Laplace Transform of Hyperbolic Cosine

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

Let $\laptrans f$ denote the Laplace transform of the real function $f$.

Then:


 * $\laptrans {\cosh a t} = \dfrac s {s^2 - a^2}$

where $a \in \R_{>0}$ is constant, and $\map \Re s > a$.