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JH
Numerade Educator

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Problem 31 Easy Difficulty

Evaluate the integral.

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

Answer

$$\sqrt{(1+x) /(1-x)}$$

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Video Transcript

Let's start off by just multiplying the intolerant by something else from multiply top and bottom by one plus X inside the radical. So go ahead and multiply out those name raiders on top one plus x, the radicals cancel in the denominator and we can go ahead and split this into two. You may remember this first inner rule And for the second for the first General, if you haven't memorized, you can take X to be signed here. That's it. Drinks up. And then when you integrate this, you get it. Send in for sex, Slim. Now, over here, we can do a use up. So then, there you have it to you. Oh, from the negative two equals X t x. So this in a girl becomes negative would have used to the negative one have to you. So go ahead and use the power ruler and and simplify and we get negative. You too, the one half. So let's just go ahead and negative. You too, the one half and then replace you back in terms of X from this equation here. So that's minus new to the one half. So that's one minus X square to the one half power. And then at our constancy, finally, and that's our final answer