# Integral of 1 formula

## Formula

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

### Introduction

Let’s denote a variable by a literal $x$. The differential element with respect to $x$ is written as $dx$ in differential calculus. Now, the indefinite integral of one with respect to $x$ is mathematically written in integral calculus as follows.

$\displaystyle \int{1} \times dx$

$\implies$ $\displaystyle \int{}dx$

The indefinite integral of one with respect to $x$ is equal to $x$ plus the constant of integration. Here, the literal $c$ denotes the integral constant.

$\,\,\,\therefore\,\,\,\,\,\,$ $\displaystyle \int{}dx$ $\,=\,$ $x$ $+$ $c$

It is called the integral of one rule and it used to find the integral of one with respect to a variable in calculus.

#### Other forms

The indefinite integral of one with respect to a variable is also popularly expressed in integral calculus in the following forms.

$(1).\,\,$ $\displaystyle \int{}dt$ $\,=\,$ $t$ $+$ $c$

$(2).\,\,$ $\displaystyle \int{}dv$ $\,=\,$ $v$ $+$ $c$

$(3).\,\,$ $\displaystyle \int{}dy$ $\,=\,$ $y$ $+$ $c$

##### Proof

Learn how to prove the integral of one rule in calculus as the variable plus the constant of integration.

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Jun 26, 2023

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