Laplace Transform of 1

Theorem
Let $f: \R \to \R$ be the function defined as:
 * $\forall t \in \R: \map f t = 1$

Let $\mathcal L$ be the Laplace Transform.

Then the Laplace transform of $\map f t$ is given by:


 * $\laptrans {\map f t} = \dfrac a s$

for $\map \Re s > 0$.