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Problem

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

02:40

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Problem 28 Medium Difficulty

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

$ \displaystyle \int \frac{dx}{\sqrt{1 - e^{2x}}} $


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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
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Problem 5
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Problem 7
Problem 8
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Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
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Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
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Problem 32
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Problem 34
Problem 35
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Problem 46

Video Transcript

Okay. This question wants us to integrate this function. Using a table so well, usually like, is having some sort of a you squared in the denominator. So let's have you equal eat of the ex. So that means that do you equals you to the x d x. But we don't have any of those. So do you. Over e to the X equals DX. So no, we can write this as d'you over either the X square roots one minus you squared. But we're still not done because we haven't eat of the ex and we're supposed to be in the u world. So if you is equal to eat of the X, then X is equal to Ellen of you. So now we can rewrite this as the integral of D'You over E to the Ellen of you Square group one minus you squared and we see the deed to the Ellen. You is just you. So we get our final integral of d U. Over you square root one minus you squared. And this is something that we can look up in our table. It's exactly one of the forms. So we get that this is equal to negative times. Ln of absolute value, one plus square root one minus You squared all over you plus C And now we can flip this fraction over and put them to get rid of the negative sign. So we get equals. Ellen of you over one plus square, one minus you squared plus c. And then the last thing we got to d'oh is plug in eat of the ex for you and now we're done.

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Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

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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