# Finding the inverse laplace transform of (2/(s+2)^4) using Convolution theorem.

1. Dec 2, 2012

### theBEAST

1. The problem statement, all variables and given/known data
Find the inverse laplace transform of (2/(s+2)^4) using the given table of identities:

2. Relevant equations
Here are the given identities:

3. The attempt at a solution
Alright, I realize that there is a simple identity that I can use with a factorial symbol, but this identity is not on our formula sheet, so I decided to try it with convolution theorem.

What did I do wrong and also is there an easier way given the table of identities? Thanks!

2. Dec 2, 2012

### lurflurf

Where did you get that flawed table? Discard it.

$$G(s)H(s) \rightarrow \int_0^t g(t-\tau)h(\tau) \mathop{d\tau}$$

Clearly both functions should depend on the integration variable.

Last edited: Dec 2, 2012
3. Dec 2, 2012

### theBEAST

Ahh, thanks!

This is the table that we get for our midterms and final lol :yuck:

Is there an easier way to solve this with another identity? The integral is pretty messy.

4. Dec 2, 2012

### lurflurf

That integral is not so bad, and you wanted to avoid using

$$\frac{1}{(s+a)^{n+1}} \rightarrow \frac{t^n}{n!} e^{-a \mathop{t}}$$

you could derive it. It helps to have a longer table with fewer errors.

Last edited: Dec 2, 2012