Showing that a finction is not integrable

Hello!

I've got what looks like a simple problem but I just can't get it right.

Here it goes: Show that , is not in .

My first thought was to simply compute the integral

and show that it diverges - however I had no luck doing that.

Then I thought that I might simply estimate it from below with something that I know is infinite but no luck there either, all I got was:

Thanks!

Re: Showing that a finction is not integrable

You don't need to compute the integral. Just notice that and the integral is divergent.