\[ \int \frac {-x^2-\log (x)+2 \log ^2(x)}{-x^2 \log (x)+\log ^3(x)} \, dx \]
Optimal antiderivative \[ \logarithmicIntegral \left (x \right )-\frac {\ln \left (x -\ln \left (x \right )\right )}{2}+\frac {\ln \left (x +\ln \left (x \right )\right )}{2} \]
command
Integrate[(-x^2 - Log[x] + 2*Log[x]^2)/(-(x^2*Log[x]) + Log[x]^3),x]
Mathematica 13.1 output
\[ -\frac {1}{2} \log (x-\log (x))+\frac {1}{2} \log (x+\log (x))+\text {li}(x) \]
Mathematica 12.3 output
\[ \int \frac {-x^2-\log (x)+2 \log ^2(x)}{-x^2 \log (x)+\log ^3(x)} \, dx \]________________________________________________________________________________________