\[ \int \frac {e^{2 x+\frac {e^{-x}}{-2 x^2+x^4}} \left (8 x^3-8 x^5+2 x^7+e^{-x} \left (4+2 x-4 x^2-x^3\right )\right )}{4 x^3-4 x^5+x^7} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{2 x} {\mathrm e}^{-\frac {{\mathrm e}^{-x}}{-x^{4}+2 x^{2}}} \]
command
integrate(((-x^3-4*x^2+2*x+4)*exp(-x)+2*x^7-8*x^5+8*x^3)*exp(2*x)/(x^7-4*x^5+4*x^3)/exp(-exp(-x)/(x^4-2*x^2)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ e^{\left (\frac {2 \, x^{5} - 4 \, x^{3} + e^{\left (-x\right )}}{x^{4} - 2 \, x^{2}}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {{\left (2 \, x^{7} - 8 \, x^{5} + 8 \, x^{3} - {\left (x^{3} + 4 \, x^{2} - 2 \, x - 4\right )} e^{\left (-x\right )}\right )} e^{\left (2 \, x + \frac {e^{\left (-x\right )}}{x^{4} - 2 \, x^{2}}\right )}}{x^{7} - 4 \, x^{5} + 4 \, x^{3}}\,{d x} \]________________________________________________________________________________________