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Integrate each of the functions.$$\int \cos ^{5} x(-\sin x d x)$$

$\frac{\cos ^{6} x}{6}+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 1

The General Power Formula

Integrals

Campbell University

Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:38

Find each integral.$\i…

02:15

Integrals of $\sin x$ or c…

02:22

Integrals of $\sin x$ and …

03:02

02:25

Evaluate the following int…

01:48

01:30

05:00

01:58

Evaluate the integrals.

02:17

Evaluate the integrals…

we want to integrate the following. The integral of the coastline. Fifth of X. Times negative Sine X. Ds. This question is testing our knowledge of methods of integration as such. We need to have a strong foundation integral calculus to solve. And particularly the question is testing our knowledge of the power rule for integration. The power rule for integration states at the integral of U. N. D. U. Is equal to U. To the N plus one divided by N plus one. That's the constant of integration. See So if we can identify you and and do you in this problem we can easily solve the the power rule. Since the negative sign is that of coastline, it's easy to see that U. As cosine X. Do you as negative sine X. D. X. And N. Is equal to five the exponent of our coastline. Thus we can use the power will to solve plugging in U. D. U. N. N. So integral U. N. D. U. Is equal to 1/6 times the coastline of exploration. Six power plus the constant of integration seat

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