Math Doubts

Integral Rule 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.

Math Doubts

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved