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Integrate each of the given functions.$$\int \frac{4 d x}{e^{\sin x} \sec x}$$

$-\frac{4}{e^{\sin x}}+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 3

The Exponential Form

Integrals

Missouri State University

Campbell University

Harvey Mudd College

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:55

Find each integral.$$\…

01:08

Find each integral.$\i…

06:07

Evaluate the following int…

01:25

00:49

03:50

Evaluate the integrals.

02:12

00:45

06:26

Repeated integration by pa…

03:43

we want to integrate the following expression. The integral of four D. X. Over even the cynics. You can't X. This question is testing our knowledge of methods of integration. We've already learned about the power rule and log arrhythmic integration in this problem. We need to make use of what's known as exponential integration to solve exponential integration states. As this formula suggests that the integral of E. To the U. D. U. Is each of you plus C. So if in our about integral we can identify you and do you we can go ahead and solve with this formula. So use whatever is raised to the power of the exponent E. Since E to the X is in the denominator we have that you is negative Synnex by this. Dus negative coast X dx but negative coast X by trig identities is identically negative dx over C. Can X. So we have an extra factor of +44 or rather negative for and are integral. Which means that our solution is negative for integral to the you. Do you buy the formula? We have negative for the negative sine X plus C.

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