\[ \int \frac {x-x^2+\left (1250-2500 x+e^x \left (-2500 x+2500 x^2\right )\right ) \log \left (-\frac {e^{2 e^x}}{-x+x^2}\right )}{-5 x+5 x^2+e \left (-4 x+4 x^2\right )} \, dx \]
Optimal antiderivative \[ \frac {625 \ln \left (\frac {{\mathrm e}^{2 \,{\mathrm e}^{x}}}{-x^{2}+x}\right )^{2}-x}{5+4 \,{\mathrm e}} \]
command
integrate((((2500*x**2-2500*x)*exp(x)-2500*x+1250)*ln(-exp(exp(x))**2/(x**2-x))-x**2+x)/((4*x**2-4*x)*exp(1)+5*x**2-5*x),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \frac {x}{5 + 4 e} + \frac {625 \log {\left (- \frac {e^{2 e^{x}}}{x^{2} - x} \right )}^{2}}{5 + 4 e} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________