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Inverse laplace transform without partial fractions

  1. Dec 9, 2014 #1
    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. jcsd
  3. Dec 9, 2014 #2

    vela

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    If you don't want to use partial fractions, you could evaluate the Bromwich integral:
    $$\frac{1}{2\pi i}\int_{\sigma-i\infty}^{\sigma+i\infty} \frac {6 e^{st}}{s^4(s-2)^2}\,ds$$
     
  4. Dec 9, 2014 #3

    LCKurtz

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    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.
     
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