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Rewrite the given integrals so that they fit the form $\int u^{n} d u,$ and identify $u, n,$ and $d u$.$$\int \frac{\tan ^{3} x d x}{\cos ^{2} x}$$

$u=\tan x, d u=\sec ^{2} x d x$ and $n=3$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 1

The General Power Formula

Integrals

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In mathematics, precalculu…

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In mathematics, a function…

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Evaluate the integrals by …

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Evaluate the integrals usi…

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Evaluate each of the follo…

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Evaluate the integral.…

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uh huh. We want to evaluate the following the integral of the tangent cubed of X. Dx over the coastline. Square X. Dx. This question is testing our knowledge of methods of integration in particular. I recently learned method called the power rule. Remember that the power rule for integration states that the integral of U. To the N. D. U. Is U. To the N plus one over N plus one plus the see the constant of integration. So if we identify you do you and end in our given integral, we can easily solve the the power rule. So we see that you as 10 cubed X. Do you as you can't square X. Dx. Which is equivalent to our given integral dx over coast squared X. And N is equal to three. So you was actually tan X. So then by the power rule you must have that are integral of U. D. N. D. U. Is U. D. M plus one for over four plus C. Or 1 4th times a tangent fourth x plus seen constant of integration.

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