Question Number 61885 by maxmathsup by imad last updated on 10/Jun/19
$${let}\:{I}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}+{i}\right)^{{n}} }\:\:{and}\:{J}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}−{i}\right)^{{n}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:{and}\:{J}\:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{thevalue}\:{of}\:{integral} \\ $$$${A}_{{n}} \:\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{\:{cos}\left({narctan}\left(\frac{\mathrm{1}}{{x}}\right)\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{{n}}{\mathrm{2}}} }{dx}\:\:\:\: \\ $$$$ \\ $$