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Problem

Evaluate the integral. $ \displaystyle \int x …

02:33

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Problem 78 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{1 + \sin x}{1 - \sin x}\ 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

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Problem 84

Video Transcript

Let's just start off by rewriting. That's right. This is two plus and then sine minus one. And then let's rewrite this. So we have one, say two and then one minus sign and then we have, unless free right, This's negative. One minus sign. No hearing. Good. Cancel. So for this one, let's multiply. It's happened, but and then for the second one, this is just in general. Negative one. So for the first but one plus sign and then here that equals one minus signs clear, which is co sign square. So let's put that in. And then here, that should have been a plus from this both pluses. And then this integral x minus x ten plus e. Now we could rewrite this. So all I did here it just break this into two fractions and then rewrite these as these two terms respectively. And then we could integrate this two ten to see can't and then our minus X and plus E. And that's our answer

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Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

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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