Inverse Laplace Transform

1. Nov 19, 2011

kiwifruit

1. The problem statement, all variables and given/known data
the questions asks to determine inverse laplace transform of

s/(s+4)^4

2. Relevant equations

3. The attempt at a solution
this can supposedly be done just using laplace transform tables so im guessing i need to simplify that to something thats workable but i dont know how.
the solution is
e^(-4t) (t^2/2 - (2/3) t^3)
anyone can help in directing me how to simplify that equation before i use tables to inverse?

2. Nov 19, 2011

I like Serena

Welcome to PF, kiwifruit!

Which transforms can you find that are somewhat close to your question?
Or transforms that perhaps may be of help?

3. Nov 19, 2011

kiwifruit

i would say
laplace of e^at = 1/(s-a)
or
laplace of cos(at) = s/(s^2 + a^2)
is similar to the question but i dont see how to simplify or factorize it to something workable

4. Nov 19, 2011

I like Serena

5. Nov 19, 2011

LCKurtz

I find this formula frequently helpful:

$$\mathcal L^{-1}f(s+a) = e^{-at}\mathcal L^{-1}f(s)$$

If you rewrite the expression like this:
$$\frac{(s+4)-4}{(s+4)^3}$$
and break it apart, the answer should fall right out.