The exercise asks that we find the IFT of $$\frac{\sin(a\omega)}{(\omega-a)^2}^2$$
Using the general formula for IFT yields integrals of the type: $$\int\limits_{-\infty}^\infty\frac{\cos(a\omega)}{(\omega-a)^2}$$ which has no apparent solution (at the known integrals tables i checked).
I suspect some of FT's properties can be of use (multiplication on frequency domain = convolution in time domain) but since i cant find a function whose FT is in terms of $\sin(a\omega)$ or $(\omega-a)^2$ I can't figure it out.