Find inverse Laplace transform of $H(s)=\frac8{s^4+4}$

Question

How can we find the inverse Laplace transform of the function $$H(s)=\frac8{s^4+4}?$$

Answer 1

Hint:

$$H(s)=\frac8{s^4+4}=\frac{2}{s+1+i}+\frac{2}{s+1-i}+\frac{2}{s-1+i}+\frac{2}{s-1-i}$$

The infverse Laplace transform of $H(s)$ is:

$$f(t)=2\exp(1+i)+2\exp(1-i)+2\exp(-1+i)+2\exp(-1-i)$$ $$=8\cos (t)\cosh(t)$$