\[ \int \frac {-14950+17450 x+32400 x^2+209952 x^3+\left (7475 x+88776 x^2-104976 x^3\right ) \log \left (\frac {89401 x^2-193752 x^3+104976 x^4}{625+16200 x+104976 x^2}\right )}{14950 x+177552 x^2-209952 x^3+\left (-7475 x-88776 x^2+104976 x^3\right ) \log \left (\frac {89401 x^2-193752 x^3+104976 x^4}{625+16200 x+104976 x^2}\right )} \, dx \]
Optimal antiderivative \[ \ln \! \left (\ln \! \left (\left (\frac {x}{x +\frac {25}{324}}-x \right )^{2}\right )-2\right )-x \]
command
Int[(-14950 + 17450*x + 32400*x^2 + 209952*x^3 + (7475*x + 88776*x^2 - 104976*x^3)*Log[(89401*x^2 - 193752*x^3 + 104976*x^4)/(625 + 16200*x + 104976*x^2)])/(14950*x + 177552*x^2 - 209952*x^3 + (-7475*x - 88776*x^2 + 104976*x^3)*Log[(89401*x^2 - 193752*x^3 + 104976*x^4)/(625 + 16200*x + 104976*x^2)]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {-14950+17450 x+32400 x^2+209952 x^3+\left (7475 x+88776 x^2-104976 x^3\right ) \log \left (\frac {89401 x^2-193752 x^3+104976 x^4}{625+16200 x+104976 x^2}\right )}{14950 x+177552 x^2-209952 x^3+\left (-7475 x-88776 x^2+104976 x^3\right ) \log \left (\frac {89401 x^2-193752 x^3+104976 x^4}{625+16200 x+104976 x^2}\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \log \left (2-\log \left (\frac {(299-324 x)^2 x^2}{(324 x+25)^2}\right )\right )-x \]