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From a little pdf I downloaded.
Where'd you get that idea?
Yes, it does but not using residues. There are a couple of ways to do a contour integration.
Well, contour integration works on that one.
it only mentions 3 forms, (14)(15) and (16) have the exact method I am using. Your integral is not of that form, so other methods have to be used.
It nowhere says that it is for those forms only.
(14)(15) and (16) show that it is only for those forms.
It seems to me the only condition is that the function is holomorphic.
You are missing the point. This will obviously not do every integral. No method does. But often is good enough. The whole integral is reduced to a line on the complex plane. That page I sent you uses the same method we are using to do an integral. We are lacking the knowledge of when this can applied.
Do you see the part after "Often". That's where your problem is. It will not always tend to zero. Also, there are some things called branch points, which I am trying to figure out, which cannot be handled regularly, So a different path must be chosen.
It is not a problem, looks like you convert it into a contour integral or something like that. Anyway the method can be used for real integrals.
I think the problem is that you are treating a regular integral as a contour integral.
Because I did understand some parts of what I redlad earlier, and some of those parts were not included in your method.
Why do you think it is not contour integration?