Complex Integration: Integrating x^0.5/(1+x^2)

[hedipaldi]

Homework Statement

integrate x^0.5/(1+x^2) by using complex integration

Homework Equations

residue theorem

The Attempt at a Solution

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

 

[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.

 

[hedipaldi]

Thank you, that works.