Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises: 75


The required formula is $$\int \frac{1}{z}dz=\ln |z|+c.$$

Work Step by Step

The integral $$\int \frac{x}{x^2+1}dx$$ can be transformed into integral $$\frac{1}{2}\int \frac{1}{z}dz$$ using substitution $z=x^2+1,$ where is $dz=2xdx$ so required formula is $$\int \frac{1}{z}dz=\ln |z|+c.$$
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