Calculating the inverse Fourier transform of two given functions

I need to calculate the inverse Fourier transform of the following functions:

1. $\displaystyle f(w) = e^{(-\pmb{i}5w)} * {\rm sinc}(2w)$

2. $\displaystyle g(w) = \frac{\pmb{i}w}{(3+\pmb{i}w)(1+\pmb{i}w)}$

I'm really stuck and I don't know where to start, any help would be appreciated!

• Is this homework? Are you having trouble evaluating the integrals, or setting them up? – Brian Mar 4 '11 at 0:44
• What did you try? – AD. Mar 4 '11 at 5:06
• The second question can be solved by staring at it and then using the residue theorem. Do you know that? For the first question: maybe you know which function gives the sinc function when Fourier transformed? – Fabian Mar 4 '11 at 22:28

1) If $e_t(x)= e^{itx}$,what is $\widehat{e_tf}$?
2) What is $\widehat{f'}$?