Fourier-Mellin Integral

The inverse of the Laplace Transform

$$F(t) = {\mathcal L}^{-1}[f(s)] = {1\over 2\pi i}\int^{\gamma +i\infty}_{\gamma -i\infty} e^{st}f(s)\,ds$$

$$f(s) = {\mathcal L}[F(t)] = \int^\infty_0 F(t)e^{-st}\,dt.$$

See also Bromwich Integral, Laplace Transform