Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Evaluate the integral.

$ \displaystyle \int \frac{\cos x}{1 - \sin x}\ dx $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$-\ln (1-\sin x)+C$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Integration Techniques

Campbell University

University of Nottingham

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.

01:41

Evaluate the integral.…

03:08

02:19

Evaluate the integral [ si…

02:41

03:29

00:27

Evaluate the indefinite in…

01:32

02:33

02:39

02:27

let's evaluate to given integral here we could go ahead and try. U Substitution will take you to be sign of X. Then we have Do you is co signed the X So plugging it into this in a girl, we have a top. That's just do you on the bottom. We have one minus you. Now, here. If this one minus he was bothering you. You could go ahead and do it. Use up. Then you could write. This inner girl is negative. One over. You won over W D w So that's negative. Natural log. Absolute value W plus e. Now we use our substitution to replace w with you. So that's one minus you on the absolute value. And then finally, we use our U substitution or original substitution to replace you with X, and that's your final answer.

View More Answers From This Book

Find Another Textbook

04:36

A bag of coins only quarters, dimes, and nickels. There are 200coins in …

03:42

1) 73 people ran a race, how many ways could they finish 1st,2nd, 3rd, 4…

Bob Nale is the owner of Nale's Quick Fill. Bob would like to estimate …

05:31

1) Measurements of the diameters of a random sample of 200 ball bearings mad…

01:46

Does it make sense? Explain in detail.8. Sample Size. A reporter for the…

03:38

Consider the following competing hypotheses: H0: ρxy = 0 HA: ρxy≠ 0 The …

05:48

Refer to the accompanying technology display. The probabilitiesin the di…

01:09

Which of the below samples will produce the best populationparameter est…

01:14

Among college-age students (18-24 years old), 9.2% havehypertension. Dur…

02:44

1. A random sample of size 30 from a normal population yields=32.8 with …