# Use comparison theorem to show if integral is convergent or divergent

## Homework Statement

int (e^-x)/(x)dx from 0 to infinity

Determine if integral is convergent or divergent

2. The attempt at a solution
I assume because the bottom limit is 0 and there is an x in the bottom of the integral that this is going to be divergent but I still have to use the comparison theorem. I'm trying to find a function less then (e^-x)/(x) that also diverges to show that (e^-x)/(x) will diverge but I'm drawing a blank. I've tried messing around with 1/x^2 or just e^-x but both of those are still larger then the original (e^-x)/(x). Any suggestions?

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Office_Shredder
Staff Emeritus
1/x is an interesting function in that it diverges both ways, the integral from 0 to 1 of 1/x is divergent, as is the integral from 1 to infinity (compare this to $$x^{1/2}$$ and $$\frac{1}{x^2}$$). So when trying to do comparison with a 1/x term, it often helps to break up the integral into one from 0 to 1 and one from 1 to infinity, and see on each of those whether it converges or diverges