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Problem

Evaluate the integral. $ \displaystyle \int x …

01:22

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Problem 14 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int \ln (1 + x^2)\ 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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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

Problem 1
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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
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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
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Problem 61
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Problem 64
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Problem 66
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Problem 68
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Problem 73
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Problem 75
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Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84

Video Transcript

Let's use integration by parts for this integral here. Let's just take you to just be the intern grand. So then go ahead and use the chain rule to differentiate us. So you get one over one plus x Square, but then take the derivative of one plus x squared. So that's our do you Then we're left over with TV equals the X. So vehicles X now using integration by parts here, recalled the formula U V minus and enroll video. So we'LL go ahead and plug in our use. Andy's here, so we have X natural log one plus X squared, so lets you times v and then we have minus in a girl VDO. So here we have the and then do you So let me go in and pull out that, too. And then X squared over one plus x squared. Now you may try partial fractions here, but first we see that they have the same degree. So here we would need to do polynomial division and we can go ahead and rewrite this. After doing the long division, we get one minus one over one plus x cleared. Yeah, and that is our partial fraction to composition, So there's no need to find the baby in the seas. And, well, we know how to integrate both of these. If the second one. If this if you don't remember what this one is, you could do a trousseau at sequel stand data. So after writing this, we have X ellen one plus X square minus two in a girl, one minus one over one plus x squared DX. So now X Ellen one plus x square. Then from this we have a minus two X when we integrate And then after doing the tricks up here, you'LL get a plus two times ten inverse x and then we'LL add our constant of integration, see? And that's your final answer.

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Top Calculus 2 / BC Educators
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Missouri State University

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Campbell University

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Baylor 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
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