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: 30


$$\frac{3}{2} x^{2}+12 x-46 \ln |x-4|+C$$

Work Step by Step

Given $$\int \frac{\left(3 x^{2}-2\right) d x}{x-4}$$ By using long division, we get \begin{aligned} \frac{\left(3 x^{2}-2\right)}{x-4}= (3 x+12)-\frac{46}{x-4} \end{aligned} Then \begin{aligned} \int \frac{3 x^{2}-2}{x-4} d x &=\int(3 x-12) d x-\int \frac{46}{x-4} d x\\ &=\frac{3}{2} x^{2}+12 x-46 \ln |x-4|+C \end{aligned}
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