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Evaluate the integral.

$ \displaystyle \int \frac{\sin 2x}{1 + \cos^4 x}\ dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Integration Techniques

Harvey Mudd College

Baylor University

Idaho State University

Boston College

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.

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Evaluate the integrals…

let's start up by re reading this in a roll. So using the double angle formula for sign and then on the denominator, we could write This is one plus co signed square and then square that And then let's try use a beer, coastlines where and then here was too negative. Do you to sign ex co sign X after used the chamber So we get negative in a girl. So we have our do you and then one plus u squared. So if you want, you could put a one up there. Now you may have memorized this formula and if so, you can just write tan inverse of you. If you forgot this fact, just do it tricks up on the cinder girl you would let you equals tan data and you have to solve that in the role. So here we have our HQ tan of you with a minus out front, plus our constancy and let's go ahead and replace you with you so that we started with. So we have negative Arc tan co science for of X plus our constancy. And that's our final answer

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