Laplace Transform of Hyperbolic Sine

Theorem
Let $\sinh t$ be the hyperbolic sine, where $t$ is real.

Let $\mathcal L$ be the Laplace Transform.

Then:


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

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