Inverse Laplace transformation of $\frac{s^2}{(s^2+1)^2}$ I am a bit lost how to compute the inverse Laplace transformation of $$ \frac {s^2}{(s^2+1)^2}$$ I think it will be some combination of sine and cosine (oscillation-like), however I ran into some weird expressions when I tried to expand the expression as $$ \frac {s}{(s^2+1)}  \frac {s}{(s^2+1)}$$
Could someone please give some suggestions? Thanks in advance!

$$
F(s)=\frac{s^2}{(s^2 + 1)^2} = \frac{s^2 + 1}{(s^2 + 1)^2} - \frac{1}{(s^2 + 1)^2}$$
$$
F(s)= \frac 1{s^2+1} +\dfrac {1}{2s}\dfrac {d}{ds}\frac 1{(s^2 + 1)}.
$$
Apply inverse Laplace Transform:
$$f(t)=\sin t -\dfrac 12 \int_0^t 1  \times \tau \sin \tau \ d\tau$$
$$f(t)=\dfrac 12 (\sin t +t \cos t)$$
