Unsure of solution to improper integral

[Satirical T-rex]

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]

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.

 

[Ssnow]

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.