The Laplace transform of a function f(t) is calculated as
\[ F(s) = \int_{0}^{\infty} f(t)e^{-st}\,dt \]
Notation:
\[ F(s) = \mathcal{L}\{f(t)\} \]
Inverse transform:
\[ f(t) = \mathcal{L}^{-1}\{F(s)\} \]
\[ F(s) = \int_{0}^{\infty} f(t)e^{-st}\,dt \]
\[ F(s) = \mathcal{L}\{f(t)\} \]
\[ f(t) = \mathcal{L}^{-1}\{F(s)\} \]