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: 12


$$\int x\,sin(3-x)dx=x\,cos(3-x)-sin(3-x)+C$$

Work Step by Step

$${[x\,cos(3-x)]}'= cos(3-x)+x\,sin(3-x)$$ $$\int x\,sin(3-x)dx=x\,cos(3-x)-\int cos(3-x)dx$$ $$=x\,cos(3-x)-sin(3-x)+C$$
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