Integration of inverse trig functions

bobsmith76
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Homework Statement

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This is an integration of an inverse trig function.
I don't see how they go from 1/2 to 1/4. I understand how they get the 1/2, du = 2dx, divide both sides by 2, but where does the 1/4 come from?
 
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Ok, I've done some more research and looks like if anything the 1/2 should just be canceled out because you're supposed to put du in the numerator, which is 2 and 2 times .5 = 1.
 
never mind, it looks like 1/4 but it's really 1/2. the book cut off the top part of 1/2 to make it look like 1/4. i found some guy on youtube doing the exact same problem.
 
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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