prove-that-0-1-t-3-4-1-t-1-4-t-dt-is-convergent-and-find-its-value-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 48491 by maxmathsup by imad last updated on 24/Nov/18

prove that ∫_0 ^∞ (((1+t)^(−(3/4)) −(1+t)^(−(1/4)) )/t)dt is convergent and find its value .

$${prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left(\mathrm{1}+{t}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} −\left(\mathrm{1}+{t}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} }{{t}}{dt}\:{is}\:{convergent}\:{and}\:{find}\:{its}\:{value}\:. \\ $$

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prove-that-0-1-t-3-4-1-t-1-4-t-dt-is-convergent-and-find-its-value-

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