\[ \int \frac {8 x^2+e^4 \left (64-32 x+4 x^2\right )}{4 x^4+e^8 \left (256-32 x^2+x^4\right )+e^4 \left (-64 x^2+4 x^4\right )} \, dx \]
Optimal antiderivative \[ \frac {x}{{\mathrm e}^{4} \left (4+x \right )-\frac {2 x^{2}}{4-x}} \]
command
integrate(((4*x^2-32*x+64)*exp(4)+8*x^2)/((x^4-32*x^2+256)*exp(4)^2+(4*x^4-64*x^2)*exp(4)+4*x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {4 \, {\left (x e^{4} + 2 \, x - 4 \, e^{4}\right )}}{{\left (x^{2} e^{4} + 2 \, x^{2} - 16 \, e^{4}\right )} {\left (e^{4} + 2\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________