Math Doubts

Integral of 1/x formula


$\displaystyle \int{\dfrac{1}{x}}dx \,=\, \log_{e}{(x)}+c$


$x$ is a variable and its reciprocal is $\dfrac{1}{x}$. The symbol $dx$ is an element of integration. Therefore, the integral of quotient of $1$ by $x$ with respect to $x$ is expressed in integral calculus in the below form.

$\displaystyle \int{\dfrac{1}{x}}dx$

The indefinite integral of ratio of $1$ to $x$ function with $dx$ is equal to sum of natural logarithm of $x$ and constant of integration.

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