How to Evaluate the Integral of x^2/(1+x^6) from 0 to Infinity?

Anabelle37
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Homework Statement



Evaluate the integral with respect to x from 0 to infinity when the integrand is x^2/(1+x^6), using complex integration techniques.

Homework Equations


The Attempt at a Solution



I have no idea where to start. Please help!
 
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how about thinking about the poles of the function and considering contour integration?
 

Thread 'Finding the nth roots of a complex number'

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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