\[ \int \frac {1-676 x-e^{2 e^2} x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{-676 x^2-e^{2 e^2} x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx \]
Optimal antiderivative \[ \ln \! \left (\ln \! \left (x \right )-x \left (2 x^{2}+26+x +{\mathrm e}^{{\mathrm e}^{2}}\right )^{2}\right ) \]
command
Int[(1 - 676*x - E^(2*E^2)*x - 104*x^2 - 315*x^3 - 16*x^4 - 20*x^5 + E^E^2*(-52*x - 4*x^2 - 12*x^3))/(-676*x^2 - E^(2*E^2)*x^2 - 52*x^3 - 105*x^4 - 4*x^5 - 4*x^6 + E^E^2*(-52*x^2 - 2*x^3 - 4*x^4) + x*Log[x]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {1-676 x-e^{2 e^2} x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{-676 x^2-e^{2 e^2} x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \log \left (x \left (2 x^2+x+e^{e^2}+26\right )^2-\log (x)\right ) \]