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Problem

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

01:42

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Problem 64 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{1}{\sqrt{\sqrt{x} + 1}}\ 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

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 start off here by doing the use up. Let's just take you to be the entire denominator. Then here we will have to use the general from calculus. Teo, do the derivative, so I do the outer one first. So I'm using the power ruler. But that I have to go and also take the derivative of the inside. So here, let me I guess Let me write it as one over to radical X. That's the derivative but the inside. So we're all here. We're using the Kane rule. And to make this problem a little easier I'd like to re write all this in terms of you. So this is just one over to you Times one over to and I'll have to fill in this blank here and then the x So I need two for just rewrite radical exterior. So I'll just get that from this equation to square both sides. It's a practice one. So you just get you squared minus one instead of radical X and was good. And take this equation here and solvent for DX. So you have d X equals two times two is four we have Are you here and then you squared minus one. Do you? So now, after using our use up, we have one over you. And then we have R D X, which was for you. You squared minus one. Do you? Let's pull off the four. Cancel those use. We have you squared minus one, So just generate this. Using the power rule. Don't forget your constant of integration. See? And then the last appears to just replace you back in with a radical. So we have here you to the third power and then minus four times you and that's your final answer.

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Top Calculus 2 / BC Educators
Grace He

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Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

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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Evaluate the following integral int 1√(x) (√(x)+1) dx

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Find the Integral of \int \frac{1}{\sqrt{1+x^2}}dx

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