\[ \int \frac {2-33 x+16 x^2-2 x^3+\left (16 x-8 x^2+x^3\right ) \log \left (3 e^{\frac {-1+\left (-8 x+2 x^2\right ) \log (x)}{-8 x+2 x^2}} x\right )}{\left (16 x-8 x^2+x^3\right ) \log ^2\left (3 e^{\frac {-1+\left (-8 x+2 x^2\right ) \log (x)}{-8 x+2 x^2}} x\right )} \, dx \]
Optimal antiderivative \[ \frac {x}{\ln \! \left (3 \,{\mathrm e}^{\ln \left (x \right )+\frac {1}{2 x \left (-x +4\right )}} x \right )} \]
command
Int[(2 - 33*x + 16*x^2 - 2*x^3 + (16*x - 8*x^2 + x^3)*Log[3*E^((-1 + (-8*x + 2*x^2)*Log[x])/(-8*x + 2*x^2))*x])/((16*x - 8*x^2 + x^3)*Log[3*E^((-1 + (-8*x + 2*x^2)*Log[x])/(-8*x + 2*x^2))*x]^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {2-33 x+16 x^2-2 x^3+\left (16 x-8 x^2+x^3\right ) \log \left (3 \exp \left (\frac {-1+\left (-8 x+2 x^2\right ) \log (x)}{-8 x+2 x^2}\right ) x\right )}{\left (16 x-8 x^2+x^3\right ) \log ^2\left (3 \exp \left (\frac {-1+\left (-8 x+2 x^2\right ) \log (x)}{-8 x+2 x^2}\right ) x\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {x}{\log \left (3 e^{\frac {1}{2 (4-x) x}} x^2\right )} \]