'numerically integrating singular function in python

I am dealing with integration over a rather singular function (such is the case in physics when dealing with Green's functions, see the attached figure) in python. What I did was the usual integration method:

quad(green_function,-cutoff,cutoff)

real and imaginary part of the typical green's function G(omega)

And the numerical integration is quite unsatisfying. I wonder if there is a better method in python other than quad that deals with this singular integration nicely?

Thanks!

python numpy

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'numerically integrating singular function in python

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