\[ \int \frac {32+2 e^{10}+512 x^3+128 x^4+128 x^8+e^5 \left (-16-32 x^4\right )}{64-64 x+16 x^2+e^{10} x^2-128 x^5+64 x^6+64 x^{10}+e^5 \left (16 x-8 x^2-16 x^6\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{2}-\frac {2}{x -\frac {4}{4 x^{4}+2-\frac {{\mathrm e}^{5}}{2}}} \]
command
integrate((2*exp(5)^2+(-32*x^4-16)*exp(5)+128*x^8+128*x^4+512*x^3+32)/(x^2*exp(5)^2+(-16*x^6-8*x^2+16*x)*exp(5)+64*x^10+64*x^6-128*x^5+16*x^2-64*x+64),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {2 \, {\left (8 \, x^{4} - e^{5} + 4\right )}}{8 \, x^{5} - x e^{5} + 4 \, x - 8} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________