Question Number 33889 by math khazana by abdo last updated on 26/Apr/18
$${prove}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }}\:=\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\:\frac{{C}_{\mathrm{2}{n}} ^{{n}} }{\mathrm{4}^{{n}} \left(\mathrm{4}{n}+\mathrm{1}\right)}\:. \\ $$