d e+f)}",1,"((e + f*x)^(1 + m)*(a + b*ArcTanh[c + d*x]))/(f*(1 + m)) + (b*d*(e + f*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (d*(e + f*x))/(d*e - f - c*f)])/(2*f*(d*e - (1 + c)*f)*(1 + m)*(2 + m)) - (b*d*(e + f*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (d*(e + f*x))/(d*e + f - c*f)])/(2*f*(d*e + f - c*f)*(1 + m)*(2 + m))","A",6,4,18,0.2222,1,"{6111, 5926, 712, 68}"
53,1,780,0,1.3952788,"\int \frac{\tanh ^{-1}(a+b x)}{c+d x^3} \, dx","Int[ArcTanh[a + b*x]/(c + d*x^3),x]","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{d} (-a-b x+1)}{(1-a) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{(-1)^{2/3} \text{PolyLog}\left(2,-\frac{\sqrt[3]{-1} \sqrt[3]{d} (-a-b x+1)}{b \sqrt[3]{c}-\sqrt[3]{-1} (1-a) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\sqrt[3]{-1} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{d} (-a-b x+1)}{(-1)^{2/3} (1-a) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\text{PolyLog}\left(2,-\frac{\sqrt[3]{d} (a+b x+1)}{b \sqrt[3]{c}-(a+1) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{(-1)^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{d} (a+b x+1)}{\sqrt[3]{-1} (a+1) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{\sqrt[3]{-1} \text{PolyLog}\left(2,-\frac{(-1)^{2/3} \sqrt[3]{d} (a+b x+1)}{b \sqrt[3]{c}-(-1)^{2/3} (a+1) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{\log (-a-b x+1) \log \left(\frac{b \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{(1-a) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\log (a+b x+1) \log \left(\frac{b \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{b \sqrt[3]{c}-(a+1) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{(-1)^{2/3} \log (-a-b x+1) \log \left(\frac{b \left(\sqrt[3]{c}-\sqrt[3]{-1} \sqrt[3]{d} x\right)}{b \sqrt[3]{c}-\sqrt[3]{-1} (1-a) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{(-1)^{2/3} \log (a+b x+1) \log \left(\frac{b \left(\sqrt[3]{c}-\sqrt[3]{-1} \sqrt[3]{d} x\right)}{\sqrt[3]{-1} (a+1) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\sqrt[3]{-1} \log (-a-b x+1) \log \left(\frac{b \left(\sqrt[3]{c}+(-1)^{2/3} \sqrt[3]{d} x\right)}{(-1)^{2/3} (1-a) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{\sqrt[3]{-1} \log (a+b x+1) \log \left(\frac{b \left(\sqrt[3]{c}+(-1)^{2/3} \sqrt[3]{d} x\right)}{b \sqrt[3]{c}-(-1)^{2/3} (a+1) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}","-\frac{\text{PolyLog}\left(2,\frac{\sqrt[3]{d} (-a-b x+1)}{(1-a) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{(-1)^{2/3} \text{PolyLog}\left(2,-\frac{\sqrt[3]{-1} \sqrt[3]{d} (-a-b x+1)}{b \sqrt[3]{c}-\sqrt[3]{-1} (1-a) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\sqrt[3]{-1} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{d} (-a-b x+1)}{(-1)^{2/3} (1-a) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\text{PolyLog}\left(2,-\frac{\sqrt[3]{d} (a+b x+1)}{b \sqrt[3]{c}-(a+1) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{(-1)^{2/3} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{d} (a+b x+1)}{\sqrt[3]{-1} (a+1) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{\sqrt[3]{-1} \text{PolyLog}\left(2,-\frac{(-1)^{2/3} \sqrt[3]{d} (a+b x+1)}{b \sqrt[3]{c}-(-1)^{2/3} (a+1) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{\log (-a-b x+1) \log \left(\frac{b \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{(1-a) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\log (a+b x+1) \log \left(\frac{b \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{b \sqrt[3]{c}-(a+1) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{(-1)^{2/3} \log (-a-b x+1) \log \left(\frac{b \left(\sqrt[3]{c}-\sqrt[3]{-1} \sqrt[3]{d} x\right)}{b \sqrt[3]{c}-\sqrt[3]{-1} (1-a) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{(-1)^{2/3} \log (a+b x+1) \log \left(\frac{b \left(\sqrt[3]{c}-\sqrt[3]{-1} \sqrt[3]{d} x\right)}{\sqrt[3]{-1} (a+1) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\sqrt[3]{-1} \log (-a-b x+1) \log \left(\frac{b \left(\sqrt[3]{c}+(-1)^{2/3} \sqrt[3]{d} x\right)}{(-1)^{2/3} (1-a) \sqrt[3]{d}+b \sqrt[3]{c}}\right)}{6 c^{2/3} \sqrt[3]{d}}-\frac{\sqrt[3]{-1} \log (a+b x+1) \log \left(\frac{b \left(\sqrt[3]{c}+(-1)^{2/3} \sqrt[3]{d} x\right)}{b \sqrt[3]{c}-(-1)^{2/3} (a+1) \sqrt[3]{d}}\right)}{6 c^{2/3} \sqrt[3]{d}}",1,"-(Log[1 - a - b*x]*Log[(b*(c^(1/3) + d^(1/3)*x))/(b*c^(1/3) + (1 - a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) + (Log[1 + a + b*x]*Log[(b*(c^(1/3) + d^(1/3)*x))/(b*c^(1/3) - (1 + a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) - ((-1)^(2/3)*Log[1 - a - b*x]*Log[(b*(c^(1/3) - (-1)^(1/3)*d^(1/3)*x))/(b*c^(1/3) - (-1)^(1/3)*(1 - a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) + ((-1)^(2/3)*Log[1 + a + b*x]*Log[(b*(c^(1/3) - (-1)^(1/3)*d^(1/3)*x))/(b*c^(1/3) + (-1)^(1/3)*(1 + a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) + ((-1)^(1/3)*Log[1 - a - b*x]*Log[(b*(c^(1/3) + (-1)^(2/3)*d^(1/3)*x))/(b*c^(1/3) + (-1)^(2/3)*(1 - a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) - ((-1)^(1/3)*Log[1 + a + b*x]*Log[(b*(c^(1/3) + (-1)^(2/3)*d^(1/3)*x))/(b*c^(1/3) - (-1)^(2/3)*(1 + a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) - PolyLog[2, (d^(1/3)*(1 - a - b*x))/(b*c^(1/3) + (1 - a)*d^(1/3))]/(6*c^(2/3)*d^(1/3)) - ((-1)^(2/3)*PolyLog[2, -(((-1)^(1/3)*d^(1/3)*(1 - a - b*x))/(b*c^(1/3) - (-1)^(1/3)*(1 - a)*d^(1/3)))])/(6*c^(2/3)*d^(1/3)) + ((-1)^(1/3)*PolyLog[2, ((-1)^(2/3)*d^(1/3)*(1 - a - b*x))/(b*c^(1/3) + (-1)^(2/3)*(1 - a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) + PolyLog[2, -((d^(1/3)*(1 + a + b*x))/(b*c^(1/3) - (1 + a)*d^(1/3)))]/(6*c^(2/3)*d^(1/3)) + ((-1)^(2/3)*PolyLog[2, ((-1)^(1/3)*d^(1/3)*(1 + a + b*x))/(b*c^(1/3) + (-1)^(1/3)*(1 + a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) - ((-1)^(1/3)*PolyLog[2, -(((-1)^(2/3)*d^(1/3)*(1 + a + b*x))/(b*c^(1/3) - (-1)^(2/3)*(1 + a)*d^(1/3)))])/(6*c^(2/3)*d^(1/3))","A",23,5,16,0.3125,1,"{6115, 2409, 2394, 2393, 2391}"
54,1,481,0,0.6055114,"\int \frac{\tanh ^{-1}(a+b x)}{c+d x^2} \, dx","Int[ArcTanh[a + b*x]/(c + d*x^2),x]","-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} (-a-b x+1)}{b \sqrt{-c}-(1-a) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} (-a-b x+1)}{(1-a) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} (a+b x+1)}{b \sqrt{-c}-(a+1) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} (a+b x+1)}{(a+1) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log (-a-b x+1) \log \left(\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{b \sqrt{-c}-(1-a) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log (a+b x+1) \log \left(\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{(a+1) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log (-a-b x+1) \log \left(\frac{b \left(\sqrt{-c}+\sqrt{d} x\right)}{(1-a) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log (a+b x+1) \log \left(\frac{b \left(\sqrt{-c}+\sqrt{d} x\right)}{b \sqrt{-c}-(a+1) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}","-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} (-a-b x+1)}{b \sqrt{-c}-(1-a) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} (-a-b x+1)}{(1-a) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} (a+b x+1)}{b \sqrt{-c}-(a+1) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} (a+b x+1)}{(a+1) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log (-a-b x+1) \log \left(\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{b \sqrt{-c}-(1-a) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log (a+b x+1) \log \left(\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{(a+1) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log (-a-b x+1) \log \left(\frac{b \left(\sqrt{-c}+\sqrt{d} x\right)}{(1-a) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log (a+b x+1) \log \left(\frac{b \left(\sqrt{-c}+\sqrt{d} x\right)}{b \sqrt{-c}-(a+1) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}",1,"-(Log[1 - a - b*x]*Log[(b*(Sqrt[-c] - Sqrt[d]*x))/(b*Sqrt[-c] - (1 - a)*Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) + (Log[1 + a + b*x]*Log[(b*(Sqrt[-c] - Sqrt[d]*x))/(b*Sqrt[-c] + (1 + a)*Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) + (Log[1 - a - b*x]*Log[(b*(Sqrt[-c] + Sqrt[d]*x))/(b*Sqrt[-c] + (1 - a)*Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) - (Log[1 + a + b*x]*Log[(b*(Sqrt[-c] + Sqrt[d]*x))/(b*Sqrt[-c] - (1 + a)*Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) - PolyLog[2, -((Sqrt[d]*(1 - a - b*x))/(b*Sqrt[-c] - (1 - a)*Sqrt[d]))]/(4*Sqrt[-c]*Sqrt[d]) + PolyLog[2, (Sqrt[d]*(1 - a - b*x))/(b*Sqrt[-c] + (1 - a)*Sqrt[d])]/(4*Sqrt[-c]*Sqrt[d]) - PolyLog[2, -((Sqrt[d]*(1 + a + b*x))/(b*Sqrt[-c] - (1 + a)*Sqrt[d]))]/(4*Sqrt[-c]*Sqrt[d]) + PolyLog[2, (Sqrt[d]*(1 + a + b*x))/(b*Sqrt[-c] + (1 + a)*Sqrt[d])]/(4*Sqrt[-c]*Sqrt[d])","A",17,5,16,0.3125,1,"{6115, 2409, 2394, 2393, 2391}"
55,1,120,0,0.1298951,"\int \frac{\tanh ^{-1}(a+b x)}{c+d x} \, dx","Int[ArcTanh[a + b*x]/(c + d*x),x]","-\frac{\text{PolyLog}\left(2,1-\frac{2 b (c+d x)}{(a+b x+1) (-a d+b c+d)}\right)}{2 d}+\frac{\text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{2 d}+\frac{\tanh ^{-1}(a+b x) \log \left(\frac{2 b (c+d x)}{(a+b x+1) (-a d+b c+d)}\right)}{d}-\frac{\log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)}{d}","-\frac{\text{PolyLog}\left(2,1-\frac{2 b (c+d x)}{(a+b x+1) (-a d+b c+d)}\right)}{2 d}+\frac{\text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{2 d}+\frac{\tanh ^{-1}(a+b x) \log \left(\frac{2 b (c+d x)}{(a+b x+1) (-a d+b c+d)}\right)}{d}-\frac{\log \left(\frac{2}{a+b x+1}\right) \tanh ^{-1}(a+b x)}{d}",1,"-((ArcTanh[a + b*x]*Log[2/(1 + a + b*x)])/d) + (ArcTanh[a + b*x]*Log[(2*b*(c + d*x))/((b*c + d - a*d)*(1 + a + b*x))])/d + PolyLog[2, 1 - 2/(1 + a + b*x)]/(2*d) - PolyLog[2, 1 - (2*b*(c + d*x))/((b*c + d - a*d)*(1 + a + b*x))]/(2*d)","A",5,5,14,0.3571,1,"{6111, 5920, 2402, 2315, 2447}"
56,1,186,0,0.2371452,"\int \frac{\tanh ^{-1}(a+b x)}{c+\frac{d}{x}} \, dx","Int[ArcTanh[a + b*x]/(c + d/x),x]","\frac{d \text{PolyLog}\left(2,\frac{c (-a-b x+1)}{-a c+b d+c}\right)}{2 c^2}-\frac{d \text{PolyLog}\left(2,\frac{c (a+b x+1)}{a c-b d+c}\right)}{2 c^2}+\frac{d \log (-a-b x+1) \log \left(\frac{b (c x+d)}{-a c+b d+c}\right)}{2 c^2}-\frac{d \log (a+b x+1) \log \left(-\frac{b (c x+d)}{a c-b d+c}\right)}{2 c^2}+\frac{(-a-b x+1) \log (-a-b x+1)}{2 b c}+\frac{(a+b x+1) \log (a+b x+1)}{2 b c}","\frac{d \text{PolyLog}\left(2,\frac{c (-a-b x+1)}{-a c+b d+c}\right)}{2 c^2}-\frac{d \text{PolyLog}\left(2,\frac{c (a+b x+1)}{a c-b d+c}\right)}{2 c^2}+\frac{d \log (-a-b x+1) \log \left(\frac{b (c x+d)}{-a c+b d+c}\right)}{2 c^2}-\frac{d \log (a+b x+1) \log \left(-\frac{b (c x+d)}{a c-b d+c}\right)}{2 c^2}+\frac{(-a-b x+1) \log (-a-b x+1)}{2 b c}+\frac{(a+b x+1) \log (a+b x+1)}{2 b c}",1,"((1 - a - b*x)*Log[1 - a - b*x])/(2*b*c) + ((1 + a + b*x)*Log[1 + a + b*x])/(2*b*c) - (d*Log[1 + a + b*x]*Log[-((b*(d + c*x))/(c + a*c - b*d))])/(2*c^2) + (d*Log[1 - a - b*x]*Log[(b*(d + c*x))/(c - a*c + b*d)])/(2*c^2) + (d*PolyLog[2, (c*(1 - a - b*x))/(c - a*c + b*d)])/(2*c^2) - (d*PolyLog[2, (c*(1 + a + b*x))/(c + a*c - b*d)])/(2*c^2)","A",15,7,16,0.4375,1,"{6115, 2409, 2389, 2295, 2394, 2393, 2391}"
57,1,545,0,0.9107141,"\int \frac{\tanh ^{-1}(a+b x)}{c+\frac{d}{x^2}} \, dx","Int[ArcTanh[a + b*x]/(c + d/x^2),x]","\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (-a-b x+1)}{a \left(-\sqrt{-c}\right)-b \sqrt{d}+\sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (-a-b x+1)}{(1-a) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+1)}{(a+1) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+1)}{(a+1) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{\sqrt{d} \log (-a-b x+1) \log \left(-\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{(1-a) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \log (-a-b x+1) \log \left(\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{(1-a) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \log (a+b x+1) \log \left(\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{(a+1) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{\sqrt{d} \log (a+b x+1) \log \left(-\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{(a+1) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{(-a-b x+1) \log (-a-b x+1)}{2 b c}+\frac{(a+b x+1) \log (a+b x+1)}{2 b c}","\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (-a-b x+1)}{a \left(-\sqrt{-c}\right)-b \sqrt{d}+\sqrt{-c}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (-a-b x+1)}{(1-a) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+1)}{(a+1) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+1)}{(a+1) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{\sqrt{d} \log (-a-b x+1) \log \left(-\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{(1-a) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \log (-a-b x+1) \log \left(\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{(1-a) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \log (a+b x+1) \log \left(\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{(a+1) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{\sqrt{d} \log (a+b x+1) \log \left(-\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{(a+1) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{(-a-b x+1) \log (-a-b x+1)}{2 b c}+\frac{(a+b x+1) \log (a+b x+1)}{2 b c}",1,"((1 - a - b*x)*Log[1 - a - b*x])/(2*b*c) + ((1 + a + b*x)*Log[1 + a + b*x])/(2*b*c) + (Sqrt[d]*Log[1 - a - b*x]*Log[-((b*(Sqrt[d] - Sqrt[-c]*x))/((1 - a)*Sqrt[-c] - b*Sqrt[d]))])/(4*(-c)^(3/2)) - (Sqrt[d]*Log[1 + a + b*x]*Log[(b*(Sqrt[d] - Sqrt[-c]*x))/((1 + a)*Sqrt[-c] + b*Sqrt[d])])/(4*(-c)^(3/2)) + (Sqrt[d]*Log[1 + a + b*x]*Log[-((b*(Sqrt[d] + Sqrt[-c]*x))/((1 + a)*Sqrt[-c] - b*Sqrt[d]))])/(4*(-c)^(3/2)) - (Sqrt[d]*Log[1 - a - b*x]*Log[(b*(Sqrt[d] + Sqrt[-c]*x))/((1 - a)*Sqrt[-c] + b*Sqrt[d])])/(4*(-c)^(3/2)) + (Sqrt[d]*PolyLog[2, (Sqrt[-c]*(1 - a - b*x))/(Sqrt[-c] - a*Sqrt[-c] - b*Sqrt[d])])/(4*(-c)^(3/2)) - (Sqrt[d]*PolyLog[2, (Sqrt[-c]*(1 - a - b*x))/((1 - a)*Sqrt[-c] + b*Sqrt[d])])/(4*(-c)^(3/2)) + (Sqrt[d]*PolyLog[2, (Sqrt[-c]*(1 + a + b*x))/((1 + a)*Sqrt[-c] - b*Sqrt[d])])/(4*(-c)^(3/2)) - (Sqrt[d]*PolyLog[2, (Sqrt[-c]*(1 + a + b*x))/((1 + a)*Sqrt[-c] + b*Sqrt[d])])/(4*(-c)^(3/2))","A",25,7,16,0.4375,1,"{6115, 2409, 2389, 2295, 2394, 2393, 2391}"
58,1,832,0,1.4297909,"\int \frac{\tanh ^{-1}(a+b x)}{c+\frac{d}{x^3}} \, dx","Int[ArcTanh[a + b*x]/(c + d/x^3),x]","\frac{(-a-b x+1) \log (-a-b x+1)}{2 b c}+\frac{\sqrt[3]{d} \log \left(\frac{b \left(\sqrt[3]{c} x+\sqrt[3]{d}\right)}{\sqrt[3]{c} (1-a)+b \sqrt[3]{d}}\right) \log (-a-b x+1)}{6 c^{4/3}}+\frac{(-1)^{2/3} \sqrt[3]{d} \log \left(-\frac{b \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{c} x\right)}{\sqrt[3]{-1} (1-a) \sqrt[3]{c}-b \sqrt[3]{d}}\right) \log (-a-b x+1)}{6 c^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{d} \log \left(\frac{b \left((-1)^{2/3} \sqrt[3]{c} x+\sqrt[3]{d}\right)}{(-1)^{2/3} \sqrt[3]{c} (1-a)+b \sqrt[3]{d}}\right) \log (-a-b x+1)}{6 c^{4/3}}+\frac{(a+b x+1) \log (a+b x+1)}{2 b c}-\frac{\sqrt[3]{d} \log (a+b x+1) \log \left(-\frac{b \left(\sqrt[3]{c} x+\sqrt[3]{d}\right)}{(a+1) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{d} \log (a+b x+1) \log \left(\frac{b \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{c} x\right)}{\sqrt[3]{-1} \sqrt[3]{c} (a+1)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{d} \log (a+b x+1) \log \left(-\frac{b \left((-1)^{2/3} \sqrt[3]{c} x+\sqrt[3]{d}\right)}{(-1)^{2/3} (a+1) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{(-1)^{2/3} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{c} (-a-b x+1)}{\sqrt[3]{-1} (1-a) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{\sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (-a-b x+1)}{\sqrt[3]{c} (1-a)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{c} (-a-b x+1)}{(-1)^{2/3} \sqrt[3]{c} (1-a)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{\sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (a+b x+1)}{(a+1) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{c} (a+b x+1)}{(-1)^{2/3} (a+1) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{c} (a+b x+1)}{\sqrt[3]{-1} \sqrt[3]{c} (a+1)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}","\frac{(-a-b x+1) \log (-a-b x+1)}{2 b c}+\frac{\sqrt[3]{d} \log \left(\frac{b \left(\sqrt[3]{c} x+\sqrt[3]{d}\right)}{\sqrt[3]{c} (1-a)+b \sqrt[3]{d}}\right) \log (-a-b x+1)}{6 c^{4/3}}+\frac{(-1)^{2/3} \sqrt[3]{d} \log \left(-\frac{b \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{c} x\right)}{\sqrt[3]{-1} (1-a) \sqrt[3]{c}-b \sqrt[3]{d}}\right) \log (-a-b x+1)}{6 c^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{d} \log \left(\frac{b \left((-1)^{2/3} \sqrt[3]{c} x+\sqrt[3]{d}\right)}{(-1)^{2/3} \sqrt[3]{c} (1-a)+b \sqrt[3]{d}}\right) \log (-a-b x+1)}{6 c^{4/3}}+\frac{(a+b x+1) \log (a+b x+1)}{2 b c}-\frac{\sqrt[3]{d} \log (a+b x+1) \log \left(-\frac{b \left(\sqrt[3]{c} x+\sqrt[3]{d}\right)}{(a+1) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{d} \log (a+b x+1) \log \left(\frac{b \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{c} x\right)}{\sqrt[3]{-1} \sqrt[3]{c} (a+1)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{d} \log (a+b x+1) \log \left(-\frac{b \left((-1)^{2/3} \sqrt[3]{c} x+\sqrt[3]{d}\right)}{(-1)^{2/3} (a+1) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{(-1)^{2/3} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{c} (-a-b x+1)}{\sqrt[3]{-1} (1-a) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{\sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (-a-b x+1)}{\sqrt[3]{c} (1-a)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{c} (-a-b x+1)}{(-1)^{2/3} \sqrt[3]{c} (1-a)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{\sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{c} (a+b x+1)}{(a+1) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{(-1)^{2/3} \sqrt[3]{c} (a+b x+1)}{(-1)^{2/3} (a+1) \sqrt[3]{c}-b \sqrt[3]{d}}\right)}{6 c^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{d} \text{PolyLog}\left(2,\frac{\sqrt[3]{-1} \sqrt[3]{c} (a+b x+1)}{\sqrt[3]{-1} \sqrt[3]{c} (a+1)+b \sqrt[3]{d}}\right)}{6 c^{4/3}}",1,"((1 - a - b*x)*Log[1 - a - b*x])/(2*b*c) + ((1 + a + b*x)*Log[1 + a + b*x])/(2*b*c) - (d^(1/3)*Log[1 + a + b*x]*Log[-((b*(d^(1/3) + c^(1/3)*x))/((1 + a)*c^(1/3) - b*d^(1/3)))])/(6*c^(4/3)) + (d^(1/3)*Log[1 - a - b*x]*Log[(b*(d^(1/3) + c^(1/3)*x))/((1 - a)*c^(1/3) + b*d^(1/3))])/(6*c^(4/3)) + ((-1)^(2/3)*d^(1/3)*Log[1 - a - b*x]*Log[-((b*(d^(1/3) - (-1)^(1/3)*c^(1/3)*x))/((-1)^(1/3)*(1 - a)*c^(1/3) - b*d^(1/3)))])/(6*c^(4/3)) - ((-1)^(2/3)*d^(1/3)*Log[1 + a + b*x]*Log[(b*(d^(1/3) - (-1)^(1/3)*c^(1/3)*x))/((-1)^(1/3)*(1 + a)*c^(1/3) + b*d^(1/3))])/(6*c^(4/3)) + ((-1)^(1/3)*d^(1/3)*Log[1 + a + b*x]*Log[-((b*(d^(1/3) + (-1)^(2/3)*c^(1/3)*x))/((-1)^(2/3)*(1 + a)*c^(1/3) - b*d^(1/3)))])/(6*c^(4/3)) - ((-1)^(1/3)*d^(1/3)*Log[1 - a - b*x]*Log[(b*(d^(1/3) + (-1)^(2/3)*c^(1/3)*x))/((-1)^(2/3)*(1 - a)*c^(1/3) + b*d^(1/3))])/(6*c^(4/3)) + ((-1)^(2/3)*d^(1/3)*PolyLog[2, ((-1)^(1/3)*c^(1/3)*(1 - a - b*x))/((-1)^(1/3)*(1 - a)*c^(1/3) - b*d^(1/3))])/(6*c^(4/3)) + (d^(1/3)*PolyLog[2, (c^(1/3)*(1 - a - b*x))/((1 - a)*c^(1/3) + b*d^(1/3))])/(6*c^(4/3)) - ((-1)^(1/3)*d^(1/3)*PolyLog[2, ((-1)^(2/3)*c^(1/3)*(1 - a - b*x))/((-1)^(2/3)*(1 - a)*c^(1/3) + b*d^(1/3))])/(6*c^(4/3)) - (d^(1/3)*PolyLog[2, (c^(1/3)*(1 + a + b*x))/((1 + a)*c^(1/3) - b*d^(1/3))])/(6*c^(4/3)) + ((-1)^(1/3)*d^(1/3)*PolyLog[2, ((-1)^(2/3)*c^(1/3)*(1 + a + b*x))/((-1)^(2/3)*(1 + a)*c^(1/3) - b*d^(1/3))])/(6*c^(4/3)) - ((-1)^(2/3)*d^(1/3)*PolyLog[2, ((-1)^(1/3)*c^(1/3)*(1 + a + b*x))/((-1)^(1/3)*(1 + a)*c^(1/3) + b*d^(1/3))])/(6*c^(4/3))","A",31,7,16,0.4375,1,"{6115, 2409, 2389, 2295, 2394, 2393, 2391}"
59,1,585,0,1.0134609,"\int \frac{\tanh ^{-1}(a+b x)}{c+d \sqrt{x}} \, dx","Int[ArcTanh[a + b*x]/(c + d*Sqrt[x]),x]","\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a-1} d}\right)}{d^2}+\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{-a-1} d+\sqrt{b} c}\right)}{d^2}-\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{1-a} d}\right)}{d^2}-\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{1-a} d+\sqrt{b} c}\right)}{d^2}+\frac{c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(\sqrt{-a-1}-\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} d+\sqrt{b} c}\right)}{d^2}-\frac{c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(\sqrt{1-a}-\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} d+\sqrt{b} c}\right)}{d^2}+\frac{c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{-a-1}+\sqrt{b} \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a-1} d}\right)}{d^2}-\frac{c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{1-a}+\sqrt{b} \sqrt{x}\right)}{\sqrt{b} c-\sqrt{1-a} d}\right)}{d^2}+\frac{c \log (-a-b x+1) \log \left(c+d \sqrt{x}\right)}{d^2}-\frac{c \log (a+b x+1) \log \left(c+d \sqrt{x}\right)}{d^2}-\frac{\sqrt{x} \log (-a-b x+1)}{d}+\frac{\sqrt{x} \log (a+b x+1)}{d}+\frac{2 \sqrt{a+1} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+1}}\right)}{\sqrt{b} d}-\frac{2 \sqrt{1-a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{1-a}}\right)}{\sqrt{b} d}","\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a-1} d}\right)}{d^2}+\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{-a-1} d+\sqrt{b} c}\right)}{d^2}-\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{1-a} d}\right)}{d^2}-\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{1-a} d+\sqrt{b} c}\right)}{d^2}+\frac{c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(\sqrt{-a-1}-\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} d+\sqrt{b} c}\right)}{d^2}-\frac{c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(\sqrt{1-a}-\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} d+\sqrt{b} c}\right)}{d^2}+\frac{c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{-a-1}+\sqrt{b} \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a-1} d}\right)}{d^2}-\frac{c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{1-a}+\sqrt{b} \sqrt{x}\right)}{\sqrt{b} c-\sqrt{1-a} d}\right)}{d^2}+\frac{c \log (-a-b x+1) \log \left(c+d \sqrt{x}\right)}{d^2}-\frac{c \log (a+b x+1) \log \left(c+d \sqrt{x}\right)}{d^2}-\frac{\sqrt{x} \log (-a-b x+1)}{d}+\frac{\sqrt{x} \log (a+b x+1)}{d}+\frac{2 \sqrt{a+1} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+1}}\right)}{\sqrt{b} d}-\frac{2 \sqrt{1-a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{1-a}}\right)}{\sqrt{b} d}",1,"(2*Sqrt[1 + a]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[1 + a]])/(Sqrt[b]*d) - (2*Sqrt[1 - a]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[1 - a]])/(Sqrt[b]*d) + (c*Log[(d*(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c + Sqrt[-1 - a]*d)]*Log[c + d*Sqrt[x]])/d^2 - (c*Log[(d*(Sqrt[1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c + Sqrt[1 - a]*d)]*Log[c + d*Sqrt[x]])/d^2 + (c*Log[-((d*(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c - Sqrt[-1 - a]*d))]*Log[c + d*Sqrt[x]])/d^2 - (c*Log[-((d*(Sqrt[1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c - Sqrt[1 - a]*d))]*Log[c + d*Sqrt[x]])/d^2 - (Sqrt[x]*Log[1 - a - b*x])/d + (c*Log[c + d*Sqrt[x]]*Log[1 - a - b*x])/d^2 + (Sqrt[x]*Log[1 + a + b*x])/d - (c*Log[c + d*Sqrt[x]]*Log[1 + a + b*x])/d^2 + (c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c - Sqrt[-1 - a]*d)])/d^2 + (c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c + Sqrt[-1 - a]*d)])/d^2 - (c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c - Sqrt[1 - a]*d)])/d^2 - (c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c + Sqrt[1 - a]*d)])/d^2","A",31,13,18,0.7222,1,"{6115, 2408, 2466, 2448, 321, 205, 2462, 260, 2416, 2394, 2393, 2391, 208}"
60,1,661,0,1.0721768,"\int \frac{\tanh ^{-1}(a+b x)}{c+\frac{d}{\sqrt{x}}} \, dx","Int[ArcTanh[a + b*x]/(c + d/Sqrt[x]),x]","-\frac{d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{-a-1} c-\sqrt{b} d}\right)}{c^3}+\frac{d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{1-a} c-\sqrt{b} d}\right)}{c^3}-\frac{d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{-a-1} c+\sqrt{b} d}\right)}{c^3}+\frac{d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{1-a} c+\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{-a-1}-\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} c+\sqrt{b} d}\right)}{c^3}+\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{1-a}-\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} c+\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{-a-1}+\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} c-\sqrt{b} d}\right)}{c^3}+\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{1-a}+\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} c-\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log (-a-b x+1) \log \left(c \sqrt{x}+d\right)}{c^3}+\frac{d^2 \log (a+b x+1) \log \left(c \sqrt{x}+d\right)}{c^3}+\frac{d \sqrt{x} \log (-a-b x+1)}{c^2}-\frac{d \sqrt{x} \log (a+b x+1)}{c^2}-\frac{2 \sqrt{a+1} d \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+1}}\right)}{\sqrt{b} c^2}+\frac{2 \sqrt{1-a} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{1-a}}\right)}{\sqrt{b} c^2}+\frac{(-a-b x+1) \log (-a-b x+1)}{2 b c}+\frac{(a+b x+1) \log (a+b x+1)}{2 b c}","-\frac{d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{-a-1} c-\sqrt{b} d}\right)}{c^3}+\frac{d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{1-a} c-\sqrt{b} d}\right)}{c^3}-\frac{d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{-a-1} c+\sqrt{b} d}\right)}{c^3}+\frac{d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{1-a} c+\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{-a-1}-\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} c+\sqrt{b} d}\right)}{c^3}+\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{1-a}-\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} c+\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{-a-1}+\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} c-\sqrt{b} d}\right)}{c^3}+\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{1-a}+\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} c-\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log (-a-b x+1) \log \left(c \sqrt{x}+d\right)}{c^3}+\frac{d^2 \log (a+b x+1) \log \left(c \sqrt{x}+d\right)}{c^3}+\frac{d \sqrt{x} \log (-a-b x+1)}{c^2}-\frac{d \sqrt{x} \log (a+b x+1)}{c^2}-\frac{2 \sqrt{a+1} d \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+1}}\right)}{\sqrt{b} c^2}+\frac{2 \sqrt{1-a} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{1-a}}\right)}{\sqrt{b} c^2}+\frac{(-a-b x+1) \log (-a-b x+1)}{2 b c}+\frac{(a+b x+1) \log (a+b x+1)}{2 b c}",1,"(-2*Sqrt[1 + a]*d*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[1 + a]])/(Sqrt[b]*c^2) + (2*Sqrt[1 - a]*d*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[1 - a]])/(Sqrt[b]*c^2) - (d^2*Log[(c*(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*c + Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 + (d^2*Log[(c*(Sqrt[1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[1 - a]*c + Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 - (d^2*Log[(c*(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*c - Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 + (d^2*Log[(c*(Sqrt[1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[1 - a]*c - Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 + (d*Sqrt[x]*Log[1 - a - b*x])/c^2 + ((1 - a - b*x)*Log[1 - a - b*x])/(2*b*c) - (d^2*Log[d + c*Sqrt[x]]*Log[1 - a - b*x])/c^3 - (d*Sqrt[x]*Log[1 + a + b*x])/c^2 + ((1 + a + b*x)*Log[1 + a + b*x])/(2*b*c) + (d^2*Log[d + c*Sqrt[x]]*Log[1 + a + b*x])/c^3 - (d^2*PolyLog[2, -((Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[-1 - a]*c - Sqrt[b]*d))])/c^3 + (d^2*PolyLog[2, -((Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[1 - a]*c - Sqrt[b]*d))])/c^3 - (d^2*PolyLog[2, (Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[-1 - a]*c + Sqrt[b]*d)])/c^3 + (d^2*PolyLog[2, (Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[1 - a]*c + Sqrt[b]*d)])/c^3","A",37,16,18,0.8889,1,"{6115, 2408, 2476, 2448, 321, 205, 2454, 2389, 2295, 2462, 260, 2416, 2394, 2393, 2391, 208}"
61,1,335,0,0.7209523,"\int \frac{\tanh ^{-1}(d+e x)}{a+b x+c x^2} \, dx","Int[ArcTanh[d + e*x]/(a + b*x + c*x^2),x]","-\frac{\text{PolyLog}\left(2,\frac{2 \left(-e \left(b-\sqrt{b^2-4 a c}\right)-2 c (d+e x)+2 c d\right)}{(d+e x+1) \left(-e \sqrt{b^2-4 a c}+b e-2 c d+2 c\right)}+1\right)}{2 \sqrt{b^2-4 a c}}+\frac{\text{PolyLog}\left(2,\frac{2 \left(-e \left(\sqrt{b^2-4 a c}+b\right)-2 c (d+e x)+2 c d\right)}{(d+e x+1) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (1-d)\right)}+1\right)}{2 \sqrt{b^2-4 a c}}+\frac{\tanh ^{-1}(d+e x) \log \left(\frac{2 e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{(d+e x+1) \left(e \left(b-\sqrt{b^2-4 a c}\right)+2 c (1-d)\right)}\right)}{\sqrt{b^2-4 a c}}-\frac{\tanh ^{-1}(d+e x) \log \left(\frac{2 e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{(d+e x+1) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (1-d)\right)}\right)}{\sqrt{b^2-4 a c}}","-\frac{\text{PolyLog}\left(2,\frac{2 \left(-e \left(b-\sqrt{b^2-4 a c}\right)-2 c (d+e x)+2 c d\right)}{(d+e x+1) \left(-e \sqrt{b^2-4 a c}+b e-2 c d+2 c\right)}+1\right)}{2 \sqrt{b^2-4 a c}}+\frac{\text{PolyLog}\left(2,\frac{2 \left(-e \left(\sqrt{b^2-4 a c}+b\right)-2 c (d+e x)+2 c d\right)}{(d+e x+1) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (1-d)\right)}+1\right)}{2 \sqrt{b^2-4 a c}}+\frac{\tanh ^{-1}(d+e x) \log \left(\frac{2 e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{(d+e x+1) \left(e \left(b-\sqrt{b^2-4 a c}\right)+2 c (1-d)\right)}\right)}{\sqrt{b^2-4 a c}}-\frac{\tanh ^{-1}(d+e x) \log \left(\frac{2 e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{(d+e x+1) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (1-d)\right)}\right)}{\sqrt{b^2-4 a c}}",1,"(ArcTanh[d + e*x]*Log[(2*e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*(1 - d) + (b - Sqrt[b^2 - 4*a*c])*e)*(1 + d + e*x))])/Sqrt[b^2 - 4*a*c] - (ArcTanh[d + e*x]*Log[(2*e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*(1 - d) + (b + Sqrt[b^2 - 4*a*c])*e)*(1 + d + e*x))])/Sqrt[b^2 - 4*a*c] - PolyLog[2, 1 + (2*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e - 2*c*(d + e*x)))/((2*c - 2*c*d + b*e - Sqrt[b^2 - 4*a*c]*e)*(1 + d + e*x))]/(2*Sqrt[b^2 - 4*a*c]) + PolyLog[2, 1 + (2*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e - 2*c*(d + e*x)))/((2*c*(1 - d) + (b + Sqrt[b^2 - 4*a*c])*e)*(1 + d + e*x))]/(2*Sqrt[b^2 - 4*a*c])","A",12,8,19,0.4211,1,"{618, 206, 6728, 6111, 5920, 2402, 2315, 2447}"
62,1,83,0,0.2629308,"\int \frac{(c e+d e x) \left(a+b \tanh ^{-1}(c+d x)\right)}{1-(c+d x)^2} \, dx","Int[((c*e + d*e*x)*(a + b*ArcTanh[c + d*x]))/(1 - (c + d*x)^2),x]","\frac{b e \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 d}-\frac{e \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 b d}+\frac{e \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d}","\frac{b e \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 d}-\frac{e \left(a+b \tanh ^{-1}(c+d x)\right)^2}{2 b d}+\frac{e \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \tanh ^{-1}(c+d x)\right)}{d}",1,"-(e*(a + b*ArcTanh[c + d*x])^2)/(2*b*d) + (e*(a + b*ArcTanh[c + d*x])*Log[2/(1 - c - d*x)])/d + (b*e*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(2*d)","A",6,5,32,0.1562,1,"{12, 5984, 5918, 2402, 2315}"