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Problem

Evaluate the integral. $ \displaystyle \int \f…
01:38

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Problem 73 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{x + \arcsin x}{\sqrt{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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Top Calculus 2 / BC Educators
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Missouri State University

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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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Watch More Solved Questions in Chapter 7

Problem 1
Problem 2
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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
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 this one by just putting it into two fractions here. Or even better, let's just right is to separate animals completely. So in the first line we have except top. And then for the second one, we have that arc sine and the other seemed denominator. Now let's do some substitution is here for the first one. Let's take you to just be that denominator. Actually, let's take it to be just the expression inside the radical, then hear negative do you over to will just give you extra e x And then for this one Over here, Let's take a w to be orc sign then DW is one over the square of one minus x square D x. So we're doing useful for both of these. So for the first Indian girl, we have this negative one half coming from the day you took and then that takes care of the ex DX. So we just have a d you up here and then we have a square of you in the bottom. So, Lucious, right? That is you to the negative one half and then we have plus and a girl w and then dw Now let's just use the Powerball twice here. So for the first integral, that's Debbie to the one half. And then you divide by a half and then for W have any squared over two. It's ad that constancy. And so here you could cross off the one half with the two. You have a negative here, so negative square of you and then replace you with X so one minus X square in the Radical plus. And then here you have W Square. So that signed inverse of X all square and then divide that expression over too, plus our constancy there at the end, and that's my final answer.

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Related Topics

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Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State 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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