Simplifying Inverse Laplace Transform of s/(s+4)^4

[kiwifruit]

Homework Statement

the questions asks to determine inverse laplace transform of

s/(s+4)^4

Homework Equations

The Attempt at a Solution

this can supposedly be done just using laplace transform tables so I am guessing i need to simplify that to something that's workable but i don't 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?

 

[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?

 

[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 don't see how to simplify or factorize it to something workable

 

[I like Serena]

If I look at the table at wikipedia:
http://en.wikipedia.org/wiki/Laplace_transform
I can find one for ${1 \over (s + \alpha)^{n+1}}$.
Another one that may be of help is sF(s) - f(0).

Can you find those?

 

[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.