\[ \int \frac {-25 e^2 x^2+e^4 \left (-200 x+50 x^2\right )}{4 x^2-4 x^3+x^4+e^4 \left (64-64 x+16 x^2\right )+e^2 \left (32 x-32 x^2+8 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {x^{2}}{\left (-x \,{\mathrm e}^{-2}-4\right ) \left (\frac {4}{25}-\frac {2 x}{25}\right )} \]
command
integrate(((50*x^2-200*x)*exp(2)^2-25*x^2*exp(2))/((16*x^2-64*x+64)*exp(2)^2+(8*x^3-32*x^2+32*x)*exp(2)+x^4-4*x^3+4*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {25 \, {\left (2 \, x e^{4} - x e^{2} - 4 \, e^{4}\right )}}{x^{2} + 4 \, x e^{2} - 2 \, x - 8 \, e^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________