Help with Laplace transform question
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Help with Laplace transform question

[From: ] [author: ] [Date: 12-03-02] [Hit: ]
x(t) = -5e^(-t) + 3te^(-t) + 5e^(-2t) + 4te^(-2t).I hope this helps!......
I'm seriously stumped on this question. All the examples I've done in class and with my teacher were completely different, so now i'm lost. So if anybody could help with this, that would be incredible and help me out so much.

Problem:
How do I find the inverse laplace transform (time domain) of the following function?

X(s)= (2s^2+5s+6)
--------------------
(s+1)^2 * (s+2)^2

-
By partial fractions,
X(s) = -5/(s+1) + 3/(s+1)^2 + 5/(s+2) + 4/(s+2)^2.

Inverting term by term yields
x(t) = -5e^(-t) + 3te^(-t) + 5e^(-2t) + 4te^(-2t).

I hope this helps!
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