\[ \int \frac {\left (32+32 x-32 x^2-32 x^3\right ) \log ^3(1+x)+\left (-6 x^5-6 x^7\right ) \log ^3\left (\frac {1+x^2}{x}\right )+\left (30 x^3+12 x^4+42 x^5+12 x^6+12 x^7\right ) \log (1+x) \log ^3\left (\frac {1+x^2}{x}\right )+\left (-60 x^2-60 x^3-60 x^4-60 x^5\right ) \log ^2(1+x) \log ^3\left (\frac {1+x^2}{x}\right )}{\left (x+x^2+x^3+x^4\right ) \log ^3(1+x) \log ^3\left (\frac {1+x^2}{x}\right )} \, dx \]
Optimal antiderivative \[ 5+3 \left (\frac {x^{2}}{\ln \! \left (1+x \right )}-5\right )^{2}+\frac {16}{\ln \! \left (x +\frac {1}{x}\right )^{2}} \]
command
Int[((32 + 32*x - 32*x^2 - 32*x^3)*Log[1 + x]^3 + (-6*x^5 - 6*x^7)*Log[(1 + x^2)/x]^3 + (30*x^3 + 12*x^4 + 42*x^5 + 12*x^6 + 12*x^7)*Log[1 + x]*Log[(1 + x^2)/x]^3 + (-60*x^2 - 60*x^3 - 60*x^4 - 60*x^5)*Log[1 + x]^2*Log[(1 + x^2)/x]^3)/((x + x^2 + x^3 + x^4)*Log[1 + x]^3*Log[(1 + x^2)/x]^3),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {\left (32+32 x-32 x^2-32 x^3\right ) \log ^3(1+x)+\left (-6 x^5-6 x^7\right ) \log ^3\left (\frac {1+x^2}{x}\right )+\left (30 x^3+12 x^4+42 x^5+12 x^6+12 x^7\right ) \log (1+x) \log ^3\left (\frac {1+x^2}{x}\right )+\left (-60 x^2-60 x^3-60 x^4-60 x^5\right ) \log ^2(1+x) \log ^3\left (\frac {1+x^2}{x}\right )}{\left (x+x^2+x^3+x^4\right ) \log ^3(1+x) \log ^3\left (\frac {1+x^2}{x}\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ -\frac {12 x^3 (x+1)}{\log (x+1)}+\frac {16}{\log ^2\left (\frac {x^2+1}{x}\right )}+\frac {3 (x+1)^4}{\log ^2(x+1)}-\frac {12 (x+1)^3}{\log ^2(x+1)}+\frac {18 (x+1)^2}{\log ^2(x+1)}-\frac {12 (x+1)}{\log ^2(x+1)}+\frac {3}{\log ^2(x+1)}+\frac {12 (x+1)^4}{\log (x+1)}-\frac {36 (x+1)^3}{\log (x+1)}+\frac {36 (x+1)^2}{\log (x+1)}-\frac {30 x (x+1)}{\log (x+1)}+\frac {18 (x+1)}{\log (x+1)}-\frac {30}{\log (x+1)} \]