p Values for which an integral converges

[cheffy]

Find the values for p for which the
integral of 1/(xln(x)^p) from 2 to infinity
converges.

I have no idea how to start this.

 

[pka]

If you know that \(\displaystyle y' = \frac{1}{{x\left( {\ln (x)} \right)^p }} \to \;y = \frac{{\left[ {\ln (x)} \right]^{1 - p} }}{{1 - p}}\),
then you can find the values for p.

 

[cheffy]

I don't understand. Would it be wherever y is defined? Wouldn't that just be p can't be 0?

 

[pka]

\(\displaystyle \L p > 1\quad \Rightarrow \quad \lim _{x \to \infty } \left( {\frac{{\left[ {\ln (x)} \right]^{1 - p} }}{{1 - p}}} \right) = ?\)