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JH
Numerade Educator

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Problem 65 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{\sin 2x}{1 + \cos^4 x}\ dx $

Answer

$-\tan ^{-1}\left(\cos ^{2} x\right)+C$

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Video Transcript

let's start up by re reading this in a roll. So using the double angle formula for sign and then on the denominator, we could write This is one plus co signed square and then square that And then let's try use a beer, coastlines where and then here was too negative. Do you to sign ex co sign X after used the chamber So we get negative in a girl. So we have our do you and then one plus u squared. So if you want, you could put a one up there. Now you may have memorized this formula and if so, you can just write tan inverse of you. If you forgot this fact, just do it tricks up on the cinder girl you would let you equals tan data and you have to solve that in the role. So here we have our HQ tan of you with a minus out front, plus our constancy and let's go ahead and replace you with you so that we started with. So we have negative Arc tan co science for of X plus our constancy. And that's our final answer