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JH
Numerade Educator

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Problem 78 Medium Difficulty

Evaluate the integral.

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

Answer

$\int \frac{1+\sin x}{1-\sin x} d x=2 \tan x+2 \sec x-x+C$

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Video Transcript

Let's just start off by rewriting. That's right. This is two plus and then sine minus one. And then let's rewrite this. So we have one, say two and then one minus sign and then we have, unless free right, This's negative. One minus sign. No hearing. Good. Cancel. So for this one, let's multiply. It's happened, but and then for the second one, this is just in general. Negative one. So for the first but one plus sign and then here that equals one minus signs clear, which is co sign square. So let's put that in. And then here, that should have been a plus from this both pluses. And then this integral x minus x ten plus e. Now we could rewrite this. So all I did here it just break this into two fractions and then rewrite these as these two terms respectively. And then we could integrate this two ten to see can't and then our minus X and plus E. And that's our answer