Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 7 - Section 7.4 - Integration of Rational Functions by Partial Fractions. - 7.4 Exercises - Page 501: 9


$$\int \frac{5x+1}{(2x+1)(x-1)}dx=\frac{ln\left | 2x+1 \right |}{2}+2ln\left | x-1 \right |+C$$

Work Step by Step

$$\int \frac{5x+1}{(2x+1)(x-1)}dx=\int \frac{(4x+2)+(x-1)}{(2x+1)(x-1)}dx$$ $$=\int (\frac{1}{2x+1}+\frac{2}{x-1})dx$$ $$=\frac{ln\left | 2x+1 \right |}{2}+2ln\left | x-1 \right |+C$$
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