Find the function f(x) which has the following Laplace transform:
F (s) =
(4s + 3) /
(s^2 − 2s + 8)

Question

Find the function f(x) which has the following Laplace transform:
F (s) =
(4s + 3) / 
(s^2 − 2s + 8)

oblivious · Answer

Well, the formula for inverting a laplace transform in a general case is rather cumbersome. Better to use a table of laplace transforms, which you should have been given.. A quick look online to find the equality you need:
$$F(s) = (s+\lambda)/((s+\alpha)^2+\beta^2)$$ Is the transform of$$\exp(-\alpha t)\(cos(\beta t)+[(\lambda-\alpha)/\beta]*sin(\beta t))$$Now you simply need to match your equation to the F(s) equation (divide num and den by 4, factor denominator leaving remainder)