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Problem

Use the Table of Integrals on Reference Pages 6-1…

02:26

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Problem 27 Easy Difficulty

Use the Table of Integrals on Reference Pages 6-10 to evaluate the integral.

$ \displaystyle \int \frac{\cos^{-1} (x^{-2})}{x^3}\ dx $


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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 6

Integration Using Tables and Computer Algebra Systems

Related Topics

Integration Techniques

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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

Video Transcript

Okay, This question wants us to integrate this function. So to do that, we want to transform this into the integral into one of our forms in the table. So to do this, let's make the substitution to make that transformation have. So we get you equal to X to the minus two. Because usually picking the argument of a coastline is a good start. So that makes d'you equal to negative, too. X to the minus three d x and we have X to the minus three d x. So we just gotta divide by negative too. So now we can transform are integral into negative 1/2 times the integral of co sign inverse of you, do you? And that's a much simply looking for him so we can look it up here, which gives us a formula for anti derivative. So let's just copy that down, keeping our negative 1/2 outside. So this is our anti derivative and now all we have to dio is substitute back in for you. So we get negative 1/2 times X to the negative to co sign in verse of X to the negative too minus square root of one minus X to the minus forth plus C and simplifying We get one over two X squared co sign in verse of one over X squared plus 1/2 square root one minus extra, the fourth plus C and that's your final answer.

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Calculus: Early Transcendentals

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Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Kristen Karbon

University of Michigan - Ann Arbor

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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