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This question already has an answer here:

$\int_{0}^{\infty}\frac{1}{1+x^{2n}}dx = ? $

Using the Beta function and Euler's reflection formula the result of the integral ought to be

$\frac{\frac{\pi}{2n}}{\sin{\frac{\pi}{2n}}}$

But I wonder how ?

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marked as duplicate by Jean Marie, Masacroso, RRL, Paul Frost, José Carlos Santos Apr 19 at 13:29

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