Got a laplace transformation question involving Heaviside Functions, just need someone to take a quick look over what I've done so far.

Find the Laplace transform of where is the unit Heaviside Function.

Well it's known that the Heaviside function is equal to 1 for , and 0 otherwise.

So for ,

For , the function is equal to

And for , we have .

So as far as I can see, we have for , and otherwise.

So would the Laplace Transform of this equation is just the Laplace Transform of 1, ie ?