## Inverse Laplace Transform

The problem statement, all variables and given/known data

Find the inverse laplace transform of:

1/(s-2)3 + 25/(s+1)(s-2)2 + s/(s-2)2

The attempt at a solution

I get (1/2)e2tt2 + (25/7)e-t-(25/7)e2t+(75/7)te2t for the first two, but I'm not even sure where to start for s/(s-2)2. I was thinking it might use convolution, but I'm not sure that I understand how convolution works... I'd really just like a hint to get me started on it...
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 Recognitions: Gold Member Homework Help Science Advisor Staff Emeritus 1/(s-2)2 looks like a shifted form of 1/s2, so you want to write numerator in terms of (s-2), i.e. s = (s-2)+2.
 Okay, so then I would have (s-2)/(s-2)2 + 2/(s-2)2 which is 1/(s-2) + 2/(s-2)2 so then I'd get e2t + 2e2tt

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## Inverse Laplace Transform

That's right. You may want to check your algebra on your earlier work. Mathematica gets a different answer than you do.