Given $$f(p)=\dfrac{p^2}{(p^2+4)^2}$$
So $$f(p)=\dfrac{p^2}{(p^2+4)^2}=\dfrac{p^2+4-4}{(p^2+4)^2}=\frac{1}{p^2+4}-\frac{4}{(p^2+4)^2}$$
I know the inverse Laplace transform of the first term but stuck on the second term. How can I do this? Any hints?
$$F(s)=\frac{s^2}{(s^2+4)^2}=s\frac{d}{ds}((\frac{1}{s^2+4})\times\frac1{2})$$
$$f(t)=\frac{d}{dt}(t\times(\frac{\sin(2t)}{2}\times\frac1{2}))=\frac1{4}(\sin(2t)+2t\cos(2t))$$