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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 ?2013-10-17

3 Answers 3

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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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In $ \int \frac{dx}{x} $, the coefficient of the numerator inside the integral, $ dx $, when there is none, is understood to be 1.

So yes, $ \int \frac{1}{x} dx $ = $ \int \frac{1 \cdot dx}{x} $ = $ \int \frac{dx}{x} $.