Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Section 8.2 - Integration by Parts - Exercises 8.2 - Page 455: 1



Work Step by Step

We use the formula $\int udv=uv-\int vdu$ with $u=x,\,dv=\sin \frac{x}{2}dx$ $du=dx,\,v=-2\cos(\frac{x}{2})$ Then, $\int x\sin\frac{x}{2}dx=x\times-2\cos(\frac{x}{2})-\int-2\cos(\frac{x}{2})dx$ $=-2x\cos(\frac{x}{2})+4\sin(\frac{x}{2})+C$
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