Question Number 226953 by Spillover last updated on 20/Dec/25
$${If}\:{I}_{{n}} =\int\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{{n}} {dx}\: \\ $$$${Show}\:{that} \\ $$$${I}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}{x}\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{{n}} +\mathrm{2}{na}^{\mathrm{2}} {I}_{{n}ā\mathrm{1}} \: \\ $$