Solving Complex Integration Homework

hedipaldi
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Homework Statement

Homework Equations

The Attempt at a Solution

 
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hedipaldi said:

Homework Statement



integrate x^0.5/(1+x^2) from 0 t0 infinity by using complex integration.

Homework Equations



residue theorem

The Attempt at a Solution


attached

Try Partial fractions?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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