Help Needed: Integrating a Complex Expression

AaronGaTech
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I need some help. I don't know how to make the intgral symbol, but here's the question. If somebody can get it started it'd be awesome.
1to e^10 1to e^6 1to e^2 1/xyz dxdydz
 
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AaronGaTech said:
I need some help. I don't know how to make the intgral symbol, but here's the question. If somebody can get it started it'd be awesome.
1to e^10 1to e^6 1to e^2 1/xyz dxdydz

so you mean

\int_1^{e^{10}} \int_1^{e^{6}} \int_1^{e^{2}} {{dxdydz} \over {xyz}

??
 
Do you know the antiderivative of 1/x?
 
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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