[Math] Find the inverse laplace transform of $F(s) = \frac{2s}{s^{4}+s^{2}+1}$

Question

I need to find the inverse Laplace transform of $F(s) = \frac{2s}{s^{4}+s^{2}+1}.$

I realise that I need to do something with the denominator so I can convert to partial fractions, but I am not able to do so. Any help will be appreciated, thanks!

Answer 1

HINT:

$$s^4+s^2+1=(s^2+1)^2-s^2=\cdots$$

$$\implies2s=s^2+s+1-(s^2-s+1)$$