\[ \int \frac {-1500+525 x+45 x^2-33 x^3+3 x^4+\left (-375 x+205 x^2-50 x^3+3 x^4\right ) \log (x)}{\left (-1500 x+525 x^2+45 x^3-33 x^4+3 x^5\right ) \log (x)} \, dx \]
Optimal antiderivative \[ 7+\frac {x^{2}}{6 \left (5-x \right )^{2}}+\ln \! \left (\left (4+x \right ) \ln \! \left (x \right )\right ) \]
command
Int[(-1500 + 525*x + 45*x^2 - 33*x^3 + 3*x^4 + (-375*x + 205*x^2 - 50*x^3 + 3*x^4)*Log[x])/((-1500*x + 525*x^2 + 45*x^3 - 33*x^4 + 3*x^5)*Log[x]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {-1500+525 x+45 x^2-33 x^3+3 x^4+\left (-375 x+205 x^2-50 x^3+3 x^4\right ) \log (x)}{\left (-1500 x+525 x^2+45 x^3-33 x^4+3 x^5\right ) \log (x)} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ -\frac {5}{3 (5-x)}+\frac {25}{6 (5-x)^2}+\log (x+4)+\log (\log (x)) \]