- #1

JulienB

- 408

- 12

## Homework Statement

Hi everybody! I'm having a hard time to find a way to cleanly prove that ∫(1/ln(x)) dx between 1 and 2 doesn't exist. At first I thought it was because it's not bounded (Riemann criterion I believe), but then I looked at another unbounded definite integral such as ∫lnx dx between 0 and 1 and it does exists! I've seen some proofs with li(x) but I haven't done that in class, so it'd be strange to use that in an exam.

## Homework Equations

Integrals, limits

## The Attempt at a Solution

Absolutely no idea. I've been trying to compare it with ∫lnx dx between 0 and 1 but it didn't really help:

∫

_{o}

^{1}ln(x) dx = lim a→0

^{+}∫

_{a}

^{1}ln(x) dx

= lim a→0

^{+}(1(ln(1) - 1) - a(ln(a) - 1)) = -1

Is there a similar method to show that the integral of 1/lnx diverges?

Thx a lot in advance for your answers.Julien.