\[ \int \frac {4+12 x+5 x^2+e^4 \left (-4+20 x-5 x^2\right )}{32+32 x-24 x^2-16 x^3+8 x^4+e^8 \left (32-32 x+8 x^2\right )+e^4 \left (64-48 x^2+16 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {-5 x^{2}+4}{\left (-2+x \right ) \left (8 x +8 \,{\mathrm e}^{4}+8\right )}+50 \]
command
integrate(((-5*x^2+20*x-4)*exp(2)^2+5*x^2+12*x+4)/((8*x^2-32*x+32)*exp(2)^4+(16*x^3-48*x^2+64)*exp(2)^2+8*x^4-16*x^3-24*x^2+32*x+32),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {5 \, x e^{4} - 5 \, x - 10 \, e^{4} - 6}{8 \, {\left (x^{2} + x e^{4} - x - 2 \, e^{4} - 2\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________