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

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 11

Integration by Use of Tables

Integrals

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31:55

In mathematics, a function…

02:08

Use a table of integrals t…

02:03

Table lookup integrals Use…

02:06

Use a substitution to chan…

01:54

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01:10

Evaluate each integral.

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11:33

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Evaluate the following int…

03:37

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'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's squared plus. See where this C. Is a constant of integration. That will come because it'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'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'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.

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