\[ \int \frac {32-72 x+72 x^2-30 x^3+4 x^4+\left (8 x-20 x^2+2 x^3+2 x^4\right ) \log \left (x^2\right )}{\left (16 x-36 x^2+36 x^3-15 x^4+2 x^5\right ) \log \left (x^2\right )} \, dx \]
Optimal antiderivative \[ \ln \! \left (\frac {\left (x -4\right )^{2} \ln \! \left (x^{2}\right )}{2 x +1-\frac {4}{2-x}}\right ) \]
command
Int[(32 - 72*x + 72*x^2 - 30*x^3 + 4*x^4 + (8*x - 20*x^2 + 2*x^3 + 2*x^4)*Log[x^2])/((16*x - 36*x^2 + 36*x^3 - 15*x^4 + 2*x^5)*Log[x^2]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {32-72 x+72 x^2-30 x^3+4 x^4+\left (8 x-20 x^2+2 x^3+2 x^4\right ) \log \left (x^2\right )}{\left (16 x-36 x^2+36 x^3-15 x^4+2 x^5\right ) \log \left (x^2\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ -\log \left (2 x^2-3 x+2\right )+\log \left (\log \left (x^2\right )\right )+\log (2-x)+2 \log (4-x) \]