I know that the Laplace transform of the delta function 
$\delta(t-a)$ is $e^{-as}$.

Now my question is to find the Laplace transform of $te^{-3(t-2)}\delta(t-2) $.

Is there any theorem or easy thumb rule to solve these kinds of problems or should I integrate the function as we conventionally do, to find its Laplace transform?