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Integrate each of the given functions.$$\int \sin ^{3} 2 x d x$$

$\frac{\cos ^{3} 2 x}{6}-\frac{\cos 2 x}{2}+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 5

Other Trigonometric Forms

Integrals

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this problem, We're gonna find the anti derivative of X Sign of the corn. The X weird. This will be a U sub problems of First. Let's assigning you value of X weird. And then we'll take the derivative to find d'you, which will be two x d x. We'll need to move the two over by divisions that we can do a proper substitution. And as we look at the original, you can see that the X squared here will be then replaced with you and then our our ex and then r D X will be replaced with 1/2 the U So are integral will look like this will have a 1/2 coefficient in front and then we replace our associated values here with sign of you D you and that are anti derivative is negative 1/2 co sign of you plus C and we substitute back to get the correct anti derivative with X. So we have negative 1/2 coastline of X squared plus C

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