How to evaluate the integral $$I=-\frac{i}{2\pi^2x}\int\limits_{-\infty}^{\infty}dp ~p\exp{\Big[i\Big(px-ct\sqrt{p^2+m^2c^2}\Big)\Big/\hslash\Big]}.$$
This is the integral that appears while calculating the amplitude of propagation of a particle of mass $m$ between the points $\textbf{x}$ and $\textbf{x}_0$, in time $t$, in relativistic quantum mechanics and $p=|\textbf{p}|$, the momentum of the particle, and $c$ in the velocity of light in vacuum.