Im trying to solve an initial value problem but can't find the inverse for the part below

Question

Can someone guide me through finding the inverse laplace for :

$$\frac{1}{(s^2+1)^2}$$

I've tried decomposition but I get the exact same thing us above.

Answer 1

You could do a partial fraction decomposition using $$ (s^2+1)^2=(s+i)^2(s-i)^2 $$

Or use that $$ \frac{\partial}{\partial \alpha}\frac1{s^2+α^2}=-\frac{2α}{(s^2+α^2)^2} $$ to reduce to a known problem and then set $α=1$