find the fourier transform of the following function in two ways , once using direct computation , and second using the convolution therom .
The Attempt at a Solution
I tried first to solve directly . used Euler's identity and got
∫e-it(w0+w)/(d2+t2) + ∫eit(w0-w)/(d2+t2)
but I think it was a deadend , unsolvable integral .
I got a hint from an internet source saying to use the Lorentzian transform but I am not familiar with it
then I tried going first from the convolution approach , which means I find the separate F transform of cos(w0t) and of 1/(d2+t2) and then calculate the convolution of them in order to get the FT of the multiplication oh them .
I couldn't do that as well because I didn't manage to integrate e-iwt/(d2+t2) and so can't find that fourier transform as well
any direction ,or explained hint would be greatly appreciated!