Math Doubts

Integral Power rule

Formula

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

Introduction

$x$ is a variable and $n$ is a constant. $x$ is raised to the power of $n$ is written as $x^n$ and $dx$ is the element of integration. Therefore, the integral of $x$ is raised to the power of $n$ with respect to $x$ is written mathematically as follows in calculus.

$\int{x^n}dx$

The indefinite integral of $x^n$ with $dx$ is equal to the sum of the quotient of $x$ is raised to the power of $n$ plus $1$ by $n$ plus one and constant of integration. It is called as power rule of integration or simply integral power rule. It is also called as reverse power rule in calculus.

Remember, the value $n$ is not equal to $-1$ ($n \ne 1$) in this case.



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