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Is the integral of $(1/x) dx$ the same as the integral of $dx/x$ ?

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What did you try ? – Felix Marin Oct 17 '13 at 9:22

Yes, $\int \frac{dx}{x}$ is simply shorthand for $\int \frac1x \, dx$; they mean precisely the same thing.

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Yes. $\int \frac{1}{x} \mathrm dx = \int \frac{\mathrm dx}{x}$.

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