$L^p$ norm of $e_n(x)=e^{2\pi inx}$

Question

I read that the $L^p$ norm of $e_n(x)=e^{2\pi inx}$ on the interval $[0,1]$ is $|e_n|_{L^p}=1$ for $1\leq p\leq\infty$. My understanding is that the $L^p$ norm is just $(\int_0^1 e^{2\pi inpx} dx)^\frac{1}{p}$ but I cannot see how this is $1$. Any help would be appreciated.

Answer 1

The norm is $(\int_{0}^{1}|e^{2\pi inx}|^{p}dx)^{1/p}=(\int_{0}^{1}1dx)^{1/p}=1$.