We know that the Fourier transform of the Dirac Delta function is defined as $$\int_{-\infty}^{\infty} \delta(t) e^{-j\omega t} dt = 1,$$
and if I were to reconstruct the function back in time domain, the inverse Fourier transform is defined as
$$\delta(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty} e^{j\omega t} d\omega.$$
How do compute I this integral analytically?