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 8.6 - Integral Tables and Computer Algebra Systems - Exercises 8.6 - Page 481: 26


$$\frac{1}{13} \sin \left(\frac{13 \theta}{2}\right)+\frac{1}{15} \sin \left(\frac{15 \theta}{2}\right) +C$$

Work Step by Step

Use the formula $$\int \cos a x \cos b x d x=\frac{\sin (a-b) x}{2(a-b)}+\frac{\sin (a+b) x}{2(a+b)}+C, \quad a^{2} \neq b^{2}$$ with $ a=\dfrac{1}{3},\ \ \ b =\dfrac{1}{4}$, then we get \begin{align*} \int \cos \frac{\theta}{2} \cos 7 \theta d \theta=\frac{1}{13} \sin \left(\frac{13 \theta}{2}\right)+\frac{1}{15} \sin \left(\frac{15 \theta}{2}\right)+ c \end{align*}
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