\[ \int \frac {8 x^5+e^8 \left (-48+8 x+16 x^2+2 x^3\right )+e^4 \left (192 x-80 x^3-8 x^4\right )}{-8 x^4+4 x^6+e^8 \left (-8+8 x+2 x^2-4 x^3+x^4\right )+e^4 \left (-16 x^2+8 x^3+8 x^4-4 x^5\right )} \, dx \]
Optimal antiderivative \[ \frac {4}{\frac {2}{3 \left (x -2 x^{2} {\mathrm e}^{-4}\right )}-\frac {1}{3}}+\ln \left (-x^{2}+2\right ) \]
command
integrate(((2*x^3+16*x^2+8*x-48)*exp(4)^2+(-8*x^4-80*x^3+192*x)*exp(4)+8*x^5)/((x^4-4*x^3+2*x^2+8*x-8)*exp(4)^2+(-4*x^5+8*x^4+8*x^3-16*x^2)*exp(4)+4*x^6-8*x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {24 \, e^{4}}{2 \, x^{2} - x e^{4} + 2 \, e^{4}} + \log \left ({\left | x^{2} - 2 \right |}\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________