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