Integrating x*sqrt(1-x^2)+(1-x^2)/2 from 0 to 1

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Homework Statement


Integrate x*sqrt(1-x^2)+(1-x^2)/2 dx from 0 to 1.

Homework Equations


None.

The Attempt at a Solution


How do I simplify this and find the integral of this?
 
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Never mind. I got it.
 
Good!
 

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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