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## Homework Statement

I'd like to prove the inexistence of [tex] \int_{-1}^1 \frac{1}{x} dx [/tex], or at least that it's not 0.

## Homework Equations

Well... :P

## The Attempt at a Solution

Since integrating is linear, we can write [tex] \int_{-1}^1 \frac{1}{x} dx = \int_{-1}^0 \frac{dx}{x} + \int_0^1 \frac{dx}{x} [/tex]. Since first integral is [tex]-\infty[/tex] and the 2nd is [tex]\infty [/tex], their sum is not known.

But I don't like this prove. Anyone can come up with a better one?