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Integrate each function by using the table in Appendix $D$.$$\int 6 x^{5} \cos x^{3} d x$$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 11

Integration by Use of Tables

Integrals

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Lectures

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In mathematics, precalculu…

31:55

In mathematics, a function…

02:45

Use tables to perform the …

02:50

Use a substitution to chan…

01:44

Use a table of integrals t…

01:57

Evaluate each integral.

01:35

Evaluate each definite int…

00:15

Use the table of integrals…

Find each integral.$$\…

03:40

Use substitution to find e…

01:15

01:34

So here on this problem we need to evaluate an indefinite integral which is integration six X to the Power five Because I mean X cube dx. And with all this entry will we have to refer to the table given the book. That is the appendix D. And let me first rewrite this integration hours. This six can be written outside this integration. So integration X to the Power five can be written as X cube times square cousin. X cube dx. I'm taking X square here. So it can also be the nurse six integration X cubed and co sign X cube X squared dx. This No we also we can right now we can refer one formula that is given in the appendix D which is integration. You can assign you do you as equals two because I mean you plus you sign you. No. If you compare this formula with the given entry level we can say that U. Is equal to X cube. So we can write that U. Is X cubed. And do you will be equal to three X squared dx. Now here we have X squared dx only but video is equal to three X squared dx. So we can multiply it with three and divide Edward tree so that the integration remains the same. Now we can exactly use this formula to evaluate the given and trickle. So it will be quilts to this. 6/3 would become too times because I knew because I knew you have cosine X cube plus, you is X cube and sign you here we have X cube plus. See where they see the concept of integration that will come because it's an indefinite in trouble. So this was a solution for the given problem. I hope you have understood the problem. Thank you.

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