# 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.

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