Integral of Exponential function formula

Formula

$\displaystyle \int{a^{\displaystyle x} \,}dx \,=\, \dfrac{a^{\displaystyle x}}{\log_{e}{a}}+c$

Introduction

$a^{\displaystyle x}$ is an exponential function, where $a$ is a constant and $x$ is a variable. The integration of $a^{\displaystyle x}$ with respect to $x$ is expressed in mathematical form as follows.

$\displaystyle \int{a^{\displaystyle x} \,}dx$

The indefinite integral of $e^{\displaystyle x}$ with respect to $x$ is equal to the sum of the natural exponential function and constant of integration.

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

Other forms

The indefinite integration of natural exponential function formula can be written in terms of any variable.

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

$(2) \,\,\,$ $\displaystyle \int{a^{\displaystyle x} \,}dx \,=\, \dfrac{a^{\displaystyle x}}{\log_{e}{a}}+c$

$(3) \,\,\,$ $\displaystyle \int{a^{\displaystyle x} \,}dx \,=\, \dfrac{a^{\displaystyle x}}{\log_{e}{a}}+c$

Proof

Learn how to derive the indefinite integration rule for the natural exponential function in integral calculus.

Latest Math Topics
Jun 26, 2023

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.