\[ \int \frac {e^4 \left (4-4 x+9 x^2-9 x^3\right )+\left (36 x^3-36 x^2 \log (x)\right ) \log \left (48+108 x^2\right )+\left (4-4 x+9 x^2-9 x^3\right ) \log ^2\left (48+108 x^2\right )}{e^8 \left (4 x+9 x^3\right )+e^4 \left (-4 x^2-9 x^4\right )+e^4 \left (4 x+9 x^3\right ) \log (x)+\left (-4 x^2-9 x^4+e^4 \left (8 x+18 x^3\right )+\left (4 x+9 x^3\right ) \log (x)\right ) \log ^2\left (48+108 x^2\right )+\left (4 x+9 x^3\right ) \log ^4\left (48+108 x^2\right )} \, dx \]
Optimal antiderivative \[ \ln \! \left (\frac {x -\ln \! \left (x \right )}{\ln \! \left (108 x^{2}+48\right )^{2}+{\mathrm e}^{4}}-1\right ) \]
command
Int[(E^4*(4 - 4*x + 9*x^2 - 9*x^3) + (36*x^3 - 36*x^2*Log[x])*Log[48 + 108*x^2] + (4 - 4*x + 9*x^2 - 9*x^3)*Log[48 + 108*x^2]^2)/(E^8*(4*x + 9*x^3) + E^4*(-4*x^2 - 9*x^4) + E^4*(4*x + 9*x^3)*Log[x] + (-4*x^2 - 9*x^4 + E^4*(8*x + 18*x^3) + (4*x + 9*x^3)*Log[x])*Log[48 + 108*x^2]^2 + (4*x + 9*x^3)*Log[48 + 108*x^2]^4),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^4 \left (4-4 x+9 x^2-9 x^3\right )+\left (36 x^3-36 x^2 \log (x)\right ) \log \left (48+108 x^2\right )+\left (4-4 x+9 x^2-9 x^3\right ) \log ^2\left (48+108 x^2\right )}{e^8 \left (4 x+9 x^3\right )+e^4 \left (-4 x^2-9 x^4\right )+e^4 \left (4 x+9 x^3\right ) \log (x)+\left (-4 x^2-9 x^4+e^4 \left (8 x+18 x^3\right )+\left (4 x+9 x^3\right ) \log (x)\right ) \log ^2\left (48+108 x^2\right )+\left (4 x+9 x^3\right ) \log ^4\left (48+108 x^2\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \log \left (\log ^2\left (12 \left (9 x^2+4\right )\right )-x+\log (x)+e^4\right )-\log \left (\log ^2\left (12 \left (9 x^2+4\right )\right )+e^4\right ) \]