\[ \int \frac {-12+4 e^2}{1444+4 e^4+e^2 (152-44 x)-836 x+121 x^2} \, dx \]
Optimal antiderivative \[ \frac {-4+x}{19-\frac {11 x}{2}+{\mathrm e}^{2}} \]
command
integrate((4*exp(2)-12)/(4*exp(2)^2+(-44*x+152)*exp(2)+121*x^2-836*x+1444),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {4 \, {\left (e^{2} - 3\right )}}{11 \, {\left (11 \, x - 2 \, e^{2} - 38\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________