In order to illustrate the procedure we will consider the integral...

(1)

... the others are similar. The integrand function has in a singulatity of the typebranch pointand we have to select an integration path that doesn't contain this point. The best cadidate is the 'red path' in the figure...

First step is to valuate the integral...

(2)

... where c is the path ABCDEFGHA... how can we proceed?...

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