Integral of sqrt(x-1)/sqrt(x): Solving Homework Equations

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Homework Statement



Integral of sqrt(x-1)/sqrt(x)


Homework Equations





The Attempt at a Solution



I think I have to sub x = sinh2 so you get sqrt(1-sinh2)/sqrt(sinh2)
I forget what to do after this
 
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I'm not totally sure that x = \sinh^2(u) will help you in this case since then x-1 = cosh^2(x)-2. Trying x= cosh^2(u) should lead to better results.
 

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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