integrate-each-of-the-given-functions-int-sqrttan-2-2-x1-d-x-3

Question

Integrate each of the given functions.
$$\int \sqrt{	an ^{2} 2 x+1} d x$$

Tyler Moulton · Accepted Answer

Uh huh. We want to integrate the following expression. The integral or rather the indefinite integral of the square root of can square. To expose one DX as I&#x27;d be written on the right by tricking metric identity. Town square to expose one is equal to see Camp square two X. So are integral is the square root of C. Can&#x27;t square two X. Dx or C can&#x27;t two X dx. We&#x27;re going to have to rely on methods of integration to solve particularly we&#x27;re going to use the method known as trigger metric integral. So you should geometric intercultural properly we have to identify which of the 10 integral Justin here has the same form as are integral. Then we can plug into the given solution to solve so for integral where she can&#x27;t square two X. Dx. We are looking for the form of C. Can you do you? So this corresponds to do equation nine. Listen here. Thus for U equals two X two U equals two dx. Our initial integral is missing a factor of two, which we carry over the solution as follows. So integral has solution one half Ln absolute values. You can&#x27;t do expose 10 2 X plus C the concept of integration.

Foster Wisusik · Answer

Okay. This question wants us to evaluate this integral. So we see that we have our arc tangent function stuck inside of this square root. So let&#x27;s pick that to be are you? Because if you take the derivative, we get that, do you is equal to 1/1 plus x squared the ex, and that shows up in our integral. So he can now substitute everything and just get the integral of square root of you. Do you? Which works out to the integral of you to the 1/2. Do you or 2/3 you to the three halves? Let&#x27;s see. Four plugging back in. We said that you was equal to our contention of X, and this is our final answer.

Robert Daugherty · Answer

seventh to 20 twos or we&#x27;re dealing with integration by parts, which tells us if I can look at an inter grand and organize. It has two functions. I function that is you and a function that is Devi. Then I can recognize the integration by parts formula and hopefully this second interval you see here it&#x27;s easier to work with in the original that I started with. So quite often when you see a inverse trick function that is going to be your substitution for you. So you is going to be the inverse tangent of X squared. Then the derivative is going to be one over one plus X squared square, and then the derivative of X squared is two x t x. So this tells me that d you is going to be, um two X over one plus X to the fourth the X Then if I look at this in a grant of taken queer of this term, what&#x27;s left is Devi is equal to x dx, which tells me that V is equal to X squared over two. So this original integral that I have is going to be UV, so that&#x27;s going to be X squared over two. The inverse tangent of X squared minus the integral of V D u. So multiplying those together. So you&#x27;re going tohave minus the integral of and you&#x27;ll have X cubed over one plus X to the fourth DX. Now, when you integrate this, you should get in the habit like that. Integration is just a puzzle. When I see X to the fourth and I see X Cube, I know that if I differentiate X to the fourth, I get X Cube. So let&#x27;s make a substitution Here Z is equal to one plus extra the fourth, then DZ is equal to four x cubed DX. So in order to get a four x cubed de acts, this is the modification that I make. And so this turns into X squared over two inverse tangent of X squared minus 1/4. And this is just the integral of one over Z, do you see? And you know that now to be the natural logarithms. So this is X squared over two inverse tangent, back squared minus 1/4 natural log. Absolute values E plus a constant of integration. Now what is easy is one plus X to the fourth. That is always positive. So I have no need for these absolute value signs. So my final answer is going to be X squared over two. The Arc Tangent of X Squared minus 1/4 and natural log of one plus next to the fourth plus constant of integration, and that is the final answer.

Pagadala Kishore Reddy · Answer

Okay, So we are going to be irradiating, though, and dig the laugh An off ex way too into second square off X ray, too. DX We know that they didn&#x27;t beat you off Dan Exes. C can square x So we really hating this integral by using u substitution with the So the next thing is let U equals Dan off ex way toe dirt in plays D&#x27;You equals seek and square off expert too into one way to DX that in place. So do you equals she can square off expert to in tow DX so no integral off 10 off X by two in tow Seek and squared off expert too d X equals when other two u equals 10 x wayto so integral off you in tow and second square X Plato The X equals to do you toe Do you? That equals two is constant indeed. I love you. Do you That equals two into. If you integrate these integral off you do u equals you square by two place See plus c they&#x27;re equals two sugars. Cancel their equals You squared plus c and we know that you is tonics wayto so you square equals town square. Expecto Bless. See? So die integral off down off expert too. In two seconds squared X ray too. The X equals dance. Great off ex way to plus C Thank you.

Linh Vu · Answer

Kanda and have the integral off the d new off. Square it on the one minus your square which you get incredulous Sigh in verse with you Prissy Now in the question were given the integral armed uh, second square. Thanks D thanks off the square root on the one minus dungeon square. Thanks. So and we would the new eco to the tension x And then do you echo to the second square X t x and isn&#x27;t exactly ecology that you hear and being one minus your square? Therefore, we should get this integral in terms of the u sending you armour square it on a one minus new square on by formula will get it Cochise Sigh Inverse you, Chris See when you equated attention x So again in cultures in verse under tension Thanks plus C

Amy Jiang · Answer

Okay, so we will do about, like the falling Integral. So let&#x27;s start by noticing that we have a tangent of X and a secret squared of X. Well, we know that the derivative of tensions, this secrets word. So we&#x27;ll be using u sub. We&#x27;ll let you be with the change in of X and into you. That&#x27;s that gives a sequence squared of X. Yet who have this portion is? Do you? So we get the integral of the square roots of you and then do you? And that gives me you the power of 1/2 plus one. So that&#x27;s 3/2, and then this is to over drink you and then we have close, see, and now replacing you in terms of X, that&#x27;s 10 years of X. You have to over three Candance of X to the power of 3/2 and then plus C for a solution

Problem

Integrate each of the given functions. $$\int 5(\…

Problem 19 Easy Difficulty

Integrate each of the given functions.
$$\int \sqrt{\tan ^{2} 2 x+1} d x$$

Answer

$\frac{1}{2} \ln |\sec 2 x+\tan 2 x|+C$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$\frac{1}{2} \ln |\sec 2 x+\tan 2 x|+C$

Basic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Kayleah T.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Catherine R.

Heather Z.

Kayleah T.

Samuel H.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus