Question

Determine whether the integral of 1/(x(lnx)^3) from 2, infinity is convergent or divergent.

Answer 1

The answer is convergent to 1/(2(ln2)^2), but I can't figure out where 1/2(ln2)^2 came from. Any help on that would be appreciated.

Answer 2

Hmmm I think this is the setup you're looking for.
The substitution look ok?

Rewriting an improper integral in a proper way can be a little tricky at first :)