Question Number 34126 by abdo imad last updated on 30/Apr/18
$${let}\:{give}\:{n}\:{natural}\:{integr}\:{not}\:{o} \\ $$$${calculate}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\prod_{{k}=\mathrm{1}} ^{{n}} \left({x}^{\mathrm{2}} \:+{k}\right)}\:. \\ $$