How to do Laplace transform in this?

Question

How to solve this problem...

I tried yo split the numerator but I still don't know what to do.

Answer 1

Using Laplace Transform formulae,

$$L^{-1}\dfrac b{(s-a)^2+b^2}=e^{at}\sin bt$$ and $$L^{-1}\dfrac{s-a}{(s-a)^2+b^2}=e^{at}\cos bt$$

Now $s^2+4s+5=(s+2)^2+1^2$

Can you recognize $a,b$ here?

Write $s+8=(s+2)+6\cdot1$