$\displaystyle \int{\dfrac{1}{x} \,} dx \,=\, \ln{x}+c$

The integral of multiplicative inverse of a variable equals to sum of natural logarithm of variable and constant of integration is called the reciprocal rule of integration.

Let $x$ be a variable. The multiplicative inverse or reciprocal of variable $x$ is expressed as $\dfrac{1}{x}$ in mathematical form. It is often appeared in integral calculus. Hence, an integral rule with reciprocal of a variable is introduction in integration.

The integration of multiplicative inverse of $x$ with respect to $x$ is written in mathematical form as follows.

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

The integration of reciprocal of $x$ with respect to $x$ is equal to natural logarithm of variable $x$ and integral constant. It is mathematically expressed in the following form in calculus.

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

This integral rule is used as a formula in calculus when a variable is involved in integration reciprocally.

The multiplicative inverse rule of integration can be written in terms of any variable in calculus.

$(1) \,\,\,$ $\displaystyle \int{\dfrac{1}{m} \,} dm \,=\, \ln{(m)}+c$

$(2) \,\,\,$ $\displaystyle \int{\dfrac{1}{y} \,} dy \,=\, \ln{(y)}+c$

Learn how to prove the integration of multiplicative inverse of a variable in integral calculus.

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved