The inverse Laplace Transform helps recover the original time-domain function from its Laplace domain representation.
\[ f(t) = \frac{1}{2\pi i} \int_{a - i\infty}^{a + i\infty} e^{st} F(s) ds \]
\[ = \sum \text{residues} \quad \text{(for } t > 0\text{)} \]