integrate-each-of-the-given-functions-int-frac5-d-xsqrtx22-x2-3

Question

Integrate each of the given functions.
$$\int \frac{5 d x}{\sqrt{x^{2}+2 x+2}}$$

Vikash Ranjan · Accepted Answer

in the problem we have been given integration five day X upon whatever off X squared plus two x plus two. Now Hill, this is written as five integration takes upon Uvarov X squared plus two X plus two. This is equal to five digression dx upon Uvarov X plus one whole square plus one. Now further we have too late assume X plus one that equals you or dx become do you? Therefore it is five condition do you upon whatever off U. S squared plus one that equals to five Ellen The road you esquire plus one Plus you. This is equal to five Ellen We got off X-plus one whole square plus one plus X plus one. Now this is equal to five Ellen and the root this is X Squire Plus two weeks plus two Plus X-plus one plus C. So we have this as our final answer to the problem.

Shamshad Waris · Answer

and the girl, it just looked under high. Plus, it&#x27;s aspiring beers. Well, it&#x27;s all about this integral using that automatic substitution. So they are Substitute X is gonna do Rubei, Dan Eggs. We&#x27;re sub student X is going to root Hi can next Because it was a to tear. Then we&#x27;ll have, like, one formula so we can remove this quadrant from here nor depend ship both side. So the acceptable toe Good bye. I don&#x27;t have that debate about Can&#x27;t get that. It is well, who seconds bracket that into digital No blood in the belly job X Andy it in this and dig it in then it yet they are excess square. So the bill you up exes. Good bye, Dan. Get that I get the whole this way Divided by Luke Under I Will us Bill o XY route by Dan Keep talking about all this Wet into the video of the exit. Good bye. Second square didn&#x27;t die in new digital. Now simply by this Expressen Then they will get I Janice Ouachita being guarded by a really like one formula. I do know second spark it physical one plus and it&#x27;s perfect that so up like this form of that. Then you will get here. Good bye. Said that in tow. Route by seconds. Where do digital now? The cancel The route five sec picked up on the numerator and denominator. Then they&#x27;ll get I&#x27;ve in tennis. Where? Get dyinto Septic in digital. Now apply the formula. Tennis squatted down the place off an escort it that we can die. Jake, it&#x27;s wet down minus one in tow. Sector garbage it my mother lying here. Then you get I&#x27;ve been to sec you Duta minus sector into Magica. As you know the formula for the security data and set it. That will apply here. Cooper, Mothers for the sec. You take that into digital will get happy too. Sick kid got in Boone Dan picked up plus Happy to fill in sick, Tiptop less. Dan Kita. Let&#x27;s see now I&#x27;m going to get some of the sector. Did you call him then? Then sec Dicta Unless and keep them. So applied this formula here, then a get hi in blue uh, sec dicta in blue Dan Kita. Let&#x27;s not Ellen checked it down last Dante dot minus Ilin Septic that unless then take dot unless see you now simply by this Expressen. Then they get I beg to sector in do and Canada minus I do earlier sec tika less then kicked up. Let&#x27;s see not blood in the village off to travel in here. Thank you. Magical explain, dude. So we hear that from here. Second technical do First we have to sample the hyper tennis off This that tingle tingle Then they&#x27;ll get It&#x27;s just where less pain divided way route So now we can plug their they don&#x27;t get I threw into route And that excess square that&#x27;s time divided by pi on the bill of authentic texts by route I minus bye bye to into Ellen Gallup Sec Tika, you can exist quite plus I divided by route by belies explain. Look, I, Lissy, not simply by this experience on Then they get one way to win Xing due under its a square less by minus. I bet you into Ellen. You can tell it&#x27;s a squared plus pi plus eggs divided way. Goodbye, lassie. So this is the sort of some of the given in figure Integra. Thank you

J Hardin · Answer

here we have the integral of DX over the switcheroo of X squared plus two x plus five. So let&#x27;s go ahead and take this quadratic and complete the square. So half of two is one. And if I square that I also get one. So let&#x27;s put a plus one. And then, since we added one we&#x27;LL make up for by subtracting one no. So let&#x27;s factor this term in apprentices. That&#x27;s X plus one square plus four. So if we want, we could write This is too square now, ideally for a truths of we would prefer something of the form ex cleared plus a square. But we don&#x27;t quite have that because we have this plus one. So if that plus one is bothering you, let&#x27;s do it use up, take you to be X plus one. Then do you is just the X so we could rewrite our general as do you over and actually say one more thing here. After this use institution, we can rewrite the quadratic is useful here plus two squared so we could replace this quadratic and X with you squared plus two squared. So that&#x27;s a no go inside the radical. And now we have a new integral that&#x27;s tailor made for tricks up here. We could take, you know, be tooth and data then do you is to seek and squared later. So let&#x27;s take this expression and the radical So replacing you with two ten data. We have four chance for data plus four. That&#x27;s a fact There on the floor. Then we have tan squared plus one so radical forest too. And we have the square room of sequence where data about the protagonist identity and taking the square root we have to seek and data so we could rewrite are integral. So do you now becomes to seek and data to seek and square debater and the radical which we just simplified down here in the bottom, right, that&#x27;s too thick and NATO canceling the twos. One of the sea cans we&#x27;re left over with integral of C can&#x27;t and we know this in a rule to be the natural log Absolute value seek and data plus tan data plus E Now I&#x27;m running on room here. Let me go to the next stage. This was our tricks up. Maybe rewrite this and the integral that we just left off with was natural log seeking data plus Dan Data. Plus he now going to our tricks up. We can rewrite this as tan data equals you over, too. So let&#x27;s draw a triangle. We know that tension is opposite over adjacent, since that equals you over to Let&#x27;s just go ahead and take Decide to be you and decide to be too. What&#x27;s the note? The high pardons by age. Bye, Petya Green Serum a squared is you squared plus two squared. So take the square root and we get H. Now we can evaluate, seek and as well so she can is high powered news over the adjacent, So each other, too. And then tangent is just you over, too, so we can rewrite this so there&#x27;s two steps we can apply here. We couldn&#x27;t first replace you with X plus one that was our U sub in the very beginning, So we have X plus one squared plus four and let&#x27;s combine these fractions because they have to have the same denominator plus you, which is X plus one all over, too. And then we could go ahead and use one of the properties for logarithms. That says Ellen, Eh, Overby is Ellen a minus? Ellen, be so here. B is two. So using a lot of property, we can write this. And then if we like, we can go ahead and replace the C minus Ellen to with another constant D. And there&#x27;s our final answer.

Bobby Barnes · Answer

if we want to use substitution to find indefinite integral here, remember, the first thing we want to do is look or what looks like notes complicated part in this integral. And then go ahead and see in that most complicated part, we can find something that if we let that be you, it&#x27;Ll help cancel something&#x27;s help in our integral and then go about solving from their wanted some. So when I look at ten at ten to the five square would&#x27;ve exposed to all of the square root of X. Well, I would think this ten to the five square root of experts to is the most complicated. And you might notice that if we let you be the power here, the derivative of this looks pretty much like one over the square root of X. So, Khun possibly eliminate the square root of X here. So let&#x27;s go ahead and do that. So But you equal five crew, the backs plus two. So first, remember that square root of X is actually next to the one half. So if I take the derivative of this with respect to X so you do you buy the Pax Sport in the world five times want, huh? Thanks to the negative one half power. And then we could just go ahead and write this five over two x to the where we can be Right Negative Half power is more over the square root of X. This is D E U X. Now notify Notice that if we divide by five halves and multiplied by DX end up with two over five. Dave, you There&#x27;s equal to one o the square root of X The X hand. This here is what we have there so we can go ahead in some fibers to get so ten to the U And then this is going to become too over five to you. And now I&#x27;LL go ahead and move to Fitz out front to five into growth ten u u And then we&#x27;ll need to recall that integrating B to the X d x will be is some number bigger than zero. This here will be so this is pretty somewhere to Eve&#x27;s. So it will be b to the X and then we divide by the base. So natural log of three See, So this here will be two over five Time&#x27;s So be so ten to you So ten to you But then we divide this by the base When it&#x27;s taken the natural and then I add our integration Hold still Now we&#x27;LL go ahead on substitute Are you and tio here? Since we really can&#x27;t simplify that much so get to over five And there the ox and the natural log of ten times ten to the So are you is five square roots of X plus two and then we add our condition and this here is the fine.

Amy Jiang · Answer

Okay, So what Cyprus setting you two are more complicated term, that is, whatever&#x27;s to appellate in that five skirt of X. That&#x27;s way we write our square root as a power. So that&#x27;s extra pair of 1/2 plus two. Now, I just wrote a derivative with that people to five no over two X to the power of negative 1/2. So that&#x27;s the square root of X X. So we see that we can multiply both sides right to over fire, and we get the following So we have one over square root of X, the X so that&#x27;s gonna be equal to R. D. You will get the integral of 10 you over four times to over five you. It&#x27;s not too quick to 2/5. I&#x27;m 10. You and Ellen up 10 plus c and then simplifying every writing, aren&#x27;t you? We get 10 to the power of why extra care of 1/2 puts two and M plus C

Sid Wan · Answer

not sixteen We have little girl acts plus two to the force Sai exposed to tow the first tr cks if we take you to be explosive too too good. See you Because five acts plus two to the force D Wade got his part. Integra equals into a girl. This part is thie over five. Look, if I sign you played, you were five. You come for the water or five. Front is constant. Signed you to you sayyou do you into grow is just nectar Because I, Detective Kasai View plus c can&#x27;t be your substitute back. Thank you x way that you want Serves coz I that&#x27;s plus to tow the fifth plus e you know that.

Problem

Integrate each of the given functions. $$\int \fr…

Problem 19 Easy Difficulty

Integrate each of the given functions.
$$\int \frac{5 d x}{\sqrt{x^{2}+2 x+2}}$$

Answer

$5 \ln \left|\sqrt{x^{2}+2 x+2}+x+1\right|+C$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$5 \ln \left|\sqrt{x^{2}+2 x+2}+x+1\right|+C$

Basic Technical Mathematics with Calculus

Heather Z.

Kristen K.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Heather Z.

Kristen K.

Michael J.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus