Compute the indefinite integral

I don’t quit understand what the question wants me to do here with ‘by choosing $u'(x) = x$ and $v(x) = ln(x)$‘

This is what I am supposed to integrate by parts by "choosing"what am I supposed to do with these u’s and v’s?
$$int :xln left(xright)dx$$

but wait it asks to do the other way around as well….