$\displaystyle \int{a^{\displaystyle x} \,}dx \,=\, \dfrac{a^{\displaystyle x}}{\log_{e}{a}}+c$
$a^{\displaystyle x}$ 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.
$\displaystyle \int{e^{\displaystyle x} \,}dx \,=\, e^{\displaystyle x}+c$
The indefinite integration of natural exponential function formula can be written in terms of any variable.
$(1) \,\,\,$ $\displaystyle \int{a^{\displaystyle x} \,}dx \,=\, \dfrac{a^{\displaystyle x}}{\log_{e}{a}}+c$
$(2) \,\,\,$ $\displaystyle \int{a^{\displaystyle x} \,}dx \,=\, \dfrac{a^{\displaystyle x}}{\log_{e}{a}}+c$
$(3) \,\,\,$ $\displaystyle \int{a^{\displaystyle x} \,}dx \,=\, \dfrac{a^{\displaystyle x}}{\log_{e}{a}}+c$
Learn how to derive the indefinite integration rule for the natural exponential function in integral calculus.
A best free mathematics education website for students, teachers and researchers.
Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.
Learn how to solve the maths problems in different methods with understandable steps.
Copyright © 2012 - 2022 Math Doubts, All Rights Reserved