Laplace Transform of Hyperbolic Cosine

Theorem
Let $\cosh t$ be the hyperbolic cosine, where $t$ is real.

Let $\mathcal L$ be the Laplace Transform.

Then:


 * $\displaystyle \mathcal L \left\{{\cosh at}\right\} = \frac s {s^2 - a^2}$

where $a \in \R$ is constant, and $\operatorname{Re}\left({s}\right) > a$.