Integration substitution rule help

p.mather
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Homework Statement


∫ x^(1/4) . (x^(5/4) +1)^6

Homework Equations



I used substitution rule with u = x^(5/4) +1

The Attempt at a Solution



I got an answer of

4/5 . (u^7/7) +c would that be correct
 
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Convert u back to x and take the derivative. Is it correct?
 

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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