\[ \int \frac {216 e^x x^3+e^x \left (-864 x^3-216 x^4\right ) \log (x)+e^x \log ^2(x)}{\log ^2(x)} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{x}-\frac {216 \,{\mathrm e}^{x} x^{4}}{\ln \left (x \right )} \]
command
Int[(216*E^x*x^3 + E^x*(-864*x^3 - 216*x^4)*Log[x] + E^x*Log[x]^2)/Log[x]^2,x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ -\frac {e^x \left (216 x^4 \log (x)-\log ^2(x)\right )}{\log ^2(x)} \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {216 e^x x^3+e^x \left (-864 x^3-216 x^4\right ) \log (x)+e^x \log ^2(x)}{\log ^2(x)} \, dx \]________________________________________________________________________________________