integral 1/(n(1+lnn^2) converge/diverge

[pamw]

\(\displaystyle \[
\int\limits_1^\infty {\frac{1}{{n(1 + \ln ^2 n)}}}
\]\)

Does this integral converge or diverge?

Would I multiply out the n or something? Help!

 

[pka]

If u=ln(n) here is what you have:
\(\displaystyle \int\limits_0^\infty {\frac{{du}}{{1 + u^2 }}} .\)