\[ \int \frac {-117+396 x-225 x^2-36 x^3+27 x^4+e^2 \left (54-198 x+162 x^2-36 x^3\right )}{4+e^4+e^2 (-4-2 x)+4 x+x^2} \, dx \]
Optimal antiderivative \[ \frac {3 \left (x^{2}-3 x +1\right ) \left (3 x^{2}-9 x +3\right )}{2-{\mathrm e}^{2}+x} \]
command
integrate(((-36*x^3+162*x^2-198*x+54)*exp(2)+27*x^4-36*x^3-225*x^2+396*x-117)/(exp(2)^2+(-2*x-4)*exp(2)+x^2+4*x+4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 9 \, x^{3} + 9 \, x^{2} e^{2} - 72 \, x^{2} + 9 \, x e^{4} - 90 \, x e^{2} + 243 \, x + \frac {9 \, {\left (e^{8} - 14 \, e^{6} + 71 \, e^{4} - 154 \, e^{2} + 121\right )}}{x - e^{2} + 2} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________