\[ \int \frac {e^{12+\frac {2-x^2-x \log (x)}{x}} \left (2+x^2\right )}{x} \, dx \]
Optimal antiderivative \[ -{\mathrm e}^{\frac {2}{x}-x -\ln \left (x \right )} x \,{\mathrm e}^{12} \]
command
Int[(E^(12 + (2 - x^2 - x*Log[x])/x)*(2 + x^2))/x,x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{12+\frac {2-x^2-x \log (x)}{x}} \left (2+x^2\right )}{x} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ -e^{-x+\frac {2}{x}+12} \]