\[ \int \frac {e^x \left (25+10 x+21 x^2+4 x^3+4 x^4\right )+e^{\frac {e^3+5 x+x^2+2 x^3}{5+x+2 x^2}} \left (25+e^3 (-1-4 x)+10 x+21 x^2+4 x^3+4 x^4\right )}{25+10 x+21 x^2+4 x^3+4 x^4} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {{\mathrm e}^{3}}{2 x^{2}+x +5}+x}+{\mathrm e}^{x}-{\mathrm e}^{5}-1 \]
command
Int[(E^x*(25 + 10*x + 21*x^2 + 4*x^3 + 4*x^4) + E^((E^3 + 5*x + x^2 + 2*x^3)/(5 + x + 2*x^2))*(25 + E^3*(-1 - 4*x) + 10*x + 21*x^2 + 4*x^3 + 4*x^4))/(25 + 10*x + 21*x^2 + 4*x^3 + 4*x^4),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^x \left (25+10 x+21 x^2+4 x^3+4 x^4\right )+e^{\frac {e^3+5 x+x^2+2 x^3}{5+x+2 x^2}} \left (25+e^3 (-1-4 x)+10 x+21 x^2+4 x^3+4 x^4\right )}{25+10 x+21 x^2+4 x^3+4 x^4} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^{\frac {e^3}{2 x^2+x+5}+x}+e^x \]