I could use some help with an integral. The problem asks to determine whether a given integral converges or diverges. I know that the answer is "diverges" but I'm not sure why.

I used integration by parts to get:

Then I evaluated

I understood to require the use of L' Hopital's rule which I applied as follows: If this were true, the improper integral would evaluate to -1 - 0 = -1 and would converge. Can anyone tell me where I went wrong?