Question Number 136402 by mathmax by abdo last updated on 21/Mar/21
$$\mathrm{find}\:\mathrm{U}_{\mathrm{n}} =\int_{\frac{\mathrm{1}}{\mathrm{n}}} ^{\mathrm{n}} \:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\right)\mathrm{arctan}\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}\right)\mathrm{dx} \\ $$$$\mathrm{and}\:\mathrm{lim}_{\mathrm{n}\rightarrow\infty} \mathrm{U}_{\mathrm{n}} \\ $$