\[ \int \frac {-600-300 x+67 x^2+8 x^3-x^4}{-1800 x+150 x^2+99 x^3-2 x^4-x^5+\left (600 x-150 x^2-8 x^3+2 x^4\right ) \log \left (\frac {300-75 x-4 x^2+x^3}{x}\right )} \, dx \]
Optimal antiderivative \[ \ln \! \left (\ln \! \left (\left (\frac {75}{x}-x \right ) \left (-x +4\right )\right )-\frac {x}{2}-3\right ) \]
command
Int[(-600 - 300*x + 67*x^2 + 8*x^3 - x^4)/(-1800*x + 150*x^2 + 99*x^3 - 2*x^4 - x^5 + (600*x - 150*x^2 - 8*x^3 + 2*x^4)*Log[(300 - 75*x - 4*x^2 + x^3)/x]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {-600-300 x+67 x^2+8 x^3-x^4}{-1800 x+150 x^2+99 x^3-2 x^4-x^5+\left (600 x-150 x^2-8 x^3+2 x^4\right ) \log \left (\frac {300-75 x-4 x^2+x^3}{x}\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \log \left (-2 \log \left (x^2-4 x+\frac {300}{x}-75\right )+x+6\right ) \]