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 ?