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Problem

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

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Problem 10 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{\cos (\frac{1}{x})}{x^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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Missouri State University

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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 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
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Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
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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 start by taking the U substitution. So looking inside the co sign, we see a one over X. So let's just try that, then using the powerful for derivatives. So here it looks like we can rewrite this using you. So it's plot of minus sign here because of this one from the use of So by writing negative, do you? We're getting one over X squared and e x so that gives us this and X squared on the bottom. So on top. So here, let's write. This is CO sign you. This is giving me this over here and by writing negative you deal. That's giving me everything else. The negative do you is giving you two of the ex is on the bottom and then multiplying by this extra you is just giving us another one over x. So that gives us the one over X cute. So this is our general. So we have negative inaugural of you times co sign you So for this new in a girl here. So it's got a little messy of here. Let me come and rewrite this. That's right. This is you co sign you. Do you now let's set ups the integration by parts for this one. So let me not use the letter you since we were to use that up here and it's in our general. What's his w equals you? T w deal TV is co sign So we assign you so using integration my parts. So remember the formula. There's UV minus integral ggo. In our case, let me go ahead and replace that with a w there. Since that's what was that we're using So negative. Then we have you time sign you minus in a girl sign you That's B and then d w which is do you? So now we can go ahead and distribute the minus sign. So that's a negative. You signed you plus integral of sign. So that's negative. You sign you minus co sign you. And now the frigate at your constancy. Now we've evaluated the intern group with the last step here will be to come up to this u substitution so that you can replace you in terms of X. So this last step here is just to do that, replace you. So you is one over X sign one over X and then we have minus co sign one of Rex and then plus C and that's your final 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

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
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