# Inverse laplace transform without partial fractions

1. Dec 9, 2014

### shreddinglicks

1. The problem statement, all variables and given/known data
take inverse laplace of:

6/[s^4(s-2)^2]

2. Relevant equations
6/[s^4(s-2)^2]

3. The attempt at a solution
I used partial fractions. I was wondering if It could be manipulated to where I could use the laplace table?

2. Dec 9, 2014

### vela

Staff Emeritus
If you don't want to use partial fractions, you could evaluate the Bromwich integral:
$$\frac{1}{2\pi i}\int_{\sigma-i\infty}^{\sigma+i\infty} \frac {6 e^{st}}{s^4(s-2)^2}\,ds$$

3. Dec 9, 2014

### LCKurtz

You could write it as$$\frac 6 {s^4}\cdot \frac 1 {(s-2)^2}$$inverse both factors using table methods, and take the convolution for your answer. Not sure it would be any easier though.