I have a question about the orthonormal basis. We consider the Hilbert space $L^2([0,1])$ with the inner product $\langle f,g\rangle = \int_0^1 f(t)g(t)dt$. So if we consider now $\int_0^1 e_i^2(t) dt$, it is equal to 1 ($e_i$ is the orthonormal basis). So my question is, what is $\int_0^1 e_i^3(t) dt$ or $\int_0^1 e_i^4(t)dt$?
Thanks in advance.