\[ \int \frac {-108+144 x^3+2 x^6+e^{-1+x} \left (-54+72 x^3+x^6\right )+\left (e^{-1+x} \left (9 x-24 x^4+16 x^7\right )+e^{-1+x} x^7 \log (x)\right ) \log \left (\frac {9-24 x^3+16 x^6+x^6 \log (x)}{x^6}\right )}{9 x-24 x^4+16 x^7+x^7 \log (x)} \, dx \]
Optimal antiderivative \[ \ln \! \left (\ln \! \left (x \right )+\left (4-\frac {3}{x^{3}}\right )^{2}\right ) \left (2+{\mathrm e}^{-1+x}\right ) \]
command
Integrate[(-108 + 144*x^3 + 2*x^6 + E^(-1 + x)*(-54 + 72*x^3 + x^6) + (E^(-1 + x)*(9*x - 24*x^4 + 16*x^7) + E^(-1 + x)*x^7*Log[x])*Log[(9 - 24*x^3 + 16*x^6 + x^6*Log[x])/x^6])/(9*x - 24*x^4 + 16*x^7 + x^7*Log[x]),x]
Mathematica 13.1 output
\[ \text {\$Aborted} \]
Mathematica 12.3 output
\[ \frac {-12 e \log (x)+e^x \log \left (\frac {\left (3-4 x^3\right )^2}{x^6}+\log (x)\right )+2 e \log \left (9-24 x^3+16 x^6+x^6 \log (x)\right )}{e} \]