Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Evaluate the integral. $ \displaystyle \int (\…

05:20

Question

Answered step-by-step

Problem 21 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{xe^{2x}}{(1 + 2x)^2} dx $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

WZ
Wen Zheng
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Wen Zheng

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Related Topics

Integration Techniques

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Grace He
Catherine Ross

Missouri State University

Caleb Elmore

Baylor University

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
Recommended Videos

14:38

Evaluate the integral.

…

00:34

Evaluate the integral by m…

00:55

Evaluate the definite inte…

01:50

Evaluate the integral.
…

01:02

Evaluate the integral.
…

01:07

Evaluate the integral.
…

01:35

Evaluate the integrals
…

03:21

Evaluate the integral.
…

06:20

Evaluate the integral.

…

10:10

Evaluate the integral.
…

0:00

Evaluate the integral. $\i…

Watch More Solved Questions in Chapter 7

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74

Video Transcript

The problem is violated the integral x times e to 2 x, over 1 plus 2 x into the square for this problem. We we can use my third integration by powers. The formula is integral of: u: v from d x is equal to u times, v minus the integral of prime v d x. Now for our problem, we can write. U is equal to x times e to 2 x and prime is equal to 1 over 1 plus 2 times x square. Then you problem is we use product rule here, so this is e to 2 x plus x times e to 2 x times 2. This is 1 plus 2 x times e to 2 x and v is equal to negative 1 half times 1 over 1 plus 2 x now use this formula. Integral of this function is equal to u times. This is negative x over 2 times 1 plus 2 x times e to 2 x. Minus you prime times we. This is minus integral of 1 plus 2 x times e to 2 x times negative 1, half 1 over 1 plus 2 x x simplified this function. We have this is equal to negative x into 2 x over 2 times 1 plus 2 x minus this plus il half integral of into 2 x x. The answer is, this is equal to negative x times e to 2 x over 2 times 1 plus 2 x plus 1 force into 2 x and plus constant number c.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
143
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
68
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Caleb Elmore

Baylor University

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
Recommended Videos

14:38

Evaluate the integral. $ \displaystyle \int \frac{x^2 + 1}{(x^2 - 2x +2)^2}\…

00:34

Evaluate the integral by making the given substitution. $ \displaystyle \in…

00:55

Evaluate the definite integral. $ \displaystyle \int^1_0 xe^{-x^2} \, dx $

01:50

Evaluate the integral. $$ \int \frac{\left(2^{x}+1\right)^{2}}{2^{x}} d x $$

01:02

Evaluate the integral. $$\int_{1}^{2}\left(2 x+x^{2}\right) d x$$

01:07

Evaluate the integral. $\int \frac{x}{\left(x^{2}+1\right)^{2}} d x$

01:35

Evaluate the integrals $$\int \frac{x^{2} d x}{\left(1+x^{2}\right)^{2}}$$

03:21

Evaluate the integral. $\int \frac{d x}{(x-1)^{2}(x-2)^{2}}$

06:20

Evaluate the integral. $ \displaystyle \int \frac{x^2 + x + 1}{(x^2 + 1)^2}\…

10:10

Evaluate the integral. $$ \int \frac{x^{2}+1}{\left(x^{2}-2 x+2\right)^{2}} d…

0:00

Evaluate the integral. $\int \frac{x-1}{x^{2}+2 x} d x$
Additional Mathematics Questions

01:47

6. We wish to estimate the mean gestational age (in days) in high-risk pregn…

01:44

USA Today/CNN/Gallup survey of 364 working parents found 203 who said they s…

01:45

The arrival of trucks at a receiving dock is a Poisson process with a mean a…

02:39

Check Your Understanding: Association vs Causation
For a sample of cities…

02:09

Name:
Statistics 214 Section
The heights of American adults can be mod…

04:16

2_ An online survey asked 1004 adults "If purchasing a used car made ce…

04:28

Beyond the examples in class, there are other models that can be linearized …

04:27

Find the area enclosed by the graphs of f(r) = 2r and g(2) = 3 ~ 2?
Find …

01:23

median price of 14,389.78. The mean price Tke same car at three different de…

05:16

2_ The continuous random variable X has pdf given by
fxkr) = 54, (o,
I…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started