What is the inverse Laplace transform of $\frac{p^2}{(p^2+4)^2}$

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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?

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$$F(s)=\frac{s^2}{(s^2+4)^2}=s\frac{d}{ds}((\frac{1}{s^2+4})\times\frac1{2})$$

$$f(t)=\frac{d}{dt}(t\times(\frac{\sin(2t)}{2}\times\frac1{2}))=\frac1{4}(\sin(2t)+2t\cos(2t))$$