# Unsure of solution to improper integral

I've been trying to solve this improper integral ∫[∞][1] ln(x) x^-1 dx. I couldn't find any way to use the comparison test to find divergence, so I used substitution and got ∞-∞ which I was pretty sure was divergence until I noticed I put 0 instead of 1 making my answer ∞. Do I need to prove divergence with a comparison test or is an answer of ∞ enough to prove it.

BvU
Homework Helper
Hi T,
You could work out $$\int_1^Y {\ln x\over x} dx$$ (As I think you did already) and take ##\lim Y\rightarrow \infty## to show the integral does not exist.

Satirical T-rex
Ssnow
Gold Member
Hi,this integral has simple antiderivative (after substituting ##\ln##), after you can take the limit of the result for ##Y\rightarrow +\infty## (as suggested by @BvU ).

Satirical T-rex
Thanks for your help and the warm welcome.

Ssnow