Problem

Integrate each function by using the table in App…

Problem 21 Easy Difficulty

Integrate each function by using the table in Appendix $D$.
$$\int 6 r \tan ^{-1} r^{2} d r$$

Answer

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 28

Methods of Integration

Section 11

Integration by Use of Tables

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Video Transcript

So here on this problem we have to evaluate an indefinite integral which is integration. Six hour changed in verse are square D. R. Now to evaluate this integral, we have to reform the appendix D. That is given in the book. Now you can do one thing. We can take three common from uh this so it would be three I'm taking outside. So here it will become too are like this tangent inverse R squared D. R. Now to evaluate this integral, will you go to use one formula which is given in the appendix D. Which is integration tangent inverse. You do you as he calls to you tangent inverse. You minus one over to natural log one plus U squared plus C. Now in our case we have U equals two. Our square. So do you would be equal to to our dear this way now we can take this to our hair. So we can write this way also to a water emptying here. So it would be to our dear rest as it is. So basically this thing would be do you and rest. We have this art square would be you know, we can exactly use this formula to evaluate this and struggle. So this will be called to this three will remain as it is. No, this is you you we have our square is so our square tangent universe. You So ancient universe. You we have our square minus one over to natural log one plus you. Square means are square. Bless C. So this is the required. This is you square. So you square means it should be out of the powerful. So this is required answer that was asking the question. I hope you have understood the problem. Thank you.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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