(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex] \int_0^\infty{ \frac{1}{x} e^{-x}} [/tex]

2. Relevant equations

Integration by parts

[tex] \int{u dv} = uv - \int{v du} [/tex]

3. The attempt at a solution

[tex] u = \frac{1}{x} [/tex]

[tex] du = \frac{1}{x^2} dx [/tex]

[tex] v = -e^{-x} [/tex]

[tex] dv = e^{-x} dx [/tex]

[tex] -\frac{1}{x} e^{-x} - \int_0^\infty{-e^{-x} \frac{1}{x^2}} dx [/tex]

It looks like this process is going to go on forever because I can't get rid of the 1/x term. Could someone please give some guidance on how this is done? Thanks.

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# Never ending integration by parts

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