I have been asked to calculate the inverse fourier transform of the equation
$$ \frac{6\exp(4iw)\sin(2w)}{(9 + w²)}$$
I have managed to see that this may fall in a case of convolution, since it is a possible product of Fourier Transforms. I have managed to see that
$$ \frac{6}{9 + w²} = \frac{6}{3² + w²} $$
Which indicates that for that part at least, the function
$$ \exp(-3|t|) $$
could be the inverse Fourier transform.
About the rest, I suspect that I could find the inverse of the sine, but its the imaginary exponential the one for which I can't seem to find its inverse.