Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.1 Integration by Parts - Exercises - Page 395: 14


$$\int x^{2}cos\,3x\,dx=\frac{x^{2}}{3}sin\,3x+\frac{2x}{9}cos\,3x-\frac{2}{27}sin\,3x+C$$

Work Step by Step

$$\int x^{2}cos\,3x\,dx$$ $$=\frac{1}{3}x^{2}sin\,3x-2x(-\frac{1}{9}cos\,3x)+2(-\frac{1}{27}sin\,3x)-\int 0\cdot (-\frac{1}{27}sin\,3x)dx$$ $$=\frac{x^{2}}{3}sin\,3x+\frac{2x}{9}cos\,3x-\frac{2}{27}sin\,3x+C$$
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