\[ \int \frac {-25-10 x-x^2+25 x^3+10 x^4+x^5+e^2 \left (-5-15 x^2+5 x^3\right )+\left (10+2 x-10 x^3-2 x^4\right ) \log \left (-2+2 x^3\right )+\left (-1+x^3\right ) \log ^2\left (-2+2 x^3\right )}{-25-10 x-x^2+25 x^3+10 x^4+x^5+\left (10+2 x-10 x^3-2 x^4\right ) \log \left (-2+2 x^3\right )+\left (-1+x^3\right ) \log ^2\left (-2+2 x^3\right )} \, dx \]
Optimal antiderivative \[ x -\frac {5 \,{\mathrm e}^{2}}{5+x -\ln \left (\ln \left ({\mathrm e}^{2 x}\right ) x^{2}-2\right )}-2 \]
command
Int[(-25 - 10*x - x^2 + 25*x^3 + 10*x^4 + x^5 + E^2*(-5 - 15*x^2 + 5*x^3) + (10 + 2*x - 10*x^3 - 2*x^4)*Log[-2 + 2*x^3] + (-1 + x^3)*Log[-2 + 2*x^3]^2)/(-25 - 10*x - x^2 + 25*x^3 + 10*x^4 + x^5 + (10 + 2*x - 10*x^3 - 2*x^4)*Log[-2 + 2*x^3] + (-1 + x^3)*Log[-2 + 2*x^3]^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ x-\frac {5 e^2}{-\log \left (2 x^3-2\right )+x+5} \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {-25-10 x-x^2+25 x^3+10 x^4+x^5+e^2 \left (-5-15 x^2+5 x^3\right )+\left (10+2 x-10 x^3-2 x^4\right ) \log \left (-2+2 x^3\right )+\left (-1+x^3\right ) \log ^2\left (-2+2 x^3\right )}{-25-10 x-x^2+25 x^3+10 x^4+x^5+\left (10+2 x-10 x^3-2 x^4\right ) \log \left (-2+2 x^3\right )+\left (-1+x^3\right ) \log ^2\left (-2+2 x^3\right )} \, dx \]________________________________________________________________________________________