How I can prove that $\int_1^N \frac{\sin ^ 2 x}{x^2}\,\mathrm dx$ asymptotically equals to $\frac{\ln N}{N}$?
I tried to use partial integration, but it didn't give me good results. I calculated that integral in terms of $Si(x)$, but it also doesn't solve my problem. Can someone tell me, where I should look for?