1,1,967,251,0.060000," ","int(x^3*arctanh(b*x+a)^2,x)","-\frac{\arctanh \left(b x +a \right) \ln \left(b x +a -1\right) a}{b^{4}}+\frac{\arctanh \left(b x +a \right) \ln \left(b x +a -1\right) a^{4}}{4 b^{4}}+\frac{3 \arctanh \left(b x +a \right) \ln \left(b x +a -1\right) a^{2}}{2 b^{4}}-\frac{\arctanh \left(b x +a \right) \ln \left(b x +a +1\right) a^{3}}{b^{4}}-\frac{3 \arctanh \left(b x +a \right) \ln \left(b x +a +1\right) a^{2}}{2 b^{4}}-\frac{\arctanh \left(b x +a \right) \ln \left(b x +a +1\right) a}{b^{4}}-\frac{\arctanh \left(b x +a \right) \ln \left(b x +a -1\right) a^{3}}{b^{4}}-\frac{\arctanh \left(b x +a \right) \ln \left(b x +a +1\right) a^{4}}{4 b^{4}}-\frac{\arctanh \left(b x +a \right) x^{2} a}{2 b^{2}}+\frac{3 \arctanh \left(b x +a \right) x \,a^{2}}{2 b^{3}}+\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{3}}{2 b^{4}}+\frac{3 \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{2}}{4 b^{4}}-\frac{3 \ln \left(b x +a +1\right) \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) a^{2}}{4 b^{4}}+\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a}{2 b^{4}}-\frac{\ln \left(b x +a +1\right) \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) a^{4}}{8 b^{4}}+\frac{\ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a}{2 b^{4}}-\frac{\ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{4}}{8 b^{4}}+\frac{\ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{3}}{2 b^{4}}-\frac{3 \ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{2}}{4 b^{4}}-\frac{\ln \left(b x +a +1\right) \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) a^{3}}{2 b^{4}}-\frac{\ln \left(b x +a +1\right) \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) a}{2 b^{4}}+\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{4}}{8 b^{4}}+\frac{x^{4} \arctanh \left(b x +a \right)^{2}}{4}-\frac{5 a x}{6 b^{3}}+\frac{a \arctanh \left(b x +a \right)}{2 b^{4}}-\frac{\arctanh \left(b x +a \right) \ln \left(b x +a +1\right)}{4 b^{4}}+\frac{13 \arctanh \left(b x +a \right) a^{3}}{6 b^{4}}+\frac{\arctanh \left(b x +a \right) \ln \left(b x +a -1\right)}{4 b^{4}}+\frac{\dilog \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{3}}{b^{4}}+\frac{\dilog \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a}{b^{4}}+\frac{\arctanh \left(b x +a \right) x^{3}}{6 b}+\frac{\arctanh \left(b x +a \right) x}{2 b^{3}}-\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(b x +a +1\right)}{8 b^{4}}+\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{8 b^{4}}+\frac{3 \ln \left(b x +a -1\right) a^{2}}{2 b^{4}}+\frac{3 \ln \left(b x +a +1\right) a^{2}}{2 b^{4}}-\frac{\ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{8 b^{4}}+\frac{3 \ln \left(b x +a +1\right)^{2} a^{2}}{8 b^{4}}+\frac{\ln \left(b x +a +1\right)^{2} a}{4 b^{4}}+\frac{\ln \left(b x +a -1\right)^{2} a^{4}}{16 b^{4}}-\frac{\ln \left(b x +a -1\right)^{2} a^{3}}{4 b^{4}}+\frac{3 \ln \left(b x +a -1\right)^{2} a^{2}}{8 b^{4}}-\frac{\ln \left(b x +a -1\right)^{2} a}{4 b^{4}}-\frac{a \ln \left(b x +a -1\right)}{2 b^{4}}+\frac{a \ln \left(b x +a +1\right)}{2 b^{4}}+\frac{\ln \left(b x +a +1\right)^{2} a^{4}}{16 b^{4}}+\frac{\ln \left(b x +a +1\right)^{2} a^{3}}{4 b^{4}}-\frac{11 a^{2}}{12 b^{4}}+\frac{x^{2}}{12 b^{2}}+\frac{\ln \left(b x +a +1\right)}{3 b^{4}}+\frac{\ln \left(b x +a -1\right)}{3 b^{4}}+\frac{\ln \left(b x +a -1\right)^{2}}{16 b^{4}}+\frac{\ln \left(b x +a +1\right)^{2}}{16 b^{4}}"," ",0,"1/2/b^4*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)*a^3+3/4/b^4*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)*a^2-3/4/b^4*ln(b*x+a+1)*ln(-1/2*b*x-1/2*a+1/2)*a^2-1/b^4*arctanh(b*x+a)*ln(b*x+a-1)*a+1/2/b^4*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)*a-1/8/b^4*ln(b*x+a+1)*ln(-1/2*b*x-1/2*a+1/2)*a^4+1/4/b^4*arctanh(b*x+a)*ln(b*x+a-1)*a^4+1/2/b^4*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)*a-1/8/b^4*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)*a^4+3/2/b^4*arctanh(b*x+a)*ln(b*x+a-1)*a^2+1/2/b^4*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)*a^3-3/4/b^4*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)*a^2-1/b^4*arctanh(b*x+a)*ln(b*x+a+1)*a^3-3/2/b^4*arctanh(b*x+a)*ln(b*x+a+1)*a^2-1/b^4*arctanh(b*x+a)*ln(b*x+a+1)*a-1/b^4*arctanh(b*x+a)*ln(b*x+a-1)*a^3-1/4/b^4*arctanh(b*x+a)*ln(b*x+a+1)*a^4-1/2/b^2*arctanh(b*x+a)*x^2*a+3/2/b^3*arctanh(b*x+a)*x*a^2-1/2/b^4*ln(b*x+a+1)*ln(-1/2*b*x-1/2*a+1/2)*a^3-1/2/b^4*ln(b*x+a+1)*ln(-1/2*b*x-1/2*a+1/2)*a+1/8/b^4*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)*a^4+1/2*a*arctanh(b*x+a)/b^4-5/6*a*x/b^3-1/4/b^4*arctanh(b*x+a)*ln(b*x+a+1)-1/8/b^4*ln(-1/2*b*x-1/2*a+1/2)*ln(b*x+a+1)+1/8/b^4*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)+13/6/b^4*arctanh(b*x+a)*a^3+3/2/b^4*ln(b*x+a-1)*a^2+3/2/b^4*ln(b*x+a+1)*a^2-1/8/b^4*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)+1/4/b^4*arctanh(b*x+a)*ln(b*x+a-1)+3/8/b^4*ln(b*x+a+1)^2*a^2+1/4/b^4*ln(b*x+a+1)^2*a+1/16/b^4*ln(b*x+a-1)^2*a^4-1/4/b^4*ln(b*x+a-1)^2*a^3+3/8/b^4*ln(b*x+a-1)^2*a^2-1/4/b^4*ln(b*x+a-1)^2*a+1/b^4*dilog(1/2+1/2*b*x+1/2*a)*a^3+1/b^4*dilog(1/2+1/2*b*x+1/2*a)*a-1/2/b^4*a*ln(b*x+a-1)+1/2/b^4*a*ln(b*x+a+1)+1/6/b*arctanh(b*x+a)*x^3+1/2/b^3*arctanh(b*x+a)*x+1/16/b^4*ln(b*x+a+1)^2*a^4+1/4/b^4*ln(b*x+a+1)^2*a^3-11/12/b^4*a^2+1/12/b^2*x^2+1/3/b^4*ln(b*x+a+1)+1/3/b^4*ln(b*x+a-1)+1/16/b^4*ln(b*x+a-1)^2+1/16/b^4*ln(b*x+a+1)^2+1/4*x^4*arctanh(b*x+a)^2","B"
2,1,729,190,0.061000," ","int(x^2*arctanh(b*x+a)^2,x)","\frac{\arctanh \left(b x +a \right) \ln \left(b x +a +1\right) a^{2}}{b^{3}}-\frac{4 \arctanh \left(b x +a \right) x a}{3 b^{2}}-\frac{\arctanh \left(b x +a \right) \ln \left(b x +a -1\right) a}{b^{3}}-\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{2}}{2 b^{3}}+\frac{\arctanh \left(b x +a \right) \ln \left(b x +a -1\right) a^{2}}{b^{3}}+\frac{\arctanh \left(b x +a \right) \ln \left(b x +a +1\right) a}{b^{3}}-\frac{\arctanh \left(b x +a \right) \ln \left(b x +a -1\right) a^{3}}{3 b^{3}}+\frac{\arctanh \left(b x +a \right) \ln \left(b x +a +1\right) a^{3}}{3 b^{3}}+\frac{\ln \left(b x +a +1\right) \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) a}{2 b^{3}}-\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{3}}{6 b^{3}}+\frac{\ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a}{2 b^{3}}-\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a}{2 b^{3}}-\frac{\ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{2}}{2 b^{3}}+\frac{\ln \left(b x +a +1\right) \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) a^{3}}{6 b^{3}}+\frac{\ln \left(b x +a +1\right) \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) a^{2}}{2 b^{3}}+\frac{\ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{3}}{6 b^{3}}+\frac{x}{3 b^{2}}-\frac{\dilog \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{3 b^{3}}+\frac{x^{3} \arctanh \left(b x +a \right)^{2}}{3}-\frac{\dilog \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a^{2}}{b^{3}}+\frac{\arctanh \left(b x +a \right) \ln \left(b x +a -1\right)}{3 b^{3}}+\frac{\arctanh \left(b x +a \right) \ln \left(b x +a +1\right)}{3 b^{3}}-\frac{5 \arctanh \left(b x +a \right) a^{2}}{3 b^{3}}+\frac{\arctanh \left(b x +a \right) x^{2}}{3 b}-\frac{\ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{6 b^{3}}+\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(b x +a +1\right)}{6 b^{3}}-\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{6 b^{3}}-\frac{\ln \left(b x +a +1\right)^{2} a^{3}}{12 b^{3}}-\frac{\ln \left(b x +a +1\right)^{2} a^{2}}{4 b^{3}}-\frac{\ln \left(b x +a +1\right)^{2} a}{4 b^{3}}-\frac{a \ln \left(b x +a -1\right)}{b^{3}}-\frac{a \ln \left(b x +a +1\right)}{b^{3}}-\frac{\ln \left(b x +a -1\right)^{2} a^{3}}{12 b^{3}}+\frac{\ln \left(b x +a -1\right)^{2} a^{2}}{4 b^{3}}-\frac{\ln \left(b x +a -1\right)^{2} a}{4 b^{3}}+\frac{a}{3 b^{3}}-\frac{\ln \left(b x +a +1\right)}{6 b^{3}}+\frac{\ln \left(b x +a -1\right)}{6 b^{3}}+\frac{\ln \left(b x +a -1\right)^{2}}{12 b^{3}}-\frac{\ln \left(b x +a +1\right)^{2}}{12 b^{3}}"," ",0,"-1/2/b^3*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)*a^2+1/2/b^3*ln(b*x+a+1)*ln(-1/2*b*x-1/2*a+1/2)*a-1/6/b^3*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)*a^3+1/2/b^3*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)*a-1/2/b^3*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)*a+1/b^3*arctanh(b*x+a)*ln(b*x+a-1)*a^2+1/b^3*arctanh(b*x+a)*ln(b*x+a+1)*a-1/3/b^3*arctanh(b*x+a)*ln(b*x+a-1)*a^3+1/3/b^3*arctanh(b*x+a)*ln(b*x+a+1)*a^3+1/b^3*arctanh(b*x+a)*ln(b*x+a+1)*a^2-4/3/b^2*arctanh(b*x+a)*x*a-1/2/b^3*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)*a^2+1/6/b^3*ln(b*x+a+1)*ln(-1/2*b*x-1/2*a+1/2)*a^3+1/2/b^3*ln(b*x+a+1)*ln(-1/2*b*x-1/2*a+1/2)*a^2-1/b^3*arctanh(b*x+a)*ln(b*x+a-1)*a+1/6/b^3*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)*a^3+1/3*x/b^2-1/b^3*dilog(1/2+1/2*b*x+1/2*a)*a^2-1/6/b^3*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)+1/3/b^3*arctanh(b*x+a)*ln(b*x+a-1)+1/3/b^3*arctanh(b*x+a)*ln(b*x+a+1)+1/6/b^3*ln(-1/2*b*x-1/2*a+1/2)*ln(b*x+a+1)-1/6/b^3*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)-5/3/b^3*arctanh(b*x+a)*a^2-1/12/b^3*ln(b*x+a+1)^2*a^3-1/4/b^3*ln(b*x+a+1)^2*a^2-1/4/b^3*ln(b*x+a+1)^2*a-1/b^3*a*ln(b*x+a-1)-1/b^3*a*ln(b*x+a+1)-1/12/b^3*ln(b*x+a-1)^2*a^3+1/4/b^3*ln(b*x+a-1)^2*a^2-1/4/b^3*ln(b*x+a-1)^2*a+1/3/b*arctanh(b*x+a)*x^2+1/3/b^3*a-1/6/b^3*ln(b*x+a+1)+1/6/b^3*ln(b*x+a-1)-1/3/b^3*dilog(1/2+1/2*b*x+1/2*a)+1/12/b^3*ln(b*x+a-1)^2-1/12/b^3*ln(b*x+a+1)^2+1/3*x^3*arctanh(b*x+a)^2","B"
3,1,365,132,0.057000," ","int(x*arctanh(b*x+a)^2,x)","\frac{x^{2} \arctanh \left(b x +a \right)^{2}}{2}-\frac{\arctanh \left(b x +a \right)^{2} a^{2}}{2 b^{2}}+\frac{\arctanh \left(b x +a \right) x}{b}+\frac{\arctanh \left(b x +a \right) a}{b^{2}}-\frac{\arctanh \left(b x +a \right) \ln \left(b x +a -1\right) a}{b^{2}}+\frac{\arctanh \left(b x +a \right) \ln \left(b x +a -1\right)}{2 b^{2}}-\frac{\arctanh \left(b x +a \right) \ln \left(b x +a +1\right) a}{b^{2}}-\frac{\arctanh \left(b x +a \right) \ln \left(b x +a +1\right)}{2 b^{2}}+\frac{\ln \left(b x +a -1\right)}{2 b^{2}}+\frac{\ln \left(b x +a +1\right)}{2 b^{2}}-\frac{\ln \left(b x +a -1\right)^{2} a}{4 b^{2}}+\frac{\dilog \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a}{b^{2}}+\frac{\ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a}{2 b^{2}}+\frac{\ln \left(b x +a -1\right)^{2}}{8 b^{2}}-\frac{\ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{4 b^{2}}+\frac{\ln \left(b x +a +1\right)^{2} a}{4 b^{2}}-\frac{\ln \left(b x +a +1\right) \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) a}{2 b^{2}}+\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right) a}{2 b^{2}}+\frac{\ln \left(b x +a +1\right)^{2}}{8 b^{2}}-\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(b x +a +1\right)}{4 b^{2}}+\frac{\ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{4 b^{2}}"," ",0,"1/2*x^2*arctanh(b*x+a)^2-1/2/b^2*arctanh(b*x+a)^2*a^2+1/b*arctanh(b*x+a)*x+1/b^2*arctanh(b*x+a)*a-1/b^2*arctanh(b*x+a)*ln(b*x+a-1)*a+1/2/b^2*arctanh(b*x+a)*ln(b*x+a-1)-1/b^2*arctanh(b*x+a)*ln(b*x+a+1)*a-1/2/b^2*arctanh(b*x+a)*ln(b*x+a+1)+1/2/b^2*ln(b*x+a-1)+1/2/b^2*ln(b*x+a+1)-1/4/b^2*ln(b*x+a-1)^2*a+1/b^2*dilog(1/2+1/2*b*x+1/2*a)*a+1/2/b^2*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)*a+1/8/b^2*ln(b*x+a-1)^2-1/4/b^2*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)+1/4/b^2*ln(b*x+a+1)^2*a-1/2/b^2*ln(b*x+a+1)*ln(-1/2*b*x-1/2*a+1/2)*a+1/2/b^2*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)*a+1/8/b^2*ln(b*x+a+1)^2-1/4/b^2*ln(-1/2*b*x-1/2*a+1/2)*ln(b*x+a+1)+1/4/b^2*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)","B"
4,1,103,83,0.275000," ","int(arctanh(b*x+a)^2,x)","x \arctanh \left(b x +a \right)^{2}+\frac{\arctanh \left(b x +a \right)^{2} a}{b}+\frac{\arctanh \left(b x +a \right)^{2}}{b}-\frac{2 \arctanh \left(b x +a \right) \ln \left(1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)}{b}-\frac{\polylog \left(2, -\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)}{b}"," ",0,"x*arctanh(b*x+a)^2+1/b*arctanh(b*x+a)^2*a+arctanh(b*x+a)^2/b-2/b*arctanh(b*x+a)*ln(1+(b*x+a+1)^2/(1-(b*x+a)^2))-1/b*polylog(2,-(b*x+a+1)^2/(1-(b*x+a)^2))","A"
5,1,1022,144,0.854000," ","int(arctanh(b*x+a)^2/x,x)","\ln \left(b x \right) \arctanh \left(b x +a \right)^{2}-\arctanh \left(b x +a \right)^{2} \ln \left(a \left(1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)-\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}+1\right)+\frac{i \pi  \left(\mathrm{csgn}\left(\frac{i}{1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}}\right) \mathrm{csgn}\left(i \left(a \left(1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)-\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}+1\right)\right) \mathrm{csgn}\left(\frac{i \left(a \left(1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)-\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}+1\right)}{1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}}\right)-\mathrm{csgn}\left(\frac{i}{1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(a \left(1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)-\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}+1\right)}{1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}}\right)^{2}+2 \mathrm{csgn}\left(\frac{i \left(a \left(1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)-\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}+1\right)}{1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}}\right)^{2}-\mathrm{csgn}\left(i \left(a \left(1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)-\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}+1\right)\right) \mathrm{csgn}\left(\frac{i \left(a \left(1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)-\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}+1\right)}{1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}}\right)^{2}-\mathrm{csgn}\left(\frac{i \left(a \left(1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)-\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}+1\right)}{1+\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}}\right)^{3}-2\right) \arctanh \left(b x +a \right)^{2}}{2}-\arctanh \left(b x +a \right) \polylog \left(2, -\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)+\frac{\polylog \left(3, -\frac{\left(b x +a +1\right)^{2}}{1-\left(b x +a \right)^{2}}\right)}{2}+\frac{a \arctanh \left(b x +a \right)^{2} \ln \left(1-\frac{\left(a -1\right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-1-a \right)}\right)}{a -1}+\frac{a \arctanh \left(b x +a \right) \polylog \left(2, \frac{\left(a -1\right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-1-a \right)}\right)}{a -1}-\frac{a \polylog \left(3, \frac{\left(a -1\right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-1-a \right)}\right)}{2 \left(a -1\right)}-\frac{\arctanh \left(b x +a \right)^{2} \ln \left(1-\frac{\left(a -1\right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-1-a \right)}\right)}{a -1}-\frac{\arctanh \left(b x +a \right) \polylog \left(2, \frac{\left(a -1\right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-1-a \right)}\right)}{a -1}+\frac{\polylog \left(3, \frac{\left(a -1\right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-1-a \right)}\right)}{2 a -2}"," ",0,"ln(b*x)*arctanh(b*x+a)^2-arctanh(b*x+a)^2*ln(a*(1+(b*x+a+1)^2/(1-(b*x+a)^2))-(b*x+a+1)^2/(1-(b*x+a)^2)+1)+1/2*I*Pi*(csgn(I/(1+(b*x+a+1)^2/(1-(b*x+a)^2)))*csgn(I*(a*(1+(b*x+a+1)^2/(1-(b*x+a)^2))-(b*x+a+1)^2/(1-(b*x+a)^2)+1))*csgn(I*(a*(1+(b*x+a+1)^2/(1-(b*x+a)^2))-(b*x+a+1)^2/(1-(b*x+a)^2)+1)/(1+(b*x+a+1)^2/(1-(b*x+a)^2)))-csgn(I/(1+(b*x+a+1)^2/(1-(b*x+a)^2)))*csgn(I*(a*(1+(b*x+a+1)^2/(1-(b*x+a)^2))-(b*x+a+1)^2/(1-(b*x+a)^2)+1)/(1+(b*x+a+1)^2/(1-(b*x+a)^2)))^2+2*csgn(I*(a*(1+(b*x+a+1)^2/(1-(b*x+a)^2))-(b*x+a+1)^2/(1-(b*x+a)^2)+1)/(1+(b*x+a+1)^2/(1-(b*x+a)^2)))^2-csgn(I*(a*(1+(b*x+a+1)^2/(1-(b*x+a)^2))-(b*x+a+1)^2/(1-(b*x+a)^2)+1))*csgn(I*(a*(1+(b*x+a+1)^2/(1-(b*x+a)^2))-(b*x+a+1)^2/(1-(b*x+a)^2)+1)/(1+(b*x+a+1)^2/(1-(b*x+a)^2)))^2-csgn(I*(a*(1+(b*x+a+1)^2/(1-(b*x+a)^2))-(b*x+a+1)^2/(1-(b*x+a)^2)+1)/(1+(b*x+a+1)^2/(1-(b*x+a)^2)))^3-2)*arctanh(b*x+a)^2-arctanh(b*x+a)*polylog(2,-(b*x+a+1)^2/(1-(b*x+a)^2))+1/2*polylog(3,-(b*x+a+1)^2/(1-(b*x+a)^2))+a/(a-1)*arctanh(b*x+a)^2*ln(1-(a-1)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-1-a))+a/(a-1)*arctanh(b*x+a)*polylog(2,(a-1)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-1-a))-1/2*a/(a-1)*polylog(3,(a-1)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-1-a))-1/(a-1)*arctanh(b*x+a)^2*ln(1-(a-1)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-1-a))-1/(a-1)*arctanh(b*x+a)*polylog(2,(a-1)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-1-a))+1/2/(a-1)*polylog(3,(a-1)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-1-a))","C"
6,1,342,249,0.069000," ","int(arctanh(b*x+a)^2/x^2,x)","-\frac{\arctanh \left(b x +a \right)^{2}}{x}+\frac{2 b \arctanh \left(b x +a \right) \ln \left(b x +a -1\right)}{2 a -2}-\frac{2 b \arctanh \left(b x +a \right) \ln \left(b x +a +1\right)}{2+2 a}-\frac{2 b \arctanh \left(b x +a \right) \ln \left(b x \right)}{\left(a -1\right) \left(1+a \right)}-\frac{b \dilog \left(\frac{b x +a -1}{a -1}\right)}{\left(a -1\right) \left(1+a \right)}-\frac{b \ln \left(b x \right) \ln \left(\frac{b x +a -1}{a -1}\right)}{\left(a -1\right) \left(1+a \right)}+\frac{b \dilog \left(\frac{b x +a +1}{1+a}\right)}{\left(a -1\right) \left(1+a \right)}+\frac{b \ln \left(b x \right) \ln \left(\frac{b x +a +1}{1+a}\right)}{\left(a -1\right) \left(1+a \right)}+\frac{b \ln \left(b x +a +1\right)^{2}}{4+4 a}-\frac{b \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(b x +a +1\right)}{2 \left(1+a \right)}+\frac{b \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{2+2 a}+\frac{b \dilog \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{2+2 a}+\frac{b \ln \left(b x +a -1\right)^{2}}{4 a -4}-\frac{b \dilog \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{2 \left(a -1\right)}-\frac{b \ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{2 \left(a -1\right)}"," ",0,"-arctanh(b*x+a)^2/x+2*b*arctanh(b*x+a)/(2*a-2)*ln(b*x+a-1)-2*b*arctanh(b*x+a)/(2+2*a)*ln(b*x+a+1)-2*b*arctanh(b*x+a)/(a-1)/(1+a)*ln(b*x)-b/(a-1)/(1+a)*dilog((b*x+a-1)/(a-1))-b/(a-1)/(1+a)*ln(b*x)*ln((b*x+a-1)/(a-1))+b/(a-1)/(1+a)*dilog((b*x+a+1)/(1+a))+b/(a-1)/(1+a)*ln(b*x)*ln((b*x+a+1)/(1+a))+1/4*b/(1+a)*ln(b*x+a+1)^2-1/2*b/(1+a)*ln(-1/2*b*x-1/2*a+1/2)*ln(b*x+a+1)+1/2*b/(1+a)*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)+1/2*b/(1+a)*dilog(1/2+1/2*b*x+1/2*a)+1/4*b/(a-1)*ln(b*x+a-1)^2-1/2*b/(a-1)*dilog(1/2+1/2*b*x+1/2*a)-1/2*b/(a-1)*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)","A"
7,1,467,358,0.077000," ","int(arctanh(b*x+a)^2/x^3,x)","-\frac{\arctanh \left(b x +a \right)^{2}}{2 x^{2}}-\frac{b^{2} \arctanh \left(b x +a \right) \ln \left(b x +a -1\right)}{2 \left(a -1\right)^{2}}+\frac{b^{2} \arctanh \left(b x +a \right) \ln \left(b x +a +1\right)}{2 \left(1+a \right)^{2}}+\frac{b \arctanh \left(b x +a \right)}{\left(a -1\right) \left(1+a \right) x}+\frac{2 b^{2} \arctanh \left(b x +a \right) a \ln \left(b x \right)}{\left(a -1\right)^{2} \left(1+a \right)^{2}}-\frac{b^{2} \ln \left(b x +a -1\right)^{2}}{8 \left(a -1\right)^{2}}+\frac{b^{2} \dilog \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{4 \left(a -1\right)^{2}}+\frac{b^{2} \ln \left(b x +a -1\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{4 \left(a -1\right)^{2}}-\frac{b^{2} \ln \left(b x +a +1\right)^{2}}{8 \left(1+a \right)^{2}}+\frac{b^{2} \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(b x +a +1\right)}{4 \left(1+a \right)^{2}}-\frac{b^{2} \ln \left(-\frac{b x}{2}-\frac{a}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{4 \left(1+a \right)^{2}}-\frac{b^{2} \dilog \left(\frac{1}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{4 \left(1+a \right)^{2}}-\frac{b^{2} \ln \left(b x +a -1\right)}{\left(a -1\right) \left(1+a \right) \left(2 a -2\right)}+\frac{b^{2} \ln \left(b x +a +1\right)}{\left(a -1\right) \left(1+a \right) \left(2+2 a \right)}+\frac{b^{2} \ln \left(b x \right)}{\left(a -1\right)^{2} \left(1+a \right)^{2}}+\frac{b^{2} a \dilog \left(\frac{b x +a -1}{a -1}\right)}{\left(a -1\right)^{2} \left(1+a \right)^{2}}+\frac{b^{2} a \ln \left(b x \right) \ln \left(\frac{b x +a -1}{a -1}\right)}{\left(a -1\right)^{2} \left(1+a \right)^{2}}-\frac{b^{2} a \dilog \left(\frac{b x +a +1}{1+a}\right)}{\left(a -1\right)^{2} \left(1+a \right)^{2}}-\frac{b^{2} a \ln \left(b x \right) \ln \left(\frac{b x +a +1}{1+a}\right)}{\left(a -1\right)^{2} \left(1+a \right)^{2}}"," ",0,"-1/2*arctanh(b*x+a)^2/x^2-1/2*b^2*arctanh(b*x+a)/(a-1)^2*ln(b*x+a-1)+1/2*b^2*arctanh(b*x+a)/(1+a)^2*ln(b*x+a+1)+b*arctanh(b*x+a)/(a-1)/(1+a)/x+2*b^2*arctanh(b*x+a)*a/(a-1)^2/(1+a)^2*ln(b*x)-1/8*b^2/(a-1)^2*ln(b*x+a-1)^2+1/4*b^2/(a-1)^2*dilog(1/2+1/2*b*x+1/2*a)+1/4*b^2/(a-1)^2*ln(b*x+a-1)*ln(1/2+1/2*b*x+1/2*a)-1/8*b^2/(1+a)^2*ln(b*x+a+1)^2+1/4*b^2/(1+a)^2*ln(-1/2*b*x-1/2*a+1/2)*ln(b*x+a+1)-1/4*b^2/(1+a)^2*ln(-1/2*b*x-1/2*a+1/2)*ln(1/2+1/2*b*x+1/2*a)-1/4*b^2/(1+a)^2*dilog(1/2+1/2*b*x+1/2*a)-b^2/(a-1)/(1+a)/(2*a-2)*ln(b*x+a-1)+b^2/(a-1)/(1+a)/(2+2*a)*ln(b*x+a+1)+b^2/(a-1)^2/(1+a)^2*ln(b*x)+b^2*a/(a-1)^2/(1+a)^2*dilog((b*x+a-1)/(a-1))+b^2*a/(a-1)^2/(1+a)^2*ln(b*x)*ln((b*x+a-1)/(a-1))-b^2*a/(a-1)^2/(1+a)^2*dilog((b*x+a+1)/(1+a))-b^2*a/(a-1)^2/(1+a)^2*ln(b*x)*ln((b*x+a+1)/(1+a))","A"
8,1,160,54,0.447000," ","int(arctanh(b*x+1)^2/x,x)","\ln \left(b x \right) \arctanh \left(b x +1\right)^{2}-\arctanh \left(b x +1\right) \polylog \left(2, -\frac{\left(b x +2\right)^{2}}{-\left(b x +1\right)^{2}+1}\right)+\frac{\polylog \left(3, -\frac{\left(b x +2\right)^{2}}{-\left(b x +1\right)^{2}+1}\right)}{2}-\left(i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(b x +2\right)^{2}}{-\left(b x +1\right)^{2}+1}}\right)^{3}-i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(b x +2\right)^{2}}{-\left(b x +1\right)^{2}+1}}\right)^{2}+i \pi +\ln \left(2\right)\right) \arctanh \left(b x +1\right)^{2}"," ",0,"ln(b*x)*arctanh(b*x+1)^2-arctanh(b*x+1)*polylog(2,-(b*x+2)^2/(-(b*x+1)^2+1))+1/2*polylog(3,-(b*x+2)^2/(-(b*x+1)^2+1))-(I*Pi*csgn(I/(1+(b*x+2)^2/(-(b*x+1)^2+1)))^3-I*Pi*csgn(I/(1+(b*x+2)^2/(-(b*x+1)^2+1)))^2+I*Pi+ln(2))*arctanh(b*x+1)^2","C"
9,1,242,64,0.033000," ","int((d*e*x+c*e)^3*(a+b*arctanh(d*x+c)),x)","\frac{d^{3} x^{4} a \,e^{3}}{4}+d^{2} x^{3} a c \,e^{3}+\frac{3 d \,x^{2} a \,c^{2} e^{3}}{2}+x a \,c^{3} e^{3}+\frac{a \,c^{4} e^{3}}{4 d}+\frac{d^{3} \arctanh \left(d x +c \right) x^{4} b \,e^{3}}{4}+d^{2} \arctanh \left(d x +c \right) x^{3} b c \,e^{3}+\frac{3 d \arctanh \left(d x +c \right) x^{2} b \,c^{2} e^{3}}{2}+\arctanh \left(d x +c \right) x b \,c^{3} e^{3}+\frac{\arctanh \left(d x +c \right) b \,c^{4} e^{3}}{4 d}+\frac{d^{2} x^{3} b \,e^{3}}{12}+\frac{d \,x^{2} b c \,e^{3}}{4}+\frac{x b \,c^{2} e^{3}}{4}+\frac{b \,c^{3} e^{3}}{12 d}+\frac{b \,e^{3} x}{4}+\frac{b c \,e^{3}}{4 d}+\frac{e^{3} b \ln \left(d x +c -1\right)}{8 d}-\frac{e^{3} b \ln \left(d x +c +1\right)}{8 d}"," ",0,"1/4*d^3*x^4*a*e^3+d^2*x^3*a*c*e^3+3/2*d*x^2*a*c^2*e^3+x*a*c^3*e^3+1/4/d*a*c^4*e^3+1/4*d^3*arctanh(d*x+c)*x^4*b*e^3+d^2*arctanh(d*x+c)*x^3*b*c*e^3+3/2*d*arctanh(d*x+c)*x^2*b*c^2*e^3+arctanh(d*x+c)*x*b*c^3*e^3+1/4/d*arctanh(d*x+c)*b*c^4*e^3+1/12*d^2*x^3*b*e^3+1/4*d*x^2*b*c*e^3+1/4*x*b*c^2*e^3+1/12/d*b*c^3*e^3+1/4*b*e^3*x+1/4/d*b*c*e^3+1/8/d*e^3*b*ln(d*x+c-1)-1/8/d*e^3*b*ln(d*x+c+1)","B"
10,1,174,63,0.033000," ","int((d*e*x+c*e)^2*(a+b*arctanh(d*x+c)),x)","\frac{d^{2} x^{3} a \,e^{2}}{3}+d \,x^{2} a c \,e^{2}+x a \,c^{2} e^{2}+\frac{a \,c^{3} e^{2}}{3 d}+\frac{d^{2} \arctanh \left(d x +c \right) x^{3} b \,e^{2}}{3}+d \arctanh \left(d x +c \right) x^{2} b c \,e^{2}+\arctanh \left(d x +c \right) x b \,c^{2} e^{2}+\frac{\arctanh \left(d x +c \right) b \,c^{3} e^{2}}{3 d}+\frac{d \,x^{2} b \,e^{2}}{6}+\frac{x b c \,e^{2}}{3}+\frac{b \,c^{2} e^{2}}{6 d}+\frac{e^{2} b \ln \left(d x +c -1\right)}{6 d}+\frac{e^{2} b \ln \left(d x +c +1\right)}{6 d}"," ",0,"1/3*d^2*x^3*a*e^2+d*x^2*a*c*e^2+x*a*c^2*e^2+1/3/d*a*c^3*e^2+1/3*d^2*arctanh(d*x+c)*x^3*b*e^2+d*arctanh(d*x+c)*x^2*b*c*e^2+arctanh(d*x+c)*x*b*c^2*e^2+1/3/d*arctanh(d*x+c)*b*c^3*e^2+1/6*d*x^2*b*e^2+1/3*x*b*c*e^2+1/6/d*b*c^2*e^2+1/6/d*e^2*b*ln(d*x+c-1)+1/6/d*e^2*b*ln(d*x+c+1)","B"
11,1,107,42,0.033000," ","int((d*e*x+c*e)*(a+b*arctanh(d*x+c)),x)","\frac{a d e \,x^{2}}{2}+x a c e +\frac{a \,c^{2} e}{2 d}+\frac{d \arctanh \left(d x +c \right) x^{2} b e}{2}+\arctanh \left(d x +c \right) x b c e +\frac{\arctanh \left(d x +c \right) b \,c^{2} e}{2 d}+\frac{b e x}{2}+\frac{b e c}{2 d}+\frac{b e \ln \left(d x +c -1\right)}{4 d}-\frac{b e \ln \left(d x +c +1\right)}{4 d}"," ",0,"1/2*a*d*e*x^2+x*a*c*e+1/2/d*a*c^2*e+1/2*d*arctanh(d*x+c)*x^2*b*e+arctanh(d*x+c)*x*b*c*e+1/2/d*arctanh(d*x+c)*b*c^2*e+1/2*b*e*x+1/2/d*b*e*c+1/4/d*b*e*ln(d*x+c-1)-1/4/d*b*e*ln(d*x+c+1)","B"
12,1,89,50,0.048000," ","int((a+b*arctanh(d*x+c))/(d*e*x+c*e),x)","\frac{a \ln \left(d x +c \right)}{d e}+\frac{b \ln \left(d x +c \right) \arctanh \left(d x +c \right)}{d e}-\frac{b \dilog \left(d x +c \right)}{2 d e}-\frac{b \dilog \left(d x +c +1\right)}{2 d e}-\frac{b \ln \left(d x +c \right) \ln \left(d x +c +1\right)}{2 d e}"," ",0,"1/d*a/e*ln(d*x+c)+1/d*b/e*ln(d*x+c)*arctanh(d*x+c)-1/2/d*b/e*dilog(d*x+c)-1/2/d*b/e*dilog(d*x+c+1)-1/2/d*b/e*ln(d*x+c)*ln(d*x+c+1)","A"
13,1,86,63,0.038000," ","int((a+b*arctanh(d*x+c))/(d*e*x+c*e)^2,x)","-\frac{a}{d \,e^{2} \left(d x +c \right)}-\frac{b \arctanh \left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}+\frac{b \ln \left(d x +c \right)}{d \,e^{2}}-\frac{b \ln \left(d x +c -1\right)}{2 d \,e^{2}}-\frac{b \ln \left(d x +c +1\right)}{2 d \,e^{2}}"," ",0,"-1/d*a/e^2/(d*x+c)-1/d*b/e^2/(d*x+c)*arctanh(d*x+c)+b*ln(d*x+c)/d/e^2-1/2/d*b/e^2*ln(d*x+c-1)-1/2/d*b/e^2*ln(d*x+c+1)","A"
14,1,88,60,0.037000," ","int((a+b*arctanh(d*x+c))/(d*e*x+c*e)^3,x)","-\frac{a}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b \arctanh \left(d x +c \right)}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b}{2 d \,e^{3} \left(d x +c \right)}-\frac{b \ln \left(d x +c -1\right)}{4 d \,e^{3}}+\frac{b \ln \left(d x +c +1\right)}{4 d \,e^{3}}"," ",0,"-1/2/d*a/e^3/(d*x+c)^2-1/2/d*b/e^3/(d*x+c)^2*arctanh(d*x+c)-1/2*b/d/e^3/(d*x+c)-1/4/d*b/e^3*ln(d*x+c-1)+1/4/d*b/e^3*ln(d*x+c+1)","A"
15,1,732,145,0.067000," ","int((d*e*x+c*e)^3*(a+b*arctanh(d*x+c))^2,x)","\frac{a b \,e^{3} x}{2}+\frac{d^{3} x^{4} a^{2} e^{3}}{4}+\frac{\arctanh \left(d x +c \right) x \,b^{2} e^{3}}{2}+2 d^{2} \arctanh \left(d x +c \right) x^{3} a b c \,e^{3}+3 d \arctanh \left(d x +c \right) x^{2} a b \,c^{2} e^{3}+\frac{e^{3} b^{2} \ln \left(d x +c -1\right)^{2}}{16 d}+\frac{e^{3} b^{2} \ln \left(d x +c +1\right)}{3 d}+\frac{e^{3} b^{2} \ln \left(d x +c -1\right)}{3 d}+\frac{e^{3} b^{2} \ln \left(d x +c +1\right)^{2}}{16 d}+\frac{e^{3} b^{2} c^{2}}{12 d}+\frac{a^{2} c^{4} e^{3}}{4 d}+2 \arctanh \left(d x +c \right) x a b \,c^{3} e^{3}+\frac{d \arctanh \left(d x +c \right) x^{2} b^{2} c \,e^{3}}{2}+\frac{3 d \arctanh \left(d x +c \right)^{2} x^{2} b^{2} c^{2} e^{3}}{2}+\frac{\arctanh \left(d x +c \right) a b \,c^{4} e^{3}}{2 d}+d^{2} \arctanh \left(d x +c \right)^{2} x^{3} b^{2} c \,e^{3}+\frac{d \,x^{2} a b c \,e^{3}}{2}+\frac{e^{3} b^{2} x c}{6}+x \,a^{2} c^{3} e^{3}+\frac{d \,e^{3} b^{2} x^{2}}{12}+\frac{x a b \,c^{2} e^{3}}{2}+\frac{3 d \,x^{2} a^{2} c^{2} e^{3}}{2}+d^{2} x^{3} a^{2} c \,e^{3}+\frac{e^{3} a b \ln \left(d x +c -1\right)}{4 d}-\frac{e^{3} a b \ln \left(d x +c +1\right)}{4 d}-\frac{e^{3} b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{8 d}+\frac{e^{3} b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{8 d}-\frac{e^{3} b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{8 d}+\frac{d^{2} x^{3} a b \,e^{3}}{6}+\frac{\arctanh \left(d x +c \right) x \,b^{2} c^{2} e^{3}}{2}+\arctanh \left(d x +c \right)^{2} x \,b^{2} c^{3} e^{3}+\frac{e^{3} b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{4 d}+\frac{\arctanh \left(d x +c \right) b^{2} c^{3} e^{3}}{6 d}+\frac{\arctanh \left(d x +c \right) b^{2} c \,e^{3}}{2 d}+\frac{d^{2} \arctanh \left(d x +c \right) x^{3} b^{2} e^{3}}{6}+\frac{d^{3} \arctanh \left(d x +c \right)^{2} x^{4} b^{2} e^{3}}{4}-\frac{e^{3} b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{4 d}+\frac{\arctanh \left(d x +c \right)^{2} b^{2} c^{4} e^{3}}{4 d}+\frac{a b \,c^{3} e^{3}}{6 d}+\frac{d^{3} \arctanh \left(d x +c \right) x^{4} a b \,e^{3}}{2}+\frac{a b c \,e^{3}}{2 d}"," ",0,"1/2*a*b*e^3*x+1/4*d^3*x^4*a^2*e^3+3*d*arctanh(d*x+c)*x^2*a*b*c^2*e^3+2*d^2*arctanh(d*x+c)*x^3*a*b*c*e^3+1/16/d*e^3*b^2*ln(d*x+c-1)^2+1/3/d*e^3*b^2*ln(d*x+c+1)+1/3/d*e^3*b^2*ln(d*x+c-1)+1/16/d*e^3*b^2*ln(d*x+c+1)^2+1/2*arctanh(d*x+c)*x*b^2*e^3+1/12/d*e^3*b^2*c^2+1/4/d*a^2*c^4*e^3+2*arctanh(d*x+c)*x*a*b*c^3*e^3+1/2*d*arctanh(d*x+c)*x^2*b^2*c*e^3+1/2*d^3*arctanh(d*x+c)*x^4*a*b*e^3+3/2*d*arctanh(d*x+c)^2*x^2*b^2*c^2*e^3+1/2/d*arctanh(d*x+c)*a*b*c^4*e^3+d^2*arctanh(d*x+c)^2*x^3*b^2*c*e^3+1/2*d*x^2*a*b*c*e^3+1/6*e^3*b^2*x*c+1/2*arctanh(d*x+c)*x*b^2*c^2*e^3+arctanh(d*x+c)^2*x*b^2*c^3*e^3+1/4/d*e^3*b^2*arctanh(d*x+c)*ln(d*x+c-1)+x*a^2*c^3*e^3+1/12*d*e^3*b^2*x^2+1/2*x*a*b*c^2*e^3+3/2*d*x^2*a^2*c^2*e^3+d^2*x^3*a^2*c*e^3+1/4/d*e^3*a*b*ln(d*x+c-1)-1/4/d*e^3*a*b*ln(d*x+c+1)+1/6/d*arctanh(d*x+c)*b^2*c^3*e^3+1/2/d*arctanh(d*x+c)*b^2*c*e^3+1/6*d^2*arctanh(d*x+c)*x^3*b^2*e^3+1/4*d^3*arctanh(d*x+c)^2*x^4*b^2*e^3-1/4/d*e^3*b^2*arctanh(d*x+c)*ln(d*x+c+1)+1/4/d*arctanh(d*x+c)^2*b^2*c^4*e^3-1/8/d*e^3*b^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+1/8/d*e^3*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)-1/8/d*e^3*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)+1/6*d^2*x^3*a*b*e^3+1/6/d*a*b*c^3*e^3+1/2/d*a*b*c*e^3","B"
16,1,583,167,0.062000," ","int((d*e*x+c*e)^2*(a+b*arctanh(d*x+c))^2,x)","-\frac{e^{2} b^{2} \ln \left(d x +c +1\right)^{2}}{12 d}+\frac{d^{2} x^{3} a^{2} e^{2}}{3}+x \,a^{2} c^{2} e^{2}-\frac{e^{2} b^{2} \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{3 d}-\frac{e^{2} b^{2} \ln \left(d x +c +1\right)}{6 d}+\frac{e^{2} b^{2} \ln \left(d x +c -1\right)}{6 d}+\frac{e^{2} b^{2} \ln \left(d x +c -1\right)^{2}}{12 d}+\frac{b^{2} c \,e^{2}}{3 d}+\frac{a^{2} c^{3} e^{2}}{3 d}+d \arctanh \left(d x +c \right)^{2} x^{2} b^{2} c \,e^{2}+2 \arctanh \left(d x +c \right) x a b \,c^{2} e^{2}+\frac{2 \arctanh \left(d x +c \right) a b \,c^{3} e^{2}}{3 d}+\frac{2 d^{2} \arctanh \left(d x +c \right) x^{3} a b \,e^{2}}{3}+2 d \arctanh \left(d x +c \right) x^{2} a b c \,e^{2}+\frac{a b \,c^{2} e^{2}}{3 d}+\frac{2 x a b c \,e^{2}}{3}+\frac{b^{2} e^{2} x}{3}+d \,x^{2} a^{2} c \,e^{2}+\frac{d \,x^{2} a b \,e^{2}}{3}-\frac{e^{2} b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{6 d}+\frac{e^{2} b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{6 d}-\frac{e^{2} b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{6 d}+\frac{e^{2} a b \ln \left(d x +c +1\right)}{3 d}+\frac{d^{2} \arctanh \left(d x +c \right)^{2} x^{3} b^{2} e^{2}}{3}+\frac{e^{2} b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{3 d}+\frac{2 \arctanh \left(d x +c \right) x \,b^{2} c \,e^{2}}{3}+\frac{e^{2} a b \ln \left(d x +c -1\right)}{3 d}+\arctanh \left(d x +c \right)^{2} x \,b^{2} c^{2} e^{2}+\frac{d \arctanh \left(d x +c \right) x^{2} b^{2} e^{2}}{3}+\frac{\arctanh \left(d x +c \right)^{2} b^{2} c^{3} e^{2}}{3 d}+\frac{\arctanh \left(d x +c \right) b^{2} c^{2} e^{2}}{3 d}+\frac{e^{2} b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{3 d}"," ",0,"-1/3/d*e^2*b^2*dilog(1/2+1/2*d*x+1/2*c)-1/12/d*e^2*b^2*ln(d*x+c+1)^2+1/3*d^2*x^3*a^2*e^2+x*a^2*c^2*e^2-1/6/d*e^2*b^2*ln(d*x+c+1)+1/6/d*e^2*b^2*ln(d*x+c-1)+1/12/d*e^2*b^2*ln(d*x+c-1)^2+1/3/d*b^2*c*e^2+1/3/d*a^2*c^3*e^2+2*d*arctanh(d*x+c)*x^2*a*b*c*e^2+d*arctanh(d*x+c)^2*x^2*b^2*c*e^2+2*arctanh(d*x+c)*x*a*b*c^2*e^2+2/3/d*arctanh(d*x+c)*a*b*c^3*e^2+2/3*d^2*arctanh(d*x+c)*x^3*a*b*e^2+1/3/d*a*b*c^2*e^2+2/3*x*a*b*c*e^2+1/3*b^2*e^2*x+1/3*d^2*arctanh(d*x+c)^2*x^3*b^2*e^2+1/3/d*e^2*b^2*arctanh(d*x+c)*ln(d*x+c-1)+d*x^2*a^2*c*e^2+1/3*d*x^2*a*b*e^2+2/3*arctanh(d*x+c)*x*b^2*c*e^2+arctanh(d*x+c)^2*x*b^2*c^2*e^2+1/3*d*arctanh(d*x+c)*x^2*b^2*e^2+1/3/d*arctanh(d*x+c)^2*b^2*c^3*e^2+1/3/d*arctanh(d*x+c)*b^2*c^2*e^2+1/3/d*e^2*b^2*arctanh(d*x+c)*ln(d*x+c+1)-1/6/d*e^2*b^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+1/6/d*e^2*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)-1/6/d*e^2*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)+1/3/d*e^2*a*b*ln(d*x+c+1)+1/3/d*e^2*a*b*ln(d*x+c-1)","B"
17,1,390,89,0.063000," ","int((d*e*x+c*e)*(a+b*arctanh(d*x+c))^2,x)","\frac{d \,x^{2} a^{2} e}{2}+x \,a^{2} c e +\frac{a^{2} c^{2} e}{2 d}+\frac{d \arctanh \left(d x +c \right)^{2} x^{2} b^{2} e}{2}+\arctanh \left(d x +c \right)^{2} x \,b^{2} c e +\frac{\arctanh \left(d x +c \right)^{2} b^{2} c^{2} e}{2 d}+\arctanh \left(d x +c \right) x \,b^{2} e +\frac{\arctanh \left(d x +c \right) b^{2} c e}{d}+\frac{e \,b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{2 d}-\frac{e \,b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{2 d}+\frac{e \,b^{2} \ln \left(d x +c -1\right)^{2}}{8 d}-\frac{e \,b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{4 d}+\frac{e \,b^{2} \ln \left(d x +c -1\right)}{2 d}+\frac{e \,b^{2} \ln \left(d x +c +1\right)}{2 d}+\frac{e \,b^{2} \ln \left(d x +c +1\right)^{2}}{8 d}-\frac{e \,b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{4 d}+\frac{e \,b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{4 d}+d \arctanh \left(d x +c \right) x^{2} a b e +2 \arctanh \left(d x +c \right) x a b c e +\frac{\arctanh \left(d x +c \right) a b \,c^{2} e}{d}+a b e x +\frac{a b c e}{d}+\frac{e a b \ln \left(d x +c -1\right)}{2 d}-\frac{e a b \ln \left(d x +c +1\right)}{2 d}"," ",0,"1/2*d*x^2*a^2*e+x*a^2*c*e+1/2/d*a^2*c^2*e+1/2*d*arctanh(d*x+c)^2*x^2*b^2*e+arctanh(d*x+c)^2*x*b^2*c*e+1/2/d*arctanh(d*x+c)^2*b^2*c^2*e+arctanh(d*x+c)*x*b^2*e+1/d*arctanh(d*x+c)*b^2*c*e+1/2/d*e*b^2*arctanh(d*x+c)*ln(d*x+c-1)-1/2/d*e*b^2*arctanh(d*x+c)*ln(d*x+c+1)+1/8/d*e*b^2*ln(d*x+c-1)^2-1/4/d*e*b^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+1/2/d*e*b^2*ln(d*x+c-1)+1/2/d*e*b^2*ln(d*x+c+1)+1/8/d*e*b^2*ln(d*x+c+1)^2-1/4/d*e*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)+1/4/d*e*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)+d*arctanh(d*x+c)*x^2*a*b*e+2*arctanh(d*x+c)*x*a*b*c*e+1/d*arctanh(d*x+c)*a*b*c^2*e+a*b*e*x+1/d*a*b*c*e+1/2/d*e*a*b*ln(d*x+c-1)-1/2/d*e*a*b*ln(d*x+c+1)","B"
18,1,893,164,0.215000," ","int((a+b*arctanh(d*x+c))^2/(d*e*x+c*e),x)","\frac{a^{2} \ln \left(d x +c \right)}{d e}+\frac{b^{2} \ln \left(d x +c \right) \arctanh \left(d x +c \right)^{2}}{d e}-\frac{b^{2} \arctanh \left(d x +c \right) \polylog \left(2, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{b^{2} \polylog \left(3, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{2 d e}-\frac{b^{2} \arctanh \left(d x +c \right)^{2} \ln \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{d e}+\frac{b^{2} \arctanh \left(d x +c \right)^{2} \ln \left(1-\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}+\frac{2 b^{2} \arctanh \left(d x +c \right) \polylog \left(2, \frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}-\frac{2 b^{2} \polylog \left(3, \frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}+\frac{b^{2} \arctanh \left(d x +c \right)^{2} \ln \left(1+\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}+\frac{2 b^{2} \arctanh \left(d x +c \right) \polylog \left(2, -\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}-\frac{2 b^{2} \polylog \left(3, -\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2} \arctanh \left(d x +c \right)^{2}}{2 d e}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{3} \arctanh \left(d x +c \right)^{2}}{2 d e}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2} \arctanh \left(d x +c \right)^{2}}{2 d e}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \arctanh \left(d x +c \right)^{2}}{2 d e}+\frac{2 a b \ln \left(d x +c \right) \arctanh \left(d x +c \right)}{d e}-\frac{a b \dilog \left(d x +c \right)}{d e}-\frac{a b \dilog \left(d x +c +1\right)}{d e}-\frac{a b \ln \left(d x +c \right) \ln \left(d x +c +1\right)}{d e}"," ",0,"1/d*a^2/e*ln(d*x+c)+1/d*b^2/e*ln(d*x+c)*arctanh(d*x+c)^2-1/d*b^2/e*arctanh(d*x+c)*polylog(2,-(d*x+c+1)^2/(1-(d*x+c)^2))+1/2/d*b^2/e*polylog(3,-(d*x+c+1)^2/(1-(d*x+c)^2))-1/d*b^2/e*arctanh(d*x+c)^2*ln((d*x+c+1)^2/(1-(d*x+c)^2)-1)+1/d*b^2/e*arctanh(d*x+c)^2*ln(1-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+2/d*b^2/e*arctanh(d*x+c)*polylog(2,(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-2/d*b^2/e*polylog(3,(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+1/d*b^2/e*arctanh(d*x+c)^2*ln(1+(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+2/d*b^2/e*arctanh(d*x+c)*polylog(2,-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-2/d*b^2/e*polylog(3,-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+1/2*I/d*b^2/e*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1))*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*arctanh(d*x+c)^2-1/2*I/d*b^2/e*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*arctanh(d*x+c)^2+1/2*I/d*b^2/e*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3*arctanh(d*x+c)^2-1/2*I/d*b^2/e*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*arctanh(d*x+c)^2+2/d*a*b/e*ln(d*x+c)*arctanh(d*x+c)-1/d*a*b/e*dilog(d*x+c)-1/d*a*b/e*dilog(d*x+c+1)-1/d*a*b/e*ln(d*x+c)*ln(d*x+c+1)","C"
19,1,396,104,0.071000," ","int((a+b*arctanh(d*x+c))^2/(d*e*x+c*e)^2,x)","-\frac{a^{2}}{d \,e^{2} \left(d x +c \right)}-\frac{b^{2} \arctanh \left(d x +c \right)^{2}}{d \,e^{2} \left(d x +c \right)}+\frac{2 b^{2} \ln \left(d x +c \right) \arctanh \left(d x +c \right)}{d \,e^{2}}-\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{d \,e^{2}}-\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{d \,e^{2}}-\frac{b^{2} \ln \left(d x +c -1\right)^{2}}{4 d \,e^{2}}+\frac{b^{2} \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d \,e^{2}}+\frac{b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,e^{2}}+\frac{b^{2} \ln \left(d x +c +1\right)^{2}}{4 d \,e^{2}}-\frac{b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{2 d \,e^{2}}+\frac{b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,e^{2}}-\frac{b^{2} \dilog \left(d x +c \right)}{d \,e^{2}}-\frac{b^{2} \dilog \left(d x +c +1\right)}{d \,e^{2}}-\frac{b^{2} \ln \left(d x +c \right) \ln \left(d x +c +1\right)}{d \,e^{2}}-\frac{2 a b \arctanh \left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}+\frac{2 a b \ln \left(d x +c \right)}{d \,e^{2}}-\frac{a b \ln \left(d x +c -1\right)}{d \,e^{2}}-\frac{a b \ln \left(d x +c +1\right)}{d \,e^{2}}"," ",0,"-1/d*a^2/e^2/(d*x+c)-1/d*b^2/e^2/(d*x+c)*arctanh(d*x+c)^2+2/d*b^2/e^2*ln(d*x+c)*arctanh(d*x+c)-1/d*b^2/e^2*arctanh(d*x+c)*ln(d*x+c-1)-1/d*b^2/e^2*arctanh(d*x+c)*ln(d*x+c+1)-1/4/d*b^2/e^2*ln(d*x+c-1)^2+1/d*b^2/e^2*dilog(1/2+1/2*d*x+1/2*c)+1/2/d*b^2/e^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+1/4/d*b^2/e^2*ln(d*x+c+1)^2-1/2/d*b^2/e^2*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)+1/2/d*b^2/e^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)-1/d*b^2/e^2*dilog(d*x+c)-1/d*b^2/e^2*dilog(d*x+c+1)-1/d*b^2/e^2*ln(d*x+c)*ln(d*x+c+1)-2/d*a*b/e^2/(d*x+c)*arctanh(d*x+c)+2/d*a*b/e^2*ln(d*x+c)-1/d*a*b/e^2*ln(d*x+c-1)-1/d*a*b/e^2*ln(d*x+c+1)","B"
20,1,371,113,0.077000," ","int((a+b*arctanh(d*x+c))^2/(d*e*x+c*e)^3,x)","-\frac{a^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b^{2} \arctanh \left(d x +c \right)^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b^{2} \arctanh \left(d x +c \right)}{d \,e^{3} \left(d x +c \right)}-\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{2 d \,e^{3}}+\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{2 d \,e^{3}}-\frac{b^{2} \ln \left(d x +c -1\right)^{2}}{8 d \,e^{3}}+\frac{b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,e^{3}}+\frac{b^{2} \ln \left(d x +c \right)}{d \,e^{3}}-\frac{b^{2} \ln \left(d x +c -1\right)}{2 d \,e^{3}}-\frac{b^{2} \ln \left(d x +c +1\right)}{2 d \,e^{3}}-\frac{b^{2} \ln \left(d x +c +1\right)^{2}}{8 d \,e^{3}}+\frac{b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{4 d \,e^{3}}-\frac{b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,e^{3}}-\frac{a b \arctanh \left(d x +c \right)}{d \,e^{3} \left(d x +c \right)^{2}}-\frac{a b}{d \,e^{3} \left(d x +c \right)}-\frac{a b \ln \left(d x +c -1\right)}{2 d \,e^{3}}+\frac{a b \ln \left(d x +c +1\right)}{2 d \,e^{3}}"," ",0,"-1/2/d*a^2/e^3/(d*x+c)^2-1/2/d*b^2/e^3/(d*x+c)^2*arctanh(d*x+c)^2-1/d*b^2/e^3*arctanh(d*x+c)/(d*x+c)-1/2/d*b^2/e^3*arctanh(d*x+c)*ln(d*x+c-1)+1/2/d*b^2/e^3*arctanh(d*x+c)*ln(d*x+c+1)-1/8/d*b^2/e^3*ln(d*x+c-1)^2+1/4/d*b^2/e^3*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+b^2*ln(d*x+c)/d/e^3-1/2/d*b^2/e^3*ln(d*x+c-1)-1/2/d*b^2/e^3*ln(d*x+c+1)-1/8/d*b^2/e^3*ln(d*x+c+1)^2+1/4/d*b^2/e^3*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)-1/4/d*b^2/e^3*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)-1/d*a*b/e^3/(d*x+c)^2*arctanh(d*x+c)-1/d*a*b/e^3/(d*x+c)-1/2/d*a*b/e^3*ln(d*x+c-1)+1/2/d*a*b/e^3*ln(d*x+c+1)","B"
21,1,492,166,0.079000," ","int((a+b*arctanh(d*x+c))^2/(d*e*x+c*e)^4,x)","-\frac{a^{2}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b^{2} \arctanh \left(d x +c \right)^{2}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b^{2} \arctanh \left(d x +c \right)}{3 d \,e^{4} \left(d x +c \right)^{2}}+\frac{2 b^{2} \ln \left(d x +c \right) \arctanh \left(d x +c \right)}{3 d \,e^{4}}-\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{3 d \,e^{4}}-\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{3 d \,e^{4}}-\frac{b^{2}}{3 d \,e^{4} \left(d x +c \right)}-\frac{b^{2} \ln \left(d x +c -1\right)}{6 d \,e^{4}}+\frac{b^{2} \ln \left(d x +c +1\right)}{6 d \,e^{4}}-\frac{b^{2} \ln \left(d x +c -1\right)^{2}}{12 d \,e^{4}}+\frac{b^{2} \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{3 d \,e^{4}}+\frac{b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{6 d \,e^{4}}+\frac{b^{2} \ln \left(d x +c +1\right)^{2}}{12 d \,e^{4}}-\frac{b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{6 d \,e^{4}}+\frac{b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{6 d \,e^{4}}-\frac{b^{2} \dilog \left(d x +c \right)}{3 d \,e^{4}}-\frac{b^{2} \dilog \left(d x +c +1\right)}{3 d \,e^{4}}-\frac{b^{2} \ln \left(d x +c \right) \ln \left(d x +c +1\right)}{3 d \,e^{4}}-\frac{2 a b \arctanh \left(d x +c \right)}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{a b}{3 d \,e^{4} \left(d x +c \right)^{2}}+\frac{2 a b \ln \left(d x +c \right)}{3 d \,e^{4}}-\frac{a b \ln \left(d x +c -1\right)}{3 d \,e^{4}}-\frac{a b \ln \left(d x +c +1\right)}{3 d \,e^{4}}"," ",0,"-1/3/d*a^2/e^4/(d*x+c)^3-1/3/d*b^2/e^4/(d*x+c)^3*arctanh(d*x+c)^2-1/3/d*b^2/e^4*arctanh(d*x+c)/(d*x+c)^2+2/3/d*b^2/e^4*ln(d*x+c)*arctanh(d*x+c)-1/3/d*b^2/e^4*arctanh(d*x+c)*ln(d*x+c-1)-1/3/d*b^2/e^4*arctanh(d*x+c)*ln(d*x+c+1)-1/3*b^2/d/e^4/(d*x+c)-1/6/d*b^2/e^4*ln(d*x+c-1)+1/6/d*b^2/e^4*ln(d*x+c+1)-1/12/d*b^2/e^4*ln(d*x+c-1)^2+1/3/d*b^2/e^4*dilog(1/2+1/2*d*x+1/2*c)+1/6/d*b^2/e^4*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+1/12/d*b^2/e^4*ln(d*x+c+1)^2-1/6/d*b^2/e^4*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)+1/6/d*b^2/e^4*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)-1/3/d*b^2/e^4*dilog(d*x+c)-1/3/d*b^2/e^4*dilog(d*x+c+1)-1/3/d*b^2/e^4*ln(d*x+c)*ln(d*x+c+1)-2/3/d*a*b/e^4/(d*x+c)^3*arctanh(d*x+c)-1/3/d*a*b/e^4/(d*x+c)^2+2/3/d*a*b/e^4*ln(d*x+c)-1/3/d*a*b/e^4*ln(d*x+c-1)-1/3/d*a*b/e^4*ln(d*x+c+1)","B"
22,1,431,158,0.077000," ","int((a+b*arctanh(d*x+c))^2/(d*e*x+c*e)^5,x)","-\frac{a^{2}}{4 d \,e^{5} \left(d x +c \right)^{4}}-\frac{b^{2} \arctanh \left(d x +c \right)^{2}}{4 d \,e^{5} \left(d x +c \right)^{4}}-\frac{b^{2} \arctanh \left(d x +c \right)}{6 d \,e^{5} \left(d x +c \right)^{3}}-\frac{b^{2} \arctanh \left(d x +c \right)}{2 d \,e^{5} \left(d x +c \right)}-\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{4 d \,e^{5}}+\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{4 d \,e^{5}}-\frac{b^{2} \ln \left(d x +c -1\right)^{2}}{16 d \,e^{5}}+\frac{b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,e^{5}}-\frac{b^{2} \ln \left(d x +c +1\right)^{2}}{16 d \,e^{5}}+\frac{b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{8 d \,e^{5}}-\frac{b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,e^{5}}-\frac{b^{2}}{12 d \,e^{5} \left(d x +c \right)^{2}}+\frac{2 b^{2} \ln \left(d x +c \right)}{3 d \,e^{5}}-\frac{b^{2} \ln \left(d x +c -1\right)}{3 d \,e^{5}}-\frac{b^{2} \ln \left(d x +c +1\right)}{3 d \,e^{5}}-\frac{a b \arctanh \left(d x +c \right)}{2 d \,e^{5} \left(d x +c \right)^{4}}-\frac{a b}{6 d \,e^{5} \left(d x +c \right)^{3}}-\frac{a b}{2 d \,e^{5} \left(d x +c \right)}-\frac{a b \ln \left(d x +c -1\right)}{4 d \,e^{5}}+\frac{a b \ln \left(d x +c +1\right)}{4 d \,e^{5}}"," ",0,"-1/4/d*a^2/e^5/(d*x+c)^4-1/4/d*b^2/e^5/(d*x+c)^4*arctanh(d*x+c)^2-1/6/d*b^2/e^5*arctanh(d*x+c)/(d*x+c)^3-1/2/d*b^2/e^5*arctanh(d*x+c)/(d*x+c)-1/4/d*b^2/e^5*arctanh(d*x+c)*ln(d*x+c-1)+1/4/d*b^2/e^5*arctanh(d*x+c)*ln(d*x+c+1)-1/16/d*b^2/e^5*ln(d*x+c-1)^2+1/8/d*b^2/e^5*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)-1/16/d*b^2/e^5*ln(d*x+c+1)^2+1/8/d*b^2/e^5*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)-1/8/d*b^2/e^5*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)-1/12*b^2/d/e^5/(d*x+c)^2+2/3*b^2*ln(d*x+c)/d/e^5-1/3/d*b^2/e^5*ln(d*x+c-1)-1/3/d*b^2/e^5*ln(d*x+c+1)-1/2/d*a*b/e^5/(d*x+c)^4*arctanh(d*x+c)-1/6/d*a*b/e^5/(d*x+c)^3-1/2/d*a*b/e^5/(d*x+c)-1/4/d*a*b/e^5*ln(d*x+c-1)+1/4/d*a*b/e^5*ln(d*x+c+1)","B"
23,1,1768,251,0.858000," ","int((d*e*x+c*e)^2*(a+b*arctanh(d*x+c))^3,x)","-\frac{i e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \pi}{2 d}+\frac{\arctanh \left(d x +c \right)^{2} a \,b^{2} c^{3} e^{2}}{d}+\frac{\arctanh \left(d x +c \right) a \,b^{2} c^{2} e^{2}}{d}+\frac{\arctanh \left(d x +c \right) a^{2} b \,c^{3} e^{2}}{d}+\frac{e^{2} a \,b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{d}+\frac{e^{2} a \,b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{d}+d \arctanh \left(d x +c \right)^{3} x^{2} b^{3} c \,e^{2}+d^{2} \arctanh \left(d x +c \right)^{2} x^{3} a \,b^{2} e^{2}+d \arctanh \left(d x +c \right) x^{2} a \,b^{2} e^{2}+d^{2} \arctanh \left(d x +c \right) x^{3} a^{2} b \,e^{2}+3 \arctanh \left(d x +c \right)^{2} x a \,b^{2} c^{2} e^{2}+2 \arctanh \left(d x +c \right) x a \,b^{2} c \,e^{2}+3 \arctanh \left(d x +c \right) x \,a^{2} b \,c^{2} e^{2}+x \,a^{2} b c \,e^{2}+\frac{e^{2} b^{3} \polylog \left(3, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{2 d}+\frac{e^{2} b^{3} \arctanh \left(d x +c \right)^{3}}{3 d}-\frac{e^{2} b^{3} \arctanh \left(d x +c \right)^{2}}{2 d}+\frac{e^{2} b^{3} \arctanh \left(d x +c \right)}{d}+\arctanh \left(d x +c \right) x \,b^{3} e^{2}+a \,b^{2} e^{2} x -\frac{i e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(d x +c \right)^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)}{\sqrt{1-\left(d x +c \right)^{2}}}\right)^{2}}{4 d}-\frac{i e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(\left(d x +c \right)^{2}-1\right) \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}\right)^{2}}{4 d}-\frac{i e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(d x +c \right)^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{2 d}+\frac{i e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(d x +c \right)^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(\left(d x +c \right)^{2}-1\right) \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}\right)}{4 d}+\frac{e^{2} a \,b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{2 d}-\frac{e^{2} a \,b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 d}-\frac{e^{2} a \,b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 d}+\frac{i e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(d x +c \right)^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(\left(d x +c \right)^{2}-1\right) \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}\right)^{2}}{4 d}+\frac{a^{3} c^{3} e^{2}}{3 d}+3 d \arctanh \left(d x +c \right)^{2} x^{2} a \,b^{2} c \,e^{2}+3 d \arctanh \left(d x +c \right) x^{2} a^{2} b c \,e^{2}-\frac{i e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{3}}{2 d}-\frac{i e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(d x +c \right)^{2}-1}\right)^{3}}{4 d}-\frac{i e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(\left(d x +c \right)^{2}-1\right) \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}\right)^{3}}{4 d}+\frac{i e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2}}{2 d}+\frac{d^{2} x^{3} a^{3} e^{2}}{3}-\frac{e^{2} b^{3} \ln \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{d}+x \,a^{3} c^{2} e^{2}+\frac{a \,b^{2} c \,e^{2}}{d}+\frac{\arctanh \left(d x +c \right)^{3} b^{3} c^{3} e^{2}}{3 d}+\frac{d^{2} \arctanh \left(d x +c \right)^{3} x^{3} b^{3} e^{2}}{3}+\frac{d \arctanh \left(d x +c \right)^{2} x^{2} b^{3} e^{2}}{2}-\frac{e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d}-\frac{e^{2} b^{3} \arctanh \left(d x +c \right) \polylog \left(2, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{d}-\frac{e^{2} a \,b^{2} \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}-\frac{e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(2\right)}{d}+\frac{e^{2} a \,b^{2} \ln \left(d x +c -1\right)}{2 d}-\frac{e^{2} a \,b^{2} \ln \left(d x +c +1\right)}{2 d}+\frac{e^{2} a \,b^{2} \ln \left(d x +c -1\right)^{2}}{4 d}-\frac{e^{2} a \,b^{2} \ln \left(d x +c +1\right)^{2}}{4 d}+\frac{e^{2} a^{2} b \ln \left(d x +c -1\right)}{2 d}+\frac{e^{2} a^{2} b \ln \left(d x +c +1\right)}{2 d}+\frac{\arctanh \left(d x +c \right)^{2} b^{3} c^{2} e^{2}}{2 d}+\frac{\arctanh \left(d x +c \right) b^{3} c \,e^{2}}{d}+\arctanh \left(d x +c \right)^{3} x \,b^{3} c^{2} e^{2}+\arctanh \left(d x +c \right)^{2} x \,b^{3} c \,e^{2}+\frac{e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(d x +c -1\right)}{2 d}+\frac{e^{2} b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(d x +c +1\right)}{2 d}+d \,x^{2} a^{3} c \,e^{2}+\frac{d \,x^{2} a^{2} b \,e^{2}}{2}+\frac{a^{2} b \,c^{2} e^{2}}{2 d}"," ",0,"-1/2*I/d*e^2*b^3*arctanh(d*x+c)^2*Pi+x*a^2*b*c*e^2+a*b^2*e^2*x+1/4*I/d*e^2*b^3*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))+1/3/d*arctanh(d*x+c)^3*b^3*c^3*e^2+1/3*d^2*arctanh(d*x+c)^3*x^3*b^3*e^2+1/2*d*arctanh(d*x+c)^2*x^2*b^3*e^2-1/4*I/d*e^2*b^3*arctanh(d*x+c)^2*Pi*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))*csgn(I*(d*x+c+1)/(1-(d*x+c)^2)^(1/2))^2-1/4*I/d*e^2*b^3*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2+1/d*arctanh(d*x+c)^2*a*b^2*c^3*e^2+1/d*arctanh(d*x+c)*a*b^2*c^2*e^2+1/d*arctanh(d*x+c)*a^2*b*c^3*e^2+1/d*e^2*a*b^2*arctanh(d*x+c)*ln(d*x+c-1)+1/d*e^2*a*b^2*arctanh(d*x+c)*ln(d*x+c+1)+1/2/d*e^2*a*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)-1/2/d*e^2*a*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)-1/2/d*e^2*a*b^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+d*arctanh(d*x+c)^3*x^2*b^3*c*e^2+d^2*arctanh(d*x+c)^2*x^3*a*b^2*e^2+d*arctanh(d*x+c)*x^2*a*b^2*e^2+d^2*arctanh(d*x+c)*x^3*a^2*b*e^2+3*arctanh(d*x+c)^2*x*a*b^2*c^2*e^2+2*arctanh(d*x+c)*x*a*b^2*c*e^2+3*arctanh(d*x+c)*x*a^2*b*c^2*e^2-1/2*I/d*e^2*b^3*arctanh(d*x+c)^2*Pi*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))^2*csgn(I*(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+1/4*I/d*e^2*b^3*arctanh(d*x+c)^2*Pi*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2+3*d*arctanh(d*x+c)^2*x^2*a*b^2*c*e^2+3*d*arctanh(d*x+c)*x^2*a^2*b*c*e^2-1/2*I/d*e^2*b^3*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3-1/4*I/d*e^2*b^3*arctanh(d*x+c)^2*Pi*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))^3-1/4*I/d*e^2*b^3*arctanh(d*x+c)^2*Pi*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3+1/2*I/d*e^2*b^3*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2+1/3/d*a^3*c^3*e^2+1/3*d^2*x^3*a^3*e^2-1/d*e^2*b^3*ln(1+(d*x+c+1)^2/(1-(d*x+c)^2))+1/2/d*e^2*b^3*polylog(3,-(d*x+c+1)^2/(1-(d*x+c)^2))+1/3/d*e^2*b^3*arctanh(d*x+c)^3-1/2/d*e^2*b^3*arctanh(d*x+c)^2+1/d*e^2*b^3*arctanh(d*x+c)+arctanh(d*x+c)*x*b^3*e^2+x*a^3*c^2*e^2+1/d*a*b^2*c*e^2-1/d*e^2*b^3*arctanh(d*x+c)^2*ln((d*x+c+1)/(1-(d*x+c)^2)^(1/2))-1/d*e^2*b^3*arctanh(d*x+c)*polylog(2,-(d*x+c+1)^2/(1-(d*x+c)^2))+1/2/d*e^2*a*b^2*ln(d*x+c-1)-1/2/d*e^2*a*b^2*ln(d*x+c+1)+1/4/d*e^2*a*b^2*ln(d*x+c-1)^2-1/d*e^2*a*b^2*dilog(1/2+1/2*d*x+1/2*c)-1/4/d*e^2*a*b^2*ln(d*x+c+1)^2+1/2/d*e^2*a^2*b*ln(d*x+c-1)+1/2/d*e^2*a^2*b*ln(d*x+c+1)-1/d*e^2*b^3*arctanh(d*x+c)^2*ln(2)+1/2/d*arctanh(d*x+c)^2*b^3*c^2*e^2+1/d*arctanh(d*x+c)*b^3*c*e^2+d*x^2*a^3*c*e^2+1/2*d*x^2*a^2*b*e^2+arctanh(d*x+c)^3*x*b^3*c^2*e^2+arctanh(d*x+c)^2*x*b^3*c*e^2+1/2/d*e^2*b^3*arctanh(d*x+c)^2*ln(d*x+c-1)+1/2/d*e^2*b^3*arctanh(d*x+c)^2*ln(d*x+c+1)+1/2/d*a^2*b*c^2*e^2","C"
24,1,6834,152,0.612000," ","int((d*e*x+c*e)*(a+b*arctanh(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
25,1,1842,245,0.183000," ","int((a+b*arctanh(d*x+c))^3/(d*e*x+c*e),x)","\frac{3 a \,b^{2} \polylog \left(3, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{2 d e}-\frac{6 a \,b^{2} \polylog \left(3, \frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}-\frac{6 a \,b^{2} \polylog \left(3, -\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}-\frac{3 a^{2} b \dilog \left(d x +c \right)}{2 d e}-\frac{3 a^{2} b \dilog \left(d x +c +1\right)}{2 d e}+\frac{b^{3} \ln \left(d x +c \right) \arctanh \left(d x +c \right)^{3}}{d e}+\frac{b^{3} \arctanh \left(d x +c \right)^{3} \ln \left(1-\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}-\frac{b^{3} \arctanh \left(d x +c \right)^{3} \ln \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{d e}+\frac{3 b^{3} \arctanh \left(d x +c \right) \polylog \left(3, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{2 d e}-\frac{3 b^{3} \arctanh \left(d x +c \right)^{2} \polylog \left(2, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{2 d e}+\frac{3 b^{3} \arctanh \left(d x +c \right)^{2} \polylog \left(2, \frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}-\frac{6 b^{3} \arctanh \left(d x +c \right) \polylog \left(3, \frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}+\frac{b^{3} \arctanh \left(d x +c \right)^{3} \ln \left(1+\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}+\frac{3 b^{3} \arctanh \left(d x +c \right)^{2} \polylog \left(2, -\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}-\frac{6 b^{3} \arctanh \left(d x +c \right) \polylog \left(3, -\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{3} \arctanh \left(d x +c \right)^{3}}{2 d e}+\frac{a^{3} \ln \left(d x +c \right)}{d e}-\frac{3 a^{2} b \ln \left(d x +c \right) \ln \left(d x +c +1\right)}{2 d e}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2} \arctanh \left(d x +c \right)^{3}}{2 d e}+\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \arctanh \left(d x +c \right)^{2}}{2 d e}+\frac{6 b^{3} \polylog \left(4, -\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}-\frac{3 b^{3} \polylog \left(4, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{4 d e}+\frac{6 b^{3} \polylog \left(4, \frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}-\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2} \arctanh \left(d x +c \right)^{2}}{2 d e}+\frac{i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \arctanh \left(d x +c \right)^{3}}{2 d e}-\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2} \arctanh \left(d x +c \right)^{2}}{2 d e}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2} \arctanh \left(d x +c \right)^{3}}{2 d e}+\frac{3 i a \,b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{3} \arctanh \left(d x +c \right)^{2}}{2 d e}+\frac{3 a \,b^{2} \arctanh \left(d x +c \right)^{2} \ln \left(1-\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}+\frac{6 a \,b^{2} \arctanh \left(d x +c \right) \polylog \left(2, \frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}+\frac{3 a \,b^{2} \ln \left(d x +c \right) \arctanh \left(d x +c \right)^{2}}{d e}+\frac{3 a \,b^{2} \arctanh \left(d x +c \right)^{2} \ln \left(1+\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}+\frac{6 a \,b^{2} \arctanh \left(d x +c \right) \polylog \left(2, -\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d e}+\frac{3 a^{2} b \ln \left(d x +c \right) \arctanh \left(d x +c \right)}{d e}-\frac{3 a \,b^{2} \arctanh \left(d x +c \right) \polylog \left(2, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{3 a \,b^{2} \arctanh \left(d x +c \right)^{2} \ln \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{d e}"," ",0,"1/d*b^3/e*arctanh(d*x+c)^3*ln(1-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-1/d*b^3/e*arctanh(d*x+c)^3*ln((d*x+c+1)^2/(1-(d*x+c)^2)-1)+3/2/d*b^3/e*arctanh(d*x+c)*polylog(3,-(d*x+c+1)^2/(1-(d*x+c)^2))-3/2/d*b^3/e*arctanh(d*x+c)^2*polylog(2,-(d*x+c+1)^2/(1-(d*x+c)^2))+3/d*b^3/e*arctanh(d*x+c)^2*polylog(2,(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-6/d*b^3/e*arctanh(d*x+c)*polylog(3,(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+1/d*b^3/e*arctanh(d*x+c)^3*ln(1+(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+3/d*b^3/e*arctanh(d*x+c)^2*polylog(2,-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-6/d*b^3/e*arctanh(d*x+c)*polylog(3,-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+3/2/d*a*b^2/e*polylog(3,-(d*x+c+1)^2/(1-(d*x+c)^2))-6/d*a*b^2/e*polylog(3,(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-6/d*a*b^2/e*polylog(3,-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-3/2/d*a^2*b/e*dilog(d*x+c)-3/2/d*a^2*b/e*dilog(d*x+c+1)+1/d*b^3/e*ln(d*x+c)*arctanh(d*x+c)^3-1/2*I/d*b^3/e*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*arctanh(d*x+c)^3-1/2*I/d*b^3/e*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*arctanh(d*x+c)^3+6/d*b^3/e*polylog(4,-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+1/d*a^3/e*ln(d*x+c)-3/4/d*b^3/e*polylog(4,-(d*x+c+1)^2/(1-(d*x+c)^2))+6/d*b^3/e*polylog(4,(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+3/d*a*b^2/e*ln(d*x+c)*arctanh(d*x+c)^2+3/d*a*b^2/e*arctanh(d*x+c)^2*ln(1+(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+6/d*a*b^2/e*arctanh(d*x+c)*polylog(2,-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+3/d*a^2*b/e*ln(d*x+c)*arctanh(d*x+c)-3/2/d*a^2*b/e*ln(d*x+c)*ln(d*x+c+1)-3/d*a*b^2/e*arctanh(d*x+c)*polylog(2,-(d*x+c+1)^2/(1-(d*x+c)^2))-3/d*a*b^2/e*arctanh(d*x+c)^2*ln((d*x+c+1)^2/(1-(d*x+c)^2)-1)+3/d*a*b^2/e*arctanh(d*x+c)^2*ln(1-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-3/2*I/d*a*b^2/e*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*arctanh(d*x+c)^2-3/2*I/d*a*b^2/e*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*arctanh(d*x+c)^2+3/2*I/d*a*b^2/e*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1))*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*arctanh(d*x+c)^2+1/2*I/d*b^3/e*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1))*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*arctanh(d*x+c)^3+1/2*I/d*b^3/e*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3*arctanh(d*x+c)^3+3/2*I/d*a*b^2/e*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3*arctanh(d*x+c)^2+6/d*a*b^2/e*arctanh(d*x+c)*polylog(2,(d*x+c+1)/(1-(d*x+c)^2)^(1/2))","C"
26,1,2001,141,0.511000," ","int((a+b*arctanh(d*x+c))^3/(d*e*x+c*e)^2,x)","\frac{3 i b^{3} \pi  \arctanh \left(d x +c \right)^{2}}{2 d \,e^{2}}-\frac{a^{3}}{d \,e^{2} \left(d x +c \right)}-\frac{3 a^{2} b \ln \left(d x +c -1\right)}{2 d \,e^{2}}-\frac{3 a^{2} b \ln \left(d x +c +1\right)}{2 d \,e^{2}}-\frac{3 a \,b^{2} \ln \left(d x +c -1\right)^{2}}{4 d \,e^{2}}+\frac{3 a \,b^{2} \ln \left(d x +c +1\right)^{2}}{4 d \,e^{2}}+\frac{3 a^{2} b \ln \left(d x +c \right)}{d \,e^{2}}+\frac{6 b^{3} \arctanh \left(d x +c \right) \polylog \left(2, -\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}-\frac{3 b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(d x +c -1\right)}{2 d \,e^{2}}-\frac{3 b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(d x +c +1\right)}{2 d \,e^{2}}+\frac{3 b^{3} \ln \left(d x +c \right) \arctanh \left(d x +c \right)^{2}}{d \,e^{2}}+\frac{3 b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(1-\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}+\frac{6 b^{3} \arctanh \left(d x +c \right) \polylog \left(2, \frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}+\frac{3 a \,b^{2} \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d \,e^{2}}-\frac{3 a \,b^{2} \dilog \left(d x +c \right)}{d \,e^{2}}-\frac{3 a \,b^{2} \dilog \left(d x +c +1\right)}{d \,e^{2}}+\frac{3 a \,b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,e^{2}}-\frac{3 a \,b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{2 d \,e^{2}}+\frac{3 a \,b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,e^{2}}-\frac{3 a \,b^{2} \ln \left(d x +c \right) \ln \left(d x +c +1\right)}{d \,e^{2}}-\frac{3 a \,b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{d \,e^{2}}-\frac{3 a^{2} b \arctanh \left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}-\frac{3 a \,b^{2} \arctanh \left(d x +c \right)^{2}}{d \,e^{2} \left(d x +c \right)}+\frac{6 a \,b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c \right)}{d \,e^{2}}-\frac{3 a \,b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{d \,e^{2}}-\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(d x +c \right)^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(\left(d x +c \right)^{2}-1\right) \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}\right) \arctanh \left(d x +c \right)^{2}}{4 d \,e^{2}}+\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \arctanh \left(d x +c \right)^{2}}{2 d \,e^{2}}-\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2} \arctanh \left(d x +c \right)^{2}}{2 d \,e^{2}}+\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(d x +c +1\right)}{\sqrt{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(d x +c \right)^{2}-1}\right)^{2} \arctanh \left(d x +c \right)^{2}}{2 d \,e^{2}}+\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(\left(d x +c \right)^{2}-1\right) \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}\right)^{2} \arctanh \left(d x +c \right)^{2}}{4 d \,e^{2}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)}{\sqrt{1-\left(d x +c \right)^{2}}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(d x +c \right)^{2}-1}\right) \arctanh \left(d x +c \right)^{2}}{4 d \,e^{2}}-\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2} \arctanh \left(d x +c \right)^{2}}{2 d \,e^{2}}-\frac{3 i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(d x +c \right)^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(\left(d x +c \right)^{2}-1\right) \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}\right)^{2} \arctanh \left(d x +c \right)^{2}}{4 d \,e^{2}}-\frac{b^{3} \arctanh \left(d x +c \right)^{3}}{d \,e^{2}}-\frac{6 b^{3} \polylog \left(3, -\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}-\frac{6 b^{3} \polylog \left(3, \frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}+\frac{3 b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(2\right)}{d \,e^{2}}-\frac{b^{3} \arctanh \left(d x +c \right)^{3}}{d \,e^{2} \left(d x +c \right)}+\frac{3 b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}-\frac{3 b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{d \,e^{2}}+\frac{3 b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(1+\frac{d x +c +1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}-\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2} \arctanh \left(d x +c \right)^{2}}{2 d \,e^{2}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(\left(d x +c \right)^{2}-1\right) \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}\right)^{3} \arctanh \left(d x +c \right)^{2}}{4 d \,e^{2}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{3} \arctanh \left(d x +c \right)^{2}}{2 d \,e^{2}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(d x +c +1\right)^{2}}{\left(d x +c \right)^{2}-1}\right)^{3} \arctanh \left(d x +c \right)^{2}}{4 d \,e^{2}}+\frac{3 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{3} \arctanh \left(d x +c \right)^{2}}{2 d \,e^{2}}"," ",0,"3/2*I/d*b^3/e^2*Pi*csgn(I*(d*x+c+1)/(1-(d*x+c)^2)^(1/2))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))^2*arctanh(d*x+c)^2-1/d*b^3/e^2*arctanh(d*x+c)^3-6/d*b^3/e^2*polylog(3,-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-6/d*b^3/e^2*polylog(3,(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-1/d*a^3/e^2/(d*x+c)-3/2*I/d*b^3/e^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*arctanh(d*x+c)^2+3/4*I/d*b^3/e^2*Pi*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3*arctanh(d*x+c)^2+3/2*I/d*b^3/e^2*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3*arctanh(d*x+c)^2+3/4*I/d*b^3/e^2*Pi*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))^3*arctanh(d*x+c)^2+3/2*I/d*b^3/e^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3*arctanh(d*x+c)^2+6/d*b^3/e^2*arctanh(d*x+c)*polylog(2,-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-3/2/d*b^3/e^2*arctanh(d*x+c)^2*ln(d*x+c-1)-3/2/d*b^3/e^2*arctanh(d*x+c)^2*ln(d*x+c+1)+3/d*b^3/e^2*ln(d*x+c)*arctanh(d*x+c)^2+3/d*b^3/e^2*arctanh(d*x+c)^2*ln(1-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+6/d*b^3/e^2*arctanh(d*x+c)*polylog(2,(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-3/2/d*a^2*b/e^2*ln(d*x+c-1)-3/2/d*a^2*b/e^2*ln(d*x+c+1)-3/4/d*a*b^2/e^2*ln(d*x+c-1)^2+3/d*a*b^2/e^2*dilog(1/2+1/2*d*x+1/2*c)+3/4/d*a*b^2/e^2*ln(d*x+c+1)^2-3/d*a*b^2/e^2*dilog(d*x+c)-3/d*a*b^2/e^2*dilog(d*x+c+1)+3/d*b^3/e^2*arctanh(d*x+c)^2*ln(2)+3/d*a^2*b/e^2*ln(d*x+c)-3/2*I/d*b^3/e^2*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*arctanh(d*x+c)^2+3/4*I/d*b^3/e^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*arctanh(d*x+c)^2+3/4*I/d*b^3/e^2*Pi*csgn(I*(d*x+c+1)/(1-(d*x+c)^2)^(1/2))^2*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))*arctanh(d*x+c)^2-3/d*a*b^2/e^2*arctanh(d*x+c)*ln(d*x+c+1)+3/2/d*a*b^2/e^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)-3/d*a^2*b/e^2/(d*x+c)*arctanh(d*x+c)-3/2/d*a*b^2/e^2*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)+3/2/d*a*b^2/e^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)-3/d*a*b^2/e^2*ln(d*x+c)*ln(d*x+c+1)-3/d*a*b^2/e^2/(d*x+c)*arctanh(d*x+c)^2+6/d*a*b^2/e^2*arctanh(d*x+c)*ln(d*x+c)-3/d*a*b^2/e^2*arctanh(d*x+c)*ln(d*x+c-1)+3/2*I/d*b^3/e^2*Pi*arctanh(d*x+c)^2-3/2*I/d*b^3/e^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*arctanh(d*x+c)^2-3/4*I/d*b^3/e^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*arctanh(d*x+c)^2+3/2*I/d*b^3/e^2*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1))*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*arctanh(d*x+c)^2-3/4*I/d*b^3/e^2*Pi*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*arctanh(d*x+c)^2-1/d*b^3/e^2/(d*x+c)*arctanh(d*x+c)^3+3/d*b^3/e^2*arctanh(d*x+c)^2*ln((d*x+c+1)/(1-(d*x+c)^2)^(1/2))-3/d*b^3/e^2*arctanh(d*x+c)^2*ln((d*x+c+1)^2/(1-(d*x+c)^2)-1)+3/d*b^3/e^2*arctanh(d*x+c)^2*ln(1+(d*x+c+1)/(1-(d*x+c)^2)^(1/2))","C"
27,1,5796,156,0.681000," ","int((a+b*arctanh(d*x+c))^3/(d*e*x+c*e)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
28,1,2247,257,0.985000," ","int((a+b*arctanh(d*x+c))^3/(d*e*x+c*e)^4,x)","\text{Expression too large to display}"," ",0,"1/2*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1))+1/4*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3+1/4*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))^3+1/2*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3-1/2*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2+1/2*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3-1/d*a*b^2/e^4/(d*x+c)-1/2/d*a^2*b/e^4/(d*x+c)^2+1/d*b^3/e^4*arctanh(d*x+c)^2*ln(2)-1/2/d*a*b^2/e^4*ln(d*x+c-1)+1/2/d*a*b^2/e^4*ln(d*x+c+1)-1/4/d*a*b^2/e^4*ln(d*x+c-1)^2-1/4*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))+1/d*a*b^2/e^4*dilog(1/2+1/2*d*x+1/2*c)+1/4/d*a*b^2/e^4*ln(d*x+c+1)^2-1/d*a*b^2/e^4*dilog(d*x+c)-1/d*a*b^2/e^4*dilog(d*x+c+1)+1/d*a^2*b/e^4*ln(d*x+c)-1/2/d*a^2*b/e^4*ln(d*x+c-1)-1/2/d*a^2*b/e^4*ln(d*x+c+1)+2/d*b^3/e^4*arctanh(d*x+c)*polylog(2,-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+1/d*b^3/e^4*ln(d*x+c)*arctanh(d*x+c)^2-1/2/d*b^3/e^4*arctanh(d*x+c)^2*ln(d*x+c-1)-1/2/d*b^3/e^4*arctanh(d*x+c)^2*ln(d*x+c+1)+2/d*b^3/e^4*arctanh(d*x+c)*polylog(2,(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+1/d*b^3/e^4*arctanh(d*x+c)^2*ln(1+(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-1/d*b^3/e^4*arctanh(d*x+c)/(d*x+c)-1/d*b^3/e^4*arctanh(d*x+c)^2*ln((d*x+c+1)^2/(1-(d*x+c)^2)-1)+1/d*b^3/e^4*arctanh(d*x+c)^2*ln((d*x+c+1)/(1-(d*x+c)^2)^(1/2))+1/d*b^3/e^4*arctanh(d*x+c)^2*ln(1-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-1/3/d*b^3/e^4/(d*x+c)^3*arctanh(d*x+c)^3-1/2/d*b^3/e^4*arctanh(d*x+c)^2/(d*x+c)^2-1/3/d*a^3/e^4/(d*x+c)^3+1/2/d*b^3/e^4*arctanh(d*x+c)^2-1/3/d*b^3/e^4*arctanh(d*x+c)^3+1/d*b^3/e^4*ln(1+(d*x+c+1)/(1-(d*x+c)^2)^(1/2))+1/d*b^3/e^4*ln((d*x+c+1)/(1-(d*x+c)^2)^(1/2)-1)-2/d*b^3/e^4*polylog(3,(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-2/d*b^3/e^4*polylog(3,-(d*x+c+1)/(1-(d*x+c)^2)^(1/2))-1/d*b^3/e^4*arctanh(d*x+c)-1/d*a*b^2/e^4*arctanh(d*x+c)*ln(d*x+c+1)+1/2/d*a*b^2/e^4*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)-1/2/d*a*b^2/e^4*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)-1/d*a^2*b/e^4/(d*x+c)^3*arctanh(d*x+c)-1/d*a*b^2/e^4/(d*x+c)^3*arctanh(d*x+c)^2-1/d*a*b^2/e^4*arctanh(d*x+c)/(d*x+c)^2+2/d*a*b^2/e^4*arctanh(d*x+c)*ln(d*x+c)-1/d*a*b^2/e^4*arctanh(d*x+c)*ln(d*x+c-1)-1/d*a*b^2/e^4*ln(d*x+c)*ln(d*x+c+1)+1/2/d*a*b^2/e^4*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)+1/2*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi-1/4*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))+1/4*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I*(d*x+c+1)/(1-(d*x+c)^2)^(1/2))^2*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))-1/2*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1))+1/2*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I*(d*x+c+1)/(1-(d*x+c)^2)^(1/2))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1))^2-1/2*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*((d*x+c+1)^2/(1-(d*x+c)^2)-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2+1/4*I/d*b^3/e^4*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(d*x+c+1)^2/((d*x+c)^2-1)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2","C"
29,1,34,17,0.046000," ","int(arctanh(1+x)/(2+2*x),x)","\frac{\ln \left(1+x \right) \arctanh \left(1+x \right)}{2}-\frac{\dilog \left(1+x \right)}{4}-\frac{\dilog \left(x +2\right)}{4}-\frac{\ln \left(1+x \right) \ln \left(x +2\right)}{4}"," ",0,"1/2*ln(1+x)*arctanh(1+x)-1/4*dilog(1+x)-1/4*dilog(x+2)-1/4*ln(1+x)*ln(x+2)","A"
30,1,59,28,0.046000," ","int(arctanh(b*x+a)/(a*d/b+d*x),x)","\frac{\ln \left(b x +a \right) \arctanh \left(b x +a \right)}{d}-\frac{\dilog \left(b x +a \right)}{2 d}-\frac{\dilog \left(b x +a +1\right)}{2 d}-\frac{\ln \left(b x +a \right) \ln \left(b x +a +1\right)}{2 d}"," ",0,"1/d*ln(b*x+a)*arctanh(b*x+a)-1/2/d*dilog(b*x+a)-1/2/d*dilog(b*x+a+1)-1/2/d*ln(b*x+a)*ln(b*x+a+1)","B"
31,1,786,156,0.043000," ","int((f*x+e)^3*(a+b*arctanh(d*x+c)),x)","\frac{b \ln \left(d x +c -1\right) e^{4}}{8 f}-\frac{b \ln \left(d x +c +1\right) e^{4}}{8 f}+\frac{b \,f^{3} \ln \left(d x +c -1\right)}{8 d^{4}}-\frac{b \,f^{3} \ln \left(d x +c +1\right)}{8 d^{4}}+\frac{b \,f^{3} x^{3}}{12 d}+\frac{b \,f^{3} x}{4 d^{3}}+a \,f^{2} x^{3} e +\frac{3 a f \,x^{2} e^{2}}{2}+\frac{b \,f^{3} \arctanh \left(d x +c \right) x^{4}}{4}+\arctanh \left(d x +c \right) x b \,e^{3}+\frac{b \arctanh \left(d x +c \right) e^{4}}{4 f}+\frac{e^{3} b \ln \left(d x +c +1\right)}{2 d}+\frac{e^{3} b \ln \left(d x +c -1\right)}{2 d}+\frac{13 b \,f^{3} c^{3}}{12 d^{4}}+\frac{a \,e^{4}}{4 f}+\frac{b \,f^{3} c}{4 d^{4}}+\frac{a \,f^{3} x^{4}}{4}+a x \,e^{3}-\frac{2 b \,f^{2} c e x}{d^{2}}-\frac{3 b f \ln \left(d x +c -1\right) c \,e^{2}}{2 d^{2}}+\frac{3 b \,f^{2} \ln \left(d x +c +1\right) c^{2} e}{2 d^{3}}-\frac{3 b f \ln \left(d x +c +1\right) c^{2} e^{2}}{4 d^{2}}-\frac{3 b \,f^{2} \ln \left(d x +c -1\right) c e}{2 d^{3}}+\frac{3 b \,f^{2} \ln \left(d x +c +1\right) c e}{2 d^{3}}+\frac{b \,f^{2} \ln \left(d x +c +1\right) c^{3} e}{2 d^{3}}+\frac{3 b f \ln \left(d x +c -1\right) c^{2} e^{2}}{4 d^{2}}+\frac{3 b \,f^{2} \ln \left(d x +c -1\right) c^{2} e}{2 d^{3}}-\frac{3 b f \ln \left(d x +c +1\right) c \,e^{2}}{2 d^{2}}-\frac{b \,f^{2} \ln \left(d x +c -1\right) c^{3} e}{2 d^{3}}+\frac{3 b \,f^{3} c^{2} x}{4 d^{3}}+\frac{3 b f \,e^{2} x}{2 d}-\frac{b \,f^{3} \ln \left(d x +c +1\right) c}{2 d^{4}}-\frac{b \,f^{3} \ln \left(d x +c -1\right) c^{3}}{2 d^{4}}-\frac{b \,f^{3} \ln \left(d x +c -1\right) c}{2 d^{4}}-\frac{b \,f^{3} \ln \left(d x +c +1\right) c^{3}}{2 d^{4}}-\frac{b \,f^{3} x^{2} c}{4 d^{2}}+\frac{b \,f^{3} \ln \left(d x +c -1\right) c^{4}}{8 d^{4}}-\frac{3 b \,f^{3} \ln \left(d x +c +1\right) c^{2}}{4 d^{4}}-\frac{b \,f^{3} \ln \left(d x +c +1\right) c^{4}}{8 d^{4}}+\frac{3 b f \ln \left(d x +c -1\right) e^{2}}{4 d^{2}}-\frac{3 b f \ln \left(d x +c +1\right) e^{2}}{4 d^{2}}+b \,f^{2} \arctanh \left(d x +c \right) e \,x^{3}+\frac{b \,f^{2} \ln \left(d x +c -1\right) e}{2 d^{3}}+\frac{3 b \,f^{3} \ln \left(d x +c -1\right) c^{2}}{4 d^{4}}+\frac{b \,f^{2} \ln \left(d x +c +1\right) e}{2 d^{3}}+\frac{b \ln \left(d x +c +1\right) c \,e^{3}}{2 d}-\frac{5 b \,f^{2} c^{2} e}{2 d^{3}}-\frac{b \ln \left(d x +c -1\right) c \,e^{3}}{2 d}+\frac{b \,f^{2} e \,x^{2}}{2 d}+\frac{3 b f c \,e^{2}}{2 d^{2}}+\frac{3 b f \arctanh \left(d x +c \right) e^{2} x^{2}}{2}"," ",0,"1/8*b/f*ln(d*x+c-1)*e^4-1/8*b/f*ln(d*x+c+1)*e^4+1/8/d^4*b*f^3*ln(d*x+c-1)-1/8/d^4*b*f^3*ln(d*x+c+1)+1/12/d*b*f^3*x^3+1/4*b/d^3*f^3*x+a*f^2*x^3*e+3/2*a*f*x^2*e^2+1/2/d*e^3*b*ln(d*x+c+1)+1/2/d*e^3*b*ln(d*x+c-1)+1/4*b*f^3*arctanh(d*x+c)*x^4+arctanh(d*x+c)*x*b*e^3+1/4*b/f*arctanh(d*x+c)*e^4+13/12/d^4*b*f^3*c^3+1/4*a/f*e^4+1/4/d^4*b*f^3*c+1/4*a*f^3*x^4+a*x*e^3-2*b/d^2*f^2*c*e*x-3/2/d^2*b*f*ln(d*x+c-1)*c*e^2+3/2/d^3*b*f^2*ln(d*x+c+1)*c^2*e-3/4/d^2*b*f*ln(d*x+c+1)*c^2*e^2-3/2/d^3*b*f^2*ln(d*x+c-1)*c*e+3/2/d^3*b*f^2*ln(d*x+c+1)*c*e+1/2/d^3*b*f^2*ln(d*x+c+1)*c^3*e+3/4/d^2*b*f*ln(d*x+c-1)*c^2*e^2+3/2/d^3*b*f^2*ln(d*x+c-1)*c^2*e-3/2/d^2*b*f*ln(d*x+c+1)*c*e^2-1/2/d^3*b*f^2*ln(d*x+c-1)*c^3*e+3/4*b/d^3*f^3*c^2*x+3/2*b/d*f*e^2*x-1/2/d^4*b*f^3*ln(d*x+c+1)*c-1/2/d^4*b*f^3*ln(d*x+c-1)*c^3-1/2/d^4*b*f^3*ln(d*x+c-1)*c-1/2/d^4*b*f^3*ln(d*x+c+1)*c^3-1/4/d^2*b*f^3*x^2*c+1/8/d^4*b*f^3*ln(d*x+c-1)*c^4+3/2*b*f*arctanh(d*x+c)*e^2*x^2+b*f^2*arctanh(d*x+c)*e*x^3-3/4/d^4*b*f^3*ln(d*x+c+1)*c^2-1/8/d^4*b*f^3*ln(d*x+c+1)*c^4+3/4/d^2*b*f*ln(d*x+c-1)*e^2-3/4/d^2*b*f*ln(d*x+c+1)*e^2+1/2/d^3*b*f^2*ln(d*x+c-1)*e+3/4/d^4*b*f^3*ln(d*x+c-1)*c^2+1/2/d^3*b*f^2*ln(d*x+c+1)*e+1/2/d*b*ln(d*x+c+1)*c*e^3-5/2/d^3*b*f^2*c^2*e-1/2/d*b*ln(d*x+c-1)*c*e^3+1/2/d*b*f^2*e*x^2+3/2/d^2*b*f*c*e^2","B"
32,1,477,112,0.038000," ","int((f*x+e)^2*(a+b*arctanh(d*x+c)),x)","\frac{b \arctanh \left(d x +c \right) e^{3}}{3 f}+\frac{b \,f^{2} x^{2}}{6 d}+a f \,x^{2} e +\frac{b \,f^{2} \arctanh \left(d x +c \right) x^{3}}{3}+\arctanh \left(d x +c \right) x b \,e^{2}+\frac{b \ln \left(d x +c -1\right) e^{3}}{6 f}+\frac{e^{2} b \ln \left(d x +c +1\right)}{2 d}+\frac{e^{2} b \ln \left(d x +c -1\right)}{2 d}+\frac{b \,f^{2} \ln \left(d x +c -1\right)}{6 d^{3}}+\frac{b \,f^{2} \ln \left(d x +c +1\right)}{6 d^{3}}-\frac{b \ln \left(d x +c +1\right) e^{3}}{6 f}+\frac{a \,e^{3}}{3 f}-\frac{5 b \,f^{2} c^{2}}{6 d^{3}}+\frac{a \,f^{2} x^{3}}{3}+a x \,e^{2}-\frac{2 b \,f^{2} c x}{3 d^{2}}-\frac{b f \ln \left(d x +c +1\right) c^{2} e}{2 d^{2}}+\frac{b f \ln \left(d x +c -1\right) c^{2} e}{2 d^{2}}-\frac{b f \ln \left(d x +c -1\right) c e}{d^{2}}-\frac{b f \ln \left(d x +c +1\right) c e}{d^{2}}+\frac{b \,f^{2} \ln \left(d x +c +1\right) c}{2 d^{3}}+\frac{b \ln \left(d x +c +1\right) c \,e^{2}}{2 d}-\frac{b \ln \left(d x +c -1\right) c \,e^{2}}{2 d}+\frac{b \,f^{2} \ln \left(d x +c +1\right) c^{2}}{2 d^{3}}+\frac{b \,f^{2} \ln \left(d x +c +1\right) c^{3}}{6 d^{3}}-\frac{b \,f^{2} \ln \left(d x +c -1\right) c}{2 d^{3}}-\frac{b f \ln \left(d x +c +1\right) e}{2 d^{2}}+b f \arctanh \left(d x +c \right) e \,x^{2}+\frac{b f c e}{d^{2}}+\frac{b f e x}{d}+\frac{b \,f^{2} \ln \left(d x +c -1\right) c^{2}}{2 d^{3}}-\frac{b \,f^{2} \ln \left(d x +c -1\right) c^{3}}{6 d^{3}}+\frac{b f \ln \left(d x +c -1\right) e}{2 d^{2}}"," ",0,"1/6/d*b*f^2*x^2+a*f*x^2*e+1/6*b/f*ln(d*x+c-1)*e^3+1/3*b*f^2*arctanh(d*x+c)*x^3+arctanh(d*x+c)*x*b*e^2+1/2/d*e^2*b*ln(d*x+c+1)+1/2/d*e^2*b*ln(d*x+c-1)+1/6/d^3*b*f^2*ln(d*x+c-1)+1/6/d^3*b*f^2*ln(d*x+c+1)-1/6*b/f*ln(d*x+c+1)*e^3+1/3*b/f*arctanh(d*x+c)*e^3+1/3*a/f*e^3-5/6/d^3*b*f^2*c^2+1/3*a*f^2*x^3+a*x*e^2-2/3*b/d^2*f^2*c*x-1/2/d^2*b*f*ln(d*x+c+1)*c^2*e+1/2/d^2*b*f*ln(d*x+c-1)*c^2*e-1/d^2*b*f*ln(d*x+c-1)*c*e-1/d^2*b*f*ln(d*x+c+1)*c*e+1/2/d^3*b*f^2*ln(d*x+c+1)*c+1/2/d*b*ln(d*x+c+1)*c*e^2-1/2/d*b*ln(d*x+c-1)*c*e^2+1/2/d^3*b*f^2*ln(d*x+c+1)*c^2+1/6/d^3*b*f^2*ln(d*x+c+1)*c^3-1/2/d^3*b*f^2*ln(d*x+c-1)*c-1/2/d^2*b*f*ln(d*x+c+1)*e+1/d^2*b*f*c*e+b/d*f*e*x+b*f*arctanh(d*x+c)*e*x^2+1/2/d^3*b*f^2*ln(d*x+c-1)*c^2-1/6/d^3*b*f^2*ln(d*x+c-1)*c^3+1/2/d^2*b*f*ln(d*x+c-1)*e","B"
33,1,184,89,0.036000," ","int((f*x+e)*(a+b*arctanh(d*x+c)),x)","\frac{a \,x^{2} f}{2}-\frac{a \,c^{2} f}{2 d^{2}}+a x e +\frac{a c e}{d}+\frac{b \arctanh \left(d x +c \right) f \,x^{2}}{2}-\frac{b \arctanh \left(d x +c \right) f \,c^{2}}{2 d^{2}}+\arctanh \left(d x +c \right) x b e +\frac{\arctanh \left(d x +c \right) b c e}{d}+\frac{b f x}{2 d}+\frac{b c f}{2 d^{2}}-\frac{b \ln \left(d x +c -1\right) c f}{2 d^{2}}+\frac{b \ln \left(d x +c -1\right) e}{2 d}+\frac{b \ln \left(d x +c -1\right) f}{4 d^{2}}-\frac{b \ln \left(d x +c +1\right) c f}{2 d^{2}}+\frac{b \ln \left(d x +c +1\right) e}{2 d}-\frac{b \ln \left(d x +c +1\right) f}{4 d^{2}}"," ",0,"1/2*a*x^2*f-1/2/d^2*a*c^2*f+a*x*e+1/d*a*c*e+1/2*b*arctanh(d*x+c)*f*x^2-1/2/d^2*b*arctanh(d*x+c)*f*c^2+arctanh(d*x+c)*x*b*e+1/d*arctanh(d*x+c)*b*c*e+1/2*b*f*x/d+1/2/d^2*b*c*f-1/2/d^2*b*ln(d*x+c-1)*c*f+1/2/d*b*ln(d*x+c-1)*e+1/4/d^2*b*ln(d*x+c-1)*f-1/2/d^2*b*ln(d*x+c+1)*c*f+1/2/d*b*ln(d*x+c+1)*e-1/4/d^2*b*ln(d*x+c+1)*f","B"
34,1,44,38,0.027000," ","int(a+b*arctanh(d*x+c),x)","a x +b \arctanh \left(d x +c \right) x +\frac{b \arctanh \left(d x +c \right) c}{d}+\frac{b \ln \left(1-\left(d x +c \right)^{2}\right)}{2 d}"," ",0,"a*x+b*arctanh(d*x+c)*x+b/d*arctanh(d*x+c)*c+1/2*b*ln(1-(d*x+c)^2)/d","A"
35,1,202,126,0.123000," ","int((a+b*arctanh(d*x+c))/(f*x+e),x)","\frac{a \ln \left(\left(d x +c \right) f -c f +d e \right)}{f}+\frac{b \ln \left(\left(d x +c \right) f -c f +d e \right) \arctanh \left(d x +c \right)}{f}+\frac{b \ln \left(\left(d x +c \right) f -c f +d e \right) \ln \left(\frac{\left(d x +c \right) f -f}{c f -d e -f}\right)}{2 f}+\frac{b \dilog \left(\frac{\left(d x +c \right) f -f}{c f -d e -f}\right)}{2 f}-\frac{b \ln \left(\left(d x +c \right) f -c f +d e \right) \ln \left(\frac{\left(d x +c \right) f +f}{c f -d e +f}\right)}{2 f}-\frac{b \dilog \left(\frac{\left(d x +c \right) f +f}{c f -d e +f}\right)}{2 f}"," ",0,"a*ln((d*x+c)*f-c*f+d*e)/f+b*ln((d*x+c)*f-c*f+d*e)/f*arctanh(d*x+c)+1/2*b/f*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f-f)/(c*f-d*e-f))+1/2*b/f*dilog(((d*x+c)*f-f)/(c*f-d*e-f))-1/2*b/f*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f+f)/(c*f-d*e+f))-1/2*b/f*dilog(((d*x+c)*f+f)/(c*f-d*e+f))","A"
36,1,141,114,0.038000," ","int((a+b*arctanh(d*x+c))/(f*x+e)^2,x)","-\frac{d a}{\left(d f x +d e \right) f}-\frac{d b \arctanh \left(d x +c \right)}{\left(d f x +d e \right) f}-\frac{d b \ln \left(\left(d x +c \right) f -c f +d e \right)}{\left(c f -d e -f \right) \left(c f -d e +f \right)}+\frac{d b \ln \left(d x +c -1\right)}{f \left(2 c f -2 d e -2 f \right)}-\frac{d b \ln \left(d x +c +1\right)}{f \left(2 c f -2 d e +2 f \right)}"," ",0,"-d*a/(d*f*x+d*e)/f-d*b/(d*f*x+d*e)/f*arctanh(d*x+c)-d*b/(c*f-d*e-f)/(c*f-d*e+f)*ln((d*x+c)*f-c*f+d*e)+d*b/f/(2*c*f-2*d*e-2*f)*ln(d*x+c-1)-d*b/f/(2*c*f-2*d*e+2*f)*ln(d*x+c+1)","A"
37,1,236,163,0.045000," ","int((a+b*arctanh(d*x+c))/(f*x+e)^3,x)","-\frac{d^{2} a}{2 \left(d f x +d e \right)^{2} f}-\frac{d^{2} b \arctanh \left(d x +c \right)}{2 \left(d f x +d e \right)^{2} f}+\frac{d^{2} b}{2 \left(c f -d e -f \right) \left(c f -d e +f \right) \left(d f x +d e \right)}+\frac{d^{2} b f \ln \left(\left(d x +c \right) f -c f +d e \right) c}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}-\frac{d^{3} b \ln \left(\left(d x +c \right) f -c f +d e \right) e}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}-\frac{d^{2} b \ln \left(d x +c -1\right)}{4 f \left(c f -d e -f \right)^{2}}+\frac{d^{2} b \ln \left(d x +c +1\right)}{4 f \left(c f -d e +f \right)^{2}}"," ",0,"-1/2*d^2*a/(d*f*x+d*e)^2/f-1/2*d^2*b/(d*f*x+d*e)^2/f*arctanh(d*x+c)+1/2*d^2*b/(c*f-d*e-f)/(c*f-d*e+f)/(d*f*x+d*e)+d^2*b*f/(c*f-d*e-f)^2/(c*f-d*e+f)^2*ln((d*x+c)*f-c*f+d*e)*c-d^3*b/(c*f-d*e-f)^2/(c*f-d*e+f)^2*ln((d*x+c)*f-c*f+d*e)*e-1/4*d^2*b/f/(c*f-d*e-f)^2*ln(d*x+c-1)+1/4*d^2*b/f/(c*f-d*e+f)^2*ln(d*x+c+1)","A"
38,1,4401,548,0.087000," ","int((f*x+e)^3*(a+b*arctanh(d*x+c))^2,x)","\text{output too large to display}"," ",0,"1/4/d*e^3*b^2*ln(d*x+c-1)^2+1/d^3*b^2*f^2*c*e-1/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c-1)*c^3*e-3/4/d^2*b^2*f*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c^2*e^2+3/2/d^3*b^2*f^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c^2*e-3/2/d^2*b^2*f*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c*e^2+3/2/d^4*b^2*f^3*ln(d*x+c+1)*c^2+1/2/d^4*b^2*f^3*ln(d*x+c+1)*c-1/8*b^2/f*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*e^4+1/8*b^2/f*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*e^4+1/4*b^2/f*arctanh(d*x+c)*ln(d*x+c-1)*e^4+1/2*a*b/f*arctanh(d*x+c)*e^4+1/6/d*a*b*f^3*x^3+b^2/d^2*e*f^2*x-5/6*b^2/d^3*c*f^3*x+1/2*a*b/d^3*f^3*x+1/d*e^3*a*b*ln(d*x+c+1)+1/d*e^3*b^2*arctanh(d*x+c)*ln(d*x+c+1)-1/2/d*e^3*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)+1/2/d*e^3*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)-1/4/d^4*a*b*f^3*ln(d*x+c+1)+3/2/d^2*b^2*f*ln(d*x+c+1)*e^2-1/8/d^4*b^2*f^3*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)-1/2/d^4*b^2*f^3*ln(d*x+c-1)*c+1/16/d^4*b^2*f^3*ln(d*x+c-1)^2*c^4+1/6/d*b^2*f^3*arctanh(d*x+c)*x^3+13/6/d^4*b^2*f^3*arctanh(d*x+c)*c^3-1/8*b^2/f*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*e^4+1/4*a*b/f*ln(d*x+c-1)*e^4-1/4*a*b/f*ln(d*x+c+1)*e^4+1/d*e^3*b^2*arctanh(d*x+c)*ln(d*x+c-1)+1/d*e^3*a*b*ln(d*x+c-1)-1/4/d*b^2*ln(d*x+c+1)^2*c*e^3-1/4/d*b^2*ln(d*x+c-1)^2*c*e^3+1/2/d^3*b^2*f^2*ln(d*x+c-1)*e+3/8/d^4*b^2*f^3*ln(d*x+c-1)^2*c^2-1/2/d^3*b^2*f^2*ln(d*x+c+1)*e-1/d^3*b^2*f^2*dilog(1/2+1/2*d*x+1/2*c)*e+3/2/d^2*b^2*f*ln(d*x+c-1)*e^2+3/2/d^4*b^2*f^3*ln(d*x+c-1)*c^2+1/8/d^4*b^2*f^3*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)+1/4/d^4*b^2*f^3*arctanh(d*x+c)*ln(d*x+c-1)-1/4/d^4*b^2*f^3*arctanh(d*x+c)*ln(d*x+c+1)-1/8/d^4*b^2*f^3*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+1/2/d^3*b^2*f^3*arctanh(d*x+c)*x+1/2/d^4*b^2*f^3*arctanh(d*x+c)*c+3/8/d^2*b^2*f*ln(d*x+c-1)^2*e^2+1/4/d^3*b^2*f^2*ln(d*x+c-1)^2*e+1/4/d^4*b^2*f^3*ln(d*x+c+1)^2*c^3-1/4/d^4*b^2*f^3*ln(d*x+c-1)^2*c^3+3/8/d^4*b^2*f^3*ln(d*x+c+1)^2*c^2+1/4/d^4*b^2*f^3*ln(d*x+c+1)^2*c+1/d^4*b^2*f^3*dilog(1/2+1/2*d*x+1/2*c)*c-1/4*b^2/f*arctanh(d*x+c)*ln(d*x+c+1)*e^4+1/4/d^4*a*b*f^3*ln(d*x+c-1)+b^2*f^2*arctanh(d*x+c)^2*e*x^3+3/2*b^2*f*arctanh(d*x+c)^2*e^2*x^2+2*arctanh(d*x+c)*x*a*b*e^3+1/16/d^4*b^2*f^3*ln(d*x+c+1)^2*c^4-1/4/d^4*b^2*f^3*ln(d*x+c-1)^2*c+1/d^4*b^2*f^3*dilog(1/2+1/2*d*x+1/2*c)*c^3+3/8/d^2*b^2*f*ln(d*x+c+1)^2*e^2-1/4/d^3*b^2*f^2*ln(d*x+c+1)^2*e-4*a*b/d^2*f^2*c*e*x+3/2/d^3*b^2*f^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c*e+a^2*x*e^3+1/4*a^2*f^3*x^4+13/6/d^4*a*b*f^3*c^3+1/2/d^4*a*b*f^3*c-1/2/d*e^3*b^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)-3/4/d^2*b^2*f*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*e^2-1/2/d^3*b^2*f^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*e-3/4/d^2*b^2*f*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*e^2+1/2/d^3*b^2*f^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*e-1/2/d^2*b^2*f^3*arctanh(d*x+c)*x^2*c+3/2/d^3*b^2*f^3*arctanh(d*x+c)*c^2*x+1/d*b^2*f^2*arctanh(d*x+c)*e*x^2-5/d^3*b^2*f^2*arctanh(d*x+c)*e*c^2+3/2*a*b/d^3*f^3*c^2*x+3*a*b/d*f*e^2*x-1/d^4*b^2*f^3*arctanh(d*x+c)*ln(d*x+c-1)*c+3/4/d^2*b^2*f*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*e^2-1/8/d^4*b^2*f^3*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c^4-3/2/d^4*a*b*f^3*ln(d*x+c+1)*c^2-1/d^4*a*b*f^3*ln(d*x+c-1)*c-1/d^4*a*b*f^3*ln(d*x+c+1)*c-1/2/d^4*b^2*f^3*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c^3-3/4/d^4*b^2*f^3*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c^2+1/2/d^4*b^2*f^3*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c-1/2/d^4*b^2*f^3*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c+1/8/d^4*b^2*f^3*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*c^4+1/2/d^4*b^2*f^3*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*c^3+3/4/d^4*b^2*f^3*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*c^2+1/2/d^4*b^2*f^3*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*c-1/d^4*b^2*f^3*arctanh(d*x+c)*ln(d*x+c+1)*c^3-3/2/d^4*b^2*f^3*arctanh(d*x+c)*ln(d*x+c+1)*c^2-1/d^4*b^2*f^3*arctanh(d*x+c)*ln(d*x+c+1)*c+1/4/d^4*b^2*f^3*arctanh(d*x+c)*ln(d*x+c-1)*c^4+3/d^3*a*b*f^2*ln(d*x+c+1)*c*e+3/d^3*a*b*f^2*ln(d*x+c+1)*c^2*e-11/12/d^4*b^2*f^3*c^2+1/4*a^2/f*e^4-3/d^2*a*b*f*ln(d*x+c+1)*c*e^2+3/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c+1)*c*e+1/3/d^4*b^2*f^3*ln(d*x+c-1)-1/4/d*e^3*b^2*ln(d*x+c+1)^2+a^2*f^2*x^3*e+3/2*a^2*f*x^2*e^2+1/12/d^2*b^2*f^3*x^2+1/16*b^2/f*ln(d*x+c-1)^2*e^4+1/4*b^2/f*arctanh(d*x+c)^2*e^4+1/16*b^2/f*ln(d*x+c+1)^2*e^4+1/4*b^2*f^3*arctanh(d*x+c)^2*x^4+arctanh(d*x+c)^2*x*b^2*e^3-1/d*b^2*dilog(1/2+1/2*d*x+1/2*c)*e^3+1/3/d^4*b^2*f^3*ln(d*x+c+1)+1/16/d^4*b^2*f^3*ln(d*x+c-1)^2+1/16/d^4*b^2*f^3*ln(d*x+c+1)^2+3/4/d^2*b^2*f*ln(d*x+c+1)^2*c*e^2-3/d^3*b^2*f^2*ln(d*x+c-1)*c*e-3/d^3*b^2*f^2*ln(d*x+c+1)*c*e-3/2/d^2*a*b*f*ln(d*x+c+1)*e^2+1/4/d^4*a*b*f^3*ln(d*x+c-1)*c^4+1/d^3*a*b*f^2*ln(d*x+c+1)*e+3/2/d^2*a*b*f*ln(d*x+c-1)*e^2+3/2/d^4*a*b*f^3*ln(d*x+c-1)*c^2-3/4/d^3*b^2*f^2*ln(d*x+c-1)^2*c*e+3/4/d^3*b^2*f^2*ln(d*x+c-1)^2*c^2*e+3/d*b^2*f*arctanh(d*x+c)*e^2*x+3/d^2*b^2*f*arctanh(d*x+c)*e^2*c-1/d*a*b*ln(d*x+c-1)*c*e^3-3/d^3*b^2*f^2*dilog(1/2+1/2*d*x+1/2*c)*c^2*e+3/d^2*b^2*f*dilog(1/2+1/2*d*x+1/2*c)*c*e^2-1/2/d^3*b^2*f^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*e+3/2/d^4*b^2*f^3*arctanh(d*x+c)*ln(d*x+c-1)*c^2-1/d^4*a*b*f^3*ln(d*x+c-1)*c^3-1/d^4*a*b*f^3*ln(d*x+c+1)*c^3-3/4/d^3*b^2*f^2*ln(d*x+c+1)^2*c*e+3/8/d^2*b^2*f*ln(d*x+c+1)^2*c^2*e^2-1/4/d^3*b^2*f^2*ln(d*x+c+1)^2*c^3*e+1/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c-1)*e+1/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c+1)*e+3/2/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c-1)*e^2-3/2/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c+1)*e^2-1/8/d^4*b^2*f^3*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c^4+1/2/d^4*b^2*f^3*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c^3-3/4/d^4*b^2*f^3*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c^2-3/4/d^2*b^2*f*ln(d*x+c-1)^2*c*e^2+1/d*a*b*ln(d*x+c+1)*c*e^3+2*a*b*f^2*arctanh(d*x+c)*e*x^3+3*a*b*f*arctanh(d*x+c)*e^2*x^2-3/4/d^3*b^2*f^2*ln(d*x+c+1)^2*c^2*e-1/2/d*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*c*e^3+1/d*b^2*arctanh(d*x+c)*ln(d*x+c+1)*c*e^3-1/d*b^2*arctanh(d*x+c)*ln(d*x+c-1)*c*e^3-3/d^2*a*b*f*ln(d*x+c-1)*c*e^2-4/d^2*b^2*f^2*arctanh(d*x+c)*e*x*c+3/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c+1)*c^2*e-3/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c+1)*c*e^2+3/2/d^2*b^2*f*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*c*e^2+1/2/d^3*b^2*f^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c^3*e-3/2/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c+1)*c^2*e^2-3/2/d^3*b^2*f^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*c*e+1/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c+1)*c^3*e+1/2*a*b*f^3*arctanh(d*x+c)*x^4+1/d^3*a*b*f^2*ln(d*x+c+1)*c^3*e+3/d^3*a*b*f^2*ln(d*x+c-1)*c^2*e+3/2/d^2*a*b*f*ln(d*x+c-1)*c^2*e^2-1/d^3*a*b*f^2*ln(d*x+c-1)*c^3*e-1/2/d^3*b^2*f^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*c^3*e-3/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c-1)*c*e-3/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c-1)*c*e^2+3/4/d^2*b^2*f*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*c^2*e^2-3/2/d^3*b^2*f^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)*c^2*e-3/d^3*a*b*f^2*ln(d*x+c-1)*c*e-3/2/d^2*a*b*f*ln(d*x+c+1)*c^2*e^2+3/2/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c-1)*c^2*e^2+1/2/d^3*b^2*f^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c^3*e-3/4/d^2*b^2*f*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c^2*e^2-3/2/d^3*b^2*f^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c^2*e+3/2/d^2*b^2*f*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c*e^2+3/2/d^3*b^2*f^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c*e+1/2/d*b^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c*e^3+1/2/d*b^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c*e^3+1/d^3*a*b*f^2*ln(d*x+c-1)*e-1/4/d^4*a*b*f^3*ln(d*x+c+1)*c^4+3/8/d^2*b^2*f*ln(d*x+c-1)^2*c^2*e^2-1/4/d^3*b^2*f^2*ln(d*x+c-1)^2*c^3*e-5/d^3*a*b*f^2*c^2*e+3/d^2*a*b*f*c*e^2+3/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c-1)*c^2*e-1/2/d^2*a*b*f^3*c*x^2+1/d*a*b*f^2*e*x^2-1/4/d^4*b^2*f^3*arctanh(d*x+c)*ln(d*x+c+1)*c^4-1/d^4*b^2*f^3*arctanh(d*x+c)*ln(d*x+c-1)*c^3","B"
39,1,2694,360,0.071000," ","int((f*x+e)^2*(a+b*arctanh(d*x+c))^2,x)","\text{Expression too large to display}"," ",0,"-1/d*e^2*b^2*dilog(1/2+1/2*d*x+1/2*c)-1/4/d*e^2*b^2*ln(d*x+c+1)^2+1/4/d*e^2*b^2*ln(d*x+c-1)^2+1/3*b^2*f^2*x/d^2-1/d*b^2*arctanh(d*x+c)*ln(d*x+c-1)*c*e^2+1/d*b^2*arctanh(d*x+c)*ln(d*x+c+1)*c*e^2+1/d*a*b*ln(d*x+c+1)*c*e^2-1/2/d^2*b^2*f*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*e+1/6/d^3*b^2*f^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c^3+1/2/d^3*b^2*f^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c^2+1/2/d^3*b^2*f^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c-1/6/d^3*b^2*f^2*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)*c^3-1/2/d^3*b^2*f^2*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)*c^2+1/6/d^3*b^2*f^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c^3-1/2/d^3*b^2*f^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c^2+1/2/d^3*b^2*f^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c-1/2/d^3*b^2*f^2*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)*c+1/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c+1)*c^2-1/3/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c-1)*c^3+1/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c-1)*c^2-1/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c-1)*c-1/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c+1)*e+1/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c-1)*e-1/2/d^2*b^2*f*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*e-1/d*a*b*ln(d*x+c-1)*c*e^2-1/3/d^3*a*b*f^2*ln(d*x+c-1)*c^3+1/2/d^2*b^2*f*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)*e+1/3/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c+1)*c^3+1/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c+1)*c+1/4/d^2*b^2*f*ln(d*x+c-1)^2*c^2*e+1/d^3*a*b*f^2*ln(d*x+c-1)*c^2+1/3/d^3*a*b*f^2*ln(d*x+c+1)*c^3+2/d*b^2*f*arctanh(d*x+c)*e*x+2/d^2*b^2*f*arctanh(d*x+c)*e*c+2/d^2*b^2*f*dilog(1/2+1/2*d*x+1/2*c)*c*e+1/d^3*a*b*f^2*ln(d*x+c+1)*c^2+1/d^3*a*b*f^2*ln(d*x+c+1)*c-1/d^3*a*b*f^2*ln(d*x+c-1)*c+2*a*b*f*arctanh(d*x+c)*e*x^2-4/3*a*b/d^2*x*c*f^2+2*a*b/d*x*e*f-4/3/d^2*b^2*f^2*arctanh(d*x+c)*x*c-1/2/d^2*b^2*f*ln(d*x+c-1)^2*c*e+1/4/d^3*b^2*f^2*ln(d*x+c-1)^2*c^2-1/4/d^3*b^2*f^2*ln(d*x+c-1)^2*c+1/4/d^2*b^2*f*ln(d*x+c-1)^2*e-1/12/d^3*b^2*f^2*ln(d*x+c-1)^2*c^3-1/d^3*b^2*f^2*ln(d*x+c+1)*c+1/4/d^2*b^2*f*ln(d*x+c+1)^2*e+1/d^2*b^2*f*ln(d*x+c+1)*e+b^2*f*arctanh(d*x+c)^2*e*x^2+1/3*a*b/f*ln(d*x+c-1)*e^3-1/6/d^3*b^2*f^2*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)+1/3/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c-1)+1/3/d^3*b^2*f^2*arctanh(d*x+c)*ln(d*x+c+1)+1/3/d*b^2*f^2*arctanh(d*x+c)*x^2-5/3/d^3*b^2*f^2*arctanh(d*x+c)*c^2-1/d^3*b^2*f^2*ln(d*x+c-1)*c+1/d^2*b^2*f*ln(d*x+c-1)*e-1/2/d^2*b^2*f*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c^2*e-1/d^2*b^2*f*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c*e+1/2/d^2*b^2*f*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)*c^2*e+1/d^2*b^2*f*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c*e+1/d^2*b^2*f*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)*c*e-2/d^2*a*b*f*ln(d*x+c-1)*c*e-1/d^2*a*b*f*ln(d*x+c+1)*c^2*e+1/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c-1)*c^2*e-1/4/d^3*b^2*f^2*ln(d*x+c+1)^2*c+1/6/d^3*b^2*f^2*ln(d*x+c-1)-1/6/d^3*b^2*f^2*ln(d*x+c+1)+1/12/d^3*b^2*f^2*ln(d*x+c-1)^2-1/3/d^3*b^2*f^2*dilog(1/2+1/2*d*x+1/2*c)-1/12/d^3*b^2*f^2*ln(d*x+c+1)^2+1/3*a^2/f*e^3+1/3/d^3*b^2*f^2*c+1/12*b^2/f*ln(d*x+c-1)^2*e^3+1/3*b^2/f*arctanh(d*x+c)^2*e^3+a^2*f*x^2*e+1/3*b^2*f^2*arctanh(d*x+c)^2*x^3+arctanh(d*x+c)^2*x*b^2*e^2+1/12*b^2/f*ln(d*x+c+1)^2*e^3+1/3/d^3*a*b*f^2*ln(d*x+c+1)+1/3/d*a*b*f^2*x^2+2/3*a*b*f^2*arctanh(d*x+c)*x^3+2*arctanh(d*x+c)*x*a*b*e^2+2/d^2*a*b*f*c*e+1/d*e^2*b^2*arctanh(d*x+c)*ln(d*x+c-1)+1/d*e^2*b^2*arctanh(d*x+c)*ln(d*x+c+1)-1/2/d*e^2*b^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+1/2/d*e^2*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)-1/2/d*e^2*b^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)+1/d*e^2*a*b*ln(d*x+c+1)+1/d*e^2*a*b*ln(d*x+c-1)+a^2*x*e^2+1/3*a^2*f^2*x^3-1/3*b^2/f*arctanh(d*x+c)*ln(d*x+c+1)*e^3-1/6*b^2/f*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*e^3-1/6*b^2/f*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*e^3-1/4/d*b^2*ln(d*x+c-1)^2*c*e^2-1/4/d*b^2*ln(d*x+c+1)^2*c*e^2-5/3/d^3*a*b*f^2*c^2-1/6/d^3*b^2*f^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+1/6/d^3*b^2*f^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)-1/d^3*b^2*f^2*dilog(1/2+1/2*d*x+1/2*c)*c^2-1/12/d^3*b^2*f^2*ln(d*x+c+1)^2*c^3+1/3/d^3*a*b*f^2*ln(d*x+c-1)-1/4/d^3*b^2*f^2*ln(d*x+c+1)^2*c^2-1/3*a*b/f*ln(d*x+c+1)*e^3+2/3*a*b/f*arctanh(d*x+c)*e^3+1/6*b^2/f*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)*e^3+1/3*b^2/f*arctanh(d*x+c)*ln(d*x+c-1)*e^3+1/d^2*a*b*f*ln(d*x+c-1)*c^2*e-2/d^2*a*b*f*ln(d*x+c+1)*c*e-2/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c+1)*c*e-2/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c-1)*c*e-1/d^2*b^2*f*arctanh(d*x+c)*ln(d*x+c+1)*c^2*e-1/2/d^2*b^2*f*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c^2*e+1/4/d^2*b^2*f*ln(d*x+c+1)^2*c^2*e+1/d^2*a*b*f*ln(d*x+c-1)*e-1/d^2*a*b*f*ln(d*x+c+1)*e+1/2/d^2*b^2*f*ln(d*x+c+1)^2*c*e+1/2/d*b^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c*e^2-1/2/d*b^2*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)*c*e^2+1/2/d*b^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c*e^2","B"
40,1,857,217,0.064000," ","int((f*x+e)*(a+b*arctanh(d*x+c))^2,x)","\frac{a b f x}{d}+\frac{b^{2} \arctanh \left(d x +c \right)^{2} f \,x^{2}}{2}+\arctanh \left(d x +c \right)^{2} x \,b^{2} e +\frac{b^{2} \ln \left(d x +c -1\right)^{2} e}{4 d}-\frac{b^{2} \ln \left(d x +c +1\right)^{2} e}{4 d}+\frac{b^{2} \ln \left(d x +c -1\right) f}{2 d^{2}}+\frac{b^{2} \ln \left(d x +c +1\right) f}{2 d^{2}}+\frac{b^{2} \ln \left(d x +c +1\right)^{2} f}{8 d^{2}}+\frac{b^{2} \ln \left(d x +c -1\right)^{2} f}{8 d^{2}}-\frac{b^{2} \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right) e}{d}+\frac{a^{2} c e}{d}-\frac{a^{2} c^{2} f}{2 d^{2}}+\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right) f}{2 d^{2}}-\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right) f}{2 d^{2}}+\frac{\arctanh \left(d x +c \right)^{2} b^{2} c e}{d}-\frac{b^{2} \arctanh \left(d x +c \right)^{2} c^{2} f}{2 d^{2}}+\frac{b^{2} \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right) c f}{d^{2}}+a b \arctanh \left(d x +c \right) f \,x^{2}+2 \arctanh \left(d x +c \right) x a b e +\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right) e}{d}+\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right) e}{d}+\frac{b^{2} \arctanh \left(d x +c \right) f x}{d}+\frac{b^{2} \arctanh \left(d x +c \right) f c}{d^{2}}-\frac{a b \ln \left(d x +c +1\right) c f}{d^{2}}-\frac{a b \ln \left(d x +c -1\right) c f}{d^{2}}-\frac{b^{2} \ln \left(d x +c +1\right) \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) c f}{2 d^{2}}+\frac{b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right) c f}{2 d^{2}}+\frac{b^{2} \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right) \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) c f}{2 d^{2}}-\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right) c f}{d^{2}}-\frac{b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right) c f}{d^{2}}-\frac{a b \arctanh \left(d x +c \right) f \,c^{2}}{d^{2}}+\frac{2 \arctanh \left(d x +c \right) a b c e}{d}-\frac{b^{2} \ln \left(d x +c +1\right) \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) f}{4 d^{2}}-\frac{e \,b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 d}-\frac{b^{2} \ln \left(d x +c -1\right)^{2} c f}{4 d^{2}}+\frac{b^{2} \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right) \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) f}{4 d^{2}}+\frac{b^{2} \ln \left(d x +c +1\right) \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) e}{2 d}-\frac{b^{2} \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right) \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) e}{2 d}+\frac{a b \ln \left(d x +c -1\right) e}{d}+\frac{a b \ln \left(d x +c +1\right) e}{d}+\frac{a^{2} x^{2} f}{2}+x e \,a^{2}+\frac{a b c f}{d^{2}}+\frac{b^{2} \ln \left(d x +c +1\right)^{2} c f}{4 d^{2}}-\frac{b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right) f}{4 d^{2}}+\frac{a b \ln \left(d x +c -1\right) f}{2 d^{2}}-\frac{a b \ln \left(d x +c +1\right) f}{2 d^{2}}"," ",0,"a*b*f*x/d+1/4/d*b^2*ln(d*x+c-1)^2*e-1/4/d*b^2*ln(d*x+c+1)^2*e-1/d*b^2*dilog(1/2+1/2*d*x+1/2*c)*e+1/2*b^2*arctanh(d*x+c)^2*f*x^2+arctanh(d*x+c)^2*x*b^2*e+1/2/d^2*b^2*ln(d*x+c-1)*f+1/2/d^2*b^2*ln(d*x+c+1)*f+1/8/d^2*b^2*ln(d*x+c+1)^2*f+1/8/d^2*b^2*ln(d*x+c-1)^2*f+1/d*a^2*c*e-1/2/d^2*a^2*c^2*f+1/2/d^2*b^2*arctanh(d*x+c)*ln(d*x+c-1)*f-1/2/d^2*b^2*arctanh(d*x+c)*ln(d*x+c+1)*f-1/d^2*a*b*ln(d*x+c+1)*c*f-1/d^2*a*b*ln(d*x+c-1)*c*f-1/d^2*b^2*arctanh(d*x+c)*ln(d*x+c-1)*c*f-1/2/d^2*b^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*c*f+1/2/d^2*b^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*c*f+1/2/d^2*b^2*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)*c*f-1/d^2*b^2*arctanh(d*x+c)*ln(d*x+c+1)*c*f-1/d^2*a*b*arctanh(d*x+c)*f*c^2+2/d*arctanh(d*x+c)*a*b*c*e-1/4/d^2*b^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*f+1/d*arctanh(d*x+c)^2*b^2*c*e-1/2/d*e*b^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)-1/2/d^2*b^2*arctanh(d*x+c)^2*c^2*f+1/d^2*b^2*dilog(1/2+1/2*d*x+1/2*c)*c*f-1/4/d^2*b^2*ln(d*x+c-1)^2*c*f+a*b*arctanh(d*x+c)*f*x^2+2*arctanh(d*x+c)*x*a*b*e+1/4/d^2*b^2*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)*f+1/d*b^2*arctanh(d*x+c)*ln(d*x+c+1)*e+1/2/d*b^2*ln(d*x+c+1)*ln(-1/2*d*x-1/2*c+1/2)*e+1/d*b^2*arctanh(d*x+c)*ln(d*x+c-1)*e-1/2/d*b^2*ln(1/2+1/2*d*x+1/2*c)*ln(-1/2*d*x-1/2*c+1/2)*e+1/d*a*b*ln(d*x+c-1)*e+1/d*a*b*ln(d*x+c+1)*e+1/2*a^2*x^2*f+x*e*a^2+1/d^2*a*b*c*f+1/d*b^2*arctanh(d*x+c)*f*x+1/d^2*b^2*arctanh(d*x+c)*f*c+1/4/d^2*b^2*ln(d*x+c+1)^2*c*f-1/4/d^2*b^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)*f+1/2/d^2*a*b*ln(d*x+c-1)*f-1/2/d^2*a*b*ln(d*x+c+1)*f","B"
41,1,174,99,0.227000," ","int((a+b*arctanh(d*x+c))^2,x)","\arctanh \left(d x +c \right)^{2} x \,b^{2}+\frac{\arctanh \left(d x +c \right)^{2} b^{2} c}{d}+2 \arctanh \left(d x +c \right) x a b +\frac{b^{2} \arctanh \left(d x +c \right)^{2}}{d}-\frac{2 \arctanh \left(d x +c \right) \ln \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) b^{2}}{d}+\frac{2 \arctanh \left(d x +c \right) a b c}{d}+a^{2} x +\frac{a b \ln \left(1-\left(d x +c \right)^{2}\right)}{d}-\frac{\polylog \left(2, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) b^{2}}{d}+\frac{a^{2} c}{d}"," ",0,"arctanh(d*x+c)^2*x*b^2+1/d*arctanh(d*x+c)^2*b^2*c+2*arctanh(d*x+c)*x*a*b+1/d*b^2*arctanh(d*x+c)^2-2/d*arctanh(d*x+c)*ln(1+(d*x+c+1)^2/(1-(d*x+c)^2))*b^2+2/d*arctanh(d*x+c)*a*b*c+a^2*x+1/d*a*b*ln(1-(d*x+c)^2)-1/d*polylog(2,-(d*x+c+1)^2/(1-(d*x+c)^2))*b^2+1/d*a^2*c","A"
42,1,1984,210,0.967000," ","int((a+b*arctanh(d*x+c))^2/(f*x+e),x)","\frac{a b \ln \left(\left(d x +c \right) f -c f +d e \right) \ln \left(\frac{\left(d x +c \right) f -f}{c f -d e -f}\right)}{f}-\frac{a b \ln \left(\left(d x +c \right) f -c f +d e \right) \ln \left(\frac{\left(d x +c \right) f +f}{c f -d e +f}\right)}{f}+\frac{i b^{2} \arctanh \left(d x +c \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(i \left(c f \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)+\left(-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right) e d +\left(1-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) f \right)\right) \mathrm{csgn}\left(\frac{i \left(c f \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)+\left(-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right) e d +\left(1-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) f \right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)}{2 f}+\frac{b^{2} \polylog \left(3, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{2 f}+\frac{b^{2} \polylog \left(3, \frac{\left(c f -d e -f \right) \left(d x +c +1\right)^{2}}{\left(1-\left(d x +c \right)^{2}\right) \left(-c f +d e -f \right)}\right)}{2 c f -2 d e -2 f}+\frac{b^{2} \ln \left(\left(d x +c \right) f -c f +d e \right) \arctanh \left(d x +c \right)^{2}}{f}-\frac{b^{2} \arctanh \left(d x +c \right)^{2} \ln \left(c f \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)+\left(-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right) e d +\left(1-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) f \right)}{f}-\frac{b^{2} \arctanh \left(d x +c \right) \polylog \left(2, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{f}-\frac{b^{2} \arctanh \left(d x +c \right) \polylog \left(2, \frac{\left(c f -d e -f \right) \left(d x +c +1\right)^{2}}{\left(1-\left(d x +c \right)^{2}\right) \left(-c f +d e -f \right)}\right)}{c f -d e -f}+\frac{a b \dilog \left(\frac{\left(d x +c \right) f -f}{c f -d e -f}\right)}{f}-\frac{b^{2} \arctanh \left(d x +c \right)^{2} \ln \left(1-\frac{\left(c f -d e -f \right) \left(d x +c +1\right)^{2}}{\left(1-\left(d x +c \right)^{2}\right) \left(-c f +d e -f \right)}\right)}{c f -d e -f}-\frac{a b \dilog \left(\frac{\left(d x +c \right) f +f}{c f -d e +f}\right)}{f}-\frac{b^{2} c \polylog \left(3, \frac{\left(c f -d e -f \right) \left(d x +c +1\right)^{2}}{\left(1-\left(d x +c \right)^{2}\right) \left(-c f +d e -f \right)}\right)}{2 \left(c f -d e -f \right)}+\frac{d \,b^{2} e \polylog \left(3, \frac{\left(c f -d e -f \right) \left(d x +c +1\right)^{2}}{\left(1-\left(d x +c \right)^{2}\right) \left(-c f +d e -f \right)}\right)}{2 f \left(c f -d e -f \right)}+\frac{i b^{2} \arctanh \left(d x +c \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c f \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)+\left(-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right) e d +\left(1-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) f \right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2}}{f}-\frac{i b^{2} \arctanh \left(d x +c \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c f \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)+\left(-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right) e d +\left(1-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) f \right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{3}}{2 f}+\frac{b^{2} c \arctanh \left(d x +c \right)^{2} \ln \left(1-\frac{\left(c f -d e -f \right) \left(d x +c +1\right)^{2}}{\left(1-\left(d x +c \right)^{2}\right) \left(-c f +d e -f \right)}\right)}{c f -d e -f}+\frac{b^{2} c \arctanh \left(d x +c \right) \polylog \left(2, \frac{\left(c f -d e -f \right) \left(d x +c +1\right)^{2}}{\left(1-\left(d x +c \right)^{2}\right) \left(-c f +d e -f \right)}\right)}{c f -d e -f}+\frac{2 a b \ln \left(\left(d x +c \right) f -c f +d e \right) \arctanh \left(d x +c \right)}{f}-\frac{i b^{2} \pi  \arctanh \left(d x +c \right)^{2}}{f}-\frac{d \,b^{2} e \arctanh \left(d x +c \right)^{2} \ln \left(1-\frac{\left(c f -d e -f \right) \left(d x +c +1\right)^{2}}{\left(1-\left(d x +c \right)^{2}\right) \left(-c f +d e -f \right)}\right)}{f \left(c f -d e -f \right)}-\frac{d \,b^{2} e \arctanh \left(d x +c \right) \polylog \left(2, \frac{\left(c f -d e -f \right) \left(d x +c +1\right)^{2}}{\left(1-\left(d x +c \right)^{2}\right) \left(-c f +d e -f \right)}\right)}{f \left(c f -d e -f \right)}-\frac{i b^{2} \arctanh \left(d x +c \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right) \mathrm{csgn}\left(\frac{i \left(c f \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)+\left(-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right) e d +\left(1-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) f \right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2}}{2 f}-\frac{i b^{2} \arctanh \left(d x +c \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(c f \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)+\left(-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right) e d +\left(1-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) f \right)\right) \mathrm{csgn}\left(\frac{i \left(c f \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)+\left(-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}-1\right) e d +\left(1-\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) f \right)}{1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}}\right)^{2}}{2 f}+\frac{a^{2} \ln \left(\left(d x +c \right) f -c f +d e \right)}{f}"," ",0,"a*b/f*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f-f)/(c*f-d*e-f))-a*b/f*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f+f)/(c*f-d*e+f))+b^2*c/(c*f-d*e-f)*arctanh(d*x+c)^2*ln(1-(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+b^2*c/(c*f-d*e-f)*arctanh(d*x+c)*polylog(2,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))-I*b^2/f*Pi*arctanh(d*x+c)^2+1/2*I*b^2/f*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))+b^2*ln((d*x+c)*f-c*f+d*e)/f*arctanh(d*x+c)^2-b^2/f*arctanh(d*x+c)^2*ln(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)-b^2/f*arctanh(d*x+c)*polylog(2,-(d*x+c+1)^2/(1-(d*x+c)^2))-b^2/(c*f-d*e-f)*arctanh(d*x+c)*polylog(2,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+a*b/f*dilog(((d*x+c)*f-f)/(c*f-d*e-f))-b^2/(c*f-d*e-f)*arctanh(d*x+c)^2*ln(1-(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))-a*b/f*dilog(((d*x+c)*f+f)/(c*f-d*e+f))-1/2*b^2*c/(c*f-d*e-f)*polylog(3,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+2*a*b*ln((d*x+c)*f-c*f+d*e)/f*arctanh(d*x+c)+1/2*d*b^2/f*e/(c*f-d*e-f)*polylog(3,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+I*b^2/f*arctanh(d*x+c)^2*Pi*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2-1/2*I*b^2/f*arctanh(d*x+c)^2*Pi*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3-1/2*I*b^2/f*arctanh(d*x+c)^2*Pi*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2-d*b^2/f*e/(c*f-d*e-f)*arctanh(d*x+c)^2*ln(1-(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))-d*b^2/f*e/(c*f-d*e-f)*arctanh(d*x+c)*polylog(2,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))-1/2*I*b^2/f*arctanh(d*x+c)^2*Pi*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2+1/2*b^2/(c*f-d*e-f)*polylog(3,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+a^2*ln((d*x+c)*f-c*f+d*e)/f+1/2*b^2/f*polylog(3,-(d*x+c+1)^2/(1-(d*x+c)^2))","C"
43,1,783,482,0.080000," ","int((a+b*arctanh(d*x+c))^2/(f*x+e)^2,x)","-\frac{d \,a^{2}}{\left(d f x +d e \right) f}-\frac{d \,b^{2} \arctanh \left(d x +c \right)^{2}}{\left(d f x +d e \right) f}-\frac{2 d \,b^{2} \arctanh \left(d x +c \right) \ln \left(\left(d x +c \right) f -c f +d e \right)}{\left(c f -d e -f \right) \left(c f -d e +f \right)}+\frac{2 d \,b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{f \left(2 c f -2 d e -2 f \right)}-\frac{2 d \,b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{f \left(2 c f -2 d e +2 f \right)}-\frac{d \,b^{2} \ln \left(\left(d x +c \right) f -c f +d e \right) \ln \left(\frac{\left(d x +c \right) f -f}{c f -d e -f}\right)}{\left(c f -d e -f \right) \left(c f -d e +f \right)}-\frac{d \,b^{2} \dilog \left(\frac{\left(d x +c \right) f -f}{c f -d e -f}\right)}{\left(c f -d e -f \right) \left(c f -d e +f \right)}+\frac{d \,b^{2} \ln \left(\left(d x +c \right) f -c f +d e \right) \ln \left(\frac{\left(d x +c \right) f +f}{c f -d e +f}\right)}{\left(c f -d e -f \right) \left(c f -d e +f \right)}+\frac{d \,b^{2} \dilog \left(\frac{\left(d x +c \right) f +f}{c f -d e +f}\right)}{\left(c f -d e -f \right) \left(c f -d e +f \right)}+\frac{d \,b^{2} \ln \left(d x +c -1\right)^{2}}{4 f \left(c f -d e -f \right)}-\frac{d \,b^{2} \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 f \left(c f -d e -f \right)}-\frac{d \,b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 f \left(c f -d e -f \right)}+\frac{d \,b^{2} \ln \left(d x +c +1\right)^{2}}{4 f \left(c f -d e +f \right)}-\frac{d \,b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{2 f \left(c f -d e +f \right)}+\frac{d \,b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 f \left(c f -d e +f \right)}+\frac{d \,b^{2} \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 f \left(c f -d e +f \right)}-\frac{2 d a b \arctanh \left(d x +c \right)}{\left(d f x +d e \right) f}-\frac{2 d a b \ln \left(\left(d x +c \right) f -c f +d e \right)}{\left(c f -d e -f \right) \left(c f -d e +f \right)}+\frac{2 d a b \ln \left(d x +c -1\right)}{f \left(2 c f -2 d e -2 f \right)}-\frac{2 d a b \ln \left(d x +c +1\right)}{f \left(2 c f -2 d e +2 f \right)}"," ",0,"-d*a^2/(d*f*x+d*e)/f-d*b^2/(d*f*x+d*e)/f*arctanh(d*x+c)^2-2*d*b^2*arctanh(d*x+c)/(c*f-d*e-f)/(c*f-d*e+f)*ln((d*x+c)*f-c*f+d*e)+2*d*b^2/f*arctanh(d*x+c)/(2*c*f-2*d*e-2*f)*ln(d*x+c-1)-2*d*b^2/f*arctanh(d*x+c)/(2*c*f-2*d*e+2*f)*ln(d*x+c+1)-d*b^2/(c*f-d*e-f)/(c*f-d*e+f)*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f-f)/(c*f-d*e-f))-d*b^2/(c*f-d*e-f)/(c*f-d*e+f)*dilog(((d*x+c)*f-f)/(c*f-d*e-f))+d*b^2/(c*f-d*e-f)/(c*f-d*e+f)*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f+f)/(c*f-d*e+f))+d*b^2/(c*f-d*e-f)/(c*f-d*e+f)*dilog(((d*x+c)*f+f)/(c*f-d*e+f))+1/4*d*b^2/f/(c*f-d*e-f)*ln(d*x+c-1)^2-1/2*d*b^2/f/(c*f-d*e-f)*dilog(1/2+1/2*d*x+1/2*c)-1/2*d*b^2/f/(c*f-d*e-f)*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+1/4*d*b^2/f/(c*f-d*e+f)*ln(d*x+c+1)^2-1/2*d*b^2/f/(c*f-d*e+f)*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)+1/2*d*b^2/f/(c*f-d*e+f)*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)+1/2*d*b^2/f/(c*f-d*e+f)*dilog(1/2+1/2*d*x+1/2*c)-2*d*a*b/(d*f*x+d*e)/f*arctanh(d*x+c)-2*d*a*b/(c*f-d*e-f)/(c*f-d*e+f)*ln((d*x+c)*f-c*f+d*e)+2*d*a*b/f/(2*c*f-2*d*e-2*f)*ln(d*x+c-1)-2*d*a*b/f/(2*c*f-2*d*e+2*f)*ln(d*x+c+1)","A"
44,1,1428,735,0.094000," ","int((a+b*arctanh(d*x+c))^2/(f*x+e)^3,x)","\frac{d^{2} a b \ln \left(d x +c +1\right)}{2 f \left(c f -d e +f \right)^{2}}+\frac{d^{2} b^{2} f \ln \left(\left(d x +c \right) f -c f +d e \right)}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}-\frac{d^{2} b^{2} \ln \left(d x +c -1\right)}{\left(c f -d e -f \right) \left(c f -d e +f \right) \left(2 c f -2 d e -2 f \right)}+\frac{d^{2} b^{2} \ln \left(d x +c +1\right)}{\left(c f -d e -f \right) \left(c f -d e +f \right) \left(2 c f -2 d e +2 f \right)}-\frac{d^{2} b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{2 f \left(c f -d e -f \right)^{2}}-\frac{d^{2} b^{2} \arctanh \left(d x +c \right)^{2}}{2 \left(d f x +d e \right)^{2} f}-\frac{d^{2} a^{2}}{2 \left(d f x +d e \right)^{2} f}+\frac{d^{2} b^{2} f \ln \left(\left(d x +c \right) f -c f +d e \right) \ln \left(\frac{\left(d x +c \right) f -f}{c f -d e -f}\right) c}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}-\frac{d^{2} b^{2} f \ln \left(\left(d x +c \right) f -c f +d e \right) \ln \left(\frac{\left(d x +c \right) f +f}{c f -d e +f}\right) c}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}+\frac{2 d^{2} a b f \ln \left(\left(d x +c \right) f -c f +d e \right) c}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}+\frac{2 d^{2} b^{2} f \arctanh \left(d x +c \right) \ln \left(\left(d x +c \right) f -c f +d e \right) c}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}+\frac{d^{2} b^{2} \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{4 f \left(c f -d e -f \right)^{2}}-\frac{d^{2} b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{4 f \left(c f -d e +f \right)^{2}}+\frac{d^{2} b^{2} \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{4 f \left(c f -d e +f \right)^{2}}-\frac{d^{2} a b \ln \left(d x +c -1\right)}{2 f \left(c f -d e -f \right)^{2}}+\frac{d^{2} a b}{\left(c f -d e -f \right) \left(c f -d e +f \right) \left(d f x +d e \right)}+\frac{d^{3} b^{2} \dilog \left(\frac{\left(d x +c \right) f +f}{c f -d e +f}\right) e}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}-\frac{d^{3} b^{2} \dilog \left(\frac{\left(d x +c \right) f -f}{c f -d e -f}\right) e}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}+\frac{d^{2} b^{2} \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{2 f \left(c f -d e +f \right)^{2}}+\frac{d^{2} b^{2} \arctanh \left(d x +c \right)}{\left(c f -d e -f \right) \left(c f -d e +f \right) \left(d f x +d e \right)}-\frac{d^{2} a b \arctanh \left(d x +c \right)}{\left(d f x +d e \right)^{2} f}-\frac{d^{2} b^{2} \ln \left(d x +c +1\right)^{2}}{8 f \left(c f -d e +f \right)^{2}}-\frac{d^{2} b^{2} \ln \left(d x +c -1\right)^{2}}{8 f \left(c f -d e -f \right)^{2}}-\frac{d^{2} b^{2} \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{4 f \left(c f -d e +f \right)^{2}}-\frac{2 d^{3} a b \ln \left(\left(d x +c \right) f -c f +d e \right) e}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}-\frac{d^{3} b^{2} \ln \left(\left(d x +c \right) f -c f +d e \right) \ln \left(\frac{\left(d x +c \right) f -f}{c f -d e -f}\right) e}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}+\frac{d^{3} b^{2} \ln \left(\left(d x +c \right) f -c f +d e \right) \ln \left(\frac{\left(d x +c \right) f +f}{c f -d e +f}\right) e}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}-\frac{d^{2} b^{2} f \dilog \left(\frac{\left(d x +c \right) f +f}{c f -d e +f}\right) c}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}-\frac{2 d^{3} b^{2} \arctanh \left(d x +c \right) \ln \left(\left(d x +c \right) f -c f +d e \right) e}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}+\frac{d^{2} b^{2} f \dilog \left(\frac{\left(d x +c \right) f -f}{c f -d e -f}\right) c}{\left(c f -d e -f \right)^{2} \left(c f -d e +f \right)^{2}}+\frac{d^{2} b^{2} \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{4 f \left(c f -d e -f \right)^{2}}"," ",0,"1/2*d^2*a*b/f/(c*f-d*e+f)^2*ln(d*x+c+1)+d^2*b^2*f/(c*f-d*e-f)^2/(c*f-d*e+f)^2*ln((d*x+c)*f-c*f+d*e)-d^2*b^2/(c*f-d*e-f)/(c*f-d*e+f)/(2*c*f-2*d*e-2*f)*ln(d*x+c-1)+d^2*b^2/(c*f-d*e-f)/(c*f-d*e+f)/(2*c*f-2*d*e+2*f)*ln(d*x+c+1)-1/2*d^2*a^2/(d*f*x+d*e)^2/f+d^2*b^2*f/(c*f-d*e-f)^2/(c*f-d*e+f)^2*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f-f)/(c*f-d*e-f))*c-d^2*b^2*f/(c*f-d*e-f)^2/(c*f-d*e+f)^2*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f+f)/(c*f-d*e+f))*c+2*d^2*a*b*f/(c*f-d*e-f)^2/(c*f-d*e+f)^2*ln((d*x+c)*f-c*f+d*e)*c+2*d^2*b^2*f*arctanh(d*x+c)/(c*f-d*e-f)^2/(c*f-d*e+f)^2*ln((d*x+c)*f-c*f+d*e)*c+1/4*d^2*b^2/f/(c*f-d*e-f)^2*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)-1/4*d^2*b^2/f/(c*f-d*e+f)^2*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)+1/4*d^2*b^2/f/(c*f-d*e+f)^2*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)-1/2*d^2*a*b/f/(c*f-d*e-f)^2*ln(d*x+c-1)+d^2*a*b/(c*f-d*e-f)/(c*f-d*e+f)/(d*f*x+d*e)+d^3*b^2/(c*f-d*e-f)^2/(c*f-d*e+f)^2*dilog(((d*x+c)*f+f)/(c*f-d*e+f))*e+1/4*d^2*b^2/f/(c*f-d*e-f)^2*dilog(1/2+1/2*d*x+1/2*c)-1/8*d^2*b^2/f/(c*f-d*e+f)^2*ln(d*x+c+1)^2-1/4*d^2*b^2/f/(c*f-d*e+f)^2*dilog(1/2+1/2*d*x+1/2*c)-1/8*d^2*b^2/f/(c*f-d*e-f)^2*ln(d*x+c-1)^2-d^3*b^2/(c*f-d*e-f)^2/(c*f-d*e+f)^2*dilog(((d*x+c)*f-f)/(c*f-d*e-f))*e+1/2*d^2*b^2/f*arctanh(d*x+c)/(c*f-d*e+f)^2*ln(d*x+c+1)+d^2*b^2*arctanh(d*x+c)/(c*f-d*e-f)/(c*f-d*e+f)/(d*f*x+d*e)-d^2*a*b/(d*f*x+d*e)^2/f*arctanh(d*x+c)-1/2*d^2*b^2/f*arctanh(d*x+c)/(c*f-d*e-f)^2*ln(d*x+c-1)-1/2*d^2*b^2/(d*f*x+d*e)^2/f*arctanh(d*x+c)^2-d^2*b^2*f/(c*f-d*e-f)^2/(c*f-d*e+f)^2*dilog(((d*x+c)*f+f)/(c*f-d*e+f))*c-2*d^3*a*b/(c*f-d*e-f)^2/(c*f-d*e+f)^2*ln((d*x+c)*f-c*f+d*e)*e-d^3*b^2/(c*f-d*e-f)^2/(c*f-d*e+f)^2*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f-f)/(c*f-d*e-f))*e+d^3*b^2/(c*f-d*e-f)^2/(c*f-d*e+f)^2*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f+f)/(c*f-d*e+f))*e-2*d^3*b^2*arctanh(d*x+c)/(c*f-d*e-f)^2/(c*f-d*e+f)^2*ln((d*x+c)*f-c*f+d*e)*e+d^2*b^2*f/(c*f-d*e-f)^2/(c*f-d*e+f)^2*dilog(((d*x+c)*f-f)/(c*f-d*e-f))*c","A"
45,1,12111,534,22.267000," ","int((f*x+e)^2*(a+b*arctanh(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
46,1,20255,316,1.684000," ","int((f*x+e)*(a+b*arctanh(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
47,1,346,130,0.286000," ","int((a+b*arctanh(d*x+c))^3,x)","a^{3} x +\frac{a^{3} c}{d}+\arctanh \left(d x +c \right)^{3} x \,b^{3}+\frac{\arctanh \left(d x +c \right)^{3} b^{3} c}{d}+\frac{b^{3} \arctanh \left(d x +c \right)^{3}}{d}-\frac{3 b^{3} \arctanh \left(d x +c \right)^{2} \ln \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{d}-\frac{3 b^{3} \arctanh \left(d x +c \right) \polylog \left(2, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{d}+\frac{3 b^{3} \polylog \left(3, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right)}{2 d}+3 \arctanh \left(d x +c \right)^{2} x a \,b^{2}+\frac{3 \arctanh \left(d x +c \right)^{2} a \,b^{2} c}{d}+\frac{3 a \,b^{2} \arctanh \left(d x +c \right)^{2}}{d}-\frac{6 \arctanh \left(d x +c \right) \ln \left(1+\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) a \,b^{2}}{d}-\frac{3 \polylog \left(2, -\frac{\left(d x +c +1\right)^{2}}{1-\left(d x +c \right)^{2}}\right) a \,b^{2}}{d}+3 \arctanh \left(d x +c \right) x \,a^{2} b +\frac{3 \arctanh \left(d x +c \right) a^{2} b c}{d}+\frac{3 a^{2} b \ln \left(1-\left(d x +c \right)^{2}\right)}{2 d}"," ",0,"a^3*x+1/d*a^3*c+arctanh(d*x+c)^3*x*b^3+1/d*arctanh(d*x+c)^3*b^3*c+1/d*b^3*arctanh(d*x+c)^3-3/d*b^3*arctanh(d*x+c)^2*ln(1+(d*x+c+1)^2/(1-(d*x+c)^2))-3/d*b^3*arctanh(d*x+c)*polylog(2,-(d*x+c+1)^2/(1-(d*x+c)^2))+3/2/d*b^3*polylog(3,-(d*x+c+1)^2/(1-(d*x+c)^2))+3*arctanh(d*x+c)^2*x*a*b^2+3/d*arctanh(d*x+c)^2*a*b^2*c+3/d*a*b^2*arctanh(d*x+c)^2-6/d*arctanh(d*x+c)*ln(1+(d*x+c+1)^2/(1-(d*x+c)^2))*a*b^2-3/d*polylog(2,-(d*x+c+1)^2/(1-(d*x+c)^2))*a*b^2+3*arctanh(d*x+c)*x*a^2*b+3/d*arctanh(d*x+c)*a^2*b*c+3/2/d*a^2*b*ln(1-(d*x+c)^2)","B"
48,1,4064,296,0.868000," ","int((a+b*arctanh(d*x+c))^3/(f*x+e),x)","\text{output too large to display}"," ",0,"-3*a*b^2/f*arctanh(d*x+c)*polylog(2,-(d*x+c+1)^2/(1-(d*x+c)^2))-3*a*b^2/(c*f-d*e-f)*arctanh(d*x+c)^2*ln(1-(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))-3*a*b^2/(c*f-d*e-f)*arctanh(d*x+c)*polylog(2,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+3*a^2*b*ln((d*x+c)*f-c*f+d*e)/f*arctanh(d*x+c)+3/2*a^2*b/f*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f-f)/(c*f-d*e-f))-3/2*a^2*b/f*ln((d*x+c)*f-c*f+d*e)*ln(((d*x+c)*f+f)/(c*f-d*e+f))+b^3*c/(c*f-d*e-f)*arctanh(d*x+c)^3*ln(1-(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+3/2*b^3*c/(c*f-d*e-f)*arctanh(d*x+c)^2*polylog(2,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))-3/2*b^3*c/(c*f-d*e-f)*arctanh(d*x+c)*polylog(3,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))-3/2*a*b^2*c/(c*f-d*e-f)*polylog(3,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+3*a*b^2*ln((d*x+c)*f-c*f+d*e)/f*arctanh(d*x+c)^2-I*b^3/f*Pi*arctanh(d*x+c)^3-b^3/(c*f-d*e-f)*arctanh(d*x+c)^3*ln(1-(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+3/2*a*b^2/f*polylog(3,-(d*x+c+1)^2/(1-(d*x+c)^2))+3/2*a*b^2/(c*f-d*e-f)*polylog(3,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))-3/4*b^3/f*polylog(4,-(d*x+c+1)^2/(1-(d*x+c)^2))-3/4*b^3/(c*f-d*e-f)*polylog(4,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+a^3*ln((d*x+c)*f-c*f+d*e)/f-3*d*a*b^2/f*e/(c*f-d*e-f)*arctanh(d*x+c)^2*ln(1-(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))-3*d*a*b^2/f*e/(c*f-d*e-f)*arctanh(d*x+c)*polylog(2,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+1/2*I*b^3/f*arctanh(d*x+c)^3*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*Pi-3/2*I*a*b^2/f*arctanh(d*x+c)^2*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*Pi-3/2*I*a*b^2/f*arctanh(d*x+c)^2*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*Pi-3*a*b^2/f*arctanh(d*x+c)^2*ln(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)+3/4*b^3*c/(c*f-d*e-f)*polylog(4,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+3/2*a^2*b/f*dilog(((d*x+c)*f-f)/(c*f-d*e-f))-3/2*a^2*b/f*dilog(((d*x+c)*f+f)/(c*f-d*e+f))-3/2*b^3/(c*f-d*e-f)*arctanh(d*x+c)^2*polylog(2,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+3/2*b^3/(c*f-d*e-f)*arctanh(d*x+c)*polylog(3,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+b^3*ln((d*x+c)*f-c*f+d*e)/f*arctanh(d*x+c)^3-b^3/f*arctanh(d*x+c)^3*ln(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)-3/2*b^3/f*arctanh(d*x+c)^2*polylog(2,-(d*x+c+1)^2/(1-(d*x+c)^2))+3/2*b^3/f*arctanh(d*x+c)*polylog(3,-(d*x+c+1)^2/(1-(d*x+c)^2))+3/2*I*a*b^2/f*arctanh(d*x+c)^2*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*Pi-3/4*d*b^3/f*e/(c*f-d*e-f)*polylog(4,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+3*a*b^2*c/(c*f-d*e-f)*arctanh(d*x+c)^2*ln(1-(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+3*a*b^2*c/(c*f-d*e-f)*arctanh(d*x+c)*polylog(2,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+I*b^3/f*arctanh(d*x+c)^3*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*Pi-1/2*I*b^3/f*arctanh(d*x+c)^3*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3*Pi-3*I*a*b^2/f*Pi*arctanh(d*x+c)^2+3/2*d*a*b^2/f*e/(c*f-d*e-f)*polylog(3,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))-1/2*I*b^3/f*arctanh(d*x+c)^3*csgn(I/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*Pi-1/2*I*b^3/f*arctanh(d*x+c)^3*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f))*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*Pi+3*I*a*b^2/f*arctanh(d*x+c)^2*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^2*Pi-3/2*I*a*b^2/f*arctanh(d*x+c)^2*csgn(I*(c*f*(1+(d*x+c+1)^2/(1-(d*x+c)^2))+(-(d*x+c+1)^2/(1-(d*x+c)^2)-1)*e*d+(1-(d*x+c+1)^2/(1-(d*x+c)^2))*f)/(1+(d*x+c+1)^2/(1-(d*x+c)^2)))^3*Pi-d*b^3/f*e/(c*f-d*e-f)*arctanh(d*x+c)^3*ln(1-(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))-3/2*d*b^3/f*e/(c*f-d*e-f)*arctanh(d*x+c)^2*polylog(2,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))+3/2*d*b^3/f*e/(c*f-d*e-f)*arctanh(d*x+c)*polylog(3,(c*f-d*e-f)*(d*x+c+1)^2/(1-(d*x+c)^2)/(-c*f+d*e-f))","C"
49,1,5728,1077,1.003000," ","int((a+b*arctanh(d*x+c))^3/(f*x+e)^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
50,0,0,22,1.619000," ","int((f*x+e)^m*(a+b*arctanh(d*x+c))^3,x)","\int \left(f x +e \right)^{m} \left(a +b \arctanh \left(d x +c \right)\right)^{3}\, dx"," ",0,"int((f*x+e)^m*(a+b*arctanh(d*x+c))^3,x)","F"
51,0,0,22,1.401000," ","int((f*x+e)^m*(a+b*arctanh(d*x+c))^2,x)","\int \left(f x +e \right)^{m} \left(a +b \arctanh \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((f*x+e)^m*(a+b*arctanh(d*x+c))^2,x)","F"
52,0,0,162,1.417000," ","int((f*x+e)^m*(a+b*arctanh(d*x+c)),x)","\int \left(f x +e \right)^{m} \left(a +b \arctanh \left(d x +c \right)\right)\, dx"," ",0,"int((f*x+e)^m*(a+b*arctanh(d*x+c)),x)","F"
53,1,587,576,0.913000," ","int(arctanh(b*x+a)/(d*x^3+c),x)","-\frac{2 b^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(\left(a^{3} d -c \,b^{3}-3 a^{2} d +3 a d -d \right) \textit{\_Z}^{6}+\left(3 a^{3} d -3 c \,b^{3}-3 a^{2} d -3 a d +3 d \right) \textit{\_Z}^{4}+\left(3 a^{3} d -3 c \,b^{3}+3 a^{2} d -3 a d -3 d \right) \textit{\_Z}^{2}+a^{3} d -c \,b^{3}+3 a^{2} d +3 a d +d \right)}{\sum}\frac{\arctanh \left(b x +a \right) \ln \left(\frac{\textit{\_R1} -\frac{b x +a +1}{\sqrt{1-\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{b x +a +1}{\sqrt{1-\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1}^{4} a^{3} d -\textit{\_R1}^{4} b^{3} c -3 \textit{\_R1}^{4} a^{2} d +3 \textit{\_R1}^{4} a d +2 \textit{\_R1}^{2} a^{3} d -2 \textit{\_R1}^{2} b^{3} c -\textit{\_R1}^{4} d -2 \textit{\_R1}^{2} a^{2} d -2 \textit{\_R1}^{2} a d +a^{3} d -c \,b^{3}+2 \textit{\_R1}^{2} d +a^{2} d -a d -d}\right)}{3}-\frac{2 b^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(\left(a^{3} d -c \,b^{3}-3 a^{2} d +3 a d -d \right) \textit{\_Z}^{6}+\left(3 a^{3} d -3 c \,b^{3}-3 a^{2} d -3 a d +3 d \right) \textit{\_Z}^{4}+\left(3 a^{3} d -3 c \,b^{3}+3 a^{2} d -3 a d -3 d \right) \textit{\_Z}^{2}+a^{3} d -c \,b^{3}+3 a^{2} d +3 a d +d \right)}{\sum}\frac{\textit{\_R1}^{2} \left(\arctanh \left(b x +a \right) \ln \left(\frac{\textit{\_R1} -\frac{b x +a +1}{\sqrt{1-\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{b x +a +1}{\sqrt{1-\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{4} a^{3} d -\textit{\_R1}^{4} b^{3} c -3 \textit{\_R1}^{4} a^{2} d +3 \textit{\_R1}^{4} a d +2 \textit{\_R1}^{2} a^{3} d -2 \textit{\_R1}^{2} b^{3} c -\textit{\_R1}^{4} d -2 \textit{\_R1}^{2} a^{2} d -2 \textit{\_R1}^{2} a d +a^{3} d -c \,b^{3}+2 \textit{\_R1}^{2} d +a^{2} d -a d -d}\right)}{3}"," ",0,"-2/3*b^2*sum(1/(_R1^4*a^3*d-_R1^4*b^3*c-3*_R1^4*a^2*d+3*_R1^4*a*d+2*_R1^2*a^3*d-2*_R1^2*b^3*c-_R1^4*d-2*_R1^2*a^2*d-2*_R1^2*a*d+a^3*d-b^3*c+2*_R1^2*d+a^2*d-a*d-d)*(arctanh(b*x+a)*ln((_R1-(b*x+a+1)/(1-(b*x+a)^2)^(1/2))/_R1)+dilog((_R1-(b*x+a+1)/(1-(b*x+a)^2)^(1/2))/_R1)),_R1=RootOf((a^3*d-b^3*c-3*a^2*d+3*a*d-d)*_Z^6+(3*a^3*d-3*b^3*c-3*a^2*d-3*a*d+3*d)*_Z^4+(3*a^3*d-3*b^3*c+3*a^2*d-3*a*d-3*d)*_Z^2+a^3*d-c*b^3+3*a^2*d+3*a*d+d))-2/3*b^2*sum(_R1^2/(_R1^4*a^3*d-_R1^4*b^3*c-3*_R1^4*a^2*d+3*_R1^4*a*d+2*_R1^2*a^3*d-2*_R1^2*b^3*c-_R1^4*d-2*_R1^2*a^2*d-2*_R1^2*a*d+a^3*d-b^3*c+2*_R1^2*d+a^2*d-a*d-d)*(arctanh(b*x+a)*ln((_R1-(b*x+a+1)/(1-(b*x+a)^2)^(1/2))/_R1)+dilog((_R1-(b*x+a+1)/(1-(b*x+a)^2)^(1/2))/_R1)),_R1=RootOf((a^3*d-b^3*c-3*a^2*d+3*a*d-d)*_Z^6+(3*a^3*d-3*b^3*c-3*a^2*d-3*a*d+3*d)*_Z^4+(3*a^3*d-3*b^3*c+3*a^2*d-3*a*d-3*d)*_Z^2+a^3*d-c*b^3+3*a^2*d+3*a*d+d))","C"
54,1,1300,377,0.742000," ","int(arctanh(b*x+a)/(d*x^2+c),x)","\frac{\sqrt{-b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d +b^{2} c -2 a d +d \right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-a^{2} d -b^{2} c -2 \sqrt{-b^{2} c d}+d \right)}\right) \arctanh \left(b x +a \right) a^{2}}{2 b c \left(a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d \right)}+\frac{b \sqrt{-b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d +b^{2} c -2 a d +d \right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-a^{2} d -b^{2} c -2 \sqrt{-b^{2} c d}+d \right)}\right) \arctanh \left(b x +a \right)}{2 d \left(a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d \right)}-\frac{\sqrt{-b^{2} c d}\, \arctanh \left(b x +a \right)^{2} a^{2}}{2 b c \left(a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d \right)}-\frac{b \sqrt{-b^{2} c d}\, \arctanh \left(b x +a \right)^{2}}{2 d \left(a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d \right)}+\frac{\sqrt{-b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d +b^{2} c -2 a d +d \right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-a^{2} d -b^{2} c -2 \sqrt{-b^{2} c d}+d \right)}\right) a^{2}}{4 b c \left(a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d \right)}+\frac{b \sqrt{-b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d +b^{2} c -2 a d +d \right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-a^{2} d -b^{2} c -2 \sqrt{-b^{2} c d}+d \right)}\right)}{4 d \left(a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d \right)}-\frac{b \ln \left(1-\frac{\left(a^{2} d +b^{2} c -2 a d +d \right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-a^{2} d -b^{2} c -2 \sqrt{-b^{2} c d}+d \right)}\right) \arctanh \left(b x +a \right)}{a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d}+\frac{b \arctanh \left(b x +a \right)^{2}}{a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d}-\frac{\sqrt{-b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d +b^{2} c -2 a d +d \right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-a^{2} d -b^{2} c -2 \sqrt{-b^{2} c d}+d \right)}\right) \arctanh \left(b x +a \right)}{2 b c \left(a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d \right)}+\frac{\sqrt{-b^{2} c d}\, \arctanh \left(b x +a \right)^{2}}{2 b c \left(a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d \right)}-\frac{b \polylog \left(2, \frac{\left(a^{2} d +b^{2} c -2 a d +d \right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-a^{2} d -b^{2} c -2 \sqrt{-b^{2} c d}+d \right)}\right)}{2 \left(a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d \right)}-\frac{\sqrt{-b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d +b^{2} c -2 a d +d \right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-a^{2} d -b^{2} c -2 \sqrt{-b^{2} c d}+d \right)}\right)}{4 b c \left(a^{2} d +b^{2} c +2 \sqrt{-b^{2} c d}-d \right)}-\frac{\sqrt{-b^{2} c d}\, \arctanh \left(b x +a \right) \ln \left(1-\frac{\left(a^{2} d +b^{2} c -2 a d +d \right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-a^{2} d -b^{2} c +2 \sqrt{-b^{2} c d}+d \right)}\right)}{2 b c d}+\frac{\sqrt{-b^{2} c d}\, \arctanh \left(b x +a \right)^{2}}{2 b c d}-\frac{\sqrt{-b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d +b^{2} c -2 a d +d \right) \left(b x +a +1\right)^{2}}{\left(1-\left(b x +a \right)^{2}\right) \left(-a^{2} d -b^{2} c +2 \sqrt{-b^{2} c d}+d \right)}\right)}{4 b c d}"," ",0,"1/2/b*(-b^2*c*d)^(1/2)/c*ln(1-(a^2*d+b^2*c-2*a*d+d)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-a^2*d-b^2*c-2*(-b^2*c*d)^(1/2)+d))*arctanh(b*x+a)*a^2/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)+1/2*b*(-b^2*c*d)^(1/2)/d*ln(1-(a^2*d+b^2*c-2*a*d+d)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-a^2*d-b^2*c-2*(-b^2*c*d)^(1/2)+d))*arctanh(b*x+a)/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)-1/2/b*(-b^2*c*d)^(1/2)/c*arctanh(b*x+a)^2*a^2/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)-1/2*b*(-b^2*c*d)^(1/2)/d*arctanh(b*x+a)^2/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)+1/4/b*(-b^2*c*d)^(1/2)/c*polylog(2,(a^2*d+b^2*c-2*a*d+d)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-a^2*d-b^2*c-2*(-b^2*c*d)^(1/2)+d))*a^2/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)+1/4*b*(-b^2*c*d)^(1/2)/d*polylog(2,(a^2*d+b^2*c-2*a*d+d)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-a^2*d-b^2*c-2*(-b^2*c*d)^(1/2)+d))/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)-b/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)*ln(1-(a^2*d+b^2*c-2*a*d+d)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-a^2*d-b^2*c-2*(-b^2*c*d)^(1/2)+d))*arctanh(b*x+a)+b/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)*arctanh(b*x+a)^2-1/2/b*(-b^2*c*d)^(1/2)/c*ln(1-(a^2*d+b^2*c-2*a*d+d)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-a^2*d-b^2*c-2*(-b^2*c*d)^(1/2)+d))*arctanh(b*x+a)/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)+1/2/b*(-b^2*c*d)^(1/2)/c*arctanh(b*x+a)^2/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)-1/2*b/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)*polylog(2,(a^2*d+b^2*c-2*a*d+d)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-a^2*d-b^2*c-2*(-b^2*c*d)^(1/2)+d))-1/4/b*(-b^2*c*d)^(1/2)/c*polylog(2,(a^2*d+b^2*c-2*a*d+d)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-a^2*d-b^2*c-2*(-b^2*c*d)^(1/2)+d))/(a^2*d+b^2*c+2*(-b^2*c*d)^(1/2)-d)-1/2/b*(-b^2*c*d)^(1/2)/c/d*arctanh(b*x+a)*ln(1-(a^2*d+b^2*c-2*a*d+d)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-a^2*d-b^2*c+2*(-b^2*c*d)^(1/2)+d))+1/2/b*(-b^2*c*d)^(1/2)/c/d*arctanh(b*x+a)^2-1/4/b*(-b^2*c*d)^(1/2)/c/d*polylog(2,(a^2*d+b^2*c-2*a*d+d)*(b*x+a+1)^2/(1-(b*x+a)^2)/(-a^2*d-b^2*c+2*(-b^2*c*d)^(1/2)+d))","B"
55,1,176,116,0.122000," ","int(arctanh(b*x+a)/(d*x+c),x)","\frac{\ln \left(d \left(b x +a \right)-a d +b c \right) \arctanh \left(b x +a \right)}{d}+\frac{\ln \left(d \left(b x +a \right)-a d +b c \right) \ln \left(\frac{d \left(b x +a \right)-d}{a d -b c -d}\right)}{2 d}+\frac{\dilog \left(\frac{d \left(b x +a \right)-d}{a d -b c -d}\right)}{2 d}-\frac{\ln \left(\frac{d \left(b x +a \right)+d}{a d -b c +d}\right) \ln \left(d \left(b x +a \right)-a d +b c \right)}{2 d}-\frac{\dilog \left(\frac{d \left(b x +a \right)+d}{a d -b c +d}\right)}{2 d}"," ",0,"ln(d*(b*x+a)-a*d+b*c)/d*arctanh(b*x+a)+1/2/d*ln(d*(b*x+a)-a*d+b*c)*ln((d*(b*x+a)-d)/(a*d-b*c-d))+1/2/d*dilog((d*(b*x+a)-d)/(a*d-b*c-d))-1/2/d*ln((d*(b*x+a)+d)/(a*d-b*c+d))*ln(d*(b*x+a)-a*d+b*c)-1/2/d*dilog((d*(b*x+a)+d)/(a*d-b*c+d))","A"
56,1,297,174,0.115000," ","int(arctanh(b*x+a)/(c+d/x),x)","\frac{\arctanh \left(b x +a \right) x}{c}+\frac{\arctanh \left(b x +a \right) a}{b c}-\frac{\arctanh \left(b x +a \right) d \ln \left(c \left(b x +a \right)-a c +b d \right)}{c^{2}}+\frac{d \ln \left(c \left(b x +a \right)-a c +b d \right) \ln \left(\frac{c \left(b x +a \right)+c}{a c -b d +c}\right)}{2 c^{2}}+\frac{d \dilog \left(\frac{c \left(b x +a \right)+c}{a c -b d +c}\right)}{2 c^{2}}-\frac{d \ln \left(c \left(b x +a \right)-a c +b d \right) \ln \left(\frac{c \left(b x +a \right)-c}{a c -b d -c}\right)}{2 c^{2}}-\frac{d \dilog \left(\frac{c \left(b x +a \right)-c}{a c -b d -c}\right)}{2 c^{2}}+\frac{\ln \left(a^{2} c^{2}-2 a b c d +b^{2} d^{2}+2 \left(c \left(b x +a \right)-a c +b d \right) a c -2 \left(c \left(b x +a \right)-a c +b d \right) b d +\left(c \left(b x +a \right)-a c +b d \right)^{2}-c^{2}\right)}{2 b c}"," ",0,"arctanh(b*x+a)/c*x+1/b*arctanh(b*x+a)/c*a-arctanh(b*x+a)/c^2*d*ln(c*(b*x+a)-a*c+b*d)+1/2/c^2*d*ln(c*(b*x+a)-a*c+b*d)*ln((c*(b*x+a)+c)/(a*c-b*d+c))+1/2/c^2*d*dilog((c*(b*x+a)+c)/(a*c-b*d+c))-1/2/c^2*d*ln(c*(b*x+a)-a*c+b*d)*ln((c*(b*x+a)-c)/(a*c-b*d-c))-1/2/c^2*d*dilog((c*(b*x+a)-c)/(a*c-b*d-c))+1/2/b/c*ln(a^2*c^2-2*a*b*c*d+b^2*d^2+2*(c*(b*x+a)-a*c+b*d)*a*c-2*(c*(b*x+a)-a*c+b*d)*b*d+(c*(b*x+a)-a*c+b*d)^2-c^2)","A"
57,1,20505,435,1.814000," ","int(arctanh(b*x+a)/(c+d/x^2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
58,1,650,624,0.890000," ","int(arctanh(b*x+a)/(c+d/x^3),x)","\frac{\arctanh \left(b x +a \right) x}{c}+\frac{\arctanh \left(b x +a \right) a}{b c}+\frac{2 b^{2} d \left(\munderset{\textit{\_R1} =\RootOf \left(\left(a^{3} c -d \,b^{3}-3 a^{2} c +3 a c -c \right) \textit{\_Z}^{6}+\left(3 a^{3} c -3 d \,b^{3}-3 a^{2} c -3 a c +3 c \right) \textit{\_Z}^{4}+\left(3 a^{3} c -3 d \,b^{3}+3 a^{2} c -3 a c -3 c \right) \textit{\_Z}^{2}+a^{3} c -d \,b^{3}+3 a^{2} c +3 a c +c \right)}{\sum}\frac{\arctanh \left(b x +a \right) \ln \left(\frac{\textit{\_R1} -\frac{b x +a +1}{\sqrt{1-\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{b x +a +1}{\sqrt{1-\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1}^{4} a^{3} c -\textit{\_R1}^{4} b^{3} d -3 \textit{\_R1}^{4} a^{2} c +3 \textit{\_R1}^{4} a c +2 \textit{\_R1}^{2} a^{3} c -2 \textit{\_R1}^{2} b^{3} d -\textit{\_R1}^{4} c -2 \textit{\_R1}^{2} a^{2} c -2 \textit{\_R1}^{2} a c +a^{3} c -d \,b^{3}+2 \textit{\_R1}^{2} c +a^{2} c -a c -c}\right)}{3 c}+\frac{2 b^{2} d \left(\munderset{\textit{\_R1} =\RootOf \left(\left(a^{3} c -d \,b^{3}-3 a^{2} c +3 a c -c \right) \textit{\_Z}^{6}+\left(3 a^{3} c -3 d \,b^{3}-3 a^{2} c -3 a c +3 c \right) \textit{\_Z}^{4}+\left(3 a^{3} c -3 d \,b^{3}+3 a^{2} c -3 a c -3 c \right) \textit{\_Z}^{2}+a^{3} c -d \,b^{3}+3 a^{2} c +3 a c +c \right)}{\sum}\frac{\textit{\_R1}^{2} \left(\arctanh \left(b x +a \right) \ln \left(\frac{\textit{\_R1} -\frac{b x +a +1}{\sqrt{1-\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{b x +a +1}{\sqrt{1-\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{4} a^{3} c -\textit{\_R1}^{4} b^{3} d -3 \textit{\_R1}^{4} a^{2} c +3 \textit{\_R1}^{4} a c +2 \textit{\_R1}^{2} a^{3} c -2 \textit{\_R1}^{2} b^{3} d -\textit{\_R1}^{4} c -2 \textit{\_R1}^{2} a^{2} c -2 \textit{\_R1}^{2} a c +a^{3} c -d \,b^{3}+2 \textit{\_R1}^{2} c +a^{2} c -a c -c}\right)}{3 c}+\frac{\ln \left(b x +a -1\right)}{2 b c}+\frac{\ln \left(b x +a +1\right)}{2 b c}"," ",0,"arctanh(b*x+a)/c*x+1/b*arctanh(b*x+a)/c*a+2/3*b^2/c*d*sum(1/(_R1^4*a^3*c-_R1^4*b^3*d-3*_R1^4*a^2*c+3*_R1^4*a*c+2*_R1^2*a^3*c-2*_R1^2*b^3*d-_R1^4*c-2*_R1^2*a^2*c-2*_R1^2*a*c+a^3*c-b^3*d+2*_R1^2*c+a^2*c-a*c-c)*(arctanh(b*x+a)*ln((_R1-(b*x+a+1)/(1-(b*x+a)^2)^(1/2))/_R1)+dilog((_R1-(b*x+a+1)/(1-(b*x+a)^2)^(1/2))/_R1)),_R1=RootOf((a^3*c-b^3*d-3*a^2*c+3*a*c-c)*_Z^6+(3*a^3*c-3*b^3*d-3*a^2*c-3*a*c+3*c)*_Z^4+(3*a^3*c-3*b^3*d+3*a^2*c-3*a*c-3*c)*_Z^2+a^3*c-d*b^3+3*a^2*c+3*a*c+c))+2/3*b^2/c*d*sum(_R1^2/(_R1^4*a^3*c-_R1^4*b^3*d-3*_R1^4*a^2*c+3*_R1^4*a*c+2*_R1^2*a^3*c-2*_R1^2*b^3*d-_R1^4*c-2*_R1^2*a^2*c-2*_R1^2*a*c+a^3*c-b^3*d+2*_R1^2*c+a^2*c-a*c-c)*(arctanh(b*x+a)*ln((_R1-(b*x+a+1)/(1-(b*x+a)^2)^(1/2))/_R1)+dilog((_R1-(b*x+a+1)/(1-(b*x+a)^2)^(1/2))/_R1)),_R1=RootOf((a^3*c-b^3*d-3*a^2*c+3*a*c-c)*_Z^6+(3*a^3*c-3*b^3*d-3*a^2*c-3*a*c+3*c)*_Z^4+(3*a^3*c-3*b^3*d+3*a^2*c-3*a*c-3*c)*_Z^2+a^3*c-d*b^3+3*a^2*c+3*a*c+c))+1/2/b/c*ln(b*x+a-1)+1/2/b/c*ln(b*x+a+1)","C"
59,1,738,477,0.100000," ","int(arctanh(b*x+a)/(c+d*x^(1/2)),x)","\frac{2 \arctanh \left(b x +a \right) \sqrt{x}}{d}-\frac{2 \arctanh \left(b x +a \right) c \ln \left(c +d \sqrt{x}\right)}{d^{2}}+\frac{c \ln \left(c +d \sqrt{x}\right) \ln \left(\frac{-b \left(c +d \sqrt{x}\right)+b c +\sqrt{-a \,d^{2} b -b \,d^{2}}}{b c +\sqrt{-a \,d^{2} b -b \,d^{2}}}\right)}{d^{2}}+\frac{c \ln \left(c +d \sqrt{x}\right) \ln \left(\frac{b \left(c +d \sqrt{x}\right)-b c +\sqrt{-a \,d^{2} b -b \,d^{2}}}{-b c +\sqrt{-a \,d^{2} b -b \,d^{2}}}\right)}{d^{2}}+\frac{c \dilog \left(\frac{-b \left(c +d \sqrt{x}\right)+b c +\sqrt{-a \,d^{2} b -b \,d^{2}}}{b c +\sqrt{-a \,d^{2} b -b \,d^{2}}}\right)}{d^{2}}+\frac{c \dilog \left(\frac{b \left(c +d \sqrt{x}\right)-b c +\sqrt{-a \,d^{2} b -b \,d^{2}}}{-b c +\sqrt{-a \,d^{2} b -b \,d^{2}}}\right)}{d^{2}}-\frac{c \ln \left(c +d \sqrt{x}\right) \ln \left(\frac{-b \left(c +d \sqrt{x}\right)+b c +\sqrt{-a \,d^{2} b +b \,d^{2}}}{b c +\sqrt{-a \,d^{2} b +b \,d^{2}}}\right)}{d^{2}}-\frac{c \ln \left(c +d \sqrt{x}\right) \ln \left(\frac{b \left(c +d \sqrt{x}\right)-b c +\sqrt{-a \,d^{2} b +b \,d^{2}}}{-b c +\sqrt{-a \,d^{2} b +b \,d^{2}}}\right)}{d^{2}}-\frac{c \dilog \left(\frac{-b \left(c +d \sqrt{x}\right)+b c +\sqrt{-a \,d^{2} b +b \,d^{2}}}{b c +\sqrt{-a \,d^{2} b +b \,d^{2}}}\right)}{d^{2}}-\frac{c \dilog \left(\frac{b \left(c +d \sqrt{x}\right)-b c +\sqrt{-a \,d^{2} b +b \,d^{2}}}{-b c +\sqrt{-a \,d^{2} b +b \,d^{2}}}\right)}{d^{2}}+\frac{2 \arctan \left(\frac{2 b \left(c +d \sqrt{x}\right)-2 b c}{2 \sqrt{a \,d^{2} b +b \,d^{2}}}\right)}{\sqrt{a \,d^{2} b +b \,d^{2}}}+\frac{2 \arctan \left(\frac{2 b \left(c +d \sqrt{x}\right)-2 b c}{2 \sqrt{a \,d^{2} b +b \,d^{2}}}\right) a}{\sqrt{a \,d^{2} b +b \,d^{2}}}+\frac{2 \arctan \left(\frac{2 b \left(c +d \sqrt{x}\right)-2 b c}{2 \sqrt{a \,d^{2} b -b \,d^{2}}}\right)}{\sqrt{a \,d^{2} b -b \,d^{2}}}-\frac{2 \arctan \left(\frac{2 b \left(c +d \sqrt{x}\right)-2 b c}{2 \sqrt{a \,d^{2} b -b \,d^{2}}}\right) a}{\sqrt{a \,d^{2} b -b \,d^{2}}}"," ",0,"2*arctanh(b*x+a)/d*x^(1/2)-2*arctanh(b*x+a)*c/d^2*ln(c+d*x^(1/2))+1/d^2*c*ln(c+d*x^(1/2))*ln((-b*(c+d*x^(1/2))+b*c+(-a*b*d^2-b*d^2)^(1/2))/(b*c+(-a*b*d^2-b*d^2)^(1/2)))+1/d^2*c*ln(c+d*x^(1/2))*ln((b*(c+d*x^(1/2))-b*c+(-a*b*d^2-b*d^2)^(1/2))/(-b*c+(-a*b*d^2-b*d^2)^(1/2)))+1/d^2*c*dilog((-b*(c+d*x^(1/2))+b*c+(-a*b*d^2-b*d^2)^(1/2))/(b*c+(-a*b*d^2-b*d^2)^(1/2)))+1/d^2*c*dilog((b*(c+d*x^(1/2))-b*c+(-a*b*d^2-b*d^2)^(1/2))/(-b*c+(-a*b*d^2-b*d^2)^(1/2)))-1/d^2*c*ln(c+d*x^(1/2))*ln((-b*(c+d*x^(1/2))+b*c+(-a*b*d^2+b*d^2)^(1/2))/(b*c+(-a*b*d^2+b*d^2)^(1/2)))-1/d^2*c*ln(c+d*x^(1/2))*ln((b*(c+d*x^(1/2))-b*c+(-a*b*d^2+b*d^2)^(1/2))/(-b*c+(-a*b*d^2+b*d^2)^(1/2)))-1/d^2*c*dilog((-b*(c+d*x^(1/2))+b*c+(-a*b*d^2+b*d^2)^(1/2))/(b*c+(-a*b*d^2+b*d^2)^(1/2)))-1/d^2*c*dilog((b*(c+d*x^(1/2))-b*c+(-a*b*d^2+b*d^2)^(1/2))/(-b*c+(-a*b*d^2+b*d^2)^(1/2)))+2/(a*b*d^2+b*d^2)^(1/2)*arctan(1/2*(2*b*(c+d*x^(1/2))-2*b*c)/(a*b*d^2+b*d^2)^(1/2))+2/(a*b*d^2+b*d^2)^(1/2)*arctan(1/2*(2*b*(c+d*x^(1/2))-2*b*c)/(a*b*d^2+b*d^2)^(1/2))*a+2/(a*b*d^2-b*d^2)^(1/2)*arctan(1/2*(2*b*(c+d*x^(1/2))-2*b*c)/(a*b*d^2-b*d^2)^(1/2))-2/(a*b*d^2-b*d^2)^(1/2)*arctan(1/2*(2*b*(c+d*x^(1/2))-2*b*c)/(a*b*d^2-b*d^2)^(1/2))*a","A"
60,1,970,549,0.104000," ","int(arctanh(b*x+a)/(c+d/x^(1/2)),x)","\frac{\arctanh \left(b x +a \right) x}{c}-\frac{2 \arctanh \left(b x +a \right) d \sqrt{x}}{c^{2}}+\frac{2 \arctanh \left(b x +a \right) d^{2} \ln \left(d +c \sqrt{x}\right)}{c^{3}}+\frac{\ln \left(b \left(d +c \sqrt{x}\right)^{2}-2 \left(d +c \sqrt{x}\right) b d +a \,c^{2}+b \,d^{2}+c^{2}\right)}{2 b c}-\frac{2 d \arctan \left(\frac{2 b \left(d +c \sqrt{x}\right)-2 b d}{2 \sqrt{a b \,c^{2}+b \,c^{2}}}\right)}{c \sqrt{a b \,c^{2}+b \,c^{2}}}+\frac{a \ln \left(b \left(d +c \sqrt{x}\right)^{2}-2 \left(d +c \sqrt{x}\right) b d +a \,c^{2}+b \,d^{2}+c^{2}\right)}{2 b c}-\frac{2 a d \arctan \left(\frac{2 b \left(d +c \sqrt{x}\right)-2 b d}{2 \sqrt{a b \,c^{2}+b \,c^{2}}}\right)}{c \sqrt{a b \,c^{2}+b \,c^{2}}}-\frac{a \ln \left(b \left(d +c \sqrt{x}\right)^{2}-2 \left(d +c \sqrt{x}\right) b d +a \,c^{2}+b \,d^{2}-c^{2}\right)}{2 b c}+\frac{2 a d \arctan \left(\frac{2 b \left(d +c \sqrt{x}\right)-2 b d}{2 \sqrt{a b \,c^{2}-b \,c^{2}}}\right)}{c \sqrt{a b \,c^{2}-b \,c^{2}}}+\frac{\ln \left(b \left(d +c \sqrt{x}\right)^{2}-2 \left(d +c \sqrt{x}\right) b d +a \,c^{2}+b \,d^{2}-c^{2}\right)}{2 b c}-\frac{2 d \arctan \left(\frac{2 b \left(d +c \sqrt{x}\right)-2 b d}{2 \sqrt{a b \,c^{2}-b \,c^{2}}}\right)}{c \sqrt{a b \,c^{2}-b \,c^{2}}}-\frac{d^{2} \ln \left(d +c \sqrt{x}\right) \ln \left(\frac{-b \left(d +c \sqrt{x}\right)+b d +\sqrt{-a b \,c^{2}-b \,c^{2}}}{b d +\sqrt{-a b \,c^{2}-b \,c^{2}}}\right)}{c^{3}}-\frac{d^{2} \ln \left(d +c \sqrt{x}\right) \ln \left(\frac{b \left(d +c \sqrt{x}\right)-b d +\sqrt{-a b \,c^{2}-b \,c^{2}}}{-b d +\sqrt{-a b \,c^{2}-b \,c^{2}}}\right)}{c^{3}}-\frac{d^{2} \dilog \left(\frac{-b \left(d +c \sqrt{x}\right)+b d +\sqrt{-a b \,c^{2}-b \,c^{2}}}{b d +\sqrt{-a b \,c^{2}-b \,c^{2}}}\right)}{c^{3}}-\frac{d^{2} \dilog \left(\frac{b \left(d +c \sqrt{x}\right)-b d +\sqrt{-a b \,c^{2}-b \,c^{2}}}{-b d +\sqrt{-a b \,c^{2}-b \,c^{2}}}\right)}{c^{3}}+\frac{d^{2} \ln \left(d +c \sqrt{x}\right) \ln \left(\frac{-b \left(d +c \sqrt{x}\right)+b d +\sqrt{-a b \,c^{2}+b \,c^{2}}}{b d +\sqrt{-a b \,c^{2}+b \,c^{2}}}\right)}{c^{3}}+\frac{d^{2} \ln \left(d +c \sqrt{x}\right) \ln \left(\frac{b \left(d +c \sqrt{x}\right)-b d +\sqrt{-a b \,c^{2}+b \,c^{2}}}{-b d +\sqrt{-a b \,c^{2}+b \,c^{2}}}\right)}{c^{3}}+\frac{d^{2} \dilog \left(\frac{-b \left(d +c \sqrt{x}\right)+b d +\sqrt{-a b \,c^{2}+b \,c^{2}}}{b d +\sqrt{-a b \,c^{2}+b \,c^{2}}}\right)}{c^{3}}+\frac{d^{2} \dilog \left(\frac{b \left(d +c \sqrt{x}\right)-b d +\sqrt{-a b \,c^{2}+b \,c^{2}}}{-b d +\sqrt{-a b \,c^{2}+b \,c^{2}}}\right)}{c^{3}}"," ",0,"arctanh(b*x+a)/c*x-2*arctanh(b*x+a)/c^2*d*x^(1/2)+2*arctanh(b*x+a)*d^2/c^3*ln(d+c*x^(1/2))+1/2/b/c*ln(b*(d+c*x^(1/2))^2-2*(d+c*x^(1/2))*b*d+a*c^2+b*d^2+c^2)-2/c*d/(a*b*c^2+b*c^2)^(1/2)*arctan(1/2*(2*b*(d+c*x^(1/2))-2*b*d)/(a*b*c^2+b*c^2)^(1/2))+1/2/b/c*a*ln(b*(d+c*x^(1/2))^2-2*(d+c*x^(1/2))*b*d+a*c^2+b*d^2+c^2)-2/c*a*d/(a*b*c^2+b*c^2)^(1/2)*arctan(1/2*(2*b*(d+c*x^(1/2))-2*b*d)/(a*b*c^2+b*c^2)^(1/2))-1/2/b/c*a*ln(b*(d+c*x^(1/2))^2-2*(d+c*x^(1/2))*b*d+a*c^2+b*d^2-c^2)+2/c*a*d/(a*b*c^2-b*c^2)^(1/2)*arctan(1/2*(2*b*(d+c*x^(1/2))-2*b*d)/(a*b*c^2-b*c^2)^(1/2))+1/2/b/c*ln(b*(d+c*x^(1/2))^2-2*(d+c*x^(1/2))*b*d+a*c^2+b*d^2-c^2)-2/c*d/(a*b*c^2-b*c^2)^(1/2)*arctan(1/2*(2*b*(d+c*x^(1/2))-2*b*d)/(a*b*c^2-b*c^2)^(1/2))-1/c^3*d^2*ln(d+c*x^(1/2))*ln((-b*(d+c*x^(1/2))+b*d+(-a*b*c^2-b*c^2)^(1/2))/(b*d+(-a*b*c^2-b*c^2)^(1/2)))-1/c^3*d^2*ln(d+c*x^(1/2))*ln((b*(d+c*x^(1/2))-b*d+(-a*b*c^2-b*c^2)^(1/2))/(-b*d+(-a*b*c^2-b*c^2)^(1/2)))-1/c^3*d^2*dilog((-b*(d+c*x^(1/2))+b*d+(-a*b*c^2-b*c^2)^(1/2))/(b*d+(-a*b*c^2-b*c^2)^(1/2)))-1/c^3*d^2*dilog((b*(d+c*x^(1/2))-b*d+(-a*b*c^2-b*c^2)^(1/2))/(-b*d+(-a*b*c^2-b*c^2)^(1/2)))+1/c^3*d^2*ln(d+c*x^(1/2))*ln((-b*(d+c*x^(1/2))+b*d+(-a*b*c^2+b*c^2)^(1/2))/(b*d+(-a*b*c^2+b*c^2)^(1/2)))+1/c^3*d^2*ln(d+c*x^(1/2))*ln((b*(d+c*x^(1/2))-b*d+(-a*b*c^2+b*c^2)^(1/2))/(-b*d+(-a*b*c^2+b*c^2)^(1/2)))+1/c^3*d^2*dilog((-b*(d+c*x^(1/2))+b*d+(-a*b*c^2+b*c^2)^(1/2))/(b*d+(-a*b*c^2+b*c^2)^(1/2)))+1/c^3*d^2*dilog((b*(d+c*x^(1/2))-b*d+(-a*b*c^2+b*c^2)^(1/2))/(-b*d+(-a*b*c^2+b*c^2)^(1/2)))","A"
61,1,2140,307,0.825000," ","int(arctanh(e*x+d)/(c*x^2+b*x+a),x)","-\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \arctanh \left(e x +d \right) \ln \left(1-\frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}+\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right)}{e \left(4 a c -b^{2}\right)}+\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \arctanh \left(e x +d \right)^{2}}{e \left(4 a c -b^{2}\right)}-\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \polylog \left(2, \frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}+\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right)}{2 e \left(4 a c -b^{2}\right)}+\frac{e \sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \ln \left(1-\frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}-\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right) \arctanh \left(e x +d \right) a}{\left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}-\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \ln \left(1-\frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}-\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right) \arctanh \left(e x +d \right) b d}{\left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}+\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \ln \left(1-\frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}-\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right) \arctanh \left(e x +d \right) c \,d^{2}}{e \left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}-\frac{e \sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \arctanh \left(e x +d \right)^{2} a}{\left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}+\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \arctanh \left(e x +d \right)^{2} b d}{\left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}-\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \arctanh \left(e x +d \right)^{2} c \,d^{2}}{e \left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}+\frac{e \sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \polylog \left(2, \frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}-\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right) a}{2 \left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}-\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \polylog \left(2, \frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}-\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right) b d}{2 \left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}+\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \polylog \left(2, \frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}-\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right) c \,d^{2}}{2 e \left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}-\frac{e \ln \left(1-\frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}-\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right) \arctanh \left(e x +d \right)}{a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c}-\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \ln \left(1-\frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}-\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right) \arctanh \left(e x +d \right) c}{e \left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}+\frac{e \arctanh \left(e x +d \right)^{2}}{a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c}+\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \arctanh \left(e x +d \right)^{2} c}{e \left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}-\frac{e \polylog \left(2, \frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}-\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right)}{2 \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}-\frac{\sqrt{e^{2} \left(-4 a c +b^{2}\right)}\, \polylog \left(2, \frac{\left(a \,e^{2}-b e d +c \,d^{2}+b e -2 c d +c \right) \left(e x +d +1\right)^{2}}{\left(-\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}+b e d -c \,d^{2}-\sqrt{-e^{2} \left(4 a c -b^{2}\right)}+c \right)}\right) c}{2 e \left(4 a c -b^{2}\right) \left(a \,e^{2}-b e d +c \,d^{2}+\sqrt{e^{2} \left(-4 a c +b^{2}\right)}-c \right)}"," ",0,"-1/e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*arctanh(e*x+d)*ln(1-(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(-e^2*(4*a*c-b^2))^(1/2)+c))+1/e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*arctanh(e*x+d)^2-1/2/e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*polylog(2,(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(-e^2*(4*a*c-b^2))^(1/2)+c))+e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*ln(1-(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(-e^2*(4*a*c-b^2))^(1/2)+c))*arctanh(e*x+d)*a/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)-(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*ln(1-(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(-e^2*(4*a*c-b^2))^(1/2)+c))*arctanh(e*x+d)*b*d/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)+1/e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*ln(1-(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(-e^2*(4*a*c-b^2))^(1/2)+c))*arctanh(e*x+d)*c*d^2/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)-e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*arctanh(e*x+d)^2*a/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)+(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*arctanh(e*x+d)^2*b*d/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)-1/e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*arctanh(e*x+d)^2*c*d^2/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)+1/2*e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*polylog(2,(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(-e^2*(4*a*c-b^2))^(1/2)+c))*a/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)-1/2*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*polylog(2,(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(-e^2*(4*a*c-b^2))^(1/2)+c))*b*d/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)+1/2/e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*polylog(2,(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(-e^2*(4*a*c-b^2))^(1/2)+c))*c*d^2/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)-e/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)*ln(1-(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(-e^2*(4*a*c-b^2))^(1/2)+c))*arctanh(e*x+d)-1/e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*ln(1-(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(-e^2*(4*a*c-b^2))^(1/2)+c))*arctanh(e*x+d)*c/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)+e/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)*arctanh(e*x+d)^2+1/e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*arctanh(e*x+d)^2*c/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)-1/2*e/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)*polylog(2,(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(-e^2*(4*a*c-b^2))^(1/2)+c))-1/2/e*(e^2*(-4*a*c+b^2))^(1/2)/(4*a*c-b^2)*polylog(2,(a*e^2-b*d*e+c*d^2+b*e-2*c*d+c)*(e*x+d+1)^2/(-(e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(-e^2*(4*a*c-b^2))^(1/2)+c))*c/(a*e^2-b*e*d+c*d^2+(e^2*(-4*a*c+b^2))^(1/2)-c)","B"
62,1,194,81,0.061000," ","int((d*e*x+c*e)*(a+b*arctanh(d*x+c))/(1-(d*x+c)^2),x)","-\frac{a e \ln \left(d x +c -1\right)}{2 d}-\frac{a e \ln \left(d x +c +1\right)}{2 d}-\frac{b e \arctanh \left(d x +c \right) \ln \left(d x +c -1\right)}{2 d}-\frac{b e \arctanh \left(d x +c \right) \ln \left(d x +c +1\right)}{2 d}-\frac{b e \ln \left(d x +c -1\right)^{2}}{8 d}+\frac{b e \dilog \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2 d}+\frac{b e \ln \left(d x +c -1\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{4 d}+\frac{b e \ln \left(d x +c +1\right)^{2}}{8 d}-\frac{b e \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(d x +c +1\right)}{4 d}+\frac{b e \ln \left(-\frac{d x}{2}-\frac{c}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{4 d}"," ",0,"-1/2/d*a*e*ln(d*x+c-1)-1/2/d*a*e*ln(d*x+c+1)-1/2/d*b*e*arctanh(d*x+c)*ln(d*x+c-1)-1/2/d*b*e*arctanh(d*x+c)*ln(d*x+c+1)-1/8/d*b*e*ln(d*x+c-1)^2+1/2/d*b*e*dilog(1/2+1/2*d*x+1/2*c)+1/4/d*b*e*ln(d*x+c-1)*ln(1/2+1/2*d*x+1/2*c)+1/8/d*b*e*ln(d*x+c+1)^2-1/4/d*b*e*ln(-1/2*d*x-1/2*c+1/2)*ln(d*x+c+1)+1/4/d*b*e*ln(-1/2*d*x-1/2*c+1/2)*ln(1/2+1/2*d*x+1/2*c)","B"