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 \f…

01:29

Question

Answered step-by-step

Problem 70 Hard Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{1}{1 + 2e^x - e^{-x}}\ dx $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

JH
J Hardin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by J Hardin

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 5

Strategy for Integration

Related Topics

Integration Techniques

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

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

04:03

Evaluate the integral.

…

02:23

Evaluate the integral.
…

01:38

Evaluate the definite inte…

01:51

Evaluate the definite inte…

03:41

Evaluate the integral.

…

05:25

Evaluate the integral.

…

03:03

Evaluate the integral.

…

04:21

Evaluate the integral.

…

01:22

Evaluate the integral.

…

00:54

Evaluate the definite inte…

0:00

evaluate Integral

0:00

Evaluate the integral.

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
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84

Video Transcript

Let's use a U substitution here. Let's take you to be either the ex then we know. Do you? Either the next T X and we could go out and solve this for X by dividing. So that's first. Let's rewrite. This is E D x. Oops as you DX since S is equal to you Some just replacing this with you here and then do you over you equals the X. So now, after using the use of you still have the one up there. Then that's one plus to you and then minus. And then here because of that minus sign well, one over you. And then here we multiply my DX do you over you. Now the next step years to just multiply this you into that denominator there. What? So that's what we have Could factor that denominator before you try partial fractions. And then here, you know the partial fractions will be of the form. Stay over to you minus one, and then be over you plus one. So, after finding in the way you find the end of the recall is you set this circle term equal to this circle term here, Then you multiply by both sides of this by the green circles from here and then saw for Andy. So after doing this, we end up with a is two thirds and then for being, we get minus one third. So I just pull off that minus. And then there's the you plus one and then here we know these in a girls if you need to, you could do it. Use up here. Here. You could do another U. So, in any case, one half and the natural log to you minus one. The one half is coming from the DW over, too. And then we also have minus one third and the natural log you plus one plus c. So just cancel those twos there. Let's go out and write this out. Cancel those twos. One over three. Also, I shouldn't circle this because we didn't back some in terms of X, new equals either the ex. So here we have one third Ellen to E X, minus one minus one third. And that here eating Ellen Ellen either the X plus one. No absolute values necessary here. This is a positive number. Plus he and that's your final answer

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
162
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
70
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

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

04:03

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

02:23

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

01:38

Evaluate the definite integral. $$\int_{1}^{2}\left(1+\frac{1}{x}+e^{x}\right) …

01:51

Evaluate the definite integral. $$\int_{-1}^{1} x e^{x^{2}+1} d x$$

03:41

Evaluate the integral. $ \displaystyle \int_{-1}^2 \mid e^x - 1 \mid dx $

05:25

Evaluate the integral. $ \displaystyle \int_0^1 (x^2 + 1) e^{-x} dx $

03:03

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

04:21

Evaluate the integral. $ \displaystyle \int \frac{dx}{1+ e^x} $

01:22

Evaluate the integral. $$ \int \frac{e^{2 x}}{1+e^{x}} d x $$

00:54

Evaluate the definite integral. $ \displaystyle \int^2_1 \frac{e^{1/x}}{x^2}…

0:00

evaluate Integral

0:00

Evaluate the integral.
Additional Mathematics Questions

01:22

At the end of the accounting period, Armstrong Corporation reports operating…

00:45

Why do journals have a Post Reference (PR) column? A. to cross reference bet…

00:24

What does effective operation of the organisation's information ensure?…

04:07

Mountainview Resorts purchased equipment for $34,000. Residual value at the …

01:08

Which of the following types of adjustments to the government fund financial…

01:25

Which of the following statements concerning approaches for the budget devel…

02:19

which of the following represents an inflow of cash to my company? a. I pay …

02:45

Liam notices that there are no safeguards over company inventory and tells h…

08:53

Your organization, located in Manitoba, will be enhancing the group benefits…

00:52

Which of the following items would not be reported in the financing activiti…

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