you can get it like this easily,
then remember that
and and where
I'm having some difficulty with what should be a simple (one sided) inverse Laplace transform:
Now, I know the answer is
I'm just not sure how to get there. I'm not looking to apply the definition - I'm looking to massage the fraction into standard transform pairs or use standard properties of the transform.
It seems to me that I need to accomplish this:
I'll probably kick myself for this, but what am I missing?