Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 90


$$ \int \frac{ x^2d t}{x^3+2}= \frac{1}{3}\ln |x^3+2|+c. $$

Work Step by Step

Le $ u=x^3+2$ and hence $ du=3x^2dx $, then we have $$ \int \frac{ x^2d t}{x^3+2}=\frac{1}{3}\int \frac{ d u}{u}= \frac{1}{3}\ln u+c=\frac{1}{3}\ln |x^3+2|+c. $$
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