# Integration of Exponential Functions

### Example 1

Find $\displaystyle \int{2e^x}dx$.

$\displaystyle \int{2e^x}dx = 2e^x +c$

### Example 2

Find $\displaystyle \int{e^{2x+1}}dx$.

$\displaystyle \int{e^{2x+1}}dx = \dfrac{1}{2}e^{2x+1} + c$

### Example 3

Find $\displaystyle \int{\dfrac{1}{e^x}}dx$.

\begin{align} \displaystyle \int{\dfrac{1}{e^x}}dx &= \int{e^{-x}}dx \\ &= \dfrac{1}{-1}e^{-x} +c \\ &= -\dfrac{1}{e^x} +c \end{align}

### Example 4

Find $\displaystyle \int{\sqrt{e^x}}dx$.

\begin{align} \displaystyle \int{\sqrt{e^x}}dx &= \int{(e^x)^{\frac{1}{2}}}dx \\ &= \int{e^{\frac{x}{2}}}dx \\ &= \dfrac{1}{2}e^{\frac{x}{2}} +c \\ &= \dfrac{1}{2}\sqrt{e^x} +c \end{align}

Discover more enlightening videos by visiting our YouTube channel!

## Mastering Integration by Parts: The Ultimate Guide

Welcome to the ultimate guide on mastering integration by parts. If you’re a student of calculus, you’ve likely encountered integration problems that seem insurmountable. That’s…

## Integration by Substitution

Integration by Substitution Integration by Substitution is performed by replacing the pronumeral (variable) with another pronumeral to simplify the expression for easier integration. Students often…

## High School Math for Life: Making Sense of Earnings

Salary Salary refers to the fixed amount of money that an employer pays an employee at regular intervals, typically on a monthly or biweekly basis,…

## Trigonometric Integration by Substitution

Substitution of Angle Parts Example 1 Find $\displaystyle \int{(2x+3) \sin (x^2+3x)}dx$. \( \begin{align} \displaystyle\text{Let } u &= x^2+3x \\\dfrac{du}{dx} &= 2x + 3 \\du &=…