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Problem

Evaluate the integral. $ \displaystyle \int_{-…
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Problem 6 Easy Difficulty

Evaluate the integral.

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

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Related Courses

Calculus 2 / BC
Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Related Topics

Integration Techniques

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Top Calculus 2 / BC Educators
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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.
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Watch More Solved Questions in Chapter 7

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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
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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
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Problem 45
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Problem 47
Problem 48
Problem 49
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Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
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Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
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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 sub for the following. Take you to be two and two plus one. Then here this's equivalents who X equals you minus one over two. And we also have do you over too equals the X for us. Rewrite this one half. Now we have X so that we could use this over here. Then we have our do you We already took out the two over here. And then here we have you. Cute. What? And let's change those limits. If X equals zero, we'LL see you equals one. If that's equals one, then we see U equals three. So that's opera limit. So here, luscious rewrite this. And then we could go ahead and split this into two two fractions and then use the power rule. No plug in your end points. So here, planning the three first? No. Then plug in one. And this should end up simplifying too. One over eighteen. Wait. And that's our answer

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Related Topics

Integration Techniques
Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Joseph Lentino

Boston College

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

06:37

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

03:17

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

08:47

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

01:09

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

06:46

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

01:07

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

09:23

Evaluate the integral. $ \displaystyle \int_0^1 \frac{x^3 + 2x}{x^4 + 4x^2 +…

01:44

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

03:24

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

01:14

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

01:48

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

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