How to write general formula for finding Laplace transform of the following function $$L[u(t)\delta(x-a)]=? $$
where $a\in \mathbb{R}$ and $\delta$ is Dirac Delta function and $u(t)$ is unknown function.
My answer:
If I am not wrong, I found $$L[u(t)\delta(x-a)]=\int_a^\infty e^{-st}u(t)\,dt$$ and then , Can we simplify more?