\[ \int \frac {e^2 (2+e)}{-e^2+6 e^{2 x+e x}} \, dx \]
Optimal antiderivative \[ \frac {1}{3}+\ln \! \left (\frac {{\mathrm e}^{2} {\mathrm e}^{-x \left ({\mathrm e}+2\right )}}{2}-3\right ) \]
command
integrate((exp(1)+2)*exp(2)/(6*exp(x*exp(1)+2*x)-exp(2)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {Exception raised: NotImplementedError} \]
Giac 1.7.0 via sagemath 9.3 output
\[ -{\left (x {\left (e + 2\right )} e^{\left (-2\right )} - e^{\left (-2\right )} \log \left ({\left | -e^{2} + 6 \, e^{\left (x {\left (e + 2\right )}\right )} \right |}\right )\right )} e^{2} \]