integrate-each-function-by-using-the-table-in-appendix-d-int-x3-ln-x2-d-x-2

Question

Integrate each function by using the table in Appendix $D$.
$$\int x^{3} \ln x^{2} d x$$

Vipender Yadav · Accepted Answer

So here on this problem we need to evaluate an indefinite interval which is integration X cubed times natural log X squared dx. And to evaluate this integral, we have to refer the appendix D. That is given in the book. Now first let me write this integration ass integration. This X cube can be written as x square dot x. Like this. Natural log x squared dx. Now I&#x27;m taking X here the six. I can write it here also. So integration, this is X square natural log X square and X dx. Now we can use one formula that is given in the appendix D. Of the book. And the formula is integration U. To the power end. Natural log you do you is it calls to do you do the power N plus one times. Natural log you divide by N plus one minus one over N plus one. And it&#x27;s squared plus. See where this C. Is a constant of integration. That will come because it&#x27;s an indefinite in trouble. Now if you compare this form law with the given interval we can say that we have U. Equals two X square and in is one. And do you will be called two weeks leaks. But here we have only X. Dx. So we can do one thing. We can multiply it with two and divide advert to. Now. We can use exactly this form law to evaluate the given and true. So let&#x27;s proceed. So the calls to this 1/2 will remain as it is times now you do the power N plus one. So you will have X square times and plus one. So one plus one is two times. Natural log you we have ex square divide one plus one is two minus 1/1 plus one is two and square will be four. Let&#x27;s see where this is a concept of integration. Now we can further simplify this and finally, we can right the answer to be won over four X. To the powerful natural log X squared minus 1/2. Blessed See So this is required, and so does the bracket here. So did he require answer that was asking the question. I hope you have understood the problem. Thank you.

Andrija Isakov · Answer

in this question will be finding the integral of X times two X quick two to the power of X quick. So first notice that we have an X squared was derivative is two X and we have X dx in the expression as well. So we noticed that we have a function inside of function and the inter function also has a derivative present. So that gives us the hint to use substitution. And we looks may substitute you for X squared, which means the value of the integral or the interval can be rewritten as to to the exponents you times 1/2 the year. This, of course, equals 1/2 of the integral of to to new to to the U, which by our integration table by formula equals to the exponents you over lawn of to plus the constant of integration. And so no, we have found the indefinite integral. We found, um, the family of anti derivatives. I would correspond to our original integral. Now we just have to substitute in terms of the variable. We had a beginning X since U equals x squared. You can write this us two to the power of X squared minus one all over long enough to close the constant of integration

Robert Daugherty · Answer

77.6 problem 21. We&#x27;re dealing with indefinite minerals here. There were using interval look up table. So I have an immigrant Internet resource that I&#x27;m using for this Look up. So the log squared of X. So I just go to many look up table and everywhere where it has locker rhythms I look and see if I can find that matches what I&#x27;m looking for and I do right here, um the integral off apartment that wrong it&#x27;s not. It&#x27;s not the one that I circle. It is the one below it. So the log square, which is right here at this one. So it&#x27;s the and this one You have to know your immigrant inner integral tables. This woman it uses elegy log that means natural, longer, so natural, long of a X squared. And it gives me the value for that and said, That&#x27;s what I&#x27;m going to use for Ah, this particular integration. So using the formula that I have so I&#x27;m going tohave the log squared and this one actually has for a X. The X is equal to x times the natural log squared of a x minus two x natural log of a X plus two acts and obviously plus a constant of integration. So in this case, I&#x27;m using the formula where a is equal to one. So in evaluating this integral, then this just becomes X natural logs squared of X minus two X natural log of X plus two x plus, a constant of integration. So that is my final answer. So, really, it&#x27;s a key about having a table and knowing how to navigate the table. You know where to look for, because tables will have hundreds of injuries, knowing how it&#x27;s organized and being able Teoh to navigate and find the right the right integral.

R M · Answer

Brooklyn 39 Integration off x cubed plus x a plus one over x x squared plus one square the X, which is equal to integration off x X squared plus one plus one over X squared plus one square E x, which is equal to integration of x X squared plus one The X over X squared plus one square plus integration off one over x x squared plus one is square the X, which is equal to integration off X X squared plus one the X A plus integration of one over X squared plus one squared and the X, which is equal to half. Then X squared plus one plus X over two X squared, plus one close, huh? Then in verse X A plus at first, See So for the first integral we use u substitution here your substitution by letting you is equal to x squared plus one. So the U is equal to X. The X and the integral can be saved. That and Britain as ah, half invigoration off, one over you being you through people to lend you And for the second integrity here we use a formula 33 from page get to

Matthew Allcock · Answer

in this video, we&#x27;re gonna go through the answer fresh number 25 after 8.7 for us to evaluate the following Integral. We&#x27;re gonna do this using intuition parts because we have a product off two functions. So the first car, we&#x27;re gonna call this function the destruction too. So we&#x27;re gonna leave for two as it is and then most quiet by insulin function want, which is X squared questions over one minus. There is one of differentiate the function of its A, I guess one of X, How&#x27;s the integral off function Walk X DX. So that&#x27;s gonna be the natural log of one times one squares minus Zira. Uh, then it&#x27;s the inter minus integral of 0 to 1 x three X. Not a lot of one is just zero. So this is just going to minus until the necks is gonna be ah X squared between zero and one. That&#x27;s gonna be minus, huh?

Matthew Allcock · Answer

in this video, we&#x27;re gonna go through the unsaid question. Number 26. I&#x27;m jumped 8.7. Arrest reevaluating following integral. So many dio using television. My parents were right size minus one time by It&#x27;s been tricked him. It doesn&#x27;t look like a product to functions, but it is a right. It is a product of the function minus one on the function natural or X, That&#x27;s what you want. So integrating by parts this is gonna be if we if the function to as it is, that&#x27;s going to natural light of X times by the integral of work, should one that&#x27;s going to be minus X rep 01 my inscriptions. Everyone of now we want to differentiate function to give us one of Rex ties by integral function. One my sex. So evaluating the first term at one and zero was gonna give us zero minus. So the minus in the mine is gonna make a plus zero. One X is gonna counselor breath. Just have the X. That&#x27;s gonna be it&#x27;s using X. What&#x27;s interesting? Warning facts. You got anything between one and the answer is just one

Problem

Integrate each function by using the table in App…

Problem 37 Easy Difficulty

Integrate each function by using the table in Appendix $D$.
$$\int x^{3} \ln x^{2} d x$$

Answer

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace H.

Kristen K.

Samuel H.

Michael J.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 28

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Kristen K.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

Basic Technical Mathematics with Calculus

Grace H.

Kristen K.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Grace H.

Kristen K.

Samuel H.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus