# Integral Rule of Natural Exponential function

## Formula

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

### Introduction

$x$ is a variable and the natural exponential function is written in mathematical form as $e^x$. The integration of $e^x$ with respect to $x$ is written in differential calculus as follows.

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

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.

$(1) \,\,\,$ $\displaystyle \int{e^m} \,}dm \,=\, e^m}+$

$(2) \,\,\,$ $\displaystyle \int{e^t} \,}dt \,=\, e^t}+$

$(3) \,\,\,$ $\displaystyle \int{e^y} \,}dy \,=\, e^y}+$

### Proof

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

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