You can reach integral of x.lnx^2 answer on this page.
What is integral of ∫x.lnx^2.dx?
Solution. In this case, the factor $X$ is easy to integrate, while the factor ln $x^2$ is simplified by differentiation. This suggests that you try integration by parts with:
$int x.lnx^2.dx=frac{1}{2}.x^2(lnx^2-1)+C$
