Integrating arcsinx: Solving a Challenging Calculus Problem

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Homework Statement



Intergrate arcsinx

Homework Equations





The Attempt at a Solution



I couldn't even touch this question. I saw the answer but still can not understand how to do this.
 
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Use the "same" method as for arctan x and for ln x.

arcsin x = (arcsin x) * 1

Now integrate by parts!
 
Thanks a lot!
 

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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