integrate-each-of-the-given-expressions-int-xx-22-d-x-3

Question

Integrate each of the given expressions.
$$\int x(x-2)^{2} d x$$

Dwijendra Rao · Accepted Answer

Hello France. We have to integrate each of the given expression the expression is given in the question is integration of X into X. Managed to holy squared dx first. We will simplify it. So this will be cause two X squared plus four minus four x into DX. So this will be cost too XQ Bliss four X minus four x squared off knicks. Yeah so this will be caused to Yeah to the power three will be Integration of actually power three DX plus four into extra power X actually parwan dx minus of four X squared dx. Okay Actually power 30 years. The integration of this will be extra about four. Mhm I do one of 14 Plus four and 2 access card to minus four Into excused by three plus constancy. So answer will be Actually about four into one way forward plus two of x squared minus of forward three X cube. Let&#x27;s constant C. So these are the answer. I hope you understood.

Amy Jiang · Answer

Okay, So looking at are integral. We see that we have a heck of a cold challenges on, and they have a role. Coast begins what we know. That the derivative of hyperbolic attentions what are people to, um, negative co seeking squared of X. And not that we have coast. You could square to backs here, So we&#x27;ll take you to be able to Khyber girl Coach engines of X. And I will do you that you go to negative happy little co ck in squared of ex DEA. Now it&#x27;s multiply both sides by negative one so that we have this portion right here. So this is the O negative. Do you? So the integral of you squared Negative, do you? And that&#x27;s equal to negative. You cube over three plus c to negative. You you is hyperbolic. Oh, attendance que kovacs over three and plus c. Okay, so this is execution

Amy Jiang · Answer

Okay, So it&#x27;s notice here for in ago that we have hyperbolic hotel agents. Aunt Hyperbolic. Does he get so notice? Or recall that the derivative of hyperbolic contingents that&#x27;s equal to negative coast chickens. Spirit of X. So I don&#x27;t leave the right Or why don&#x27;t we use you? Stop. We cannot you be equal to the following and then do you is equal to negative? Have got a hybrid ball coast against. We can bring that to the other side to negative. Yes, you can squared X for this portion right here. This is equal to do you and then we have intentions squared of you are acceptable to use word so he gets the integral of you squared. Do you taking the interval? We get YouTube over three. But see, when we can get you in terms of X, that is hyperbolic. Coach engines cubed, abets over three busting

Amy Jiang · Answer

Okay, so it started noticing that the derivative of this term is equal to this. So why don&#x27;t we let you equal to that term? Do we get to you that you go to two x plus one d x? So we have the you that&#x27;s equal to this portion and in here and that&#x27;s you. So we get the integral of you over you to party. I&#x27;ll rewrite that in terms of our negative exponents of executed happening. Three. You and I want to take her integral. What&#x27;s using? Probably good three plus one. So that&#x27;s negative, too. Over negative to see replacing are you gets X squared plus to the power of negative overnight two men plus seats.

Sid Wan · Answer

Okay. Finds an integral off That&#x27;s over full. Tend Actual full square the ah, that&#x27;s C If we take at our four square you to be that he was Explorer over sixteen D&#x27;You equals axe over Ate the X so we can run this a cz This guy is to see you, Tad. You too. Do you on your hands? You Because ah, well two in front collective national off cause I you we&#x27;LL see if you plugging you to be x square over sixteens that give to natural log because I asked Square over sixteen c, yeah.

Amy Jiang · Answer

Okay, so we want to use use up here. So why don&#x27;t we let are you equal are, um, larger polynomial, that is, Let&#x27;s let it equal X squared plus two x. But it&#x27;s what you know, if we take the derivative of that, you get to acts plus two and Indy X, So notice that we have two x puts to here and a DX so that&#x27;s equal to do you. So now let&#x27;s replace what we have. So we have do you over u to the power of four. Okay. So look to your right that as a negative exported so that you to the part of negative four. Do you? And I want to take her in a girl So he gets, um You took out negative three over negative three. Let&#x27;s see. And now, um, what&#x27;s your place? Are you with our X? So we have X squared plus two minus four to the part of negative three over the next three. Your name, plus C

Problem

Integrate each of the given expressions. $$\int\l…

Problem 16 Easy Difficulty

Integrate each of the given expressions.
$$\int x(x-2)^{2} d x$$

Answer

$\frac{x^{4}}{4}-\frac{4}{3} x^{3}+2 x^{2}+C$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Heather Z.

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Samuel H.

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$\frac{x^{4}}{4}-\frac{4}{3} x^{3}+2 x^{2}+C$

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