[tex]\mathop\int\limits_{\infty} \log[(z-1)(z+1)]dz=A(z)\biggr|_0^0=4\pi i[/tex](adsbygoogle = window.adsbygoogle || []).push({});

The infinity symbol below the integral is a positive-oriented, closed, and differentiable path over the function looping around both branch-points and A(z) is the antiderivative of the integrand. I mean would that hold for all of them? You know, like 2 pi i times the number of branch-points? Don't know but probably depends on what direction you're going around them. Integrals like this I think are interesting but not really discussed in classes right? I mean, when have you ever seen something like this anyway? Not really in books and yet it is perfectly consistent with the Fundamental Theorem of Calculus. Isn't it? I think we should explicitly identify them as a particular type of integral more than just a 2-dimensional contour integral. Maybe a 3-D contour integal but that's too wordy. What do you guys think? Have they already been named and I just don't know?

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# How shall we call these types of integrals in Complex Analysis?

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