Integral rules of Exponential functions

In integral calculus, some functions are formed with exponential functions. For calculating the integrals of such functions, some special rules are required. The following is the list of integration formulas with proofs for finding the integration of the functions in which the exponential functions are involved.

Exponential function

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

The integral of the exponential function is equal to the sum of the quotient of exponential function by the natural logarithm of the base and the integral constant.

Natural exponential function

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

The integral of the natural exponential function is equal to the sum of the natural exponential function and the integral constant.

Problems

List of the integral problems with solutions to learn how to use the integral rules of exponential functions to find the integrals of the functions in which exponential functions are involved.