Why is it that this integral equals zero as the limits go to infinity?

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SUMMARY

The integral of x^s/s over a semicircular contour with radius R, where R approaches infinity and c>0, equals zero. This conclusion is based on the behavior of the integrand as it approaches the singularities on the real axis. The discussion emphasizes the importance of indenting the contour to avoid these singularities, particularly when the imaginary part of c is greater than zero (Im(c)>0). This method is crucial for correctly evaluating integrals in complex analysis.

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jack5322
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x^s/s integrated on the semicircular contour with radius R and center c>0, where x>1, s is the complex variable, and R is meant to go to infinity. please help.
 
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do you mean Im(c)>0 ? usually this example is supposed to illustrate the need to indent the contour to get around singularities on the real axis
 
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