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…

04:21

Question

Answered step-by-step

Problem 26 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int_0^1 \frac{3x^2 + 1}{x^3 + x^2 + x + 1}\ 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
Grace He
Catherine Ross

Missouri State University

Caleb Elmore

Baylor University

Samuel Hannah

University of Nottingham

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

04:34

Evaluate the integral.
…

08:47

Evaluate the integral.

…

06:37

Evaluate the integral.

…

01:14

Evaluate the integral.
…

03:17

Evaluate the integral.
…

01:49

Evaluate the integral.
…

04:56

Evaluate the integral.
…

02:15

Evaluate the integral.

…

01:09

Evaluate the integral.
…

04:29

Evaluate the integral.
…

00:42

Evaluate the indefinite in…

04:52

Evaluate the integral.
…

06:41

Evaluate the integral.
…

01:20

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

for this integral. Let's use partial fractions. So do that. We really should look at the denominator to see if this factors so this what you could do here they see that X equals minus one is a route. So if you plug it into that denominator, you get zero. So this tells you the X minus negative one or just X plus one divides the denominator. So go ahead and do the long division there. So you would like to divide over X Plus one. And after doing the polynomial division, we X Square plus one. So that tells us that we can go ahead and write the original and so grand and the denominator. We can now write that as X plus one times x squared plus one. And we get that by just multiplying this to both sides. And then we'LL get a factor on the right so we can replace this cubic polynomial with X square plus one Times X plus one. So now we would do the partial fractions. This's a over X plus one bye B X plus C explored plus one. Now go ahead and multiply both sides of this equation by the denominator on the left. Then we get a and then b X plus C with X plus one. Now go ahead and simplify this friendly hand side. And we could rewrite this by pulling out of X Square by pulling out of X and then we're left over with our constant term. So look at the coefficients on the left we see a three in front of the X Square, so a plus b is three. Then we see no ex term over here on the left. That means D plus he must be zero. And in the constant term is one. So the constants of here must be want that gives us three by three system to solve. Come. So here, for example, you could be equals negative c and then we can write This's a minus. B equals one and then plug this equation and right below we can go ahead and add these equations together. You get ankles, too. From this equation up here, B equals one. And then from here we have C equals negative one. So let's go ahead and on to the next page. And let's plug in these values for a B and c into our partial fraction. So it was to be was one. So we just have a one x there and then see was minus one. So we get the mine. Is there exploring? Plus one. Now let's split this into three in a girls Then for the second one, we have X and then finally So for this first integral if this plus one is bothering you, do you sub? And then when we integrate that we'LL get to natural log absolute value It's close one and point zero one for the second Integral Here you Khun do another use, um let you be the denominator Then do you over two equals x t x So there we'LL get one half natural log explorer plus one zero one and then finally over here You may remember this one already, but if not, you can do it Tricks up here X equals tan data after using that you should get But now including this minus here will have minus Artie Innovex zero one and then we just plug in. So here's the first one plug in one for X to national log to when you plug it zero for X you get natural other one, which is zero. And then over here, plug in X equals one. Plug it zero than the whole term zero and then ten inverse of one. And then plus, because of this minus here, it's an inverse of zero. So this is just five over to natural log to combining these and then this is minus pira for And this is because this is over. Here is power for in this term over here. Zero. So we have the minus right there, 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
191
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
81
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

Samuel Hannah

University of Nottingham

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

04:34

Evaluate the integral. $$ \int_{0}^{1} \frac{3 x^{2}+1}{x^{3}+x^{2}+x+1} d x $$

08:47

Evaluate the integral. $ \displaystyle \int_{-1}^0 \frac{x^3 - 4x + 1}{x^2 -…

06:37

Evaluate the integral. $ \displaystyle \int_0^1 \frac{2}{2x^2 + 3x + 1}\ dx $

01:14

Evaluate the integral. $$\int_{0}^{1} \frac{x-1}{x^{2}+3 x+2} d x$$

03:17

Evaluate the integral. $$ \int_{0}^{1} \frac{x}{(2 x+1)^{3}} d x $$

01:49

Evaluate the integral. $$\int_{0}^{1} 3 x^{2}\left(x^{3}+1\right) d x$$

04:56

Evaluate the integral. $\int_{-1}^{0} \frac{x^{3}-4 x+1}{x^{2}-3 x+2} d x$

02:15

Evaluate the integral. $ \displaystyle \int_0^1 \frac{x}{(2x + 1)^3}\ dx $

01:09

Evaluate the integral. $$\int_{0}^{1}\left(1+x^{2}\right)^{3} d x$$

04:29

Evaluate the integral. $$\int_{0}^{1} \frac{2}{2 x^{2}+3 x+1} d x$$

00:42

Evaluate the indefinite integral. $ \displaystyle \int (x^2 + 1)(x^3 + 3x)^4…

04:52

Evaluate the integral. $$ \int_{0}^{1} \frac{3 x^{2}+1}{x^{3}+x^{2}+x+1} d x $$

06:41

Evaluate the integral. $$ \int_{-1}^{0} \frac{x^{3}-4 x+1}{x^{2}-3 x+2} d x $$

01:20

Evaluate the integral. $ \displaystyle \int_0^1 \frac{2}{2x^2 + 3x + 1}\ dx $
Additional Mathematics Questions

02:00

6 students secured 34, 23, 29, 32, 11, 43 out of 50 marks in a paper. What i…

01:22

Varun had to travel 12 km from town A to town B. he travelled 5/8 km by bus.…

01:15

What is the first step in writing f(x) = 6x2 + 5 – 42x in vertex form?

02:07

what is the probability of drawing a ace from a deck of 52 cards

00:17

The square robot of 12.25is ??
A)3.5
B)2.5
C)35
D)25

02:01

Find the value of K so that quadratic equation 3x2 - kx + 38 = 0 has equal r…

02:06

the range of x, 32, 41, 62,64 & 71 is 45. What is the value of x

01:18

find the equation of the line passess through (x1, y1 ,z1) and parallel to t…

01:14

determine the time taken when distance is 7150 km and speed is 780 km / h

01:14

determine the time taken when distance is 7150 km and speed is 780 km / h

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