\[ \int \frac {-2 e^{5/2}-3 e^5}{4 x^2+e^5 \left (121+66 x+9 x^2\right )+e^{5/2} \left (44 x+12 x^2\right )} \, dx \]
Optimal antiderivative \[ \frac {1}{11+2 x \,{\mathrm e}^{-\frac {5}{2}}+3 x}-4 \]
command
integrate((-3*exp(5/2)^2-2*exp(5/2))/((9*x^2+66*x+121)*exp(5/2)^2+(12*x^2+44*x)*exp(5/2)+4*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {3 \, e^{5} + 2 \, e^{\frac {5}{2}}}{{\left (3 \, x e^{\frac {5}{2}} + 2 \, x + 11 \, e^{\frac {5}{2}}\right )} {\left (3 \, e^{\frac {5}{2}} + 2\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________