I'm given $\Psi(x,t)$ as a proposal for a wave function. $\Psi(x,t)=\int_{1}^{1+\Delta k} e^{i(kx-wt)} k^2 dk$
Now I try to compute $\Psi^*(x,t)\Psi(x,t)$ wich is the product
$(\int_{1}^{1+\Delta k} e^{-i(kx-wt)} k^2 dk) (\int_{1}^{1+\Delta k} e^{i(kx-wt)}k^2 dk)$
In wich way should I transform this to a double integral? Taking into account that $w=w(|k|)$
Thanks for your time.