Integrating a Double Integral: A Stumped Math Student's Attempt

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http://home.comcast.net/~andykovacs/integral.JPG

I had to reverse a double integral and evaluate, and I was able to do the reversal, but I was stumped on how to integrate this. I imagine there's a way to simplify it since I can't see how any of the integration techniques I've learned will help, but nothing comes to mind.
 
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TMFKAN64 said:
When in doubt, try Mathematica: http://integrals.wolfram.com/index.jsp.

hehehe... did you actually try it?

I don't think that's the answer he's looking for
 
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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