\[ \int \frac {-2+x+((-12+7 x) \log (3)+(12-7 x) \log (x)) \log (-\log (3)+\log (x))}{\left (-256 x^7+256 x^8-64 x^9\right ) \log (3)+\left (256 x^7-256 x^8+64 x^9\right ) \log (x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left (\ln \! \left (x \right )-\ln \! \left (3\right )\right )}{64 x^{6} \left (-2+x \right )} \]
command
Integrate[(-2 + x + ((-12 + 7*x)*Log[3] + (12 - 7*x)*Log[x])*Log[-Log[3] + Log[x]])/((-256*x^7 + 256*x^8 - 64*x^9)*Log[3] + (256*x^7 - 256*x^8 + 64*x^9)*Log[x]),x]
Mathematica 13.1 output
\[ \int \frac {-2+x+((-12+7 x) \log (3)+(12-7 x) \log (x)) \log (-\log (3)+\log (x))}{\left (-256 x^7+256 x^8-64 x^9\right ) \log (3)+\left (256 x^7-256 x^8+64 x^9\right ) \log (x)} \, dx \]
Mathematica 12.3 output
\[ \frac {\log \left (\log \left (\frac {x}{3}\right )\right )}{64 (-2+x) x^6} \]