\[ \int \frac {e^{\frac {-2+(-14+2 x) \log (\log (x))}{\log (\log (x))}} \left (1+x \log (x) \log ^2(\log (x))\right )}{2 x \log (x) \log ^2(\log (x))} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{-14+2 x -\frac {2}{\ln \left (\ln \left (x \right )\right )}}}{4}+8 \]
command
Int[(E^((-2 + (-14 + 2*x)*Log[Log[x]])/Log[Log[x]])*(1 + x*Log[x]*Log[Log[x]]^2))/(2*x*Log[x]*Log[Log[x]]^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{\frac {-2+(-14+2 x) \log (\log (x))}{\log (\log (x))}} \left (1+x \log (x) \log ^2(\log (x))\right )}{2 x \log (x) \log ^2(\log (x))} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {1}{4} e^{-2 \left (-x+\frac {1}{\log (\log (x))}+7\right )} \]