How Can Integral Substitutions Simplify \(\int \frac{dx}{x^{2} e^{-2/x}}\)?

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Homework Statement


\int \frac{dx}{x^{2} e^{\frac{-2}{x}}}

The Attempt at a Solution


I'm not sure where to begin.
 
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Have you tried any substitutions?
 
What happens if you make a substitution, say: u = =\frac{2}{x} ?
 
I got it with u = -2/x, thanks. I'm not sure why I didn't do that in the first place.
 
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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