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Evaluate the integral.

$ \displaystyle \int \frac{\sin^3 x}{\cos x}\ dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Integration Techniques

Missouri State University

Baylor 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.

02:49

05:51

Evaluate the integral.…

01:24

Evaluate the indicated int…

01:08

Evaluate the given integra…

Let's evaluate the given integral. So here, let's start off by pulling off a factor of Science Square, and then we can go ahead and rewrite This term here, that's queer is one minus close and squares. So let's do that. There it is. That's our sign square. And then we have sine X cosign still in the bottom. And then here we can go ahead and do a use up U equals co sign. Then negative, you equal sign So we can write this as pause that minus from over here, one minus use where over you and then let's go ahead and rewrite this and then just use the powerful here. So for the first term, we get negative national log groups you and then here Watch out for that double whiteness. No. And then finally come back to your use up here and replace you with X two up there and then plus see. And that's a final answer

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