\[ \int \frac {5832-3420 x+668 x^2-58 x^3+2 x^4+\left (-738 x+206 x^2-27 x^3+x^4\right ) \log \left (\frac {1}{x^2}\right )}{\left (2916 x-1710 x^2+334 x^3-29 x^4+x^5\right ) \log \left (\frac {1}{x^2}\right )} \, dx \]
Optimal antiderivative \[ \ln \! \left (\frac {\frac {\left (1+2 x \right ) x}{\left (x -9\right )^{2}}+x -4}{4 \ln \! \left (\frac {1}{x^{2}}\right )}\right ) \]
command
Int[(5832 - 3420*x + 668*x^2 - 58*x^3 + 2*x^4 + (-738*x + 206*x^2 - 27*x^3 + x^4)*Log[x^(-2)])/((2916*x - 1710*x^2 + 334*x^3 - 29*x^4 + x^5)*Log[x^(-2)]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {5832-3420 x+668 x^2-58 x^3+2 x^4+\left (-738 x+206 x^2-27 x^3+x^4\right ) \log \left (\frac {1}{x^2}\right )}{\left (2916 x-1710 x^2+334 x^3-29 x^4+x^5\right ) \log \left (\frac {1}{x^2}\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ -\log \left (\log \left (\frac {1}{x^2}\right )\right )+\log \left (-x^3+20 x^2-154 x+324\right )-2 \log (9-x) \]