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## Homework Statement

My professor gave us the problem: "Explain why not all antiderivatives of [itex]\frac{dx}{x}[/itex] are in the form of [itex]ln|x|[/itex]"

## Homework Equations

[itex]\int \frac{dx}{x} = {ln|x|, x\neq 0}[/itex]

## The Attempt at a Solution

I honestly don't know where to even start on this one, from all of my background I have been taught that [itex]\int \frac{dx}{x} = {ln|x|, x\neq 0}[/itex]. I have some clue that it has something to do with what happens when [itex] x = 0 [/itex] because of the fourm at this link (http://forums.xkcd.com/viewtopic.php?f=17&t=68042) but the poster that proposed [itex]\int \frac{dx}{x}[/itex] may not equal [itex]ln|x|[/itex] never explained why. Any help would be greatly appreciated.