Question Number 28068 by abdo imad last updated on 19/Jan/18
$${let}\:{give}\:\:\:{I}_{{a}} \:\:=\:\:\int_{\mathrm{0}} ^{+\propto} \:\:\:\:\frac{{t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}}{dt}\:\:\:{by}\:{using}\:{Residus}\:{theorem} \\ $$ $${find}\:{the}\:{value}\:{of}\:\:{I}_{{a}} \:\:\:\:\:{with}\:\:\mathrm{0}<{a}<\mathrm{1}\:\:\:. \\ $$