Simple Integral. I'm a bit rusty.

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Homework Statement



Take the integral of
1/[(z^2 + x^2) ^ 3/2] dx where z is a constant.



Homework Equations





The Attempt at a Solution



I tried substitution, but couldn't get it to work. Thanks in advance.
 
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Have you tried x=ztanθ ?
 
Yes but I was confused on the next step. I tried to look into trig substitutions.
 
Could you post your entire working?
 
Oh, never mind I think I just figured it out. Thanks for your help!
 
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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