Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.2 Trigonometric Integrals - Exercises - Page 403: 19


$$ -\frac{1}{2}\cot^2 x-\ln \sin x+c$$

Work Step by Step

\begin{align*} \int \cot^3 xdx&= \int \cot x\cot^2 xdx\\ &= \int \cot x(\csc^2 x-1)dx\\ &= \int \cot x\csc^2 xdx-\int \cot x dx\\ &= -\frac{1}{2}\cot^2 x-\ln \sin x+c \end{align*}
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