Laplace Transform of Hyperbolic Sine

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

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

Then:


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

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