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JH

# Evaluate the integral.$\displaystyle \int \frac{\sin^3 x}{\cos x}\ dx$

## $\int \frac{\sin ^{3} x}{\cos x} d x=-\ln |\cos x|+\frac{1}{2} \cos ^{2} x+c$

#### Topics

Integration Techniques

### Discussion

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

Let's evaluate the given integral. So here, let's start off by pulling off a factor of Science Square, and then we can go ahead and rewrite This term here, that's queer is one minus close and squares. So let's do that. There it is. That's our sign square. And then we have sine X cosign still in the bottom. And then here we can go ahead and do a use up U equals co sign. Then negative, you equal sign So we can write this as pause that minus from over here, one minus use where over you and then let's go ahead and rewrite this and then just use the powerful here. So for the first term, we get negative national log groups you and then here Watch out for that double whiteness. No. And then finally come back to your use up here and replace you with X two up there and then plus see. And that's a final answer

JH

#### Topics

Integration Techniques

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp