Calculus, 10th Edition (Anton)

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

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2: 64

Answer

$=\frac{1}{2}ln|x|+C$

Work Step by Step

Since $\frac{1}{2x}$ equals $(\frac{1}{2})(\frac{1}{x})$ and $\frac{1}{2}$ is a constant, the constant can be brought outside of the integral. This yields $$\frac{1}{2}\int\frac{dx}{x}=\boxed{\frac{1}{2}ln|x|+C}$$
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