\[ \int \frac {32 x+16 e^3 x+2 e^6 x}{1+e^5-2 x^2+x^4+e^{5/2} \left (-2+2 x^2\right )} \, dx \]
Optimal antiderivative \[ \frac {\left (4+{\mathrm e}^{3}\right )^{2}}{1-{\mathrm e}^{\frac {5}{2}}-x^{2}} \]
command
integrate((2*x*exp(3)^2+16*x*exp(3)+32*x)/(exp(5/4)^4+(2*x^2-2)*exp(5/4)^2+x^4-2*x^2+1),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {e^{12} + 16 \, e^{9} + 96 \, e^{6} + 256 \, e^{3} + 256}{x^{2} e^{6} + 8 \, x^{2} e^{3} + 16 \, x^{2} + e^{\frac {17}{2}} - e^{6} + 8 \, e^{\frac {11}{2}} - 8 \, e^{3} + 16 \, e^{\frac {5}{2}} - 16} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________