Inverse Laplace of $\frac{s}{(s+3)^{5}}$

Question

Struggling to answer this transform. Anyone able to give me a walkthrough?

I know that the inverse transform of $$\frac{1}{(s+a)^{n}}$$ is $$\frac{1}{(s+a){!}}{t}^{n-1} {e}^{-at}$$

But I am unsure how to get to that position as I have "s" instead of a number. I assume I can use partial fractions but with it being to the power five I feel like that would be difficult and length to solve, so I'm not sure if I'm missing something here.

Thanks.

Answer 1

Hint:

Write $\frac {s}{(s+3)^5}$ as $$\frac {s+3-3}{(s+3)^5} = \frac {s+3}{(s+3)^5} -\frac {3}{(s+3)^5}$$

$$= \frac {1}{(s+3)^4} -\frac {3}{(s+3)^5}$$