Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 7 - Principles Of Integral Evaluation - 7.1 An Overview Of Integration Methods - Exercises Set 7.1 - Page 490: 2

Answer

$${\left( {4 + 2x} \right)^{3/2}} + C$$

Work Step by Step

$$\eqalign{ & \int {3\sqrt {4 + 2x} dx} \cr & \int {3{{\left( {4 + 2x} \right)}^{1/2}}dx} \cr & {\text{substitute }}u = 4 + 2x,{\text{ }}du = 2dx \cr & \int {3{{\left( {4 + 2x} \right)}^{1/2}}dx} = \int {3{u^{1/2}}} \left( {\frac{1}{2}du} \right) \cr & = \frac{3}{2}\int {{u^{1/2}}} du \cr & {\text{power rule}} \cr & = \frac{3}{2}\left( {\frac{{{u^{3/2}}}}{{3/2}}} \right) + C \cr & = {u^{3/2}} + C \cr & {\text{write in terms of }}x \cr & = {\left( {4 + 2x} \right)^{3/2}} + C \cr} $$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.