Partial fraction decomposition of $\frac{21}{s^{2}+4}$ for inverse-Laplace transform

Question

So I have this number which I want to do inverse-Laplace transformation on, which is kind of complicated. So it would be easier to do some partial fraction decomposition first.

I am trying to do the following: However I cannot seem to get it right at all.

$$\frac{21}{s^{2}+4} = \frac{A}{s^{2}+4} + \frac{B}{s^{2}+4}$$

Answer 1

Hint: You don't need partial fractions. That is the Laplace transform of an elementary function.

Answer 2

Notice, using the fact that $\mathcal{L}_{s}^{-1}\left[\frac{\omega}{s^2+\omega^2}\right]_{(t)}=\sin(\omega t)$: :

$$\mathcal{L}_{s}^{-1}\left[\frac{21}{s^2+4}\right]_{(t)}=21\mathcal{L}_{s}^{-1}\left[\frac{1}{s^2+4}\right]_{(t)}=\frac{21}{2}\mathcal{L}_{s}^{-1}\left[\frac{2}{s^2+2^2}\right]_{(t)}=\frac{21}{2}\sin\left(2t\right)$$