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Evaluate the integral.

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

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Integration Techniques

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

01:53

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.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

01:03

Evaluate the indefinite in…

00:32

00:30

01:05

01:26

Evaluate each integral.

03:32

02:18

Evaluate the integral.…

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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