## Calculus (3rd Edition)

Published by W. H. Freeman

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

#### Answer

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

#### 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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