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Integrate each of the given functions.$$\int \frac{e^{\cos 3 x} d x}{\csc 3 x}$$

$-\frac{1}{3} e^{\cos 3 x}+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 3

The Exponential Form

Integrals

Campbell University

Baylor University

University of Nottingham

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:47

Evaluate each of the follo…

01:44

Evaluate the following int…

00:48

Evaluate the integrals.

01:17

Evaluate the integrals…

01:28

02:42

07:21

Evaluate the integral.…

01:35

Evaluate each definite int…

01:57

Evaluate each integral.

Mhm. We want to integrate the following expression. The integral of E. Race of the coastline of three X. D. X. Divided by the coast ticket of three X. This question was testing our knowledge of methods of integration. We've already learned about the power rule and algorithmic rules for integration and this particular problem were being challenged to use exponential integration. What today's of the integral of each of the U. D. U. Is each of you plus C. If we identify you and do you in this problem we can easily solve. So since you're whatever raised to the power of E we see that you must be co sign three X. Do you would then be negative three signed three X. Dx. Which we can also write as negative three D. X. Over cause you can't three X. Because sign is one of our coast. You can thus are integral is either you D. You but it's missing a factor of negative three. So we must have are integral is negative one third integral to the U. D. U. Or negative one third E. To the coastline of three X. Plus C. The constant of integration.

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