Inegration with square roots - calc 1

Aimee79
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1. Homework Statement [/b]
∫x/√(x-1)dx

2. Homework Equations [/b]
I'm just stumped. I have tried u substituion with
u=√(x-1)
x=u^2+1

((u^2+1)/u)du
=(u+1/u)du

but it doesn't seem to work and I can't integrate 1/u.

I just don't know where to go with this any help would be greatly appreciated.

Aimee
 
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If I were doing this question, I wouldn't make the substitution you made, but would instead use the substitution u=x-1.
 
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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