evaluate-the-integral-intlefttan-2-xtan-4-xright-d-x-2

Question

Evaluate the integral.
$\int\left(	an ^{2} x+	an ^{4} xight) d x$

Vipender Yadav · Accepted Answer

we have to evaluate the integral ancient square X plus danger to the power four x dot leagues Now we can ride this intriguing as I&#x27;m taking opinion squared X common. So you get Union Square X one bless Kenyans critics Norton DX now one Palestinian square x is sickens Quicks, cylindrical become dangerous heritage X ancient square x times sick and squeaks Not DX no, I&#x27;m taking danger X s d. So now differentiating board decide. So you get, uh, second square x dot Be excessive cools to duty so the interval becomes integral P square beauty on weaken right. Listening s integration off the square The square is the cube do Edward tree. Let&#x27;s see, we see the constant of integration simply we have to put the value of 50 de Here was a change in X sort of become change in Cuba X divide by three plus c So finally we can conclude that the intruder tangent square X plus staging to the power four x bx is it cools to dangerous Que Bix divide by three Blessed see So this is the required and so

J Hardin · Answer

this problem is from Chapter seven section to problem number twenty four in the book Calculus Early. Transcendental. Lt&#x27;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&#x27;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&#x27;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&#x27;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&#x27;s our answer

Geena Pullo · Answer

Hi. Some of this question we&#x27;re going to be solving for the tan of X to the fourth times the seeking of X, t X and so from here, what we&#x27;re going to do is we&#x27;re just manipulate our equation a little bit and we&#x27;re going to have the tan of X squared times he tan of X squared times the Sikh end of acts d x on from here. We&#x27;re gonna use the trick. Equations were going to use the trick equation that states that the tan of X squared plus one is equal to the Seacon of X squared. Andi So the tan of X squared is equal to the seeking of X squared minus one. Now we&#x27;re going to just right this into our equation. Substituting in are seeking of X squared minus one for all the chance in the equation. So we&#x27;re going to now have the seek and of X squared minus one time, See, seek in of X squared minus one times the seek it of X d x. Uh, now from here, we&#x27;re gonna just distribute, so we&#x27;re gonna have the integral of the Sikh in of X to the fourth minus two times the Sikh int of X squared plus one times the seek and of acts X on from here. We&#x27;re just going to, um, distributed through our sequence would have seek IND of acts to the fifth minus two times the Sikh int of, um X cubed plus the seeking of x d. X on from here. We&#x27;re gonna split this into three different integral. So we&#x27;re going to have the integral of the stick in of activated three F&#x27;s minus the axe. Sorry, Linus, to times the integral of the Sikh and of exe cute d X plus the integral of the Sikh and of X de X. And now from here, we&#x27;re gonna be, ah, using a couple of equations. So, um, first thing we can do is we can solve for, um, are seeking of X to the fifth. Using the equation that states that the integral of the second toothy on of Axe D X is equal to the speak int of a new minus to x 10 x over and minus one plus and minus two over on minus one times the integral of the Sikh int of X of on my Penis to D X and so we&#x27;re going to have her our first integral. We&#x27;re gonna have be, um, seeking of and minus two. So five minus two, which is three. So the secret of X cute times the tan of acts over five minus one. So four plus five minus two, which is three over five minutes for one which is four times the integral of the Sikh int of X to the third or the seeking of X cubed d X Andi. Now we&#x27;re going to used the There&#x27;s an equation actually, for this Seacon of x cubed and we&#x27;re gonna be using that. Just offer next one So that one states that the secret of X cubed D X is equal to one half times the seeking of acts Tan X plus one half times the Ellen plus the tan of acts. Um, on then from here, we&#x27;re going to be using the another equation for the seeking of X dx. And that equation is just going to be plus the I&#x27;ll on of the Sikh int of X plus thicket tan of x. And of course, we have a plus C For all of these, the each would have an individual C but it would all just end up being one. See anyway, um, so I&#x27;m just gonna one see there so we&#x27;re going to multiply by each of these by two. Negative to actually said, this is going to cross out and so we could make this and negative and we the negative there. So that is going to cause these two to be able to cross out. And so we&#x27;re going to be left with e seek IND of X cubed and fax over four plus 3/4 of the integral of the Sikh in of X cubed D X minus the Sikh end of X tan of X plus. See, And so from here, or going to do is we&#x27;re gonna use the same equation that we used to solve for the secret of three x dx Teoh Saul for are integral. So now we&#x27;re going to have the second of X cubed times the tan of X over four plus 3/4 of one half the second of axe of acts, plus one half of the Ellen of the second of acts, plus each hand of X. And then this is going to be minus be seek and of X, take a fax plus C. And so from here we can just simplify. So we&#x27;re going to have the seeking of acts cubed times the tan of acts over fourth plus 3/8 times the seek and of X Tanna Axe closed 3/8 times the on of the seeking of X plus the tan of X minus the seek and of X tan of X plus c. And now we can make this instead be eight over eight. And so we&#x27;re going to have as our final answer the second of X cute times the tan of acts over four, my Penis five AIDS of the Sikh and of x times, the tan of X us 3/8 of the L on of the Sikh and of acts plus the tan of Axe plus see And that is going to be our final answer

Geena Pullo · Answer

I think this question. We have the tangent of X to the fourth DX so we can use Thean Quay Asian that states that the integral of the attack t d end of acts D X is equal to be 10 to the n minus one of acts over on minus one minus the integral of the and to the on minus to of acts de Adickes. And so we&#x27;re going to have the can of acts to the M minus monitor and is equal to four. So four minus one is gonna be free. So the tan of active cues over and minus one again, and is for though three minus the integral of the can of X to the N minus two. The and my is equal to four so and my s two is equal to two. So the tan of ax squared the X on. So from here, we&#x27;re going to be using another equation. Um, that states that the girl of the of X squared DX is equal it and bent of axe My x. What? See, On DSO our final I wanted to be the engine of FC huge oh, birth maybe minus the tangent of ataques But the axe cross see on that is our final answer

Enkhzaya Enkhtaivan · Answer

This is from fairy age from chapter 8.3. We have seconds to the fourth x times changing square x t x So here, when they were. So this kind of internal is a special family off intercourse it on Lee or seconds and change it functions and they&#x27;re usually one of two substitution. Sze usually work so the 1st 1 it&#x27;s so so either we do you in course second off. No Max, Are you seacoast? Ancient off axe One of the substitution Sze will usually work and let&#x27;s see which one would work. So if you&#x27;re not sure what to dio which one is the crest one right away So in this the 1st 1 we have this&#x27;s second of exchange int of x t x So if you look at this that we have So this implies that our interim function will become you Cube And then there&#x27;s one power of tension left and so that is going to be a problem because tangent off X again is equal to by definition Well, it&#x27;s squared the U squared minus one. No! So in this substitution, we will deal with descend around. So while this isn&#x27;t the worst into a weird thing. This this&#x27;s over something that Khun Dubai intuited my parts several times. But that&#x27;s what happens in the second substitution. In this case, we will have do you or bees will be just second squared X the X So in this case, our interim will become, um since so would see So I will have our 10. So we have second to afford extension squared off axe DX Here it&#x27;s here and this is going to be a call to Well, if you in course tension and change of squares simply you You squared that two powers off the second who simply become tea, do you and then what&#x27;s left? Here&#x27;s tension squared of X But this is good because we have tension square. So it is simply you squared times you squared minus one. Do you so hear this thiss is obviously the better idea. So it&#x27;s this proceeded with this one. I&#x27;m going to cross off this here so this will only become simply into a future for you my city of second to you that a suitor fish are fished this year, Harry. Third plus C there is equal to home so Now he&#x27;s back. Substitute, sir. It&#x27;s simply attention tw to her first over five, my ass tangent to certain over. Very close. See? Now, let me finish is probably saying this This is very similar to problem through six of this chapter where we have our powers of seconds intentions. So as you&#x27;ve seen and here we have even powers here both, uh, our foreign part two. And in this case, this substitution Rico&#x27;s tension ex works out the best while in problem 36. If you chicken out who we will see, there&#x27;s odd powers for both and in that case, the other substitution works the best.

Robert Daugherty · Answer

section eight dot to number 38. So we&#x27;re looking for the indefinite, Integral. Ah, the secret to the fourth of X changes squared of x d x. The key with many of these is to get our powers in terms of squares. So if I write, this is seeking squared of eggs seeking squared If x changes squared of x t x I know the seeking squared is one plus the tension squared So this is the integral of the secret squared of X one plus changes squared of X times attention&#x27;s great of X, d x and the puzzle with many into grows If I can look at a function and his derivative appearing, I can usually make a U substitution. Well, I do see that here, if you is equal to the tangent of X then I know that Do you iss seeking squared of x d x So this becomes the integral of one plus u squared times you squared to you which is the interval of you to the fourth plus u squared Do you which is you to the fifth over five plus you cubed over three plus a constant of integration and we know you is equal to the change it of X. Therefore, this answer is just 1/5 attention to the fifth of X plus 1/3 tension cubed of X plus a constant of integration.

Problem

Evaluate the integral. $\int \tan ^{4} x \sec ^{…

Problem 20 Easy Difficulty

Evaluate the integral.
$\int\left(\tan ^{2} x+\tan ^{4} x\right) d x$

Answer

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

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James Stewart

Essential Calculus Early Transcendentals

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Integration Review - Intro

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

Essential Calculus Early Transcendentals

Catherine R.

Kayleah T.

Kristen K.

Samuel H.

Integration Review - Intro

Definite vs Indefinite

James StewartEssential Calculus Early Transcendentals

Catherine R.

Kayleah T.

Kristen K.

Samuel H.

James Stewart

Essential Calculus Early Transcendentals