\[ \int \frac {2\ 3^{e^x (12-6 x)}+3^{e^x (12-6 x)} \left (2+e^x \left (12 x-12 x^2\right ) \log (3)\right ) \log (x) \log (\log (x))}{\log (x)} \, dx \]
Optimal antiderivative \[ 2 x \,{\mathrm e}^{6 \ln \left (3\right ) \left (2-x \right ) {\mathrm e}^{x}} \ln \left (\ln \left (x \right )\right ) \]
command
Int[(2*3^(E^x*(12 - 6*x)) + 3^(E^x*(12 - 6*x))*(2 + E^x*(12*x - 12*x^2)*Log[3])*Log[x]*Log[Log[x]])/Log[x],x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ -\frac {2\ 3^{6 e^x (2-x)} \left (e^x x \log (x) \log (\log (x))-e^x x^2 \log (x) \log (\log (x))\right )}{\left (e^x-e^x (2-x)\right ) \log (x)} \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {2\ 3^{e^x (12-6 x)}+3^{e^x (12-6 x)} \left (2+e^x \left (12 x-12 x^2\right ) \log (3)\right ) \log (x) \log (\log (x))}{\log (x)} \, dx \]________________________________________________________________________________________