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.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
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