Calculus (3rd Edition)

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

Chapter 5 - The Integral - Chapter Review Exercises - Page 278: 63

Answer

$\frac{1}{2}\cot(9-2\theta)+c.$

Work Step by Step

Since $(\cot(9-2\theta))'=2\csc^2(9-2\theta)$, we have \begin{align*} \int\csc^2(9-2\theta) d\theta &=\frac{1}{2}\int 2\csc^2(9-2\theta) d\theta \\ &=\frac{1}{2}\cot(9-2\theta)+c. \end{align*}
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