## I don't understand the Gram-Schmidt process on a function

I have been given a weight function $w = xe^{-x}$ and $u_n = x^n, n = 0,1,2,..$. I don't exactly get what bit to use to integrate because in my definition it says:

$\displaystyle \varphi_i = \frac{\psi_i}{\left(\int \psi_{i}^{2}wdx\right)^{1/2}}$

where $\psi_i = u_i + a_{i,0}\varphi_0 + a_{i,1}\varphi_1 + ...$

But how can you work out $\psi_i$ if you need $\varphi_i$ and to work out $\varphi_i$ you need $\psi_i$?