# Integral of Exponential function formula

## Formula

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

### Introduction

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

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

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

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

#### Other forms

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

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

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

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

### Proof

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

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