Inverse Laplace

1. Nov 7, 2008

tommyhakinen

1. The problem statement, all variables and given/known data
$$F(s) = \frac{s^2 + 1}{s^2 + 4s + 3}$$
Find the inverse laplace transform?

3. The attempt at a solution
Since the nominator's degree is not smaller that the denominator, i have to do the long division before doing the inverse laplace.

$$F(s) = \frac{- 4s - 2}{(s+1)(s+3)} + 1$$

I can get the inverse laplace for the first term. However, I was stopped at L-1{1}. Need help. Thank you.

2. Nov 7, 2008

gabbagabbahey

Hint: What is $$\int_{0^-}^{\infty} \delta (t) e^{-st}dt$$ ? (where $\delta$ is the dirac delta function)

3. Nov 7, 2008

lurflurf

L-1{1}=diracdelta