If you remember the antiderivative of ln x you could rewrite the integrand as
take both u and v' to be ln x, and go from there.
If you don't remember the antiderivative of ln x then you'll have to use the hidden factor of 1 and take
u = (ln x)2
v' = 1.
We put stuff in the formula:
Again, we use the hidden factor of 1 to get
Wrapping this expression in brackets and putting it in where we left off,