Question

A travelling wave is given by;

$ C(x,t) = \exp(i(k_0x-w_0t)) \ \int_{-∞}^∞ A_0 \exp(-a(k-k_0)^2)\exp(iE(k-k_0)) \ \mathrm{d} k$

I need to get it into the form;

$ C(x,t) = A_0 \sqrt{\frac{pi}{a}} \exp(-\frac{(x-c_gt)^2}{4a}) \exp(i(k_0x-w_0t))$

I know that I need;

$\int_{-∞}^∞ \exp(-ay^2) \ \mathrm{d} y = \sqrt{\frac{pi}{a}}$

I've been trying to work it through but I'm getting nowhere