# Residue theorem

1. Jun 14, 2012

### hedipaldi

1. The problem statement, all variables and given/known data
integrate x^0.5/(1+x^2) by using complex integration

2. Relevant equations

residue theorem

3. The attempt at a solution
my attempt at a solution is attached.i need help in finding where am i mistaken.
thank's
Hedi

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2. Jun 14, 2012

### jackmell

. . . that's too messy to read. For me at least. Try and learn the math formatting language Latex to nicely format your math. Is this what you want to integrate:

$$\int_0^{\infty} \frac{\sqrt{x}}{1+x^2}dx$$

If so, how about taking a half-disc contour in the upper half-plane, indented around the branch-point at the origin. For now, just suppose the small and large half-circle contours go to zero and you're left with the two legs on the real axis. Then the integral over those two legs is equal to 2pi i times the residue at i right.

3. Jun 14, 2012

### hedipaldi

Thank you, that works.