How Can You Integrate Complex Fractions Like This One?

heisgirl20
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I've tried to used integration by parts and u substitution and I've also tried just multiplying the fraction by the denominator (6-x)^(1/2) but I am still confused at how to approach this.
 
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Multiply and divide by \sqrt{6+x}.
 

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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