\[ \int \frac {e^2 \left (-e x-x^2\right )+e^{\frac {\log (e+x)+e^2 \log (5 x \log (4))}{e^2}} \left (x+e^2 (e+x)\right )}{e^2 \left (e x+x^2\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\ln \left (10 x \ln \left (2\right )\right )+\ln \left (x +{\mathrm e}\right ) {\mathrm e}^{-2}}-x \]
command
integrate((((x+exp(1))*exp(2)+x)*exp((exp(2)*ln(10*x*ln(2))+ln(x+exp(1)))/exp(2))+(-x*exp(1)-x**2)*exp(2))/(x*exp(1)+x**2)/exp(2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {\frac {10 x \left (x + e\right )^{e^{-2}} e^{2} \log {\left (2 \right )}}{1 + e^{2}} + \frac {10 x \left (x + e\right )^{e^{-2}} e^{4} \log {\left (2 \right )}}{1 + e^{2}} - x e^{2} - \frac {10 \left (x + e\right )^{e^{-2}} e^{7} \log {\left (2 \right )}}{1 + e^{2}} - \frac {10 \left (x + e\right )^{e^{-2}} e^{5} \log {\left (2 \right )}}{1 + e^{2}} + 10 \left (x + e\right )^{e^{-2}} e^{5} \log {\left (2 \right )}}{e^{2}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {\int \left (- \frac {e^{3}}{x + e}\right )\, dx + \int \left (- \frac {x e^{2}}{x + e}\right )\, dx + \int \frac {10 x \left (x + e\right )^{e^{-2}} \log {\left (2 \right )}}{x + e}\, dx + \int \frac {10 \left (x + e\right )^{e^{-2}} e^{3} \log {\left (2 \right )}}{x + e}\, dx + \int \frac {10 x \left (x + e\right )^{e^{-2}} e^{2} \log {\left (2 \right )}}{x + e}\, dx}{e^{2}} \]________________________________________________________________________________________