\[ \int \frac {e^{-e^{-5+e^5-x}} \left (20 x-4 x^2-x^3\right ) \left (-20+8 x+3 x^2+e^{-5+e^5-x} \left (-20 x+4 x^2+x^3\right )\right )}{-20 x+4 x^2+x^3} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\ln \left (\left (-x^{2}-4 x +20\right ) x \right )-{\mathrm e}^{{\mathrm e}^{5}-x -5}} \]
command
integrate(((x^3+4*x^2-20*x)*exp(exp(5)-x-5)+3*x^2+8*x-20)*exp(log(-x^3-4*x^2+20*x)-exp(exp(5)-x-5))/(x^3+4*x^2-20*x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ -{\left (x^{3} e^{\left (-x + e^{5} - e^{\left (-x + e^{5} - 5\right )} - 5\right )} + 4 \, x^{2} e^{\left (-x + e^{5} - e^{\left (-x + e^{5} - 5\right )} - 5\right )} - 20 \, x e^{\left (-x + e^{5} - e^{\left (-x + e^{5} - 5\right )} - 5\right )}\right )} e^{\left (x - e^{5} + 5\right )} \]