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Evaluate the integral. $ \displaystyle \int_0^…

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Problem 39 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{\sec \theta \tan \theta}{\sec^2 \theta - \sec \theta}\ d \theta $

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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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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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Video Transcript

Let's try use up here. Let's take you'd be C cam. Send to you seeking times. Damn. So we can rewrite this. We see appear This is equal to this. So we just have do you of top and then we have use Claire minus you. Oh, it's the factor that then here you have to do partial fractions. So here will end up with one over. You minus one minus one over you. That's natural log. Absolute value. You minus one minus Ellen. Absolute value. You don't forget the constancy and then here and finally go back and tio original use, um, and replace you, and that's your final answer.

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Related Topics

Integration Techniques

Top Calculus 2 / BC Educators

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Oregon State University

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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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