1,1,67,49,0.008000," ","int(x^5*(a+b*arctanh(c*x)),x)","\frac{x^{6} a}{6}+\frac{b \,x^{6} \arctanh \left(c x \right)}{6}+\frac{b \,x^{5}}{30 c}+\frac{b \,x^{3}}{18 c^{3}}+\frac{b x}{6 c^{5}}+\frac{b \ln \left(c x -1\right)}{12 c^{6}}-\frac{b \ln \left(c x +1\right)}{12 c^{6}}"," ",0,"1/6*x^6*a+1/6*b*x^6*arctanh(c*x)+1/30*b*x^5/c+1/18*b*x^3/c^3+1/6*b*x/c^5+1/12/c^6*b*ln(c*x-1)-1/12/c^6*b*ln(c*x+1)","A"
2,1,60,49,0.009000," ","int(x^4*(a+b*arctanh(c*x)),x)","\frac{a \,x^{5}}{5}+\frac{b \,x^{5} \arctanh \left(c x \right)}{5}+\frac{b \,x^{4}}{20 c}+\frac{b \,x^{2}}{10 c^{3}}+\frac{b \ln \left(c x -1\right)}{10 c^{5}}+\frac{b \ln \left(c x +1\right)}{10 c^{5}}"," ",0,"1/5*a*x^5+1/5*b*x^5*arctanh(c*x)+1/20*b*x^4/c+1/10*b*x^2/c^3+1/10/c^5*b*ln(c*x-1)+1/10/c^5*b*ln(c*x+1)","A"
3,1,58,40,0.008000," ","int(x^3*(a+b*arctanh(c*x)),x)","\frac{x^{4} a}{4}+\frac{b \,x^{4} \arctanh \left(c x \right)}{4}+\frac{b \,x^{3}}{12 c}+\frac{b x}{4 c^{3}}+\frac{b \ln \left(c x -1\right)}{8 c^{4}}-\frac{b \ln \left(c x +1\right)}{8 c^{4}}"," ",0,"1/4*x^4*a+1/4*b*x^4*arctanh(c*x)+1/12*b*x^3/c+1/4*b*x/c^3+1/8/c^4*b*ln(c*x-1)-1/8/c^4*b*ln(c*x+1)","A"
4,1,51,40,0.008000," ","int(x^2*(a+b*arctanh(c*x)),x)","\frac{x^{3} a}{3}+\frac{b \,x^{3} \arctanh \left(c x \right)}{3}+\frac{b \,x^{2}}{6 c}+\frac{b \ln \left(c x -1\right)}{6 c^{3}}+\frac{b \ln \left(c x +1\right)}{6 c^{3}}"," ",0,"1/3*x^3*a+1/3*b*x^3*arctanh(c*x)+1/6*b*x^2/c+1/6/c^3*b*ln(c*x-1)+1/6/c^3*b*ln(c*x+1)","A"
5,1,49,31,0.007000," ","int(x*(a+b*arctanh(c*x)),x)","\frac{a \,x^{2}}{2}+\frac{b \,x^{2} \arctanh \left(c x \right)}{2}+\frac{b x}{2 c}+\frac{b \ln \left(c x -1\right)}{4 c^{2}}-\frac{b \ln \left(c x +1\right)}{4 c^{2}}"," ",0,"1/2*a*x^2+1/2*b*x^2*arctanh(c*x)+1/2*b*x/c+1/4/c^2*b*ln(c*x-1)-1/4/c^2*b*ln(c*x+1)","A"
6,1,29,28,0.003000," ","int(a+b*arctanh(c*x),x)","a x +b x \arctanh \left(c x \right)+\frac{b \ln \left(-c^{2} x^{2}+1\right)}{2 c}"," ",0,"a*x+b*x*arctanh(c*x)+1/2*b*ln(-c^2*x^2+1)/c","A"
7,1,47,22,0.014000," ","int((a+b*arctanh(c*x))/x,x)","a \ln \left(c x \right)+b \ln \left(c x \right) \arctanh \left(c x \right)-\frac{b \dilog \left(c x \right)}{2}-\frac{b \dilog \left(c x +1\right)}{2}-\frac{b \ln \left(c x \right) \ln \left(c x +1\right)}{2}"," ",0,"a*ln(c*x)+b*ln(c*x)*arctanh(c*x)-1/2*b*dilog(c*x)-1/2*b*dilog(c*x+1)-1/2*b*ln(c*x)*ln(c*x+1)","B"
8,1,45,36,0.010000," ","int((a+b*arctanh(c*x))/x^2,x)","-\frac{a}{x}-\frac{b \arctanh \left(c x \right)}{x}+c b \ln \left(c x \right)-\frac{c b \ln \left(c x -1\right)}{2}-\frac{c b \ln \left(c x +1\right)}{2}"," ",0,"-a/x-b/x*arctanh(c*x)+c*b*ln(c*x)-1/2*c*b*ln(c*x-1)-1/2*c*b*ln(c*x+1)","A"
9,1,49,34,0.011000," ","int((a+b*arctanh(c*x))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arctanh \left(c x \right)}{2 x^{2}}-\frac{b c}{2 x}-\frac{c^{2} b \ln \left(c x -1\right)}{4}+\frac{c^{2} b \ln \left(c x +1\right)}{4}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arctanh(c*x)-1/2*b*c/x-1/4*c^2*b*ln(c*x-1)+1/4*c^2*b*ln(c*x+1)","A"
10,1,59,49,0.012000," ","int((a+b*arctanh(c*x))/x^4,x)","-\frac{a}{3 x^{3}}-\frac{b \arctanh \left(c x \right)}{3 x^{3}}-\frac{b c}{6 x^{2}}+\frac{c^{3} b \ln \left(c x \right)}{3}-\frac{c^{3} b \ln \left(c x -1\right)}{6}-\frac{c^{3} b \ln \left(c x +1\right)}{6}"," ",0,"-1/3*a/x^3-1/3*b/x^3*arctanh(c*x)-1/6*b*c/x^2+1/3*c^3*b*ln(c*x)-1/6*c^3*b*ln(c*x-1)-1/6*c^3*b*ln(c*x+1)","A"
11,1,58,43,0.013000," ","int((a+b*arctanh(c*x))/x^5,x)","-\frac{a}{4 x^{4}}-\frac{b \arctanh \left(c x \right)}{4 x^{4}}-\frac{b c}{12 x^{3}}-\frac{b \,c^{3}}{4 x}-\frac{c^{4} b \ln \left(c x -1\right)}{8}+\frac{c^{4} b \ln \left(c x +1\right)}{8}"," ",0,"-1/4*a/x^4-1/4*b/x^4*arctanh(c*x)-1/12*b*c/x^3-1/4*b*c^3/x-1/8*c^4*b*ln(c*x-1)+1/8*c^4*b*ln(c*x+1)","A"
12,1,68,58,0.013000," ","int((a+b*arctanh(c*x))/x^6,x)","-\frac{a}{5 x^{5}}-\frac{b \arctanh \left(c x \right)}{5 x^{5}}-\frac{b c}{20 x^{4}}-\frac{b \,c^{3}}{10 x^{2}}+\frac{c^{5} b \ln \left(c x \right)}{5}-\frac{c^{5} b \ln \left(c x -1\right)}{10}-\frac{c^{5} b \ln \left(c x +1\right)}{10}"," ",0,"-1/5*a/x^5-1/5*b/x^5*arctanh(c*x)-1/20*b*c/x^4-1/10*b*c^3/x^2+1/5*c^5*b*ln(c*x)-1/10*c^5*b*ln(c*x-1)-1/10*c^5*b*ln(c*x+1)","A"
13,1,314,127,0.032000," ","int(x^5*(a+b*arctanh(c*x))^2,x)","\frac{x^{6} a^{2}}{6}+\frac{b^{2} x^{6} \arctanh \left(c x \right)^{2}}{6}+\frac{b^{2} \arctanh \left(c x \right) x^{5}}{15 c}+\frac{b^{2} \arctanh \left(c x \right) x^{3}}{9 c^{3}}+\frac{b^{2} x \arctanh \left(c x \right)}{3 c^{5}}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{6 c^{6}}-\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{6 c^{6}}+\frac{b^{2} \ln \left(c x -1\right)^{2}}{24 c^{6}}-\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{12 c^{6}}+\frac{b^{2} \ln \left(c x +1\right)^{2}}{24 c^{6}}-\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{12 c^{6}}+\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{12 c^{6}}+\frac{b^{2} x^{4}}{60 c^{2}}+\frac{4 b^{2} x^{2}}{45 c^{4}}+\frac{23 b^{2} \ln \left(c x -1\right)}{90 c^{6}}+\frac{23 b^{2} \ln \left(c x +1\right)}{90 c^{6}}+\frac{a b \,x^{6} \arctanh \left(c x \right)}{3}+\frac{x^{5} a b}{15 c}+\frac{a b \,x^{3}}{9 c^{3}}+\frac{a b x}{3 c^{5}}+\frac{a b \ln \left(c x -1\right)}{6 c^{6}}-\frac{a b \ln \left(c x +1\right)}{6 c^{6}}"," ",0,"1/6*x^6*a^2+1/6*b^2*x^6*arctanh(c*x)^2+1/15/c*b^2*arctanh(c*x)*x^5+1/9/c^3*b^2*arctanh(c*x)*x^3+1/3*b^2*x*arctanh(c*x)/c^5+1/6/c^6*b^2*arctanh(c*x)*ln(c*x-1)-1/6/c^6*b^2*arctanh(c*x)*ln(c*x+1)+1/24/c^6*b^2*ln(c*x-1)^2-1/12/c^6*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/24/c^6*b^2*ln(c*x+1)^2-1/12/c^6*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/12/c^6*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/60*b^2*x^4/c^2+4/45*b^2*x^2/c^4+23/90/c^6*b^2*ln(c*x-1)+23/90/c^6*b^2*ln(c*x+1)+1/3*a*b*x^6*arctanh(c*x)+1/15/c*x^5*a*b+1/9*a*b*x^3/c^3+1/3*a*b*x/c^5+1/6/c^6*a*b*ln(c*x-1)-1/6/c^6*a*b*ln(c*x+1)","B"
14,1,306,144,0.018000," ","int(x^4*(a+b*arctanh(c*x))^2,x)","\frac{x^{5} a^{2}}{5}+\frac{x^{5} b^{2} \arctanh \left(c x \right)^{2}}{5}+\frac{b^{2} \arctanh \left(c x \right) x^{4}}{10 c}+\frac{b^{2} \arctanh \left(c x \right) x^{2}}{5 c^{3}}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{5 c^{5}}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{5 c^{5}}+\frac{b^{2} x^{3}}{30 c^{2}}+\frac{3 b^{2} x}{10 c^{4}}+\frac{3 b^{2} \ln \left(c x -1\right)}{20 c^{5}}-\frac{3 b^{2} \ln \left(c x +1\right)}{20 c^{5}}+\frac{b^{2} \ln \left(c x -1\right)^{2}}{20 c^{5}}-\frac{b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{5 c^{5}}-\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{10 c^{5}}-\frac{b^{2} \ln \left(c x +1\right)^{2}}{20 c^{5}}+\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{10 c^{5}}-\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{10 c^{5}}+\frac{2 x^{5} a b \arctanh \left(c x \right)}{5}+\frac{x^{4} a b}{10 c}+\frac{a b \,x^{2}}{5 c^{3}}+\frac{a b \ln \left(c x -1\right)}{5 c^{5}}+\frac{a b \ln \left(c x +1\right)}{5 c^{5}}"," ",0,"1/5*x^5*a^2+1/5*x^5*b^2*arctanh(c*x)^2+1/10/c*b^2*arctanh(c*x)*x^4+1/5/c^3*b^2*arctanh(c*x)*x^2+1/5/c^5*b^2*arctanh(c*x)*ln(c*x-1)+1/5/c^5*b^2*arctanh(c*x)*ln(c*x+1)+1/30*b^2*x^3/c^2+3/10*b^2*x/c^4+3/20/c^5*b^2*ln(c*x-1)-3/20/c^5*b^2*ln(c*x+1)+1/20/c^5*b^2*ln(c*x-1)^2-1/5/c^5*b^2*dilog(1/2+1/2*c*x)-1/10/c^5*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/20/c^5*b^2*ln(c*x+1)^2+1/10/c^5*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/10/c^5*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+2/5*x^5*a*b*arctanh(c*x)+1/10/c*x^4*a*b+1/5*a*b*x^2/c^3+1/5/c^5*a*b*ln(c*x-1)+1/5/c^5*a*b*ln(c*x+1)","B"
15,1,278,99,0.017000," ","int(x^3*(a+b*arctanh(c*x))^2,x)","\frac{a^{2} x^{4}}{4}+\frac{b^{2} x^{4} \arctanh \left(c x \right)^{2}}{4}+\frac{b^{2} \arctanh \left(c x \right) x^{3}}{6 c}+\frac{b^{2} x \arctanh \left(c x \right)}{2 c^{3}}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{4 c^{4}}-\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{4 c^{4}}+\frac{b^{2} \ln \left(c x -1\right)^{2}}{16 c^{4}}-\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{8 c^{4}}+\frac{b^{2} \ln \left(c x +1\right)^{2}}{16 c^{4}}-\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{8 c^{4}}+\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{8 c^{4}}+\frac{b^{2} x^{2}}{12 c^{2}}+\frac{b^{2} \ln \left(c x -1\right)}{3 c^{4}}+\frac{b^{2} \ln \left(c x +1\right)}{3 c^{4}}+\frac{x^{4} a b \arctanh \left(c x \right)}{2}+\frac{a b \,x^{3}}{6 c}+\frac{a b x}{2 c^{3}}+\frac{a b \ln \left(c x -1\right)}{4 c^{4}}-\frac{a b \ln \left(c x +1\right)}{4 c^{4}}"," ",0,"1/4*a^2*x^4+1/4*b^2*x^4*arctanh(c*x)^2+1/6/c*b^2*arctanh(c*x)*x^3+1/2*b^2*x*arctanh(c*x)/c^3+1/4/c^4*b^2*arctanh(c*x)*ln(c*x-1)-1/4/c^4*b^2*arctanh(c*x)*ln(c*x+1)+1/16/c^4*b^2*ln(c*x-1)^2-1/8/c^4*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/16/c^4*b^2*ln(c*x+1)^2-1/8/c^4*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/8/c^4*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/12*b^2*x^2/c^2+1/3/c^4*b^2*ln(c*x-1)+1/3/c^4*b^2*ln(c*x+1)+1/2*x^4*a*b*arctanh(c*x)+1/6*a*b*x^3/c+1/2*a*b*x/c^3+1/4/c^4*a*b*ln(c*x-1)-1/4/c^4*a*b*ln(c*x+1)","B"
16,1,270,116,0.013000," ","int(x^2*(a+b*arctanh(c*x))^2,x)","\frac{x^{3} a^{2}}{3}+\frac{b^{2} x^{3} \arctanh \left(c x \right)^{2}}{3}+\frac{b^{2} \arctanh \left(c x \right) x^{2}}{3 c}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{3 c^{3}}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{3 c^{3}}+\frac{b^{2} x}{3 c^{2}}+\frac{b^{2} \ln \left(c x -1\right)}{6 c^{3}}-\frac{b^{2} \ln \left(c x +1\right)}{6 c^{3}}+\frac{b^{2} \ln \left(c x -1\right)^{2}}{12 c^{3}}-\frac{b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{3 c^{3}}-\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{6 c^{3}}-\frac{b^{2} \ln \left(c x +1\right)^{2}}{12 c^{3}}-\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{6 c^{3}}+\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{6 c^{3}}+\frac{2 a b \,x^{3} \arctanh \left(c x \right)}{3}+\frac{a b \,x^{2}}{3 c}+\frac{a b \ln \left(c x -1\right)}{3 c^{3}}+\frac{a b \ln \left(c x +1\right)}{3 c^{3}}"," ",0,"1/3*x^3*a^2+1/3*b^2*x^3*arctanh(c*x)^2+1/3/c*b^2*arctanh(c*x)*x^2+1/3/c^3*b^2*arctanh(c*x)*ln(c*x-1)+1/3/c^3*b^2*arctanh(c*x)*ln(c*x+1)+1/3*b^2*x/c^2+1/6/c^3*b^2*ln(c*x-1)-1/6/c^3*b^2*ln(c*x+1)+1/12/c^3*b^2*ln(c*x-1)^2-1/3/c^3*b^2*dilog(1/2+1/2*c*x)-1/6/c^3*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/12/c^3*b^2*ln(c*x+1)^2-1/6/c^3*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/6/c^3*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+2/3*a*b*x^3*arctanh(c*x)+1/3*a*b*x^2/c+1/3/c^3*a*b*ln(c*x-1)+1/3/c^3*a*b*ln(c*x+1)","B"
17,1,239,69,0.016000," ","int(x*(a+b*arctanh(c*x))^2,x)","\frac{a^{2} x^{2}}{2}+\frac{x^{2} b^{2} \arctanh \left(c x \right)^{2}}{2}+\frac{b^{2} x \arctanh \left(c x \right)}{c}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{2 c^{2}}-\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{2 c^{2}}+\frac{b^{2} \ln \left(c x -1\right)^{2}}{8 c^{2}}-\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c^{2}}+\frac{b^{2} \ln \left(c x -1\right)}{2 c^{2}}+\frac{b^{2} \ln \left(c x +1\right)}{2 c^{2}}+\frac{b^{2} \ln \left(c x +1\right)^{2}}{8 c^{2}}+\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c^{2}}-\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{4 c^{2}}+a b \,x^{2} \arctanh \left(c x \right)+\frac{a b x}{c}+\frac{a b \ln \left(c x -1\right)}{2 c^{2}}-\frac{a b \ln \left(c x +1\right)}{2 c^{2}}"," ",0,"1/2*a^2*x^2+1/2*x^2*b^2*arctanh(c*x)^2+b^2*x*arctanh(c*x)/c+1/2/c^2*b^2*arctanh(c*x)*ln(c*x-1)-1/2/c^2*b^2*arctanh(c*x)*ln(c*x+1)+1/8/c^2*b^2*ln(c*x-1)^2-1/4/c^2*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/2/c^2*b^2*ln(c*x-1)+1/2/c^2*b^2*ln(c*x+1)+1/8/c^2*b^2*ln(c*x+1)^2+1/4/c^2*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/4/c^2*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+a*b*x^2*arctanh(c*x)+a*b*x/c+1/2/c^2*a*b*ln(c*x-1)-1/2/c^2*a*b*ln(c*x+1)","B"
18,1,123,74,0.189000," ","int((a+b*arctanh(c*x))^2,x)","x \,b^{2} \arctanh \left(c x \right)^{2}+2 x a b \arctanh \left(c x \right)+\frac{b^{2} \arctanh \left(c x \right)^{2}}{c}-\frac{2 \arctanh \left(c x \right) \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right) b^{2}}{c}+a^{2} x +\frac{a b \ln \left(-c^{2} x^{2}+1\right)}{c}-\frac{\polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right) b^{2}}{c}"," ",0,"x*b^2*arctanh(c*x)^2+2*x*a*b*arctanh(c*x)+1/c*b^2*arctanh(c*x)^2-2/c*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))*b^2+a^2*x+1/c*a*b*ln(-c^2*x^2+1)-1/c*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))*b^2","A"
19,1,701,113,0.280000," ","int((a+b*arctanh(c*x))^2/x,x)","a^{2} \ln \left(c x \right)+b^{2} \ln \left(c x \right) \arctanh \left(c x \right)^{2}-b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)+\frac{b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2}-b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)+b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+2 b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-2 b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+2 b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-2 b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}+2 a b \ln \left(c x \right) \arctanh \left(c x \right)-a b \ln \left(c x \right) \ln \left(c x +1\right)-a b \dilog \left(c x \right)-a b \dilog \left(c x +1\right)"," ",0,"a^2*ln(c*x)+b^2*ln(c*x)*arctanh(c*x)^2-b^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/2*b^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-b^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+b^2*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*b^2*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))-2*b^2*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))+b^2*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+2*b^2*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))-2*b^2*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2*I*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-1/2*I*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+2*a*b*ln(c*x)*arctanh(c*x)-a*b*ln(c*x)*ln(c*x+1)-a*b*dilog(c*x)-a*b*dilog(c*x+1)","C"
20,1,248,71,0.023000," ","int((a+b*arctanh(c*x))^2/x^2,x)","-\frac{a^{2}}{x}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{x}+2 c \,b^{2} \ln \left(c x \right) \arctanh \left(c x \right)-c \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)-c \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)-\frac{c \,b^{2} \ln \left(c x -1\right)^{2}}{4}+c \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)+\frac{c \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2}+\frac{c \,b^{2} \ln \left(c x +1\right)^{2}}{4}-\frac{c \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2}+\frac{c \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2}-c \,b^{2} \dilog \left(c x \right)-c \,b^{2} \dilog \left(c x +1\right)-c \,b^{2} \ln \left(c x \right) \ln \left(c x +1\right)-\frac{2 a b \arctanh \left(c x \right)}{x}+2 c a b \ln \left(c x \right)-c a b \ln \left(c x -1\right)-c a b \ln \left(c x +1\right)"," ",0,"-a^2/x-b^2/x*arctanh(c*x)^2+2*c*b^2*ln(c*x)*arctanh(c*x)-c*b^2*arctanh(c*x)*ln(c*x-1)-c*b^2*arctanh(c*x)*ln(c*x+1)-1/4*c*b^2*ln(c*x-1)^2+c*b^2*dilog(1/2+1/2*c*x)+1/2*c*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/4*c*b^2*ln(c*x+1)^2-1/2*c*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/2*c*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-c*b^2*dilog(c*x)-c*b^2*dilog(c*x+1)-c*b^2*ln(c*x)*ln(c*x+1)-2*a*b/x*arctanh(c*x)+2*c*a*b*ln(c*x)-c*a*b*ln(c*x-1)-c*a*b*ln(c*x+1)","B"
21,1,253,74,0.019000," ","int((a+b*arctanh(c*x))^2/x^3,x)","-\frac{a^{2}}{2 x^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{2 x^{2}}-\frac{c \,b^{2} \arctanh \left(c x \right)}{x}-\frac{c^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{2}+\frac{c^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{2}-\frac{c^{2} b^{2} \ln \left(c x -1\right)^{2}}{8}+\frac{c^{2} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4}+c^{2} b^{2} \ln \left(c x \right)-\frac{c^{2} b^{2} \ln \left(c x -1\right)}{2}-\frac{c^{2} b^{2} \ln \left(c x +1\right)}{2}-\frac{c^{2} b^{2} \ln \left(c x +1\right)^{2}}{8}+\frac{c^{2} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{4}-\frac{c^{2} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4}-\frac{a b \arctanh \left(c x \right)}{x^{2}}-\frac{a b c}{x}-\frac{c^{2} a b \ln \left(c x -1\right)}{2}+\frac{c^{2} a b \ln \left(c x +1\right)}{2}"," ",0,"-1/2*a^2/x^2-1/2*b^2/x^2*arctanh(c*x)^2-c*b^2*arctanh(c*x)/x-1/2*c^2*b^2*arctanh(c*x)*ln(c*x-1)+1/2*c^2*b^2*arctanh(c*x)*ln(c*x+1)-1/8*c^2*b^2*ln(c*x-1)^2+1/4*c^2*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+c^2*b^2*ln(c*x)-1/2*c^2*b^2*ln(c*x-1)-1/2*c^2*b^2*ln(c*x+1)-1/8*c^2*b^2*ln(c*x+1)^2+1/4*c^2*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/4*c^2*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-a*b/x^2*arctanh(c*x)-a*b*c/x-1/2*c^2*a*b*ln(c*x-1)+1/2*c^2*a*b*ln(c*x+1)","B"
22,1,339,116,0.023000," ","int((a+b*arctanh(c*x))^2/x^4,x)","-\frac{a^{2}}{3 x^{3}}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{3 x^{3}}-\frac{c \,b^{2} \arctanh \left(c x \right)}{3 x^{2}}+\frac{2 c^{3} b^{2} \ln \left(c x \right) \arctanh \left(c x \right)}{3}-\frac{c^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{3}-\frac{c^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{3}-\frac{b^{2} c^{2}}{3 x}-\frac{c^{3} b^{2} \ln \left(c x -1\right)}{6}+\frac{c^{3} b^{2} \ln \left(c x +1\right)}{6}-\frac{c^{3} b^{2} \ln \left(c x -1\right)^{2}}{12}+\frac{c^{3} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{3}+\frac{c^{3} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{6}+\frac{c^{3} b^{2} \ln \left(c x +1\right)^{2}}{12}+\frac{c^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{6}-\frac{c^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{6}-\frac{c^{3} b^{2} \dilog \left(c x \right)}{3}-\frac{c^{3} b^{2} \dilog \left(c x +1\right)}{3}-\frac{c^{3} b^{2} \ln \left(c x \right) \ln \left(c x +1\right)}{3}-\frac{2 a b \arctanh \left(c x \right)}{3 x^{3}}-\frac{c a b}{3 x^{2}}+\frac{2 c^{3} a b \ln \left(c x \right)}{3}-\frac{c^{3} a b \ln \left(c x -1\right)}{3}-\frac{c^{3} a b \ln \left(c x +1\right)}{3}"," ",0,"-1/3*a^2/x^3-1/3*b^2/x^3*arctanh(c*x)^2-1/3*c*b^2*arctanh(c*x)/x^2+2/3*c^3*b^2*ln(c*x)*arctanh(c*x)-1/3*c^3*b^2*arctanh(c*x)*ln(c*x-1)-1/3*c^3*b^2*arctanh(c*x)*ln(c*x+1)-1/3*b^2*c^2/x-1/6*c^3*b^2*ln(c*x-1)+1/6*c^3*b^2*ln(c*x+1)-1/12*c^3*b^2*ln(c*x-1)^2+1/3*c^3*b^2*dilog(1/2+1/2*c*x)+1/6*c^3*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/12*c^3*b^2*ln(c*x+1)^2+1/6*c^3*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/6*c^3*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/3*c^3*b^2*dilog(c*x)-1/3*c^3*b^2*dilog(c*x+1)-1/3*c^3*b^2*ln(c*x)*ln(c*x+1)-2/3*a*b/x^3*arctanh(c*x)-1/3*c*a*b/x^2+2/3*c^3*a*b*ln(c*x)-1/3*c^3*a*b*ln(c*x-1)-1/3*c^3*a*b*ln(c*x+1)","B"
23,1,290,103,0.027000," ","int((a+b*arctanh(c*x))^2/x^5,x)","-\frac{a^{2}}{4 x^{4}}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{4 x^{4}}-\frac{c \,b^{2} \arctanh \left(c x \right)}{6 x^{3}}-\frac{c^{3} b^{2} \arctanh \left(c x \right)}{2 x}-\frac{c^{4} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{4}+\frac{c^{4} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{4}-\frac{c^{4} b^{2} \ln \left(c x -1\right)^{2}}{16}+\frac{c^{4} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{8}-\frac{c^{4} b^{2} \ln \left(c x +1\right)^{2}}{16}-\frac{c^{4} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{8}+\frac{c^{4} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{8}-\frac{b^{2} c^{2}}{12 x^{2}}+\frac{2 c^{4} b^{2} \ln \left(c x \right)}{3}-\frac{c^{4} b^{2} \ln \left(c x -1\right)}{3}-\frac{c^{4} b^{2} \ln \left(c x +1\right)}{3}-\frac{a b \arctanh \left(c x \right)}{2 x^{4}}-\frac{a b c}{6 x^{3}}-\frac{c^{3} a b}{2 x}-\frac{c^{4} a b \ln \left(c x -1\right)}{4}+\frac{c^{4} a b \ln \left(c x +1\right)}{4}"," ",0,"-1/4*a^2/x^4-1/4*b^2/x^4*arctanh(c*x)^2-1/6*c*b^2*arctanh(c*x)/x^3-1/2*c^3*b^2*arctanh(c*x)/x-1/4*c^4*b^2*arctanh(c*x)*ln(c*x-1)+1/4*c^4*b^2*arctanh(c*x)*ln(c*x+1)-1/16*c^4*b^2*ln(c*x-1)^2+1/8*c^4*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/16*c^4*b^2*ln(c*x+1)^2-1/8*c^4*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/8*c^4*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/12*b^2*c^2/x^2+2/3*c^4*b^2*ln(c*x)-1/3*c^4*b^2*ln(c*x-1)-1/3*c^4*b^2*ln(c*x+1)-1/2*a*b/x^4*arctanh(c*x)-1/6*a*b*c/x^3-1/2*c^3*a*b/x-1/4*c^4*a*b*ln(c*x-1)+1/4*c^4*a*b*ln(c*x+1)","B"
24,1,1330,221,2.326000," ","int(x^5*(a+b*arctanh(c*x))^3,x)","-\frac{19 b^{3} \arctanh \left(c x \right)}{60 c^{6}}+\frac{b^{3} x^{6} \arctanh \left(c x \right)^{3}}{6}+\frac{23 b^{3} \arctanh \left(c x \right)^{2}}{30 c^{6}}-\frac{b^{3} \arctanh \left(c x \right)^{3}}{6 c^{6}}+\frac{b^{3} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{2 c^{6}}+\frac{a^{2} b \,x^{6} \arctanh \left(c x \right)}{2}+\frac{a \,b^{2} x^{6} \arctanh \left(c x \right)^{2}}{2}-\frac{b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{4 c^{6}}+\frac{b^{3} \arctanh \left(c x \right)^{2} x^{5}}{10 c}+\frac{b^{3} \arctanh \left(c x \right)^{2} x^{3}}{6 c^{3}}+\frac{b^{3} \arctanh \left(c x \right)^{2} x}{2 c^{5}}+\frac{b^{3} \arctanh \left(c x \right) x^{4}}{20 c^{2}}+\frac{4 b^{3} \arctanh \left(c x \right) x^{2}}{15 c^{4}}+\frac{b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right)}{4 c^{6}}-\frac{23 b^{3} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{15 c^{6}}-\frac{23 b^{3} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{15 c^{6}}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \arctanh \left(c x \right)^{2}}{8 c^{6}}+\frac{a \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{2 c^{6}}-\frac{a \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{2 c^{6}}+\frac{a \,b^{2} \arctanh \left(c x \right) x^{3}}{3 c^{3}}+\frac{a \,b^{2} \arctanh \left(c x \right) x}{c^{5}}+\frac{a \,b^{2} x^{5} \arctanh \left(c x \right)}{5 c}-\frac{i b^{3} \pi  \arctanh \left(c x \right)^{2}}{4 c^{6}}+\frac{19 b^{3} x}{60 c^{5}}+\frac{b^{3} x^{3}}{60 c^{3}}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{8 c^{6}}+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2}}{8 c^{6}}+\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \arctanh \left(c x \right)^{2}}{4 c^{6}}+\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{8 c^{6}}-\frac{b^{3}}{3 c^{6}}+\frac{x^{6} a^{3}}{6}-\frac{23 b^{3} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{15 c^{6}}-\frac{23 b^{3} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{15 c^{6}}-\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{4 c^{6}}+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{4 c^{6}}+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2}}{8 c^{6}}+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{8 c^{6}}-\frac{a \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c^{6}}-\frac{a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{4 c^{6}}+\frac{a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c^{6}}+\frac{4 x^{2} a \,b^{2}}{15 c^{4}}+\frac{x \,a^{2} b}{2 c^{5}}+\frac{x^{5} a^{2} b}{10 c}+\frac{a \,b^{2} x^{4}}{20 c^{2}}+\frac{a^{2} b \,x^{3}}{6 c^{3}}+\frac{a \,b^{2} \ln \left(c x -1\right)^{2}}{8 c^{6}}+\frac{a \,b^{2} \ln \left(c x +1\right)^{2}}{8 c^{6}}+\frac{23 a \,b^{2} \ln \left(c x -1\right)}{30 c^{6}}+\frac{23 a \,b^{2} \ln \left(c x +1\right)}{30 c^{6}}+\frac{a^{2} b \ln \left(c x -1\right)}{4 c^{6}}-\frac{a^{2} b \ln \left(c x +1\right)}{4 c^{6}}"," ",0,"-23/15/c^6*b^3*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-23/15/c^6*b^3*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2/c^6*b^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*a^2*b*x^6*arctanh(c*x)+1/2*a*b^2*x^6*arctanh(c*x)^2-1/8*I/c^6*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+19/60*b^3*x/c^5+1/60*b^3*x^3/c^3-19/60*b^3*arctanh(c*x)/c^6+1/8*I/c^6*b^3*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2+1/4*I/c^6*b^3*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)^2+1/8*I/c^6*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/8*I/c^6*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/4/c^6*b^3*arctanh(c*x)^2*ln(c*x+1)+1/6*b^3*x^6*arctanh(c*x)^3+23/30/c^6*b^3*arctanh(c*x)^2-1/6/c^6*b^3*arctanh(c*x)^3-23/15/c^6*b^3*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-23/15/c^6*b^3*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/3/c^6*b^3+1/6*x^6*a^3-1/4*I/c^6*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/4*I/c^6*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/8*I/c^6*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2+1/8*I/c^6*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/2/c^6*a*b^2*arctanh(c*x)*ln(c*x-1)-1/2/c^6*a*b^2*arctanh(c*x)*ln(c*x+1)-1/4/c^6*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/4/c^6*a*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/4/c^6*a*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/3/c^3*a*b^2*arctanh(c*x)*x^3+1/c^5*a*b^2*arctanh(c*x)*x+1/5/c*a*b^2*x^5*arctanh(c*x)-1/4*I/c^6*b^3*Pi*arctanh(c*x)^2+4/15/c^4*x^2*a*b^2+1/2/c^5*x*a^2*b+1/10/c*x^5*a^2*b+1/20/c^2*a*b^2*x^4+1/6/c^3*a^2*b*x^3+1/10/c*b^3*arctanh(c*x)^2*x^5+1/6/c^3*b^3*arctanh(c*x)^2*x^3+1/2/c^5*b^3*arctanh(c*x)^2*x+1/20/c^2*b^3*arctanh(c*x)*x^4+4/15/c^4*b^3*arctanh(c*x)*x^2+1/8/c^6*a*b^2*ln(c*x-1)^2+1/8/c^6*a*b^2*ln(c*x+1)^2+23/30/c^6*a*b^2*ln(c*x-1)+23/30/c^6*a*b^2*ln(c*x+1)+1/4/c^6*a^2*b*ln(c*x-1)-1/4/c^6*a^2*b*ln(c*x+1)+1/4/c^6*b^3*arctanh(c*x)^2*ln(c*x-1)","C"
25,1,1275,236,2.219000," ","int(x^4*(a+b*arctanh(c*x))^3,x)","\frac{9 a \,b^{2} x}{10 c^{4}}+\frac{3 x^{4} a^{2} b}{20 c}+\frac{3 a^{2} b \,x^{2}}{10 c^{3}}+\frac{3 b^{3} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{10 c^{5}}+\frac{x^{5} b^{3} \arctanh \left(c x \right)^{3}}{5}-\frac{9 b^{3} \arctanh \left(c x \right)^{2}}{20 c^{5}}+\frac{b^{3} \arctanh \left(c x \right)^{3}}{5 c^{5}}+\frac{b^{3} \arctanh \left(c x \right)}{c^{5}}-\frac{b^{3} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{5}}-\frac{3 a \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{10 c^{5}}+\frac{3 a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{10 c^{5}}-\frac{3 a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{10 c^{5}}+\frac{3 a \,b^{2} \ln \left(c x -1\right)^{2}}{20 c^{5}}-\frac{3 a \,b^{2} \ln \left(c x +1\right)^{2}}{20 c^{5}}+\frac{9 a \,b^{2} \ln \left(c x -1\right)}{20 c^{5}}-\frac{9 a \,b^{2} \ln \left(c x +1\right)}{20 c^{5}}+\frac{3 a^{2} b \ln \left(c x -1\right)}{10 c^{5}}+\frac{3 a^{2} b \ln \left(c x +1\right)}{10 c^{5}}+\frac{9 b^{3} x \arctanh \left(c x \right)}{10 c^{4}}+\frac{b^{3} \arctanh \left(c x \right) x^{3}}{10 c^{2}}+\frac{3 b^{3} \arctanh \left(c x \right)^{2} x^{2}}{10 c^{3}}+\frac{3 b^{3} \arctanh \left(c x \right)^{2} x^{4}}{20 c}-\frac{3 a \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{5 c^{5}}-\frac{3 b^{3} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{5 c^{5}}+\frac{3 b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right)}{10 c^{5}}+\frac{3 b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{10 c^{5}}-\frac{3 b^{3} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{5 c^{5}}-\frac{3 b^{3} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{5 c^{5}}+\frac{3 x^{5} a^{2} b \arctanh \left(c x \right)}{5}+\frac{3 a \,b^{2} \arctanh \left(c x \right) x^{2}}{5 c^{3}}+\frac{3 a \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{5 c^{5}}+\frac{3 a \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{5 c^{5}}+\frac{3 a \,b^{2} x^{4} \arctanh \left(c x \right)}{10 c}-\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \pi}{10 c^{5}}+\frac{a \,b^{2} x^{3}}{10 c^{2}}+\frac{b^{3} x^{2}}{20 c^{3}}-\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \pi}{20 c^{5}}-\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \pi}{10 c^{5}}-\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \pi}{20 c^{5}}+\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \pi}{10 c^{5}}-\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \pi}{10 c^{5}}-\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \pi}{20 c^{5}}+\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \pi}{20 c^{5}}-\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \pi}{20 c^{5}}+\frac{x^{5} a^{3}}{5}+\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \pi}{20 c^{5}}-\frac{b^{3}}{20 c^{5}}+\frac{3 x^{5} a \,b^{2} \arctanh \left(c x \right)^{2}}{5}"," ",0,"9/10*a*b^2*x/c^4+9/10*b^3*x*arctanh(c*x)/c^4+3/20/c*x^4*a^2*b+3/10/c^3*a^2*b*x^2+1/10/c^2*b^3*arctanh(c*x)*x^3+3/10/c^3*b^3*arctanh(c*x)^2*x^2+3/20/c*b^3*arctanh(c*x)^2*x^4+3/10/c^5*b^3*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-1/c^5*b^3*ln(1+(c*x+1)^2/(-c^2*x^2+1))+3/5/c^3*a*b^2*arctanh(c*x)*x^2+3/5/c^5*a*b^2*arctanh(c*x)*ln(c*x-1)+3/5/c^5*a*b^2*arctanh(c*x)*ln(c*x+1)-3/10/c^5*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+3/10/c^5*a*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-3/10/c^5*a*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-3/10*I/c^5*b^3*arctanh(c*x)^2*Pi+3/20/c^5*a*b^2*ln(c*x-1)^2-3/20/c^5*a*b^2*ln(c*x+1)^2+9/20/c^5*a*b^2*ln(c*x-1)-9/20/c^5*a*b^2*ln(c*x+1)+3/10/c^5*a^2*b*ln(c*x-1)+3/10/c^5*a^2*b*ln(c*x+1)-3/5/c^5*a*b^2*dilog(1/2+1/2*c*x)-3/5/c^5*b^3*arctanh(c*x)^2*ln(2)+3/10/c^5*b^3*arctanh(c*x)^2*ln(c*x-1)+3/10/c^5*b^3*arctanh(c*x)^2*ln(c*x+1)-3/5/c^5*b^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-3/5/c^5*b^3*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+3/5*x^5*a^2*b*arctanh(c*x)+3/5*x^5*a*b^2*arctanh(c*x)^2-3/10*I/c^5*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*Pi-3/20*I/c^5*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*Pi+3/20*I/c^5*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi-3/20*I/c^5*b^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi+1/10*a*b^2*x^3/c^2+1/20*b^3*x^2/c^3-3/20*I/c^5*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi-3/10*I/c^5*b^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi-3/20*I/c^5*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi+3/10*I/c^5*b^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi+1/5*x^5*a^3+3/20*I/c^5*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi-1/20/c^5*b^3+3/10/c*a*b^2*x^4*arctanh(c*x)+1/5*x^5*b^3*arctanh(c*x)^3-9/20/c^5*b^3*arctanh(c*x)^2+1/5/c^5*b^3*arctanh(c*x)^3+1/c^5*b^3*arctanh(c*x)","C"
26,1,1245,171,1.412000," ","int(x^3*(a+b*arctanh(c*x))^3,x)","\frac{3 b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right)}{8 c^{4}}-\frac{3 b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{8 c^{4}}+\frac{3 b^{3} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{4 c^{4}}+\frac{b^{3} \arctanh \left(c x \right)^{2} x^{3}}{4 c}+\frac{3 b^{3} \arctanh \left(c x \right)^{2} x}{4 c^{3}}+\frac{b^{3} \arctanh \left(c x \right) x^{2}}{4 c^{2}}+\frac{3 x^{4} a^{2} b \arctanh \left(c x \right)}{4}+\frac{3 a \,b^{2} x^{4} \arctanh \left(c x \right)^{2}}{4}-\frac{2 b^{3} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{4}}-\frac{2 b^{3} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{4}}+\frac{b^{3} \arctanh \left(c x \right)^{2}}{c^{4}}-\frac{b^{3} \arctanh \left(c x \right)^{3}}{4 c^{4}}+\frac{x^{4} b^{3} \arctanh \left(c x \right)^{3}}{4}-\frac{b^{3} \arctanh \left(c x \right)}{4 c^{4}}-\frac{3 a \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{8 c^{4}}-\frac{3 a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{8 c^{4}}+\frac{3 a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{8 c^{4}}+\frac{3 a \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{4 c^{4}}-\frac{3 a \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{4 c^{4}}+\frac{3 a \,b^{2} \arctanh \left(c x \right) x}{2 c^{3}}+\frac{a \,b^{2} \arctanh \left(c x \right) x^{3}}{2 c}-\frac{3 i b^{3} \pi  \arctanh \left(c x \right)^{2}}{8 c^{4}}+\frac{b^{3} x}{4 c^{3}}-\frac{2 b^{3} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{4}}-\frac{2 b^{3} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{4}}-\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \arctanh \left(c x \right)^{2}}{16 c^{4}}-\frac{b^{3}}{4 c^{4}}+\frac{x^{4} a^{3}}{4}+\frac{x^{2} a \,b^{2}}{4 c^{2}}+\frac{3 x \,a^{2} b}{4 c^{3}}+\frac{a^{2} b \,x^{3}}{4 c}+\frac{3 a \,b^{2} \ln \left(c x -1\right)^{2}}{16 c^{4}}+\frac{3 a \,b^{2} \ln \left(c x +1\right)^{2}}{16 c^{4}}+\frac{a \,b^{2} \ln \left(c x -1\right)}{c^{4}}+\frac{a \,b^{2} \ln \left(c x +1\right)}{c^{4}}+\frac{3 a^{2} b \ln \left(c x -1\right)}{8 c^{4}}-\frac{3 a^{2} b \ln \left(c x +1\right)}{8 c^{4}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2}}{16 c^{4}}+\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{16 c^{4}}-\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{16 c^{4}}+\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \arctanh \left(c x \right)^{2}}{8 c^{4}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{8 c^{4}}-\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{8 c^{4}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2}}{16 c^{4}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{16 c^{4}}"," ",0,"3/16*I/c^4*b^3*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2+3/16*I/c^4*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-3/16*I/c^4*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+3/8*I/c^4*b^3*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)^2-2/c^4*b^3*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-2/c^4*b^3*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/c^4*b^3*arctanh(c*x)^2-1/4/c^4*b^3*arctanh(c*x)^3+1/4*x^4*b^3*arctanh(c*x)^3+3/4/c^4*a*b^2*arctanh(c*x)*ln(c*x-1)-3/4/c^4*a*b^2*arctanh(c*x)*ln(c*x+1)-3/8/c^4*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-3/8/c^4*a*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+3/8/c^4*a*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+3/2/c^3*a*b^2*arctanh(c*x)*x+1/2/c*a*b^2*arctanh(c*x)*x^3-3/8*I/c^4*b^3*Pi*arctanh(c*x)^2+1/4*b^3*x/c^3-1/4*b^3*arctanh(c*x)/c^4-3/16*I/c^4*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-1/4/c^4*b^3+1/4*x^4*a^3+1/4/c^2*x^2*a*b^2+3/4/c^3*x*a^2*b+1/4/c*a^2*b*x^3+3/16/c^4*a*b^2*ln(c*x-1)^2+3/16/c^4*a*b^2*ln(c*x+1)^2+1/c^4*a*b^2*ln(c*x-1)+1/c^4*a*b^2*ln(c*x+1)+3/8/c^4*a^2*b*ln(c*x-1)-3/8/c^4*a^2*b*ln(c*x+1)+3/8/c^4*b^3*arctanh(c*x)^2*ln(c*x-1)-3/8/c^4*b^3*arctanh(c*x)^2*ln(c*x+1)-2/c^4*b^3*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-2/c^4*b^3*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+3/4/c^4*b^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+1/4/c*b^3*arctanh(c*x)^2*x^3+3/4/c^3*b^3*arctanh(c*x)^2*x+1/4/c^2*b^3*arctanh(c*x)*x^2+3/4*x^4*a^2*b*arctanh(c*x)+3/4*a*b^2*x^4*arctanh(c*x)^2+3/8*I/c^4*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-3/8*I/c^4*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+3/16*I/c^4*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2+3/16*I/c^4*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2","C"
27,1,1177,185,1.411000," ","int(x^2*(a+b*arctanh(c*x))^3,x)","\frac{x^{3} a^{3}}{3}-\frac{i b^{3} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)}{4 c^{3}}-\frac{i b^{3} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{2 c^{3}}+\frac{i b^{3} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{4 c^{3}}-\frac{i b^{3} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2}}{4 c^{3}}+\frac{a \,b^{2} x}{c^{2}}-\frac{i b^{3} \arctanh \left(c x \right)^{2} \pi}{2 c^{3}}+\frac{i b^{3} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)}{4 c^{3}}+\frac{b^{3} x \arctanh \left(c x \right)}{c^{2}}+a^{2} b \,x^{3} \arctanh \left(c x \right)+a \,b^{2} x^{3} \arctanh \left(c x \right)^{2}+\frac{b^{3} \arctanh \left(c x \right)^{2} x^{2}}{2 c}-\frac{b^{3} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{3}}-\frac{b^{3} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c^{3}}-\frac{a \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{3}}+\frac{b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right)}{2 c^{3}}+\frac{b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{2 c^{3}}-\frac{b^{3} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{3}}-\frac{i b^{3} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3}}{4 c^{3}}-\frac{i b^{3} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3}}{4 c^{3}}-\frac{i b^{3} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3}}{2 c^{3}}+\frac{i b^{3} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 c^{3}}+\frac{x^{3} b^{3} \arctanh \left(c x \right)^{3}}{3}-\frac{b^{3} \arctanh \left(c x \right)^{2}}{2 c^{3}}+\frac{b^{3} \arctanh \left(c x \right)^{3}}{3 c^{3}}+\frac{b^{3} \arctanh \left(c x \right)}{c^{3}}+\frac{b^{3} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c^{3}}+\frac{a \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{c^{3}}+\frac{a \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{3}}-\frac{a \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{3}}+\frac{a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 c^{3}}-\frac{a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{3}}+\frac{a \,b^{2} \arctanh \left(c x \right) x^{2}}{c}-\frac{b^{3} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{3}}+\frac{a^{2} b \,x^{2}}{2 c}+\frac{a \,b^{2} \ln \left(c x -1\right)^{2}}{4 c^{3}}-\frac{a \,b^{2} \ln \left(c x +1\right)^{2}}{4 c^{3}}+\frac{a \,b^{2} \ln \left(c x -1\right)}{2 c^{3}}-\frac{a \,b^{2} \ln \left(c x +1\right)}{2 c^{3}}+\frac{a^{2} b \ln \left(c x -1\right)}{2 c^{3}}+\frac{a^{2} b \ln \left(c x +1\right)}{2 c^{3}}"," ",0,"1/3*x^3*a^3+a*b^2*x/c^2+b^3*x*arctanh(c*x)/c^2+1/4*I/c^3*b^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))+1/c*a*b^2*arctanh(c*x)*x^2+1/c^3*a*b^2*arctanh(c*x)*ln(c*x-1)+1/c^3*a*b^2*arctanh(c*x)*ln(c*x+1)-1/2/c^3*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/2/c^3*a*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/2/c^3*a*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/2*I/c^3*b^3*arctanh(c*x)^2*Pi+1/3*x^3*b^3*arctanh(c*x)^3-1/2/c^3*b^3*arctanh(c*x)^2+1/3/c^3*b^3*arctanh(c*x)^3+1/c^3*b^3*arctanh(c*x)+1/2/c^3*b^3*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-1/c^3*b^3*ln(1+(c*x+1)^2/(-c^2*x^2+1))-1/4*I/c^3*b^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-1/4*I/c^3*b^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-1/2*I/c^3*b^3*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3+1/2*I/c^3*b^3*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+1/2/c*a^2*b*x^2+a^2*b*x^3*arctanh(c*x)+a*b^2*x^3*arctanh(c*x)^2+1/2/c*b^3*arctanh(c*x)^2*x^2-1/c^3*b^3*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-1/c^3*b^3*arctanh(c*x)^2*ln(2)-1/c^3*a*b^2*dilog(1/2+1/2*c*x)+1/2/c^3*b^3*arctanh(c*x)^2*ln(c*x-1)+1/2/c^3*b^3*arctanh(c*x)^2*ln(c*x+1)-1/c^3*b^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+1/4/c^3*a*b^2*ln(c*x-1)^2-1/4/c^3*a*b^2*ln(c*x+1)^2+1/2/c^3*a*b^2*ln(c*x-1)-1/2/c^3*a*b^2*ln(c*x+1)+1/2/c^3*a^2*b*ln(c*x-1)+1/2/c^3*a^2*b*ln(c*x+1)-1/2*I/c^3*b^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/4*I/c^3*b^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-1/4*I/c^3*b^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2-1/4*I/c^3*b^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))","C"
28,1,6097,113,0.636000," ","int(x*(a+b*arctanh(c*x))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
29,1,261,106,0.243000," ","int((a+b*arctanh(c*x))^3,x)","x \,a^{3}+b^{3} x \arctanh \left(c x \right)^{3}+\frac{b^{3} \arctanh \left(c x \right)^{3}}{c}-\frac{3 b^{3} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c}-\frac{3 b^{3} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c}+\frac{3 b^{3} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c}+3 x a \,b^{2} \arctanh \left(c x \right)^{2}+\frac{3 a \,b^{2} \arctanh \left(c x \right)^{2}}{c}-\frac{6 \arctanh \left(c x \right) \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right) a \,b^{2}}{c}-\frac{3 \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right) a \,b^{2}}{c}+3 x \,a^{2} b \arctanh \left(c x \right)+\frac{3 a^{2} b \ln \left(-c^{2} x^{2}+1\right)}{2 c}"," ",0,"x*a^3+b^3*x*arctanh(c*x)^3+1/c*b^3*arctanh(c*x)^3-3/c*b^3*arctanh(c*x)^2*ln(1+(c*x+1)^2/(-c^2*x^2+1))-3/c*b^3*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+3/2/c*b^3*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+3*x*a*b^2*arctanh(c*x)^2+3/c*a*b^2*arctanh(c*x)^2-6/c*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))*a*b^2-3/c*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))*a*b^2+3*x*a^2*b*arctanh(c*x)+3/2/c*a^2*b*ln(-c^2*x^2+1)","B"
30,1,1470,172,0.263000," ","int((a+b*arctanh(c*x))^3/x,x)","a^{3} \ln \left(c x \right)-\frac{3 b^{3} \polylog \left(4, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{4}+6 b^{3} \polylog \left(4, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+6 b^{3} \polylog \left(4, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2}-\frac{3 a^{2} b \dilog \left(c x \right)}{2}-\frac{3 a^{2} b \dilog \left(c x +1\right)}{2}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{3}}{2}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{3}}{2}+\frac{3 i a \,b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2}-\frac{3 a^{2} b \ln \left(c x \right) \ln \left(c x +1\right)}{2}-3 a \,b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)+3 a \,b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+6 a \,b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 a \,b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+6 a \,b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 a \,b^{2} \ln \left(c x \right) \arctanh \left(c x \right)^{2}-3 a \,b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)+3 a^{2} b \ln \left(c x \right) \arctanh \left(c x \right)+\frac{3 a \,b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2}-6 a \,b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-6 a \,b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+b^{3} \arctanh \left(c x \right)^{3} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 b^{3} \arctanh \left(c x \right)^{2} \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-6 b^{3} \arctanh \left(c x \right) \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+b^{3} \ln \left(c x \right) \arctanh \left(c x \right)^{3}-b^{3} \arctanh \left(c x \right)^{3} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)-\frac{3 b^{3} \arctanh \left(c x \right)^{2} \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2}+\frac{3 b^{3} \arctanh \left(c x \right) \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2}+b^{3} \arctanh \left(c x \right)^{3} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 b^{3} \arctanh \left(c x \right)^{2} \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-6 b^{3} \arctanh \left(c x \right) \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{3}}{2}-\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}-\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}+\frac{i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{3}}{2}"," ",0,"a^3*ln(c*x)-3/4*b^3*polylog(4,-(c*x+1)^2/(-c^2*x^2+1))+6*b^3*polylog(4,(c*x+1)/(-c^2*x^2+1)^(1/2))+6*b^3*polylog(4,-(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*b^3*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^3+3/2*I*a*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-3/2*a^2*b*dilog(c*x)-3/2*a^2*b*dilog(c*x+1)+3/2*a*b^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-6*a*b^2*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-6*a*b^2*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+b^3*arctanh(c*x)^3*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+3*b^3*arctanh(c*x)^2*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))-6*b^3*arctanh(c*x)*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+b^3*ln(c*x)*arctanh(c*x)^3-b^3*arctanh(c*x)^3*ln((c*x+1)^2/(-c^2*x^2+1)-1)-3/2*b^3*arctanh(c*x)^2*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+3/2*b^3*arctanh(c*x)*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+b^3*arctanh(c*x)^3*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+3*b^3*arctanh(c*x)^2*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))-6*b^3*arctanh(c*x)*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2*I*b^3*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^3-1/2*I*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^3+3/2*I*a*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-3*a*b^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+3*a*b^2*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+6*a*b^2*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+3*a*b^2*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+6*a*b^2*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))+3*a*b^2*ln(c*x)*arctanh(c*x)^2-3*a*b^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+3*a^2*b*ln(c*x)*arctanh(c*x)-3/2*a^2*b*ln(c*x)*ln(c*x+1)-3/2*I*a*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-3/2*I*a*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*b^3*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^3","C"
31,1,1583,100,0.535000," ","int((a+b*arctanh(c*x))^3/x^2,x)","\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2}+\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2}}{4}-6 c \,b^{3} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-6 c \,b^{3} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-c \,b^{3} \arctanh \left(c x \right)^{3}-\frac{b^{3} \arctanh \left(c x \right)^{3}}{x}-3 c a \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)-3 c a \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)+\frac{3 i c \,b^{3} \pi  \arctanh \left(c x \right)^{2}}{2}-\frac{a^{3}}{x}-\frac{3 c a \,b^{2} \ln \left(c x -1\right)^{2}}{4}+\frac{3 c a \,b^{2} \ln \left(c x +1\right)^{2}}{4}-\frac{3 c \,a^{2} b \ln \left(c x -1\right)}{2}-\frac{3 c \,a^{2} b \ln \left(c x +1\right)}{2}+3 c \,a^{2} b \ln \left(c x \right)-3 c a \,b^{2} \dilog \left(c x \right)-\frac{3 a^{2} b \arctanh \left(c x \right)}{x}-\frac{3 a \,b^{2} \arctanh \left(c x \right)^{2}}{x}+\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2}-\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \arctanh \left(c x \right)^{2}}{4}-3 c a \,b^{2} \dilog \left(c x +1\right)-\frac{3 c \,b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right)}{2}-\frac{3 c \,b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{2}+3 c \,b^{3} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 c \,b^{3} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 c \,b^{3} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+6 c \,b^{3} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 c \,b^{3} \ln \left(c x \right) \arctanh \left(c x \right)^{2}+6 c \,b^{3} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-3 c \,b^{3} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)+3 c \,b^{3} \arctanh \left(c x \right)^{2} \ln \left(2\right)+3 c a \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)+\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \arctanh \left(c x \right)^{2}}{2}+\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2}}{4}-\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}-\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}+\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2}-\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{4}+\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{4}-3 c a \,b^{2} \ln \left(c x \right) \ln \left(c x +1\right)+\frac{3 c a \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2}-\frac{3 c a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2}+\frac{3 c a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2}+6 c a \,b^{2} \arctanh \left(c x \right) \ln \left(c x \right)-\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}+\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{4}"," ",0,"-6*c*b^3*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-6*c*b^3*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))-c*b^3*arctanh(c*x)^3-b^3/x*arctanh(c*x)^3+3/4*I*c*b^3*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2-3/2*I*c*b^3*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-a^3/x+3/2*I*c*b^3*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-3/4*I*c*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-3*c*a*b^2*dilog(c*x+1)-3/2*c*b^3*arctanh(c*x)^2*ln(c*x-1)-3/2*c*b^3*arctanh(c*x)^2*ln(c*x+1)+3*c*b^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+3*c*b^3*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+3*c*b^3*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+6*c*b^3*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))+3*c*b^3*ln(c*x)*arctanh(c*x)^2+6*c*b^3*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))-3*c*b^3*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)-3/4*c*a*b^2*ln(c*x-1)^2+3/4*c*a*b^2*ln(c*x+1)^2-3/2*c*a^2*b*ln(c*x-1)-3/2*c*a^2*b*ln(c*x+1)+3*c*b^3*arctanh(c*x)^2*ln(2)+3*c*a*b^2*dilog(1/2+1/2*c*x)+3*c*a^2*b*ln(c*x)-3*c*a*b^2*dilog(c*x)-3*a^2*b/x*arctanh(c*x)-3*a*b^2/x*arctanh(c*x)^2+3/4*I*c*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2-3/2*I*c*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+3/4*I*c*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+3/2*I*c*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+3/2*I*c*b^3*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-3/2*I*c*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-3/4*I*c*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+3/4*I*c*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+3/2*I*c*b^3*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)^2+6*c*a*b^2*arctanh(c*x)*ln(c*x)-3*c*a*b^2*ln(c*x)*ln(c*x+1)-3*c*a*b^2*arctanh(c*x)*ln(c*x-1)-3*c*a*b^2*arctanh(c*x)*ln(c*x+1)+3/2*c*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-3/2*c*a*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+3/2*c*a*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+3/2*I*c*b^3*Pi*arctanh(c*x)^2","C"
32,1,5098,113,0.710000," ","int((a+b*arctanh(c*x))^3/x^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
33,1,1838,188,1.943000," ","int((a+b*arctanh(c*x))^3/x^4,x)","\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \pi}{2}-\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \pi}{4}-\frac{a^{3}}{3 x^{3}}+c^{3} b^{3} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}-1\right)+c^{3} b^{3} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-c^{3} a \,b^{2} \dilog \left(c x \right)-c^{3} a \,b^{2} \dilog \left(c x +1\right)+c^{3} a \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)-\frac{c \,b^{3} \arctanh \left(c x \right)^{2}}{2 x^{2}}-\frac{c^{2} b^{3} \arctanh \left(c x \right)}{x}+c^{3} b^{3} \arctanh \left(c x \right)^{2} \ln \left(2\right)-\frac{c^{3} b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right)}{2}-\frac{c^{3} b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{2}+c^{3} b^{3} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+c^{3} b^{3} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \pi}{2}-\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \pi}{2}+\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \pi}{4}+\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \pi}{2}-\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \pi}{4}+\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \pi}{4}-\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \pi}{2}+\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \pi}{2}+\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \pi}{4}+\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \pi}{2}+\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \pi}{4}+\frac{c^{3} b^{3} \arctanh \left(c x \right)^{2}}{2}-\frac{c^{3} b^{3} \arctanh \left(c x \right)^{3}}{3}-c^{3} b^{3} \arctanh \left(c x \right)-\frac{b^{3} \arctanh \left(c x \right)^{3}}{3 x^{3}}-2 c^{3} b^{3} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-2 c^{3} b^{3} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+c^{3} b^{3} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+2 c^{3} b^{3} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+c^{3} b^{3} \ln \left(c x \right) \arctanh \left(c x \right)^{2}+2 c^{3} b^{3} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-c^{3} b^{3} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)-\frac{a^{2} b \arctanh \left(c x \right)}{x^{3}}-\frac{a \,b^{2} \arctanh \left(c x \right)^{2}}{x^{3}}-\frac{c^{2} a \,b^{2}}{x}-\frac{c \,a^{2} b}{2 x^{2}}+\frac{c^{3} a \,b^{2} \ln \left(c x +1\right)}{2}-\frac{c^{3} a^{2} b \ln \left(c x -1\right)}{2}-\frac{c^{3} a^{2} b \ln \left(c x +1\right)}{2}+c^{3} a^{2} b \ln \left(c x \right)-\frac{c^{3} a \,b^{2} \ln \left(c x -1\right)^{2}}{4}+\frac{c^{3} a \,b^{2} \ln \left(c x +1\right)^{2}}{4}-\frac{c^{3} a \,b^{2} \ln \left(c x -1\right)}{2}+\frac{c^{3} a \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2}-\frac{c^{3} a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2}+\frac{c^{3} a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2}-c^{3} a \,b^{2} \ln \left(c x \right) \ln \left(c x +1\right)-c^{3} a \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)+2 c^{3} a \,b^{2} \arctanh \left(c x \right) \ln \left(c x \right)-c^{3} a \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)-\frac{c a \,b^{2} \arctanh \left(c x \right)}{x^{2}}+\frac{i c^{3} b^{3} \arctanh \left(c x \right)^{2} \pi}{2}"," ",0,"-1/2*I*c^3*b^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi+1/2*I*c^3*b^3*arctanh(c*x)^2*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi+1/4*I*c^3*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi+1/2*I*c^3*b^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi+1/4*I*c^3*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi+1/2*I*c^3*b^3*arctanh(c*x)^2*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi-1/4*I*c^3*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi-1/3*a^3/x^3-1/2*I*c^3*b^3*arctanh(c*x)^2*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi-1/2*I*c^3*b^3*arctanh(c*x)^2*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi+1/4*I*c^3*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi+1/2*I*c^3*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*Pi-1/4*I*c^3*b^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi+1/4*I*c^3*b^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi+c^3*b^3*ln((c*x+1)/(-c^2*x^2+1)^(1/2)-1)+c^3*b^3*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*c^3*b^3*arctanh(c*x)^2-1/3*c^3*b^3*arctanh(c*x)^3-c^3*b^3*arctanh(c*x)-1/3*b^3/x^3*arctanh(c*x)^3-2*c^3*b^3*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^3*b^3*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))-c^2*a*b^2/x-1/2*c*a^2*b/x^2+1/2*c^3*a*b^2*ln(c*x+1)-1/2*c^3*a^2*b*ln(c*x-1)-1/2*c^3*a^2*b*ln(c*x+1)+c^3*a^2*b*ln(c*x)-c^3*a*b^2*dilog(c*x)-c^3*a*b^2*dilog(c*x+1)+c^3*a*b^2*dilog(1/2+1/2*c*x)-1/2*c*b^3*arctanh(c*x)^2/x^2-c^2*b^3*arctanh(c*x)/x-1/4*c^3*a*b^2*ln(c*x-1)^2+1/4*c^3*a*b^2*ln(c*x+1)^2-1/2*c^3*a*b^2*ln(c*x-1)+c^3*b^3*arctanh(c*x)^2*ln(2)-1/2*c^3*b^3*arctanh(c*x)^2*ln(c*x-1)-1/2*c^3*b^3*arctanh(c*x)^2*ln(c*x+1)+c^3*b^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+c^3*b^3*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+c^3*b^3*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c^3*b^3*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))+c^3*b^3*ln(c*x)*arctanh(c*x)^2+2*c^3*b^3*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))-c^3*b^3*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)-a^2*b/x^3*arctanh(c*x)-a*b^2/x^3*arctanh(c*x)^2-c^3*a*b^2*arctanh(c*x)*ln(c*x+1)+1/2*c^3*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/2*c^3*a*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/2*c^3*a*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+2*c^3*a*b^2*arctanh(c*x)*ln(c*x)-c^3*a*b^2*ln(c*x)*ln(c*x+1)-c^3*a*b^2*arctanh(c*x)*ln(c*x-1)-c*a*b^2*arctanh(c*x)/x^2+1/2*I*c^3*b^3*arctanh(c*x)^2*Pi","C"
34,1,1281,173,1.707000," ","int((a+b*arctanh(c*x))^3/x^5,x)","\frac{3 c^{4} a \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{8}-\frac{3 c^{4} a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{8}+\frac{3 c^{4} a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{8}-\frac{c a \,b^{2} \arctanh \left(c x \right)}{2 x^{3}}-\frac{3 c^{3} a \,b^{2} \arctanh \left(c x \right)}{2 x}-\frac{3 c^{4} a \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{4}+\frac{3 c^{4} a \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{4}+\frac{3 i c^{4} b^{3} \pi  \arctanh \left(c x \right)^{2}}{8}+\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \arctanh \left(c x \right)^{2}}{16}-\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2}}{16}-\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{16}-\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{8}+\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{8}-\frac{a^{3}}{4 x^{4}}-\frac{c \,a^{2} b}{4 x^{3}}-\frac{c^{2} a \,b^{2}}{4 x^{2}}-\frac{3 c^{3} a^{2} b}{4 x}-\frac{3 c^{4} a \,b^{2} \ln \left(c x -1\right)^{2}}{16}-\frac{3 c^{4} a \,b^{2} \ln \left(c x +1\right)^{2}}{16}-c^{4} a \,b^{2} \ln \left(c x -1\right)-c^{4} a \,b^{2} \ln \left(c x +1\right)-\frac{3 c^{4} a^{2} b \ln \left(c x -1\right)}{8}+\frac{3 c^{4} a^{2} b \ln \left(c x +1\right)}{8}+2 c^{4} a \,b^{2} \ln \left(c x \right)-\frac{c^{4} b^{3} \sqrt{-c^{2} x^{2}+1}}{4 \left(c x +1-\sqrt{-c^{2} x^{2}+1}\right)}-\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2}}{16}+\frac{c^{4} b^{3} \sqrt{-c^{2} x^{2}+1}}{4 \sqrt{-c^{2} x^{2}+1}+4 c x +4}-\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \arctanh \left(c x \right)^{2}}{8}+\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{16}-\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{16}+\frac{b^{3} c^{4} \arctanh \left(c x \right)}{4}-\frac{b^{3} \arctanh \left(c x \right)^{3}}{4 x^{4}}-c^{4} b^{3} \arctanh \left(c x \right)^{2}+\frac{c^{4} b^{3} \arctanh \left(c x \right)^{3}}{4}+2 c^{4} b^{3} \dilog \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-2 c^{4} b^{3} \dilog \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{c^{2} b^{3} \arctanh \left(c x \right)}{4 x^{2}}-\frac{c \,b^{3} \arctanh \left(c x \right)^{2}}{4 x^{3}}-\frac{3 c^{3} b^{3} \arctanh \left(c x \right)^{2}}{4 x}-\frac{3 c^{4} b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right)}{8}+\frac{3 c^{4} b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{8}-\frac{3 c^{4} b^{3} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{4}+2 c^{4} b^{3} \arctanh \left(c x \right) \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{3 a^{2} b \arctanh \left(c x \right)}{4 x^{4}}-\frac{3 a \,b^{2} \arctanh \left(c x \right)^{2}}{4 x^{4}}"," ",0,"3/8*c^4*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-3/8*c^4*a*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/2*c*a*b^2*arctanh(c*x)/x^3-3/2*c^3*a*b^2*arctanh(c*x)/x+3/8*I*c^4*b^3*Pi*arctanh(c*x)^2+3/8*c^4*a*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-3/4*c^4*a*b^2*arctanh(c*x)*ln(c*x-1)+3/16*I*c^4*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+1/4*b^3*c^4*arctanh(c*x)+3/8*I*c^4*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-3/16*I*c^4*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2-3/16*I*c^4*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-3/8*I*c^4*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/4*a^3/x^4-1/4*c*a^2*b/x^3-1/4*c^2*a*b^2/x^2-3/4*c^3*a^2*b/x-1/4*c^2*b^3*arctanh(c*x)/x^2-1/4*c*b^3*arctanh(c*x)^2/x^3-3/4*c^3*b^3*arctanh(c*x)^2/x-3/16*c^4*a*b^2*ln(c*x-1)^2-3/16*c^4*a*b^2*ln(c*x+1)^2-c^4*a*b^2*ln(c*x-1)-c^4*a*b^2*ln(c*x+1)-3/8*c^4*a^2*b*ln(c*x-1)+3/8*c^4*a^2*b*ln(c*x+1)+2*c^4*a*b^2*ln(c*x)-3/8*c^4*b^3*arctanh(c*x)^2*ln(c*x-1)+3/8*c^4*b^3*arctanh(c*x)^2*ln(c*x+1)-3/4*c^4*b^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-1/4*c^4*b^3/(c*x+1-(-c^2*x^2+1)^(1/2))*(-c^2*x^2+1)^(1/2)+1/4*c^4*b^3/((-c^2*x^2+1)^(1/2)+c*x+1)*(-c^2*x^2+1)^(1/2)+2*c^4*b^3*arctanh(c*x)*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-3/4*a^2*b/x^4*arctanh(c*x)-3/4*a*b^2/x^4*arctanh(c*x)^2+3/4*c^4*a*b^2*arctanh(c*x)*ln(c*x+1)-3/8*I*c^4*b^3*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)^2+3/16*I*c^4*b^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-3/16*I*c^4*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-3/16*I*c^4*b^3*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2-1/4*b^3/x^4*arctanh(c*x)^3-c^4*b^3*arctanh(c*x)^2+1/4*c^4*b^3*arctanh(c*x)^3+2*c^4*b^3*dilog(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^4*b^3*dilog((c*x+1)/(-c^2*x^2+1)^(1/2))","C"
35,1,107,88,0.045000," ","int((d*x)^(5/2)*(a+b*arctanh(c*x)),x)","\frac{2 \left(d x \right)^{\frac{7}{2}} a}{7 d}+\frac{2 b \left(d x \right)^{\frac{7}{2}} \arctanh \left(c x \right)}{7 d}+\frac{4 b \left(d x \right)^{\frac{5}{2}}}{35 c}+\frac{4 b \,d^{2} \sqrt{d x}}{7 c^{3}}-\frac{2 d^{3} b \arctan \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{7 c^{3} \sqrt{c d}}-\frac{2 d^{3} b \arctanh \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{7 c^{3} \sqrt{c d}}"," ",0,"2/7/d*(d*x)^(7/2)*a+2/7/d*b*(d*x)^(7/2)*arctanh(c*x)+4/35*b*(d*x)^(5/2)/c+4/7*b*d^2*(d*x)^(1/2)/c^3-2/7*d^3*b/c^3/(c*d)^(1/2)*arctan(c*(d*x)^(1/2)/(c*d)^(1/2))-2/7*d^3*b/c^3/(c*d)^(1/2)*arctanh(c*(d*x)^(1/2)/(c*d)^(1/2))","A"
36,1,93,74,0.036000," ","int((d*x)^(3/2)*(a+b*arctanh(c*x)),x)","\frac{2 \left(d x \right)^{\frac{5}{2}} a}{5 d}+\frac{2 b \left(d x \right)^{\frac{5}{2}} \arctanh \left(c x \right)}{5 d}+\frac{4 b \left(d x \right)^{\frac{3}{2}}}{15 c}+\frac{2 d^{2} b \arctan \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{5 c^{2} \sqrt{c d}}-\frac{2 d^{2} b \arctanh \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{5 c^{2} \sqrt{c d}}"," ",0,"2/5/d*(d*x)^(5/2)*a+2/5/d*b*(d*x)^(5/2)*arctanh(c*x)+4/15*b*(d*x)^(3/2)/c+2/5*d^2*b/c^2/(c*d)^(1/2)*arctan(c*(d*x)^(1/2)/(c*d)^(1/2))-2/5*d^2*b/c^2/(c*d)^(1/2)*arctanh(c*(d*x)^(1/2)/(c*d)^(1/2))","A"
37,1,89,74,0.034000," ","int((d*x)^(1/2)*(a+b*arctanh(c*x)),x)","\frac{2 \left(d x \right)^{\frac{3}{2}} a}{3 d}+\frac{2 b \left(d x \right)^{\frac{3}{2}} \arctanh \left(c x \right)}{3 d}+\frac{4 b \sqrt{d x}}{3 c}-\frac{2 d b \arctan \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{3 c \sqrt{c d}}-\frac{2 d b \arctanh \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{3 c \sqrt{c d}}"," ",0,"2/3/d*(d*x)^(3/2)*a+2/3/d*b*(d*x)^(3/2)*arctanh(c*x)+4/3*b*(d*x)^(1/2)/c-2/3*d*b/c/(c*d)^(1/2)*arctan(c*(d*x)^(1/2)/(c*d)^(1/2))-2/3*d*b/c/(c*d)^(1/2)*arctanh(c*(d*x)^(1/2)/(c*d)^(1/2))","A"
38,1,70,63,0.035000," ","int((a+b*arctanh(c*x))/(d*x)^(1/2),x)","\frac{2 a \sqrt{d x}}{d}+\frac{2 b \sqrt{d x}\, \arctanh \left(c x \right)}{d}+\frac{2 b \arctan \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{\sqrt{c d}}-\frac{2 b \arctanh \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{\sqrt{c d}}"," ",0,"2/d*a*(d*x)^(1/2)+2/d*b*(d*x)^(1/2)*arctanh(c*x)+2*b/(c*d)^(1/2)*arctan(c*(d*x)^(1/2)/(c*d)^(1/2))-2*b/(c*d)^(1/2)*arctanh(c*(d*x)^(1/2)/(c*d)^(1/2))","A"
39,1,78,63,0.031000," ","int((a+b*arctanh(c*x))/(d*x)^(3/2),x)","-\frac{2 a}{d \sqrt{d x}}-\frac{2 b \arctanh \left(c x \right)}{d \sqrt{d x}}+\frac{2 b c \arctan \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{d \sqrt{c d}}+\frac{2 b c \arctanh \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{d \sqrt{c d}}"," ",0,"-2/d*a/(d*x)^(1/2)-2/d*b/(d*x)^(1/2)*arctanh(c*x)+2/d*b*c/(c*d)^(1/2)*arctan(c*(d*x)^(1/2)/(c*d)^(1/2))+2/d*b*c/(c*d)^(1/2)*arctanh(c*(d*x)^(1/2)/(c*d)^(1/2))","A"
40,1,94,75,0.037000," ","int((a+b*arctanh(c*x))/(d*x)^(5/2),x)","-\frac{2 a}{3 d \left(d x \right)^{\frac{3}{2}}}-\frac{2 b \arctanh \left(c x \right)}{3 d \left(d x \right)^{\frac{3}{2}}}-\frac{4 b c}{3 d^{2} \sqrt{d x}}-\frac{2 b \,c^{2} \arctan \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{3 d^{2} \sqrt{c d}}+\frac{2 b \,c^{2} \arctanh \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{3 d^{2} \sqrt{c d}}"," ",0,"-2/3/d*a/(d*x)^(3/2)-2/3/d*b/(d*x)^(3/2)*arctanh(c*x)-4/3*b*c/d^2/(d*x)^(1/2)-2/3/d^2*b*c^2/(c*d)^(1/2)*arctan(c*(d*x)^(1/2)/(c*d)^(1/2))+2/3/d^2*b*c^2/(c*d)^(1/2)*arctanh(c*(d*x)^(1/2)/(c*d)^(1/2))","A"
41,1,94,75,0.034000," ","int((a+b*arctanh(c*x))/(d*x)^(7/2),x)","-\frac{2 a}{5 d \left(d x \right)^{\frac{5}{2}}}-\frac{2 b \arctanh \left(c x \right)}{5 d \left(d x \right)^{\frac{5}{2}}}-\frac{4 b c}{15 d^{2} \left(d x \right)^{\frac{3}{2}}}+\frac{2 b \,c^{3} \arctan \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{5 d^{3} \sqrt{c d}}+\frac{2 b \,c^{3} \arctanh \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{5 d^{3} \sqrt{c d}}"," ",0,"-2/5/d*a/(d*x)^(5/2)-2/5/d*b/(d*x)^(5/2)*arctanh(c*x)-4/15*b*c/d^2/(d*x)^(3/2)+2/5/d^3*b*c^3/(c*d)^(1/2)*arctan(c*(d*x)^(1/2)/(c*d)^(1/2))+2/5/d^3*b*c^3/(c*d)^(1/2)*arctanh(c*(d*x)^(1/2)/(c*d)^(1/2))","A"
42,1,108,89,0.038000," ","int((a+b*arctanh(c*x))/(d*x)^(9/2),x)","-\frac{2 a}{7 d \left(d x \right)^{\frac{7}{2}}}-\frac{2 b \arctanh \left(c x \right)}{7 d \left(d x \right)^{\frac{7}{2}}}-\frac{4 b c}{35 d^{2} \left(d x \right)^{\frac{5}{2}}}-\frac{4 b \,c^{3}}{7 d^{4} \sqrt{d x}}-\frac{2 b \,c^{4} \arctan \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{7 d^{4} \sqrt{c d}}+\frac{2 b \,c^{4} \arctanh \left(\frac{c \sqrt{d x}}{\sqrt{c d}}\right)}{7 d^{4} \sqrt{c d}}"," ",0,"-2/7/d*a/(d*x)^(7/2)-2/7/d*b/(d*x)^(7/2)*arctanh(c*x)-4/35*b*c/d^2/(d*x)^(5/2)-4/7*b*c^3/d^4/(d*x)^(1/2)-2/7/d^4*b*c^4/(c*d)^(1/2)*arctan(c*(d*x)^(1/2)/(c*d)^(1/2))+2/7/d^4*b*c^4/(c*d)^(1/2)*arctanh(c*(d*x)^(1/2)/(c*d)^(1/2))","A"
43,0,0,18,1.756000," ","int((d*x)^m*(a+b*arctanh(c*x))^3,x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c x \right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x))^3,x)","F"
44,0,0,18,1.411000," ","int((d*x)^m*(a+b*arctanh(c*x))^2,x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c x \right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x))^2,x)","F"
45,0,0,70,1.470000," ","int((d*x)^m*(a+b*arctanh(c*x)),x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c x \right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x)),x)","F"
46,0,0,18,0.883000," ","int((d*x)^m/(a+b*arctanh(c*x)),x)","\int \frac{\left(d x \right)^{m}}{a +b \arctanh \left(c x \right)}\, dx"," ",0,"int((d*x)^m/(a+b*arctanh(c*x)),x)","F"
47,0,0,18,0.900000," ","int((d*x)^m/(a+b*arctanh(c*x))^2,x)","\int \frac{\left(d x \right)^{m}}{\left(a +b \arctanh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((d*x)^m/(a+b*arctanh(c*x))^2,x)","F"
48,0,0,12,0.303000," ","int((a+b*arctanh(c*x))^p,x)","\int \left(a +b \arctanh \left(c x \right)\right)^{p}\, dx"," ",0,"int((a+b*arctanh(c*x))^p,x)","F"
49,0,0,18,0.565000," ","int((d*x)^m*(a+b*arctanh(c*x))^p,x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c x \right)\right)^{p}\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x))^p,x)","F"
50,1,66,46,0.030000," ","int(x^7*(a+b*arctanh(c*x^2)),x)","\frac{x^{8} a}{8}+\frac{b \,x^{8} \arctanh \left(c \,x^{2}\right)}{8}+\frac{b \,x^{6}}{24 c}+\frac{b \,x^{2}}{8 c^{3}}-\frac{b \ln \left(c \,x^{2}+1\right)}{16 c^{4}}+\frac{b \ln \left(c \,x^{2}-1\right)}{16 c^{4}}"," ",0,"1/8*x^8*a+1/8*b*x^8*arctanh(c*x^2)+1/24*b*x^6/c+1/8*b*x^2/c^3-1/16*b/c^4*ln(c*x^2+1)+1/16*b/c^4*ln(c*x^2-1)","A"
51,1,45,42,0.025000," ","int(x^5*(a+b*arctanh(c*x^2)),x)","\frac{x^{6} a}{6}+\frac{b \,x^{6} \arctanh \left(c \,x^{2}\right)}{6}+\frac{b \,x^{4}}{12 c}+\frac{b \ln \left(c^{2} x^{4}-1\right)}{12 c^{3}}"," ",0,"1/6*x^6*a+1/6*b*x^6*arctanh(c*x^2)+1/12*b*x^4/c+1/12*b/c^3*ln(c^2*x^4-1)","A"
52,1,57,37,0.031000," ","int(x^3*(a+b*arctanh(c*x^2)),x)","\frac{x^{4} a}{4}+\frac{b \,x^{4} \arctanh \left(c \,x^{2}\right)}{4}+\frac{b \,x^{2}}{4 c}-\frac{b \ln \left(c \,x^{2}+1\right)}{8 c^{2}}+\frac{b \ln \left(c \,x^{2}-1\right)}{8 c^{2}}"," ",0,"1/4*x^4*a+1/4*b*x^4*arctanh(c*x^2)+1/4*b*x^2/c-1/8*b/c^2*ln(c*x^2+1)+1/8*b/c^2*ln(c*x^2-1)","A"
53,1,37,33,0.021000," ","int(x*(a+b*arctanh(c*x^2)),x)","\frac{a \,x^{2}}{2}+\frac{b \,x^{2} \arctanh \left(c \,x^{2}\right)}{2}+\frac{b \ln \left(-c^{2} x^{4}+1\right)}{4 c}"," ",0,"1/2*a*x^2+1/2*b*x^2*arctanh(c*x^2)+1/4*b*ln(-c^2*x^4+1)/c","A"
54,1,124,26,0.055000," ","int((a+b*arctanh(c*x^2))/x,x)","a \ln \left(x \right)+b \ln \left(x \right) \arctanh \left(c \,x^{2}\right)-\frac{b \ln \left(x \right) \ln \left(1+x \sqrt{-c}\right)}{2}-\frac{b \ln \left(x \right) \ln \left(1-x \sqrt{-c}\right)}{2}-\frac{b \dilog \left(1+x \sqrt{-c}\right)}{2}-\frac{b \dilog \left(1-x \sqrt{-c}\right)}{2}+\frac{b \ln \left(x \right) \ln \left(1-x \sqrt{c}\right)}{2}+\frac{b \ln \left(x \right) \ln \left(1+x \sqrt{c}\right)}{2}+\frac{b \dilog \left(1-x \sqrt{c}\right)}{2}+\frac{b \dilog \left(1+x \sqrt{c}\right)}{2}"," ",0,"a*ln(x)+b*ln(x)*arctanh(c*x^2)-1/2*b*ln(x)*ln(1+x*(-c)^(1/2))-1/2*b*ln(x)*ln(1-x*(-c)^(1/2))-1/2*b*dilog(1+x*(-c)^(1/2))-1/2*b*dilog(1-x*(-c)^(1/2))+1/2*b*ln(x)*ln(1-x*c^(1/2))+1/2*b*ln(x)*ln(1+x*c^(1/2))+1/2*b*dilog(1-x*c^(1/2))+1/2*b*dilog(1+x*c^(1/2))","B"
55,1,49,39,0.032000," ","int((a+b*arctanh(c*x^2))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arctanh \left(c \,x^{2}\right)}{2 x^{2}}+b c \ln \left(x \right)-\frac{b c \ln \left(c \,x^{2}+1\right)}{4}-\frac{b c \ln \left(c \,x^{2}-1\right)}{4}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arctanh(c*x^2)+b*c*ln(x)-1/4*b*c*ln(c*x^2+1)-1/4*b*c*ln(c*x^2-1)","A"
56,1,55,38,0.033000," ","int((a+b*arctanh(c*x^2))/x^5,x)","-\frac{a}{4 x^{4}}-\frac{b \arctanh \left(c \,x^{2}\right)}{4 x^{4}}-\frac{b c}{4 x^{2}}+\frac{b \,c^{2} \ln \left(c \,x^{2}+1\right)}{8}-\frac{b \,c^{2} \ln \left(c \,x^{2}-1\right)}{8}"," ",0,"-1/4*a/x^4-1/4*b/x^4*arctanh(c*x^2)-1/4*b*c/x^2+1/8*b*c^2*ln(c*x^2+1)-1/8*b*c^2*ln(c*x^2-1)","A"
57,1,63,51,0.033000," ","int((a+b*arctanh(c*x^2))/x^7,x)","-\frac{a}{6 x^{6}}-\frac{b \arctanh \left(c \,x^{2}\right)}{6 x^{6}}-\frac{b c}{12 x^{4}}+\frac{b \,c^{3} \ln \left(x \right)}{3}-\frac{b \,c^{3} \ln \left(c \,x^{2}+1\right)}{12}-\frac{b \,c^{3} \ln \left(c \,x^{2}-1\right)}{12}"," ",0,"-1/6*a/x^6-1/6*b/x^6*arctanh(c*x^2)-1/12*b*c/x^4+1/3*b*c^3*ln(x)-1/12*b*c^3*ln(c*x^2+1)-1/12*b*c^3*ln(c*x^2-1)","A"
58,1,53,49,0.030000," ","int(x^4*(a+b*arctanh(c*x^2)),x)","\frac{a \,x^{5}}{5}+\frac{b \,x^{5} \arctanh \left(c \,x^{2}\right)}{5}+\frac{2 b \,x^{3}}{15 c}+\frac{b \arctan \left(x \sqrt{c}\right)}{5 c^{\frac{5}{2}}}-\frac{b \arctanh \left(x \sqrt{c}\right)}{5 c^{\frac{5}{2}}}"," ",0,"1/5*a*x^5+1/5*b*x^5*arctanh(c*x^2)+2/15*b*x^3/c+1/5*b*arctan(x*c^(1/2))/c^(5/2)-1/5*b*arctanh(x*c^(1/2))/c^(5/2)","A"
59,1,51,47,0.032000," ","int(x^2*(a+b*arctanh(c*x^2)),x)","\frac{x^{3} a}{3}+\frac{b \,x^{3} \arctanh \left(c \,x^{2}\right)}{3}+\frac{2 b x}{3 c}-\frac{b \arctan \left(x \sqrt{c}\right)}{3 c^{\frac{3}{2}}}-\frac{b \arctanh \left(x \sqrt{c}\right)}{3 c^{\frac{3}{2}}}"," ",0,"1/3*x^3*a+1/3*b*x^3*arctanh(c*x^2)+2/3*b*x/c-1/3*b*arctan(x*c^(1/2))/c^(3/2)-1/3*b*arctanh(x*c^(1/2))/c^(3/2)","A"
60,1,37,36,0.030000," ","int(a+b*arctanh(c*x^2),x)","a x +b x \arctanh \left(c \,x^{2}\right)+\frac{b \arctan \left(x \sqrt{c}\right)}{\sqrt{c}}-\frac{b \arctanh \left(x \sqrt{c}\right)}{\sqrt{c}}"," ",0,"a*x+b*x*arctanh(c*x^2)+b*arctan(x*c^(1/2))/c^(1/2)-b*arctanh(x*c^(1/2))/c^(1/2)","A"
61,1,42,40,0.030000," ","int((a+b*arctanh(c*x^2))/x^2,x)","-\frac{a}{x}-\frac{b \arctanh \left(c \,x^{2}\right)}{x}+b \arctan \left(x \sqrt{c}\right) \sqrt{c}+b \arctanh \left(x \sqrt{c}\right) \sqrt{c}"," ",0,"-a/x-b/x*arctanh(c*x^2)+b*arctan(x*c^(1/2))*c^(1/2)+b*arctanh(x*c^(1/2))*c^(1/2)","A"
62,1,51,50,0.033000," ","int((a+b*arctanh(c*x^2))/x^4,x)","-\frac{a}{3 x^{3}}-\frac{b \arctanh \left(c \,x^{2}\right)}{3 x^{3}}-\frac{2 b c}{3 x}-\frac{b \,c^{\frac{3}{2}} \arctan \left(x \sqrt{c}\right)}{3}+\frac{b \,c^{\frac{3}{2}} \arctanh \left(x \sqrt{c}\right)}{3}"," ",0,"-1/3*a/x^3-1/3*b/x^3*arctanh(c*x^2)-2/3*b*c/x-1/3*b*c^(3/2)*arctan(x*c^(1/2))+1/3*b*c^(3/2)*arctanh(x*c^(1/2))","A"
63,1,51,50,0.034000," ","int((a+b*arctanh(c*x^2))/x^6,x)","-\frac{a}{5 x^{5}}-\frac{b \arctanh \left(c \,x^{2}\right)}{5 x^{5}}-\frac{2 b c}{15 x^{3}}+\frac{b \,c^{\frac{5}{2}} \arctan \left(x \sqrt{c}\right)}{5}+\frac{b \,c^{\frac{5}{2}} \arctanh \left(x \sqrt{c}\right)}{5}"," ",0,"-1/5*a/x^5-1/5*b/x^5*arctanh(c*x^2)-2/15*b*c/x^3+1/5*b*c^(5/2)*arctan(x*c^(1/2))+1/5*b*c^(5/2)*arctanh(x*c^(1/2))","A"
64,-2,0,111,180.000000," ","int(x^7*(a+b*arctanh(c*x^2))^2,x)","\int x^{7} \left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int(x^7*(a+b*arctanh(c*x^2))^2,x)","F"
65,-2,0,132,180.000000," ","int(x^5*(a+b*arctanh(c*x^2))^2,x)","\int x^{5} \left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int(x^5*(a+b*arctanh(c*x^2))^2,x)","F"
66,1,247,81,0.264000," ","int(x^3*(a+b*arctanh(c*x^2))^2,x)","\frac{b^{2} \left(c^{2} x^{4}-1\right) \ln \left(c \,x^{2}+1\right)^{2}}{16 c^{2}}+\frac{b \left(-x^{4} b \ln \left(-c \,x^{2}+1\right) c^{2}+2 a \,c^{2} x^{4}+2 b c \,x^{2}+b \ln \left(-c \,x^{2}+1\right)\right) \ln \left(c \,x^{2}+1\right)}{8 c^{2}}+\frac{b^{2} x^{4} \ln \left(-c \,x^{2}+1\right)^{2}}{16}-\frac{a b \,x^{4} \ln \left(-c \,x^{2}+1\right)}{4}+\frac{a^{2} x^{4}}{4}-\frac{b^{2} x^{2} \ln \left(-c \,x^{2}+1\right)}{4 c}+\frac{a b \,x^{2}}{2 c}-\frac{b^{2} \ln \left(-c \,x^{2}+1\right)^{2}}{16 c^{2}}-\frac{b \ln \left(-c \,x^{2}-1\right) a}{4 c^{2}}+\frac{b^{2} \ln \left(-c \,x^{2}-1\right)}{4 c^{2}}+\frac{b \ln \left(-c \,x^{2}+1\right) a}{4 c^{2}}+\frac{b^{2} \ln \left(-c \,x^{2}+1\right)}{4 c^{2}}"," ",0,"1/16*b^2*(c^2*x^4-1)/c^2*ln(c*x^2+1)^2+1/8*b*(-x^4*b*ln(-c*x^2+1)*c^2+2*a*c^2*x^4+2*b*c*x^2+b*ln(-c*x^2+1))/c^2*ln(c*x^2+1)+1/16*b^2*x^4*ln(-c*x^2+1)^2-1/4*a*b*x^4*ln(-c*x^2+1)+1/4*a^2*x^4-1/4/c*b^2*x^2*ln(-c*x^2+1)+1/2*a*b*x^2/c-1/16/c^2*b^2*ln(-c*x^2+1)^2-1/4/c^2*b*ln(-c*x^2-1)*a+1/4/c^2*b^2*ln(-c*x^2-1)+1/4/c^2*b*ln(-c*x^2+1)*a+1/4/c^2*b^2*ln(-c*x^2+1)","B"
67,1,144,88,0.178000," ","int(x*(a+b*arctanh(c*x^2))^2,x)","\frac{x^{2} b^{2} \arctanh \left(c \,x^{2}\right)^{2}}{2}+x^{2} a b \arctanh \left(c \,x^{2}\right)+\frac{a^{2} x^{2}}{2}+\frac{b^{2} \arctanh \left(c \,x^{2}\right)^{2}}{2 c}-\frac{\arctanh \left(c \,x^{2}\right) \ln \left(1+\frac{\left(c \,x^{2}+1\right)^{2}}{-c^{2} x^{4}+1}\right) b^{2}}{c}+\frac{a b \ln \left(-c^{2} x^{4}+1\right)}{2 c}-\frac{\polylog \left(2, -\frac{\left(c \,x^{2}+1\right)^{2}}{-c^{2} x^{4}+1}\right) b^{2}}{2 c}"," ",0,"1/2*x^2*b^2*arctanh(c*x^2)^2+x^2*a*b*arctanh(c*x^2)+1/2*a^2*x^2+1/2/c*b^2*arctanh(c*x^2)^2-1/c*arctanh(c*x^2)*ln(1+(c*x^2+1)^2/(-c^2*x^4+1))*b^2+1/2/c*a*b*ln(-c^2*x^4+1)-1/2/c*polylog(2,-(c*x^2+1)^2/(-c^2*x^4+1))*b^2","A"
68,0,0,130,0.216000," ","int((a+b*arctanh(c*x^2))^2/x,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}}{x}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^2/x,x)","F"
69,-2,0,81,180.000000," ","int((a+b*arctanh(c*x^2))^2/x^3,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}}{x^{3}}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^2/x^3,x)","F"
70,1,257,80,0.273000," ","int((a+b*arctanh(c*x^2))^2/x^5,x)","\frac{b^{2} \left(c^{2} x^{4}-1\right) \ln \left(c \,x^{2}+1\right)^{2}}{16 x^{4}}-\frac{b \left(x^{4} b \ln \left(-c \,x^{2}+1\right) c^{2}+2 b c \,x^{2}-b \ln \left(-c \,x^{2}+1\right)+2 a \right) \ln \left(c \,x^{2}+1\right)}{8 x^{4}}+\frac{b^{2} c^{2} x^{4} \ln \left(-c \,x^{2}+1\right)^{2}+4 b \,c^{2} \ln \left(c \,x^{2}+1\right) x^{4} a -4 b^{2} c^{2} \ln \left(c \,x^{2}+1\right) x^{4}-4 b \,c^{2} \ln \left(c \,x^{2}-1\right) x^{4} a -4 b^{2} c^{2} \ln \left(c \,x^{2}-1\right) x^{4}+16 b^{2} c^{2} \ln \left(x \right) x^{4}+4 b^{2} c \,x^{2} \ln \left(-c \,x^{2}+1\right)-8 a b c \,x^{2}-b^{2} \ln \left(-c \,x^{2}+1\right)^{2}+4 b \ln \left(-c \,x^{2}+1\right) a -4 a^{2}}{16 x^{4}}"," ",0,"1/16*b^2*(c^2*x^4-1)/x^4*ln(c*x^2+1)^2-1/8*b*(x^4*b*ln(-c*x^2+1)*c^2+2*b*c*x^2-b*ln(-c*x^2+1)+2*a)/x^4*ln(c*x^2+1)+1/16*(b^2*c^2*x^4*ln(-c*x^2+1)^2+4*b*c^2*ln(c*x^2+1)*x^4*a-4*b^2*c^2*ln(c*x^2+1)*x^4-4*b*c^2*ln(c*x^2-1)*x^4*a-4*b^2*c^2*ln(c*x^2-1)*x^4+16*b^2*c^2*ln(x)*x^4+4*b^2*c*x^2*ln(-c*x^2+1)-8*a*b*c*x^2-b^2*ln(-c*x^2+1)^2+4*b*ln(-c*x^2+1)*a-4*a^2)/x^4","B"
71,0,0,930,0.383000," ","int(x^4*(a+b*arctanh(c*x^2))^2,x)","\int x^{4} \left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int(x^4*(a+b*arctanh(c*x^2))^2,x)","F"
72,0,0,890,0.344000," ","int(x^2*(a+b*arctanh(c*x^2))^2,x)","\int x^{2} \left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int(x^2*(a+b*arctanh(c*x^2))^2,x)","F"
73,0,0,779,0.288000," ","int((a+b*arctanh(c*x^2))^2,x)","\int \left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^2,x)","F"
74,0,0,767,0.342000," ","int((a+b*arctanh(c*x^2))^2/x^2,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}}{x^{2}}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^2/x^2,x)","F"
75,0,0,867,0.290000," ","int((a+b*arctanh(c*x^2))^2/x^4,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}}{x^{4}}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^2/x^4,x)","F"
76,0,0,933,0.296000," ","int((a+b*arctanh(c*x^2))^2/x^6,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}}{x^{6}}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^2/x^6,x)","F"
77,1,748,129,0.390000," ","int(x^3*(a+b*arctanh(c*x^2))^3,x)","\frac{b^{3} \left(c^{2} x^{4}-1\right) \ln \left(c \,x^{2}+1\right)^{3}}{32 c^{2}}+\frac{3 b^{2} \left(-x^{4} b \ln \left(-c \,x^{2}+1\right) c^{2}+2 a \,c^{2} x^{4}+2 b c \,x^{2}+b \ln \left(-c \,x^{2}+1\right)-2 a +2 b \right) \ln \left(c \,x^{2}+1\right)^{2}}{32 c^{2}}+\left(\frac{3 b^{3} \left(c^{2} x^{4}-1\right) \ln \left(-c \,x^{2}+1\right)^{2}}{32 c^{2}}-\frac{3 b^{2} x^{2} \left(a c \,x^{2}+b \right) \ln \left(-c \,x^{2}+1\right)}{8 c}+\frac{3 b \left(a^{2} c^{2} x^{4}+2 a b c \,x^{2}+b \ln \left(-c \,x^{2}+1\right) a +b^{2} \ln \left(-c \,x^{2}+1\right)\right)}{8 c^{2}}\right) \ln \left(c \,x^{2}+1\right)+\frac{3 b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{2}+1\right)}{\sum}\left(-\frac{\left(\ln \left(x -\underline{\hspace{1.25 ex}}\alpha  \right) \ln \left(-c \,x^{2}+1\right)+2 c \left(-\frac{\ln \left(x -\underline{\hspace{1.25 ex}}\alpha  \right) \left(\ln \left(\frac{\RootOf \left(c \,\textit{\_Z}^{2}+2 \textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  c -2, \mathit{index} =1\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(c \,\textit{\_Z}^{2}+2 \textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  c -2, \mathit{index} =1\right)}\right)+\ln \left(\frac{\RootOf \left(c \,\textit{\_Z}^{2}+2 \textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  c -2, \mathit{index} =2\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(c \,\textit{\_Z}^{2}+2 \textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  c -2, \mathit{index} =2\right)}\right)\right)}{2 c}-\frac{\dilog \left(\frac{\RootOf \left(c \,\textit{\_Z}^{2}+2 \textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  c -2, \mathit{index} =1\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(c \,\textit{\_Z}^{2}+2 \textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  c -2, \mathit{index} =1\right)}\right)+\dilog \left(\frac{\RootOf \left(c \,\textit{\_Z}^{2}+2 \textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  c -2, \mathit{index} =2\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(c \,\textit{\_Z}^{2}+2 \textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  c -2, \mathit{index} =2\right)}\right)}{2 c}\right)\right) b}{c}\right)\right)}{4 c}+\frac{3 b^{2} a \ln \left(c \,x^{2}-1\right)}{16 c^{2}}-\frac{3 a^{2} b \ln \left(c \,x^{2}+1\right)}{8 c^{2}}+\frac{3 a \,b^{2} \ln \left(c \,x^{2}+1\right)}{4 c^{2}}+\frac{3 b^{3} \ln \left(-c \,x^{2}+1\right)}{8 c^{2}}-\frac{3 b^{3} \ln \left(c \,x^{2}-1\right)}{8 c^{2}}-\frac{b^{3} x^{4} \ln \left(-c \,x^{2}+1\right)^{3}}{32}-\frac{3 b^{3} \ln \left(-c \,x^{2}+1\right)^{2}}{16 c^{2}}+\frac{b^{3} \ln \left(-c \,x^{2}+1\right)^{3}}{32 c^{2}}-\frac{3 b^{3}}{16 c^{2}}+\frac{x^{4} a^{3}}{4}+\frac{3 a^{2} b \,x^{2}}{4 c}+\frac{3 b^{3} x^{2} \ln \left(-c \,x^{2}+1\right)^{2}}{16 c}-\frac{3 a^{2} b \,x^{4} \ln \left(-c \,x^{2}+1\right)}{8}+\frac{3 a^{2} b \ln \left(c \,x^{2}-1\right)}{8 c^{2}}+\frac{3 a \,b^{2} x^{4} \ln \left(-c \,x^{2}+1\right)^{2}}{16}+\frac{9 a \,b^{2} \ln \left(-c \,x^{2}+1\right)}{16 c^{2}}-\frac{3 a \,b^{2} \ln \left(-c \,x^{2}+1\right)^{2}}{16 c^{2}}-\frac{3 a \,b^{2} x^{2} \ln \left(-c \,x^{2}+1\right)}{4 c}"," ",0,"1/32*b^3*(c^2*x^4-1)/c^2*ln(c*x^2+1)^3+3/32*b^2*(-x^4*b*ln(-c*x^2+1)*c^2+2*a*c^2*x^4+2*b*c*x^2+b*ln(-c*x^2+1)-2*a+2*b)/c^2*ln(c*x^2+1)^2+(3/32*b^3*(c^2*x^4-1)/c^2*ln(-c*x^2+1)^2-3/8*b^2*x^2*(a*c*x^2+b)/c*ln(-c*x^2+1)+3/8*b*(a^2*c^2*x^4+2*a*b*c*x^2+b*ln(-c*x^2+1)*a+b^2*ln(-c*x^2+1))/c^2)*ln(c*x^2+1)+3/4*b^2/c*Sum(-(ln(x-_alpha)*ln(-c*x^2+1)+2*c*(-1/2*ln(x-_alpha)*(ln((RootOf(_Z^2*c+2*_Z*_alpha*c-2,index=1)-x+_alpha)/RootOf(_Z^2*c+2*_Z*_alpha*c-2,index=1))+ln((RootOf(_Z^2*c+2*_Z*_alpha*c-2,index=2)-x+_alpha)/RootOf(_Z^2*c+2*_Z*_alpha*c-2,index=2)))/c-1/2*(dilog((RootOf(_Z^2*c+2*_Z*_alpha*c-2,index=1)-x+_alpha)/RootOf(_Z^2*c+2*_Z*_alpha*c-2,index=1))+dilog((RootOf(_Z^2*c+2*_Z*_alpha*c-2,index=2)-x+_alpha)/RootOf(_Z^2*c+2*_Z*_alpha*c-2,index=2)))/c))*b/c,_alpha=RootOf(_Z^2*c+1))+3/16*b^2/c^2*a*ln(c*x^2-1)-3/8*a^2*b/c^2*ln(c*x^2+1)+3/4*a*b^2/c^2*ln(c*x^2+1)+3/8/c^2*b^3*ln(-c*x^2+1)-3/8/c^2*b^3*ln(c*x^2-1)-1/32*b^3*x^4*ln(-c*x^2+1)^3-3/16*b^3/c^2*ln(-c*x^2+1)^2+1/32*b^3/c^2*ln(-c*x^2+1)^3-3/16*b^3/c^2+1/4*x^4*a^3+3/4/c*a^2*b*x^2+3/16*b^3/c*x^2*ln(-c*x^2+1)^2-3/8*a^2*b*x^4*ln(-c*x^2+1)+3/8*a^2*b/c^2*ln(c*x^2-1)+3/16*a*b^2*x^4*ln(-c*x^2+1)^2+9/16*a*b^2/c^2*ln(-c*x^2+1)-3/16*a*b^2/c^2*ln(-c*x^2+1)^2-3/4*a*b^2/c*x^2*ln(-c*x^2+1)","C"
78,1,298,124,0.200000," ","int(x*(a+b*arctanh(c*x^2))^3,x)","\frac{x^{2} a^{3}}{2}+\frac{b^{3} x^{2} \arctanh \left(c \,x^{2}\right)^{3}}{2}+\frac{b^{3} \arctanh \left(c \,x^{2}\right)^{3}}{2 c}-\frac{3 b^{3} \arctanh \left(c \,x^{2}\right)^{2} \ln \left(1+\frac{\left(c \,x^{2}+1\right)^{2}}{-c^{2} x^{4}+1}\right)}{2 c}-\frac{3 b^{3} \arctanh \left(c \,x^{2}\right) \polylog \left(2, -\frac{\left(c \,x^{2}+1\right)^{2}}{-c^{2} x^{4}+1}\right)}{2 c}+\frac{3 b^{3} \polylog \left(3, -\frac{\left(c \,x^{2}+1\right)^{2}}{-c^{2} x^{4}+1}\right)}{4 c}+\frac{3 x^{2} a \,b^{2} \arctanh \left(c \,x^{2}\right)^{2}}{2}+\frac{3 a \,b^{2} \arctanh \left(c \,x^{2}\right)^{2}}{2 c}-\frac{3 \arctanh \left(c \,x^{2}\right) \ln \left(1+\frac{\left(c \,x^{2}+1\right)^{2}}{-c^{2} x^{4}+1}\right) a \,b^{2}}{c}-\frac{3 \polylog \left(2, -\frac{\left(c \,x^{2}+1\right)^{2}}{-c^{2} x^{4}+1}\right) a \,b^{2}}{2 c}+\frac{3 x^{2} a^{2} b \arctanh \left(c \,x^{2}\right)}{2}+\frac{3 a^{2} b \ln \left(-c^{2} x^{4}+1\right)}{4 c}"," ",0,"1/2*x^2*a^3+1/2*b^3*x^2*arctanh(c*x^2)^3+1/2/c*b^3*arctanh(c*x^2)^3-3/2/c*b^3*arctanh(c*x^2)^2*ln(1+(c*x^2+1)^2/(-c^2*x^4+1))-3/2/c*b^3*arctanh(c*x^2)*polylog(2,-(c*x^2+1)^2/(-c^2*x^4+1))+3/4/c*b^3*polylog(3,-(c*x^2+1)^2/(-c^2*x^4+1))+3/2*x^2*a*b^2*arctanh(c*x^2)^2+3/2/c*a*b^2*arctanh(c*x^2)^2-3/c*arctanh(c*x^2)*ln(1+(c*x^2+1)^2/(-c^2*x^4+1))*a*b^2-3/2/c*polylog(2,-(c*x^2+1)^2/(-c^2*x^4+1))*a*b^2+3/2*x^2*a^2*b*arctanh(c*x^2)+3/4/c*a^2*b*ln(-c^2*x^4+1)","B"
79,0,0,196,0.214000," ","int((a+b*arctanh(c*x^2))^3/x,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{3}}{x}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^3/x,x)","F"
80,0,0,115,0.289000," ","int((a+b*arctanh(c*x^2))^3/x^3,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{3}}{x^{3}}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^3/x^3,x)","F"
81,0,0,127,0.338000," ","int((a+b*arctanh(c*x^2))^3/x^5,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{3}}{x^{5}}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^3/x^5,x)","F"
82,1,302,212,0.056000," ","int((d*x)^(5/2)*(a+b*arctanh(c*x^2)),x)","\frac{2 \left(d x \right)^{\frac{7}{2}} a}{7 d}+\frac{2 b \left(d x \right)^{\frac{7}{2}} \arctanh \left(c \,x^{2}\right)}{7 d}+\frac{8 b d \left(d x \right)^{\frac{3}{2}}}{21 c}+\frac{2 d^{3} b \arctan \left(\frac{\sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{7 c^{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-\frac{d^{3} b \ln \left(\frac{\sqrt{d x}+\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}{\sqrt{d x}-\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{7 c^{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-\frac{d^{3} b \sqrt{2}\, \ln \left(\frac{d x -\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}{d x +\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}\right)}{14 c^{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-\frac{d^{3} b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+1\right)}{7 c^{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-\frac{d^{3} b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-1\right)}{7 c^{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}"," ",0,"2/7/d*(d*x)^(7/2)*a+2/7/d*b*(d*x)^(7/2)*arctanh(c*x^2)+8/21*b*d*(d*x)^(3/2)/c+2/7*d^3*b/c^2/(d^2/c)^(1/4)*arctan((d*x)^(1/2)/(d^2/c)^(1/4))-1/7*d^3*b/c^2/(d^2/c)^(1/4)*ln(((d*x)^(1/2)+(d^2/c)^(1/4))/((d*x)^(1/2)-(d^2/c)^(1/4)))-1/14*d^3*b/c^2/(d^2/c)^(1/4)*2^(1/2)*ln((d*x-(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2))/(d*x+(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2)))-1/7*d^3*b/c^2/(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)+1)-1/7*d^3*b/c^2/(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)-1)","A"
83,1,292,212,0.038000," ","int((d*x)^(3/2)*(a+b*arctanh(c*x^2)),x)","\frac{2 \left(d x \right)^{\frac{5}{2}} a}{5 d}+\frac{2 b \left(d x \right)^{\frac{5}{2}} \arctanh \left(c \,x^{2}\right)}{5 d}+\frac{8 b d \sqrt{d x}}{5 c}-\frac{d b \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{d x}+\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}{\sqrt{d x}-\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{5 c}-\frac{2 d b \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{5 c}-\frac{d b \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d x +\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}{d x -\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}\right)}{10 c}-\frac{d b \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+1\right)}{5 c}-\frac{d b \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-1\right)}{5 c}"," ",0,"2/5/d*(d*x)^(5/2)*a+2/5/d*b*(d*x)^(5/2)*arctanh(c*x^2)+8/5*b*d*(d*x)^(1/2)/c-1/5*d*b/c*(d^2/c)^(1/4)*ln(((d*x)^(1/2)+(d^2/c)^(1/4))/((d*x)^(1/2)-(d^2/c)^(1/4)))-2/5*d*b/c*(d^2/c)^(1/4)*arctan((d*x)^(1/2)/(d^2/c)^(1/4))-1/10*d*b/c*(d^2/c)^(1/4)*2^(1/2)*ln((d*x+(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2))/(d*x-(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2)))-1/5*d*b/c*(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)+1)-1/5*d*b/c*(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)-1)","A"
84,1,280,200,0.039000," ","int((d*x)^(1/2)*(a+b*arctanh(c*x^2)),x)","\frac{2 \left(d x \right)^{\frac{3}{2}} a}{3 d}+\frac{2 b \left(d x \right)^{\frac{3}{2}} \arctanh \left(c \,x^{2}\right)}{3 d}+\frac{2 d b \arctan \left(\frac{\sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{3 c \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-\frac{d b \ln \left(\frac{\sqrt{d x}+\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}{\sqrt{d x}-\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{3 c \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+\frac{d b \sqrt{2}\, \ln \left(\frac{d x -\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}{d x +\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}\right)}{6 c \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+\frac{d b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+1\right)}{3 c \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+\frac{d b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-1\right)}{3 c \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}"," ",0,"2/3/d*(d*x)^(3/2)*a+2/3/d*b*(d*x)^(3/2)*arctanh(c*x^2)+2/3*d*b/c/(d^2/c)^(1/4)*arctan((d*x)^(1/2)/(d^2/c)^(1/4))-1/3*d*b/c/(d^2/c)^(1/4)*ln(((d*x)^(1/2)+(d^2/c)^(1/4))/((d*x)^(1/2)-(d^2/c)^(1/4)))+1/6*d*b/c/(d^2/c)^(1/4)*2^(1/2)*ln((d*x-(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2))/(d*x+(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2)))+1/3*d*b/c/(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)+1)+1/3*d*b/c/(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)-1)","A"
85,1,273,198,0.038000," ","int((a+b*arctanh(c*x^2))/(d*x)^(1/2),x)","\frac{2 a \sqrt{d x}}{d}+\frac{2 b \sqrt{d x}\, \arctanh \left(c \,x^{2}\right)}{d}-\frac{b \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{d x}+\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}{\sqrt{d x}-\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{d}-\frac{2 b \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{d}+\frac{b \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d x +\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}{d x -\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}\right)}{2 d}+\frac{b \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+1\right)}{d}+\frac{b \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-1\right)}{d}"," ",0,"2/d*a*(d*x)^(1/2)+2/d*b*(d*x)^(1/2)*arctanh(c*x^2)-1/d*b*(d^2/c)^(1/4)*ln(((d*x)^(1/2)+(d^2/c)^(1/4))/((d*x)^(1/2)-(d^2/c)^(1/4)))-2/d*b*(d^2/c)^(1/4)*arctan((d*x)^(1/2)/(d^2/c)^(1/4))+1/2/d*b*(d^2/c)^(1/4)*2^(1/2)*ln((d*x+(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2))/(d*x-(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2)))+1/d*b*(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)+1)+1/d*b*(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)-1)","A"
86,1,272,198,0.034000," ","int((a+b*arctanh(c*x^2))/(d*x)^(3/2),x)","-\frac{2 a}{d \sqrt{d x}}-\frac{2 b \arctanh \left(c \,x^{2}\right)}{d \sqrt{d x}}-\frac{2 b \arctan \left(\frac{\sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{d \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+\frac{b \ln \left(\frac{\sqrt{d x}+\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}{\sqrt{d x}-\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{d \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \ln \left(\frac{d x -\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}{d x +\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}\right)}{2 d \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+1\right)}{d \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-1\right)}{d \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}"," ",0,"-2/d*a/(d*x)^(1/2)-2/d*b/(d*x)^(1/2)*arctanh(c*x^2)-2/d*b/(d^2/c)^(1/4)*arctan((d*x)^(1/2)/(d^2/c)^(1/4))+1/d*b/(d^2/c)^(1/4)*ln(((d*x)^(1/2)+(d^2/c)^(1/4))/((d*x)^(1/2)-(d^2/c)^(1/4)))+1/2/d*b/(d^2/c)^(1/4)*2^(1/2)*ln((d*x-(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2))/(d*x+(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2)))+1/d*b/(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)+1)+1/d*b/(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)-1)","A"
87,1,280,200,0.037000," ","int((a+b*arctanh(c*x^2))/(d*x)^(5/2),x)","-\frac{2 a}{3 d \left(d x \right)^{\frac{3}{2}}}-\frac{2 b \arctanh \left(c \,x^{2}\right)}{3 d \left(d x \right)^{\frac{3}{2}}}+\frac{b c \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{d x}+\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}{\sqrt{d x}-\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{3 d^{3}}+\frac{2 b c \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{3 d^{3}}+\frac{b c \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d x +\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}{d x -\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}\right)}{6 d^{3}}+\frac{b c \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+1\right)}{3 d^{3}}+\frac{b c \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-1\right)}{3 d^{3}}"," ",0,"-2/3/d*a/(d*x)^(3/2)-2/3/d*b/(d*x)^(3/2)*arctanh(c*x^2)+1/3/d^3*b*c*(d^2/c)^(1/4)*ln(((d*x)^(1/2)+(d^2/c)^(1/4))/((d*x)^(1/2)-(d^2/c)^(1/4)))+2/3/d^3*b*c*(d^2/c)^(1/4)*arctan((d*x)^(1/2)/(d^2/c)^(1/4))+1/6/d^3*b*c*(d^2/c)^(1/4)*2^(1/2)*ln((d*x+(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2))/(d*x-(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2)))+1/3/d^3*b*c*(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)+1)+1/3/d^3*b*c*(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)-1)","A"
88,1,292,212,0.040000," ","int((a+b*arctanh(c*x^2))/(d*x)^(7/2),x)","-\frac{2 a}{5 d \left(d x \right)^{\frac{5}{2}}}-\frac{2 b \arctanh \left(c \,x^{2}\right)}{5 d \left(d x \right)^{\frac{5}{2}}}-\frac{2 b c \arctan \left(\frac{\sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{5 d^{3} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+\frac{b c \ln \left(\frac{\sqrt{d x}+\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}{\sqrt{d x}-\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{5 d^{3} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-\frac{8 b c}{5 d^{3} \sqrt{d x}}-\frac{b c \sqrt{2}\, \ln \left(\frac{d x -\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}{d x +\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}\right)}{10 d^{3} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-\frac{b c \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+1\right)}{5 d^{3} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-\frac{b c \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-1\right)}{5 d^{3} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}"," ",0,"-2/5/d*a/(d*x)^(5/2)-2/5/d*b/(d*x)^(5/2)*arctanh(c*x^2)-2/5/d^3*b*c/(d^2/c)^(1/4)*arctan((d*x)^(1/2)/(d^2/c)^(1/4))+1/5/d^3*b*c/(d^2/c)^(1/4)*ln(((d*x)^(1/2)+(d^2/c)^(1/4))/((d*x)^(1/2)-(d^2/c)^(1/4)))-8/5*b*c/d^3/(d*x)^(1/2)-1/10/d^3*b*c/(d^2/c)^(1/4)*2^(1/2)*ln((d*x-(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2))/(d*x+(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2)))-1/5/d^3*b*c/(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)+1)-1/5/d^3*b*c/(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)-1)","A"
89,1,302,212,0.038000," ","int((a+b*arctanh(c*x^2))/(d*x)^(9/2),x)","-\frac{2 a}{7 d \left(d x \right)^{\frac{7}{2}}}-\frac{2 b \arctanh \left(c \,x^{2}\right)}{7 d \left(d x \right)^{\frac{7}{2}}}+\frac{b \,c^{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{d x}+\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}{\sqrt{d x}-\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{7 d^{5}}+\frac{2 b \,c^{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{7 d^{5}}-\frac{8 b c}{21 d^{3} \left(d x \right)^{\frac{3}{2}}}-\frac{b \,c^{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d x +\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}{d x -\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{d^{2}}{c}}}\right)}{14 d^{5}}-\frac{b \,c^{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}+1\right)}{7 d^{5}}-\frac{b \,c^{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}-1\right)}{7 d^{5}}"," ",0,"-2/7/d*a/(d*x)^(7/2)-2/7/d*b/(d*x)^(7/2)*arctanh(c*x^2)+1/7/d^5*b*c^2*(d^2/c)^(1/4)*ln(((d*x)^(1/2)+(d^2/c)^(1/4))/((d*x)^(1/2)-(d^2/c)^(1/4)))+2/7/d^5*b*c^2*(d^2/c)^(1/4)*arctan((d*x)^(1/2)/(d^2/c)^(1/4))-8/21*b*c/d^3/(d*x)^(3/2)-1/14/d^5*b*c^2*(d^2/c)^(1/4)*2^(1/2)*ln((d*x+(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2))/(d*x-(d^2/c)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2/c)^(1/2)))-1/7/d^5*b*c^2*(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)+1)-1/7/d^5*b*c^2*(d^2/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/c)^(1/4)*(d*x)^(1/2)-1)","A"
90,0,0,4596,0.465000," ","int((d*x)^(1/2)*(a+b*arctanh(c*x^2))^2,x)","\int \sqrt{d x}\, \left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int((d*x)^(1/2)*(a+b*arctanh(c*x^2))^2,x)","F"
91,0,0,4598,0.386000," ","int((a+b*arctanh(c*x^2))^2/(d*x)^(1/2),x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}}{\sqrt{d x}}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^2/(d*x)^(1/2),x)","F"
92,0,0,4779,0.474000," ","int((a+b*arctanh(c*x^2))^2/(d*x)^(3/2),x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}}{\left(d x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^2/(d*x)^(3/2),x)","F"
93,0,0,4801,0.476000," ","int((a+b*arctanh(c*x^2))^2/(d*x)^(5/2),x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}}{\left(d x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^2/(d*x)^(5/2),x)","F"
94,0,0,20,0.183000," ","int((d*x)^m*(a+b*arctanh(c*x^2))^3,x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c \,x^{2}\right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x^2))^3,x)","F"
95,0,0,20,0.179000," ","int((d*x)^m*(a+b*arctanh(c*x^2))^2,x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x^2))^2,x)","F"
96,0,0,72,0.179000," ","int((d*x)^m*(a+b*arctanh(c*x^2)),x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c \,x^{2}\right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x^2)),x)","F"
97,0,0,20,0.110000," ","int((d*x)^m/(a+b*arctanh(c*x^2)),x)","\int \frac{\left(d x \right)^{m}}{a +b \arctanh \left(c \,x^{2}\right)}\, dx"," ",0,"int((d*x)^m/(a+b*arctanh(c*x^2)),x)","F"
98,0,0,20,0.114000," ","int((d*x)^m/(a+b*arctanh(c*x^2))^2,x)","\int \frac{\left(d x \right)^{m}}{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}}\, dx"," ",0,"int((d*x)^m/(a+b*arctanh(c*x^2))^2,x)","F"
99,1,66,46,0.031000," ","int(x^11*(a+b*arctanh(c*x^3)),x)","\frac{x^{12} a}{12}+\frac{b \,x^{12} \arctanh \left(c \,x^{3}\right)}{12}+\frac{b \,x^{9}}{36 c}+\frac{b \,x^{3}}{12 c^{3}}-\frac{b \ln \left(c \,x^{3}+1\right)}{24 c^{4}}+\frac{b \ln \left(c \,x^{3}-1\right)}{24 c^{4}}"," ",0,"1/12*x^12*a+1/12*b*x^12*arctanh(c*x^3)+1/36*b*x^9/c+1/12*b*x^3/c^3-1/24*b/c^4*ln(c*x^3+1)+1/24*b/c^4*ln(c*x^3-1)","A"
100,1,45,42,0.023000," ","int(x^8*(a+b*arctanh(c*x^3)),x)","\frac{x^{9} a}{9}+\frac{b \,x^{9} \arctanh \left(c \,x^{3}\right)}{9}+\frac{b \,x^{6}}{18 c}+\frac{b \ln \left(c^{2} x^{6}-1\right)}{18 c^{3}}"," ",0,"1/9*x^9*a+1/9*b*x^9*arctanh(c*x^3)+1/18*b*x^6/c+1/18*b/c^3*ln(c^2*x^6-1)","A"
101,1,57,37,0.029000," ","int(x^5*(a+b*arctanh(c*x^3)),x)","\frac{x^{6} a}{6}+\frac{b \,x^{6} \arctanh \left(c \,x^{3}\right)}{6}+\frac{b \,x^{3}}{6 c}-\frac{b \ln \left(c \,x^{3}+1\right)}{12 c^{2}}+\frac{b \ln \left(c \,x^{3}-1\right)}{12 c^{2}}"," ",0,"1/6*x^6*a+1/6*b*x^6*arctanh(c*x^3)+1/6*b*x^3/c-1/12*b/c^2*ln(c*x^3+1)+1/12*b/c^2*ln(c*x^3-1)","A"
102,1,37,33,0.021000," ","int(x^2*(a+b*arctanh(c*x^3)),x)","\frac{x^{3} a}{3}+\frac{b \,x^{3} \arctanh \left(c \,x^{3}\right)}{3}+\frac{b \ln \left(-c^{2} x^{6}+1\right)}{6 c}"," ",0,"1/3*x^3*a+1/3*b*x^3*arctanh(c*x^3)+1/6*b*ln(-c^2*x^6+1)/c","A"
103,1,92,26,0.098000," ","int((a+b*arctanh(c*x^3))/x,x)","a \ln \left(x \right)+b \ln \left(x \right) \arctanh \left(c \,x^{3}\right)+\frac{b \left(\munderset{\textit{\_R1} =\RootOf \left(c \,\textit{\_Z}^{3}-1\right)}{\sum}\left(\ln \left(x \right) \ln \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)\right)\right)}{2}-\frac{b \left(\munderset{\textit{\_R1} =\RootOf \left(c \,\textit{\_Z}^{3}+1\right)}{\sum}\left(\ln \left(x \right) \ln \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)\right)\right)}{2}"," ",0,"a*ln(x)+b*ln(x)*arctanh(c*x^3)+1/2*b*sum(ln(x)*ln((_R1-x)/_R1)+dilog((_R1-x)/_R1),_R1=RootOf(_Z^3*c-1))-1/2*b*sum(ln(x)*ln((_R1-x)/_R1)+dilog((_R1-x)/_R1),_R1=RootOf(_Z^3*c+1))","C"
104,1,49,39,0.033000," ","int((a+b*arctanh(c*x^3))/x^4,x)","-\frac{a}{3 x^{3}}-\frac{b \arctanh \left(c \,x^{3}\right)}{3 x^{3}}+b c \ln \left(x \right)-\frac{b c \ln \left(c \,x^{3}-1\right)}{6}-\frac{b c \ln \left(c \,x^{3}+1\right)}{6}"," ",0,"-1/3*a/x^3-1/3*b/x^3*arctanh(c*x^3)+b*c*ln(x)-1/6*b*c*ln(c*x^3-1)-1/6*b*c*ln(c*x^3+1)","A"
105,1,55,38,0.033000," ","int((a+b*arctanh(c*x^3))/x^7,x)","-\frac{a}{6 x^{6}}-\frac{b \arctanh \left(c \,x^{3}\right)}{6 x^{6}}-\frac{b c}{6 x^{3}}-\frac{b \,c^{2} \ln \left(c \,x^{3}-1\right)}{12}+\frac{b \,c^{2} \ln \left(c \,x^{3}+1\right)}{12}"," ",0,"-1/6*a/x^6-1/6*b/x^6*arctanh(c*x^3)-1/6*b*c/x^3-1/12*b*c^2*ln(c*x^3-1)+1/12*b*c^2*ln(c*x^3+1)","A"
106,1,63,51,0.036000," ","int((a+b*arctanh(c*x^3))/x^10,x)","-\frac{a}{9 x^{9}}-\frac{b \arctanh \left(c \,x^{3}\right)}{9 x^{9}}-\frac{b c}{18 x^{6}}+\frac{b \,c^{3} \ln \left(x \right)}{3}-\frac{b \,c^{3} \ln \left(c \,x^{3}-1\right)}{18}-\frac{b \,c^{3} \ln \left(c \,x^{3}+1\right)}{18}"," ",0,"-1/9*a/x^9-1/9*b/x^9*arctanh(c*x^3)-1/18*b*c/x^6+1/3*b*c^3*ln(x)-1/18*b*c^3*ln(c*x^3-1)-1/18*b*c^3*ln(c*x^3+1)","A"
107,1,184,128,0.035000," ","int(x^3*(a+b*arctanh(c*x^3)),x)","\frac{x^{4} a}{4}+\frac{b \,x^{4} \arctanh \left(c \,x^{3}\right)}{4}+\frac{3 b x}{4 c}+\frac{b \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{8 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \ln \left(x^{2}+\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{16 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{8 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{8 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b \ln \left(x^{2}-\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{16 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{8 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}"," ",0,"1/4*x^4*a+1/4*b*x^4*arctanh(c*x^3)+3/4*b*x/c+1/8*b/c^2/(1/c)^(2/3)*ln(x-(1/c)^(1/3))-1/16*b/c^2/(1/c)^(2/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))-1/8*b/c^2/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))-1/8*b/c^2/(1/c)^(2/3)*ln(x+(1/c)^(1/3))+1/16*b/c^2/(1/c)^(2/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))-1/8*b/c^2/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))","A"
108,1,99,78,0.030000," ","int(a+b*arctanh(c*x^3),x)","a x +b x \arctanh \left(c \,x^{3}\right)+\frac{b \ln \left(x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}-\frac{b \ln \left(x^{4}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}} x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x^{2}}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}"," ",0,"a*x+b*x*arctanh(c*x^3)+1/2*b/c/(1/c^2)^(1/3)*ln(x^2-(1/c^2)^(1/3))-1/4*b/c/(1/c^2)^(1/3)*ln(x^4+(1/c^2)^(1/3)*x^2+(1/c^2)^(2/3))+1/2*b*3^(1/2)/c/(1/c^2)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c^2)^(1/3)*x^2+1))","A"
109,1,159,124,0.032000," ","int((a+b*arctanh(c*x^3))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arctanh \left(c \,x^{3}\right)}{2 x^{2}}-\frac{b \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{4 \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b \ln \left(x^{2}+\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{8 \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{4 \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{4 \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \ln \left(x^{2}-\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{8 \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{4 \left(\frac{1}{c}\right)^{\frac{2}{3}}}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arctanh(c*x^3)-1/4*b/(1/c)^(2/3)*ln(x-(1/c)^(1/3))+1/8*b/(1/c)^(2/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))+1/4*b/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))+1/4*b/(1/c)^(2/3)*ln(x+(1/c)^(1/3))-1/8*b/(1/c)^(2/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))+1/4*b/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))","A"
110,1,172,91,0.035000," ","int((a+b*arctanh(c*x^3))/x^6,x)","-\frac{a}{5 x^{5}}-\frac{b \arctanh \left(c \,x^{3}\right)}{5 x^{5}}-\frac{3 b c}{10 x^{2}}-\frac{b c \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{10 \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b c \ln \left(x^{2}+\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{20 \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b c \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{10 \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b c \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{10 \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b c \ln \left(x^{2}-\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{20 \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b c \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{10 \left(\frac{1}{c}\right)^{\frac{2}{3}}}"," ",0,"-1/5*a/x^5-1/5*b/x^5*arctanh(c*x^3)-3/10*b*c/x^2-1/10*b*c/(1/c)^(2/3)*ln(x-(1/c)^(1/3))+1/20*b*c/(1/c)^(2/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))+1/10*b*c/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))-1/10*b*c/(1/c)^(2/3)*ln(x+(1/c)^(1/3))+1/20*b*c/(1/c)^(2/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))-1/10*b*c/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))","A"
111,1,186,130,0.032000," ","int(x^7*(a+b*arctanh(c*x^3)),x)","\frac{x^{8} a}{8}+\frac{b \,x^{8} \arctanh \left(c \,x^{3}\right)}{8}+\frac{3 b \,x^{5}}{40 c}+\frac{b \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{16 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b \ln \left(x^{2}+\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{32 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{16 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{16 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \ln \left(x^{2}-\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{32 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{16 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}"," ",0,"1/8*x^8*a+1/8*b*x^8*arctanh(c*x^3)+3/40*b*x^5/c+1/16*b/c^3/(1/c)^(1/3)*ln(x-(1/c)^(1/3))-1/32*b/c^3/(1/c)^(1/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))+1/16*b/c^3*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))-1/16*b/c^3/(1/c)^(1/3)*ln(x+(1/c)^(1/3))+1/32*b/c^3/(1/c)^(1/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))+1/16*b/c^3*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))","A"
112,1,114,90,0.026000," ","int(x^4*(a+b*arctanh(c*x^3)),x)","\frac{a \,x^{5}}{5}+\frac{b \,x^{5} \arctanh \left(c \,x^{3}\right)}{5}+\frac{3 b \,x^{2}}{10 c}+\frac{b \ln \left(x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{10 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}-\frac{b \ln \left(x^{4}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}} x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}\right)}{20 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}-\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x^{2}}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{10 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}"," ",0,"1/5*a*x^5+1/5*b*x^5*arctanh(c*x^3)+3/10*b*x^2/c+1/10*b/c^3/(1/c^2)^(2/3)*ln(x^2-(1/c^2)^(1/3))-1/20*b/c^3/(1/c^2)^(2/3)*ln(x^4+(1/c^2)^(1/3)*x^2+(1/c^2)^(2/3))-1/10*b/c^3/(1/c^2)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c^2)^(1/3)*x^2+1))","A"
113,1,177,121,0.031000," ","int(x*(a+b*arctanh(c*x^3)),x)","\frac{a \,x^{2}}{2}+\frac{b \,x^{2} \arctanh \left(c \,x^{3}\right)}{2}+\frac{b \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b \ln \left(x^{2}+\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{8 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \ln \left(x^{2}-\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{8 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}"," ",0,"1/2*a*x^2+1/2*b*x^2*arctanh(c*x^3)+1/4*b/c/(1/c)^(1/3)*ln(x-(1/c)^(1/3))-1/8*b/c/(1/c)^(1/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))+1/4*b*3^(1/2)/c/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))-1/4*b/c/(1/c)^(1/3)*ln(x+(1/c)^(1/3))+1/8*b/c/(1/c)^(1/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))+1/4*b*3^(1/2)/c/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))","A"
114,1,105,83,0.026000," ","int((a+b*arctanh(c*x^3))/x^2,x)","-\frac{a}{x}-\frac{b \arctanh \left(c \,x^{3}\right)}{x}-\frac{b \ln \left(x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}+\frac{b \ln \left(x^{4}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}} x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x^{2}}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}"," ",0,"-a/x-b/x*arctanh(c*x^3)-1/2*b/c/(1/c^2)^(2/3)*ln(x^2-(1/c^2)^(1/3))+1/4*b/c/(1/c^2)^(2/3)*ln(x^4+(1/c^2)^(1/3)*x^2+(1/c^2)^(2/3))+1/2*b/c/(1/c^2)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c^2)^(1/3)*x^2+1))","A"
115,1,172,131,0.035000," ","int((a+b*arctanh(c*x^3))/x^5,x)","-\frac{a}{4 x^{4}}-\frac{b \arctanh \left(c \,x^{3}\right)}{4 x^{4}}-\frac{3 b c}{4 x}-\frac{b c \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{8 \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b c \ln \left(x^{2}+\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{16 \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b c \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{8 \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b c \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{8 \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b c \ln \left(x^{2}-\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{16 \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b c \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{8 \left(\frac{1}{c}\right)^{\frac{1}{3}}}"," ",0,"-1/4*a/x^4-1/4*b/x^4*arctanh(c*x^3)-3/4*b*c/x-1/8*b*c/(1/c)^(1/3)*ln(x-(1/c)^(1/3))+1/16*b*c/(1/c)^(1/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))-1/8*b*c*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))+1/8*b*c/(1/c)^(1/3)*ln(x+(1/c)^(1/3))-1/16*b*c/(1/c)^(1/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))-1/8*b*c*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))","A"
116,-2,0,111,180.000000," ","int(x^11*(a+b*arctanh(c*x^3))^2,x)","\int x^{11} \left(a +b \arctanh \left(c \,x^{3}\right)\right)^{2}\, dx"," ",0,"int(x^11*(a+b*arctanh(c*x^3))^2,x)","F"
117,-2,0,132,180.000000," ","int(x^8*(a+b*arctanh(c*x^3))^2,x)","\int x^{8} \left(a +b \arctanh \left(c \,x^{3}\right)\right)^{2}\, dx"," ",0,"int(x^8*(a+b*arctanh(c*x^3))^2,x)","F"
118,1,247,81,0.276000," ","int(x^5*(a+b*arctanh(c*x^3))^2,x)","\frac{b^{2} \left(c^{2} x^{6}-1\right) \ln \left(c \,x^{3}+1\right)^{2}}{24 c^{2}}+\frac{b \left(-x^{6} b \ln \left(-c \,x^{3}+1\right) c^{2}+2 a \,c^{2} x^{6}+2 b c \,x^{3}+b \ln \left(-c \,x^{3}+1\right)\right) \ln \left(c \,x^{3}+1\right)}{12 c^{2}}+\frac{b^{2} x^{6} \ln \left(-c \,x^{3}+1\right)^{2}}{24}-\frac{a b \,x^{6} \ln \left(-c \,x^{3}+1\right)}{6}+\frac{x^{6} a^{2}}{6}-\frac{b^{2} x^{3} \ln \left(-c \,x^{3}+1\right)}{6 c}+\frac{a b \,x^{3}}{3 c}-\frac{b^{2} \ln \left(-c \,x^{3}+1\right)^{2}}{24 c^{2}}+\frac{b \ln \left(-c \,x^{3}+1\right) a}{6 c^{2}}+\frac{b^{2} \ln \left(-c \,x^{3}+1\right)}{6 c^{2}}-\frac{b \ln \left(-c \,x^{3}-1\right) a}{6 c^{2}}+\frac{b^{2} \ln \left(-c \,x^{3}-1\right)}{6 c^{2}}"," ",0,"1/24*b^2*(c^2*x^6-1)/c^2*ln(c*x^3+1)^2+1/12*b*(-x^6*b*ln(-c*x^3+1)*c^2+2*a*c^2*x^6+2*b*c*x^3+b*ln(-c*x^3+1))/c^2*ln(c*x^3+1)+1/24*b^2*x^6*ln(-c*x^3+1)^2-1/6*a*b*x^6*ln(-c*x^3+1)+1/6*x^6*a^2-1/6/c*b^2*x^3*ln(-c*x^3+1)+1/3*a*b*x^3/c-1/24/c^2*b^2*ln(-c*x^3+1)^2+1/6/c^2*b*ln(-c*x^3+1)*a+1/6/c^2*b^2*ln(-c*x^3+1)-1/6/c^2*b*ln(-c*x^3-1)*a+1/6/c^2*b^2*ln(-c*x^3-1)","B"
119,1,145,88,0.179000," ","int(x^2*(a+b*arctanh(c*x^3))^2,x)","\frac{x^{3} b^{2} \arctanh \left(c \,x^{3}\right)^{2}}{3}+\frac{2 x^{3} a b \arctanh \left(c \,x^{3}\right)}{3}+\frac{x^{3} a^{2}}{3}+\frac{b^{2} \arctanh \left(c \,x^{3}\right)^{2}}{3 c}-\frac{2 \arctanh \left(c \,x^{3}\right) \ln \left(1+\frac{\left(c \,x^{3}+1\right)^{2}}{-c^{2} x^{6}+1}\right) b^{2}}{3 c}+\frac{a b \ln \left(-c^{2} x^{6}+1\right)}{3 c}-\frac{\polylog \left(2, -\frac{\left(c \,x^{3}+1\right)^{2}}{-c^{2} x^{6}+1}\right) b^{2}}{3 c}"," ",0,"1/3*x^3*b^2*arctanh(c*x^3)^2+2/3*x^3*a*b*arctanh(c*x^3)+1/3*x^3*a^2+1/3/c*b^2*arctanh(c*x^3)^2-2/3/c*arctanh(c*x^3)*ln(1+(c*x^3+1)^2/(-c^2*x^6+1))*b^2+1/3/c*a*b*ln(-c^2*x^6+1)-1/3/c*polylog(2,-(c*x^3+1)^2/(-c^2*x^6+1))*b^2","A"
120,0,0,130,0.220000," ","int((a+b*arctanh(c*x^3))^2/x,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{3}\right)\right)^{2}}{x}\, dx"," ",0,"int((a+b*arctanh(c*x^3))^2/x,x)","F"
121,-2,0,82,180.000000," ","int((a+b*arctanh(c*x^3))^2/x^4,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{3}\right)\right)^{2}}{x^{4}}\, dx"," ",0,"int((a+b*arctanh(c*x^3))^2/x^4,x)","F"
122,1,257,80,0.283000," ","int((a+b*arctanh(c*x^3))^2/x^7,x)","\frac{b^{2} \left(c^{2} x^{6}-1\right) \ln \left(c \,x^{3}+1\right)^{2}}{24 x^{6}}-\frac{b \left(x^{6} b \ln \left(-c \,x^{3}+1\right) c^{2}+2 b c \,x^{3}-b \ln \left(-c \,x^{3}+1\right)+2 a \right) \ln \left(c \,x^{3}+1\right)}{12 x^{6}}+\frac{b^{2} c^{2} x^{6} \ln \left(-c \,x^{3}+1\right)^{2}+24 b^{2} c^{2} \ln \left(x \right) x^{6}+4 b \,c^{2} \ln \left(c \,x^{3}+1\right) x^{6} a -4 b^{2} c^{2} \ln \left(c \,x^{3}+1\right) x^{6}-4 b \,c^{2} \ln \left(c \,x^{3}-1\right) x^{6} a -4 b^{2} c^{2} \ln \left(c \,x^{3}-1\right) x^{6}+4 b^{2} c \,x^{3} \ln \left(-c \,x^{3}+1\right)-8 a b c \,x^{3}-b^{2} \ln \left(-c \,x^{3}+1\right)^{2}+4 b \ln \left(-c \,x^{3}+1\right) a -4 a^{2}}{24 x^{6}}"," ",0,"1/24*b^2*(c^2*x^6-1)/x^6*ln(c*x^3+1)^2-1/12*b*(x^6*b*ln(-c*x^3+1)*c^2+2*b*c*x^3-b*ln(-c*x^3+1)+2*a)/x^6*ln(c*x^3+1)+1/24*(b^2*c^2*x^6*ln(-c*x^3+1)^2+24*b^2*c^2*ln(x)*x^6+4*b*c^2*ln(c*x^3+1)*x^6*a-4*b^2*c^2*ln(c*x^3+1)*x^6-4*b*c^2*ln(c*x^3-1)*x^6*a-4*b^2*c^2*ln(c*x^3-1)*x^6+4*b^2*c*x^3*ln(-c*x^3+1)-8*a*b*c*x^3-b^2*ln(-c*x^3+1)^2+4*b*ln(-c*x^3+1)*a-4*a^2)/x^6","B"
123,0,0,130,0.273000," ","int((a+b*arctanh(c*x^3))^2/x^10,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{3}\right)\right)^{2}}{x^{10}}\, dx"," ",0,"int((a+b*arctanh(c*x^3))^2/x^10,x)","F"
124,0,0,211,0.343000," ","int(x^8*(a+b*arctanh(c*x^3))^3,x)","\int x^{8} \left(a +b \arctanh \left(c \,x^{3}\right)\right)^{3}\, dx"," ",0,"int(x^8*(a+b*arctanh(c*x^3))^3,x)","F"
125,1,750,129,0.436000," ","int(x^5*(a+b*arctanh(c*x^3))^3,x)","\frac{b^{3} \left(c^{2} x^{6}-1\right) \ln \left(c \,x^{3}+1\right)^{3}}{48 c^{2}}+\frac{b^{2} \left(-x^{6} b \ln \left(-c \,x^{3}+1\right) c^{2}+2 a \,c^{2} x^{6}+2 b c \,x^{3}+b \ln \left(-c \,x^{3}+1\right)-2 a +2 b \right) \ln \left(c \,x^{3}+1\right)^{2}}{16 c^{2}}+\left(\frac{b^{3} \left(c^{2} x^{6}-1\right) \ln \left(-c \,x^{3}+1\right)^{2}}{16 c^{2}}-\frac{b^{2} x^{3} \left(a c \,x^{3}+b \right) \ln \left(-c \,x^{3}+1\right)}{4 c}+\frac{b \left(a^{2} c^{2} x^{6}+2 a b c \,x^{3}+b \ln \left(-c \,x^{3}+1\right) a +b^{2} \ln \left(-c \,x^{3}+1\right)\right)}{4 c^{2}}\right) \ln \left(c \,x^{3}+1\right)+\frac{b^{2} a \ln \left(c \,x^{3}-1\right)}{8 c^{2}}-\frac{a^{2} b \ln \left(c \,x^{3}+1\right)}{4 c^{2}}+\frac{a \,b^{2} \ln \left(c \,x^{3}+1\right)}{2 c^{2}}+\frac{a^{2} b \ln \left(c \,x^{3}-1\right)}{4 c^{2}}+\frac{a \,b^{2} x^{6} \ln \left(-c \,x^{3}+1\right)^{2}}{8}+\frac{3 a \,b^{2} \ln \left(-c \,x^{3}+1\right)}{8 c^{2}}-\frac{a \,b^{2} \ln \left(-c \,x^{3}+1\right)^{2}}{8 c^{2}}+\frac{b^{3} x^{3} \ln \left(-c \,x^{3}+1\right)^{2}}{8 c}-\frac{a^{2} b \,x^{6} \ln \left(-c \,x^{3}+1\right)}{4}+\frac{x^{6} a^{3}}{6}+\frac{b^{3} \ln \left(-c \,x^{3}+1\right)}{4 c^{2}}-\frac{b^{3} \ln \left(c \,x^{3}-1\right)}{4 c^{2}}-\frac{b^{3} x^{6} \ln \left(-c \,x^{3}+1\right)^{3}}{48}-\frac{b^{3} \ln \left(-c \,x^{3}+1\right)^{2}}{8 c^{2}}+\frac{b^{3} \ln \left(-c \,x^{3}+1\right)^{3}}{48 c^{2}}+\frac{3 b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3} c +1\right)}{\sum}\left(-\frac{2 \left(\ln \left(x -\underline{\hspace{1.25 ex}}\alpha  \right) \ln \left(-c \,x^{3}+1\right)+3 c \left(-\frac{\ln \left(x -\underline{\hspace{1.25 ex}}\alpha  \right) \left(\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  +\underline{\hspace{1.25 ex}}\alpha^{2}, \mathit{index} =1\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  +\underline{\hspace{1.25 ex}}\alpha^{2}, \mathit{index} =1\right)}\right)+\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  +\underline{\hspace{1.25 ex}}\alpha^{2}, \mathit{index} =2\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  +\underline{\hspace{1.25 ex}}\alpha^{2}, \mathit{index} =2\right)}\right)+\ln \left(\frac{x +\underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha }\right)\right)}{3 c}-\frac{\dilog \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  +\underline{\hspace{1.25 ex}}\alpha^{2}, \mathit{index} =1\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  +\underline{\hspace{1.25 ex}}\alpha^{2}, \mathit{index} =1\right)}\right)+\dilog \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  +\underline{\hspace{1.25 ex}}\alpha^{2}, \mathit{index} =2\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \underline{\hspace{1.25 ex}}\alpha  +\underline{\hspace{1.25 ex}}\alpha^{2}, \mathit{index} =2\right)}\right)+\dilog \left(\frac{x +\underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha }\right)}{3 c}\right)\right) b}{3 c}\right)\right)}{4 c}-\frac{a \,b^{2} x^{3} \ln \left(-c \,x^{3}+1\right)}{2 c}-\frac{b^{3}}{8 c^{2}}+\frac{a^{2} b \,x^{3}}{2 c}"," ",0,"1/48*b^3*(c^2*x^6-1)/c^2*ln(c*x^3+1)^3+1/16*b^2*(-x^6*b*ln(-c*x^3+1)*c^2+2*a*c^2*x^6+2*b*c*x^3+b*ln(-c*x^3+1)-2*a+2*b)/c^2*ln(c*x^3+1)^2+(1/16*b^3*(c^2*x^6-1)/c^2*ln(-c*x^3+1)^2-1/4*b^2*x^3*(a*c*x^3+b)/c*ln(-c*x^3+1)+1/4*b*(a^2*c^2*x^6+2*a*b*c*x^3+b*ln(-c*x^3+1)*a+b^2*ln(-c*x^3+1))/c^2)*ln(c*x^3+1)+1/8*b^2/c^2*a*ln(c*x^3-1)-1/4*a^2*b/c^2*ln(c*x^3+1)+1/2*a*b^2/c^2*ln(c*x^3+1)+1/4*a^2*b/c^2*ln(c*x^3-1)+1/8*a*b^2*x^6*ln(-c*x^3+1)^2+3/8*a*b^2/c^2*ln(-c*x^3+1)-1/8*a*b^2/c^2*ln(-c*x^3+1)^2+1/8*b^3/c*x^3*ln(-c*x^3+1)^2-1/4*a^2*b*x^6*ln(-c*x^3+1)+1/6*x^6*a^3+1/4/c^2*b^3*ln(-c*x^3+1)-1/4/c^2*b^3*ln(c*x^3-1)-1/48*b^3*x^6*ln(-c*x^3+1)^3-1/8*b^3/c^2*ln(-c*x^3+1)^2+1/48*b^3/c^2*ln(-c*x^3+1)^3+3/4*b^2/c*Sum(-2/3*(ln(x-_alpha)*ln(-c*x^3+1)+3*c*(-1/3*ln(x-_alpha)*(ln((RootOf(_Z^2+_Z*_alpha+_alpha^2,index=1)-x+_alpha)/RootOf(_Z^2+_Z*_alpha+_alpha^2,index=1))+ln((RootOf(_Z^2+_Z*_alpha+_alpha^2,index=2)-x+_alpha)/RootOf(_Z^2+_Z*_alpha+_alpha^2,index=2))+ln(1/2*(x+_alpha)/_alpha))/c-1/3*(dilog((RootOf(_Z^2+_Z*_alpha+_alpha^2,index=1)-x+_alpha)/RootOf(_Z^2+_Z*_alpha+_alpha^2,index=1))+dilog((RootOf(_Z^2+_Z*_alpha+_alpha^2,index=2)-x+_alpha)/RootOf(_Z^2+_Z*_alpha+_alpha^2,index=2))+dilog(1/2*(x+_alpha)/_alpha))/c))*b/c,_alpha=RootOf(_Z^3*c+1))-1/2*a*b^2/c*x^3*ln(-c*x^3+1)-1/8*b^3/c^2+1/2/c*a^2*b*x^3","C"
126,1,295,124,0.205000," ","int(x^2*(a+b*arctanh(c*x^3))^3,x)","\frac{x^{3} a^{3}}{3}+\frac{b^{3} x^{3} \arctanh \left(c \,x^{3}\right)^{3}}{3}+\frac{b^{3} \arctanh \left(c \,x^{3}\right)^{3}}{3 c}-\frac{b^{3} \arctanh \left(c \,x^{3}\right)^{2} \ln \left(1+\frac{\left(c \,x^{3}+1\right)^{2}}{-c^{2} x^{6}+1}\right)}{c}-\frac{b^{3} \arctanh \left(c \,x^{3}\right) \polylog \left(2, -\frac{\left(c \,x^{3}+1\right)^{2}}{-c^{2} x^{6}+1}\right)}{c}+\frac{b^{3} \polylog \left(3, -\frac{\left(c \,x^{3}+1\right)^{2}}{-c^{2} x^{6}+1}\right)}{2 c}+x^{3} a \,b^{2} \arctanh \left(c \,x^{3}\right)^{2}+\frac{a \,b^{2} \arctanh \left(c \,x^{3}\right)^{2}}{c}-\frac{2 \arctanh \left(c \,x^{3}\right) \ln \left(1+\frac{\left(c \,x^{3}+1\right)^{2}}{-c^{2} x^{6}+1}\right) a \,b^{2}}{c}-\frac{\polylog \left(2, -\frac{\left(c \,x^{3}+1\right)^{2}}{-c^{2} x^{6}+1}\right) a \,b^{2}}{c}+x^{3} a^{2} b \arctanh \left(c \,x^{3}\right)+\frac{a^{2} b \ln \left(-c^{2} x^{6}+1\right)}{2 c}"," ",0,"1/3*x^3*a^3+1/3*b^3*x^3*arctanh(c*x^3)^3+1/3/c*b^3*arctanh(c*x^3)^3-1/c*b^3*arctanh(c*x^3)^2*ln(1+(c*x^3+1)^2/(-c^2*x^6+1))-1/c*b^3*arctanh(c*x^3)*polylog(2,-(c*x^3+1)^2/(-c^2*x^6+1))+1/2/c*b^3*polylog(3,-(c*x^3+1)^2/(-c^2*x^6+1))+x^3*a*b^2*arctanh(c*x^3)^2+1/c*a*b^2*arctanh(c*x^3)^2-2/c*arctanh(c*x^3)*ln(1+(c*x^3+1)^2/(-c^2*x^6+1))*a*b^2-1/c*polylog(2,-(c*x^3+1)^2/(-c^2*x^6+1))*a*b^2+x^3*a^2*b*arctanh(c*x^3)+1/2/c*a^2*b*ln(-c^2*x^6+1)","B"
127,0,0,196,0.222000," ","int((a+b*arctanh(c*x^3))^3/x,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{3}\right)\right)^{3}}{x}\, dx"," ",0,"int((a+b*arctanh(c*x^3))^3/x,x)","F"
128,0,0,114,0.312000," ","int((a+b*arctanh(c*x^3))^3/x^4,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{3}\right)\right)^{3}}{x^{4}}\, dx"," ",0,"int((a+b*arctanh(c*x^3))^3/x^4,x)","F"
129,0,0,126,0.327000," ","int((a+b*arctanh(c*x^3))^3/x^7,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{3}\right)\right)^{3}}{x^{7}}\, dx"," ",0,"int((a+b*arctanh(c*x^3))^3/x^7,x)","F"
130,0,0,20,0.192000," ","int((d*x)^m*(a+b*arctanh(c*x^3))^3,x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c \,x^{3}\right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x^3))^3,x)","F"
131,0,0,20,0.193000," ","int((d*x)^m*(a+b*arctanh(c*x^3))^2,x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c \,x^{3}\right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x^3))^2,x)","F"
132,0,0,72,0.183000," ","int((d*x)^m*(a+b*arctanh(c*x^3)),x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c \,x^{3}\right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x^3)),x)","F"
133,0,0,20,0.113000," ","int((d*x)^m/(a+b*arctanh(c*x^3)),x)","\int \frac{\left(d x \right)^{m}}{a +b \arctanh \left(c \,x^{3}\right)}\, dx"," ",0,"int((d*x)^m/(a+b*arctanh(c*x^3)),x)","F"
134,0,0,20,0.118000," ","int((d*x)^m/(a+b*arctanh(c*x^3))^2,x)","\int \frac{\left(d x \right)^{m}}{\left(a +b \arctanh \left(c \,x^{3}\right)\right)^{2}}\, dx"," ",0,"int((d*x)^m/(a+b*arctanh(c*x^3))^2,x)","F"
135,1,62,42,0.041000," ","int(x^3*(a+b*arctanh(c/x)),x)","\frac{x^{4} a}{4}+\frac{b \,x^{4} \arctanh \left(\frac{c}{x}\right)}{4}+\frac{b c \,x^{3}}{12}+\frac{b \,c^{3} x}{4}+\frac{c^{4} b \ln \left(\frac{c}{x}-1\right)}{8}-\frac{c^{4} b \ln \left(1+\frac{c}{x}\right)}{8}"," ",0,"1/4*x^4*a+1/4*b*x^4*arctanh(c/x)+1/12*b*c*x^3+1/4*b*c^3*x+1/8*c^4*b*ln(c/x-1)-1/8*c^4*b*ln(1+c/x)","A"
136,1,67,39,0.040000," ","int(x^2*(a+b*arctanh(c/x)),x)","\frac{x^{3} a}{3}+\frac{b \,x^{3} \arctanh \left(\frac{c}{x}\right)}{3}+\frac{b c \,x^{2}}{6}-\frac{c^{3} b \ln \left(\frac{c}{x}\right)}{3}+\frac{c^{3} b \ln \left(\frac{c}{x}-1\right)}{6}+\frac{c^{3} b \ln \left(1+\frac{c}{x}\right)}{6}"," ",0,"1/3*x^3*a+1/3*b*x^3*arctanh(c/x)+1/6*b*c*x^2-1/3*c^3*b*ln(c/x)+1/6*c^3*b*ln(c/x-1)+1/6*c^3*b*ln(1+c/x)","A"
137,1,53,33,0.037000," ","int(x*(a+b*arctanh(c/x)),x)","\frac{a \,x^{2}}{2}+\frac{\arctanh \left(\frac{c}{x}\right) b \,x^{2}}{2}+\frac{x b c}{2}+\frac{c^{2} b \ln \left(\frac{c}{x}-1\right)}{4}-\frac{c^{2} b \ln \left(1+\frac{c}{x}\right)}{4}"," ",0,"1/2*a*x^2+1/2*arctanh(c/x)*b*x^2+1/2*x*b*c+1/4*c^2*b*ln(c/x-1)-1/4*c^2*b*ln(1+c/x)","A"
138,1,48,27,0.034000," ","int(a+b*arctanh(c/x),x)","a x +b x \arctanh \left(\frac{c}{x}\right)-b c \ln \left(\frac{c}{x}\right)+\frac{b c \ln \left(\frac{c}{x}-1\right)}{2}+\frac{b c \ln \left(1+\frac{c}{x}\right)}{2}"," ",0,"a*x+b*x*arctanh(c/x)-b*c*ln(c/x)+1/2*b*c*ln(c/x-1)+1/2*b*c*ln(1+c/x)","A"
139,1,63,26,0.043000," ","int((a+b*arctanh(c/x))/x,x)","-a \ln \left(\frac{c}{x}\right)-b \ln \left(\frac{c}{x}\right) \arctanh \left(\frac{c}{x}\right)+\frac{b \dilog \left(\frac{c}{x}\right)}{2}+\frac{b \dilog \left(1+\frac{c}{x}\right)}{2}+\frac{b \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)}{2}"," ",0,"-a*ln(c/x)-b*ln(c/x)*arctanh(c/x)+1/2*b*dilog(c/x)+1/2*b*dilog(1+c/x)+1/2*b*ln(c/x)*ln(1+c/x)","B"
140,1,37,35,0.023000," ","int((a+b*arctanh(c/x))/x^2,x)","-\frac{a}{x}-\frac{b \arctanh \left(\frac{c}{x}\right)}{x}-\frac{b \ln \left(1-\frac{c^{2}}{x^{2}}\right)}{2 c}"," ",0,"-a/x-b/x*arctanh(c/x)-1/2*b*ln(1-c^2/x^2)/c","A"
141,1,57,40,0.030000," ","int((a+b*arctanh(c/x))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arctanh \left(\frac{c}{x}\right)}{2 x^{2}}-\frac{b}{2 c x}-\frac{b \ln \left(\frac{c}{x}-1\right)}{4 c^{2}}+\frac{b \ln \left(1+\frac{c}{x}\right)}{4 c^{2}}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arctanh(c/x)-1/2*b/c/x-1/4/c^2*b*ln(c/x-1)+1/4/c^2*b*ln(1+c/x)","A"
142,1,57,52,0.034000," ","int((a+b*arctanh(c/x))/x^4,x)","-\frac{a}{3 x^{3}}-\frac{b \arctanh \left(\frac{c}{x}\right)}{3 x^{3}}-\frac{b}{6 c \,x^{2}}-\frac{b \ln \left(\frac{c}{x}-1\right)}{6 c^{3}}-\frac{b \ln \left(1+\frac{c}{x}\right)}{6 c^{3}}"," ",0,"-1/3*a/x^3-1/3*b/x^3*arctanh(c/x)-1/6*b/c/x^2-1/6/c^3*b*ln(c/x-1)-1/6/c^3*b*ln(1+c/x)","A"
143,1,328,109,0.064000," ","int(x^3*(a+b*arctanh(c/x))^2,x)","\frac{a^{2} x^{4}}{4}+\frac{b^{2} x^{4} \arctanh \left(\frac{c}{x}\right)^{2}}{4}+\frac{c \,b^{2} \arctanh \left(\frac{c}{x}\right) x^{3}}{6}+\frac{c^{3} b^{2} \arctanh \left(\frac{c}{x}\right) x}{2}+\frac{c^{4} b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}-1\right)}{4}-\frac{c^{4} b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)}{4}+\frac{c^{4} b^{2} \ln \left(\frac{c}{x}-1\right)^{2}}{16}-\frac{c^{4} b^{2} \ln \left(\frac{c}{x}-1\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{8}+\frac{c^{4} b^{2} \ln \left(1+\frac{c}{x}\right)^{2}}{16}+\frac{c^{4} b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{8}-\frac{c^{4} b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(1+\frac{c}{x}\right)}{8}+\frac{b^{2} c^{2} x^{2}}{12}-\frac{2 c^{4} b^{2} \ln \left(\frac{c}{x}\right)}{3}+\frac{c^{4} b^{2} \ln \left(\frac{c}{x}-1\right)}{3}+\frac{c^{4} b^{2} \ln \left(1+\frac{c}{x}\right)}{3}+\frac{a b \,x^{4} \arctanh \left(\frac{c}{x}\right)}{2}+\frac{a b c \,x^{3}}{6}+\frac{c^{3} x a b}{2}+\frac{c^{4} a b \ln \left(\frac{c}{x}-1\right)}{4}-\frac{c^{4} a b \ln \left(1+\frac{c}{x}\right)}{4}"," ",0,"1/4*a^2*x^4+1/4*b^2*x^4*arctanh(c/x)^2+1/6*c*b^2*arctanh(c/x)*x^3+1/2*c^3*b^2*arctanh(c/x)*x+1/4*c^4*b^2*arctanh(c/x)*ln(c/x-1)-1/4*c^4*b^2*arctanh(c/x)*ln(1+c/x)+1/16*c^4*b^2*ln(c/x-1)^2-1/8*c^4*b^2*ln(c/x-1)*ln(1/2+1/2*c/x)+1/16*c^4*b^2*ln(1+c/x)^2+1/8*c^4*b^2*ln(-1/2*c/x+1/2)*ln(1/2+1/2*c/x)-1/8*c^4*b^2*ln(-1/2*c/x+1/2)*ln(1+c/x)+1/12*b^2*c^2*x^2-2/3*c^4*b^2*ln(c/x)+1/3*c^4*b^2*ln(c/x-1)+1/3*c^4*b^2*ln(1+c/x)+1/2*a*b*x^4*arctanh(c/x)+1/6*a*b*c*x^3+1/2*c^3*x*a*b+1/4*c^4*a*b*ln(c/x-1)-1/4*c^4*a*b*ln(1+c/x)","B"
144,1,391,128,0.069000," ","int(x^2*(a+b*arctanh(c/x))^2,x)","\frac{x^{3} a^{2}}{3}+\frac{b^{2} x^{3} \arctanh \left(\frac{c}{x}\right)^{2}}{3}+\frac{c \,b^{2} \arctanh \left(\frac{c}{x}\right) x^{2}}{3}-\frac{2 c^{3} b^{2} \ln \left(\frac{c}{x}\right) \arctanh \left(\frac{c}{x}\right)}{3}+\frac{c^{3} b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}-1\right)}{3}+\frac{c^{3} b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)}{3}+\frac{b^{2} c^{2} x}{3}+\frac{c^{3} b^{2} \ln \left(\frac{c}{x}-1\right)}{6}-\frac{c^{3} b^{2} \ln \left(1+\frac{c}{x}\right)}{6}+\frac{c^{3} b^{2} \ln \left(\frac{c}{x}-1\right)^{2}}{12}-\frac{c^{3} b^{2} \dilog \left(\frac{1}{2}+\frac{c}{2 x}\right)}{3}-\frac{c^{3} b^{2} \ln \left(\frac{c}{x}-1\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{6}-\frac{c^{3} b^{2} \ln \left(1+\frac{c}{x}\right)^{2}}{12}-\frac{c^{3} b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{6}+\frac{c^{3} b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(1+\frac{c}{x}\right)}{6}+\frac{c^{3} b^{2} \dilog \left(\frac{c}{x}\right)}{3}+\frac{c^{3} b^{2} \dilog \left(1+\frac{c}{x}\right)}{3}+\frac{c^{3} b^{2} \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)}{3}+\frac{2 a b \,x^{3} \arctanh \left(\frac{c}{x}\right)}{3}+\frac{a b c \,x^{2}}{3}-\frac{2 c^{3} a b \ln \left(\frac{c}{x}\right)}{3}+\frac{c^{3} a b \ln \left(\frac{c}{x}-1\right)}{3}+\frac{c^{3} a b \ln \left(1+\frac{c}{x}\right)}{3}"," ",0,"1/3*x^3*a^2+1/3*b^2*x^3*arctanh(c/x)^2+1/3*c*b^2*arctanh(c/x)*x^2-2/3*c^3*b^2*ln(c/x)*arctanh(c/x)+1/3*c^3*b^2*arctanh(c/x)*ln(c/x-1)+1/3*c^3*b^2*arctanh(c/x)*ln(1+c/x)+1/3*b^2*c^2*x+1/6*c^3*b^2*ln(c/x-1)-1/6*c^3*b^2*ln(1+c/x)+1/12*c^3*b^2*ln(c/x-1)^2-1/3*c^3*b^2*dilog(1/2+1/2*c/x)-1/6*c^3*b^2*ln(c/x-1)*ln(1/2+1/2*c/x)-1/12*c^3*b^2*ln(1+c/x)^2-1/6*c^3*b^2*ln(-1/2*c/x+1/2)*ln(1/2+1/2*c/x)+1/6*c^3*b^2*ln(-1/2*c/x+1/2)*ln(1+c/x)+1/3*c^3*b^2*dilog(c/x)+1/3*c^3*b^2*dilog(1+c/x)+1/3*c^3*b^2*ln(c/x)*ln(1+c/x)+2/3*a*b*x^3*arctanh(c/x)+1/3*a*b*c*x^2-2/3*c^3*a*b*ln(c/x)+1/3*c^3*a*b*ln(c/x-1)+1/3*c^3*a*b*ln(1+c/x)","B"
145,1,287,77,0.062000," ","int(x*(a+b*arctanh(c/x))^2,x)","\frac{a^{2} x^{2}}{2}+\frac{b^{2} x^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{2}+c \,b^{2} \arctanh \left(\frac{c}{x}\right) x +\frac{c^{2} b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}-1\right)}{2}-\frac{c^{2} b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)}{2}+\frac{c^{2} b^{2} \ln \left(\frac{c}{x}-1\right)^{2}}{8}-\frac{c^{2} b^{2} \ln \left(\frac{c}{x}-1\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{4}-c^{2} b^{2} \ln \left(\frac{c}{x}\right)+\frac{c^{2} b^{2} \ln \left(\frac{c}{x}-1\right)}{2}+\frac{c^{2} b^{2} \ln \left(1+\frac{c}{x}\right)}{2}+\frac{c^{2} b^{2} \ln \left(1+\frac{c}{x}\right)^{2}}{8}-\frac{c^{2} b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(1+\frac{c}{x}\right)}{4}+\frac{c^{2} b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{4}+a b \,x^{2} \arctanh \left(\frac{c}{x}\right)+a b c x +\frac{c^{2} a b \ln \left(\frac{c}{x}-1\right)}{2}-\frac{c^{2} a b \ln \left(1+\frac{c}{x}\right)}{2}"," ",0,"1/2*a^2*x^2+1/2*b^2*x^2*arctanh(c/x)^2+c*b^2*arctanh(c/x)*x+1/2*c^2*b^2*arctanh(c/x)*ln(c/x-1)-1/2*c^2*b^2*arctanh(c/x)*ln(1+c/x)+1/8*c^2*b^2*ln(c/x-1)^2-1/4*c^2*b^2*ln(c/x-1)*ln(1/2+1/2*c/x)-c^2*b^2*ln(c/x)+1/2*c^2*b^2*ln(c/x-1)+1/2*c^2*b^2*ln(1+c/x)+1/8*c^2*b^2*ln(1+c/x)^2-1/4*c^2*b^2*ln(-1/2*c/x+1/2)*ln(1+c/x)+1/4*c^2*b^2*ln(-1/2*c/x+1/2)*ln(1/2+1/2*c/x)+a*b*x^2*arctanh(c/x)+a*b*c*x+1/2*c^2*a*b*ln(c/x-1)-1/2*c^2*a*b*ln(1+c/x)","B"
146,1,282,77,0.059000," ","int((a+b*arctanh(c/x))^2,x)","a^{2} x +b^{2} x \arctanh \left(\frac{c}{x}\right)^{2}-2 c \,b^{2} \ln \left(\frac{c}{x}\right) \arctanh \left(\frac{c}{x}\right)+c \,b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}-1\right)+c \,b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)+\frac{c \,b^{2} \ln \left(\frac{c}{x}-1\right)^{2}}{4}-c \,b^{2} \dilog \left(\frac{1}{2}+\frac{c}{2 x}\right)-\frac{c \,b^{2} \ln \left(\frac{c}{x}-1\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{2}-\frac{c \,b^{2} \ln \left(1+\frac{c}{x}\right)^{2}}{4}+\frac{c \,b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(1+\frac{c}{x}\right)}{2}-\frac{c \,b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{2}+c \,b^{2} \dilog \left(\frac{c}{x}\right)+c \,b^{2} \dilog \left(1+\frac{c}{x}\right)+c \,b^{2} \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)+2 a b x \arctanh \left(\frac{c}{x}\right)-2 c a b \ln \left(\frac{c}{x}\right)+c a b \ln \left(\frac{c}{x}-1\right)+c a b \ln \left(1+\frac{c}{x}\right)"," ",0,"a^2*x+b^2*x*arctanh(c/x)^2-2*c*b^2*ln(c/x)*arctanh(c/x)+c*b^2*arctanh(c/x)*ln(c/x-1)+c*b^2*arctanh(c/x)*ln(1+c/x)+1/4*c*b^2*ln(c/x-1)^2-c*b^2*dilog(1/2+1/2*c/x)-1/2*c*b^2*ln(c/x-1)*ln(1/2+1/2*c/x)-1/4*c*b^2*ln(1+c/x)^2+1/2*c*b^2*ln(-1/2*c/x+1/2)*ln(1+c/x)-1/2*c*b^2*ln(-1/2*c/x+1/2)*ln(1/2+1/2*c/x)+c*b^2*dilog(c/x)+c*b^2*dilog(1+c/x)+c*b^2*ln(c/x)*ln(1+c/x)+2*a*b*x*arctanh(c/x)-2*c*a*b*ln(c/x)+c*a*b*ln(c/x-1)+c*a*b*ln(1+c/x)","B"
147,1,780,129,0.201000," ","int((a+b*arctanh(c/x))^2/x,x)","-a^{2} \ln \left(\frac{c}{x}\right)-b^{2} \ln \left(\frac{c}{x}\right) \arctanh \left(\frac{c}{x}\right)^{2}+b^{2} \arctanh \left(\frac{c}{x}\right) \polylog \left(2, -\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)-\frac{b^{2} \polylog \left(3, -\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}{2}+b^{2} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)-b^{2} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1-\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-2 b^{2} \arctanh \left(\frac{c}{x}\right) \polylog \left(2, \frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+2 b^{2} \polylog \left(3, \frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-b^{2} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1+\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-2 b^{2} \arctanh \left(\frac{c}{x}\right) \polylog \left(2, -\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+2 b^{2} \polylog \left(3, -\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{3} \arctanh \left(\frac{c}{x}\right)^{2}}{2}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{2}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{2}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \arctanh \left(\frac{c}{x}\right)^{2}}{2}-2 a b \ln \left(\frac{c}{x}\right) \arctanh \left(\frac{c}{x}\right)+a b \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)+a b \dilog \left(\frac{c}{x}\right)+a b \dilog \left(1+\frac{c}{x}\right)"," ",0,"-a^2*ln(c/x)-b^2*ln(c/x)*arctanh(c/x)^2+b^2*arctanh(c/x)*polylog(2,-(1+c/x)^2/(1-c^2/x^2))-1/2*b^2*polylog(3,-(1+c/x)^2/(1-c^2/x^2))+b^2*arctanh(c/x)^2*ln((1+c/x)^2/(1-c^2/x^2)-1)-b^2*arctanh(c/x)^2*ln(1-(1+c/x)/(1-c^2/x^2)^(1/2))-2*b^2*arctanh(c/x)*polylog(2,(1+c/x)/(1-c^2/x^2)^(1/2))+2*b^2*polylog(3,(1+c/x)/(1-c^2/x^2)^(1/2))-b^2*arctanh(c/x)^2*ln(1+(1+c/x)/(1-c^2/x^2)^(1/2))-2*b^2*arctanh(c/x)*polylog(2,-(1+c/x)/(1-c^2/x^2)^(1/2))+2*b^2*polylog(3,-(1+c/x)/(1-c^2/x^2)^(1/2))-1/2*I*b^2*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1))*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))*arctanh(c/x)^2+1/2*I*b^2*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2+1/2*I*b^2*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2-1/2*I*b^2*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^3*arctanh(c/x)^2-2*a*b*ln(c/x)*arctanh(c/x)+a*b*ln(c/x)*ln(1+c/x)+a*b*dilog(c/x)+a*b*dilog(1+c/x)","C"
148,1,144,87,0.181000," ","int((a+b*arctanh(c/x))^2/x^2,x)","-\frac{a^{2}}{x}-\frac{b^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{x}-\frac{b^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{c}+\frac{2 \arctanh \left(\frac{c}{x}\right) \ln \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right) b^{2}}{c}+\frac{\polylog \left(2, -\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right) b^{2}}{c}-\frac{2 a b \arctanh \left(\frac{c}{x}\right)}{x}-\frac{a b \ln \left(1-\frac{c^{2}}{x^{2}}\right)}{c}"," ",0,"-a^2/x-1/x*b^2*arctanh(c/x)^2-1/c*b^2*arctanh(c/x)^2+2/c*arctanh(c/x)*ln(1+(1+c/x)^2/(1-c^2/x^2))*b^2+1/c*polylog(2,-(1+c/x)^2/(1-c^2/x^2))*b^2-2/x*a*b*arctanh(c/x)-1/c*a*b*ln(1-c^2/x^2)","A"
149,1,284,81,0.051000," ","int((a+b*arctanh(c/x))^2/x^3,x)","-\frac{a^{2}}{2 x^{2}}-\frac{b^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{2 x^{2}}-\frac{b^{2} \arctanh \left(\frac{c}{x}\right)}{c x}-\frac{b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}-1\right)}{2 c^{2}}+\frac{b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)}{2 c^{2}}-\frac{b^{2} \ln \left(\frac{c}{x}-1\right)^{2}}{8 c^{2}}+\frac{b^{2} \ln \left(\frac{c}{x}-1\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{4 c^{2}}-\frac{b^{2} \ln \left(\frac{c}{x}-1\right)}{2 c^{2}}-\frac{b^{2} \ln \left(1+\frac{c}{x}\right)}{2 c^{2}}-\frac{b^{2} \ln \left(1+\frac{c}{x}\right)^{2}}{8 c^{2}}-\frac{b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{4 c^{2}}+\frac{b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(1+\frac{c}{x}\right)}{4 c^{2}}-\frac{a b \arctanh \left(\frac{c}{x}\right)}{x^{2}}-\frac{a b}{c x}-\frac{a b \ln \left(\frac{c}{x}-1\right)}{2 c^{2}}+\frac{a b \ln \left(1+\frac{c}{x}\right)}{2 c^{2}}"," ",0,"-1/2*a^2/x^2-1/2/x^2*b^2*arctanh(c/x)^2-1/c*b^2*arctanh(c/x)/x-1/2/c^2*b^2*arctanh(c/x)*ln(c/x-1)+1/2/c^2*b^2*arctanh(c/x)*ln(1+c/x)-1/8/c^2*b^2*ln(c/x-1)^2+1/4/c^2*b^2*ln(c/x-1)*ln(1/2+1/2*c/x)-1/2/c^2*b^2*ln(c/x-1)-1/2/c^2*b^2*ln(1+c/x)-1/8/c^2*b^2*ln(1+c/x)^2-1/4/c^2*b^2*ln(-1/2*c/x+1/2)*ln(1/2+1/2*c/x)+1/4/c^2*b^2*ln(-1/2*c/x+1/2)*ln(1+c/x)-a*b/x^2*arctanh(c/x)-a*b/c/x-1/2/c^2*a*b*ln(c/x-1)+1/2/c^2*a*b*ln(1+c/x)","B"
150,1,1410,189,0.707000," ","int(x^3*(a+b*arctanh(c/x))^3,x)","\frac{3 c^{4} a^{2} b \ln \left(\frac{c}{x}-1\right)}{8}-\frac{3 c^{4} a^{2} b \ln \left(1+\frac{c}{x}\right)}{8}+\frac{3 c^{4} a \,b^{2} \ln \left(\frac{c}{x}-1\right)^{2}}{16}-2 c^{4} a \,b^{2} \ln \left(\frac{c}{x}\right)+\frac{3 c^{4} a \,b^{2} \ln \left(1+\frac{c}{x}\right)^{2}}{16}-\frac{c^{4} b^{3} \sqrt{1-\frac{c^{2}}{x^{2}}}}{4 \left(\sqrt{1-\frac{c^{2}}{x^{2}}}+\frac{c}{x}+1\right)}+c^{4} a \,b^{2} \ln \left(\frac{c}{x}-1\right)+c^{4} a \,b^{2} \ln \left(1+\frac{c}{x}\right)+\frac{3 c^{3} x \,a^{2} b}{4}+\frac{c \,a^{2} b \,x^{3}}{4}+\frac{c^{2} a \,b^{2} x^{2}}{4}-\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right) \arctanh \left(\frac{c}{x}\right)^{2}}{16}+\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right)^{3} \arctanh \left(\frac{c}{x}\right)^{2}}{16}+\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right)^{3} \arctanh \left(\frac{c}{x}\right)^{2}}{16}-\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{3} \arctanh \left(\frac{c}{x}\right)^{2}}{8}+\frac{3 a \,b^{2} x^{4} \arctanh \left(\frac{c}{x}\right)^{2}}{4}+\frac{3 c^{4} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(\frac{c}{x}-1\right)}{8}-2 c^{4} b^{3} \arctanh \left(\frac{c}{x}\right) \ln \left(1+\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+\frac{3 c^{4} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)}{4}+\frac{c \,b^{3} \arctanh \left(\frac{c}{x}\right)^{2} x^{3}}{4}+\frac{3 c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} x}{4}+\frac{c^{2} b^{3} \arctanh \left(\frac{c}{x}\right) x^{2}}{4}-\frac{3 c^{4} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1+\frac{c}{x}\right)}{8}+\frac{3 a^{2} b \,x^{4} \arctanh \left(\frac{c}{x}\right)}{4}-\frac{3 i c^{4} b^{3} \pi  \arctanh \left(\frac{c}{x}\right)^{2}}{8}-\frac{3 c^{4} a \,b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)}{4}+\frac{c a \,b^{2} \arctanh \left(\frac{c}{x}\right) x^{3}}{2}+\frac{3 c^{3} a \,b^{2} \arctanh \left(\frac{c}{x}\right) x}{2}+\frac{3 c^{4} a \,b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}-1\right)}{4}+\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{8}+\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{16}+\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{8}-\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{16}+\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right) \arctanh \left(\frac{c}{x}\right)^{2}}{16}+\frac{x^{4} a^{3}}{4}+c^{4} b^{3} \arctanh \left(\frac{c}{x}\right)^{2}+\frac{b^{3} x^{4} \arctanh \left(\frac{c}{x}\right)^{3}}{4}-2 c^{4} b^{3} \dilog \left(1+\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-\frac{c^{4} b^{3} \arctanh \left(\frac{c}{x}\right)^{3}}{4}-\frac{c^{4} b^{3} \arctanh \left(\frac{c}{x}\right)}{4}+2 c^{4} b^{3} \dilog \left(\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+\frac{c^{4} b^{3} \sqrt{1-\frac{c^{2}}{x^{2}}}}{\frac{4 c}{x}+4-4 \sqrt{1-\frac{c^{2}}{x^{2}}}}-\frac{3 c^{4} a \,b^{2} \ln \left(\frac{c}{x}-1\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{8}-\frac{3 c^{4} a \,b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(1+\frac{c}{x}\right)}{8}+\frac{3 c^{4} a \,b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{8}"," ",0,"3/16*I*c^4*b^3*Pi*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))^3*arctanh(c/x)^2+3/16*I*c^4*b^3*Pi*csgn(I*(1+c/x)^2/(-1+c^2/x^2))^3*arctanh(c/x)^2+c^4*b^3*arctanh(c/x)^2-3/16*I*c^4*b^3*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*(1+c/x)^2/(-1+c^2/x^2))*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))*arctanh(c/x)^2+3/4*a*b^2*x^4*arctanh(c/x)^2+3/8*c^4*b^3*arctanh(c/x)^2*ln(c/x-1)+3/8*c^4*a^2*b*ln(c/x-1)-3/8*c^4*a^2*b*ln(1+c/x)-2*c^4*b^3*arctanh(c/x)*ln(1+(1+c/x)/(1-c^2/x^2)^(1/2))+3/4*c^4*b^3*arctanh(c/x)^2*ln((1+c/x)/(1-c^2/x^2)^(1/2))+3/16*c^4*a*b^2*ln(c/x-1)^2+1/4*c^4*b^3/(c/x+1-(1-c^2/x^2)^(1/2))*(1-c^2/x^2)^(1/2)-2*c^4*a*b^2*ln(c/x)+3/16*c^4*a*b^2*ln(1+c/x)^2+1/4*c*b^3*arctanh(c/x)^2*x^3+3/4*c^3*b^3*arctanh(c/x)^2*x+1/4*c^2*b^3*arctanh(c/x)*x^2-3/8*c^4*b^3*arctanh(c/x)^2*ln(1+c/x)-1/4*c^4*b^3/((1-c^2/x^2)^(1/2)+c/x+1)*(1-c^2/x^2)^(1/2)+c^4*a*b^2*ln(c/x-1)+c^4*a*b^2*ln(1+c/x)+3/4*c^3*x*a^2*b+1/4*c*a^2*b*x^3+1/4*c^2*a*b^2*x^2+3/4*a^2*b*x^4*arctanh(c/x)+3/16*I*c^4*b^3*Pi*csgn(I*(1+c/x)/(1-c^2/x^2)^(1/2))^2*csgn(I*(1+c/x)^2/(-1+c^2/x^2))*arctanh(c/x)^2-3/8*I*c^4*b^3*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))^3*arctanh(c/x)^2+3/8*I*c^4*b^3*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2+3/16*I*c^4*b^3*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2+3/8*I*c^4*b^3*Pi*csgn(I*(1+c/x)/(1-c^2/x^2)^(1/2))*csgn(I*(1+c/x)^2/(-1+c^2/x^2))^2*arctanh(c/x)^2+1/4*b^3*x^4*arctanh(c/x)^3-2*c^4*b^3*dilog(1+(1+c/x)/(1-c^2/x^2)^(1/2))-1/4*c^4*b^3*arctanh(c/x)^3-1/4*c^4*b^3*arctanh(c/x)-3/16*I*c^4*b^3*Pi*csgn(I*(1+c/x)^2/(-1+c^2/x^2))*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2+1/4*x^4*a^3-3/4*c^4*a*b^2*arctanh(c/x)*ln(1+c/x)-3/8*I*c^4*b^3*Pi*arctanh(c/x)^2+2*c^4*b^3*dilog((1+c/x)/(1-c^2/x^2)^(1/2))-3/8*c^4*a*b^2*ln(c/x-1)*ln(1/2+1/2*c/x)+1/2*c*a*b^2*arctanh(c/x)*x^3+3/2*c^3*a*b^2*arctanh(c/x)*x-3/8*c^4*a*b^2*ln(-1/2*c/x+1/2)*ln(1+c/x)+3/8*c^4*a*b^2*ln(-1/2*c/x+1/2)*ln(1/2+1/2*c/x)+3/4*c^4*a*b^2*arctanh(c/x)*ln(c/x-1)","C"
151,1,2033,205,0.871000," ","int(x^2*(a+b*arctanh(c/x))^3,x)","\frac{x^{3} a^{3}}{3}-\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right)^{3} \pi}{4}-c^{3} a \,b^{2} \dilog \left(\frac{1}{2}+\frac{c}{2 x}\right)-2 c^{3} b^{3} \arctanh \left(\frac{c}{x}\right) \polylog \left(2, -\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+\frac{c^{3} a^{2} b \ln \left(1+\frac{c}{x}\right)}{2}+\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right) \pi}{4}-\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \pi}{2}+\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \pi}{2}-\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{3} \pi}{2}-\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{3} \pi}{2}+\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \pi}{2}-\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right) \pi}{4}-\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right)^{2} \pi}{2}-\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right)^{2} \pi}{4}-c^{3} b^{3} \ln \left(\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}-1\right)-c^{3} b^{3} \ln \left(1+\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+\frac{c \,b^{3} \arctanh \left(\frac{c}{x}\right)^{2} x^{2}}{2}+c^{2} b^{3} \arctanh \left(\frac{c}{x}\right) x -c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1+\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+2 c^{3} b^{3} \polylog \left(3, -\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-\frac{c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2}}{2}+\frac{c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{3}}{3}+c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)+2 c^{3} b^{3} \polylog \left(3, \frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+\frac{b^{3} x^{3} \arctanh \left(\frac{c}{x}\right)^{3}}{3}+\frac{c \,a^{2} b \,x^{2}}{2}+c^{2} a \,b^{2} x -c^{3} a^{2} b \ln \left(\frac{c}{x}\right)+\frac{c^{3} a \,b^{2} \ln \left(\frac{c}{x}-1\right)^{2}}{4}-\frac{c^{3} a \,b^{2} \ln \left(1+\frac{c}{x}\right)^{2}}{4}+c^{3} a \,b^{2} \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)-\frac{c^{3} a \,b^{2} \ln \left(\frac{c}{x}-1\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{2}+\frac{c^{3} a \,b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(1+\frac{c}{x}\right)}{2}-\frac{c^{3} a \,b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{2}-\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right)^{3} \pi}{4}+a^{2} b \,x^{3} \arctanh \left(\frac{c}{x}\right)+a \,b^{2} x^{3} \arctanh \left(\frac{c}{x}\right)^{2}-c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(2\right)+c^{3} a \,b^{2} \dilog \left(\frac{c}{x}\right)+c^{3} a \,b^{2} \dilog \left(1+\frac{c}{x}\right)+\frac{c^{3} a^{2} b \ln \left(\frac{c}{x}-1\right)}{2}-c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1-\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-c^{3} b^{3} \ln \left(\frac{c}{x}\right) \arctanh \left(\frac{c}{x}\right)^{2}-2 c^{3} b^{3} \arctanh \left(\frac{c}{x}\right) \polylog \left(2, \frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)+\frac{c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(\frac{c}{x}-1\right)}{2}+\frac{c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1+\frac{c}{x}\right)}{2}-c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \pi}{2}-\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \pi}{2}+\frac{i c^{3} b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right)^{2} \pi}{4}-2 c^{3} a \,b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}\right)+c a \,b^{2} \arctanh \left(\frac{c}{x}\right) x^{2}+c^{3} a \,b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}-1\right)+c^{3} a \,b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)+\frac{c^{3} a \,b^{2} \ln \left(\frac{c}{x}-1\right)}{2}-\frac{c^{3} a \,b^{2} \ln \left(1+\frac{c}{x}\right)}{2}"," ",0,"1/3*x^3*a^3-2*c^3*a*b^2*arctanh(c/x)*ln(c/x)+1/2*c^3*a^2*b*ln(1+c/x)+1/2*c*b^3*arctanh(c/x)^2*x^2+c^2*b^3*arctanh(c/x)*x-c^3*b^3*arctanh(c/x)^2*ln(1+(1+c/x)/(1-c^2/x^2)^(1/2))-c^3*b^3*arctanh(c/x)^2*ln(1-(1+c/x)/(1-c^2/x^2)^(1/2))-1/2*I*c^3*b^3*arctanh(c/x)^2*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*Pi-1/4*I*c^3*b^3*arctanh(c/x)^2*csgn(I*(1+c/x)/(1-c^2/x^2)^(1/2))^2*csgn(I*(1+c/x)^2/(-1+c^2/x^2))*Pi-1/2*I*c^3*b^3*arctanh(c/x)^2*csgn(I*(1+c/x)/(1-c^2/x^2)^(1/2))*csgn(I*(1+c/x)^2/(-1+c^2/x^2))^2*Pi-1/4*I*c^3*b^3*arctanh(c/x)^2*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*Pi+1/4*I*c^3*b^3*arctanh(c/x)^2*csgn(I*(1+c/x)^2/(-1+c^2/x^2))*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*Pi+1/4*I*c^3*b^3*arctanh(c/x)^2*csgn(I*(1+c/x)^2/(-1+c^2/x^2))*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))*Pi+2*c^3*b^3*polylog(3,-(1+c/x)/(1-c^2/x^2)^(1/2))-c^3*b^3*ln((1+c/x)/(1-c^2/x^2)^(1/2)-1)-c^3*b^3*ln(1+(1+c/x)/(1-c^2/x^2)^(1/2))-1/2*c^3*b^3*arctanh(c/x)^2+1/3*c^3*b^3*arctanh(c/x)^3+c^3*b^3*arctanh(c/x)+2*c^3*b^3*polylog(3,(1+c/x)/(1-c^2/x^2)^(1/2))+1/3*b^3*x^3*arctanh(c/x)^3+1/2*I*c^3*b^3*arctanh(c/x)^2*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))^2*Pi-1/2*I*c^3*b^3*arctanh(c/x)^2*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^3*Pi-1/2*I*c^3*b^3*arctanh(c/x)^2*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))^3*Pi-c^3*b^3*ln(c/x)*arctanh(c/x)^2-2*c^3*b^3*arctanh(c/x)*polylog(2,(1+c/x)/(1-c^2/x^2)^(1/2))+c^3*b^3*arctanh(c/x)^2*ln((1+c/x)^2/(1-c^2/x^2)-1)+1/2*c^3*b^3*arctanh(c/x)^2*ln(c/x-1)+1/2*c^3*b^3*arctanh(c/x)^2*ln(1+c/x)-c^3*b^3*arctanh(c/x)^2*ln((1+c/x)/(1-c^2/x^2)^(1/2))+1/2*c*a^2*b*x^2+c^2*a*b^2*x+a^2*b*x^3*arctanh(c/x)+a*b^2*x^3*arctanh(c/x)^2-c^3*b^3*arctanh(c/x)^2*ln(2)-c^3*a^2*b*ln(c/x)+c^3*a*b^2*dilog(c/x)+c^3*a*b^2*dilog(1+c/x)-c^3*a*b^2*dilog(1/2+1/2*c/x)+1/4*c^3*a*b^2*ln(c/x-1)^2-1/4*c^3*a*b^2*ln(1+c/x)^2-2*c^3*b^3*arctanh(c/x)*polylog(2,-(1+c/x)/(1-c^2/x^2)^(1/2))+c^3*a*b^2*ln(c/x)*ln(1+c/x)-1/2*c^3*a*b^2*ln(c/x-1)*ln(1/2+1/2*c/x)+c*a*b^2*arctanh(c/x)*x^2+1/2*c^3*a*b^2*ln(-1/2*c/x+1/2)*ln(1+c/x)-1/2*c^3*a*b^2*ln(-1/2*c/x+1/2)*ln(1/2+1/2*c/x)+c^3*a*b^2*arctanh(c/x)*ln(c/x-1)+1/2*I*c^3*b^3*arctanh(c/x)^2*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*Pi+1/2*c^3*a^2*b*ln(c/x-1)-1/4*I*c^3*b^3*arctanh(c/x)^2*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))^3*Pi+1/2*I*c^3*b^3*arctanh(c/x)^2*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*Pi+c^3*a*b^2*arctanh(c/x)*ln(1+c/x)-1/2*I*c^3*b^3*arctanh(c/x)^2*Pi-1/4*I*c^3*b^3*arctanh(c/x)^2*csgn(I*(1+c/x)^2/(-1+c^2/x^2))^3*Pi+1/2*c^3*a*b^2*ln(c/x-1)-1/2*c^3*a*b^2*ln(1+c/x)","C"
152,1,5536,125,0.596000," ","int(x*(a+b*arctanh(c/x))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
153,1,1756,106,0.363000," ","int((a+b*arctanh(c/x))^3,x)","3 c a \,b^{2} \dilog \left(\frac{c}{x}\right)+3 c a \,b^{2} \dilog \left(1+\frac{c}{x}\right)-3 c a \,b^{2} \dilog \left(\frac{1}{2}+\frac{c}{2 x}\right)-3 c \,b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1-\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-6 c \,b^{3} \arctanh \left(\frac{c}{x}\right) \polylog \left(2, -\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-3 c \,b^{3} \ln \left(\frac{c}{x}\right) \arctanh \left(\frac{c}{x}\right)^{2}-6 c \,b^{3} \arctanh \left(\frac{c}{x}\right) \polylog \left(2, \frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+3 c \,b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)+\frac{3 c \,b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(\frac{c}{x}-1\right)}{2}+\frac{3 c \,b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1+\frac{c}{x}\right)}{2}-3 c \,b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-3 c \,b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1+\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+3 a \,b^{2} x \arctanh \left(\frac{c}{x}\right)^{2}+3 a^{2} b x \arctanh \left(\frac{c}{x}\right)-3 c \,b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(2\right)+\frac{3 c \,a^{2} b \ln \left(1+\frac{c}{x}\right)}{2}-3 c \,a^{2} b \ln \left(\frac{c}{x}\right)+\frac{3 c a \,b^{2} \ln \left(\frac{c}{x}-1\right)^{2}}{4}-\frac{3 c a \,b^{2} \ln \left(1+\frac{c}{x}\right)^{2}}{4}+\frac{3 c \,a^{2} b \ln \left(\frac{c}{x}-1\right)}{2}-\frac{3 c a \,b^{2} \ln \left(\frac{c}{x}-1\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{2}+\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right) \arctanh \left(\frac{c}{x}\right)^{2}}{4}-\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \arctanh \left(\frac{c}{x}\right)^{2}}{2}+b^{3} x \arctanh \left(\frac{c}{x}\right)^{3}+6 c \,b^{3} \polylog \left(3, \frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+6 c \,b^{3} \polylog \left(3, -\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+c \,b^{3} \arctanh \left(\frac{c}{x}\right)^{3}+\frac{3 c a \,b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(1+\frac{c}{x}\right)}{2}-\frac{3 c a \,b^{2} \ln \left(-\frac{c}{2 x}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c}{2 x}\right)}{2}-\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right)^{3} \arctanh \left(\frac{c}{x}\right)^{2}}{4}-\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right)^{3} \arctanh \left(\frac{c}{x}\right)^{2}}{4}-\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{3} \arctanh \left(\frac{c}{x}\right)^{2}}{2}+\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{2}-\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{3} \arctanh \left(\frac{c}{x}\right)^{2}}{2}+3 c a \,b^{2} \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)+\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{4}+\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{2}+\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{2}-\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right) \arctanh \left(\frac{c}{x}\right)^{2}}{4}-\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{-1+\frac{c^{2}}{x^{2}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{2}-\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(1+\frac{c}{x}\right)^{2}}{\left(-1+\frac{c^{2}}{x^{2}}\right) \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{4}+x \,a^{3}+3 c a \,b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}-1\right)+3 c a \,b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)-6 c a \,b^{2} \arctanh \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}\right)-\frac{3 i c \,b^{3} \pi  \arctanh \left(\frac{c}{x}\right)^{2}}{2}"," ",0,"3/4*I*c*b^3*Pi*csgn(I*(1+c/x)^2/(-1+c^2/x^2))*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2-3/4*I*c*b^3*Pi*csgn(I*(1+c/x)^2/(-1+c^2/x^2))^3*arctanh(c/x)^2-3/4*I*c*b^3*Pi*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))^3*arctanh(c/x)^2+3/2*I*c*b^3*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2+3/2*I*c*b^3*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2+3/2*c*a^2*b*ln(1+c/x)-3*c*b^3*arctanh(c/x)^2*ln(1+(1+c/x)/(1-c^2/x^2)^(1/2))+3*a*b^2*x*arctanh(c/x)^2+3*a^2*b*x*arctanh(c/x)-3*c*b^3*arctanh(c/x)^2*ln(2)-3*c*a^2*b*ln(c/x)+3*c*a*b^2*dilog(c/x)+3*c*a*b^2*dilog(1+c/x)-3*c*a*b^2*dilog(1/2+1/2*c/x)-3*c*b^3*arctanh(c/x)^2*ln(1-(1+c/x)/(1-c^2/x^2)^(1/2))-6*c*b^3*arctanh(c/x)*polylog(2,-(1+c/x)/(1-c^2/x^2)^(1/2))-3*c*b^3*ln(c/x)*arctanh(c/x)^2-6*c*b^3*arctanh(c/x)*polylog(2,(1+c/x)/(1-c^2/x^2)^(1/2))+3*c*b^3*arctanh(c/x)^2*ln((1+c/x)^2/(1-c^2/x^2)-1)+3/2*c*b^3*arctanh(c/x)^2*ln(c/x-1)+3/2*c*b^3*arctanh(c/x)^2*ln(1+c/x)-3*c*b^3*arctanh(c/x)^2*ln((1+c/x)/(1-c^2/x^2)^(1/2))+3/4*c*a*b^2*ln(c/x-1)^2-3/4*c*a*b^2*ln(1+c/x)^2+3/2*c*a^2*b*ln(c/x-1)-3/2*c*a*b^2*ln(c/x-1)*ln(1/2+1/2*c/x)+3/4*I*c*b^3*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*(1+c/x)^2/(-1+c^2/x^2))*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))*arctanh(c/x)^2+b^3*x*arctanh(c/x)^3+6*c*b^3*polylog(3,(1+c/x)/(1-c^2/x^2)^(1/2))+6*c*b^3*polylog(3,-(1+c/x)/(1-c^2/x^2)^(1/2))+c*b^3*arctanh(c/x)^3-3/4*I*c*b^3*Pi*csgn(I*(1+c/x)/(1-c^2/x^2)^(1/2))^2*csgn(I*(1+c/x)^2/(-1+c^2/x^2))*arctanh(c/x)^2-3/2*I*c*b^3*Pi*csgn(I*(1+c/x)/(1-c^2/x^2)^(1/2))*csgn(I*(1+c/x)^2/(-1+c^2/x^2))^2*arctanh(c/x)^2-3/4*I*c*b^3*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*(1+c/x)^2/(-1+c^2/x^2)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2-3/2*I*c*b^3*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1))*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))*arctanh(c/x)^2+3/2*c*a*b^2*ln(-1/2*c/x+1/2)*ln(1+c/x)-3/2*c*a*b^2*ln(-1/2*c/x+1/2)*ln(1/2+1/2*c/x)-3/2*I*c*b^3*Pi*arctanh(c/x)^2-3/2*I*c*b^3*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))^3*arctanh(c/x)^2+3/2*I*c*b^3*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2-3/2*I*c*b^3*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^3*arctanh(c/x)^2+3*c*a*b^2*arctanh(c/x)*ln(c/x-1)+3*c*a*b^2*arctanh(c/x)*ln(1+c/x)-6*c*a*b^2*arctanh(c/x)*ln(c/x)+3*c*a*b^2*ln(c/x)*ln(1+c/x)+x*a^3","C"
154,1,1631,196,0.129000," ","int((a+b*arctanh(c/x))^3/x,x)","-3 a \,b^{2} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1+\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-6 a \,b^{2} \arctanh \left(\frac{c}{x}\right) \polylog \left(2, -\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-3 a \,b^{2} \ln \left(\frac{c}{x}\right) \arctanh \left(\frac{c}{x}\right)^{2}-3 a^{2} b \ln \left(\frac{c}{x}\right) \arctanh \left(\frac{c}{x}\right)+3 a \,b^{2} \arctanh \left(\frac{c}{x}\right) \polylog \left(2, -\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)+3 a \,b^{2} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)-3 a \,b^{2} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1-\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-6 a \,b^{2} \arctanh \left(\frac{c}{x}\right) \polylog \left(2, \frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+\frac{3 a^{2} b \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{c}{x}\right)}{2}-\frac{3 i a \,b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{3} \arctanh \left(\frac{c}{x}\right)^{2}}{2}+\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{3}}{2}+\frac{i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{3}}{2}-6 b^{3} \polylog \left(4, -\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+\frac{3 b^{3} \polylog \left(4, -\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}{4}+\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{2}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \arctanh \left(\frac{c}{x}\right)^{3}}{2}-3 b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \polylog \left(2, -\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+6 b^{3} \arctanh \left(\frac{c}{x}\right) \polylog \left(3, -\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+\frac{3 a^{2} b \dilog \left(\frac{c}{x}\right)}{2}+\frac{3 a^{2} b \dilog \left(1+\frac{c}{x}\right)}{2}+6 a \,b^{2} \polylog \left(3, -\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-\frac{3 a \,b^{2} \polylog \left(3, -\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}{2}+6 a \,b^{2} \polylog \left(3, \frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-b^{3} \ln \left(\frac{c}{x}\right) \arctanh \left(\frac{c}{x}\right)^{3}+b^{3} \arctanh \left(\frac{c}{x}\right)^{3} \ln \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)+\frac{3 b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \polylog \left(2, -\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}{2}-\frac{3 b^{3} \arctanh \left(\frac{c}{x}\right) \polylog \left(3, -\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}{2}-b^{3} \arctanh \left(\frac{c}{x}\right)^{3} \ln \left(1-\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-3 b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \polylog \left(2, \frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)+6 b^{3} \arctanh \left(\frac{c}{x}\right) \polylog \left(3, \frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-b^{3} \arctanh \left(\frac{c}{x}\right)^{3} \ln \left(1+\frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \arctanh \left(\frac{c}{x}\right)^{2}}{2}+\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{2}-a^{3} \ln \left(\frac{c}{x}\right)-6 b^{3} \polylog \left(4, \frac{1+\frac{c}{x}}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)-\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}-1\right)}{1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}}\right)^{3} \arctanh \left(\frac{c}{x}\right)^{3}}{2}"," ",0,"-3*a*b^2*arctanh(c/x)^2*ln(1+(1+c/x)/(1-c^2/x^2)^(1/2))-6*a*b^2*arctanh(c/x)*polylog(2,-(1+c/x)/(1-c^2/x^2)^(1/2))-3*a*b^2*ln(c/x)*arctanh(c/x)^2-3*a^2*b*ln(c/x)*arctanh(c/x)+3/2*a^2*b*ln(c/x)*ln(1+c/x)+3*a*b^2*arctanh(c/x)*polylog(2,-(1+c/x)^2/(1-c^2/x^2))+3*a*b^2*arctanh(c/x)^2*ln((1+c/x)^2/(1-c^2/x^2)-1)-3*a*b^2*arctanh(c/x)^2*ln(1-(1+c/x)/(1-c^2/x^2)^(1/2))-6*a*b^2*arctanh(c/x)*polylog(2,(1+c/x)/(1-c^2/x^2)^(1/2))-3/2*I*a*b^2*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^3*arctanh(c/x)^2+1/2*I*b^3*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^3+1/2*I*b^3*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^3+3/2*I*a*b^2*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2-1/2*I*b^3*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1))*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))*arctanh(c/x)^3+3/2*I*a*b^2*Pi*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^2*arctanh(c/x)^2+6*a*b^2*polylog(3,(1+c/x)/(1-c^2/x^2)^(1/2))-b^3*ln(c/x)*arctanh(c/x)^3+b^3*arctanh(c/x)^3*ln((1+c/x)^2/(1-c^2/x^2)-1)+3/2*b^3*arctanh(c/x)^2*polylog(2,-(1+c/x)^2/(1-c^2/x^2))-3/2*b^3*arctanh(c/x)*polylog(3,-(1+c/x)^2/(1-c^2/x^2))-b^3*arctanh(c/x)^3*ln(1-(1+c/x)/(1-c^2/x^2)^(1/2))-3*b^3*arctanh(c/x)^2*polylog(2,(1+c/x)/(1-c^2/x^2)^(1/2))+6*b^3*arctanh(c/x)*polylog(3,(1+c/x)/(1-c^2/x^2)^(1/2))-b^3*arctanh(c/x)^3*ln(1+(1+c/x)/(1-c^2/x^2)^(1/2))-3*b^3*arctanh(c/x)^2*polylog(2,-(1+c/x)/(1-c^2/x^2)^(1/2))+6*b^3*arctanh(c/x)*polylog(3,-(1+c/x)/(1-c^2/x^2)^(1/2))+3/2*a^2*b*dilog(c/x)+3/2*a^2*b*dilog(1+c/x)+6*a*b^2*polylog(3,-(1+c/x)/(1-c^2/x^2)^(1/2))-3/2*a*b^2*polylog(3,-(1+c/x)^2/(1-c^2/x^2))-3/2*I*a*b^2*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1))*csgn(I/(1+(1+c/x)^2/(1-c^2/x^2)))*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))*arctanh(c/x)^2-1/2*I*b^3*Pi*csgn(I*((1+c/x)^2/(1-c^2/x^2)-1)/(1+(1+c/x)^2/(1-c^2/x^2)))^3*arctanh(c/x)^3-6*b^3*polylog(4,-(1+c/x)/(1-c^2/x^2)^(1/2))-a^3*ln(c/x)+3/4*b^3*polylog(4,-(1+c/x)^2/(1-c^2/x^2))-6*b^3*polylog(4,(1+c/x)/(1-c^2/x^2)^(1/2))","C"
155,1,298,124,0.209000," ","int((a+b*arctanh(c/x))^3/x^2,x)","-\frac{a^{3}}{x}-\frac{b^{3} \arctanh \left(\frac{c}{x}\right)^{3}}{x}-\frac{b^{3} \arctanh \left(\frac{c}{x}\right)^{3}}{c}+\frac{3 b^{3} \arctanh \left(\frac{c}{x}\right)^{2} \ln \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}{c}+\frac{3 b^{3} \arctanh \left(\frac{c}{x}\right) \polylog \left(2, -\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}{c}-\frac{3 b^{3} \polylog \left(3, -\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right)}{2 c}-\frac{3 a \,b^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{x}-\frac{3 a \,b^{2} \arctanh \left(\frac{c}{x}\right)^{2}}{c}+\frac{6 \arctanh \left(\frac{c}{x}\right) \ln \left(1+\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right) a \,b^{2}}{c}+\frac{3 \polylog \left(2, -\frac{\left(1+\frac{c}{x}\right)^{2}}{1-\frac{c^{2}}{x^{2}}}\right) a \,b^{2}}{c}-\frac{3 a^{2} b \arctanh \left(\frac{c}{x}\right)}{x}-\frac{3 a^{2} b \ln \left(1-\frac{c^{2}}{x^{2}}\right)}{2 c}"," ",0,"-a^3/x-b^3/x*arctanh(c/x)^3-1/c*b^3*arctanh(c/x)^3+3/c*b^3*arctanh(c/x)^2*ln(1+(1+c/x)^2/(1-c^2/x^2))+3/c*b^3*arctanh(c/x)*polylog(2,-(1+c/x)^2/(1-c^2/x^2))-3/2/c*b^3*polylog(3,-(1+c/x)^2/(1-c^2/x^2))-3/x*a*b^2*arctanh(c/x)^2-3/c*a*b^2*arctanh(c/x)^2+6/c*arctanh(c/x)*ln(1+(1+c/x)^2/(1-c^2/x^2))*a*b^2+3/c*polylog(2,-(1+c/x)^2/(1-c^2/x^2))*a*b^2-3/x*a^2*b*arctanh(c/x)-3/2/c*a^2*b*ln(1-c^2/x^2)","B"
156,1,6645,129,0.565000," ","int((a+b*arctanh(c/x))^3/x^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
157,1,64,46,0.043000," ","int(x^7*(a+b*arctanh(c/x^2)),x)","\frac{x^{8} a}{8}+\frac{b \,x^{8} \arctanh \left(\frac{c}{x^{2}}\right)}{8}+\frac{b c \,x^{6}}{24}+\frac{b \,c^{3} x^{2}}{8}-\frac{b \,c^{4} \ln \left(1+\frac{c}{x^{2}}\right)}{16}+\frac{b \,c^{4} \ln \left(\frac{c}{x^{2}}-1\right)}{16}"," ",0,"1/8*x^8*a+1/8*b*x^8*arctanh(c/x^2)+1/24*b*c*x^6+1/8*b*c^3*x^2-1/16*b*c^4*ln(1+c/x^2)+1/16*b*c^4*ln(c/x^2-1)","A"
158,1,65,39,0.061000," ","int(x^5*(a+b*arctanh(c/x^2)),x)","\frac{x^{6} a}{6}+\frac{b \,x^{6} \arctanh \left(\frac{c}{x^{2}}\right)}{6}+\frac{b c \,x^{4}}{12}-\frac{b \,c^{3} \ln \left(\frac{1}{x}\right)}{3}+\frac{b \,c^{3} \ln \left(1+\frac{c}{x^{2}}\right)}{12}+\frac{b \,c^{3} \ln \left(\frac{c}{x^{2}}-1\right)}{12}"," ",0,"1/6*x^6*a+1/6*b*x^6*arctanh(c/x^2)+1/12*b*c*x^4-1/3*b*c^3*ln(1/x)+1/12*b*c^3*ln(1+c/x^2)+1/12*b*c^3*ln(c/x^2-1)","A"
159,1,55,37,0.040000," ","int(x^3*(a+b*arctanh(c/x^2)),x)","\frac{x^{4} a}{4}+\frac{\arctanh \left(\frac{c}{x^{2}}\right) b \,x^{4}}{4}+\frac{b c \,x^{2}}{4}-\frac{b \,c^{2} \ln \left(1+\frac{c}{x^{2}}\right)}{8}+\frac{b \,c^{2} \ln \left(\frac{c}{x^{2}}-1\right)}{8}"," ",0,"1/4*x^4*a+1/4*arctanh(c/x^2)*b*x^4+1/4*b*c*x^2-1/8*b*c^2*ln(1+c/x^2)+1/8*b*c^2*ln(c/x^2-1)","A"
160,1,52,30,0.057000," ","int(x*(a+b*arctanh(c/x^2)),x)","\frac{a \,x^{2}}{2}+\frac{b \,x^{2} \arctanh \left(\frac{c}{x^{2}}\right)}{2}-b c \ln \left(\frac{1}{x}\right)+\frac{b c \ln \left(1+\frac{c}{x^{2}}\right)}{4}+\frac{b c \ln \left(\frac{c}{x^{2}}-1\right)}{4}"," ",0,"1/2*a*x^2+1/2*b*x^2*arctanh(c/x^2)-b*c*ln(1/x)+1/4*b*c*ln(1+c/x^2)+1/4*b*c*ln(c/x^2-1)","A"
161,1,154,26,0.058000," ","int((a+b*arctanh(c/x^2))/x,x)","-a \ln \left(\frac{1}{x}\right)-b \ln \left(\frac{1}{x}\right) \arctanh \left(\frac{c}{x^{2}}\right)+\frac{b \ln \left(\frac{1}{x}\right) \ln \left(1+\frac{\sqrt{-c}}{x}\right)}{2}+\frac{b \ln \left(\frac{1}{x}\right) \ln \left(1-\frac{\sqrt{-c}}{x}\right)}{2}+\frac{b \dilog \left(1+\frac{\sqrt{-c}}{x}\right)}{2}+\frac{b \dilog \left(1-\frac{\sqrt{-c}}{x}\right)}{2}-\frac{b \ln \left(\frac{1}{x}\right) \ln \left(1-\frac{\sqrt{c}}{x}\right)}{2}-\frac{b \ln \left(\frac{1}{x}\right) \ln \left(1+\frac{\sqrt{c}}{x}\right)}{2}-\frac{b \dilog \left(1-\frac{\sqrt{c}}{x}\right)}{2}-\frac{b \dilog \left(1+\frac{\sqrt{c}}{x}\right)}{2}"," ",0,"-a*ln(1/x)-b*ln(1/x)*arctanh(c/x^2)+1/2*b*ln(1/x)*ln(1+(-c)^(1/2)/x)+1/2*b*ln(1/x)*ln(1-(-c)^(1/2)/x)+1/2*b*dilog(1+(-c)^(1/2)/x)+1/2*b*dilog(1-(-c)^(1/2)/x)-1/2*b*ln(1/x)*ln(1-1/x*c^(1/2))-1/2*b*ln(1/x)*ln(1+1/x*c^(1/2))-1/2*b*dilog(1-1/x*c^(1/2))-1/2*b*dilog(1+1/x*c^(1/2))","B"
162,1,37,36,0.023000," ","int((a+b*arctanh(c/x^2))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arctanh \left(\frac{c}{x^{2}}\right)}{2 x^{2}}-\frac{b \ln \left(1-\frac{c^{2}}{x^{4}}\right)}{4 c}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arctanh(c/x^2)-1/4*b*ln(1-c^2/x^4)/c","A"
163,1,57,42,0.038000," ","int((a+b*arctanh(c/x^2))/x^5,x)","-\frac{a}{4 x^{4}}-\frac{b \arctanh \left(\frac{c}{x^{2}}\right)}{4 x^{4}}-\frac{b}{4 c \,x^{2}}+\frac{b \ln \left(1+\frac{c}{x^{2}}\right)}{8 c^{2}}-\frac{b \ln \left(\frac{c}{x^{2}}-1\right)}{8 c^{2}}"," ",0,"-1/4*a/x^4-1/4*b/x^4*arctanh(c/x^2)-1/4*b/c/x^2+1/8*b/c^2*ln(1+c/x^2)-1/8*b/c^2*ln(c/x^2-1)","A"
164,1,45,52,0.037000," ","int((a+b*arctanh(c/x^2))/x^7,x)","-\frac{a}{6 x^{6}}-\frac{b \arctanh \left(\frac{c}{x^{2}}\right)}{6 x^{6}}-\frac{b}{12 c \,x^{4}}-\frac{b \ln \left(\frac{c^{2}}{x^{4}}-1\right)}{12 c^{3}}"," ",0,"-1/6*a/x^6-1/6*b/x^6*arctanh(c/x^2)-1/12*b/c/x^4-1/12*b/c^3*ln(c^2/x^4-1)","A"
165,1,53,47,0.042000," ","int(x^4*(a+b*arctanh(c/x^2)),x)","\frac{a \,x^{5}}{5}+\frac{b \,x^{5} \arctanh \left(\frac{c}{x^{2}}\right)}{5}+\frac{2 b c \,x^{3}}{15}+\frac{b \,c^{\frac{5}{2}} \arctan \left(\frac{x}{\sqrt{c}}\right)}{5}-\frac{b \,c^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{c}}{x}\right)}{5}"," ",0,"1/5*a*x^5+1/5*b*x^5*arctanh(c/x^2)+2/15*b*c*x^3+1/5*b*c^(5/2)*arctan(x/c^(1/2))-1/5*b*c^(5/2)*arctanh(1/x*c^(1/2))","A"
166,1,51,45,0.040000," ","int(x^2*(a+b*arctanh(c/x^2)),x)","\frac{x^{3} a}{3}+\frac{b \,x^{3} \arctanh \left(\frac{c}{x^{2}}\right)}{3}+\frac{2 x b c}{3}-\frac{b \,c^{\frac{3}{2}} \arctan \left(\frac{x}{\sqrt{c}}\right)}{3}-\frac{b \,c^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{c}}{x}\right)}{3}"," ",0,"1/3*x^3*a+1/3*b*x^3*arctanh(c/x^2)+2/3*x*b*c-1/3*b*c^(3/2)*arctan(x/c^(1/2))-1/3*b*c^(3/2)*arctanh(1/x*c^(1/2))","A"
167,1,39,36,0.036000," ","int(a+b*arctanh(c/x^2),x)","a x +b x \arctanh \left(\frac{c}{x^{2}}\right)-\arctanh \left(\frac{\sqrt{c}}{x}\right) \sqrt{c}\, b +b \arctan \left(\frac{x}{\sqrt{c}}\right) \sqrt{c}"," ",0,"a*x+b*x*arctanh(c/x^2)-arctanh(1/x*c^(1/2))*c^(1/2)*b+b*arctan(x/c^(1/2))*c^(1/2)","A"
168,1,44,40,0.037000," ","int((a+b*arctanh(c/x^2))/x^2,x)","-\frac{a}{x}-\frac{b \arctanh \left(\frac{c}{x^{2}}\right)}{x}+\frac{b \arctan \left(\frac{x}{\sqrt{c}}\right)}{\sqrt{c}}+\frac{b \arctanh \left(\frac{\sqrt{c}}{x}\right)}{\sqrt{c}}"," ",0,"-a/x-b/x*arctanh(c/x^2)+b*arctan(x/c^(1/2))/c^(1/2)+b/c^(1/2)*arctanh(1/x*c^(1/2))","A"
169,1,55,52,0.039000," ","int((a+b*arctanh(c/x^2))/x^4,x)","-\frac{a}{3 x^{3}}-\frac{b \arctanh \left(\frac{c}{x^{2}}\right)}{3 x^{3}}-\frac{2 b}{3 c x}-\frac{b \arctan \left(\frac{x}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}+\frac{b \arctanh \left(\frac{\sqrt{c}}{x}\right)}{3 c^{\frac{3}{2}}}"," ",0,"-1/3*a/x^3-1/3*b/x^3*arctanh(c/x^2)-2/3*b/c/x-1/3*b*arctan(x/c^(1/2))/c^(3/2)+1/3*b/c^(3/2)*arctanh(1/x*c^(1/2))","A"
170,1,55,52,0.040000," ","int((a+b*arctanh(c/x^2))/x^6,x)","-\frac{a}{5 x^{5}}-\frac{b \arctanh \left(\frac{c}{x^{2}}\right)}{5 x^{5}}-\frac{2 b}{15 c \,x^{3}}+\frac{b \arctan \left(\frac{x}{\sqrt{c}}\right)}{5 c^{\frac{5}{2}}}+\frac{b \arctanh \left(\frac{\sqrt{c}}{x}\right)}{5 c^{\frac{5}{2}}}"," ",0,"-1/5*a/x^5-1/5*b/x^5*arctanh(c/x^2)-2/15*b/c/x^3+1/5*b*arctan(x/c^(1/2))/c^(5/2)+1/5*b/c^(5/2)*arctanh(1/x*c^(1/2))","A"
171,-2,0,86,180.000000," ","int(x^3*(a+b*arctanh(c/x^2))^2,x)","\int x^{3} \left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}\, dx"," ",0,"int(x^3*(a+b*arctanh(c/x^2))^2,x)","F"
172,-2,0,88,180.000000," ","int(x*(a+b*arctanh(c/x^2))^2,x)","\int x \left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}\, dx"," ",0,"int(x*(a+b*arctanh(c/x^2))^2,x)","F"
173,0,0,135,0.711000," ","int((a+b*arctanh(c/x^2))^2/x,x)","\int \frac{\left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}}{x}\, dx"," ",0,"int((a+b*arctanh(c/x^2))^2/x,x)","F"
174,1,144,93,0.193000," ","int((a+b*arctanh(c/x^2))^2/x^3,x)","-\frac{a^{2}}{2 x^{2}}-\frac{b^{2} \arctanh \left(\frac{c}{x^{2}}\right)^{2}}{2 x^{2}}-\frac{b^{2} \arctanh \left(\frac{c}{x^{2}}\right)^{2}}{2 c}+\frac{\arctanh \left(\frac{c}{x^{2}}\right) \ln \left(1+\frac{\left(1+\frac{c}{x^{2}}\right)^{2}}{1-\frac{c^{2}}{x^{4}}}\right) b^{2}}{c}+\frac{\polylog \left(2, -\frac{\left(1+\frac{c}{x^{2}}\right)^{2}}{1-\frac{c^{2}}{x^{4}}}\right) b^{2}}{2 c}-\frac{a b \arctanh \left(\frac{c}{x^{2}}\right)}{x^{2}}-\frac{a b \ln \left(1-\frac{c^{2}}{x^{4}}\right)}{2 c}"," ",0,"-1/2*a^2/x^2-1/2/x^2*b^2*arctanh(c/x^2)^2-1/2/c*b^2*arctanh(c/x^2)^2+1/c*arctanh(c/x^2)*ln(1+(1+c/x^2)^2/(1-c^2/x^4))*b^2+1/2/c*polylog(2,-(1+c/x^2)^2/(1-c^2/x^4))*b^2-1/x^2*a*b*arctanh(c/x^2)-1/2/c*a*b*ln(1-c^2/x^4)","A"
175,-1,0,87,180.000000," ","int((a+b*arctanh(c/x^2))^2/x^5,x)","\int \frac{\left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}}{x^{5}}\, dx"," ",0,"int((a+b*arctanh(c/x^2))^2/x^5,x)","F"
176,0,0,933,1.013000," ","int(x^4*(a+b*arctanh(c/x^2))^2,x)","\int x^{4} \left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}\, dx"," ",0,"int(x^4*(a+b*arctanh(c/x^2))^2,x)","F"
177,0,0,895,0.843000," ","int(x^2*(a+b*arctanh(c/x^2))^2,x)","\int x^{2} \left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}\, dx"," ",0,"int(x^2*(a+b*arctanh(c/x^2))^2,x)","F"
178,0,0,1208,0.767000," ","int((a+b*arctanh(c/x^2))^2,x)","\int \left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}\, dx"," ",0,"int((a+b*arctanh(c/x^2))^2,x)","F"
179,0,0,918,0.888000," ","int((a+b*arctanh(c/x^2))^2/x^2,x)","\int \frac{\left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}}{x^{2}}\, dx"," ",0,"int((a+b*arctanh(c/x^2))^2/x^2,x)","F"
180,0,0,978,0.832000," ","int((a+b*arctanh(c/x^2))^2/x^4,x)","\int \frac{\left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}}{x^{4}}\, dx"," ",0,"int((a+b*arctanh(c/x^2))^2/x^4,x)","F"
181,0,0,1044,0.932000," ","int((a+b*arctanh(c/x^2))^2/x^6,x)","\int \frac{\left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}}{x^{6}}\, dx"," ",0,"int((a+b*arctanh(c/x^2))^2/x^6,x)","F"
182,0,0,20,0.921000," ","int((d*x)^m*(a+b*arctanh(c/x^2))^3,x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c/x^2))^3,x)","F"
183,0,0,20,0.405000," ","int((d*x)^m*(a+b*arctanh(c/x^2))^2,x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c/x^2))^2,x)","F"
184,0,0,69,0.311000," ","int((d*x)^m*(a+b*arctanh(c/x^2)),x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c/x^2)),x)","F"
185,0,0,20,0.181000," ","int((d*x)^m/(a+b*arctanh(c/x^2)),x)","\int \frac{\left(d x \right)^{m}}{a +b \arctanh \left(\frac{c}{x^{2}}\right)}\, dx"," ",0,"int((d*x)^m/(a+b*arctanh(c/x^2)),x)","F"
186,0,0,20,0.203000," ","int((d*x)^m/(a+b*arctanh(c/x^2))^2,x)","\int \frac{\left(d x \right)^{m}}{\left(a +b \arctanh \left(\frac{c}{x^{2}}\right)\right)^{2}}\, dx"," ",0,"int((d*x)^m/(a+b*arctanh(c/x^2))^2,x)","F"
187,1,84,64,0.030000," ","int(x^3*(a+b*arctanh(c*x^(1/2))),x)","\frac{x^{4} a}{4}+\frac{b \,x^{4} \arctanh \left(c \sqrt{x}\right)}{4}+\frac{b \,x^{\frac{7}{2}}}{28 c}+\frac{b \,x^{\frac{5}{2}}}{20 c^{3}}+\frac{b \,x^{\frac{3}{2}}}{12 c^{5}}+\frac{b \sqrt{x}}{4 c^{7}}+\frac{b \ln \left(c \sqrt{x}-1\right)}{8 c^{8}}-\frac{b \ln \left(1+c \sqrt{x}\right)}{8 c^{8}}"," ",0,"1/4*x^4*a+1/4*b*x^4*arctanh(c*x^(1/2))+1/28*b*x^(7/2)/c+1/20*b*x^(5/2)/c^3+1/12*b*x^(3/2)/c^5+1/4*b*x^(1/2)/c^7+1/8/c^8*b*ln(c*x^(1/2)-1)-1/8/c^8*b*ln(1+c*x^(1/2))","A"
188,1,75,55,0.030000," ","int(x^2*(a+b*arctanh(c*x^(1/2))),x)","\frac{x^{3} a}{3}+\frac{b \,x^{3} \arctanh \left(c \sqrt{x}\right)}{3}+\frac{b \,x^{\frac{5}{2}}}{15 c}+\frac{b \,x^{\frac{3}{2}}}{9 c^{3}}+\frac{b \sqrt{x}}{3 c^{5}}+\frac{b \ln \left(c \sqrt{x}-1\right)}{6 c^{6}}-\frac{b \ln \left(1+c \sqrt{x}\right)}{6 c^{6}}"," ",0,"1/3*x^3*a+1/3*b*x^3*arctanh(c*x^(1/2))+1/15*b*x^(5/2)/c+1/9*b*x^(3/2)/c^3+1/3*b*x^(1/2)/c^5+1/6/c^6*b*ln(c*x^(1/2)-1)-1/6/c^6*b*ln(1+c*x^(1/2))","A"
189,1,66,46,0.029000," ","int(x*(a+b*arctanh(c*x^(1/2))),x)","\frac{a \,x^{2}}{2}+\frac{b \,x^{2} \arctanh \left(c \sqrt{x}\right)}{2}+\frac{b \,x^{\frac{3}{2}}}{6 c}+\frac{b \sqrt{x}}{2 c^{3}}+\frac{b \ln \left(c \sqrt{x}-1\right)}{4 c^{4}}-\frac{b \ln \left(1+c \sqrt{x}\right)}{4 c^{4}}"," ",0,"1/2*a*x^2+1/2*b*x^2*arctanh(c*x^(1/2))+1/6*b*x^(3/2)/c+1/2*b*x^(1/2)/c^3+1/4/c^4*b*ln(c*x^(1/2)-1)-1/4/c^4*b*ln(1+c*x^(1/2))","A"
190,1,50,33,0.027000," ","int(a+b*arctanh(c*x^(1/2)),x)","a x +b x \arctanh \left(c \sqrt{x}\right)+\frac{b \sqrt{x}}{c}+\frac{b \ln \left(c \sqrt{x}-1\right)}{2 c^{2}}-\frac{b \ln \left(1+c \sqrt{x}\right)}{2 c^{2}}"," ",0,"a*x+b*x*arctanh(c*x^(1/2))+b*x^(1/2)/c+1/2*b/c^2*ln(c*x^(1/2)-1)-1/2*b/c^2*ln(1+c*x^(1/2))","A"
191,1,63,25,0.042000," ","int((a+b*arctanh(c*x^(1/2)))/x,x)","2 a \ln \left(c \sqrt{x}\right)+2 b \ln \left(c \sqrt{x}\right) \arctanh \left(c \sqrt{x}\right)-b \dilog \left(c \sqrt{x}\right)-b \dilog \left(1+c \sqrt{x}\right)-b \ln \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)"," ",0,"2*a*ln(c*x^(1/2))+2*b*ln(c*x^(1/2))*arctanh(c*x^(1/2))-b*dilog(c*x^(1/2))-b*dilog(1+c*x^(1/2))-b*ln(c*x^(1/2))*ln(1+c*x^(1/2))","B"
192,1,55,36,0.033000," ","int((a+b*arctanh(c*x^(1/2)))/x^2,x)","-\frac{a}{x}-\frac{b \arctanh \left(c \sqrt{x}\right)}{x}-\frac{b c}{\sqrt{x}}-\frac{c^{2} b \ln \left(c \sqrt{x}-1\right)}{2}+\frac{c^{2} b \ln \left(1+c \sqrt{x}\right)}{2}"," ",0,"-a/x-b/x*arctanh(c*x^(1/2))-b*c/x^(1/2)-1/2*c^2*b*ln(c*x^(1/2)-1)+1/2*c^2*b*ln(1+c*x^(1/2))","A"
193,1,64,47,0.035000," ","int((a+b*arctanh(c*x^(1/2)))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arctanh \left(c \sqrt{x}\right)}{2 x^{2}}-\frac{b c}{6 x^{\frac{3}{2}}}-\frac{b \,c^{3}}{2 \sqrt{x}}-\frac{c^{4} b \ln \left(c \sqrt{x}-1\right)}{4}+\frac{c^{4} b \ln \left(1+c \sqrt{x}\right)}{4}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arctanh(c*x^(1/2))-1/6*b*c/x^(3/2)-1/2*b*c^3/x^(1/2)-1/4*c^4*b*ln(c*x^(1/2)-1)+1/4*c^4*b*ln(1+c*x^(1/2))","A"
194,1,73,56,0.036000," ","int((a+b*arctanh(c*x^(1/2)))/x^4,x)","-\frac{a}{3 x^{3}}-\frac{b \arctanh \left(c \sqrt{x}\right)}{3 x^{3}}-\frac{b c}{15 x^{\frac{5}{2}}}-\frac{b \,c^{3}}{9 x^{\frac{3}{2}}}-\frac{b \,c^{5}}{3 \sqrt{x}}-\frac{c^{6} b \ln \left(c \sqrt{x}-1\right)}{6}+\frac{c^{6} b \ln \left(1+c \sqrt{x}\right)}{6}"," ",0,"-1/3*a/x^3-1/3*b/x^3*arctanh(c*x^(1/2))-1/15*b*c/x^(5/2)-1/9*b*c^3/x^(3/2)-1/3*b*c^5/x^(1/2)-1/6*c^6*b*ln(c*x^(1/2)-1)+1/6*c^6*b*ln(1+c*x^(1/2))","A"
195,1,396,167,0.060000," ","int(x^3*(a+b*arctanh(c*x^(1/2)))^2,x)","\frac{b^{2} \arctanh \left(c \sqrt{x}\right) \sqrt{x}}{2 c^{7}}-\frac{a b \ln \left(1+c \sqrt{x}\right)}{4 c^{8}}+\frac{a b \ln \left(c \sqrt{x}-1\right)}{4 c^{8}}+\frac{x^{\frac{5}{2}} a b}{10 c^{3}}+\frac{a b \,x^{\frac{3}{2}}}{6 c^{5}}+\frac{x^{\frac{7}{2}} a b}{14 c}+\frac{b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{4 c^{8}}-\frac{b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{4 c^{8}}+\frac{b^{2} \arctanh \left(c \sqrt{x}\right) x^{\frac{3}{2}}}{6 c^{5}}+\frac{b^{2} \arctanh \left(c \sqrt{x}\right) x^{\frac{5}{2}}}{10 c^{3}}+\frac{b^{2} \arctanh \left(c \sqrt{x}\right) x^{\frac{7}{2}}}{14 c}+\frac{a b \,x^{4} \arctanh \left(c \sqrt{x}\right)}{2}-\frac{b^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{8 c^{8}}-\frac{b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{8 c^{8}}+\frac{b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{8 c^{8}}+\frac{a b \sqrt{x}}{2 c^{7}}+\frac{71 b^{2} x}{420 c^{6}}+\frac{a^{2} x^{4}}{4}+\frac{3 b^{2} x^{2}}{70 c^{4}}+\frac{b^{2} x^{3}}{84 c^{2}}+\frac{44 b^{2} \ln \left(1+c \sqrt{x}\right)}{105 c^{8}}+\frac{b^{2} \ln \left(c \sqrt{x}-1\right)^{2}}{16 c^{8}}+\frac{b^{2} \ln \left(1+c \sqrt{x}\right)^{2}}{16 c^{8}}+\frac{44 b^{2} \ln \left(c \sqrt{x}-1\right)}{105 c^{8}}+\frac{b^{2} x^{4} \arctanh \left(c \sqrt{x}\right)^{2}}{4}"," ",0,"-1/4/c^8*a*b*ln(1+c*x^(1/2))+1/4/c^8*a*b*ln(c*x^(1/2)-1)+1/10/c^3*x^(5/2)*a*b+1/6/c^5*a*b*x^(3/2)+1/14/c*x^(7/2)*a*b+1/4/c^8*b^2*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-1/4/c^8*b^2*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-1/8/c^8*b^2*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))-1/8/c^8*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+1/8/c^8*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))+1/6/c^5*b^2*arctanh(c*x^(1/2))*x^(3/2)+1/10/c^3*b^2*arctanh(c*x^(1/2))*x^(5/2)+1/14/c*b^2*arctanh(c*x^(1/2))*x^(7/2)+1/2*a*b*x^4*arctanh(c*x^(1/2))+1/2*a*b*x^(1/2)/c^7+1/2*b^2*arctanh(c*x^(1/2))*x^(1/2)/c^7+71/420*b^2*x/c^6+1/4*a^2*x^4+3/70*b^2*x^2/c^4+1/84*b^2*x^3/c^2+44/105/c^8*b^2*ln(1+c*x^(1/2))+1/16/c^8*b^2*ln(c*x^(1/2)-1)^2+1/16/c^8*b^2*ln(1+c*x^(1/2))^2+1/4*b^2*x^4*arctanh(c*x^(1/2))^2+44/105/c^8*b^2*ln(c*x^(1/2)-1)","B"
196,1,358,137,0.059000," ","int(x^2*(a+b*arctanh(c*x^(1/2)))^2,x)","\frac{x^{3} a^{2}}{3}+\frac{b^{2} x^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{3}+\frac{2 b^{2} \arctanh \left(c \sqrt{x}\right) x^{\frac{5}{2}}}{15 c}+\frac{2 b^{2} \arctanh \left(c \sqrt{x}\right) x^{\frac{3}{2}}}{9 c^{3}}+\frac{2 b^{2} \arctanh \left(c \sqrt{x}\right) \sqrt{x}}{3 c^{5}}+\frac{b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{3 c^{6}}-\frac{b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{3 c^{6}}+\frac{b^{2} \ln \left(c \sqrt{x}-1\right)^{2}}{12 c^{6}}-\frac{b^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{6 c^{6}}+\frac{b^{2} \ln \left(1+c \sqrt{x}\right)^{2}}{12 c^{6}}-\frac{b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{6 c^{6}}+\frac{b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{6 c^{6}}+\frac{b^{2} x^{2}}{30 c^{2}}+\frac{8 b^{2} x}{45 c^{4}}+\frac{23 b^{2} \ln \left(c \sqrt{x}-1\right)}{45 c^{6}}+\frac{23 b^{2} \ln \left(1+c \sqrt{x}\right)}{45 c^{6}}+\frac{2 a b \,x^{3} \arctanh \left(c \sqrt{x}\right)}{3}+\frac{2 x^{\frac{5}{2}} a b}{15 c}+\frac{2 a b \,x^{\frac{3}{2}}}{9 c^{3}}+\frac{2 a b \sqrt{x}}{3 c^{5}}+\frac{a b \ln \left(c \sqrt{x}-1\right)}{3 c^{6}}-\frac{a b \ln \left(1+c \sqrt{x}\right)}{3 c^{6}}"," ",0,"1/3*x^3*a^2+1/3*b^2*x^3*arctanh(c*x^(1/2))^2+2/15/c*b^2*arctanh(c*x^(1/2))*x^(5/2)+2/9/c^3*b^2*arctanh(c*x^(1/2))*x^(3/2)+2/3*b^2*arctanh(c*x^(1/2))*x^(1/2)/c^5+1/3/c^6*b^2*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-1/3/c^6*b^2*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))+1/12/c^6*b^2*ln(c*x^(1/2)-1)^2-1/6/c^6*b^2*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+1/12/c^6*b^2*ln(1+c*x^(1/2))^2-1/6/c^6*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+1/6/c^6*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))+1/30*b^2*x^2/c^2+8/45*b^2*x/c^4+23/45/c^6*b^2*ln(c*x^(1/2)-1)+23/45/c^6*b^2*ln(1+c*x^(1/2))+2/3*a*b*x^3*arctanh(c*x^(1/2))+2/15/c*x^(5/2)*a*b+2/9/c^3*a*b*x^(3/2)+2/3*a*b*x^(1/2)/c^5+1/3/c^6*a*b*ln(c*x^(1/2)-1)-1/3/c^6*a*b*ln(1+c*x^(1/2))","B"
197,1,317,105,0.052000," ","int(x*(a+b*arctanh(c*x^(1/2)))^2,x)","\frac{a^{2} x^{2}}{2}+\frac{b^{2} x^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{2}+\frac{b^{2} \arctanh \left(c \sqrt{x}\right) x^{\frac{3}{2}}}{3 c}+\frac{b^{2} \arctanh \left(c \sqrt{x}\right) \sqrt{x}}{c^{3}}+\frac{b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{2 c^{4}}-\frac{b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{2 c^{4}}+\frac{b^{2} \ln \left(c \sqrt{x}-1\right)^{2}}{8 c^{4}}-\frac{b^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{4 c^{4}}+\frac{b^{2} \ln \left(1+c \sqrt{x}\right)^{2}}{8 c^{4}}-\frac{b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{4 c^{4}}+\frac{b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{4 c^{4}}+\frac{b^{2} x}{6 c^{2}}+\frac{2 b^{2} \ln \left(c \sqrt{x}-1\right)}{3 c^{4}}+\frac{2 b^{2} \ln \left(1+c \sqrt{x}\right)}{3 c^{4}}+x^{2} a b \arctanh \left(c \sqrt{x}\right)+\frac{a b \,x^{\frac{3}{2}}}{3 c}+\frac{a b \sqrt{x}}{c^{3}}+\frac{a b \ln \left(c \sqrt{x}-1\right)}{2 c^{4}}-\frac{a b \ln \left(1+c \sqrt{x}\right)}{2 c^{4}}"," ",0,"1/2*a^2*x^2+1/2*b^2*x^2*arctanh(c*x^(1/2))^2+1/3/c*b^2*arctanh(c*x^(1/2))*x^(3/2)+b^2*arctanh(c*x^(1/2))*x^(1/2)/c^3+1/2/c^4*b^2*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-1/2/c^4*b^2*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))+1/8/c^4*b^2*ln(c*x^(1/2)-1)^2-1/4/c^4*b^2*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+1/8/c^4*b^2*ln(1+c*x^(1/2))^2-1/4/c^4*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+1/4/c^4*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))+1/6*b^2*x/c^2+2/3/c^4*b^2*ln(c*x^(1/2)-1)+2/3/c^4*b^2*ln(1+c*x^(1/2))+x^2*a*b*arctanh(c*x^(1/2))+1/3*a*b*x^(3/2)/c+a*b*x^(1/2)/c^3+1/2/c^4*a*b*ln(c*x^(1/2)-1)-1/2/c^4*a*b*ln(1+c*x^(1/2))","B"
198,1,272,75,0.053000," ","int((a+b*arctanh(c*x^(1/2)))^2,x)","a^{2} x +x \,b^{2} \arctanh \left(c \sqrt{x}\right)^{2}+\frac{2 b^{2} \arctanh \left(c \sqrt{x}\right) \sqrt{x}}{c}+\frac{b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{c^{2}}-\frac{b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{c^{2}}+\frac{b^{2} \ln \left(c \sqrt{x}-1\right)^{2}}{4 c^{2}}-\frac{b^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2 c^{2}}+\frac{b^{2} \ln \left(c \sqrt{x}-1\right)}{c^{2}}+\frac{b^{2} \ln \left(1+c \sqrt{x}\right)}{c^{2}}+\frac{b^{2} \ln \left(1+c \sqrt{x}\right)^{2}}{4 c^{2}}+\frac{b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2 c^{2}}-\frac{b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{2 c^{2}}+2 a b x \arctanh \left(c \sqrt{x}\right)+\frac{2 a b \sqrt{x}}{c}+\frac{a b \ln \left(c \sqrt{x}-1\right)}{c^{2}}-\frac{a b \ln \left(1+c \sqrt{x}\right)}{c^{2}}"," ",0,"a^2*x+x*b^2*arctanh(c*x^(1/2))^2+2*b^2*arctanh(c*x^(1/2))*x^(1/2)/c+1/c^2*b^2*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-1/c^2*b^2*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))+1/4/c^2*b^2*ln(c*x^(1/2)-1)^2-1/2/c^2*b^2*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+1/c^2*b^2*ln(c*x^(1/2)-1)+1/c^2*b^2*ln(1+c*x^(1/2))+1/4/c^2*b^2*ln(1+c*x^(1/2))^2+1/2/c^2*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))-1/2/c^2*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+2*a*b*x*arctanh(c*x^(1/2))+2*a*b*x^(1/2)/c+1/c^2*a*b*ln(c*x^(1/2)-1)-1/c^2*a*b*ln(1+c*x^(1/2))","B"
199,1,742,129,0.227000," ","int((a+b*arctanh(c*x^(1/2)))^2/x,x)","2 a^{2} \ln \left(c \sqrt{x}\right)+2 b^{2} \ln \left(c \sqrt{x}\right) \arctanh \left(c \sqrt{x}\right)^{2}-2 b^{2} \arctanh \left(c \sqrt{x}\right) \polylog \left(2, -\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)+b^{2} \polylog \left(3, -\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)-2 b^{2} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)+2 b^{2} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(1-\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+4 b^{2} \arctanh \left(c \sqrt{x}\right) \polylog \left(2, \frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)-4 b^{2} \polylog \left(3, \frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+2 b^{2} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(1+\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+4 b^{2} \arctanh \left(c \sqrt{x}\right) \polylog \left(2, -\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)-4 b^{2} \polylog \left(3, -\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}-i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}+i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \arctanh \left(c \sqrt{x}\right)^{2}-i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}+4 a b \ln \left(c \sqrt{x}\right) \arctanh \left(c \sqrt{x}\right)-2 a b \ln \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)-2 a b \dilog \left(c \sqrt{x}\right)-2 a b \dilog \left(1+c \sqrt{x}\right)"," ",0,"2*a^2*ln(c*x^(1/2))+2*b^2*ln(c*x^(1/2))*arctanh(c*x^(1/2))^2-2*b^2*arctanh(c*x^(1/2))*polylog(2,-(1+c*x^(1/2))^2/(-c^2*x+1))+b^2*polylog(3,-(1+c*x^(1/2))^2/(-c^2*x+1))-2*b^2*arctanh(c*x^(1/2))^2*ln((1+c*x^(1/2))^2/(-c^2*x+1)-1)+2*b^2*arctanh(c*x^(1/2))^2*ln(1-(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+4*b^2*arctanh(c*x^(1/2))*polylog(2,(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-4*b^2*polylog(3,(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+2*b^2*arctanh(c*x^(1/2))^2*ln(1+(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+4*b^2*arctanh(c*x^(1/2))*polylog(2,-(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-4*b^2*polylog(3,-(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-I*b^2*Pi*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1))*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2-I*b^2*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2+I*b^2*Pi*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^3*arctanh(c*x^(1/2))^2+I*b^2*Pi*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1))*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*arctanh(c*x^(1/2))^2+4*a*b*ln(c*x^(1/2))*arctanh(c*x^(1/2))-2*a*b*ln(c*x^(1/2))*ln(1+c*x^(1/2))-2*a*b*dilog(c*x^(1/2))-2*a*b*dilog(1+c*x^(1/2))","C"
200,1,292,77,0.067000," ","int((a+b*arctanh(c*x^(1/2)))^2/x^2,x)","-\frac{a^{2}}{x}-\frac{b^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{x}-\frac{2 c \,b^{2} \arctanh \left(c \sqrt{x}\right)}{\sqrt{x}}-c^{2} b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)+c^{2} b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)-\frac{c^{2} b^{2} \ln \left(c \sqrt{x}-1\right)^{2}}{4}+\frac{c^{2} b^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2}+2 c^{2} b^{2} \ln \left(c \sqrt{x}\right)-c^{2} b^{2} \ln \left(c \sqrt{x}-1\right)-c^{2} b^{2} \ln \left(1+c \sqrt{x}\right)-\frac{c^{2} b^{2} \ln \left(1+c \sqrt{x}\right)^{2}}{4}+\frac{c^{2} b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{2}-\frac{c^{2} b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2}-\frac{2 a b \arctanh \left(c \sqrt{x}\right)}{x}-\frac{2 c a b}{\sqrt{x}}-c^{2} a b \ln \left(c \sqrt{x}-1\right)+c^{2} a b \ln \left(1+c \sqrt{x}\right)"," ",0,"-a^2/x-b^2/x*arctanh(c*x^(1/2))^2-2*c*b^2*arctanh(c*x^(1/2))/x^(1/2)-c^2*b^2*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)+c^2*b^2*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-1/4*c^2*b^2*ln(c*x^(1/2)-1)^2+1/2*c^2*b^2*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+2*c^2*b^2*ln(c*x^(1/2))-c^2*b^2*ln(c*x^(1/2)-1)-c^2*b^2*ln(1+c*x^(1/2))-1/4*c^2*b^2*ln(1+c*x^(1/2))^2+1/2*c^2*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))-1/2*c^2*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))-2*a*b/x*arctanh(c*x^(1/2))-2*c*a*b/x^(1/2)-c^2*a*b*ln(c*x^(1/2)-1)+c^2*a*b*ln(1+c*x^(1/2))","B"
201,1,332,109,0.071000," ","int((a+b*arctanh(c*x^(1/2)))^2/x^3,x)","-\frac{a^{2}}{2 x^{2}}-\frac{b^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{2 x^{2}}-\frac{c \,b^{2} \arctanh \left(c \sqrt{x}\right)}{3 x^{\frac{3}{2}}}-\frac{c^{3} b^{2} \arctanh \left(c \sqrt{x}\right)}{\sqrt{x}}-\frac{c^{4} b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{2}+\frac{c^{4} b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{2}-\frac{c^{4} b^{2} \ln \left(c \sqrt{x}-1\right)^{2}}{8}+\frac{c^{4} b^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{4}-\frac{c^{4} b^{2} \ln \left(1+c \sqrt{x}\right)^{2}}{8}-\frac{c^{4} b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{4}+\frac{c^{4} b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{4}-\frac{b^{2} c^{2}}{6 x}+\frac{4 c^{4} b^{2} \ln \left(c \sqrt{x}\right)}{3}-\frac{2 c^{4} b^{2} \ln \left(c \sqrt{x}-1\right)}{3}-\frac{2 c^{4} b^{2} \ln \left(1+c \sqrt{x}\right)}{3}-\frac{a b \arctanh \left(c \sqrt{x}\right)}{x^{2}}-\frac{c a b}{3 x^{\frac{3}{2}}}-\frac{c^{3} a b}{\sqrt{x}}-\frac{c^{4} a b \ln \left(c \sqrt{x}-1\right)}{2}+\frac{c^{4} a b \ln \left(1+c \sqrt{x}\right)}{2}"," ",0,"-1/2*a^2/x^2-1/2*b^2/x^2*arctanh(c*x^(1/2))^2-1/3*c*b^2*arctanh(c*x^(1/2))/x^(3/2)-c^3*b^2*arctanh(c*x^(1/2))/x^(1/2)-1/2*c^4*b^2*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)+1/2*c^4*b^2*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-1/8*c^4*b^2*ln(c*x^(1/2)-1)^2+1/4*c^4*b^2*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))-1/8*c^4*b^2*ln(1+c*x^(1/2))^2-1/4*c^4*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))+1/4*c^4*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))-1/6*b^2*c^2/x+4/3*c^4*b^2*ln(c*x^(1/2))-2/3*c^4*b^2*ln(c*x^(1/2)-1)-2/3*c^4*b^2*ln(1+c*x^(1/2))-a*b/x^2*arctanh(c*x^(1/2))-1/3*c*a*b/x^(3/2)-c^3*a*b/x^(1/2)-1/2*c^4*a*b*ln(c*x^(1/2)-1)+1/2*c^4*a*b*ln(1+c*x^(1/2))","B"
202,1,1518,300,3.658000," ","int(x^3*(a+b*arctanh(c*x^(1/2)))^3,x)","-\frac{88 b^{3} \dilog \left(1-\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{35 c^{8}}+\frac{47 b^{3} \sqrt{x}}{70 c^{7}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \arctanh \left(c \sqrt{x}\right)^{2}}{16 c^{8}}-\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{16 c^{8}}+\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{16 c^{8}}+\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{8 c^{8}}-\frac{3 a \,b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{8 c^{8}}-\frac{3 a \,b^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{8 c^{8}}+\frac{3 a \,b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{8 c^{8}}+\frac{3 a \,b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{4 c^{8}}-\frac{3 a \,b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{4 c^{8}}+\frac{3 a \,b^{2} x^{\frac{5}{2}} \arctanh \left(c \sqrt{x}\right)}{10 c^{3}}+\frac{a \,b^{2} \arctanh \left(c \sqrt{x}\right) x^{\frac{3}{2}}}{2 c^{5}}+\frac{a \,b^{2} x^{3}}{28 c^{2}}+\frac{23 b^{3} x^{\frac{3}{2}}}{420 c^{5}}+\frac{b^{3} x^{\frac{5}{2}}}{140 c^{3}}-\frac{47 b^{3} \arctanh \left(c \sqrt{x}\right)}{70 c^{8}}+\frac{b^{3} x^{4} \arctanh \left(c \sqrt{x}\right)^{3}}{4}+\frac{44 b^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{35 c^{8}}-\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{3}}{4 c^{8}}-\frac{88 b^{3} \dilog \left(1+\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{35 c^{8}}+\frac{3 a \,b^{2} \arctanh \left(c \sqrt{x}\right) \sqrt{x}}{2 c^{7}}+\frac{3 a \,b^{2} \arctanh \left(c \sqrt{x}\right) x^{\frac{7}{2}}}{14 c}-\frac{3 i b^{3} \pi  \arctanh \left(c \sqrt{x}\right)^{2}}{8 c^{8}}+\frac{9 a \,b^{2} x^{2}}{70 c^{4}}+\frac{71 x a \,b^{2}}{140 c^{6}}+\frac{a^{2} b \,x^{\frac{3}{2}}}{4 c^{5}}+\frac{3 \sqrt{x}\, a^{2} b}{4 c^{7}}+\frac{3 x^{\frac{5}{2}} a^{2} b}{20 c^{3}}+\frac{3 x^{\frac{7}{2}} a^{2} b}{28 c}+\frac{3 a \,b^{2} \ln \left(c \sqrt{x}-1\right)^{2}}{16 c^{8}}+\frac{3 a \,b^{2} \ln \left(1+c \sqrt{x}\right)^{2}}{16 c^{8}}+\frac{44 a \,b^{2} \ln \left(c \sqrt{x}-1\right)}{35 c^{8}}+\frac{44 a \,b^{2} \ln \left(1+c \sqrt{x}\right)}{35 c^{8}}+\frac{3 a^{2} b \ln \left(c \sqrt{x}-1\right)}{8 c^{8}}-\frac{3 a^{2} b \ln \left(1+c \sqrt{x}\right)}{8 c^{8}}+\frac{x^{4} a^{3}}{4}-\frac{11 b^{3}}{15 c^{8}}+\frac{3 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} x^{\frac{5}{2}}}{20 c^{3}}+\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{2} x^{\frac{3}{2}}}{4 c^{5}}+\frac{3 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \sqrt{x}}{4 c^{7}}+\frac{9 b^{3} \arctanh \left(c \sqrt{x}\right) x^{2}}{70 c^{4}}+\frac{71 b^{3} \arctanh \left(c \sqrt{x}\right) x}{140 c^{6}}+\frac{3 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} x^{\frac{7}{2}}}{28 c}+\frac{b^{3} \arctanh \left(c \sqrt{x}\right) x^{3}}{28 c^{2}}+\frac{3 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(c \sqrt{x}-1\right)}{8 c^{8}}-\frac{3 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(1+c \sqrt{x}\right)}{8 c^{8}}+\frac{3 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)}{4 c^{8}}+\frac{3 a \,b^{2} x^{4} \arctanh \left(c \sqrt{x}\right)^{2}}{4}+\frac{3 a^{2} b \,x^{4} \arctanh \left(c \sqrt{x}\right)}{4}-\frac{88 b^{3} \arctanh \left(c \sqrt{x}\right) \ln \left(1+\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{35 c^{8}}-\frac{88 b^{3} \arctanh \left(c \sqrt{x}\right) \ln \left(1-\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{35 c^{8}}-\frac{3 i b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)}{16 c^{8}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{16 c^{8}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{16 c^{8}}-\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{8 c^{8}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{8 c^{8}}"," ",0,"-47/70*b^3*arctanh(c*x^(1/2))/c^8+47/70*b^3*x^(1/2)/c^7+3/16*I/c^8*b^3*Pi*csgn(I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))^2*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*arctanh(c*x^(1/2))^2-3/16*I/c^8*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2-3/8/c^8*a*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+3/4/c^8*a*b^2*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-3/4/c^8*a*b^2*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-3/8/c^8*a*b^2*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+3/8/c^8*a*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))+3/10/c^3*a*b^2*x^(5/2)*arctanh(c*x^(1/2))+1/2/c^5*a*b^2*arctanh(c*x^(1/2))*x^(3/2)+3/2/c^7*a*b^2*arctanh(c*x^(1/2))*x^(1/2)+3/14/c*a*b^2*arctanh(c*x^(1/2))*x^(7/2)-3/8*I/c^8*b^3*Pi*arctanh(c*x^(1/2))^2+1/28*a*b^2*x^3/c^2+23/420*b^3*x^(3/2)/c^5+1/140*b^3*x^(5/2)/c^3+9/70/c^4*a*b^2*x^2+71/140/c^6*x*a*b^2+3/20/c^3*b^3*arctanh(c*x^(1/2))^2*x^(5/2)+1/4/c^5*b^3*arctanh(c*x^(1/2))^2*x^(3/2)+3/4/c^7*b^3*arctanh(c*x^(1/2))^2*x^(1/2)+9/70/c^4*b^3*arctanh(c*x^(1/2))*x^2+71/140/c^6*b^3*arctanh(c*x^(1/2))*x+3/28/c*b^3*arctanh(c*x^(1/2))^2*x^(7/2)+1/28/c^2*b^3*arctanh(c*x^(1/2))*x^3+1/4/c^5*a^2*b*x^(3/2)+3/4/c^7*x^(1/2)*a^2*b+3/20/c^3*x^(5/2)*a^2*b+3/28/c*x^(7/2)*a^2*b+3/16/c^8*a*b^2*ln(c*x^(1/2)-1)^2+3/16/c^8*a*b^2*ln(1+c*x^(1/2))^2+44/35/c^8*a*b^2*ln(c*x^(1/2)-1)+44/35/c^8*a*b^2*ln(1+c*x^(1/2))+3/8/c^8*a^2*b*ln(c*x^(1/2)-1)-3/8/c^8*a^2*b*ln(1+c*x^(1/2))+3/8/c^8*b^3*arctanh(c*x^(1/2))^2*ln(c*x^(1/2)-1)-3/8/c^8*b^3*arctanh(c*x^(1/2))^2*ln(1+c*x^(1/2))-88/35/c^8*b^3*arctanh(c*x^(1/2))*ln(1+I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-88/35/c^8*b^3*arctanh(c*x^(1/2))*ln(1-I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+3/4/c^8*b^3*arctanh(c*x^(1/2))^2*ln((1+c*x^(1/2))/(-c^2*x+1)^(1/2))+3/4*a*b^2*x^4*arctanh(c*x^(1/2))^2+3/4*a^2*b*x^4*arctanh(c*x^(1/2))+1/4*x^4*a^3-11/15/c^8*b^3+3/16*I/c^8*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2+3/8*I/c^8*b^3*Pi*csgn(I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))^2*arctanh(c*x^(1/2))^2+1/4*b^3*x^4*arctanh(c*x^(1/2))^3-88/35/c^8*b^3*dilog(1+I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-88/35/c^8*b^3*dilog(1-I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+44/35/c^8*b^3*arctanh(c*x^(1/2))^2-1/4/c^8*b^3*arctanh(c*x^(1/2))^3-3/16*I/c^8*b^3*arctanh(c*x^(1/2))^2*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))+3/16*I/c^8*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^3*arctanh(c*x^(1/2))^2+3/16*I/c^8*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))^3*arctanh(c*x^(1/2))^2-3/8*I/c^8*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^3*arctanh(c*x^(1/2))^2+3/8*I/c^8*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2","C"
203,1,1423,246,0.579000," ","int(x^2*(a+b*arctanh(c*x^(1/2)))^3,x)","\frac{x^{3} a^{3}}{3}+\frac{8 a \,b^{2} x}{15 c^{4}}+\frac{b^{3} \arctanh \left(c \sqrt{x}\right) x^{2}}{10 c^{2}}+\frac{8 b^{3} \arctanh \left(c \sqrt{x}\right) x}{15 c^{4}}+\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{2} x^{\frac{5}{2}}}{5 c}+\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(c \sqrt{x}-1\right)}{2 c^{6}}-\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(1+c \sqrt{x}\right)}{2 c^{6}}+\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)}{c^{6}}+a^{2} b \,x^{3} \arctanh \left(c \sqrt{x}\right)+a \,b^{2} x^{3} \arctanh \left(c \sqrt{x}\right)^{2}+\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{2} x^{\frac{3}{2}}}{3 c^{3}}+\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \sqrt{x}}{c^{5}}-\frac{46 b^{3} \arctanh \left(c \sqrt{x}\right) \ln \left(1+\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{15 c^{6}}-\frac{46 b^{3} \arctanh \left(c \sqrt{x}\right) \ln \left(1-\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{15 c^{6}}+\frac{a^{2} b \,x^{\frac{3}{2}}}{3 c^{3}}+\frac{\sqrt{x}\, a^{2} b}{c^{5}}+\frac{x^{\frac{5}{2}} a^{2} b}{5 c}+\frac{23 a \,b^{2} \ln \left(c \sqrt{x}-1\right)}{15 c^{6}}+\frac{23 a \,b^{2} \ln \left(1+c \sqrt{x}\right)}{15 c^{6}}+\frac{a^{2} b \ln \left(c \sqrt{x}-1\right)}{2 c^{6}}-\frac{a^{2} b \ln \left(1+c \sqrt{x}\right)}{2 c^{6}}+\frac{a \,b^{2} x^{2}}{10 c^{2}}+\frac{a \,b^{2} \ln \left(c \sqrt{x}-1\right)^{2}}{4 c^{6}}+\frac{a \,b^{2} \ln \left(1+c \sqrt{x}\right)^{2}}{4 c^{6}}+\frac{19 b^{3} \sqrt{x}}{30 c^{5}}+\frac{b^{3} x^{\frac{3}{2}}}{30 c^{3}}+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \arctanh \left(c \sqrt{x}\right)^{2}}{4 c^{6}}+\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{2 c^{6}}+\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{4 c^{6}}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{4 c^{6}}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right) \arctanh \left(c \sqrt{x}\right)^{2}}{4 c^{6}}+\frac{2 a \,b^{2} \arctanh \left(c \sqrt{x}\right) \sqrt{x}}{c^{5}}-\frac{i b^{3} \pi  \arctanh \left(c \sqrt{x}\right)^{2}}{2 c^{6}}-\frac{46 b^{3} \dilog \left(1+\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{15 c^{6}}-\frac{46 b^{3} \dilog \left(1-\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{15 c^{6}}-\frac{19 b^{3} \arctanh \left(c \sqrt{x}\right)}{30 c^{6}}+\frac{b^{3} x^{3} \arctanh \left(c \sqrt{x}\right)^{3}}{3}+\frac{23 b^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{15 c^{6}}-\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{3}}{3 c^{6}}+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{2 c^{6}}+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{4 c^{6}}+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{4 c^{6}}-\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{2 c^{6}}-\frac{a \,b^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2 c^{6}}+\frac{a \,b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2 c^{6}}-\frac{a \,b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{2 c^{6}}+\frac{a \,b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{c^{6}}-\frac{a \,b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{c^{6}}+\frac{2 a \,b^{2} x^{\frac{5}{2}} \arctanh \left(c \sqrt{x}\right)}{5 c}+\frac{2 a \,b^{2} \arctanh \left(c \sqrt{x}\right) x^{\frac{3}{2}}}{3 c^{3}}-\frac{2 b^{3}}{3 c^{6}}"," ",0,"1/3*x^3*a^3+8/15*a*b^2*x/c^4+1/10/c^2*b^3*arctanh(c*x^(1/2))*x^2+8/15/c^4*b^3*arctanh(c*x^(1/2))*x+1/5/c*b^3*arctanh(c*x^(1/2))^2*x^(5/2)+1/3/c^3*a^2*b*x^(3/2)+1/c^5*x^(1/2)*a^2*b+1/5/c*x^(5/2)*a^2*b+23/15/c^6*a*b^2*ln(c*x^(1/2)-1)+23/15/c^6*a*b^2*ln(1+c*x^(1/2))+1/2/c^6*a^2*b*ln(c*x^(1/2)-1)-1/2/c^6*a^2*b*ln(1+c*x^(1/2))+1/2/c^6*b^3*arctanh(c*x^(1/2))^2*ln(c*x^(1/2)-1)-1/2/c^6*b^3*arctanh(c*x^(1/2))^2*ln(1+c*x^(1/2))-46/15/c^6*b^3*arctanh(c*x^(1/2))*ln(1+I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-46/15/c^6*b^3*arctanh(c*x^(1/2))*ln(1-I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+1/c^6*b^3*arctanh(c*x^(1/2))^2*ln((1+c*x^(1/2))/(-c^2*x+1)^(1/2))+a^2*b*x^3*arctanh(c*x^(1/2))+a*b^2*x^3*arctanh(c*x^(1/2))^2+1/10/c^2*a*b^2*x^2+1/4/c^6*a*b^2*ln(c*x^(1/2)-1)^2+1/4/c^6*a*b^2*ln(1+c*x^(1/2))^2+1/3/c^3*b^3*arctanh(c*x^(1/2))^2*x^(3/2)+1/c^5*b^3*arctanh(c*x^(1/2))^2*x^(1/2)+1/4*I/c^6*b^3*Pi*csgn(I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))^2*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*arctanh(c*x^(1/2))^2+1/2*I/c^6*b^3*Pi*csgn(I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))^2*arctanh(c*x^(1/2))^2+1/4*I/c^6*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2-1/4*I/c^6*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2-19/30*b^3*arctanh(c*x^(1/2))/c^6+19/30*b^3*x^(1/2)/c^5+1/2*I/c^6*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2-1/4*I/c^6*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*arctanh(c*x^(1/2))^2+1/30*b^3*x^(3/2)/c^3+1/3*b^3*x^3*arctanh(c*x^(1/2))^3-46/15/c^6*b^3*dilog(1+I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-46/15/c^6*b^3*dilog(1-I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+23/15/c^6*b^3*arctanh(c*x^(1/2))^2-1/3/c^6*b^3*arctanh(c*x^(1/2))^3+1/4*I/c^6*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))^3*arctanh(c*x^(1/2))^2+1/4*I/c^6*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^3*arctanh(c*x^(1/2))^2-1/2*I/c^6*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^3*arctanh(c*x^(1/2))^2+1/c^6*a*b^2*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-1/c^6*a*b^2*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-1/2/c^6*a*b^2*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+1/2/c^6*a*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))-1/2/c^6*a*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+2/5/c*a*b^2*x^(5/2)*arctanh(c*x^(1/2))+2/3/c^3*a*b^2*arctanh(c*x^(1/2))*x^(3/2)+2/c^5*a*b^2*arctanh(c*x^(1/2))*x^(1/2)-1/2*I/c^6*b^3*Pi*arctanh(c*x^(1/2))^2-2/3/c^6*b^3","C"
204,1,1339,194,0.419000," ","int(x*(a+b*arctanh(c*x^(1/2)))^3,x)","\frac{a \,b^{2} x}{2 c^{2}}-\frac{b^{3}}{2 c^{4}}-\frac{3 i b^{3} \pi  \arctanh \left(c \sqrt{x}\right)^{2}}{4 c^{4}}+\frac{a \,b^{2} \arctanh \left(c \sqrt{x}\right) x^{\frac{3}{2}}}{c}+\frac{3 a \,b^{2} \arctanh \left(c \sqrt{x}\right) \sqrt{x}}{c^{3}}+\frac{3 a \,b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{2 c^{4}}-\frac{3 a \,b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{2 c^{4}}+\frac{3 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(c \sqrt{x}-1\right)}{4 c^{4}}-\frac{3 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(1+c \sqrt{x}\right)}{4 c^{4}}+\frac{3 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)}{2 c^{4}}+\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{2} x^{\frac{3}{2}}}{2 c}+\frac{3 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \sqrt{x}}{2 c^{3}}+\frac{b^{3} \arctanh \left(c \sqrt{x}\right) x}{2 c^{2}}+\frac{3 a \,b^{2} x^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{2}+\frac{3 a^{2} b \,x^{2} \arctanh \left(c \sqrt{x}\right)}{2}-\frac{4 b^{3} \arctanh \left(c \sqrt{x}\right) \ln \left(1+\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{c^{4}}-\frac{4 b^{3} \arctanh \left(c \sqrt{x}\right) \ln \left(1-\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{c^{4}}+\frac{2 a \,b^{2} \ln \left(1+c \sqrt{x}\right)}{c^{4}}+\frac{3 a^{2} b \ln \left(c \sqrt{x}-1\right)}{4 c^{4}}-\frac{3 a^{2} b \ln \left(1+c \sqrt{x}\right)}{4 c^{4}}+\frac{a^{2} b \,x^{\frac{3}{2}}}{2 c}+\frac{3 \sqrt{x}\, a^{2} b}{2 c^{3}}+\frac{3 a \,b^{2} \ln \left(c \sqrt{x}-1\right)^{2}}{8 c^{4}}+\frac{3 a \,b^{2} \ln \left(1+c \sqrt{x}\right)^{2}}{8 c^{4}}+\frac{2 a \,b^{2} \ln \left(c \sqrt{x}-1\right)}{c^{4}}-\frac{b^{3} \arctanh \left(c \sqrt{x}\right)}{2 c^{4}}+\frac{b^{3} x^{2} \arctanh \left(c \sqrt{x}\right)^{3}}{2}+\frac{2 b^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{c^{4}}-\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{3}}{2 c^{4}}-\frac{4 b^{3} \dilog \left(1+\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{c^{4}}-\frac{4 b^{3} \dilog \left(1-\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)}{c^{4}}+\frac{b^{3} \sqrt{x}}{2 c^{3}}-\frac{3 a \,b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{4 c^{4}}-\frac{3 a \,b^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{4 c^{4}}+\frac{3 a \,b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{4 c^{4}}-\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right) \arctanh \left(c \sqrt{x}\right)^{2}}{8 c^{4}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{8 c^{4}}-\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{4 c^{4}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{8 c^{4}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{4 c^{4}}+\frac{x^{2} a^{3}}{2}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \arctanh \left(c \sqrt{x}\right)^{2}}{8 c^{4}}+\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{4 c^{4}}-\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{8 c^{4}}+\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{8 c^{4}}"," ",0,"1/2*a*b^2*x/c^2-1/2/c^4*b^3+2/c^4*a*b^2*ln(1+c*x^(1/2))+3/4/c^4*a^2*b*ln(c*x^(1/2)-1)-3/4/c^4*a^2*b*ln(1+c*x^(1/2))+3/4/c^4*b^3*arctanh(c*x^(1/2))^2*ln(c*x^(1/2)-1)-3/4/c^4*b^3*arctanh(c*x^(1/2))^2*ln(1+c*x^(1/2))-4/c^4*b^3*arctanh(c*x^(1/2))*ln(1+I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-4/c^4*b^3*arctanh(c*x^(1/2))*ln(1-I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+3/2/c^4*b^3*arctanh(c*x^(1/2))^2*ln((1+c*x^(1/2))/(-c^2*x+1)^(1/2))+1/2/c*b^3*arctanh(c*x^(1/2))^2*x^(3/2)+3/2/c^3*b^3*arctanh(c*x^(1/2))^2*x^(1/2)+1/2/c^2*b^3*arctanh(c*x^(1/2))*x+1/2/c*a^2*b*x^(3/2)+3/2/c^3*x^(1/2)*a^2*b+3/2*a*b^2*x^2*arctanh(c*x^(1/2))^2+3/2*a^2*b*x^2*arctanh(c*x^(1/2))+3/8/c^4*a*b^2*ln(c*x^(1/2)-1)^2+3/8/c^4*a*b^2*ln(1+c*x^(1/2))^2+2/c^4*a*b^2*ln(c*x^(1/2)-1)-1/2*b^3*arctanh(c*x^(1/2))/c^4+1/2*b^3*x^(1/2)/c^3+1/c*a*b^2*arctanh(c*x^(1/2))*x^(3/2)+3/c^3*a*b^2*arctanh(c*x^(1/2))*x^(1/2)-3/4*I/c^4*b^3*Pi*arctanh(c*x^(1/2))^2-3/4/c^4*a*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+3/2/c^4*a*b^2*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-3/2/c^4*a*b^2*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-3/4/c^4*a*b^2*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+3/4/c^4*a*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))+3/8*I/c^4*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))^3*arctanh(c*x^(1/2))^2+1/2*b^3*x^2*arctanh(c*x^(1/2))^3-4/c^4*b^3*dilog(1+I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-4/c^4*b^3*dilog(1-I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+2/c^4*b^3*arctanh(c*x^(1/2))^2-1/2/c^4*b^3*arctanh(c*x^(1/2))^3-3/8*I/c^4*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*arctanh(c*x^(1/2))^2+1/2*x^2*a^3-3/4*I/c^4*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^3*arctanh(c*x^(1/2))^2+3/8*I/c^4*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^3*arctanh(c*x^(1/2))^2+3/4*I/c^4*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2+3/8*I/c^4*b^3*Pi*csgn(I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))^2*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*arctanh(c*x^(1/2))^2+3/4*I/c^4*b^3*Pi*csgn(I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))^2*arctanh(c*x^(1/2))^2-3/8*I/c^4*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2+3/8*I/c^4*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2","C"
205,1,6235,126,0.320000," ","int((a+b*arctanh(c*x^(1/2)))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
206,1,1542,196,0.183000," ","int((a+b*arctanh(c*x^(1/2)))^3/x,x)","-6 a \,b^{2} \arctanh \left(c \sqrt{x}\right) \polylog \left(2, -\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)-6 a \,b^{2} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)+6 a^{2} b \ln \left(c \sqrt{x}\right) \arctanh \left(c \sqrt{x}\right)+6 a \,b^{2} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(1-\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+12 a \,b^{2} \arctanh \left(c \sqrt{x}\right) \polylog \left(2, \frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+6 a \,b^{2} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(1+\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+12 a \,b^{2} \arctanh \left(c \sqrt{x}\right) \polylog \left(2, -\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+6 a \,b^{2} \ln \left(c \sqrt{x}\right) \arctanh \left(c \sqrt{x}\right)^{2}-3 a^{2} b \ln \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)+2 a^{3} \ln \left(c \sqrt{x}\right)-i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{3}-i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{3}+3 i a \,b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}-\frac{3 b^{3} \polylog \left(4, -\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}{2}+12 b^{3} \polylog \left(4, \frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+12 b^{3} \polylog \left(4, -\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+3 a \,b^{2} \polylog \left(3, -\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)-12 a \,b^{2} \polylog \left(3, \frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)-12 a \,b^{2} \polylog \left(3, -\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)-3 a^{2} b \dilog \left(c \sqrt{x}\right)-3 a^{2} b \dilog \left(1+c \sqrt{x}\right)+2 b^{3} \arctanh \left(c \sqrt{x}\right)^{3} \ln \left(1+\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+6 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \polylog \left(2, -\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)-12 b^{3} \arctanh \left(c \sqrt{x}\right) \polylog \left(3, -\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+2 b^{3} \ln \left(c \sqrt{x}\right) \arctanh \left(c \sqrt{x}\right)^{3}-2 b^{3} \arctanh \left(c \sqrt{x}\right)^{3} \ln \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)-3 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \polylog \left(2, -\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)+3 b^{3} \arctanh \left(c \sqrt{x}\right) \polylog \left(3, -\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)+2 b^{3} \arctanh \left(c \sqrt{x}\right)^{3} \ln \left(1-\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+6 b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \polylog \left(2, \frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)-12 b^{3} \arctanh \left(c \sqrt{x}\right) \polylog \left(3, \frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{3}-3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}-3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}+i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \arctanh \left(c \sqrt{x}\right)^{3}+3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}-1\right)}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \arctanh \left(c \sqrt{x}\right)^{2}"," ",0,"I*b^3*Pi*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^3*arctanh(c*x^(1/2))^3+6*a*b^2*ln(c*x^(1/2))*arctanh(c*x^(1/2))^2-6*a*b^2*arctanh(c*x^(1/2))*polylog(2,-(1+c*x^(1/2))^2/(-c^2*x+1))-6*a*b^2*arctanh(c*x^(1/2))^2*ln((1+c*x^(1/2))^2/(-c^2*x+1)-1)+6*a^2*b*ln(c*x^(1/2))*arctanh(c*x^(1/2))-3*a^2*b*ln(c*x^(1/2))*ln(1+c*x^(1/2))+6*a*b^2*arctanh(c*x^(1/2))^2*ln(1-(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+12*a*b^2*arctanh(c*x^(1/2))*polylog(2,(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+6*a*b^2*arctanh(c*x^(1/2))^2*ln(1+(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+12*a*b^2*arctanh(c*x^(1/2))*polylog(2,-(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-3/2*b^3*polylog(4,-(1+c*x^(1/2))^2/(-c^2*x+1))+12*b^3*polylog(4,(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+12*b^3*polylog(4,-(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+2*a^3*ln(c*x^(1/2))-I*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^3-I*b^3*Pi*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1))*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^3+3*I*a*b^2*Pi*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^3*arctanh(c*x^(1/2))^2+3*a*b^2*polylog(3,-(1+c*x^(1/2))^2/(-c^2*x+1))-12*a*b^2*polylog(3,(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-12*a*b^2*polylog(3,-(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-3*a^2*b*dilog(c*x^(1/2))-3*a^2*b*dilog(1+c*x^(1/2))+2*b^3*arctanh(c*x^(1/2))^3*ln(1+(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+6*b^3*arctanh(c*x^(1/2))^2*polylog(2,-(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-12*b^3*arctanh(c*x^(1/2))*polylog(3,-(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+2*b^3*ln(c*x^(1/2))*arctanh(c*x^(1/2))^3-2*b^3*arctanh(c*x^(1/2))^3*ln((1+c*x^(1/2))^2/(-c^2*x+1)-1)-3*b^3*arctanh(c*x^(1/2))^2*polylog(2,-(1+c*x^(1/2))^2/(-c^2*x+1))+3*b^3*arctanh(c*x^(1/2))*polylog(3,-(1+c*x^(1/2))^2/(-c^2*x+1))+2*b^3*arctanh(c*x^(1/2))^3*ln(1-(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+6*b^3*arctanh(c*x^(1/2))^2*polylog(2,(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-12*b^3*arctanh(c*x^(1/2))*polylog(3,(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+3*I*a*b^2*Pi*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1))*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*arctanh(c*x^(1/2))^2-3*I*a*b^2*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2-3*I*a*b^2*Pi*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1))*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2+I*b^3*Pi*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1))*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*((1+c*x^(1/2))^2/(-c^2*x+1)-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*arctanh(c*x^(1/2))^3","C"
207,1,5199,126,0.634000," ","int((a+b*arctanh(c*x^(1/2)))^3/x^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
208,1,1365,194,0.593000," ","int((a+b*arctanh(c*x^(1/2)))^3/x^3,x)","\frac{3 c^{4} a \,b^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{4}+\frac{3 c^{4} a \,b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{4}-\frac{3 c^{4} a \,b^{2} \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{4}-\frac{c a \,b^{2} \arctanh \left(c \sqrt{x}\right)}{x^{\frac{3}{2}}}-\frac{3 c^{4} b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)}{2}+\frac{3 c^{4} b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(1+c \sqrt{x}\right)}{4}-\frac{3 a^{2} b \arctanh \left(c \sqrt{x}\right)}{2 x^{2}}-\frac{3 a \,b^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{2 x^{2}}-\frac{3 c^{4} b^{3} \arctanh \left(c \sqrt{x}\right)^{2} \ln \left(c \sqrt{x}-1\right)}{4}+\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right) \arctanh \left(c \sqrt{x}\right)^{2}}{8}-\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{8}+\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{4}-\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right)^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{8}-\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{4}-\frac{b^{3} \arctanh \left(c \sqrt{x}\right)^{3}}{2 x^{2}}-4 c^{4} b^{3} \dilog \left(\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)-2 c^{4} b^{3} \arctanh \left(c \sqrt{x}\right)^{2}+\frac{c^{4} b^{3} \arctanh \left(c \sqrt{x}\right)^{3}}{2}+4 c^{4} b^{3} \dilog \left(1+\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)+\frac{b^{3} c^{4} \arctanh \left(c \sqrt{x}\right)}{2}+\frac{c^{4} b^{3} \sqrt{-c^{2} x +1}}{2 \sqrt{-c^{2} x +1}+2 c \sqrt{x}+2}-\frac{3 i c^{4} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \arctanh \left(c \sqrt{x}\right)^{2}}{8}-\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{8}-\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)}{\sqrt{-c^{2} x +1}}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{4}+\frac{3 i c^{4} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{c^{2} x -1}\right) \mathrm{csgn}\left(\frac{i \left(1+c \sqrt{x}\right)^{2}}{\left(c^{2} x -1\right) \left(1+\frac{\left(1+c \sqrt{x}\right)^{2}}{-c^{2} x +1}\right)}\right)^{2} \arctanh \left(c \sqrt{x}\right)^{2}}{8}-\frac{3 c^{3} a \,b^{2} \arctanh \left(c \sqrt{x}\right)}{\sqrt{x}}-\frac{3 c^{4} a \,b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{2}+\frac{3 c^{4} a \,b^{2} \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{2}+\frac{3 i c^{4} b^{3} \pi  \arctanh \left(c \sqrt{x}\right)^{2}}{4}-\frac{c^{4} b^{3} \sqrt{-c^{2} x +1}}{2 \left(c \sqrt{x}+1-\sqrt{-c^{2} x +1}\right)}-\frac{c^{2} a \,b^{2}}{2 x}-2 c^{4} a \,b^{2} \ln \left(c \sqrt{x}-1\right)-2 c^{4} a \,b^{2} \ln \left(1+c \sqrt{x}\right)-\frac{c \,a^{2} b}{2 x^{\frac{3}{2}}}-\frac{3 c^{4} a^{2} b \ln \left(c \sqrt{x}-1\right)}{4}+4 c^{4} b^{3} \arctanh \left(c \sqrt{x}\right) \ln \left(1+\frac{1+c \sqrt{x}}{\sqrt{-c^{2} x +1}}\right)-\frac{c^{2} b^{3} \arctanh \left(c \sqrt{x}\right)}{2 x}-\frac{3 c^{3} b^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{2 \sqrt{x}}-\frac{c \,b^{3} \arctanh \left(c \sqrt{x}\right)^{2}}{2 x^{\frac{3}{2}}}+\frac{3 c^{4} a^{2} b \ln \left(1+c \sqrt{x}\right)}{4}+4 c^{4} a \,b^{2} \ln \left(c \sqrt{x}\right)-\frac{3 c^{3} a^{2} b}{2 \sqrt{x}}-\frac{3 c^{4} a \,b^{2} \ln \left(c \sqrt{x}-1\right)^{2}}{8}-\frac{3 c^{4} a \,b^{2} \ln \left(1+c \sqrt{x}\right)^{2}}{8}-\frac{a^{3}}{2 x^{2}}"," ",0,"-3/8*I*c^4*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^3*arctanh(c*x^(1/2))^2+3/4*I*c^4*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^3*arctanh(c*x^(1/2))^2-3/8*I*c^4*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))^3*arctanh(c*x^(1/2))^2-3/4*I*c^4*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2-c*a*b^2*arctanh(c*x^(1/2))/x^(3/2)-3*c^3*a*b^2*arctanh(c*x^(1/2))/x^(1/2)+3/4*c^4*a*b^2*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))-3/2*c^4*a*b^2*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)+3/2*c^4*a*b^2*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))+3/4*c^4*a*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))-3/4*c^4*a*b^2*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))+3/4*I*c^4*b^3*Pi*arctanh(c*x^(1/2))^2-1/2*b^3/x^2*arctanh(c*x^(1/2))^3-4*c^4*b^3*dilog((1+c*x^(1/2))/(-c^2*x+1)^(1/2))-2*c^4*b^3*arctanh(c*x^(1/2))^2+1/2*c^4*b^3*arctanh(c*x^(1/2))^3+4*c^4*b^3*dilog(1+(1+c*x^(1/2))/(-c^2*x+1)^(1/2))+1/2*b^3*c^4*arctanh(c*x^(1/2))+3/8*I*c^4*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*arctanh(c*x^(1/2))^2-3/8*I*c^4*b^3*Pi*csgn(I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))^2*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*arctanh(c*x^(1/2))^2-3/8*I*c^4*b^3*Pi*csgn(I/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2-3/4*I*c^4*b^3*Pi*csgn(I*(1+c*x^(1/2))/(-c^2*x+1)^(1/2))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))^2*arctanh(c*x^(1/2))^2+3/8*I*c^4*b^3*Pi*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1))*csgn(I*(1+c*x^(1/2))^2/(c^2*x-1)/(1+(1+c*x^(1/2))^2/(-c^2*x+1)))^2*arctanh(c*x^(1/2))^2+4*c^4*b^3*arctanh(c*x^(1/2))*ln(1+(1+c*x^(1/2))/(-c^2*x+1)^(1/2))-1/2*c^2*b^3*arctanh(c*x^(1/2))/x-3/2*c^3*b^3*arctanh(c*x^(1/2))^2/x^(1/2)-1/2*c*b^3*arctanh(c*x^(1/2))^2/x^(3/2)-1/2*c^4*b^3/(c*x^(1/2)+1-(-c^2*x+1)^(1/2))*(-c^2*x+1)^(1/2)-1/2*c^2*a*b^2/x-3/2*c^4*b^3*arctanh(c*x^(1/2))^2*ln((1+c*x^(1/2))/(-c^2*x+1)^(1/2))+1/2*c^4*b^3/((-c^2*x+1)^(1/2)+c*x^(1/2)+1)*(-c^2*x+1)^(1/2)-2*c^4*a*b^2*ln(c*x^(1/2)-1)-2*c^4*a*b^2*ln(1+c*x^(1/2))-1/2*c*a^2*b/x^(3/2)-3/4*c^4*a^2*b*ln(c*x^(1/2)-1)+3/4*c^4*b^3*arctanh(c*x^(1/2))^2*ln(1+c*x^(1/2))+3/4*c^4*a^2*b*ln(1+c*x^(1/2))+4*c^4*a*b^2*ln(c*x^(1/2))-3/2*a^2*b/x^2*arctanh(c*x^(1/2))-3/2*a*b^2/x^2*arctanh(c*x^(1/2))^2-3/2*c^3*a^2*b/x^(1/2)-3/8*c^4*a*b^2*ln(c*x^(1/2)-1)^2-3/8*c^4*a*b^2*ln(1+c*x^(1/2))^2-3/4*c^4*b^3*arctanh(c*x^(1/2))^2*ln(c*x^(1/2)-1)-1/2*a^3/x^2","C"
209,1,35,26,0.025000," ","int(x^(3/2)*arctanh(x^(1/2)),x)","\frac{2 x^{\frac{5}{2}} \arctanh \left(\sqrt{x}\right)}{5}+\frac{x^{2}}{10}+\frac{x}{5}+\frac{\ln \left(-1+\sqrt{x}\right)}{5}+\frac{\ln \left(1+\sqrt{x}\right)}{5}"," ",0,"2/5*x^(5/2)*arctanh(x^(1/2))+1/10*x^2+1/5*x+1/5*ln(-1+x^(1/2))+1/5*ln(1+x^(1/2))","A"
210,1,30,21,0.024000," ","int(arctanh(x^(1/2))*x^(1/2),x)","\frac{2 x^{\frac{3}{2}} \arctanh \left(\sqrt{x}\right)}{3}+\frac{x}{3}+\frac{\ln \left(-1+\sqrt{x}\right)}{3}+\frac{\ln \left(1+\sqrt{x}\right)}{3}"," ",0,"2/3*x^(3/2)*arctanh(x^(1/2))+1/3*x+1/3*ln(-1+x^(1/2))+1/3*ln(1+x^(1/2))","A"
211,1,17,16,0.025000," ","int(arctanh(x^(1/2))/x^(1/2),x)","\ln \left(1-x \right)+2 \arctanh \left(\sqrt{x}\right) \sqrt{x}"," ",0,"ln(1-x)+2*arctanh(x^(1/2))*x^(1/2)","A"
212,1,29,20,0.031000," ","int(arctanh(x^(1/2))/x^(3/2),x)","-\frac{2 \arctanh \left(\sqrt{x}\right)}{\sqrt{x}}+\ln \left(x \right)-\ln \left(-1+\sqrt{x}\right)-\ln \left(1+\sqrt{x}\right)"," ",0,"-2*arctanh(x^(1/2))/x^(1/2)+ln(x)-ln(-1+x^(1/2))-ln(1+x^(1/2))","A"
213,1,194,132,0.036000," ","int(x^3*(a+b*arctanh(c*x^(3/2))),x)","\frac{x^{4} a}{4}+\frac{b \,x^{4} \arctanh \left(c \,x^{\frac{3}{2}}\right)}{4}+\frac{3 b \,x^{\frac{5}{2}}}{20 c}+\frac{b \ln \left(\sqrt{x}-\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{8 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}} \sqrt{x}+\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{16 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sqrt{x}}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{8 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b \ln \left(\sqrt{x}+\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{8 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}} \sqrt{x}+\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{16 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sqrt{x}}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{8 c^{3} \left(\frac{1}{c}\right)^{\frac{1}{3}}}"," ",0,"1/4*x^4*a+1/4*b*x^4*arctanh(c*x^(3/2))+3/20*b*x^(5/2)/c+1/8*b/c^3/(1/c)^(1/3)*ln(x^(1/2)-(1/c)^(1/3))-1/16*b/c^3/(1/c)^(1/3)*ln(x+(1/c)^(1/3)*x^(1/2)+(1/c)^(2/3))+1/8*b/c^3*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x^(1/2)+1))-1/8*b/c^3/(1/c)^(1/3)*ln(x^(1/2)+(1/c)^(1/3))+1/16*b/c^3/(1/c)^(1/3)*ln(x-(1/c)^(1/3)*x^(1/2)+(1/c)^(2/3))+1/8*b/c^3*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x^(1/2)-1))","A"
214,1,57,37,0.025000," ","int(x^2*(a+b*arctanh(c*x^(3/2))),x)","\frac{x^{3} a}{3}+\frac{b \,x^{3} \arctanh \left(c \,x^{\frac{3}{2}}\right)}{3}+\frac{b \,x^{\frac{3}{2}}}{3 c}+\frac{b \ln \left(c \,x^{\frac{3}{2}}-1\right)}{6 c^{2}}-\frac{b \ln \left(c \,x^{\frac{3}{2}}+1\right)}{6 c^{2}}"," ",0,"1/3*x^3*a+1/3*b*x^3*arctanh(c*x^(3/2))+1/3*b*x^(3/2)/c+1/6/c^2*b*ln(c*x^(3/2)-1)-1/6/c^2*b*ln(c*x^(3/2)+1)","A"
215,1,194,132,0.036000," ","int(x*(a+b*arctanh(c*x^(3/2))),x)","\frac{a \,x^{2}}{2}+\frac{b \,x^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right)}{2}+\frac{3 b \sqrt{x}}{2 c}+\frac{b \ln \left(\sqrt{x}-\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{4 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}} \sqrt{x}+\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{8 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sqrt{x}}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{4 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \ln \left(\sqrt{x}+\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{4 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}} \sqrt{x}+\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{8 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sqrt{x}}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{4 c^{2} \left(\frac{1}{c}\right)^{\frac{2}{3}}}"," ",0,"1/2*a*x^2+1/2*b*x^2*arctanh(c*x^(3/2))+3/2*b*x^(1/2)/c+1/4*b/c^2/(1/c)^(2/3)*ln(x^(1/2)-(1/c)^(1/3))-1/8*b/c^2/(1/c)^(2/3)*ln(x+(1/c)^(1/3)*x^(1/2)+(1/c)^(2/3))-1/4*b/c^2/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x^(1/2)+1))-1/4*b/c^2/(1/c)^(2/3)*ln(x^(1/2)+(1/c)^(1/3))+1/8*b/c^2/(1/c)^(2/3)*ln(x-(1/c)^(1/3)*x^(1/2)+(1/c)^(2/3))-1/4*b/c^2/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x^(1/2)-1))","A"
216,1,179,120,0.033000," ","int(a+b*arctanh(c*x^(3/2)),x)","a x +b x \arctanh \left(c \,x^{\frac{3}{2}}\right)+\frac{b \ln \left(\sqrt{x}-\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}} \sqrt{x}+\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sqrt{x}}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b \ln \left(\sqrt{x}+\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}} \sqrt{x}+\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sqrt{x}}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}"," ",0,"a*x+b*x*arctanh(c*x^(3/2))+1/2*b/c/(1/c)^(1/3)*ln(x^(1/2)-(1/c)^(1/3))-1/4*b/c/(1/c)^(1/3)*ln(x+(1/c)^(1/3)*x^(1/2)+(1/c)^(2/3))+1/2*b*3^(1/2)/c/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x^(1/2)+1))-1/2*b/c/(1/c)^(1/3)*ln(x^(1/2)+(1/c)^(1/3))+1/4*b/c/(1/c)^(1/3)*ln(x-(1/c)^(1/3)*x^(1/2)+(1/c)^(2/3))+1/2*b*3^(1/2)/c/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x^(1/2)-1))","A"
217,1,63,26,0.042000," ","int((a+b*arctanh(c*x^(3/2)))/x,x)","\frac{2 a \ln \left(c \,x^{\frac{3}{2}}\right)}{3}+\frac{2 b \ln \left(c \,x^{\frac{3}{2}}\right) \arctanh \left(c \,x^{\frac{3}{2}}\right)}{3}-\frac{b \dilog \left(c \,x^{\frac{3}{2}}\right)}{3}-\frac{b \dilog \left(c \,x^{\frac{3}{2}}+1\right)}{3}-\frac{b \ln \left(c \,x^{\frac{3}{2}}\right) \ln \left(c \,x^{\frac{3}{2}}+1\right)}{3}"," ",0,"2/3*a*ln(c*x^(3/2))+2/3*b*ln(c*x^(3/2))*arctanh(c*x^(3/2))-1/3*b*dilog(c*x^(3/2))-1/3*b*dilog(c*x^(3/2)+1)-1/3*b*ln(c*x^(3/2))*ln(c*x^(3/2)+1)","B"
218,1,167,124,0.036000," ","int((a+b*arctanh(c*x^(3/2)))/x^2,x)","-\frac{a}{x}-\frac{b \arctanh \left(c \,x^{\frac{3}{2}}\right)}{x}-\frac{b \ln \left(\sqrt{x}-\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{2 \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}} \sqrt{x}+\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{4 \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sqrt{x}}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{2 \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b \ln \left(\sqrt{x}+\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{2 \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}} \sqrt{x}+\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{4 \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sqrt{x}}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{2 \left(\frac{1}{c}\right)^{\frac{2}{3}}}"," ",0,"-a/x-b/x*arctanh(c*x^(3/2))-1/2*b/(1/c)^(2/3)*ln(x^(1/2)-(1/c)^(1/3))+1/4*b/(1/c)^(2/3)*ln(x+(1/c)^(1/3)*x^(1/2)+(1/c)^(2/3))+1/2*b/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x^(1/2)+1))+1/2*b/(1/c)^(2/3)*ln(x^(1/2)+(1/c)^(1/3))-1/4*b/(1/c)^(2/3)*ln(x-(1/c)^(1/3)*x^(1/2)+(1/c)^(2/3))+1/2*b/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x^(1/2)-1))","A"
219,1,180,133,0.040000," ","int((a+b*arctanh(c*x^(3/2)))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arctanh \left(c \,x^{\frac{3}{2}}\right)}{2 x^{2}}-\frac{3 b c}{2 \sqrt{x}}-\frac{b c \ln \left(\sqrt{x}-\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{4 \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b c \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}} \sqrt{x}+\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{8 \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b c \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sqrt{x}}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{4 \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b c \ln \left(\sqrt{x}+\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{4 \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b c \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}} \sqrt{x}+\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{8 \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b c \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sqrt{x}}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{4 \left(\frac{1}{c}\right)^{\frac{1}{3}}}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arctanh(c*x^(3/2))-3/2*b*c/x^(1/2)-1/4*b*c/(1/c)^(1/3)*ln(x^(1/2)-(1/c)^(1/3))+1/8*b*c/(1/c)^(1/3)*ln(x+(1/c)^(1/3)*x^(1/2)+(1/c)^(2/3))-1/4*b*c*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x^(1/2)+1))+1/4*b*c/(1/c)^(1/3)*ln(x^(1/2)+(1/c)^(1/3))-1/8*b*c/(1/c)^(1/3)*ln(x-(1/c)^(1/3)*x^(1/2)+(1/c)^(2/3))-1/4*b*c*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x^(1/2)-1))","A"
220,1,55,38,0.035000," ","int((a+b*arctanh(c*x^(3/2)))/x^4,x)","-\frac{a}{3 x^{3}}-\frac{b \arctanh \left(c \,x^{\frac{3}{2}}\right)}{3 x^{3}}-\frac{b c}{3 x^{\frac{3}{2}}}-\frac{b \,c^{2} \ln \left(c \,x^{\frac{3}{2}}-1\right)}{6}+\frac{b \,c^{2} \ln \left(c \,x^{\frac{3}{2}}+1\right)}{6}"," ",0,"-1/3*a/x^3-1/3*b/x^3*arctanh(c*x^(3/2))-1/3*b*c/x^(3/2)-1/6*b*c^2*ln(c*x^(3/2)-1)+1/6*b*c^2*ln(c*x^(3/2)+1)","A"
221,1,284,81,0.054000," ","int(x^2*(a+b*arctanh(c*x^(3/2)))^2,x)","\frac{x^{3} a^{2}}{3}+\frac{x^{3} b^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right)^{2}}{3}+\frac{2 b^{2} x^{\frac{3}{2}} \arctanh \left(c \,x^{\frac{3}{2}}\right)}{3 c}+\frac{b^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right) \ln \left(c \,x^{\frac{3}{2}}-1\right)}{3 c^{2}}-\frac{b^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right) \ln \left(c \,x^{\frac{3}{2}}+1\right)}{3 c^{2}}+\frac{b^{2} \ln \left(c \,x^{\frac{3}{2}}-1\right)^{2}}{12 c^{2}}-\frac{b^{2} \ln \left(c \,x^{\frac{3}{2}}-1\right) \ln \left(\frac{1}{2}+\frac{c \,x^{\frac{3}{2}}}{2}\right)}{6 c^{2}}+\frac{b^{2} \ln \left(c \,x^{\frac{3}{2}}-1\right)}{3 c^{2}}+\frac{b^{2} \ln \left(c \,x^{\frac{3}{2}}+1\right)}{3 c^{2}}+\frac{b^{2} \ln \left(c \,x^{\frac{3}{2}}+1\right)^{2}}{12 c^{2}}+\frac{b^{2} \ln \left(-\frac{c \,x^{\frac{3}{2}}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \,x^{\frac{3}{2}}}{2}\right)}{6 c^{2}}-\frac{b^{2} \ln \left(-\frac{c \,x^{\frac{3}{2}}}{2}+\frac{1}{2}\right) \ln \left(c \,x^{\frac{3}{2}}+1\right)}{6 c^{2}}+\frac{2 a b \,x^{3} \arctanh \left(c \,x^{\frac{3}{2}}\right)}{3}+\frac{2 a b \,x^{\frac{3}{2}}}{3 c}+\frac{a b \ln \left(c \,x^{\frac{3}{2}}-1\right)}{3 c^{2}}-\frac{a b \ln \left(c \,x^{\frac{3}{2}}+1\right)}{3 c^{2}}"," ",0,"1/3*x^3*a^2+1/3*x^3*b^2*arctanh(c*x^(3/2))^2+2/3*b^2*x^(3/2)*arctanh(c*x^(3/2))/c+1/3/c^2*b^2*arctanh(c*x^(3/2))*ln(c*x^(3/2)-1)-1/3/c^2*b^2*arctanh(c*x^(3/2))*ln(c*x^(3/2)+1)+1/12/c^2*b^2*ln(c*x^(3/2)-1)^2-1/6/c^2*b^2*ln(c*x^(3/2)-1)*ln(1/2+1/2*c*x^(3/2))+1/3/c^2*b^2*ln(c*x^(3/2)-1)+1/3/c^2*b^2*ln(c*x^(3/2)+1)+1/12/c^2*b^2*ln(c*x^(3/2)+1)^2+1/6/c^2*b^2*ln(-1/2*c*x^(3/2)+1/2)*ln(1/2+1/2*c*x^(3/2))-1/6/c^2*b^2*ln(-1/2*c*x^(3/2)+1/2)*ln(c*x^(3/2)+1)+2/3*a*b*x^3*arctanh(c*x^(3/2))+2/3*a*b*x^(3/2)/c+1/3/c^2*a*b*ln(c*x^(3/2)-1)-1/3/c^2*a*b*ln(c*x^(3/2)+1)","B"
222,1,785,130,0.248000," ","int((a+b*arctanh(c*x^(3/2)))^2/x,x)","\frac{2 a^{2} \ln \left(c \,x^{\frac{3}{2}}\right)}{3}+\frac{2 b^{2} \ln \left(c \,x^{\frac{3}{2}}\right) \arctanh \left(c \,x^{\frac{3}{2}}\right)^{2}}{3}-\frac{2 b^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right) \polylog \left(2, -\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}\right)}{3}+\frac{b^{2} \polylog \left(3, -\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}\right)}{3}-\frac{2 b^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right)^{2} \ln \left(\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}-1\right)}{3}+\frac{2 b^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right)^{2} \ln \left(1-\frac{c \,x^{\frac{3}{2}}+1}{\sqrt{-c^{2} x^{3}+1}}\right)}{3}+\frac{4 b^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right) \polylog \left(2, \frac{c \,x^{\frac{3}{2}}+1}{\sqrt{-c^{2} x^{3}+1}}\right)}{3}-\frac{4 b^{2} \polylog \left(3, \frac{c \,x^{\frac{3}{2}}+1}{\sqrt{-c^{2} x^{3}+1}}\right)}{3}+\frac{2 b^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right)^{2} \ln \left(1+\frac{c \,x^{\frac{3}{2}}+1}{\sqrt{-c^{2} x^{3}+1}}\right)}{3}+\frac{4 b^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right) \polylog \left(2, -\frac{c \,x^{\frac{3}{2}}+1}{\sqrt{-c^{2} x^{3}+1}}\right)}{3}-\frac{4 b^{2} \polylog \left(3, -\frac{c \,x^{\frac{3}{2}}+1}{\sqrt{-c^{2} x^{3}+1}}\right)}{3}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}-1\right)}{1+\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}}\right)^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right)^{2}}{3}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}-1\right)}{1+\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}}\right)^{2} \arctanh \left(c \,x^{\frac{3}{2}}\right)^{2}}{3}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}-1\right)}{1+\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}}\right) \arctanh \left(c \,x^{\frac{3}{2}}\right)^{2}}{3}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}-1\right)}{1+\frac{\left(c \,x^{\frac{3}{2}}+1\right)^{2}}{-c^{2} x^{3}+1}}\right)^{3} \arctanh \left(c \,x^{\frac{3}{2}}\right)^{2}}{3}+\frac{4 a b \ln \left(c \,x^{\frac{3}{2}}\right) \arctanh \left(c \,x^{\frac{3}{2}}\right)}{3}-\frac{2 a b \ln \left(c \,x^{\frac{3}{2}}\right) \ln \left(c \,x^{\frac{3}{2}}+1\right)}{3}-\frac{2 a b \dilog \left(c \,x^{\frac{3}{2}}\right)}{3}-\frac{2 a b \dilog \left(c \,x^{\frac{3}{2}}+1\right)}{3}"," ",0,"2/3*a^2*ln(c*x^(3/2))+2/3*b^2*ln(c*x^(3/2))*arctanh(c*x^(3/2))^2-2/3*b^2*arctanh(c*x^(3/2))*polylog(2,-(c*x^(3/2)+1)^2/(-c^2*x^3+1))+1/3*b^2*polylog(3,-(c*x^(3/2)+1)^2/(-c^2*x^3+1))-2/3*b^2*arctanh(c*x^(3/2))^2*ln((c*x^(3/2)+1)^2/(-c^2*x^3+1)-1)+2/3*b^2*arctanh(c*x^(3/2))^2*ln(1-(c*x^(3/2)+1)/(-c^2*x^3+1)^(1/2))+4/3*b^2*arctanh(c*x^(3/2))*polylog(2,(c*x^(3/2)+1)/(-c^2*x^3+1)^(1/2))-4/3*b^2*polylog(3,(c*x^(3/2)+1)/(-c^2*x^3+1)^(1/2))+2/3*b^2*arctanh(c*x^(3/2))^2*ln(1+(c*x^(3/2)+1)/(-c^2*x^3+1)^(1/2))+4/3*b^2*arctanh(c*x^(3/2))*polylog(2,-(c*x^(3/2)+1)/(-c^2*x^3+1)^(1/2))-4/3*b^2*polylog(3,-(c*x^(3/2)+1)/(-c^2*x^3+1)^(1/2))-1/3*I*b^2*Pi*csgn(I/(1+(c*x^(3/2)+1)^2/(-c^2*x^3+1)))*csgn(I*((c*x^(3/2)+1)^2/(-c^2*x^3+1)-1)/(1+(c*x^(3/2)+1)^2/(-c^2*x^3+1)))^2*arctanh(c*x^(3/2))^2+1/3*I*b^2*Pi*csgn(I*((c*x^(3/2)+1)^2/(-c^2*x^3+1)-1))*csgn(I/(1+(c*x^(3/2)+1)^2/(-c^2*x^3+1)))*csgn(I*((c*x^(3/2)+1)^2/(-c^2*x^3+1)-1)/(1+(c*x^(3/2)+1)^2/(-c^2*x^3+1)))*arctanh(c*x^(3/2))^2+1/3*I*b^2*Pi*csgn(I*((c*x^(3/2)+1)^2/(-c^2*x^3+1)-1)/(1+(c*x^(3/2)+1)^2/(-c^2*x^3+1)))^3*arctanh(c*x^(3/2))^2-1/3*I*b^2*Pi*csgn(I*((c*x^(3/2)+1)^2/(-c^2*x^3+1)-1))*csgn(I*((c*x^(3/2)+1)^2/(-c^2*x^3+1)-1)/(1+(c*x^(3/2)+1)^2/(-c^2*x^3+1)))^2*arctanh(c*x^(3/2))^2+4/3*a*b*ln(c*x^(3/2))*arctanh(c*x^(3/2))-2/3*a*b*ln(c*x^(3/2))*ln(c*x^(3/2)+1)-2/3*a*b*dilog(c*x^(3/2))-2/3*a*b*dilog(c*x^(3/2)+1)","C"
223,0,0,80,0.432000," ","int((a+b*arctanh(c*x^(3/2)))^2/x^4,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{\frac{3}{2}}\right)\right)^{2}}{x^{4}}\, dx"," ",0,"int((a+b*arctanh(c*x^(3/2)))^2/x^4,x)","F"
224,0,0,60,0.138000," ","int(x^2*(a+b*arctanh(c*x^n)),x)","\int x^{2} \left(a +b \arctanh \left(c \,x^{n}\right)\right)\, dx"," ",0,"int(x^2*(a+b*arctanh(c*x^n)),x)","F"
225,0,0,57,0.277000," ","int(x*(a+b*arctanh(c*x^n)),x)","\int x \left(a +b \arctanh \left(c \,x^{n}\right)\right)\, dx"," ",0,"int(x*(a+b*arctanh(c*x^n)),x)","F"
226,0,0,56,0.220000," ","int(a+b*arctanh(c*x^n),x)","\int a +b \arctanh \left(c \,x^{n}\right)\, dx"," ",0,"int(a+b*arctanh(c*x^n),x)","F"
227,1,76,32,0.045000," ","int((a+b*arctanh(c*x^n))/x,x)","\frac{a \ln \left(c \,x^{n}\right)}{n}+\frac{b \ln \left(c \,x^{n}\right) \arctanh \left(c \,x^{n}\right)}{n}-\frac{b \dilog \left(c \,x^{n}\right)}{2 n}-\frac{b \dilog \left(c \,x^{n}+1\right)}{2 n}-\frac{b \ln \left(c \,x^{n}\right) \ln \left(c \,x^{n}+1\right)}{2 n}"," ",0,"1/n*a*ln(c*x^n)+1/n*b*ln(c*x^n)*arctanh(c*x^n)-1/2/n*b*dilog(c*x^n)-1/2/n*b*dilog(c*x^n+1)-1/2/n*b*ln(c*x^n)*ln(c*x^n+1)","B"
228,0,0,63,0.122000," ","int((a+b*arctanh(c*x^n))/x^2,x)","\int \frac{a +b \arctanh \left(c \,x^{n}\right)}{x^{2}}\, dx"," ",0,"int((a+b*arctanh(c*x^n))/x^2,x)","F"
229,0,0,63,0.127000," ","int((a+b*arctanh(c*x^n))/x^3,x)","\int \frac{a +b \arctanh \left(c \,x^{n}\right)}{x^{3}}\, dx"," ",0,"int((a+b*arctanh(c*x^n))/x^3,x)","F"
230,0,0,67,0.131000," ","int((a+b*arctanh(c*x^n))/x^4,x)","\int \frac{a +b \arctanh \left(c \,x^{n}\right)}{x^{4}}\, dx"," ",0,"int((a+b*arctanh(c*x^n))/x^4,x)","F"
231,0,0,16,0.194000," ","int(x*(a+b*arctanh(c*x^n))^2,x)","\int x \left(a +b \arctanh \left(c \,x^{n}\right)\right)^{2}\, dx"," ",0,"int(x*(a+b*arctanh(c*x^n))^2,x)","F"
232,0,0,14,0.233000," ","int((a+b*arctanh(c*x^n))^2,x)","\int \left(a +b \arctanh \left(c \,x^{n}\right)\right)^{2}\, dx"," ",0,"int((a+b*arctanh(c*x^n))^2,x)","F"
233,1,880,144,0.241000," ","int((a+b*arctanh(c*x^n))^2/x,x)","\frac{a^{2} \ln \left(c \,x^{n}\right)}{n}+\frac{b^{2} \ln \left(c \,x^{n}\right) \arctanh \left(c \,x^{n}\right)^{2}}{n}-\frac{b^{2} \arctanh \left(c \,x^{n}\right) \polylog \left(2, -\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}\right)}{n}+\frac{b^{2} \polylog \left(3, -\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}\right)}{2 n}-\frac{b^{2} \arctanh \left(c \,x^{n}\right)^{2} \ln \left(\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}-1\right)}{n}+\frac{b^{2} \arctanh \left(c \,x^{n}\right)^{2} \ln \left(1-\frac{c \,x^{n}+1}{\sqrt{-c^{2} x^{2 n}+1}}\right)}{n}+\frac{2 b^{2} \arctanh \left(c \,x^{n}\right) \polylog \left(2, \frac{c \,x^{n}+1}{\sqrt{-c^{2} x^{2 n}+1}}\right)}{n}-\frac{2 b^{2} \polylog \left(3, \frac{c \,x^{n}+1}{\sqrt{-c^{2} x^{2 n}+1}}\right)}{n}+\frac{b^{2} \arctanh \left(c \,x^{n}\right)^{2} \ln \left(1+\frac{c \,x^{n}+1}{\sqrt{-c^{2} x^{2 n}+1}}\right)}{n}+\frac{2 b^{2} \arctanh \left(c \,x^{n}\right) \polylog \left(2, -\frac{c \,x^{n}+1}{\sqrt{-c^{2} x^{2 n}+1}}\right)}{n}-\frac{2 b^{2} \polylog \left(3, -\frac{c \,x^{n}+1}{\sqrt{-c^{2} x^{2 n}+1}}\right)}{n}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}-1\right)}{1+\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}}\right)^{3} \arctanh \left(c \,x^{n}\right)^{2}}{2 n}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}-1\right)}{1+\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}}\right)^{2} \arctanh \left(c \,x^{n}\right)^{2}}{2 n}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}-1\right)}{1+\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}}\right)^{2} \arctanh \left(c \,x^{n}\right)^{2}}{2 n}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}-1\right)}{1+\frac{\left(c \,x^{n}+1\right)^{2}}{-c^{2} x^{2 n}+1}}\right) \arctanh \left(c \,x^{n}\right)^{2}}{2 n}+\frac{2 a b \ln \left(c \,x^{n}\right) \arctanh \left(c \,x^{n}\right)}{n}-\frac{a b \ln \left(c \,x^{n}\right) \ln \left(c \,x^{n}+1\right)}{n}-\frac{a b \dilog \left(c \,x^{n}\right)}{n}-\frac{a b \dilog \left(c \,x^{n}+1\right)}{n}"," ",0,"1/n*a^2*ln(c*x^n)+1/n*b^2*ln(c*x^n)*arctanh(c*x^n)^2-1/n*b^2*arctanh(c*x^n)*polylog(2,-(c*x^n+1)^2/(-c^2*(x^n)^2+1))+1/2/n*b^2*polylog(3,-(c*x^n+1)^2/(-c^2*(x^n)^2+1))-1/n*b^2*arctanh(c*x^n)^2*ln((c*x^n+1)^2/(-c^2*(x^n)^2+1)-1)+1/n*b^2*arctanh(c*x^n)^2*ln(1-(c*x^n+1)/(-c^2*(x^n)^2+1)^(1/2))+2/n*b^2*arctanh(c*x^n)*polylog(2,(c*x^n+1)/(-c^2*(x^n)^2+1)^(1/2))-2/n*b^2*polylog(3,(c*x^n+1)/(-c^2*(x^n)^2+1)^(1/2))+1/n*b^2*arctanh(c*x^n)^2*ln(1+(c*x^n+1)/(-c^2*(x^n)^2+1)^(1/2))+2/n*b^2*arctanh(c*x^n)*polylog(2,-(c*x^n+1)/(-c^2*(x^n)^2+1)^(1/2))-2/n*b^2*polylog(3,-(c*x^n+1)/(-c^2*(x^n)^2+1)^(1/2))-1/2*I/n*b^2*Pi*csgn(I*((c*x^n+1)^2/(-c^2*(x^n)^2+1)-1))*csgn(I*((c*x^n+1)^2/(-c^2*(x^n)^2+1)-1)/(1+(c*x^n+1)^2/(-c^2*(x^n)^2+1)))^2*arctanh(c*x^n)^2+1/2*I/n*b^2*Pi*csgn(I*((c*x^n+1)^2/(-c^2*(x^n)^2+1)-1)/(1+(c*x^n+1)^2/(-c^2*(x^n)^2+1)))^3*arctanh(c*x^n)^2+1/2*I/n*b^2*Pi*csgn(I*((c*x^n+1)^2/(-c^2*(x^n)^2+1)-1))*csgn(I/(1+(c*x^n+1)^2/(-c^2*(x^n)^2+1)))*csgn(I*((c*x^n+1)^2/(-c^2*(x^n)^2+1)-1)/(1+(c*x^n+1)^2/(-c^2*(x^n)^2+1)))*arctanh(c*x^n)^2-1/2*I/n*b^2*Pi*csgn(I/(1+(c*x^n+1)^2/(-c^2*(x^n)^2+1)))*csgn(I*((c*x^n+1)^2/(-c^2*(x^n)^2+1)-1)/(1+(c*x^n+1)^2/(-c^2*(x^n)^2+1)))^2*arctanh(c*x^n)^2+2/n*a*b*ln(c*x^n)*arctanh(c*x^n)-1/n*a*b*ln(c*x^n)*ln(c*x^n+1)-1/n*a*b*dilog(c*x^n)-1/n*a*b*dilog(c*x^n+1)","C"
234,0,0,18,0.123000," ","int((a+b*arctanh(c*x^n))^2/x^2,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{n}\right)\right)^{2}}{x^{2}}\, dx"," ",0,"int((a+b*arctanh(c*x^n))^2/x^2,x)","F"
235,0,0,18,0.129000," ","int((a+b*arctanh(c*x^n))^2/x^3,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{n}\right)\right)^{2}}{x^{3}}\, dx"," ",0,"int((a+b*arctanh(c*x^n))^2/x^3,x)","F"
236,1,61,26,0.042000," ","int(arctanh(a*x^n)/x,x)","\frac{\ln \left(a \,x^{n}\right) \arctanh \left(a \,x^{n}\right)}{n}-\frac{\dilog \left(a \,x^{n}\right)}{2 n}-\frac{\dilog \left(a \,x^{n}+1\right)}{2 n}-\frac{\ln \left(a \,x^{n}\right) \ln \left(a \,x^{n}+1\right)}{2 n}"," ",0,"1/n*ln(a*x^n)*arctanh(a*x^n)-1/2/n*dilog(a*x^n)-1/2/n*dilog(a*x^n+1)-1/2/n*ln(a*x^n)*ln(a*x^n+1)","B"
237,1,85,20,0.104000," ","int(arctanh(a*x^5)/x,x)","\ln \left(x \right) \arctanh \left(a \,x^{5}\right)-\frac{\left(\munderset{\textit{\_R1} =\RootOf \left(a \,\textit{\_Z}^{5}+1\right)}{\sum}\left(\ln \left(x \right) \ln \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)\right)\right)}{2}+\frac{\left(\munderset{\textit{\_R1} =\RootOf \left(a \,\textit{\_Z}^{5}-1\right)}{\sum}\left(\ln \left(x \right) \ln \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)\right)\right)}{2}"," ",0,"ln(x)*arctanh(a*x^5)-1/2*sum(ln(x)*ln((_R1-x)/_R1)+dilog((_R1-x)/_R1),_R1=RootOf(_Z^5*a+1))+1/2*sum(ln(x)*ln((_R1-x)/_R1)+dilog((_R1-x)/_R1),_R1=RootOf(_Z^5*a-1))","C"
238,1,30,17,0.046000," ","int(arctanh(1/x),x)","x \arctanh \left(\frac{1}{x}\right)-\ln \left(\frac{1}{x}\right)+\frac{\ln \left(\frac{1}{x}-1\right)}{2}+\frac{\ln \left(\frac{1}{x}+1\right)}{2}"," ",0,"x*arctanh(1/x)-ln(1/x)+1/2*ln(1/x-1)+1/2*ln(1/x+1)","A"
239,0,0,20,0.246000," ","int((d*x)^m*(a+b*arctanh(c*x^n))^3,x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c \,x^{n}\right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x^n))^3,x)","F"
240,0,0,20,0.234000," ","int((d*x)^m*(a+b*arctanh(c*x^n))^2,x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c \,x^{n}\right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x^n))^2,x)","F"
241,0,0,82,0.286000," ","int((d*x)^m*(a+b*arctanh(c*x^n)),x)","\int \left(d x \right)^{m} \left(a +b \arctanh \left(c \,x^{n}\right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arctanh(c*x^n)),x)","F"
242,0,0,20,0.064000," ","int((d*x)^m/(a+b*arctanh(c*x^n)),x)","\int \frac{\left(d x \right)^{m}}{a +b \arctanh \left(c \,x^{n}\right)}\, dx"," ",0,"int((d*x)^m/(a+b*arctanh(c*x^n)),x)","F"
243,0,0,20,0.296000," ","int((d*x)^m/(a+b*arctanh(c*x^n))^2,x)","\int \frac{\left(d x \right)^{m}}{\left(a +b \arctanh \left(c \,x^{n}\right)\right)^{2}}\, dx"," ",0,"int((d*x)^m/(a+b*arctanh(c*x^n))^2,x)","F"