What is the Inverse Laplace Transform of (2s^2 + 20s + 36) / (s^3 + 6s^2 + 9s)?

[minuswhale]

Homework Statement

F(s) = (2s² + 20s + 36) / (s³ + 6s² + 9s)

Homework Equations

L[e^-at] = 1 / (s + a)
L^-1[(s+a) / ((s+a)² + w²)] = e^-atcos(wt)
L^-1[w / ((s+a)² + w²)] = e^-atsin(wt)

The Attempt at a Solution

Factored the top by 2 and the bottom by s, but the rest of the top seems unfactorable. Stuck after that
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[Char. Limit]

I would try factoring the denominator and then applying partial fractions, if you can.

 

[minuswhale]

Somehow I got from partial fraction 4 unknowns with 3 equations?

A/s + B/(s+3) + (Cs+D) / (s+3)²

 

[vela]

You don't need the C in the last term. Your expansion should be

$$\frac{A}{s} + \frac{B}{s+3} + \frac{C}{(s+3)^2}$$

You use Cs+D in the numerator when the denominator is irreducible, e.g. x²+1.

 

[lurflurf]

^c=0