\[ \int \frac {\left (6-30 x+5 x^2\right ) \log (x)+\left (150 x^2-25 x^3+\left (30 x-5 x^2\right ) \log \left (\frac {6-x}{x}\right )\right ) \log ^2(x)+\left (30 x-5 x^2+(6-x) \log \left (\frac {6-x}{x}\right )\right ) \log \left (5 x+\log \left (\frac {6-x}{x}\right )\right )}{\left (150 x^3-25 x^4+\left (30 x^2-5 x^3\right ) \log \left (\frac {6-x}{x}\right )\right ) \log ^2(x)+\left (-30 x^2+5 x^3+\left (-6 x+x^2\right ) \log \left (\frac {6-x}{x}\right )\right ) \log (x) \log \left (5 x+\log \left (\frac {6-x}{x}\right )\right )} \, dx \]
Optimal antiderivative \[ \ln \! \left (\frac {\ln \! \left (\ln \! \left (\frac {6-x}{x}\right )+5 x \right )}{\ln \! \left (x \right )}-5 x \right ) \]
command
Int[((6 - 30*x + 5*x^2)*Log[x] + (150*x^2 - 25*x^3 + (30*x - 5*x^2)*Log[(6 - x)/x])*Log[x]^2 + (30*x - 5*x^2 + (6 - x)*Log[(6 - x)/x])*Log[5*x + Log[(6 - x)/x]])/((150*x^3 - 25*x^4 + (30*x^2 - 5*x^3)*Log[(6 - x)/x])*Log[x]^2 + (-30*x^2 + 5*x^3 + (-6*x + x^2)*Log[(6 - x)/x])*Log[x]*Log[5*x + Log[(6 - x)/x]]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {\left (6-30 x+5 x^2\right ) \log (x)+\left (150 x^2-25 x^3+\left (30 x-5 x^2\right ) \log \left (\frac {6-x}{x}\right )\right ) \log ^2(x)+\left (30 x-5 x^2+(6-x) \log \left (\frac {6-x}{x}\right )\right ) \log \left (5 x+\log \left (\frac {6-x}{x}\right )\right )}{\left (150 x^3-25 x^4+\left (30 x^2-5 x^3\right ) \log \left (\frac {6-x}{x}\right )\right ) \log ^2(x)+\left (-30 x^2+5 x^3+\left (-6 x+x^2\right ) \log \left (\frac {6-x}{x}\right )\right ) \log (x) \log \left (5 x+\log \left (\frac {6-x}{x}\right )\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \log \left (5 x \log (x)-\log \left (5 x+\log \left (\frac {6}{x}-1\right )\right )\right )-\log (\log (x)) \]