Finding the Inverse Laplace of F(s)

[tommyhakinen]

Homework Statement

$$F(s) = \frac{s^2 + 1}{s^2 + 4s + 3}$$
Find the inverse laplace transform?

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.

 

[gabbagabbahey]

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

 

[lurflurf]

L-1{1}=diracdelta