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

Question

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.