\[ \int \frac {e^{\frac {5 x-\log \left (\frac {1}{9} (-100+9 \log (\log (-2+x)))\right )}{x}} \left (-9 e^4 x+\left (e^4 (200-100 x) \log (-2+x)+e^4 (-18+9 x) \log (-2+x) \log (\log (-2+x))\right ) \log \left (\frac {1}{9} (-100+9 \log (\log (-2+x)))\right )\right )}{\left (200 x^2-100 x^3\right ) \log (-2+x)+\left (-18 x^2+9 x^3\right ) \log (-2+x) \log (\log (-2+x))} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{4} {\mathrm e}^{5-\frac {\ln \left (\ln \left (\ln \left (-2+x \right )\right )-\frac {100}{9}\right )}{x}} \]
command
Int[(E^((5*x - Log[(-100 + 9*Log[Log[-2 + x]])/9])/x)*(-9*E^4*x + (E^4*(200 - 100*x)*Log[-2 + x] + E^4*(-18 + 9*x)*Log[-2 + x]*Log[Log[-2 + x]])*Log[(-100 + 9*Log[Log[-2 + x]])/9]))/((200*x^2 - 100*x^3)*Log[-2 + x] + (-18*x^2 + 9*x^3)*Log[-2 + x]*Log[Log[-2 + x]]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \exp \left (\frac {5 x-\log \left (\frac {1}{9} (9 \log (\log (x-2))-100)\right )}{x}+4\right ) \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {\exp \left (\frac {5 x-\log \left (\frac {1}{9} (-100+9 \log (\log (-2+x)))\right )}{x}\right ) \left (-9 e^4 x+\left (e^4 (200-100 x) \log (-2+x)+e^4 (-18+9 x) \log (-2+x) \log (\log (-2+x))\right ) \log \left (\frac {1}{9} (-100+9 \log (\log (-2+x)))\right )\right )}{\left (200 x^2-100 x^3\right ) \log (-2+x)+\left (-18 x^2+9 x^3\right ) \log (-2+x) \log (\log (-2+x))} \, dx \]________________________________________________________________________________________