I need to show that two Hermite polynomials are orthogonal, but I'm a little confused.
I have: $H_2(x) = 4x^2-2$ and $H_3(x) = 8x^3-12x$
I know I need to integrate $$\int_{-L}^L (4x^2-2)(8x^3-12x) dx=0,$$ because it says I need to show it's orthogonal on $[-L,L]$, where $L$ is a constant.
Do I just pick random values for $L$, or is there some sort of procedure?