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Evaluate the integral.

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

Idaho State University

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.

02:38

03:29

01:38

Evaluate the integral.…

01:30

03:11

02:36

01:34

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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