Dummy DSP student request for IDTFT Calculation and Integration Process We have one DSP course in biomedical engineering, so i have been for 10 years away from mathematical calculation and working in this years by programing by c and ..., so one of our exercise is to calculating the IDTFT of some signals like this from this eBook "Digital Signal Processing Using MATLAB 3rd Edition":


  Using the definition of the inverse DTFT in (3.2), determine the
  sequences corresponding to the following DTFTs:




so the manual book solved this question by summery like this:



So, i don't know how it reached this part:



could you give me some ...?
It is possible to do this calculation by some software and seeing the formulation changing mode from base question to the answer like those shown above?

Thanks for your attention.
This is using Euler's Identity for a sine which should get you past the point where you are stuck:

$$ \sin(\phi) = \frac{e^{j\phi}-e^{-j\phi}}{2j}$$