integrate-each-of-the-given-expressions-intleft12-x2right2-d-x-2

Question

Integrate each of the given expressions.
$$\int\left(1+2 x^{2}\right)^{2} d x$$

Dwijendra Rao · Accepted Answer

Hello Friends we have to integration of this. We have to do integration of this given expression that is integration of one plus two x squared to the power of to DX. Okay so first we can simplify it. So this will it cost to one plus four extra. About four Plus four XS. Where dx So integration of Wendy X. That is a costume In 2004. Actually leave our four. Do you express for indication of X squared dx. So this will be a cost to X. Integration of this will be extremely well. Photo integration of this will be actually have high plus five And extra the power to integration of extra the power to will be executed upon three plus constancy. Okay so if you can add it X. There&#x27;s four upon 5 Back to the par five plus four by three Extra the power three plus constant to see. So this is the and that I hope you understood. Thank you.

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.

Amy Jiang · Answer

So it started everything that we have this X plus one turn here and in our denominator you have X squared plus two x minus one. So we know that if we take the derivative purpose, we get some X terms and some constant term. So let&#x27;s start by reading you be equal to what&#x27;s inside or what&#x27;s in our denominator in this power here. So that&#x27;s X squared. Plus two acts minus one. Okay, so we have Do you that&#x27;s equal to two X plus to and then the ex senators that we have a two in common so we can factor that out. And then we have what we want for inter numerator here. Except that we need to divide by two on both sides to get rid of it to that. Okay, Now let&#x27;s rewrite this in terms of you. So we have X plus one, the X that&#x27;s equal. Teoh, do you over to and then we have one over X squared plus two x minus one. That&#x27;s now you could a part two. Okay, so let&#x27;s pull out that 1/2 and all. It&#x27;s also rewrite this as a negative export it, that is, We get you to far native to you are not taking our inner Rome. He gets you to part of bigger two plus one, but expected of one over negative one plus. So that gives me negative 1/2 and then within rewrites are you in our denominated? That&#x27;s two times you and you is X squared, of course, to minus one part of one and then plus C, that&#x27;s where we get our fallen pollution.

Linh Vu · Answer

in the question. When did you find an indefinite integral on the X squared plus one over X square, The Yanks record under power room with an expert and the ex getting coaching the X and this one off and risk one classic constancy before we can have bled a formula. We need to rewrite a second term here. Expert. Your plus injured A power form will be expert minuscule g x then I am not a formal organic origin. The expert tree over three now, um honest Juba&#x27;s only be bel minus one of a minus one plus c. We can understand you&#x27;re the expert three with three minus one number. Thanks. Let&#x27;s see.

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

Fuzail Shakir · Answer

we have the integral over off X over X squared plus one. The whole thing is squared. The X we&#x27;re gonna let you is equal to X squared plus one so that d&#x27;you is equal to two. X t x or d&#x27;you divided by two is equal to x t X pulling the 1/2 out and then substituting the stuff in. We end up with you to the power of native to do you which is equal to a negative 1/2 you to the power of negative one plus c back substituting. We end up with negative 1/2 times x squared plus one to the power of negative one plus seat.

Problem

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

Problem 23 Easy Difficulty

Integrate each of the given expressions.
$$\int\left(1+2 x^{2}\right)^{2} d x$$

Answer

$x+8 x^{3}+\frac{144}{5} x^{5}+C$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$x+8 x^{3}+\frac{144}{5} x^{5}+C$

Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kayleah T.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Catherine R.

Anna Marie V.

Kayleah T.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus