\[ \int \frac {-400 x^2+800 x^3-400 x^4+\left (800 x-1600 x^2+800 x^3\right ) \log (-1+x)+\left (-400+800 x-400 x^2\right ) \log ^2(-1+x)+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (200 x^2-400 x^4+200 x^5+\left (200 x-400 x^2+800 x^3-400 x^4\right ) \log (-1+x)+\left (200 x-400 x^2+200 x^3\right ) \log ^2(-1+x)\right )}{e^{\frac {3 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (x^3-2 x^4+x^5+\left (-2 x^2+4 x^3-2 x^4\right ) \log (-1+x)+\left (x-2 x^2+x^3\right ) \log ^2(-1+x)\right )+e^{\frac {2 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (-3 x^3+6 x^4-3 x^5+\left (6 x^2-12 x^3+6 x^4\right ) \log (-1+x)+\left (-3 x+6 x^2-3 x^3\right ) \log ^2(-1+x)\right ) \log \left (x^2\right )+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (3 x^3-6 x^4+3 x^5+\left (-6 x^2+12 x^3-6 x^4\right ) \log (-1+x)+\left (3 x-6 x^2+3 x^3\right ) \log ^2(-1+x)\right ) \log ^2\left (x^2\right )+\left (-x^3+2 x^4-x^5+\left (2 x^2-4 x^3+2 x^4\right ) \log (-1+x)+\left (-x+2 x^2-x^3\right ) \log ^2(-1+x)\right ) \log ^3\left (x^2\right )} \, dx \]
Optimal antiderivative \[ 1-\frac {4}{\left (\frac {\ln \left (x^{2}\right )}{5}-\frac {{\mathrm e}^{\frac {x}{\left (x -\ln \left (-1+x \right )\right ) \left (-1+x \right )}+x}}{5}\right )^{2}} \]
command
integrate((((200*x^3-400*x^2+200*x)*log(-1+x)^2+(-400*x^4+800*x^3-400*x^2+200*x)*log(-1+x)+200*x^5-400*x^4+200*x^2)*exp(((x^2-x)*log(-1+x)-x^3+x^2-x)/((-1+x)*log(-1+x)-x^2+x))+(-400*x^2+800*x-400)*log(-1+x)^2+(800*x^3-1600*x^2+800*x)*log(-1+x)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*log(-1+x)^2+(-2*x^4+4*x^3-2*x^2)*log(-1+x)+x^5-2*x^4+x^3)*exp(((x^2-x)*log(-1+x)-x^3+x^2-x)/((-1+x)*log(-1+x)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*log(-1+x)^2+(6*x^4-12*x^3+6*x^2)*log(-1+x)-3*x^5+6*x^4-3*x^3)*log(x^2)*exp(((x^2-x)*log(-1+x)-x^3+x^2-x)/((-1+x)*log(-1+x)-x^2+x))^2+((3*x^3-6*x^2+3*x)*log(-1+x)^2+(-6*x^4+12*x^3-6*x^2)*log(-1+x)+3*x^5-6*x^4+3*x^3)*log(x^2)^2*exp(((x^2-x)*log(-1+x)-x^3+x^2-x)/((-1+x)*log(-1+x)-x^2+x))+((-x^3+2*x^2-x)*log(-1+x)^2+(2*x^4-4*x^3+2*x^2)*log(-1+x)-x^5+2*x^4-x^3)*log(x^2)^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {100}{2 \, e^{\left (\frac {x^{3} - x^{2} \log \left (x - 1\right ) - x^{2} + x \log \left (x - 1\right ) + x}{x^{2} - x \log \left (x - 1\right ) - x + \log \left (x - 1\right )}\right )} \log \left (x^{2}\right ) - \log \left (x^{2}\right )^{2} - e^{\left (\frac {2 \, {\left (x^{3} - x^{2} \log \left (x - 1\right ) - x^{2} + x \log \left (x - 1\right ) + x\right )}}{x^{2} - x \log \left (x - 1\right ) - x + \log \left (x - 1\right )}\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________