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JH
Numerade Educator

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Problem 16 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int \tan^2 x \cos^3 x dx $

Answer

$\frac{\sin ^{3} x}{3}+C$

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Video Transcript

this problem is from chapter seven section to problem number sixteen in the book Calculus Early transcendence, ALS a condition by James store. And here we have an indefinite integral of tangents where times co sank you. So first thing we can do is use the definition of tangent tangent assigned over co sign so we can rewrite Tan Square is sine squared X overcoats and square Becks. And here we see that we could cancel off some of these co sign so we could cross off these two in the denominator, we could take off two of the coastlines in the numerator, and then we're just left with Cho since the first power. So that gives us in a girl sine squared X times close antibiotics. So here we can use the u substitution take you to be signing books so that do you is co sign of X d X. And then our general simply becomes the integral of use. Claire, do you? Which we can evaluate using the power rule. We had you cubed over three plus e. And then for the final answer, we should go back to our u sub in back substitute from you back into sign of X. And there's a garment. Final answer