- #1

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## Main Question or Discussion Point

I know that the improper integral

[itex]

\int_2^\infty \left(\frac{1}{x\log^2x}\right)^p \, dx

[/itex]

converges for p=1, but does it diverge for p>1? How do you show this?

[itex]

\int_2^\infty \left(\frac{1}{x\log^2x}\right)^p \, dx

[/itex]

converges for p=1, but does it diverge for p>1? How do you show this?