integral convergence - does this integration converge

Question

i just ran into this problem and i'm having a hard time solving it:

i would like to know if this integral converges or not, and why.

i'd prefer the normal convergence tests.

$$ \int_2^\infty\frac{x}{\ln^3 x}dx $$

Any help will be greatly appreciated.

thanks,

yaron.

Answer 1

Community wiki answer so the question can be marked as answered: No, the integral does not converge, since any power of $\ln x$ grows more slowly than $x$.