Question Number 28988 by abdo imad last updated on 02/Feb/18
$${let}\:{give}\:\mathrm{0}<\alpha<\mathrm{1}\:{find}\:{in}\:{terms}\:{of}\:\alpha\:{the}\:{value}\:{of}\:{integral} \\ $$ $$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{{x}^{\alpha} \left(\mathrm{1}+{x}\right)}\:. \\ $$