Say I have a function $f(K_\alpha) = \frac{1}{\sqrt{\pi}} e^{-\frac{(D-K_\alpha)^2}{2}} \times \frac{1}{\sqrt{\pi}} e^{\frac{-K_\alpha^2}{2}}$.
I want to get the integral of $f(K_\alpha)$ over all $K_\alpha$.
$\int_{K_\alpha} \frac{1}{\sqrt{\pi}} e^{-\frac{(D-K_\alpha)^2}{2}} \times \frac{1}{\sqrt{\pi}} e^{\frac{-K_\alpha^2}{2}}$
I started like this.
$\int_{K_\alpha} \frac{1}{\sqrt{\pi}} e^{-\frac{(D-K_\alpha)^2}{2}} \times \frac{1}{\sqrt{\pi}} e^{\frac{-K_\alpha^2}{2}} dK_\alpha \\ = \int_{K_\alpha} \frac{1}{\pi} e^{-K_\alpha^2+DK_\alpha-(D^2/2)} \\ $
I am not sure what to do after this.