Have a integration problem that i am stuck on

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Homework Statement



integral of (x^2)*sqrt(6x+7) from 0 to 1


The Attempt at a Solution


i am thinking this has something to do with u substitution but i can't figure out what u should be?
 
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Put u=6x+7, then x=(u-7)/6, right?
 
Yes, that should work.
 
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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