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

$x$ 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.

List of most recently solved mathematics problems.

Jul 04, 2018

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Evaluate $\displaystyle \large \lim_{x \,\to\, \tan^{-1}{3}} \normalsize {\dfrac{\tan^2{x}-2\tan{x}-3}{\tan^2{x}-4\tan{x}+3}}$

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Evaluate $\displaystyle \large \lim_{x \to 0} \normalsize \dfrac{e^{x^2}-\cos{x}}{x^2}$

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Evaluate $\displaystyle \int \dfrac{1+\cos{4x}}{\cot{x}-\tan{x}} dx$

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Evaluate $\displaystyle \large \lim_{x \to \infty} \normalsize {\sqrt{x^2+x+1}-\sqrt{x^2+1}}$

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