By the way, with the precise purpose to avoid waste of time, I suggest to read the following recent post...

http://www.mathhelpforum.com/math-he...es-186754.html
Here for the computation of the integral....

(1)

... has been proposed the integration of the complex function

along the path in the figure...

Now it is evident that if

is not analytic inside the 'circular proximity' of

of radious r the method fails and the computation of the integral (1) becomes [really...] 'impossible'... fortunately that is not the case

...

Kind regards