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JH
Numerade Educator

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Problem 39 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{\sec \theta \tan \theta}{\sec^2 \theta - \sec \theta}\ d \theta $

Answer

$\ln |1-\cos \theta|+C \quad$ or $\quad \ln |\sec \theta-1|-\ln |\sec \theta|+C$

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Video Transcript

Let's try use up here. Let's take you'd be C cam. Send to you seeking times. Damn. So we can rewrite this. We see appear This is equal to this. So we just have do you of top and then we have use Claire minus you. Oh, it's the factor that then here you have to do partial fractions. So here will end up with one over. You minus one minus one over you. That's natural log. Absolute value. You minus one minus Ellen. Absolute value. You don't forget the constancy and then here and finally go back and tio original use, um, and replace you, and that's your final answer.