Question Number 160439 by qaz last updated on 29/Nov/21
$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{3}\pi}\int_{\pi} ^{\mathrm{2}\pi} \frac{\mathrm{x}}{\mathrm{arctan}\:\left(\mathrm{nx}\right)}\mathrm{dx}\right)^{\mathrm{n}} =? \\ $$