I want to integrate [itex]\int_0^e \ln(x)[/itex] but first, I wondered if it would be divergent. I figured if xx goes to zero as x goes to zero then the integral would diverge (because xln(x)-x would diverge).
2. The attempt at a solution
I'm wondering how you could show that this limit (xx as x→0) is 1. It makes intuitive sense that it should approach 1, and it's clear from the graph, but I'm curious as to how someone would find this limit mathematically.