Solving the Laplace Transform of an Irreducible Quadratic Factor

[sunshine21]

Homework Statement

i need to find the laplace transform of this equation by using the partial fraction. it is an irreducible quadratic factor that i don't really know how to solve it.

Homework Equations

[(s+1)^2 + 6]/[(s+1)^2 +4]^2

The Attempt at a Solution

please help me, thanks. =)

 

[Mark44]

Actually, you want the inverse Laplace transform.

Instead of using partial fractions, I think it might be helpful to rewrite the numerator this way:
$$\frac{(s + 1)^2 + 6}{((s + 1)^2 + 4)^2} = \frac{(s + 1)^2 + 4 + 2}{((s + 1)^2 + 4)^2} = \frac{(s + 1)^2 + 4}{((s + 1)^2 + 4)^2} + \frac{2}{((s + 1)^2 + 4)^2}$$

 

[sunshine21]

ouh..when you make it simple, now i can see how to solve it.
i didnt realize it. maybe i think to much on how to cancel out the square at the denominator.
thanks Mark44. your information is very helpful. thank you so much =))