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Problem 34 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{\sin \phi}{\cos^3 \phi} d \phi $


$\frac{1}{2 \cos ^{2} \phi}+C$


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Video Transcript

this problem is from Chapter seven section to problem number thirty four in the book Calculus Early. Transcendental. Lt's a Tradition by James Door. We have an indefinite integral sign of fee. Time's coast. Thank you, Sophie. Here, it looks like we can apply u substitution. Let's take you to be the denominator or actually just call signs, because when we do to you, we have negative sign fee. We have this negative sign out here that's not in the room right here. So let's go out and multiply this latest equation by a negative one. Yeah, After a substitution, we have a negative coming from this negative over here in a girl. The numerator is, Do you? We already pulled out the negative. And now the denominator is just you, Cube. Let's set herself up to use the power rule so we can rewrite. This is you to the minus three. Do you so buying the power? We have you to the minus two overnegative too. Plus he so they cancel those negative signs. So we get a positive one half who have you square Plus he. And at this point, we've evaluated the new girl. But we should put our final answer back in terms of the original variable fee. So what use are you substitution? To do that? We have one over two. Use clear that becomes co signed Square Plus E and that's your answer.