I'm not terribly sure why you tell us that A=1, as it is the only parameter that is not used at all here. I'm also not at all sure why you have C1=eval(C1) in there, as we never see C1 either. And your title claims that this somehow includes the gamma function. Don't see that either.
You have unknown parameters X and Y. How could you expect to do a numerical integration with them as unknowns? Or are X and Y known, and you are not telling us what they are? Can we guess? If so, then I pick:
If X and Y are known parameters, then I don't see the problem with a numerical integration, since an analytical solution is clearly not to be found. Not every problem has a clean solution. I'd start with quadgk or integral.
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