integrate-each-of-the-given-functions-int-fracln-xx3-d-x-2

Question

Integrate each of the given functions.
$$\int \frac{\ln x}{x^{3}} d x$$

Vikash Ranjan · Accepted Answer

And the problem we have to find the integral which is integration and annex upon xQ dx. So this is equal to integration Erin X into Extra Power -3 DX. So further this is equal to LNX into extra power -2 upon -2 minus indication went up on X. Into extra power minus two upon minus two dicks. So this is equal to -1 upon to Ln X into one upon x Squire. Plus half. Integration. Extra power minus three D. X. This equals -1 upon to mm X squared L N X Plus one upon to Extra Power -2 upon minus two. Let&#x27;s see this is equal to- went upon two x Squire, L N X. Mhm -1 upon four X squared plus C. So finally we have this as our answer.

Aishwarya Krishnakumar · Answer

Robin, 29 were asked to use substitution to find this indefinite integral. So we&#x27;re gonna let our you equal the thing that&#x27;s inside the parentheses. So one plus three Ellen of eggs and the next step is to take the derivative off both sides. So do you. Because so since one is the constant, we don&#x27;t have to take the derivative of that. But we do have to take the druid of of Three Ellen of X, which would be three over x t x. And you can move this three to the other side by dividing. Would be d u over three equals won over eggs DX. And as you can see, we have a one over. So we have won over JIA one over x d x. And as you can see, this is a one over X. It&#x27;s an imaginary one. Appear. You have a DX so we can go ahead and rewrite this you see in a girl of you squared do you over three and we can move this three to the outside because it&#x27;s the constants of one over three interval of you squared. Do you and the Sequels you to the three we&#x27;re And this 1/3 is from here, while this 1/3 is from the integration. Lucy, and you can&#x27;t have a you in the final answer. So we plug in this. You? I didn&#x27;t get one plus three Ellen eggs to the third power Plus e. This is the final answer.

Amy Jiang · Answer

this was separating you equal C one plus three x Because I know that derivative of L O Island relaxes you put one over X So do you. That&#x27;s people to three over X g x And now I&#x27;ll divide by three on both sides. So I get the following. Okay, A knowledge to replace what what we have. So we have you squared and then do you over three. Well, that&#x27;s equal to 1/3 in a row View square, do you? And I&#x27;ll solve them for interval gets you cubed over three c So that&#x27;s you go to 1/9 or you is one plus 30 in effect to the power of three plus e.

Matt Just · Answer

Okay, So twenty six, we have Ah, definite integral. One, two, three. I have written long necks all over x dx. All right in the red flag here is that we have this natural longer necks into the square root and the derivative of natural Log X is one over X And then I&#x27;ll get a factor tx especially you Bee National X Teo Year is just one over x thanks. And like, that was exactly what we have here one over x d. X. So it&#x27;s just a direct substitution. So when x is one natural log one zero when Axis three years naturalized three and then we just have I&#x27;m just going to write It is, you know, the one half dating you, that&#x27;s nice. And then an anti derivative you to the three has over three House evaluated from zero to block three. When I evaluate it, zero, it&#x27;s going to be zero cents. Get two thirds and national lockers three to the tree house, which we can plug in, get an approximate value and it&#x27;s approximately equal to zero point seven six seven. So

Xiaomeng Zhang · Answer

so we know the derogative off low on axe dress. Eco&#x27;s Who won over acts, overuse of substitution here that a close to the anti grow off the square rules off along acts but the robber to off lawn acts. So we need to change our our ring here. So we&#x27;re how pero long. Three briar root off key key key. It&#x27;s grassroots off P that as teach the power off one over to so teach the power off three over. True, and we need to come to over three here. Go to to over three times long. Three to the power off. 3/2. Reach approximately e kale soup on 7676

Robert Daugherty · Answer

7.1 problem 13. We&#x27;re dealing with integration by parts which says, if I can look at it in a grand and recognize it as two functions you and Devi that would integrate into u V minus the integral of the D u. I said quite often were let you be the polynomial. The exception is with logarithms. When you see logarithms quite often, your you term is just going to be the logarithms term. Because when we differentiate logarithms, we do get a simplification here. So d you is going to be one over x cubed using the chain roll times the derivative of X cubed the X So this just becomes three over x dx. So that is my do you term. And that&#x27;s nice, because now there are no longer rhythms and they&#x27;re gonna be in this next integral. Then Devi, in this case is going to be X squared DX when you integrate, that&#x27;s just the power rule polynomial. So V is going to be executed over three. So this integral evaluates to UV so that&#x27;s gonna be X cubed. Natural log of X cubed Oh, that over three minus the integral of V d you. So when you multiply the and d you together, you&#x27;re going to get this is just gonna be the integral of X cubed over x the X So this is 1/3 X cube log of X cubed minus the integral X squared DX. And so this is 1/3 X cubed natural log of X cubed minus X cubed over three, plus a constant of integration. And now you can factor out this 1/3 x cubed and you&#x27;re left with natural log of X cubed minus one plus constant of integration.

Problem

Integrate each of the given functions. $$\int_{0}…

Problem 15 Easy Difficulty

Integrate each of the given functions.
$$\int \frac{\ln x}{x^{3}} d x$$

Answer

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

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus