\[ \int \frac {e^{2 e^4} \left (512 x-1024 x^2+768 x^3-256 x^4+32 x^5+e^8 \left (-4+x^2\right )\right )}{e^{16} x^2+4096 x^4-8192 x^5+6144 x^6-2048 x^7+256 x^8+e^8 \left (-128 x^3+128 x^4-32 x^5\right )} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{2 \,{\mathrm e}^{4}}}{\left (\frac {{\mathrm e}^{8}}{\left (-2+x \right )^{2} x}-16\right ) x^{2}} \]
command
integrate(((x^2-4)*exp(4)^2+32*x^5-256*x^4+768*x^3-1024*x^2+512*x)*exp(2*exp(4))/(x^2*exp(4)^4+(-32*x^5+128*x^4-128*x^3)*exp(4)^2+256*x^8-2048*x^7+6144*x^6-8192*x^5+4096*x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {{\left (x^{2} - 4 \, x + 4\right )} e^{\left (2 \, e^{4}\right )}}{16 \, x^{4} - 64 \, x^{3} + 64 \, x^{2} - x e^{8}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________