Is the integral of $(1/x) dx$ the same as the integral of $dx/x$ ?
Is $\int \frac{1}{x} dx = \int \frac{dx}{x}$?
3
$\begingroup$
calculus
integration
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0What did you try ? – 2013-10-17
3 Answers
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Yes, $\int \frac{dx}{x}$ is simply shorthand for $\int \frac1x \, dx$; they mean precisely the same thing.
5
Yes. $\int \frac{1}{x} \mathrm dx = \int \frac{\mathrm dx}{x}$.
0
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} $.