Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.5 The Method of Partial Fractions - Exercises - Page 423: 5

Answer

$\frac{1}{3}x-\frac{4}{9}\ln|9x-12|+C$

Work Step by Step

long division give $\frac{x}{3x-4}$ = $\frac{1}{3}+\frac{\frac{4}{3}}{3x-4}$ so $\int{\frac{x}{3x-4}dx}$ = $\int({\frac{1}{3}+\frac{\frac{4}{3}}{3x-4}})dx$ = $\frac{1}{3}x-\frac{4}{9}\ln|9x-12|+C$
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