Limit with definite Integral

[man111]

Evaluation of

[tex]\displaystyle \lim_{n\rightarrow \infty}\bigg[\bigg(\ln(n^2+n^{-2})\bigg)^{-1}\cdot \int^{\pi n}_{1}\frac{\sin^2(5x)}{x}dx\bigg][/tex]

[pipi langstrump]

Use L'Hôpital's rule