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JH
Numerade Educator

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Problem 79 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int x \sin^2 x \cos x\ dx $

Answer

$$\frac{1}{3} x \sin ^{3} x+\frac{1}{3} \cos x-\frac{1}{9} \cos ^{3} x+C$$

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Video Transcript

Let's try this one by using parts. Let's take you to be this X over here. Do you use the X? And then we're left over with this for our D V. And then here you can do a U sub that you be signed. And he's the power rule. So here, using the formula, the by parts formula there we have U times V. So that's X. Thank you. Be over three and then minus integral. And then we have Z do pull over three and then here. Let's go ahead and rewrite this as science square time sign and then use the Pythagorean identity. And then yeah, right that So we have actually, let's go to the next page here and then split this up into two winner girls double negative turns into a plus. And then here you could do another use of and after evaluating this, Okay, so here we have a plus co sign over three and then here a minus co sign cubed. And then here we'll have to divide by another three from the power rule. Sell 10 9. Wow! And that's our final answer.