Transform of $\frac{u^3}{u^4+4}$: Fourier Analysis

[nhrock3]

$$\frac{u^3}{u^4+4}$$
what is the transform of this function?

 

[White]

if you ask just for the result here it is:
http://www.wolframalpha.com/input/?i=Fourier+transform+u^3%2F%28u^4%2B4%29