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Evaluate the integrals$$\int \cos ^{3} x \sin x d x$$

$$-\frac{1}{4} \cos ^{4} x+C$$

Calculus 1 / AB

Calculus 2 / BC

Chapter 8

Techniques of Integration

Section 2

Trigonometric Integrals

Integrals

Integration

Integration Techniques

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:28

Evaluate the integrals.

02:42

Evaluate the integrals…

00:48

01:17

01:24

Evaluate the indicated int…

05:51

Evaluate the integral.…

04:22

Evaluate the integral.

01:35

Evaluate the following int…

02:07

02:00

Section eight that to problem number three We've got the integral of the cosign cubed of x times the sign of X so integration. Sometimes it's just like a puzzle. Sometimes the puzzles that you see sometimes the puzzles hard but one of the key things If I can ever identify ah function and it's derivative coexisting, that can be a key. So if I look at this well, it looks like the Ellicott co sign the derivative coastline is minus sign. So what if I were to let you equal the co sign of X? Then d'you is going to be minus sign of eggs DX so I could rewrite this as wth e integral. So negative co sign cubed of X minus Sign of x d x and you know that minus sign of X t X. That is just simply, do you and then you is able to co sign X. So this is just simply you cubed. So this is the Inderal minus you, Cube, do you? This integrates to be minus you to the fourth over for plus a constant of integration. So this final answer is just minus the co sign to the fourth power of X over four, plus a constant of integration

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