(Hopefully easy) integration question

Heyo,

I'm having difficulty seeing how these two lines follow. I'm fairly sure I'm being an eejit and the answer's straightforward, but would appreciate a quick explanation of what's going on.

$$\frac{1}{2\pi}\int d^3p e^{-i(\emph{p}^2/2m)t} \\ \times e^{i\emph{p.(x-x_0)}} \\ = (\frac{m}{2 \pi it})^{3/2}e^{\frac{im(\emph{x-x_0}^2}{2t}}$$

Last edited:

CompuChip
$$\frac{1}{2\pi}\int d^3p e^{-i(\vec{p}^2/2m)t} e^{i\vec{p}\cdot(\vec{x}-\vec{x_0})} = \left (\frac{m}{2 \pi it}\right )^{3/2}e^{\frac{im(\vec{x-x_0})^2}{2t}}$$