What is the method for finding f(t) for F(s) = (s-1)/(s+1)^3?

[kahless2005]

Given:
F(s) = (s-1)/(s+1)^3

Find:
f(t)

Solution:

Using the equation that when F(s) = n!/(s-a)^(n=1), L^(-1){F(s)} = t^n*e^(at)

So far I find that f(t) = e^(-t)*(-t^2+__)

The book says that f(t) = e^(-t)*(t-t^2)
How did they get the t?

 

[pocoman]

You should rewrite F(s)
<br /> F(s) \equiv \frac{s-1}{(s+1)^3} \equiv \frac{1}{(s+1)^2} - \frac{2}{(s+1)^3}<br />
and apply the inverse laplace transform
when F(s) = n!/(s-a)^(n=1), L^(-1){F(s)} = t^n*e^(at)
for each term.