Wednesday, July 25, 2018

integration - $int^infty_0 frac{dx}{x^n + 1}$, n odd

Well, I saw this integral :


$$\int^\infty_0 \frac{dx}{x^n + 1}$$


on some questions (like this one : Calculating a real integral using complex integration )


But it has always been for $n$ even. Is there something wrong with $n$ odd ? Is not, how do you compute this ? by the same argument ?


thank you and sorry if this is easy. I can't figure out how to do it since it's neither odd nor even.

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