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JH
Numerade Educator

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Problem 24 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int (\tan^2 x + \tan^4 x) dx $

Answer

$\frac{\tan ^{3} x}{3}+C$

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Video Transcript

this problem is from Chapter seven section to problem number twenty four in the book Calculus Early. Transcendental. Lt's a tradition. My James store. Here we have an indefinite animal of Tangent Square plus tensions of the four power. So one way to proceed here suggest factor out its hand square. If we do that, we pull out its hand squared and we're left over with one plus ten square of X. And now we can apply our path. Agron Identities too. Rewrite one plus tan squared is sequence where at this point, we can apply u sub Let's take you two be tangent of X so that do you is sick and scared of x e x So here the sea cans Word of the X That's our do you in this tan square of X, this is Wilby. You squared so that our interval becomes you. Swear to you. Okay, we can use the power all to evaluate this General factions becomes you cued over three plus e and then we could These are useless institution toe back, substitute from you back in terms of X. So us you cue becomes Tan Cube X. We have to divide that by three and then we are see and there's our answer