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JH
Numerade Educator

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Problem 1 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{\cos x}{1 - \sin x}\ dx $

Answer

$-\ln (1-\sin x)+C$

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Video Transcript

let's evaluate to given integral here we could go ahead and try. U Substitution will take you to be sign of X. Then we have Do you is co signed the X So plugging it into this in a girl, we have a top. That's just do you on the bottom. We have one minus you. Now, here. If this one minus he was bothering you. You could go ahead and do it. Use up. Then you could write. This inner girl is negative. One over. You won over W D w So that's negative. Natural log. Absolute value W plus e. Now we use our substitution to replace w with you. So that's one minus you on the absolute value. And then finally, we use our U substitution or original substitution to replace you with X, and that's your final answer.