\[ \int \frac {e^4 (225-150 x)+1125 e^2 x^2}{e^4-30 e^2 x+225 x^2} \, dx \]
Optimal antiderivative \[ \frac {5 \left (3-x \right ) x}{\frac {1}{15}-x \,{\mathrm e}^{-2}} \]
command
integrate(((-150*x+225)*exp(2)^2+1125*x^2*exp(2))/(exp(2)^2-30*exp(2)*x+225*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 5 \, x e^{2} + \frac {e^{6} - 45 \, e^{4}}{3 \, {\left (15 \, x - e^{2}\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________