How to go about integrating this

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Homework Statement



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The Attempt at a Solution



I'm not sure how to go about integrating this, i.e. integration by parts, substitution etc?

Any ideas?
 

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samjohnny said:

Homework Statement



Attached

The Attempt at a Solution



I'm not sure how to go about integrating this, i.e. integration by parts, substitution etc?

Any ideas?

Hint: I would probably make it a little easier by making the sub y = wt first to get a simple argument for the cosine. Then sub y = 2x and apply the double angle formula for cosine and simplify the integrand.
 
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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