Question Number 121858 by Bird last updated on 12/Nov/20
$${decompose}\:{F}\left({x}\right)\:=\frac{{x}^{{n}} }{{x}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{1}} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{x}^{{n}} }{{x}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{1}}{dx} \\ $$$${n}\:{integr}\:{natural} \\ $$