Math Doubts

Integral of Natural Exponential function

Formula

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

Introduction

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

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

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.

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

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

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

Proof

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



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