let-I-0-1-x-1-4-1-x-3-4-x-dx-prove-that-I-isconvergent-and-find-its-value-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 34308 by prof Abdo imad last updated on 03/May/18

let I = ∫_0 ^(+∞) (((1+x)^(−(1/4)) −(1+x)^(−(3/4)) )/x)dx prove that I isconvergent and find its value .

$${let}\:\:{I}\:=\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} \:\:−\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} }{{x}}{dx} \\ $$$${prove}\:{that}\:{I}\:{isconvergent}\:{and}\:{find}\:{its}\:{value}\:. \\ $$

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let-I-0-1-x-1-4-1-x-3-4-x-dx-prove-that-I-isconvergent-and-find-its-value-

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