Inverse Laplace transform of 1/(s^4+1)

[plexus0208]

Homework Statement

Find the unit impulse response for the operator D^4 + I, using the Laplace transform.

Homework Equations

The Attempt at a Solution

w^(4) + w = δ(t)

s^4W + W = 1

W = 1 / (s^4 +1)

Now, I need to find the inverse laplace transform of W. But I don't know how to simplify W. Should I use partial fractions? If so, how do I factor the denominator?

(Note: In the first line "^(4)" refers to the fourth derivative with respect to t.

 

[rock.freak667]

you could replace 1 with -i² where i is the imaginary unit. But you may need to convert that to a better form in the final solution.