integrate-each-of-the-given-functions-int-2-tan-1-x-d-x-2

Question

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

Vikash Ranjan · Accepted Answer

the problem we have twice integration dying words X. So first of all this equals two. Two times 10 Universe X. Indignation one into the X minus integration. The upon the exhaust the universe X indication one dx the X hole. Make it closed. Therefore this equals two. Twice in two universe X into x minus in the mission. one upon 1 plus x Squire and two X. The X. So this is equal to Twice in two X. The universe X -1 upon to integration DP upon P As we have assumed one plus excess choir sp So twice of X dx become DP or we have X. D X equal D. P. A point to. So this is given us twice of X. The universe X minus. This is twice into one upon to Ellen mud one plus x square plus C. So further this is twice affects the universe X minus two Ellen so tomorrow one plus X square plus C. So this is the 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.

Amy Jiang · Answer

Okay, so we have the integral attendants Were ex tickets where X the experts let you equal to and it&#x27;s of excuse. You know, that&#x27;s for you is able to sequence where x X and this is what one. So we have integral of you squared you. This is equal to you. Three over three, which is equal to 10 Jin&#x27;s extra part three over three plus c.

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.

Amit Srivastava · Answer

I could annex sickest X dx select tennis sickle Tohti. So shake your square x bx picking No de dick 33 Beto by Roberto Blessing Sir Timothy Answer will be to buy three Annex three battle this.

Amit Srivastava · Answer

let Eichel toe DX by one minus stand square. So, yeah, I could do a 15 10 as a sign This correx by Costco X. So finally it is caused square x bx and it is called square X minus Sinus square exterior. So can we write this as one plus cost two x by two And this part as cost two x formula as we know cost corrects minor stance. Correct this cost to it. So final part will be won by two cost West will be sick to x and here one by two Dick So one by two integration off sick two x will be logged sick to X plus 10 2 x by toe And here it is X by toe Plessy.

Problem

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

Problem 9 Easy Difficulty

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

Answer

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

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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

Basic Technical Mathematics with Calculus

Heather Z.

Kayleah T.

Kristen K.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Heather Z.

Kayleah T.

Kristen K.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus