Laplace Transform of Bessel Function of the First Kind of Order Zero/Corollary

Corollary to Laplace Transform of Bessel Function of the First Kind of Order Zero
Let $J_0$ denote the Bessel function of the first kind of order $0$.

Then the Laplace transform of $\map {J_0} {a t}$ is given as:
 * $\laptrans {\map {J_0} {a t} } = \dfrac 1 {\sqrt {s^2 + a^2} }$