Question Number 113632 by mathmax by abdo last updated on 14/Sep/20
$$\mathrm{calculate}\:\mathrm{U}_{\mathrm{n}} =\int_{\frac{\mathrm{1}}{\mathrm{n}}} ^{\mathrm{n}} \left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{t}^{\mathrm{2}} }\right)\mathrm{arctan}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{t}}\right)\mathrm{dt} \\ $$$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{U}_{\mathrm{n}} \\ $$