\[ \int \frac {e^{e^{-4+2 x}} \left (1+8 x+e^{-4+2 x} \left (10-2 x-8 x^2\right )\right )}{25-10 x-39 x^2+8 x^3+16 x^4} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{{\mathrm e}^{2 x -4}}}{-4 x^{2}-x +5} \]
command
Int[(E^E^(-4 + 2*x)*(1 + 8*x + E^(-4 + 2*x)*(10 - 2*x - 8*x^2)))/(25 - 10*x - 39*x^2 + 8*x^3 + 16*x^4),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{e^{-4+2 x}} \left (1+8 x+e^{-4+2 x} \left (10-2 x-8 x^2\right )\right )}{25-10 x-39 x^2+8 x^3+16 x^4} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {e^{e^{2 x-4}} \left (-4 x^2-x+5\right )}{16 x^4+8 x^3-39 x^2-10 x+25} \]