Compute the integral $\int_{0}^{\infty} \exp(in\omega t-\gamma^2 t^2)dt$
Show that $\frac{1}{\sqrt{2\pi}} \cdot \left(\int_{- \infty}^{\infty} e^{itx} \cdot e^{-\frac{1}{2}t^2 } dx \right) = e^{-\frac{1}{2}t^2}$