\[ \int \frac {e^3 \left (160-40 x^4\right )+e^6 \left (-48 x+13 x^3+4 x^5+e^2 \left (-32+8 x^4\right )\right )}{25 x^3+e^3 \left (-10 e^2 x^3-10 x^4\right )+e^6 \left (e^4 x^3+2 e^2 x^4+x^5\right )} \, dx \]
Optimal antiderivative \[ \frac {3+\left (2 x -\frac {4}{x}\right )^{2}}{x +{\mathrm e}^{2}-5 \,{\mathrm e}^{-3}} \]
command
integrate((((8*x^4-32)*exp(2)+4*x^5+13*x^3-48*x)*exp(3)^2+(-40*x^4+160)*exp(3))/((x^3*exp(2)^2+2*x^4*exp(2)+x^5)*exp(3)^2+(-10*x^3*exp(2)-10*x^4)*exp(3)+25*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 4 \, x + \frac {4 \, e^{20} - 13 \, e^{16} - 80 \, e^{15} + 16 \, e^{12} + 130 \, e^{11} + 600 \, e^{10} - 325 \, e^{6} - 2000 \, e^{5} + 2500}{{\left (x e^{3} + e^{5} - 5\right )} {\left (e^{13} - 10 \, e^{8} + 25 \, e^{3}\right )}} - \frac {16 \, {\left (x e^{6} - e^{8} + 5 \, e^{3}\right )}}{x^{2} {\left (e^{10} - 10 \, e^{5} + 25\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________