\[ \int \frac {-x^3+e^{-2+x+\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left ((2-x) \log (2)+e^{5/x} \left (5 x-x^3\right ) \log (2)\right )}{25 x^3+10 x^4+x^5+e^{\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left (10 x^3+2 x^4\right ) \log (2)+e^{\frac {2 e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} x^3 \log ^2(2)} \, dx \]
Optimal antiderivative \[ \frac {1}{5+\ln \! \left (2\right ) {\mathrm e}^{\left ({\mathrm e}^{\frac {5}{x}}+\frac {1}{x^{2}}\right ) {\mathrm e}^{-2+x}}+x} \]
command
Integrate[(-x^3 + E^(-2 + x + (E^(-2 + x)*(1 + E^(5/x)*x^2))/x^2)*((2 - x)*Log[2] + E^(5/x)*(5*x - x^3)*Log[2]))/(25*x^3 + 10*x^4 + x^5 + E^((E^(-2 + x)*(1 + E^(5/x)*x^2))/x^2)*(10*x^3 + 2*x^4)*Log[2] + E^((2*E^(-2 + x)*(1 + E^(5/x)*x^2))/x^2)*x^3*Log[2]^2),x]
Mathematica 13.1 output
\[ \text {\$Aborted} \]
Mathematica 12.3 output
\[ \frac {-e^4 x^3 \log (2)+e^{2+x} (5+x) (x \log (2)-\log (4))+e^{2+\frac {5}{x}+x} x (5+x) \left (x^2 \log (2)-\log (32)\right )}{e^2 \left (-e^2 x^3+e^x \left (-10+3 x+x^2\right )+e^{\frac {5}{x}+x} x \left (-25-5 x+5 x^2+x^3\right )\right ) \log (2) \left (5+x+e^{e^{-2+x} \left (e^{5/x}+\frac {1}{x^2}\right )} \log (2)\right )} \]