let-give-I-a-0-t-a-1-1-t-dt-by-using-Residus-theorem-find-the-value-of-I-a-with-0-lt-a-lt-1-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 28068 by abdo imad last updated on 19/Jan/18

let give I_a = ∫_0 ^(+∝) (t^(a−1) /(1+t))dt by using Residus theorem find the value of I_a with 0<a<1 .

$${let}\:{give}\:\:\:{I}_{{a}} \:\:=\:\:\int_{\mathrm{0}} ^{+\propto} \:\:\:\:\frac{{t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}}{dt}\:\:\:{by}\:{using}\:{Residus}\:{theorem} \\ $$$${find}\:{the}\:{value}\:{of}\:\:{I}_{{a}} \:\:\:\:\:{with}\:\:\mathrm{0}<{a}<\mathrm{1}\:\:\:. \\ $$

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let-give-I-a-0-t-a-1-1-t-dt-by-using-Residus-theorem-find-the-value-of-I-a-with-0-lt-a-lt-1-

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