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find-the-value-of-A-n-1-dt-t-n-1-t-1-withn-N-




Question Number 28832 by abdo imad last updated on 30/Jan/18
find the value of  A_n = ∫_1 ^(+∞)    (dt/(t^(n+1) (√(t−1)))) .withn∈N .
$${find}\:{the}\:{value}\:{of}\:\:{A}_{{n}} =\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{{dt}}{{t}^{{n}+\mathrm{1}} \sqrt{{t}−\mathrm{1}}}\:.{withn}\in{N}\:. \\ $$

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