Question Number 34270 by math khazana by abdo last updated on 03/May/18
$${let}\:{give}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{{n}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{for}\:{n}\geqslant\mathrm{2}\:{find}\:{a}\:{relation}\:{between}\:{A}_{{n}+\mathrm{1}} \:{and}\:{A}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:{A}_{{n}} . \\ $$