let-give-0-lt-lt-1-find-in-terms-of-the-value-of-integral-0-dx-x-1-x-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 28988 by abdo imad last updated on 02/Feb/18

let give 0<α<1 find in terms of α the value of integral ∫_0 ^∞ (dx/(x^α (1+x))) .

$${let}\:{give}\:\mathrm{0}<\alpha<\mathrm{1}\:{find}\:{in}\:{terms}\:{of}\:\alpha\:{the}\:{value}\:{of}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{{x}^{\alpha} \left(\mathrm{1}+{x}\right)}\:. \\ $$

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let-give-0-lt-lt-1-find-in-terms-of-the-value-of-integral-0-dx-x-1-x-

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