\[ \int \frac {-1+6 e^x+e^x \log \left (\frac {5 e^x}{-e^5+\log (5)}\right )}{5 e^x-x+e^x \log \left (\frac {5 e^x}{-e^5+\log (5)}\right )} \, dx \]
Optimal antiderivative \[ \ln \left ({\mathrm e}^{x} \left (\ln \left (\frac {5 \,{\mathrm e}^{x}}{\ln \left (5\right )-{\mathrm e}^{5}}\right )+5\right )-x \right ) \]
command
integrate((exp(x)*ln(5*exp(x)/(ln(5)-exp(5)))+6*exp(x)-1)/(exp(x)*ln(5*exp(x)/(ln(5)-exp(5)))+5*exp(x)-x),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \log {\left (- \frac {x}{x - \log {\left (- \log {\left (5 \right )} + e^{5} \right )} + \log {\left (5 \right )} + 5 + i \pi } + e^{x} \right )} + \log {\left (x - \log {\left (- \log {\left (5 \right )} + e^{5} \right )} + \log {\left (5 \right )} + 5 + i \pi \right )} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________