1,1,395,137,0.034000," ","int((e*x+d)^4*(a+b*arctanh(c*x)),x)","\frac{b \,e^{3} d x}{c^{3}}+\frac{b \,e^{4} \arctanh \left(c x \right) x^{5}}{5}+b \arctanh \left(c x \right) x \,d^{4}+\frac{b \arctanh \left(c x \right) d^{5}}{5 e}-\frac{b \ln \left(c x +1\right) d^{5}}{10 e}+\frac{b \,e^{4} x^{2}}{10 c^{3}}+2 a e \,x^{2} d^{3}+2 a \,e^{2} x^{3} d^{2}+a \,e^{3} x^{4} d +\frac{b \,e^{4} \ln \left(c x -1\right)}{10 c^{5}}+\frac{b \,e^{4} \ln \left(c x +1\right)}{10 c^{5}}+\frac{b \ln \left(c x -1\right) d^{4}}{2 c}+\frac{b \ln \left(c x +1\right) d^{4}}{2 c}+\frac{b \ln \left(c x -1\right) d^{5}}{10 e}+\frac{a \,d^{5}}{5 e}+\frac{a \,e^{4} x^{5}}{5}+a x \,d^{4}+\frac{b \,e^{2} x^{2} d^{2}}{c}+b \,e^{3} \arctanh \left(c x \right) x^{4} d +2 b \,e^{2} \arctanh \left(c x \right) x^{3} d^{2}+2 b e \arctanh \left(c x \right) x^{2} d^{3}+\frac{b e \ln \left(c x -1\right) d^{3}}{c^{2}}+\frac{b \,e^{2} \ln \left(c x -1\right) d^{2}}{c^{3}}+\frac{b \,e^{3} \ln \left(c x -1\right) d}{2 c^{4}}-\frac{b \,e^{3} \ln \left(c x +1\right) d}{2 c^{4}}-\frac{b e \ln \left(c x +1\right) d^{3}}{c^{2}}+\frac{b \,e^{2} \ln \left(c x +1\right) d^{2}}{c^{3}}+\frac{2 b e \,d^{3} x}{c}+\frac{b d \,e^{3} x^{3}}{3 c}+\frac{b \,e^{4} x^{4}}{20 c}"," ",0,"b/c^3*e^3*d*x-1/10*b/e*ln(c*x+1)*d^5+1/5*b*e^4*arctanh(c*x)*x^5+1/10/c^3*b*e^4*x^2+2*a*e*x^2*d^3+2*a*e^2*x^3*d^2+a*e^3*x^4*d+b*arctanh(c*x)*x*d^4+1/10/c^5*b*e^4*ln(c*x-1)+1/10/c^5*b*e^4*ln(c*x+1)+1/2/c*b*ln(c*x-1)*d^4+1/2/c*b*ln(c*x+1)*d^4+1/10*b/e*ln(c*x-1)*d^5+1/5*b/e*arctanh(c*x)*d^5+1/5*a/e*d^5+1/5*a*e^4*x^5+a*x*d^4+1/c*b*e^2*x^2*d^2+b*e^3*arctanh(c*x)*x^4*d+2*b*e^2*arctanh(c*x)*x^3*d^2+2*b*e*arctanh(c*x)*x^2*d^3+1/c^2*b*e*ln(c*x-1)*d^3+1/c^3*b*e^2*ln(c*x-1)*d^2+1/2/c^4*b*e^3*ln(c*x-1)*d-1/2/c^4*b*e^3*ln(c*x+1)*d-1/c^2*b*e*ln(c*x+1)*d^3+1/c^3*b*e^2*ln(c*x+1)*d^2+2*b/c*e*d^3*x+1/3*b*d*e^3*x^3/c+1/20*b*e^4*x^4/c","B"
2,1,308,113,0.031000," ","int((e*x+d)^3*(a+b*arctanh(c*x)),x)","\frac{a \,x^{4} e^{3}}{4}+a d \,e^{2} x^{3}+\frac{3 a \,d^{2} e \,x^{2}}{2}+a x \,d^{3}+\frac{a \,d^{4}}{4 e}+\frac{b \,e^{3} \arctanh \left(c x \right) x^{4}}{4}+b \,e^{2} \arctanh \left(c x \right) x^{3} d +\frac{3 b e \arctanh \left(c x \right) x^{2} d^{2}}{2}+b \arctanh \left(c x \right) x \,d^{3}+\frac{b \arctanh \left(c x \right) d^{4}}{4 e}+\frac{b \,e^{3} x^{3}}{12 c}+\frac{b d \,e^{2} x^{2}}{2 c}+\frac{3 b e x \,d^{2}}{2 c}+\frac{b x \,e^{3}}{4 c^{3}}+\frac{b \ln \left(c x -1\right) d^{4}}{8 e}+\frac{b \ln \left(c x -1\right) d^{3}}{2 c}+\frac{3 b e \ln \left(c x -1\right) d^{2}}{4 c^{2}}+\frac{b \,e^{2} \ln \left(c x -1\right) d}{2 c^{3}}+\frac{b \,e^{3} \ln \left(c x -1\right)}{8 c^{4}}-\frac{b \ln \left(c x +1\right) d^{4}}{8 e}+\frac{b \ln \left(c x +1\right) d^{3}}{2 c}-\frac{3 b e \ln \left(c x +1\right) d^{2}}{4 c^{2}}+\frac{b \,e^{2} \ln \left(c x +1\right) d}{2 c^{3}}-\frac{b \,e^{3} \ln \left(c x +1\right)}{8 c^{4}}"," ",0,"1/4*a*x^4*e^3+a*d*e^2*x^3+3/2*a*d^2*e*x^2+a*x*d^3+1/4*a/e*d^4+1/4*b*e^3*arctanh(c*x)*x^4+b*e^2*arctanh(c*x)*x^3*d+3/2*b*e*arctanh(c*x)*x^2*d^2+b*arctanh(c*x)*x*d^3+1/4*b/e*arctanh(c*x)*d^4+1/12*b*e^3*x^3/c+1/2*b*d*e^2*x^2/c+3/2*b/c*e*x*d^2+1/4*b/c^3*x*e^3+1/8*b/e*ln(c*x-1)*d^4+1/2/c*b*ln(c*x-1)*d^3+3/4/c^2*b*e*ln(c*x-1)*d^2+1/2/c^3*b*e^2*ln(c*x-1)*d+1/8/c^4*b*e^3*ln(c*x-1)-1/8*b/e*ln(c*x+1)*d^4+1/2/c*b*ln(c*x+1)*d^3-3/4/c^2*b*e*ln(c*x+1)*d^2+1/2/c^3*b*e^2*ln(c*x+1)*d-1/8/c^4*b*e^3*ln(c*x+1)","B"
3,1,218,88,0.032000," ","int((e*x+d)^2*(a+b*arctanh(c*x)),x)","\frac{a \,x^{3} e^{2}}{3}+a d e \,x^{2}+a x \,d^{2}+\frac{a \,d^{3}}{3 e}+\frac{b \,e^{2} \arctanh \left(c x \right) x^{3}}{3}+b e \arctanh \left(c x \right) x^{2} d +b \arctanh \left(c x \right) x \,d^{2}+\frac{b \arctanh \left(c x \right) d^{3}}{3 e}+\frac{b \,e^{2} x^{2}}{6 c}+\frac{b d e x}{c}+\frac{b \ln \left(c x -1\right) d^{3}}{6 e}+\frac{b \ln \left(c x -1\right) d^{2}}{2 c}+\frac{b e \ln \left(c x -1\right) d}{2 c^{2}}+\frac{b \,e^{2} \ln \left(c x -1\right)}{6 c^{3}}-\frac{b \ln \left(c x +1\right) d^{3}}{6 e}+\frac{b \ln \left(c x +1\right) d^{2}}{2 c}-\frac{b e \ln \left(c x +1\right) d}{2 c^{2}}+\frac{b \,e^{2} \ln \left(c x +1\right)}{6 c^{3}}"," ",0,"1/3*a*x^3*e^2+a*d*e*x^2+a*x*d^2+1/3*a/e*d^3+1/3*b*e^2*arctanh(c*x)*x^3+b*e*arctanh(c*x)*x^2*d+b*arctanh(c*x)*x*d^2+1/3*b/e*arctanh(c*x)*d^3+1/6*b*e^2*x^2/c+b*d*e*x/c+1/6*b/e*ln(c*x-1)*d^3+1/2/c*b*ln(c*x-1)*d^2+1/2/c^2*b*e*ln(c*x-1)*d+1/6/c^3*b*e^2*ln(c*x-1)-1/6*b/e*ln(c*x+1)*d^3+1/2/c*b*ln(c*x+1)*d^2-1/2/c^2*b*e*ln(c*x+1)*d+1/6/c^3*b*e^2*ln(c*x+1)","B"
4,1,92,76,0.029000," ","int((e*x+d)*(a+b*arctanh(c*x)),x)","\frac{a \,x^{2} e}{2}+a d x +\frac{b \arctanh \left(c x \right) x^{2} e}{2}+b \arctanh \left(c x \right) x d +\frac{b e x}{2 c}+\frac{b \ln \left(c x -1\right) d}{2 c}+\frac{b \ln \left(c x -1\right) e}{4 c^{2}}+\frac{b \ln \left(c x +1\right) d}{2 c}-\frac{b \ln \left(c x +1\right) e}{4 c^{2}}"," ",0,"1/2*a*x^2*e+a*d*x+1/2*b*arctanh(c*x)*x^2*e+b*arctanh(c*x)*x*d+1/2*b*e*x/c+1/2/c*b*ln(c*x-1)*d+1/4/c^2*b*ln(c*x-1)*e+1/2/c*b*ln(c*x+1)*d-1/4/c^2*b*ln(c*x+1)*e","A"
5,1,148,110,0.089000," ","int((a+b*arctanh(c*x))/(e*x+d),x)","\frac{a \ln \left(c x e +c d \right)}{e}+\frac{b \ln \left(c x e +c d \right) \arctanh \left(c x \right)}{e}+\frac{b \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{2 e}+\frac{b \dilog \left(\frac{c x e -e}{-c d -e}\right)}{2 e}-\frac{b \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{2 e}-\frac{b \dilog \left(\frac{c x e +e}{-c d +e}\right)}{2 e}"," ",0,"a*ln(c*e*x+c*d)/e+b*ln(c*e*x+c*d)/e*arctanh(c*x)+1/2*b/e*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))+1/2*b/e*dilog((c*e*x-e)/(-c*d-e))-1/2*b/e*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))-1/2*b/e*dilog((c*e*x+e)/(-c*d+e))","A"
6,1,114,91,0.036000," ","int((a+b*arctanh(c*x))/(e*x+d)^2,x)","-\frac{c a}{\left(c x e +c d \right) e}-\frac{c b \arctanh \left(c x \right)}{\left(c x e +c d \right) e}-\frac{c b \ln \left(c x e +c d \right)}{\left(c d +e \right) \left(c d -e \right)}-\frac{c b \ln \left(c x -1\right)}{e \left(2 c d +2 e \right)}+\frac{c b \ln \left(c x +1\right)}{e \left(2 c d -2 e \right)}"," ",0,"-c*a/(c*e*x+c*d)/e-c*b/(c*e*x+c*d)/e*arctanh(c*x)-c*b/(c*d+e)/(c*d-e)*ln(c*e*x+c*d)-c*b/e/(2*c*d+2*e)*ln(c*x-1)+c*b/e/(2*c*d-2*e)*ln(c*x+1)","A"
7,1,154,125,0.039000," ","int((a+b*arctanh(c*x))/(e*x+d)^3,x)","-\frac{c^{2} a}{2 \left(c x e +c d \right)^{2} e}-\frac{c^{2} b \arctanh \left(c x \right)}{2 \left(c x e +c d \right)^{2} e}+\frac{c^{2} b}{2 \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)}-\frac{c^{3} b d \ln \left(c x e +c d \right)}{\left(c d +e \right)^{2} \left(c d -e \right)^{2}}-\frac{c^{2} b \ln \left(c x -1\right)}{4 e \left(c d +e \right)^{2}}+\frac{b \,c^{2} \ln \left(c x +1\right)}{4 \left(c d -e \right)^{2} e}"," ",0,"-1/2*c^2*a/(c*e*x+c*d)^2/e-1/2*c^2*b/(c*e*x+c*d)^2/e*arctanh(c*x)+1/2*c^2*b/(c*d+e)/(c*d-e)/(c*e*x+c*d)-c^3*b*d/(c*d+e)^2/(c*d-e)^2*ln(c*e*x+c*d)-1/4*c^2*b/e/(c*d+e)^2*ln(c*x-1)+1/4*b*c^2*ln(c*x+1)/(c*d-e)^2/e","A"
8,1,223,165,0.040000," ","int((a+b*arctanh(c*x))/(e*x+d)^4,x)","-\frac{c^{3} a}{3 \left(c x e +c d \right)^{3} e}-\frac{c^{3} b \arctanh \left(c x \right)}{3 \left(c x e +c d \right)^{3} e}+\frac{c^{3} b}{6 \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)^{2}}-\frac{c^{5} b \ln \left(c x e +c d \right) d^{2}}{\left(c d +e \right)^{3} \left(c d -e \right)^{3}}-\frac{c^{3} b \,e^{2} \ln \left(c x e +c d \right)}{3 \left(c d +e \right)^{3} \left(c d -e \right)^{3}}+\frac{2 c^{4} b d}{3 \left(c d +e \right)^{2} \left(c d -e \right)^{2} \left(c x e +c d \right)}-\frac{c^{3} b \ln \left(c x -1\right)}{6 e \left(c d +e \right)^{3}}+\frac{b \,c^{3} \ln \left(c x +1\right)}{6 \left(c d -e \right)^{3} e}"," ",0,"-1/3*c^3*a/(c*e*x+c*d)^3/e-1/3*c^3*b/(c*e*x+c*d)^3/e*arctanh(c*x)+1/6*c^3*b/(c*d+e)/(c*d-e)/(c*e*x+c*d)^2-c^5*b/(c*d+e)^3/(c*d-e)^3*ln(c*e*x+c*d)*d^2-1/3*c^3*b*e^2/(c*d+e)^3/(c*d-e)^3*ln(c*e*x+c*d)+2/3*c^4*b*d/(c*d+e)^2/(c*d-e)^2/(c*e*x+c*d)-1/6*c^3*b/e/(c*d+e)^3*ln(c*x-1)+1/6*b*c^3*ln(c*x+1)/(c*d-e)^3/e","A"
9,1,1430,343,0.069000," ","int((e*x+d)^3*(a+b*arctanh(c*x))^2,x)","\frac{a^{2} d^{4}}{4 e}+a^{2} e^{2} x^{3} d +\frac{3 a^{2} e \,x^{2} d^{2}}{2}+b^{2} \arctanh \left(c x \right)^{2} x \,d^{3}+\frac{b^{2} \arctanh \left(c x \right)^{2} d^{4}}{4 e}+\frac{b^{2} e^{3} \arctanh \left(c x \right)^{2} x^{4}}{4}-\frac{b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right) d^{3}}{c}+\frac{b^{2} \ln \left(c x -1\right)^{2} d^{4}}{16 e}+\frac{b^{2} \ln \left(c x +1\right)^{2} d^{4}}{16 e}+\frac{b^{2} e^{3} \ln \left(c x +1\right)^{2}}{16 c^{4}}+\frac{b^{2} e^{3} \ln \left(c x -1\right)}{3 c^{4}}+\frac{b^{2} e^{3} \ln \left(c x +1\right)}{3 c^{4}}+\frac{b^{2} e^{3} \ln \left(c x -1\right)^{2}}{16 c^{4}}+\frac{b^{2} \ln \left(c x -1\right)^{2} d^{3}}{4 c}-\frac{b^{2} \ln \left(c x +1\right)^{2} d^{3}}{4 c}+\frac{b^{2} e^{3} \arctanh \left(c x \right) x}{2 c^{3}}+b^{2} e^{2} \arctanh \left(c x \right)^{2} x^{3} d +\frac{3 b^{2} e \arctanh \left(c x \right)^{2} x^{2} d^{2}}{2}+\frac{b^{2} e^{3} \arctanh \left(c x \right) \ln \left(c x -1\right)}{4 c^{4}}-\frac{b^{2} e^{3} \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) d^{4}}{4 e}-\frac{b^{2} \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d^{3}}{2 c}-\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right) d^{3}}{2 c}+\frac{a b \ln \left(c x -1\right) d^{4}}{4 e}-\frac{a b \ln \left(c x +1\right) d^{4}}{4 e}-\frac{b^{2} \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d^{4}}{8 e}+\frac{b^{2} \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d^{4}}{8 e}+\frac{b^{2} \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d^{3}}{2 c}+\frac{a b x \,e^{3}}{2 c^{3}}+\frac{a b \ln \left(c x +1\right) d^{3}}{c}+\frac{a b \ln \left(c x -1\right) d^{3}}{c}+\frac{b^{2} e^{2} \ln \left(c x -1\right)^{2} d}{4 c^{3}}-\frac{b^{2} e^{2} \ln \left(c x +1\right)^{2} d}{4 c^{3}}+\frac{3 b^{2} e \ln \left(c x +1\right)^{2} d^{2}}{8 c^{2}}-\frac{a b \,e^{3} \ln \left(c x +1\right)}{4 c^{4}}+\frac{a b \,e^{3} \ln \left(c x -1\right)}{4 c^{4}}+\frac{3 b^{2} e \ln \left(c x -1\right) d^{2}}{2 c^{2}}+\frac{3 b^{2} e \ln \left(c x +1\right) d^{2}}{2 c^{2}}+\frac{b^{2} e^{2} \ln \left(c x -1\right) d}{2 c^{3}}-\frac{b^{2} e^{2} \ln \left(c x +1\right) d}{2 c^{3}}+\frac{b^{2} e^{3} x^{2}}{12 c^{2}}-\frac{b^{2} e^{3} \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right)}{8 c^{4}}+\frac{b^{2} e^{3} \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right)}{8 c^{4}}-\frac{b^{2} e^{3} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{8 c^{4}}+\frac{a b \,x^{3} e^{3}}{6 c}+\frac{3 b^{2} e \ln \left(c x -1\right)^{2} d^{2}}{8 c^{2}}+a^{2} x \,d^{3}+\frac{a^{2} e^{3} x^{4}}{4}-\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right) d^{4}}{8 e}+\frac{a b \arctanh \left(c x \right) d^{4}}{2 e}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right) d^{3}}{c}+\frac{a b \,e^{3} \arctanh \left(c x \right) x^{4}}{2}+\frac{b^{2} e^{3} \arctanh \left(c x \right) x^{3}}{6 c}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right) d^{3}}{c}-\frac{b^{2} e^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right) d}{c^{3}}-\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right) d^{4}}{4 e}+2 a b \arctanh \left(c x \right) x \,d^{3}+\frac{b^{2} d \,e^{2} x}{c^{2}}+\frac{3 b^{2} e \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d^{2}}{4 c^{2}}-\frac{b^{2} e^{2} \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d}{2 c^{3}}-\frac{3 b^{2} e \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right) d^{2}}{4 c^{2}}-\frac{b^{2} e^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right) d}{2 c^{3}}+\frac{b^{2} e^{2} \arctanh \left(c x \right) \ln \left(c x +1\right) d}{c^{3}}+\frac{3 b^{2} e \arctanh \left(c x \right) \ln \left(c x -1\right) d^{2}}{2 c^{2}}+\frac{3 b^{2} e \arctanh \left(c x \right) x \,d^{2}}{c}+\frac{b^{2} e^{2} \arctanh \left(c x \right) x^{2} d}{c}+2 a b \,e^{2} \arctanh \left(c x \right) x^{3} d +3 a b e \arctanh \left(c x \right) x^{2} d^{2}+\frac{b^{2} e^{2} \arctanh \left(c x \right) \ln \left(c x -1\right) d}{c^{3}}-\frac{3 b^{2} e \arctanh \left(c x \right) \ln \left(c x +1\right) d^{2}}{2 c^{2}}+\frac{3 a b e x \,d^{2}}{c}+\frac{a b \,e^{2} x^{2} d}{c}+\frac{3 a b e \ln \left(c x -1\right) d^{2}}{2 c^{2}}+\frac{a b \,e^{2} \ln \left(c x -1\right) d}{c^{3}}-\frac{3 a b e \ln \left(c x +1\right) d^{2}}{2 c^{2}}+\frac{a b \,e^{2} \ln \left(c x +1\right) d}{c^{3}}-\frac{3 b^{2} e \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d^{2}}{4 c^{2}}+\frac{b^{2} e^{2} \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d}{2 c^{3}}"," ",0,"1/4*a^2/e*d^4+a^2*e^2*x^3*d+3/2*a^2*e*x^2*d^2+b^2*arctanh(c*x)^2*x*d^3+1/4*b^2/e*arctanh(c*x)^2*d^4+1/16*b^2/e*ln(c*x-1)^2*d^4+1/16*b^2/e*ln(c*x+1)^2*d^4+1/4*b^2*e^3*arctanh(c*x)^2*x^4+1/16/c^4*b^2*e^3*ln(c*x+1)^2+1/3/c^4*b^2*e^3*ln(c*x-1)+1/3/c^4*b^2*e^3*ln(c*x+1)+1/16/c^4*b^2*e^3*ln(c*x-1)^2+1/4/c*b^2*ln(c*x-1)^2*d^3-1/c*b^2*dilog(1/2+1/2*c*x)*d^3-1/4/c*b^2*ln(c*x+1)^2*d^3-1/2/c*b^2*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)*d^3-1/2/c*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)*d^3+1/2*a*b/e*arctanh(c*x)*d^4+1/4*a*b/e*ln(c*x-1)*d^4-1/4*a*b/e*ln(c*x+1)*d^4-1/8*b^2/e*ln(c*x+1)*ln(-1/2*c*x+1/2)*d^4+1/8*b^2/e*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)*d^4+1/c*b^2*arctanh(c*x)*ln(c*x-1)*d^3+1/2*a*b*e^3*arctanh(c*x)*x^4+1/2/c*b^2*ln(c*x+1)*ln(-1/2*c*x+1/2)*d^3+1/6/c*b^2*e^3*arctanh(c*x)*x^3+1/c*b^2*arctanh(c*x)*ln(c*x+1)*d^3+1/2*a*b/c^3*x*e^3+1/c*a*b*ln(c*x+1)*d^3+1/c*a*b*ln(c*x-1)*d^3+1/4/c^3*b^2*e^2*ln(c*x-1)^2*d-1/c^3*b^2*e^2*dilog(1/2+1/2*c*x)*d+1/2/c^3*b^2*e^3*arctanh(c*x)*x-1/4/c^3*b^2*e^2*ln(c*x+1)^2*d+3/8/c^2*b^2*e*ln(c*x+1)^2*d^2-1/4/c^4*a*b*e^3*ln(c*x+1)+1/4/c^4*a*b*e^3*ln(c*x-1)+3/2/c^2*b^2*e*ln(c*x-1)*d^2+3/2/c^2*b^2*e*ln(c*x+1)*d^2+1/2/c^3*b^2*e^2*ln(c*x-1)*d-1/2/c^3*b^2*e^2*ln(c*x+1)*d+b^2*e^2*arctanh(c*x)^2*x^3*d+3/2*b^2*e*arctanh(c*x)^2*x^2*d^2+1/12*b^2*e^3*x^2/c^2-1/8/c^4*b^2*e^3*ln(c*x+1)*ln(-1/2*c*x+1/2)+1/8/c^4*b^2*e^3*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)+1/4/c^4*b^2*e^3*arctanh(c*x)*ln(c*x-1)-1/4/c^4*b^2*e^3*arctanh(c*x)*ln(c*x+1)-1/8/c^4*b^2*e^3*ln(c*x-1)*ln(1/2+1/2*c*x)+1/6/c*a*b*x^3*e^3+3/8/c^2*b^2*e*ln(c*x-1)^2*d^2+a^2*x*d^3+1/4*a^2*e^3*x^4+1/4*b^2/e*arctanh(c*x)*ln(c*x-1)*d^4-1/8*b^2/e*ln(c*x-1)*ln(1/2+1/2*c*x)*d^4-1/4*b^2/e*arctanh(c*x)*ln(c*x+1)*d^4+2*a*b*arctanh(c*x)*x*d^3+b^2*d*e^2*x/c^2+1/c^3*b^2*e^2*arctanh(c*x)*ln(c*x+1)*d+3/2/c^2*b^2*e*arctanh(c*x)*ln(c*x-1)*d^2+3/4/c^2*b^2*e*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)*d^2-1/2/c^3*b^2*e^2*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)*d-3/4/c^2*b^2*e*ln(c*x-1)*ln(1/2+1/2*c*x)*d^2-1/2/c^3*b^2*e^2*ln(c*x-1)*ln(1/2+1/2*c*x)*d+3/c*b^2*e*arctanh(c*x)*x*d^2+1/c*b^2*e^2*arctanh(c*x)*x^2*d+3*a*b/c*e*x*d^2+1/c*a*b*e^2*x^2*d+2*a*b*e^2*arctanh(c*x)*x^3*d+3*a*b*e*arctanh(c*x)*x^2*d^2+3/2/c^2*a*b*e*ln(c*x-1)*d^2+1/c^3*a*b*e^2*ln(c*x-1)*d-3/2/c^2*a*b*e*ln(c*x+1)*d^2+1/c^3*a*b*e^2*ln(c*x+1)*d-3/4/c^2*b^2*e*ln(c*x+1)*ln(-1/2*c*x+1/2)*d^2+1/2/c^3*b^2*e^2*ln(c*x+1)*ln(-1/2*c*x+1/2)*d+1/c^3*b^2*e^2*arctanh(c*x)*ln(c*x-1)*d-3/2/c^2*b^2*e*arctanh(c*x)*ln(c*x+1)*d^2","B"
10,1,1050,241,0.066000," ","int((e*x+d)^2*(a+b*arctanh(c*x))^2,x)","-\frac{b^{2} e^{2} \ln \left(c x +1\right)^{2}}{12 c^{3}}+a^{2} e \,x^{2} d +\frac{b^{2} e^{2} \arctanh \left(c x \right)^{2} x^{3}}{3}-\frac{b^{2} e^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{3 c^{3}}-\frac{b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right) d^{2}}{c}+\frac{b^{2} \arctanh \left(c x \right)^{2} d^{3}}{3 e}+b^{2} \arctanh \left(c x \right)^{2} x \,d^{2}+\frac{b^{2} e^{2} \ln \left(c x -1\right)^{2}}{12 c^{3}}-\frac{b^{2} \ln \left(c x +1\right)^{2} d^{2}}{4 c}+\frac{b^{2} \ln \left(c x -1\right)^{2} d^{2}}{4 c}+\frac{b^{2} \ln \left(c x -1\right)^{2} d^{3}}{12 e}+\frac{b^{2} \ln \left(c x +1\right)^{2} d^{3}}{12 e}+\frac{b^{2} e^{2} \ln \left(c x -1\right)}{6 c^{3}}-\frac{b^{2} e^{2} \ln \left(c x +1\right)}{6 c^{3}}+\frac{a^{2} d^{3}}{3 e}+\frac{a b \,e^{2} \ln \left(c x +1\right)}{3 c^{3}}+\frac{b^{2} e^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{3 c^{3}}+\frac{b^{2} e^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{3 c^{3}}+\frac{2 a b \arctanh \left(c x \right) d^{3}}{3 e}+b^{2} e \arctanh \left(c x \right)^{2} x^{2} d +\frac{2 a b \,e^{2} \arctanh \left(c x \right) x^{3}}{3}-\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right) d^{3}}{3 e}+2 a b \arctanh \left(c x \right) x \,d^{2}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right) d^{3}}{3 e}+\frac{b^{2} e^{2} \arctanh \left(c x \right) x^{2}}{3 c}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right) d^{2}}{c}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right) d^{2}}{c}+\frac{b^{2} e^{2} x}{3 c^{2}}+\frac{a b e \ln \left(c x -1\right) d}{c^{2}}-\frac{a b e \ln \left(c x +1\right) d}{c^{2}}-\frac{b^{2} e \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right) d}{2 c^{2}}+\frac{b^{2} e \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d}{2 c^{2}}-\frac{b^{2} e \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d}{2 c^{2}}+2 a b e \arctanh \left(c x \right) x^{2} d +\frac{b^{2} e \arctanh \left(c x \right) \ln \left(c x -1\right) d}{c^{2}}-\frac{b^{2} e \arctanh \left(c x \right) \ln \left(c x +1\right) d}{c^{2}}+\frac{2 b^{2} d e x \arctanh \left(c x \right)}{c}+\frac{b^{2} e \ln \left(c x -1\right)^{2} d}{4 c^{2}}+\frac{b^{2} e \ln \left(c x -1\right) d}{c^{2}}+\frac{b^{2} e \ln \left(c x +1\right) d}{c^{2}}+\frac{b^{2} e \ln \left(c x +1\right)^{2} d}{4 c^{2}}-\frac{b^{2} e^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{6 c^{3}}-\frac{b^{2} e^{2} \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right)}{6 c^{3}}+\frac{b^{2} e^{2} \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right)}{6 c^{3}}+\frac{a b \ln \left(c x -1\right) d^{3}}{3 e}-\frac{a b \ln \left(c x +1\right) d^{3}}{3 e}+\frac{a b \,e^{2} \ln \left(c x -1\right)}{3 c^{3}}+\frac{a^{2} e^{2} x^{3}}{3}+a^{2} x \,d^{2}-\frac{b^{2} \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d^{3}}{6 e}+\frac{b^{2} \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d^{3}}{6 e}-\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right) d^{3}}{6 e}-\frac{b^{2} \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d^{2}}{2 c}+\frac{b^{2} \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d^{2}}{2 c}-\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right) d^{2}}{2 c}+\frac{a b \,x^{2} e^{2}}{3 c}+\frac{a b \ln \left(c x -1\right) d^{2}}{c}+\frac{a b \ln \left(c x +1\right) d^{2}}{c}+\frac{2 a b d e x}{c}"," ",0,"1/3*b^2*e^2*arctanh(c*x)^2*x^3-1/12/c^3*b^2*e^2*ln(c*x+1)^2+a^2*e*x^2*d+1/12/c^3*b^2*e^2*ln(c*x-1)^2-1/3/c^3*b^2*e^2*dilog(1/2+1/2*c*x)-1/c*b^2*dilog(1/2+1/2*c*x)*d^2-1/4/c*b^2*ln(c*x+1)^2*d^2+1/4/c*b^2*ln(c*x-1)^2*d^2+1/12*b^2/e*ln(c*x-1)^2*d^3+1/3*b^2/e*arctanh(c*x)^2*d^3+1/12*b^2/e*ln(c*x+1)^2*d^3+b^2*arctanh(c*x)^2*x*d^2+1/6/c^3*b^2*e^2*ln(c*x-1)-1/6/c^3*b^2*e^2*ln(c*x+1)+1/3*a^2/e*d^3+1/3/c^3*a*b*e^2*ln(c*x+1)+1/3*b^2*e^2*x/c^2+2*a*b*e*arctanh(c*x)*x^2*d+1/c^2*a*b*e*ln(c*x-1)*d-1/c^2*a*b*e*ln(c*x+1)*d+1/c^2*b^2*e*arctanh(c*x)*ln(c*x-1)*d-1/2/c^2*b^2*e*ln(c*x-1)*ln(1/2+1/2*c*x)*d+1/2/c^2*b^2*e*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)*d-1/2/c^2*b^2*e*ln(c*x+1)*ln(-1/2*c*x+1/2)*d-1/c^2*b^2*e*arctanh(c*x)*ln(c*x+1)*d+1/4/c^2*b^2*e*ln(c*x-1)^2*d+1/c^2*b^2*e*ln(c*x-1)*d+1/c^2*b^2*e*ln(c*x+1)*d+1/4/c^2*b^2*e*ln(c*x+1)^2*d-1/6/c^3*b^2*e^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/3/c^3*b^2*e^2*arctanh(c*x)*ln(c*x-1)+1/3/c^3*b^2*e^2*arctanh(c*x)*ln(c*x+1)-1/6/c^3*b^2*e^2*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)+1/6/c^3*b^2*e^2*ln(c*x+1)*ln(-1/2*c*x+1/2)+1/3*a*b/e*ln(c*x-1)*d^3+2/3*a*b/e*arctanh(c*x)*d^3-1/3*a*b/e*ln(c*x+1)*d^3+1/3/c^3*a*b*e^2*ln(c*x-1)+1/3*a^2*e^2*x^3+a^2*x*d^2+b^2*e*arctanh(c*x)^2*x^2*d+2/3*a*b*e^2*arctanh(c*x)*x^3-1/3*b^2/e*arctanh(c*x)*ln(c*x+1)*d^3+2*a*b*arctanh(c*x)*x*d^2-1/6*b^2/e*ln(c*x+1)*ln(-1/2*c*x+1/2)*d^3+1/6*b^2/e*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)*d^3-1/6*b^2/e*ln(c*x-1)*ln(1/2+1/2*c*x)*d^3+1/3*b^2/e*arctanh(c*x)*ln(c*x-1)*d^3-1/2/c*b^2*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)*d^2+1/3/c*b^2*e^2*arctanh(c*x)*x^2+1/2/c*b^2*ln(c*x+1)*ln(-1/2*c*x+1/2)*d^2-1/2/c*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)*d^2+1/c*b^2*arctanh(c*x)*ln(c*x+1)*d^2+1/3/c*a*b*x^2*e^2+1/c*b^2*arctanh(c*x)*ln(c*x-1)*d^2+1/c*a*b*ln(c*x-1)*d^2+1/c*a*b*ln(c*x+1)*d^2+2*a*b*d*e*x/c+2*b^2*d*e*x*arctanh(c*x)/c","B"
11,1,462,154,0.058000," ","int((e*x+d)*(a+b*arctanh(c*x))^2,x)","-\frac{b^{2} \ln \left(c x +1\right)^{2} d}{4 c}+\frac{b^{2} \ln \left(c x +1\right) e}{2 c^{2}}-\frac{b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right) d}{c}+b^{2} \arctanh \left(c x \right)^{2} x d +\frac{b^{2} \arctanh \left(c x \right)^{2} x^{2} e}{2}+\frac{b^{2} \ln \left(c x +1\right)^{2} e}{8 c^{2}}+\frac{b^{2} \ln \left(c x -1\right)^{2} e}{8 c^{2}}+\frac{b^{2} \ln \left(c x -1\right) e}{2 c^{2}}+\frac{b^{2} \ln \left(c x -1\right)^{2} d}{4 c}+a^{2} d x +\frac{a b e x}{c}-\frac{a b \ln \left(c x +1\right) e}{2 c^{2}}-\frac{b^{2} \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) e}{4 c^{2}}+\frac{b^{2} \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) e}{4 c^{2}}+\frac{a b \ln \left(c x -1\right) e}{2 c^{2}}+\frac{b^{2} \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d}{2 c}-\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right) d}{2 c}-\frac{b^{2} \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d}{2 c}+\frac{a b \ln \left(c x +1\right) d}{c}+\frac{a b \ln \left(c x -1\right) d}{c}-\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right) e}{4 c^{2}}+\frac{a^{2} x^{2} e}{2}+\frac{b^{2} e x \arctanh \left(c x \right)}{c}-\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right) e}{2 c^{2}}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right) e}{2 c^{2}}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right) d}{c}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right) d}{c}+a b \arctanh \left(c x \right) x^{2} e +2 a b \arctanh \left(c x \right) x d"," ",0,"-1/4/c*b^2*ln(c*x+1)^2*d+1/2/c^2*b^2*ln(c*x+1)*e-1/c*b^2*dilog(1/2+1/2*c*x)*d+b^2*arctanh(c*x)^2*x*d+1/2*b^2*arctanh(c*x)^2*x^2*e+1/8/c^2*b^2*ln(c*x+1)^2*e+1/8/c^2*b^2*ln(c*x-1)^2*e+1/2/c^2*b^2*ln(c*x-1)*e+1/4/c*b^2*ln(c*x-1)^2*d+a^2*d*x+a*b*e*x/c+b^2*e*x*arctanh(c*x)/c-1/2/c^2*a*b*ln(c*x+1)*e-1/2/c^2*b^2*arctanh(c*x)*ln(c*x+1)*e-1/4/c^2*b^2*ln(c*x+1)*ln(-1/2*c*x+1/2)*e+1/4/c^2*b^2*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)*e+1/2/c^2*b^2*arctanh(c*x)*ln(c*x-1)*e+1/2/c^2*a*b*ln(c*x-1)*e+1/2/c*b^2*ln(c*x+1)*ln(-1/2*c*x+1/2)*d-1/2/c*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)*d+1/c*b^2*arctanh(c*x)*ln(c*x-1)*d+1/c*b^2*arctanh(c*x)*ln(c*x+1)*d-1/2/c*b^2*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)*d+1/c*a*b*ln(c*x+1)*d+1/c*a*b*ln(c*x-1)*d-1/4/c^2*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)*e+1/2*a^2*x^2*e+a*b*arctanh(c*x)*x^2*e+2*a*b*arctanh(c*x)*x*d","B"
12,1,1170,184,0.743000," ","int((a+b*arctanh(c*x))^2/(e*x+d),x)","\frac{a^{2} \ln \left(c x e +c d \right)}{e}+\frac{b^{2} \ln \left(c x e +c d \right) \arctanh \left(c x \right)^{2}}{e}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{e}+\frac{i b^{2} \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) \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)\right)}{2 e}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3}}{2 e}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)\right)}{2 e}-\frac{i b^{2} \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) \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 e}-\frac{b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{e}+\frac{b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 e}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{c d +e}+\frac{b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{c d +e}-\frac{b^{2} \polylog \left(3, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{2 \left(c d +e \right)}+\frac{c \,b^{2} d \arctanh \left(c x \right)^{2} \ln \left(1-\frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{e \left(c d +e \right)}+\frac{c \,b^{2} d \arctanh \left(c x \right) \polylog \left(2, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{e \left(c d +e \right)}-\frac{c \,b^{2} d \polylog \left(3, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{2 e \left(c d +e \right)}+\frac{2 a b \ln \left(c x e +c d \right) \arctanh \left(c x \right)}{e}+\frac{a b \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{e}+\frac{a b \dilog \left(\frac{c x e -e}{-c d -e}\right)}{e}-\frac{a b \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{e}-\frac{a b \dilog \left(\frac{c x e +e}{-c d +e}\right)}{e}"," ",0,"a^2*ln(c*e*x+c*d)/e+b^2*ln(c*e*x+c*d)/e*arctanh(c*x)^2-b^2/e*arctanh(c*x)^2*ln(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))-1/2*I*b^2/e*arctanh(c*x)^2*Pi*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))-1/2*I*b^2/e*arctanh(c*x)^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)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+1/2*I*b^2/e*arctanh(c*x)^2*Pi*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^3+1/2*I*b^2/e*arctanh(c*x)^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)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))-b^2/e*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/2*b^2/e*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+b^2/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+b^2/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-1/2*b^2/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+c*b^2/e*d/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+c*b^2/e*d/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-1/2*c*b^2/e*d/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+2*a*b*ln(c*e*x+c*d)/e*arctanh(c*x)+a*b/e*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))+a*b/e*dilog((c*e*x-e)/(-c*d-e))-a*b/e*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))-a*b/e*dilog((c*e*x+e)/(-c*d+e))","C"
13,1,605,317,0.072000," ","int((a+b*arctanh(c*x))^2/(e*x+d)^2,x)","-\frac{c \,a^{2}}{\left(c x e +c d \right) e}-\frac{c \,b^{2} \arctanh \left(c x \right)^{2}}{\left(c x e +c d \right) e}-\frac{2 c \,b^{2} \arctanh \left(c x \right) \ln \left(c x e +c d \right)}{\left(c d +e \right) \left(c d -e \right)}-\frac{2 c \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{e \left(2 c d +2 e \right)}+\frac{2 c \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{e \left(2 c d -2 e \right)}-\frac{c \,b^{2} \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{\left(c d +e \right) \left(c d -e \right)}-\frac{c \,b^{2} \dilog \left(\frac{c x e -e}{-c d -e}\right)}{\left(c d +e \right) \left(c d -e \right)}+\frac{c \,b^{2} \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{\left(c d +e \right) \left(c d -e \right)}+\frac{c \,b^{2} \dilog \left(\frac{c x e +e}{-c d +e}\right)}{\left(c d +e \right) \left(c d -e \right)}-\frac{c \,b^{2} \ln \left(c x +1\right)^{2}}{4 e \left(c d -e \right)}+\frac{c \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 e \left(c d -e \right)}-\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 e \left(c d -e \right)}-\frac{c \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 e \left(c d -e \right)}-\frac{c \,b^{2} \ln \left(c x -1\right)^{2}}{4 e \left(c d +e \right)}+\frac{c \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 e \left(c d +e \right)}+\frac{c \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 e \left(c d +e \right)}-\frac{2 c a b \arctanh \left(c x \right)}{\left(c x e +c d \right) e}-\frac{2 c a b \ln \left(c x e +c d \right)}{\left(c d +e \right) \left(c d -e \right)}-\frac{2 c a b \ln \left(c x -1\right)}{e \left(2 c d +2 e \right)}+\frac{2 c a b \ln \left(c x +1\right)}{e \left(2 c d -2 e \right)}"," ",0,"-c*a^2/(c*e*x+c*d)/e-c*b^2/(c*e*x+c*d)/e*arctanh(c*x)^2-2*c*b^2*arctanh(c*x)/(c*d+e)/(c*d-e)*ln(c*e*x+c*d)-2*c*b^2/e*arctanh(c*x)/(2*c*d+2*e)*ln(c*x-1)+2*c*b^2/e*arctanh(c*x)/(2*c*d-2*e)*ln(c*x+1)-c*b^2/(c*d+e)/(c*d-e)*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))-c*b^2/(c*d+e)/(c*d-e)*dilog((c*e*x-e)/(-c*d-e))+c*b^2/(c*d+e)/(c*d-e)*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))+c*b^2/(c*d+e)/(c*d-e)*dilog((c*e*x+e)/(-c*d+e))-1/4*c*b^2/e/(c*d-e)*ln(c*x+1)^2+1/2*c*b^2/e/(c*d-e)*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/2*c*b^2/e/(c*d-e)*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/2*c*b^2/e/(c*d-e)*dilog(1/2+1/2*c*x)-1/4*c*b^2/e/(c*d+e)*ln(c*x-1)^2+1/2*c*b^2/e/(c*d+e)*dilog(1/2+1/2*c*x)+1/2*c*b^2/e/(c*d+e)*ln(c*x-1)*ln(1/2+1/2*c*x)-2*c*a*b/(c*e*x+c*d)/e*arctanh(c*x)-2*c*a*b/(c*d+e)/(c*d-e)*ln(c*e*x+c*d)-2*c*a*b/e/(2*c*d+2*e)*ln(c*x-1)+2*c*a*b/e/(2*c*d-2*e)*ln(c*x+1)","A"
14,1,824,461,0.079000," ","int((a+b*arctanh(c*x))^2/(e*x+d)^3,x)","\frac{c^{2} a b}{\left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)}+\frac{c^{2} a b \ln \left(c x +1\right)}{2 e \left(c d -e \right)^{2}}+\frac{c^{2} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 e \left(c d +e \right)^{2}}+\frac{c^{2} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{4 e \left(c d -e \right)^{2}}-\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 e \left(c d -e \right)^{2}}-\frac{c^{2} a b \ln \left(c x -1\right)}{2 e \left(c d +e \right)^{2}}+\frac{c^{2} b^{2} e \ln \left(c x e +c d \right)}{\left(c d +e \right)^{2} \left(c d -e \right)^{2}}+\frac{c^{2} b^{2} \ln \left(c x -1\right)}{\left(c d +e \right) \left(c d -e \right) \left(2 c d +2 e \right)}-\frac{c^{2} b^{2} \ln \left(c x +1\right)}{\left(c d +e \right) \left(c d -e \right) \left(2 c d -2 e \right)}+\frac{c^{2} b^{2} \arctanh \left(c x \right)}{\left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)}-\frac{c^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{2 e \left(c d +e \right)^{2}}+\frac{c^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{2 e \left(c d -e \right)^{2}}-\frac{c^{2} a b \arctanh \left(c x \right)}{\left(c x e +c d \right)^{2} e}-\frac{c^{3} b^{2} d \dilog \left(\frac{c x e -e}{-c d -e}\right)}{\left(c d +e \right)^{2} \left(c d -e \right)^{2}}+\frac{c^{3} b^{2} d \dilog \left(\frac{c x e +e}{-c d +e}\right)}{\left(c d +e \right)^{2} \left(c d -e \right)^{2}}-\frac{c^{2} a^{2}}{2 \left(c x e +c d \right)^{2} e}-\frac{2 c^{3} a b d \ln \left(c x e +c d \right)}{\left(c d +e \right)^{2} \left(c d -e \right)^{2}}-\frac{c^{3} b^{2} d \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{\left(c d +e \right)^{2} \left(c d -e \right)^{2}}-\frac{2 c^{3} b^{2} \arctanh \left(c x \right) d \ln \left(c x e +c d \right)}{\left(c d +e \right)^{2} \left(c d -e \right)^{2}}+\frac{c^{3} b^{2} d \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{\left(c d +e \right)^{2} \left(c d -e \right)^{2}}+\frac{c^{2} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 e \left(c d +e \right)^{2}}-\frac{c^{2} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 e \left(c d -e \right)^{2}}-\frac{c^{2} b^{2} \arctanh \left(c x \right)^{2}}{2 \left(c x e +c d \right)^{2} e}-\frac{c^{2} b^{2} \ln \left(c x +1\right)^{2}}{8 e \left(c d -e \right)^{2}}-\frac{c^{2} b^{2} \ln \left(c x -1\right)^{2}}{8 e \left(c d +e \right)^{2}}"," ",0,"c^2*a*b/(c*d+e)/(c*d-e)/(c*e*x+c*d)+1/2*c^2*a*b/e/(c*d-e)^2*ln(c*x+1)+c^2*b^2*arctanh(c*x)/(c*d+e)/(c*d-e)/(c*e*x+c*d)-1/2*c^2*b^2/e*arctanh(c*x)/(c*d+e)^2*ln(c*x-1)+1/2*c^2*b^2/e*arctanh(c*x)/(c*d-e)^2*ln(c*x+1)+1/4*c^2*b^2/e/(c*d+e)^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/4*c^2*b^2/e/(c*d-e)^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/4*c^2*b^2/e/(c*d-e)^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-c^2*a*b/(c*e*x+c*d)^2/e*arctanh(c*x)-c^3*b^2*d/(c*d+e)^2/(c*d-e)^2*dilog((c*e*x-e)/(-c*d-e))+c^3*b^2*d/(c*d+e)^2/(c*d-e)^2*dilog((c*e*x+e)/(-c*d+e))-1/2*c^2*a*b/e/(c*d+e)^2*ln(c*x-1)+c^2*b^2*e/(c*d+e)^2/(c*d-e)^2*ln(c*e*x+c*d)+c^2*b^2/(c*d+e)/(c*d-e)/(2*c*d+2*e)*ln(c*x-1)-c^2*b^2/(c*d+e)/(c*d-e)/(2*c*d-2*e)*ln(c*x+1)-1/2*c^2*a^2/(c*e*x+c*d)^2/e-2*c^3*a*b*d/(c*d+e)^2/(c*d-e)^2*ln(c*e*x+c*d)-2*c^3*b^2*arctanh(c*x)*d/(c*d+e)^2/(c*d-e)^2*ln(c*e*x+c*d)-c^3*b^2*d/(c*d+e)^2/(c*d-e)^2*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))+c^3*b^2*d/(c*d+e)^2/(c*d-e)^2*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))+1/4*c^2*b^2/e/(c*d+e)^2*dilog(1/2+1/2*c*x)-1/8*c^2*b^2/e/(c*d-e)^2*ln(c*x+1)^2-1/4*c^2*b^2/e/(c*d-e)^2*dilog(1/2+1/2*c*x)-1/2*c^2*b^2/(c*e*x+c*d)^2/e*arctanh(c*x)^2-1/8*c^2*b^2/e/(c*d+e)^2*ln(c*x-1)^2","A"
15,1,6104,580,11.293000," ","int((e*x+d)^3*(a+b*arctanh(c*x))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
16,1,4600,373,6.212000," ","int((e*x+d)^2*(a+b*arctanh(c*x))^3,x)","\text{output too large to display}"," ",0,"d*x^2*a^3*e+1/2/c^3*a^2*b*e^2*ln(c*x-1)+1/2/c^3*a^2*b*e^2*ln(c*x+1)-6/c^2*b^3*e*d*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-6/c^2*b^3*e*d*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/c^2*b^3*e*d*arctanh(c*x)^3+1/4*a*b^2/e*ln(c*x+1)^2*d^3+a*b^2*e^2*x/c^2+b^3*e^2*x*arctanh(c*x)/c^2-3/4*I/c^2*b^3*e*Pi*d*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+a^2*b*e^2*arctanh(c*x)*x^3+a*b^2*e^2*arctanh(c*x)^2*x^3+b^3*e*arctanh(c*x)^3*x^2*d+3*a*b^2*arctanh(c*x)^2*x*d^2+1/2*b^3/e*arctanh(c*x)^2*ln(c*x-1)*d^3-1/2*b^3/e*arctanh(c*x)^2*ln(c*x+1)*d^3+b^3/e*ln((c*x+1)/(-c^2*x^2+1)^(1/2))*arctanh(c*x)^2*d^3+3*a^2*b*arctanh(c*x)*x*d^2-1/2*a^2*b/e*ln(c*x+1)*d^3+1/4*a*b^2/e*ln(c*x-1)^2*d^3+a*b^2/e*arctanh(c*x)^2*d^3+a^2*b/e*arctanh(c*x)*d^3+1/2*a^2*b/e*ln(c*x-1)*d^3+1/2/c*a^2*b*x^2*e^2+3/c^2*b^3*e*arctanh(c*x)^2*d+1/2/c^3*a*b^2*e^2*ln(c*x-1)-1/2/c^3*a*b^2*e^2*ln(c*x+1)+3/2/c*b^3*arctanh(c*x)^2*ln(c*x-1)*d^2-3/c*b^3*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))*arctanh(c*x)*d^2-3/c*b^3*ln((c*x+1)/(-c^2*x^2+1)^(1/2))*arctanh(c*x)^2*d^2+3/2/c*b^3*arctanh(c*x)^2*ln(c*x+1)*d^2-3/4/c*a*b^2*ln(c*x+1)^2*d^2+3/4/c*a*b^2*ln(c*x-1)^2*d^2-3/c*a*b^2*dilog(1/2+1/2*c*x)*d^2-3/c*b^3*ln(2)*d^2*arctanh(c*x)^2+1/2/c*b^3*e^2*arctanh(c*x)^2*x^2+3/2/c*a^2*b*ln(c*x-1)*d^2+3/2/c*a^2*b*ln(c*x+1)*d^2-1/c^3*b^3*e^2*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))*arctanh(c*x)-1/c^3*b^3*e^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))*arctanh(c*x)^2+1/2/c^3*b^3*e^2*arctanh(c*x)^2*ln(c*x-1)+1/2/c^3*b^3*e^2*arctanh(c*x)^2*ln(c*x+1)+1/4/c^3*a*b^2*e^2*ln(c*x-1)^2-1/c^3*a*b^2*e^2*dilog(1/2+1/2*c*x)-1/4/c^3*a*b^2*e^2*ln(c*x+1)^2-1/c^3*b^3*e^2*ln(2)*arctanh(c*x)^2+3/4*I/c^2*b^3*e*Pi*d*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*d^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*arctanh(c*x)^2-3/4*I/c*b^3*Pi*d^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*arctanh(c*x)^2+3/4*I/c*b^3*Pi*d^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*arctanh(c*x)^2-3/4*I/c*b^3*Pi*d^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))*arctanh(c*x)^2+1/4*I/c^3*b^3*e^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*arctanh(c*x)^2+1/4*I*b^3/e*Pi*d^3*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+1/4*I*b^3/e*Pi*d^3*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+1/2*I*b^3/e*Pi*d^3*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)^2-1/4*I*b^3/e*Pi*d^3*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*I/c^3*b^3*e^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+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I/c^3*b^3*e^2*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)^2-1/4*I/c^3*b^3*e^2*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+3/4*I/c^2*b^3*e*Pi*d*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2+3/2*I/c^2*b^3*e*Pi*d*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-3/2*I/c^2*b^3*e*Pi*d*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+6/c*a*b^2*e*arctanh(c*x)*x*d-3/2/c^2*a*b^2*e*ln(c*x+1)*ln(-1/2*c*x+1/2)*d+3/2/c^2*a*b^2*e*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)*d-3/2/c^2*a*b^2*e*ln(c*x-1)*ln(1/2+1/2*c*x)*d+3/c^2*a*b^2*e*arctanh(c*x)*ln(c*x-1)*d-3/c^2*a*b^2*e*arctanh(c*x)*ln(c*x+1)*d-1/2*I/c^3*b^3*e^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-1/4*I/c^3*b^3*e^2*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*I/c^3*b^3*e^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/4*I/c^3*b^3*e^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2-3/2*I/c^2*b^3*e*Pi*d*arctanh(c*x)^2-3/4*I/c*b^3*Pi*d^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2-3/4*I/c*b^3*Pi*d^2*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*d^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-3/2*I/c*b^3*Pi*d^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-1/2*I*b^3/e*Pi*d^3*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/2*I*b^3/e*Pi*d^3*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/4*I*b^3/e*Pi*d^3*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2+1/4*I*b^3/e*Pi*d^3*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+a^3*x*d^2+1/3*a^3*e^2*x^3-1/2/c^3*a*b^2*e^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/2/c^3*a*b^2*e^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/c^3*a*b^2*e^2*arctanh(c*x)*ln(c*x-1)+1/c^3*a*b^2*e^2*arctanh(c*x)*ln(c*x+1)+1/2/c^3*a*b^2*e^2*ln(c*x+1)*ln(-1/2*c*x+1/2)-6/c^2*b^3*e*d*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-3/2/c^2*b^3*e*arctanh(c*x)^2*ln(c*x+1)*d+3/2/c^2*b^3*e*arctanh(c*x)^2*ln(c*x-1)*d-6/c^2*b^3*e*d*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+3/c^2*b^3*e*ln((c*x+1)/(-c^2*x^2+1)^(1/2))*arctanh(c*x)^2*d+3/2/c^2*a^2*b*e*ln(c*x-1)*d-3/2/c^2*a^2*b*e*ln(c*x+1)*d+3/c^2*a*b^2*e*ln(c*x+1)*d+3/c^2*a*b^2*e*ln(c*x-1)*d+3/4/c^2*a*b^2*e*ln(c*x+1)^2*d+3/4/c^2*a*b^2*e*ln(c*x-1)^2*d-1/2*I*b^3/e*Pi*d^3*arctanh(c*x)^2-3/2*I/c*b^3*Pi*d^2*arctanh(c*x)^2-1/2*I/c^3*b^3*e^2*Pi*arctanh(c*x)^2+3*a^2*b/c*x*d*e+3*a^2*b*e*arctanh(c*x)*x^2*d+a*b^2/e*arctanh(c*x)*ln(c*x-1)*d^3-a*b^2/e*arctanh(c*x)*ln(c*x+1)*d^3-1/2*a*b^2/e*ln(c*x+1)*ln(-1/2*c*x+1/2)*d^3+1/2*a*b^2/e*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)*d^3-1/2*a*b^2/e*ln(c*x-1)*ln(1/2+1/2*c*x)*d^3+3*a*b^2*e*arctanh(c*x)^2*x^2*d+1/c*a*b^2*e^2*arctanh(c*x)*x^2+3/c*b^3*e*arctanh(c*x)^2*x*d+3/2/c*a*b^2*ln(c*x+1)*ln(-1/2*c*x+1/2)*d^2-3/2/c*a*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)*d^2-3/2/c*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)*d^2+3/c*a*b^2*arctanh(c*x)*ln(c*x-1)*d^2+3/c*a*b^2*arctanh(c*x)*ln(c*x+1)*d^2+1/3*b^3*e^2*arctanh(c*x)^3*x^3+b^3*arctanh(c*x)^3*x*d^2+1/c*b^3*d^2*arctanh(c*x)^3+3/2/c*b^3*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))*d^2+1/3/c^3*b^3*e^2*arctanh(c*x)^3-1/2/c^3*b^3*e^2*arctanh(c*x)^2+1/2/c^3*b^3*e^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-1/c^3*b^3*e^2*ln(1+(c*x+1)^2/(-c^2*x^2+1))+1/c^3*b^3*e^2*arctanh(c*x)+1/3*a^3/e*d^3+3/4*I/c*b^3*Pi*d^2*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)^2-3/4*I/c^2*b^3*e*Pi*d*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^2*b^3*e*Pi*d*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+3/4*I/c^2*b^3*e*Pi*d*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+1/4*I/c^3*b^3*e^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))*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+3/2*I/c^2*b^3*e*Pi*d*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)^2-1/4*I*b^3/e*Pi*d^3*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","C"
17,1,12404,232,1.246000," ","int((e*x+d)*(a+b*arctanh(c*x))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
18,1,2367,260,0.655000," ","int((a+b*arctanh(c*x))^3/(e*x+d),x)","\text{Expression too large to display}"," ",0,"3/4*c*b^3/e*d/(c*d+e)*polylog(4,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+1/2*I*b^3/e*arctanh(c*x)^3*Pi*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-3/2*c*a*b^2/e*d/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+c*b^3/e*d/(c*d+e)*arctanh(c*x)^3*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+3/2*c*b^3/e*d/(c*d+e)*arctanh(c*x)^2*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-3/2*c*b^3/e*d/(c*d+e)*arctanh(c*x)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+3/2*I*a*b^2/e*arctanh(c*x)^2*Pi*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-1/2*I*b^3/e*arctanh(c*x)^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)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-1/2*I*b^3/e*arctanh(c*x)^3*Pi*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))+3*c*a*b^2/e*d/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+3*c*a*b^2/e*d/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-3/2*I*a*b^2/e*arctanh(c*x)^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)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-3/2*I*a*b^2/e*arctanh(c*x)^2*Pi*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))+1/2*I*b^3/e*arctanh(c*x)^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)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))-3/4*b^3/e*polylog(4,-(c*x+1)^2/(-c^2*x^2+1))-3*a*b^2/e*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+3*a*b^2/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+3*a*b^2/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+3*a^2*b*ln(c*e*x+c*d)/e*arctanh(c*x)+3/2*a^2*b/e*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))-3/2*a^2*b/e*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))+3*a*b^2*ln(c*e*x+c*d)/e*arctanh(c*x)^2-3*a*b^2/e*arctanh(c*x)^2*ln(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))+3/4*b^3/(c*d+e)*polylog(4,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+a^3*ln(c*e*x+c*d)/e+3/2*b^3/e*arctanh(c*x)*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+b^3/(c*d+e)*arctanh(c*x)^3*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+3/2*b^3/(c*d+e)*arctanh(c*x)^2*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-3/2*b^3/(c*d+e)*arctanh(c*x)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+b^3*ln(c*e*x+c*d)/e*arctanh(c*x)^3-b^3/e*arctanh(c*x)^3*ln(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))-3/2*b^3/e*arctanh(c*x)^2*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+3/2*a^2*b/e*dilog((c*e*x-e)/(-c*d-e))-3/2*a^2*b/e*dilog((c*e*x+e)/(-c*d+e))+3/2*a*b^2/e*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-3/2*a*b^2/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+3/2*I*a*b^2/e*arctanh(c*x)^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)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))","C"
19,1,3497,501,0.888000," ","int((a+b*arctanh(c*x))^3/(e*x+d)^2,x)","\text{output too large to display}"," ",0,"-c*a^3/(c*e*x+c*d)/e+3/4*I*c^2*b^3/e/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*d*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)))^2-3/2*I*c^2*b^3/e/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*d*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2-3/4*I*c^2*b^3/e/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*d*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)))^2-3/4*I*c^2*b^3/e/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*d*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))-3/4*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-3/2*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-3/2*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3+3/2*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-3/4*I*c*b^3/(c*d+e)/(c*d-e)*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-c*b^3/(c*e*x+c*d)/e*arctanh(c*x)^3+c*b^3/e*arctanh(c*x)^3/(c*d-e)+3/4*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^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))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))-3/4*I*c^2*b^3/e/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*d*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-3/4*I*c^2*b^3/e/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*d*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-3/2*I*c^2*b^3/e/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*d*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+3/2*I*c^2*b^3/e/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*d*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-3/2*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^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)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))+3/4*I*c^2*b^3/e/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*d*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)))-3*c*b^3/e*arctanh(c*x)^2/(2*c*d+2*e)*ln(c*x-1)+3*c*b^3/e*arctanh(c*x)^2/(2*c*d-2*e)*ln(c*x+1)-3*c*b^3/e*arctanh(c*x)^2/(c*d-e)*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+3*c*b^3*arctanh(c*x)^2/(c*d+e)/(c*d-e)*ln(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))-3*c*b^3*arctanh(c*x)^2/(c*d+e)/(c*d-e)*ln(c*e*x+c*d)-3*c*a*b^2/(c*e*x+c*d)/e*arctanh(c*x)^2+3/2*c*a*b^2/e/(c*d+e)*dilog(1/2+1/2*c*x)+3/2*c*b^3*e/(c*d+e)^2/(c*d-e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-3*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^2*ln(2)+3/2*c^2*b^3/(c*d+e)^2/(c*d-e)*d*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-3*c*a^2*b/(c*d+e)/(c*d-e)*ln(c*e*x+c*d)-3*c*a^2*b/e/(2*c*d+2*e)*ln(c*x-1)+3*c*a^2*b/e/(2*c*d-2*e)*ln(c*x+1)-3*c*a*b^2/(c*d+e)/(c*d-e)*dilog((c*e*x-e)/(-c*d-e))+3*c*a*b^2/(c*d+e)/(c*d-e)*dilog((c*e*x+e)/(-c*d+e))-3/4*c*a*b^2/e/(c*d-e)*ln(c*x+1)^2-3/2*c*a*b^2/e/(c*d-e)*dilog(1/2+1/2*c*x)-3/4*c*a*b^2/e/(c*d+e)*ln(c*x-1)^2-3*c*a^2*b/(c*e*x+c*d)/e*arctanh(c*x)-6*c*a*b^2/e*arctanh(c*x)/(2*c*d+2*e)*ln(c*x-1)+6*c*a*b^2/e*arctanh(c*x)/(2*c*d-2*e)*ln(c*x+1)-3*c*a*b^2/(c*d+e)/(c*d-e)*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))+3*c*a*b^2/(c*d+e)/(c*d-e)*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))-3*c*b^3*e/(c*d+e)^2/(c*d-e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-3*c*b^3*e/(c*d+e)^2/(c*d-e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-3*c^2*b^3/(c*d+e)^2/(c*d-e)*d*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-3*c^2*b^3/(c*d+e)^2/(c*d-e)*d*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-3/2*c*a*b^2/e/(c*d-e)*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-3/2*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi+3/2*c*a*b^2/e/(c*d-e)*ln(-1/2*c*x+1/2)*ln(c*x+1)+3/2*c*a*b^2/e/(c*d+e)*ln(c*x-1)*ln(1/2+1/2*c*x)-6*c*a*b^2*arctanh(c*x)/(c*d+e)/(c*d-e)*ln(c*e*x+c*d)+3/2*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^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)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+3/4*I*c*b^3/(c*d+e)/(c*d-e)*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)))^2-3/4*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^2*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))-3/4*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^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+(c*x+1)^2/(-c^2*x^2+1)))^2-3/2*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^2*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+3/2*I*c*b^3/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+3/2*I*c^2*b^3/e/(c*d+e)/(c*d-e)*arctanh(c*x)^2*Pi*d","C"
20,1,53538,911,3.862000," ","int((a+b*arctanh(c*x))^3/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
21,1,118,53,0.043000," ","int((a+b*arctanh(c*x))/(2*c*x+1),x)","\frac{a \ln \left(2 c x +1\right)}{2 c}+\frac{b \ln \left(2 c x +1\right) \arctanh \left(c x \right)}{2 c}+\frac{b \ln \left(\frac{2}{3}-\frac{2 c x}{3}\right) \ln \left(2 c x +1\right)}{4 c}-\frac{b \ln \left(\frac{2}{3}-\frac{2 c x}{3}\right) \ln \left(\frac{2 c x}{3}+\frac{1}{3}\right)}{4 c}-\frac{b \dilog \left(\frac{2 c x}{3}+\frac{1}{3}\right)}{4 c}-\frac{b \dilog \left(2 c x +2\right)}{4 c}-\frac{b \ln \left(2 c x +1\right) \ln \left(2 c x +2\right)}{4 c}"," ",0,"1/2/c*a*ln(2*c*x+1)+1/2/c*b*ln(2*c*x+1)*arctanh(c*x)+1/4/c*b*ln(2/3-2/3*c*x)*ln(2*c*x+1)-1/4/c*b*ln(2/3-2/3*c*x)*ln(2/3*c*x+1/3)-1/4/c*b*dilog(2/3*c*x+1/3)-1/4/c*b*dilog(2*c*x+2)-1/4/c*b*ln(2*c*x+1)*ln(2*c*x+2)","B"
22,1,127,69,0.043000," ","int(arctanh(x)/(1-x*2^(1/2)),x)","-\frac{\ln \left(x \sqrt{2}-1\right) \sqrt{2}\, \arctanh \left(x \right)}{2}-\frac{\sqrt{2}\, \ln \left(x \sqrt{2}-1\right) \ln \left(\frac{\sqrt{2}-x \sqrt{2}}{\sqrt{2}-1}\right)}{4}+\frac{\sqrt{2}\, \ln \left(x \sqrt{2}-1\right) \ln \left(\frac{\sqrt{2}+x \sqrt{2}}{1+\sqrt{2}}\right)}{4}-\frac{\sqrt{2}\, \dilog \left(\frac{\sqrt{2}-x \sqrt{2}}{\sqrt{2}-1}\right)}{4}+\frac{\sqrt{2}\, \dilog \left(\frac{\sqrt{2}+x \sqrt{2}}{1+\sqrt{2}}\right)}{4}"," ",0,"-1/2*ln(x*2^(1/2)-1)*2^(1/2)*arctanh(x)-1/4*2^(1/2)*ln(x*2^(1/2)-1)*ln((2^(1/2)-x*2^(1/2))/(2^(1/2)-1))+1/4*2^(1/2)*ln(x*2^(1/2)-1)*ln((2^(1/2)+x*2^(1/2))/(1+2^(1/2)))-1/4*2^(1/2)*dilog((2^(1/2)-x*2^(1/2))/(2^(1/2)-1))+1/4*2^(1/2)*dilog((2^(1/2)+x*2^(1/2))/(1+2^(1/2)))","A"
23,1,306,166,0.036000," ","int((e*x+d)^3*(a+b*arctanh(c*x^2)),x)","\frac{a \,x^{4} e^{3}}{4}+a d \,e^{2} x^{3}+\frac{3 a \,d^{2} e \,x^{2}}{2}+a x \,d^{3}+\frac{a \,d^{4}}{4 e}+\frac{b \,e^{3} \arctanh \left(c \,x^{2}\right) x^{4}}{4}+b \,e^{2} \arctanh \left(c \,x^{2}\right) x^{3} d +\frac{3 b e \arctanh \left(c \,x^{2}\right) x^{2} d^{2}}{2}+b \arctanh \left(c \,x^{2}\right) x \,d^{3}+\frac{b \arctanh \left(c \,x^{2}\right) d^{4}}{4 e}+\frac{b \,e^{3} x^{2}}{4 c}+\frac{2 b d \,e^{2} x}{c}-\frac{b \ln \left(c \,x^{2}+1\right) d^{4}}{8 e}+\frac{3 b e \ln \left(c \,x^{2}+1\right) d^{2}}{4 c}-\frac{b \,e^{3} \ln \left(c \,x^{2}+1\right)}{8 c^{2}}+\frac{b \arctan \left(x \sqrt{c}\right) d^{3}}{\sqrt{c}}-\frac{b \,e^{2} \arctan \left(x \sqrt{c}\right) d}{c^{\frac{3}{2}}}+\frac{b \ln \left(c \,x^{2}-1\right) d^{4}}{8 e}+\frac{3 b e \ln \left(c \,x^{2}-1\right) d^{2}}{4 c}+\frac{b \,e^{3} \ln \left(c \,x^{2}-1\right)}{8 c^{2}}-\frac{b \arctanh \left(x \sqrt{c}\right) d^{3}}{\sqrt{c}}-\frac{b \,e^{2} \arctanh \left(x \sqrt{c}\right) d}{c^{\frac{3}{2}}}"," ",0,"1/4*a*x^4*e^3+a*d*e^2*x^3+3/2*a*d^2*e*x^2+a*x*d^3+1/4*a/e*d^4+1/4*b*e^3*arctanh(c*x^2)*x^4+b*e^2*arctanh(c*x^2)*x^3*d+3/2*b*e*arctanh(c*x^2)*x^2*d^2+b*arctanh(c*x^2)*x*d^3+1/4*b/e*arctanh(c*x^2)*d^4+1/4*b*e^3*x^2/c+2*b*d*e^2*x/c-1/8*b/e*ln(c*x^2+1)*d^4+3/4*b*e/c*ln(c*x^2+1)*d^2-1/8*b*e^3/c^2*ln(c*x^2+1)+b/c^(1/2)*arctan(x*c^(1/2))*d^3-b*e^2/c^(3/2)*arctan(x*c^(1/2))*d+1/8*b/e*ln(c*x^2-1)*d^4+3/4*b*e/c*ln(c*x^2-1)*d^2+1/8*b*e^3/c^2*ln(c*x^2-1)-b/c^(1/2)*arctanh(x*c^(1/2))*d^3-b*e^2/c^(3/2)*arctanh(x*c^(1/2))*d","A"
24,1,223,138,0.031000," ","int((e*x+d)^2*(a+b*arctanh(c*x^2)),x)","\frac{a \,x^{3} e^{2}}{3}+a d e \,x^{2}+a x \,d^{2}+\frac{a \,d^{3}}{3 e}+\frac{b \,e^{2} \arctanh \left(c \,x^{2}\right) x^{3}}{3}+b e \arctanh \left(c \,x^{2}\right) x^{2} d +b \arctanh \left(c \,x^{2}\right) x \,d^{2}+\frac{b \arctanh \left(c \,x^{2}\right) d^{3}}{3 e}+\frac{2 b \,e^{2} x}{3 c}-\frac{b \ln \left(c \,x^{2}+1\right) d^{3}}{6 e}+\frac{b e \ln \left(c \,x^{2}+1\right) d}{2 c}+\frac{b \arctan \left(x \sqrt{c}\right) d^{2}}{\sqrt{c}}-\frac{b \,e^{2} \arctan \left(x \sqrt{c}\right)}{3 c^{\frac{3}{2}}}+\frac{b \ln \left(c \,x^{2}-1\right) d^{3}}{6 e}+\frac{b e \ln \left(c \,x^{2}-1\right) d}{2 c}-\frac{b \arctanh \left(x \sqrt{c}\right) d^{2}}{\sqrt{c}}-\frac{b \,e^{2} \arctanh \left(x \sqrt{c}\right)}{3 c^{\frac{3}{2}}}"," ",0,"1/3*a*x^3*e^2+a*d*e*x^2+a*x*d^2+1/3*a/e*d^3+1/3*b*e^2*arctanh(c*x^2)*x^3+b*e*arctanh(c*x^2)*x^2*d+b*arctanh(c*x^2)*x*d^2+1/3*b/e*arctanh(c*x^2)*d^3+2/3*b*e^2*x/c-1/6*b/e*ln(c*x^2+1)*d^3+1/2*b*e/c*ln(c*x^2+1)*d+b/c^(1/2)*arctan(x*c^(1/2))*d^2-1/3*b*e^2/c^(3/2)*arctan(x*c^(1/2))+1/6*b/e*ln(c*x^2-1)*d^3+1/2*b*e/c*ln(c*x^2-1)*d-b/c^(1/2)*arctanh(x*c^(1/2))*d^2-1/3*b*e^2/c^(3/2)*arctanh(x*c^(1/2))","A"
25,1,91,103,0.030000," ","int((e*x+d)*(a+b*arctanh(c*x^2)),x)","\frac{a \,x^{2} e}{2}+a d x +\frac{b \arctanh \left(c \,x^{2}\right) x^{2} e}{2}+b \arctanh \left(c \,x^{2}\right) d x +\frac{b e \ln \left(c \,x^{2}+1\right)}{4 c}+\frac{b d \arctan \left(x \sqrt{c}\right)}{\sqrt{c}}+\frac{b e \ln \left(c \,x^{2}-1\right)}{4 c}-\frac{b d \arctanh \left(x \sqrt{c}\right)}{\sqrt{c}}"," ",0,"1/2*a*x^2*e+a*d*x+1/2*b*arctanh(c*x^2)*x^2*e+b*arctanh(c*x^2)*d*x+1/4*b*e/c*ln(c*x^2+1)+b*d*arctan(x*c^(1/2))/c^(1/2)+1/4*b*e/c*ln(c*x^2-1)-b*d*arctanh(x*c^(1/2))/c^(1/2)","A"
26,1,362,277,0.072000," ","int((a+b*arctanh(c*x^2))/(e*x+d),x)","\frac{a \ln \left(e x +d \right)}{e}+\frac{b \ln \left(e x +d \right) \arctanh \left(c \,x^{2}\right)}{e}+\frac{b \ln \left(e x +d \right) \ln \left(\frac{e \sqrt{c}-\left(e x +d \right) c +c d}{e \sqrt{c}+c d}\right)}{2 e}+\frac{b \ln \left(e x +d \right) \ln \left(\frac{e \sqrt{c}+\left(e x +d \right) c -c d}{e \sqrt{c}-c d}\right)}{2 e}+\frac{b \dilog \left(\frac{e \sqrt{c}-\left(e x +d \right) c +c d}{e \sqrt{c}+c d}\right)}{2 e}+\frac{b \dilog \left(\frac{e \sqrt{c}+\left(e x +d \right) c -c d}{e \sqrt{c}-c d}\right)}{2 e}-\frac{b \ln \left(e x +d \right) \ln \left(\frac{e \sqrt{-c}-\left(e x +d \right) c +c d}{e \sqrt{-c}+c d}\right)}{2 e}-\frac{b \ln \left(e x +d \right) \ln \left(\frac{e \sqrt{-c}+\left(e x +d \right) c -c d}{e \sqrt{-c}-c d}\right)}{2 e}-\frac{b \dilog \left(\frac{e \sqrt{-c}-\left(e x +d \right) c +c d}{e \sqrt{-c}+c d}\right)}{2 e}-\frac{b \dilog \left(\frac{e \sqrt{-c}+\left(e x +d \right) c -c d}{e \sqrt{-c}-c d}\right)}{2 e}"," ",0,"a*ln(e*x+d)/e+b*ln(e*x+d)/e*arctanh(c*x^2)+1/2*b/e*ln(e*x+d)*ln((e*c^(1/2)-(e*x+d)*c+c*d)/(e*c^(1/2)+c*d))+1/2*b/e*ln(e*x+d)*ln((e*c^(1/2)+(e*x+d)*c-c*d)/(e*c^(1/2)-c*d))+1/2*b/e*dilog((e*c^(1/2)-(e*x+d)*c+c*d)/(e*c^(1/2)+c*d))+1/2*b/e*dilog((e*c^(1/2)+(e*x+d)*c-c*d)/(e*c^(1/2)-c*d))-1/2*b/e*ln(e*x+d)*ln((e*(-c)^(1/2)-(e*x+d)*c+c*d)/(e*(-c)^(1/2)+c*d))-1/2*b/e*ln(e*x+d)*ln((e*(-c)^(1/2)+(e*x+d)*c-c*d)/(e*(-c)^(1/2)-c*d))-1/2*b/e*dilog((e*(-c)^(1/2)-(e*x+d)*c+c*d)/(e*(-c)^(1/2)+c*d))-1/2*b/e*dilog((e*(-c)^(1/2)+(e*x+d)*c-c*d)/(e*(-c)^(1/2)-c*d))","A"
27,1,181,156,0.038000," ","int((a+b*arctanh(c*x^2))/(e*x+d)^2,x)","-\frac{a}{\left(e x +d \right) e}-\frac{b \arctanh \left(c \,x^{2}\right)}{\left(e x +d \right) e}+\frac{b c d \ln \left(c \,x^{2}+1\right)}{e \left(2 c \,d^{2}+2 e^{2}\right)}+\frac{2 b \sqrt{c}\, \arctan \left(x \sqrt{c}\right)}{2 c \,d^{2}+2 e^{2}}+\frac{2 b e c d \ln \left(e x +d \right)}{\left(c \,d^{2}-e^{2}\right) \left(c \,d^{2}+e^{2}\right)}-\frac{b c d \ln \left(c \,x^{2}-1\right)}{e \left(2 c \,d^{2}-2 e^{2}\right)}-\frac{2 b \sqrt{c}\, \arctanh \left(x \sqrt{c}\right)}{2 c \,d^{2}-2 e^{2}}"," ",0,"-a/(e*x+d)/e-b/(e*x+d)/e*arctanh(c*x^2)+b/e*c/(2*c*d^2+2*e^2)*d*ln(c*x^2+1)+2*b*c^(1/2)/(2*c*d^2+2*e^2)*arctan(x*c^(1/2))+2*b*e*c*d/(c*d^2-e^2)/(c*d^2+e^2)*ln(e*x+d)-b/e*c/(2*c*d^2-2*e^2)*d*ln(c*x^2-1)-2*b*c^(1/2)/(2*c*d^2-2*e^2)*arctanh(x*c^(1/2))","A"
28,1,310,215,0.044000," ","int((a+b*arctanh(c*x^2))/(e*x+d)^3,x)","-\frac{a}{2 \left(e x +d \right)^{2} e}-\frac{b \arctanh \left(c \,x^{2}\right)}{2 \left(e x +d \right)^{2} e}+\frac{b \,c^{2} \ln \left(c \,x^{2}+1\right) d^{2}}{4 e \left(c \,d^{2}+e^{2}\right)^{2}}-\frac{b e c \ln \left(c \,x^{2}+1\right)}{4 \left(c \,d^{2}+e^{2}\right)^{2}}+\frac{b \,c^{\frac{3}{2}} d \arctan \left(x \sqrt{c}\right)}{\left(c \,d^{2}+e^{2}\right)^{2}}-\frac{b e c d}{\left(c \,d^{2}-e^{2}\right) \left(c \,d^{2}+e^{2}\right) \left(e x +d \right)}+\frac{3 b e \,c^{3} \ln \left(e x +d \right) d^{4}}{\left(c \,d^{2}-e^{2}\right)^{2} \left(c \,d^{2}+e^{2}\right)^{2}}+\frac{b \,e^{5} c \ln \left(e x +d \right)}{\left(c \,d^{2}-e^{2}\right)^{2} \left(c \,d^{2}+e^{2}\right)^{2}}-\frac{b \,c^{2} \ln \left(c \,x^{2}-1\right) d^{2}}{4 e \left(c \,d^{2}-e^{2}\right)^{2}}-\frac{b e c \ln \left(c \,x^{2}-1\right)}{4 \left(c \,d^{2}-e^{2}\right)^{2}}-\frac{b \,c^{\frac{3}{2}} d \arctanh \left(x \sqrt{c}\right)}{\left(c \,d^{2}-e^{2}\right)^{2}}"," ",0,"-1/2*a/(e*x+d)^2/e-1/2*b/(e*x+d)^2/e*arctanh(c*x^2)+1/4*b/e*c^2/(c*d^2+e^2)^2*ln(c*x^2+1)*d^2-1/4*b*e*c/(c*d^2+e^2)^2*ln(c*x^2+1)+b*c^(3/2)*d*arctan(x*c^(1/2))/(c*d^2+e^2)^2-b*e*c*d/(c*d^2-e^2)/(c*d^2+e^2)/(e*x+d)+3*b*e*c^3/(c*d^2-e^2)^2/(c*d^2+e^2)^2*ln(e*x+d)*d^4+b*e^5*c/(c*d^2-e^2)^2/(c*d^2+e^2)^2*ln(e*x+d)-1/4*b/e*c^2/(c*d^2-e^2)^2*ln(c*x^2-1)*d^2-1/4*b*e*c/(c*d^2-e^2)^2*ln(c*x^2-1)-b*c^(3/2)*d*arctanh(x*c^(1/2))/(c*d^2-e^2)^2","A"
29,0,0,900,0.421000," ","int((e*x+d)*(a+b*arctanh(c*x^2))^2,x)","\int \left(e x +d \right) \left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int((e*x+d)*(a+b*arctanh(c*x^2))^2,x)","F"
30,0,0,22,0.352000," ","int((a+b*arctanh(c*x^2))^2/(e*x+d),x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}}{e x +d}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^2/(e*x+d),x)","F"
31,0,0,22,0.612000," ","int((a+b*arctanh(c*x^2))^2/(e*x+d)^2,x)","\int \frac{\left(a +b \arctanh \left(c \,x^{2}\right)\right)^{2}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((a+b*arctanh(c*x^2))^2/(e*x+d)^2,x)","F"
32,1,500,267,0.035000," ","int((e*x+d)^2*(a+b*arctanh(c*x^3)),x)","\frac{a \,x^{3} e^{2}}{3}+a d e \,x^{2}+a x \,d^{2}+\frac{a \,d^{3}}{3 e}+\frac{b \,e^{2} \arctanh \left(c \,x^{3}\right) x^{3}}{3}+b e \arctanh \left(c \,x^{3}\right) x^{2} d +b \arctanh \left(c \,x^{3}\right) x \,d^{2}+\frac{b \arctanh \left(c \,x^{3}\right) d^{3}}{3 e}+\frac{b \,d^{2} \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \,d^{2} \ln \left(x^{2}+\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \,d^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b e d \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b e d \ln \left(x^{2}+\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b e d \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 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(c \,x^{3}-1\right) d^{3}}{6 e}+\frac{b \,e^{2} \ln \left(c \,x^{3}-1\right)}{6 c}+\frac{b \,d^{2} \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b \,d^{2} \ln \left(x^{2}-\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b \,d^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b e d \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b e d \ln \left(x^{2}-\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b e d \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 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(c \,x^{3}+1\right) d^{3}}{6 e}+\frac{b \,e^{2} \ln \left(c \,x^{3}+1\right)}{6 c}"," ",0,"1/3*a*x^3*e^2+a*d*e*x^2+a*x*d^2+1/3*a/e*d^3+1/3*b*e^2*arctanh(c*x^3)*x^3+b*e*arctanh(c*x^3)*x^2*d+b*arctanh(c*x^3)*x*d^2+1/3*b/e*arctanh(c*x^3)*d^3+1/2*b/c*d^2/(1/c)^(2/3)*ln(x-(1/c)^(1/3))-1/4*b/c*d^2/(1/c)^(2/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))-1/2*b/c*d^2/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))+1/2*b*e/c*d/(1/c)^(1/3)*ln(x-(1/c)^(1/3))-1/4*b*e/c*d/(1/c)^(1/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))+1/2*b*e/c*d*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))+1/6*b/e*ln(c*x^3-1)*d^3+1/6*b*e^2/c*ln(c*x^3-1)+1/2*b/c*d^2/(1/c)^(2/3)*ln(x+(1/c)^(1/3))-1/4*b/c*d^2/(1/c)^(2/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))+1/2*b/c*d^2/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))-1/2*b*e/c*d/(1/c)^(1/3)*ln(x+(1/c)^(1/3))+1/4*b*e/c*d/(1/c)^(1/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))+1/2*b*e/c*d*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))-1/6*b/e*ln(c*x^3+1)*d^3+1/6*b*e^2/c*ln(c*x^3+1)","A"
33,1,362,216,0.031000," ","int((e*x+d)*(a+b*arctanh(c*x^3)),x)","\frac{a \,x^{2} e}{2}+a d x +\frac{b \arctanh \left(c \,x^{3}\right) x^{2} e}{2}+b \arctanh \left(c \,x^{3}\right) d x +\frac{b d \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b d \ln \left(x^{2}+\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b d \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b e \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b e \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 e \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 d \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b d \ln \left(x^{2}-\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b d \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{2 c \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b e \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{4 c \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b e \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 e \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*e+a*d*x+1/2*b*arctanh(c*x^3)*x^2*e+b*arctanh(c*x^3)*d*x+1/2*b*d/c/(1/c)^(2/3)*ln(x-(1/c)^(1/3))-1/4*b*d/c/(1/c)^(2/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))-1/2*b*d/c/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))+1/4*b*e/c/(1/c)^(1/3)*ln(x-(1/c)^(1/3))-1/8*b*e/c/(1/c)^(1/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))+1/4*b*e*3^(1/2)/c/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))+1/2*b*d/c/(1/c)^(2/3)*ln(x+(1/c)^(1/3))-1/4*b*d/c/(1/c)^(2/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))+1/2*b*d/c/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))-1/4*b*e/c/(1/c)^(1/3)*ln(x+(1/c)^(1/3))+1/8*b*e/c/(1/c)^(1/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))+1/4*b*e*3^(1/2)/c/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))","A"
34,1,182,423,0.150000," ","int((a+b*arctanh(c*x^3))/(e*x+d),x)","\frac{a \ln \left(e x +d \right)}{e}+\frac{b \ln \left(e x +d \right) \arctanh \left(c \,x^{3}\right)}{e}-\frac{b \left(\munderset{\textit{\_R1} =\RootOf \left(\textit{\_Z}^{3} c -3 c d \,\textit{\_Z}^{2}+3 c \,d^{2} \textit{\_Z} -c \,d^{3}+e^{3}\right)}{\sum}\left(\ln \left(e x +d \right) \ln \left(\frac{-e x +\textit{\_R1} -d}{\textit{\_R1}}\right)+\dilog \left(\frac{-e x +\textit{\_R1} -d}{\textit{\_R1}}\right)\right)\right)}{2 e}+\frac{b \left(\munderset{\textit{\_R1} =\RootOf \left(\textit{\_Z}^{3} c -3 c d \,\textit{\_Z}^{2}+3 c \,d^{2} \textit{\_Z} -c \,d^{3}-e^{3}\right)}{\sum}\left(\ln \left(e x +d \right) \ln \left(\frac{-e x +\textit{\_R1} -d}{\textit{\_R1}}\right)+\dilog \left(\frac{-e x +\textit{\_R1} -d}{\textit{\_R1}}\right)\right)\right)}{2 e}"," ",0,"a*ln(e*x+d)/e+b*ln(e*x+d)/e*arctanh(c*x^3)-1/2*b/e*sum(ln(e*x+d)*ln((-e*x+_R1-d)/_R1)+dilog((-e*x+_R1-d)/_R1),_R1=RootOf(_Z^3*c-3*_Z^2*c*d+3*_Z*c*d^2-c*d^3+e^3))+1/2*b/e*sum(ln(e*x+d)*ln((-e*x+_R1-d)/_R1)+dilog((-e*x+_R1-d)/_R1),_R1=RootOf(_Z^3*c-3*_Z^2*c*d+3*_Z*c*d^2-c*d^3-e^3))","C"
35,1,591,352,0.043000," ","int((a+b*arctanh(c*x^3))/(e*x+d)^2,x)","-\frac{a}{\left(e x +d \right) e}-\frac{b \arctanh \left(c \,x^{3}\right)}{\left(e x +d \right) e}+\frac{b d \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{\left(2 c \,d^{3}+2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b d \ln \left(x^{2}+\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{2 \left(2 c \,d^{3}+2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b d \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{\left(2 c \,d^{3}+2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b e \ln \left(x -\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{\left(2 c \,d^{3}+2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b e \ln \left(x^{2}+\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{2 \left(2 c \,d^{3}+2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b e \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{\left(2 c \,d^{3}+2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b c \,d^{2} \ln \left(c \,x^{3}-1\right)}{e \left(2 c \,d^{3}+2 e^{3}\right)}+\frac{b d \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{\left(2 c \,d^{3}-2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{2}{3}}}-\frac{b d \ln \left(x^{2}-\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{2 \left(2 c \,d^{3}-2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b d \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(2 c \,d^{3}-2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{2}{3}}}+\frac{b e \ln \left(x +\left(\frac{1}{c}\right)^{\frac{1}{3}}\right)}{\left(2 c \,d^{3}-2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b e \ln \left(x^{2}-\left(\frac{1}{c}\right)^{\frac{1}{3}} x +\left(\frac{1}{c}\right)^{\frac{2}{3}}\right)}{2 \left(2 c \,d^{3}-2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{1}{3}}}-\frac{b e \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{1}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(2 c \,d^{3}-2 e^{3}\right) \left(\frac{1}{c}\right)^{\frac{1}{3}}}+\frac{b c \,d^{2} \ln \left(c \,x^{3}+1\right)}{e \left(2 c \,d^{3}-2 e^{3}\right)}-\frac{3 b \,e^{2} c \,d^{2} \ln \left(e x +d \right)}{\left(c \,d^{3}+e^{3}\right) \left(c \,d^{3}-e^{3}\right)}"," ",0,"-a/(e*x+d)/e-b/(e*x+d)/e*arctanh(c*x^3)+b/(2*c*d^3+2*e^3)*d/(1/c)^(2/3)*ln(x-(1/c)^(1/3))-1/2*b/(2*c*d^3+2*e^3)*d/(1/c)^(2/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))-b/(2*c*d^3+2*e^3)*d/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))-b*e/(2*c*d^3+2*e^3)/(1/c)^(1/3)*ln(x-(1/c)^(1/3))+1/2*b*e/(2*c*d^3+2*e^3)/(1/c)^(1/3)*ln(x^2+(1/c)^(1/3)*x+(1/c)^(2/3))-b*e/(2*c*d^3+2*e^3)*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x+1))-b/e*c/(2*c*d^3+2*e^3)*d^2*ln(c*x^3-1)+b/(2*c*d^3-2*e^3)*d/(1/c)^(2/3)*ln(x+(1/c)^(1/3))-1/2*b/(2*c*d^3-2*e^3)*d/(1/c)^(2/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))+b/(2*c*d^3-2*e^3)*d/(1/c)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))+b*e/(2*c*d^3-2*e^3)/(1/c)^(1/3)*ln(x+(1/c)^(1/3))-1/2*b*e/(2*c*d^3-2*e^3)/(1/c)^(1/3)*ln(x^2-(1/c)^(1/3)*x+(1/c)^(2/3))-b*e/(2*c*d^3-2*e^3)*3^(1/2)/(1/c)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c)^(1/3)*x-1))+b/e*c/(2*c*d^3-2*e^3)*d^2*ln(c*x^3+1)-3*b*e^2*c*d^2/(c*d^3+e^3)/(c*d^3-e^3)*ln(e*x+d)","A"
36,1,309,161,0.057000," ","int(x^3*(a+b*arctanh(c*x^(1/2)))/(-c^2*x+1),x)","-\frac{a \,x^{3}}{3 c^{2}}-\frac{x^{2} a}{2 c^{4}}-\frac{x a}{c^{6}}-\frac{a \ln \left(c \sqrt{x}-1\right)}{c^{8}}-\frac{a \ln \left(1+c \sqrt{x}\right)}{c^{8}}-\frac{b \arctanh \left(c \sqrt{x}\right) x^{3}}{3 c^{2}}-\frac{b \arctanh \left(c \sqrt{x}\right) x^{2}}{2 c^{4}}-\frac{b \arctanh \left(c \sqrt{x}\right) x}{c^{6}}-\frac{b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{c^{8}}-\frac{b \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{c^{8}}-\frac{b \ln \left(c \sqrt{x}-1\right)^{2}}{4 c^{8}}+\frac{b \dilog \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{c^{8}}+\frac{b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2 c^{8}}+\frac{b \ln \left(1+c \sqrt{x}\right)^{2}}{4 c^{8}}-\frac{b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{2 c^{8}}+\frac{b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2 c^{8}}-\frac{b \,x^{\frac{5}{2}}}{15 c^{3}}-\frac{5 b \,x^{\frac{3}{2}}}{18 c^{5}}-\frac{11 b \sqrt{x}}{6 c^{7}}-\frac{11 b \ln \left(c \sqrt{x}-1\right)}{12 c^{8}}+\frac{11 b \ln \left(1+c \sqrt{x}\right)}{12 c^{8}}"," ",0,"-1/3/c^2*a*x^3-1/2/c^4*x^2*a-1/c^6*x*a-1/c^8*a*ln(c*x^(1/2)-1)-1/c^8*a*ln(1+c*x^(1/2))-1/3/c^2*b*arctanh(c*x^(1/2))*x^3-1/2/c^4*b*arctanh(c*x^(1/2))*x^2-1/c^6*b*arctanh(c*x^(1/2))*x-1/c^8*b*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-1/c^8*b*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-1/4/c^8*b*ln(c*x^(1/2)-1)^2+1/c^8*b*dilog(1/2+1/2*c*x^(1/2))+1/2/c^8*b*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+1/4/c^8*b*ln(1+c*x^(1/2))^2-1/2/c^8*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+1/2/c^8*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))-1/15*b*x^(5/2)/c^3-5/18*b*x^(3/2)/c^5-11/6*b*x^(1/2)/c^7-11/12/c^8*b*ln(c*x^(1/2)-1)+11/12/c^8*b*ln(1+c*x^(1/2))","A"
37,1,276,134,0.056000," ","int(x^2*(a+b*arctanh(c*x^(1/2)))/(-c^2*x+1),x)","-\frac{x^{2} a}{2 c^{2}}-\frac{x a}{c^{4}}-\frac{a \ln \left(c \sqrt{x}-1\right)}{c^{6}}-\frac{a \ln \left(1+c \sqrt{x}\right)}{c^{6}}-\frac{b \arctanh \left(c \sqrt{x}\right) x^{2}}{2 c^{2}}-\frac{b \arctanh \left(c \sqrt{x}\right) x}{c^{4}}-\frac{b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{c^{6}}-\frac{b \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{c^{6}}-\frac{b \ln \left(c \sqrt{x}-1\right)^{2}}{4 c^{6}}+\frac{b \dilog \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{c^{6}}+\frac{b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2 c^{6}}+\frac{b \ln \left(1+c \sqrt{x}\right)^{2}}{4 c^{6}}+\frac{b \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{b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{2 c^{6}}-\frac{b \,x^{\frac{3}{2}}}{6 c^{3}}-\frac{3 b \sqrt{x}}{2 c^{5}}-\frac{3 b \ln \left(c \sqrt{x}-1\right)}{4 c^{6}}+\frac{3 b \ln \left(1+c \sqrt{x}\right)}{4 c^{6}}"," ",0,"-1/2/c^2*x^2*a-1/c^4*x*a-1/c^6*a*ln(c*x^(1/2)-1)-1/c^6*a*ln(1+c*x^(1/2))-1/2/c^2*b*arctanh(c*x^(1/2))*x^2-1/c^4*b*arctanh(c*x^(1/2))*x-1/c^6*b*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-1/c^6*b*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-1/4/c^6*b*ln(c*x^(1/2)-1)^2+1/c^6*b*dilog(1/2+1/2*c*x^(1/2))+1/2/c^6*b*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+1/4/c^6*b*ln(1+c*x^(1/2))^2+1/2/c^6*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))-1/2/c^6*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))-1/6*b*x^(3/2)/c^3-3/2*b*x^(1/2)/c^5-3/4/c^6*b*ln(c*x^(1/2)-1)+3/4/c^6*b*ln(1+c*x^(1/2))","B"
38,1,243,106,0.056000," ","int(x*(a+b*arctanh(c*x^(1/2)))/(-c^2*x+1),x)","-\frac{x a}{c^{2}}-\frac{a \ln \left(c \sqrt{x}-1\right)}{c^{4}}-\frac{a \ln \left(1+c \sqrt{x}\right)}{c^{4}}-\frac{b \arctanh \left(c \sqrt{x}\right) x}{c^{2}}-\frac{b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{c^{4}}-\frac{b \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{c^{4}}-\frac{b \sqrt{x}}{c^{3}}-\frac{b \ln \left(c \sqrt{x}-1\right)}{2 c^{4}}+\frac{b \ln \left(1+c \sqrt{x}\right)}{2 c^{4}}-\frac{b \ln \left(c \sqrt{x}-1\right)^{2}}{4 c^{4}}+\frac{b \dilog \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{c^{4}}+\frac{b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2 c^{4}}+\frac{b \ln \left(1+c \sqrt{x}\right)^{2}}{4 c^{4}}-\frac{b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{2 c^{4}}+\frac{b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2 c^{4}}"," ",0,"-1/c^2*x*a-1/c^4*a*ln(c*x^(1/2)-1)-1/c^4*a*ln(1+c*x^(1/2))-1/c^2*b*arctanh(c*x^(1/2))*x-1/c^4*b*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-1/c^4*b*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-b*x^(1/2)/c^3-1/2/c^4*b*ln(c*x^(1/2)-1)+1/2/c^4*b*ln(1+c*x^(1/2))-1/4/c^4*b*ln(c*x^(1/2)-1)^2+1/c^4*b*dilog(1/2+1/2*c*x^(1/2))+1/2/c^4*b*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+1/4/c^4*b*ln(1+c*x^(1/2))^2-1/2/c^4*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+1/2/c^4*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))","B"
39,1,186,70,0.051000," ","int((a+b*arctanh(c*x^(1/2)))/(-c^2*x+1),x)","-\frac{a \ln \left(c \sqrt{x}-1\right)}{c^{2}}-\frac{a \ln \left(1+c \sqrt{x}\right)}{c^{2}}-\frac{b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)}{c^{2}}-\frac{b \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{c^{2}}-\frac{b \ln \left(c \sqrt{x}-1\right)^{2}}{4 c^{2}}+\frac{b \dilog \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{c^{2}}+\frac{b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2 c^{2}}+\frac{b \ln \left(1+c \sqrt{x}\right)^{2}}{4 c^{2}}-\frac{b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{2 c^{2}}+\frac{b \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}}"," ",0,"-1/c^2*a*ln(c*x^(1/2)-1)-1/c^2*a*ln(1+c*x^(1/2))-1/c^2*b*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-1/c^2*b*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-1/4/c^2*b*ln(c*x^(1/2)-1)^2+1/c^2*b*dilog(1/2+1/2*c*x^(1/2))+1/2/c^2*b*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+1/4/c^2*b*ln(1+c*x^(1/2))^2-1/2/c^2*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+1/2/c^2*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))","B"
40,1,217,61,0.059000," ","int((a+b*arctanh(c*x^(1/2)))/x/(-c^2*x+1),x)","2 a \ln \left(c \sqrt{x}\right)-a \ln \left(c \sqrt{x}-1\right)-a \ln \left(1+c \sqrt{x}\right)+2 b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}\right)-b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)-b \arctanh \left(c \sqrt{x}\right) \ln \left(1+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)-\frac{b \ln \left(c \sqrt{x}-1\right)^{2}}{4}+b \dilog \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)+\frac{b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2}+\frac{b \ln \left(1+c \sqrt{x}\right)^{2}}{4}-\frac{b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{2}+\frac{b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2}"," ",0,"2*a*ln(c*x^(1/2))-a*ln(c*x^(1/2)-1)-a*ln(1+c*x^(1/2))+2*b*arctanh(c*x^(1/2))*ln(c*x^(1/2))-b*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-b*arctanh(c*x^(1/2))*ln(1+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))-1/4*b*ln(c*x^(1/2)-1)^2+b*dilog(1/2+1/2*c*x^(1/2))+1/2*b*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+1/4*b*ln(1+c*x^(1/2))^2-1/2*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+1/2*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))","B"
41,1,315,105,0.067000," ","int((a+b*arctanh(c*x^(1/2)))/x^2/(-c^2*x+1),x)","-\frac{a}{x}+2 c^{2} a \ln \left(c \sqrt{x}\right)-c^{2} a \ln \left(c \sqrt{x}-1\right)-c^{2} a \ln \left(1+c \sqrt{x}\right)-\frac{b \arctanh \left(c \sqrt{x}\right)}{x}+2 c^{2} b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}\right)-c^{2} b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)-c^{2} b \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)-\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}-c^{2} b \dilog \left(c \sqrt{x}\right)-c^{2} b \dilog \left(1+c \sqrt{x}\right)-c^{2} b \ln \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)-\frac{c^{2} b \ln \left(c \sqrt{x}-1\right)^{2}}{4}+c^{2} b \dilog \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)+\frac{c^{2} b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2}+\frac{c^{2} b \ln \left(1+c \sqrt{x}\right)^{2}}{4}-\frac{c^{2} b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{2}+\frac{c^{2} b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2}"," ",0,"-a/x+2*c^2*a*ln(c*x^(1/2))-c^2*a*ln(c*x^(1/2)-1)-c^2*a*ln(1+c*x^(1/2))-b*arctanh(c*x^(1/2))/x+2*c^2*b*arctanh(c*x^(1/2))*ln(c*x^(1/2))-c^2*b*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-c^2*b*arctanh(c*x^(1/2))*ln(1+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))-c^2*b*dilog(c*x^(1/2))-c^2*b*dilog(1+c*x^(1/2))-c^2*b*ln(c*x^(1/2))*ln(1+c*x^(1/2))-1/4*c^2*b*ln(c*x^(1/2)-1)^2+c^2*b*dilog(1/2+1/2*c*x^(1/2))+1/2*c^2*b*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+1/4*c^2*b*ln(1+c*x^(1/2))^2-1/2*c^2*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+1/2*c^2*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))","B"
42,1,348,134,0.071000," ","int((a+b*arctanh(c*x^(1/2)))/x^3/(-c^2*x+1),x)","-\frac{a}{2 x^{2}}-\frac{c^{2} a}{x}+2 c^{4} a \ln \left(c \sqrt{x}\right)-c^{4} a \ln \left(c \sqrt{x}-1\right)-c^{4} a \ln \left(1+c \sqrt{x}\right)-\frac{b \arctanh \left(c \sqrt{x}\right)}{2 x^{2}}-\frac{c^{2} b \arctanh \left(c \sqrt{x}\right)}{x}+2 c^{4} b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}\right)-c^{4} b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)-c^{4} b \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)-c^{4} b \dilog \left(c \sqrt{x}\right)-c^{4} b \dilog \left(1+c \sqrt{x}\right)-c^{4} b \ln \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)-\frac{c^{4} b \ln \left(c \sqrt{x}-1\right)^{2}}{4}+c^{4} b \dilog \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)+\frac{c^{4} b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2}+\frac{c^{4} b \ln \left(1+c \sqrt{x}\right)^{2}}{4}-\frac{c^{4} b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{2}+\frac{c^{4} b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2}-\frac{b c}{6 x^{\frac{3}{2}}}-\frac{3 b \,c^{3}}{2 \sqrt{x}}-\frac{3 c^{4} b \ln \left(c \sqrt{x}-1\right)}{4}+\frac{3 c^{4} b \ln \left(1+c \sqrt{x}\right)}{4}"," ",0,"-1/2*a/x^2-c^2*a/x+2*c^4*a*ln(c*x^(1/2))-c^4*a*ln(c*x^(1/2)-1)-c^4*a*ln(1+c*x^(1/2))-1/2*b*arctanh(c*x^(1/2))/x^2-c^2*b*arctanh(c*x^(1/2))/x+2*c^4*b*arctanh(c*x^(1/2))*ln(c*x^(1/2))-c^4*b*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-c^4*b*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-c^4*b*dilog(c*x^(1/2))-c^4*b*dilog(1+c*x^(1/2))-c^4*b*ln(c*x^(1/2))*ln(1+c*x^(1/2))-1/4*c^4*b*ln(c*x^(1/2)-1)^2+c^4*b*dilog(1/2+1/2*c*x^(1/2))+1/2*c^4*b*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))+1/4*c^4*b*ln(1+c*x^(1/2))^2-1/2*c^4*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+1/2*c^4*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))-1/6*b*c/x^(3/2)-3/2*b*c^3/x^(1/2)-3/4*c^4*b*ln(c*x^(1/2)-1)+3/4*c^4*b*ln(1+c*x^(1/2))","B"
43,1,381,161,0.071000," ","int((a+b*arctanh(c*x^(1/2)))/x^4/(-c^2*x+1),x)","-\frac{c^{2} b \arctanh \left(c \sqrt{x}\right)}{2 x^{2}}-c^{6} b \ln \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)+\frac{c^{6} b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2}-\frac{c^{6} b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(1+c \sqrt{x}\right)}{2}-\frac{c^{4} b \arctanh \left(c \sqrt{x}\right)}{x}-c^{6} b \arctanh \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)+2 c^{6} b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}\right)-c^{6} b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}-1\right)+\frac{c^{6} b \ln \left(-\frac{c \sqrt{x}}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)}{2}-\frac{11 b \,c^{5}}{6 \sqrt{x}}-\frac{5 b \,c^{3}}{18 x^{\frac{3}{2}}}-\frac{b c}{15 x^{\frac{5}{2}}}-\frac{c^{4} a}{x}-\frac{c^{2} a}{2 x^{2}}-c^{6} a \ln \left(c \sqrt{x}-1\right)-c^{6} a \ln \left(1+c \sqrt{x}\right)-\frac{c^{6} b \ln \left(c \sqrt{x}-1\right)^{2}}{4}+\frac{c^{6} b \ln \left(1+c \sqrt{x}\right)^{2}}{4}-\frac{11 c^{6} b \ln \left(c \sqrt{x}-1\right)}{12}+2 c^{6} a \ln \left(c \sqrt{x}\right)+\frac{11 c^{6} b \ln \left(1+c \sqrt{x}\right)}{12}-c^{6} b \dilog \left(c \sqrt{x}\right)+c^{6} b \dilog \left(\frac{1}{2}+\frac{c \sqrt{x}}{2}\right)-\frac{b \arctanh \left(c \sqrt{x}\right)}{3 x^{3}}-c^{6} b \dilog \left(1+c \sqrt{x}\right)-\frac{a}{3 x^{3}}"," ",0,"-c^4*b*arctanh(c*x^(1/2))/x-c^6*b*arctanh(c*x^(1/2))*ln(1+c*x^(1/2))-c^6*b*ln(c*x^(1/2))*ln(1+c*x^(1/2))+2*c^6*b*arctanh(c*x^(1/2))*ln(c*x^(1/2))+1/2*c^6*b*ln(c*x^(1/2)-1)*ln(1/2+1/2*c*x^(1/2))-1/2*c^6*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1+c*x^(1/2))+1/2*c^6*b*ln(-1/2*c*x^(1/2)+1/2)*ln(1/2+1/2*c*x^(1/2))-c^6*b*arctanh(c*x^(1/2))*ln(c*x^(1/2)-1)-1/2*c^2*b*arctanh(c*x^(1/2))/x^2-11/6*b*c^5/x^(1/2)-5/18*b*c^3/x^(3/2)-1/15*b*c/x^(5/2)-c^6*b*dilog(c*x^(1/2))-c^4*a/x-1/2*c^2*a/x^2-c^6*a*ln(c*x^(1/2)-1)-c^6*a*ln(1+c*x^(1/2))-1/4*c^6*b*ln(c*x^(1/2)-1)^2+c^6*b*dilog(1/2+1/2*c*x^(1/2))+1/4*c^6*b*ln(1+c*x^(1/2))^2-1/3*b*arctanh(c*x^(1/2))/x^3-11/12*c^6*b*ln(c*x^(1/2)-1)-c^6*b*dilog(1+c*x^(1/2))+2*c^6*a*ln(c*x^(1/2))+11/12*c^6*b*ln(1+c*x^(1/2))-1/3*a/x^3","B"
44,1,651,376,0.097000," ","int(x^2*(a+b*arctanh(c*x^(1/2)))/(e*x+d),x)","-\frac{a d x}{e^{2}}+\frac{a \,x^{2}}{2 e}+\frac{a \,d^{2} \ln \left(c^{2} e x +c^{2} d \right)}{e^{3}}-\frac{b \arctanh \left(c \sqrt{x}\right) x d}{e^{2}}+\frac{b \arctanh \left(c \sqrt{x}\right) x^{2}}{2 e}+\frac{b \arctanh \left(c \sqrt{x}\right) d^{2} \ln \left(c^{2} e x +c^{2} d \right)}{e^{3}}+\frac{b \,x^{\frac{3}{2}}}{6 c e}-\frac{b d \sqrt{x}}{c \,e^{2}}+\frac{b \sqrt{x}}{2 c^{3} e}-\frac{b \ln \left(c \sqrt{x}-1\right) d}{2 c^{2} e^{2}}+\frac{b \ln \left(c \sqrt{x}-1\right)}{4 c^{4} e}+\frac{b \ln \left(1+c \sqrt{x}\right) d}{2 c^{2} e^{2}}-\frac{b \ln \left(1+c \sqrt{x}\right)}{4 c^{4} e}+\frac{b \,d^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 e^{3}}-\frac{b \,d^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 e^{3}}-\frac{b \,d^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 e^{3}}-\frac{b \,d^{2} \dilog \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 e^{3}}-\frac{b \,d^{2} \dilog \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 e^{3}}-\frac{b \,d^{2} \ln \left(1+c \sqrt{x}\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 e^{3}}+\frac{b \,d^{2} \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 e^{3}}+\frac{b \,d^{2} \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 e^{3}}+\frac{b \,d^{2} \dilog \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 e^{3}}+\frac{b \,d^{2} \dilog \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 e^{3}}"," ",0,"-a*d*x/e^2+1/2*a*x^2/e+a*d^2/e^3*ln(c^2*e*x+c^2*d)-b*arctanh(c*x^(1/2))*x*d/e^2+1/2*b*arctanh(c*x^(1/2))*x^2/e+b*arctanh(c*x^(1/2))*d^2/e^3*ln(c^2*e*x+c^2*d)+1/6*b*x^(3/2)/c/e-b*d*x^(1/2)/c/e^2+1/2*b*x^(1/2)/c^3/e-1/2/c^2*b/e^2*ln(c*x^(1/2)-1)*d+1/4/c^4*b*ln(c*x^(1/2)-1)/e+1/2/c^2*b/e^2*ln(1+c*x^(1/2))*d-1/4/c^4*b*ln(1+c*x^(1/2))/e+1/2*b*d^2/e^3*ln(c*x^(1/2)-1)*ln(c^2*e*x+c^2*d)-1/2*b*d^2/e^3*ln(c*x^(1/2)-1)*ln((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))-1/2*b*d^2/e^3*ln(c*x^(1/2)-1)*ln((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))-1/2*b*d^2/e^3*dilog((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))-1/2*b*d^2/e^3*dilog((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))-1/2*b*d^2/e^3*ln(1+c*x^(1/2))*ln(c^2*e*x+c^2*d)+1/2*b*d^2/e^3*ln(1+c*x^(1/2))*ln((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))+1/2*b*d^2/e^3*ln(1+c*x^(1/2))*ln((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))+1/2*b*d^2/e^3*dilog((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))+1/2*b*d^2/e^3*dilog((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))","A"
45,1,539,306,0.065000," ","int(x*(a+b*arctanh(c*x^(1/2)))/(e*x+d),x)","\frac{a x}{e}-\frac{a d \ln \left(c^{2} e x +c^{2} d \right)}{e^{2}}+\frac{b \arctanh \left(c \sqrt{x}\right) x}{e}-\frac{b \arctanh \left(c \sqrt{x}\right) d \ln \left(c^{2} e x +c^{2} d \right)}{e^{2}}-\frac{b d \ln \left(c \sqrt{x}-1\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 e^{2}}+\frac{b d \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 e^{2}}+\frac{b d \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 e^{2}}+\frac{b d \dilog \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 e^{2}}+\frac{b d \dilog \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 e^{2}}+\frac{b d \ln \left(1+c \sqrt{x}\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 e^{2}}-\frac{b d \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 e^{2}}-\frac{b d \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 e^{2}}-\frac{b d \dilog \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 e^{2}}-\frac{b d \dilog \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 e^{2}}+\frac{b \sqrt{x}}{c e}+\frac{b \ln \left(c \sqrt{x}-1\right)}{2 c^{2} e}-\frac{b \ln \left(1+c \sqrt{x}\right)}{2 c^{2} e}"," ",0,"a*x/e-a/e^2*d*ln(c^2*e*x+c^2*d)+b*arctanh(c*x^(1/2))*x/e-b*arctanh(c*x^(1/2))/e^2*d*ln(c^2*e*x+c^2*d)-1/2*b/e^2*d*ln(c*x^(1/2)-1)*ln(c^2*e*x+c^2*d)+1/2*b/e^2*d*ln(c*x^(1/2)-1)*ln((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))+1/2*b/e^2*d*ln(c*x^(1/2)-1)*ln((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))+1/2*b/e^2*d*dilog((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))+1/2*b/e^2*d*dilog((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))+1/2*b/e^2*d*ln(1+c*x^(1/2))*ln(c^2*e*x+c^2*d)-1/2*b/e^2*d*ln(1+c*x^(1/2))*ln((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))-1/2*b/e^2*d*ln(1+c*x^(1/2))*ln((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))-1/2*b/e^2*d*dilog((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))-1/2*b/e^2*d*dilog((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))+b*x^(1/2)/c/e+1/2/c^2*b*ln(c*x^(1/2)-1)/e-1/2/c^2*b*ln(1+c*x^(1/2))/e","A"
46,1,462,256,0.062000," ","int((a+b*arctanh(c*x^(1/2)))/(e*x+d),x)","\frac{a \ln \left(c^{2} e x +c^{2} d \right)}{e}+\frac{b \ln \left(c^{2} e x +c^{2} d \right) \arctanh \left(c \sqrt{x}\right)}{e}+\frac{b \ln \left(c \sqrt{x}-1\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 e}-\frac{b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 e}-\frac{b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 e}-\frac{b \dilog \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 e}-\frac{b \dilog \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 e}-\frac{b \ln \left(1+c \sqrt{x}\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 e}+\frac{b \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 e}+\frac{b \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 e}+\frac{b \dilog \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 e}+\frac{b \dilog \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 e}"," ",0,"a/e*ln(c^2*e*x+c^2*d)+b/e*ln(c^2*e*x+c^2*d)*arctanh(c*x^(1/2))+1/2*b/e*ln(c*x^(1/2)-1)*ln(c^2*e*x+c^2*d)-1/2*b*ln(c*x^(1/2)-1)/e*ln((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))-1/2*b*ln(c*x^(1/2)-1)/e*ln((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))-1/2*b/e*dilog((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))-1/2*b/e*dilog((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))-1/2*b/e*ln(1+c*x^(1/2))*ln(c^2*e*x+c^2*d)+1/2*b*ln(1+c*x^(1/2))/e*ln((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))+1/2*b*ln(1+c*x^(1/2))/e*ln((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))+1/2*b/e*dilog((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))+1/2*b/e*dilog((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))","A"
47,1,540,292,0.070000," ","int((a+b*arctanh(c*x^(1/2)))/x/(e*x+d),x)","\frac{2 a \ln \left(c \sqrt{x}\right)}{d}-\frac{a \ln \left(c^{2} e x +c^{2} d \right)}{d}+\frac{2 b \arctanh \left(c \sqrt{x}\right) \ln \left(c \sqrt{x}\right)}{d}-\frac{b \arctanh \left(c \sqrt{x}\right) \ln \left(c^{2} e x +c^{2} d \right)}{d}-\frac{b \ln \left(c \sqrt{x}-1\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 d}+\frac{b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 d}+\frac{b \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 d}+\frac{b \dilog \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 d}+\frac{b \dilog \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 d}+\frac{b \ln \left(1+c \sqrt{x}\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 d}-\frac{b \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 d}-\frac{b \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 d}-\frac{b \dilog \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 d}-\frac{b \dilog \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 d}-\frac{b \dilog \left(c \sqrt{x}\right)}{d}-\frac{b \dilog \left(1+c \sqrt{x}\right)}{d}-\frac{b \ln \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{d}"," ",0,"2*a/d*ln(c*x^(1/2))-a/d*ln(c^2*e*x+c^2*d)+2*b*arctanh(c*x^(1/2))/d*ln(c*x^(1/2))-b*arctanh(c*x^(1/2))/d*ln(c^2*e*x+c^2*d)-1/2*b/d*ln(c*x^(1/2)-1)*ln(c^2*e*x+c^2*d)+1/2*b/d*ln(c*x^(1/2)-1)*ln((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))+1/2*b/d*ln(c*x^(1/2)-1)*ln((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))+1/2*b/d*dilog((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))+1/2*b/d*dilog((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))+1/2*b/d*ln(1+c*x^(1/2))*ln(c^2*e*x+c^2*d)-1/2*b/d*ln(1+c*x^(1/2))*ln((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))-1/2*b/d*ln(1+c*x^(1/2))*ln((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))-1/2*b/d*dilog((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))-1/2*b/d*dilog((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))-b/d*dilog(c*x^(1/2))-b/d*dilog(1+c*x^(1/2))-b/d*ln(c*x^(1/2))*ln(1+c*x^(1/2))","A"
48,1,620,343,0.074000," ","int((a+b*arctanh(c*x^(1/2)))/x^2/(e*x+d),x)","-\frac{a}{d x}-\frac{2 a e \ln \left(c \sqrt{x}\right)}{d^{2}}+\frac{a e \ln \left(c^{2} e x +c^{2} d \right)}{d^{2}}-\frac{b \arctanh \left(c \sqrt{x}\right)}{d x}-\frac{2 b \arctanh \left(c \sqrt{x}\right) e \ln \left(c \sqrt{x}\right)}{d^{2}}+\frac{b \arctanh \left(c \sqrt{x}\right) e \ln \left(c^{2} e x +c^{2} d \right)}{d^{2}}-\frac{b c}{d \sqrt{x}}-\frac{c^{2} b \ln \left(c \sqrt{x}-1\right)}{2 d}+\frac{c^{2} b \ln \left(1+c \sqrt{x}\right)}{2 d}+\frac{b e \dilog \left(c \sqrt{x}\right)}{d^{2}}+\frac{b e \dilog \left(1+c \sqrt{x}\right)}{d^{2}}+\frac{b e \ln \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{d^{2}}+\frac{b e \ln \left(c \sqrt{x}-1\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 d^{2}}-\frac{b e \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 d^{2}}-\frac{b e \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 d^{2}}-\frac{b e \dilog \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 d^{2}}-\frac{b e \dilog \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 d^{2}}-\frac{b e \ln \left(1+c \sqrt{x}\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 d^{2}}+\frac{b e \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 d^{2}}+\frac{b e \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 d^{2}}+\frac{b e \dilog \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 d^{2}}+\frac{b e \dilog \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 d^{2}}"," ",0,"-a/d/x-2*a/d^2*e*ln(c*x^(1/2))+a*e/d^2*ln(c^2*e*x+c^2*d)-b*arctanh(c*x^(1/2))/d/x-2*b*arctanh(c*x^(1/2))/d^2*e*ln(c*x^(1/2))+b*arctanh(c*x^(1/2))*e/d^2*ln(c^2*e*x+c^2*d)-b*c/d/x^(1/2)-1/2*c^2*b/d*ln(c*x^(1/2)-1)+1/2*c^2*b/d*ln(1+c*x^(1/2))+b/d^2*e*dilog(c*x^(1/2))+b/d^2*e*dilog(1+c*x^(1/2))+b/d^2*e*ln(c*x^(1/2))*ln(1+c*x^(1/2))+1/2*b/d^2*e*ln(c*x^(1/2)-1)*ln(c^2*e*x+c^2*d)-1/2*b/d^2*e*ln(c*x^(1/2)-1)*ln((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))-1/2*b/d^2*e*ln(c*x^(1/2)-1)*ln((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))-1/2*b/d^2*e*dilog((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))-1/2*b/d^2*e*dilog((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))-1/2*b/d^2*e*ln(1+c*x^(1/2))*ln(c^2*e*x+c^2*d)+1/2*b/d^2*e*ln(1+c*x^(1/2))*ln((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))+1/2*b/d^2*e*ln(1+c*x^(1/2))*ln((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))+1/2*b/d^2*e*dilog((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))+1/2*b/d^2*e*dilog((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))","A"
49,1,741,421,0.081000," ","int((a+b*arctanh(c*x^(1/2)))/x^3/(e*x+d),x)","-\frac{b \,e^{2} \dilog \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 d^{3}}-\frac{b \,e^{2} \dilog \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 d^{3}}-\frac{b \arctanh \left(c \sqrt{x}\right)}{2 d \,x^{2}}+\frac{c^{4} b \ln \left(1+c \sqrt{x}\right)}{4 d}-\frac{c^{4} b \ln \left(c \sqrt{x}-1\right)}{4 d}-\frac{b \,e^{2} \dilog \left(c \sqrt{x}\right)}{d^{3}}-\frac{b \,e^{2} \dilog \left(1+c \sqrt{x}\right)}{d^{3}}+\frac{b \,e^{2} \dilog \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 d^{3}}+\frac{b \,e^{2} \dilog \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 d^{3}}+\frac{2 a \,e^{2} \ln \left(c \sqrt{x}\right)}{d^{3}}-\frac{a \,e^{2} \ln \left(c^{2} e x +c^{2} d \right)}{d^{3}}+\frac{a e}{d^{2} x}-\frac{c^{2} b \ln \left(1+c \sqrt{x}\right) e}{2 d^{2}}-\frac{a}{2 d \,x^{2}}+\frac{b c e}{d^{2} \sqrt{x}}-\frac{b \,e^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 d^{3}}+\frac{b \,e^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}-e \left(c \sqrt{x}-1\right)-e}{c \sqrt{-d e}-e}\right)}{2 d^{3}}+\frac{b \,e^{2} \ln \left(c \sqrt{x}-1\right) \ln \left(\frac{c \sqrt{-d e}+e \left(c \sqrt{x}-1\right)+e}{c \sqrt{-d e}+e}\right)}{2 d^{3}}+\frac{b \,e^{2} \ln \left(1+c \sqrt{x}\right) \ln \left(c^{2} e x +c^{2} d \right)}{2 d^{3}}-\frac{b \,e^{2} \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}-e \left(1+c \sqrt{x}\right)+e}{c \sqrt{-d e}+e}\right)}{2 d^{3}}-\frac{b \,e^{2} \ln \left(1+c \sqrt{x}\right) \ln \left(\frac{c \sqrt{-d e}+e \left(1+c \sqrt{x}\right)-e}{c \sqrt{-d e}-e}\right)}{2 d^{3}}+\frac{c^{2} b \ln \left(c \sqrt{x}-1\right) e}{2 d^{2}}-\frac{b \arctanh \left(c \sqrt{x}\right) e^{2} \ln \left(c^{2} e x +c^{2} d \right)}{d^{3}}+\frac{b \arctanh \left(c \sqrt{x}\right) e}{d^{2} x}+\frac{2 b \arctanh \left(c \sqrt{x}\right) e^{2} \ln \left(c \sqrt{x}\right)}{d^{3}}-\frac{b \,e^{2} \ln \left(c \sqrt{x}\right) \ln \left(1+c \sqrt{x}\right)}{d^{3}}-\frac{b c}{6 d \,x^{\frac{3}{2}}}-\frac{b \,c^{3}}{2 d \sqrt{x}}"," ",0,"1/4*c^4*b/d*ln(1+c*x^(1/2))-1/4*c^4*b/d*ln(c*x^(1/2)-1)-b/d^3*e^2*dilog(c*x^(1/2))-b/d^3*e^2*dilog(1+c*x^(1/2))+1/2*b/d^3*e^2*dilog((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))+1/2*b/d^3*e^2*dilog((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))-1/2*b/d^3*e^2*dilog((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))-1/2*b/d^3*e^2*dilog((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))-1/2*b*arctanh(c*x^(1/2))/d/x^2+2*a/d^3*e^2*ln(c*x^(1/2))-a*e^2/d^3*ln(c^2*e*x+c^2*d)+a/d^2*e/x-1/2*c^2*b/d^2*ln(1+c*x^(1/2))*e-1/2*a/d/x^2+b*c*e/d^2/x^(1/2)-b*arctanh(c*x^(1/2))*e^2/d^3*ln(c^2*e*x+c^2*d)-1/2*b/d^3*e^2*ln(c*x^(1/2)-1)*ln(c^2*e*x+c^2*d)+1/2*b/d^3*e^2*ln(c*x^(1/2)-1)*ln((c*(-d*e)^(1/2)-e*(c*x^(1/2)-1)-e)/(c*(-d*e)^(1/2)-e))+b*arctanh(c*x^(1/2))/d^2*e/x+1/2*b/d^3*e^2*ln(c*x^(1/2)-1)*ln((c*(-d*e)^(1/2)+e*(c*x^(1/2)-1)+e)/(c*(-d*e)^(1/2)+e))+1/2*b/d^3*e^2*ln(1+c*x^(1/2))*ln(c^2*e*x+c^2*d)-1/2*b/d^3*e^2*ln(1+c*x^(1/2))*ln((c*(-d*e)^(1/2)-e*(1+c*x^(1/2))+e)/(c*(-d*e)^(1/2)+e))-1/2*b/d^3*e^2*ln(1+c*x^(1/2))*ln((c*(-d*e)^(1/2)+e*(1+c*x^(1/2))-e)/(c*(-d*e)^(1/2)-e))+1/2*c^2*b/d^2*ln(c*x^(1/2)-1)*e-b/d^3*e^2*ln(c*x^(1/2))*ln(1+c*x^(1/2))+2*b*arctanh(c*x^(1/2))/d^3*e^2*ln(c*x^(1/2))-1/6*b*c/d/x^(3/2)-1/2*b*c^3/d/x^(1/2)","A"