Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.6 Strategies for Integration - Exercises - Page 431: 14


$$-x \csc x-\ln |\csc x+\cot x|+C$$

Work Step by Step

Given $$\int x \csc x \cot x \, d x$$ Let \begin{align*} u&= x\ \ \ \ \ \ dv= \csc x \cot x \, d x\\ du&= dx\ \ \ \ \ \ v=- \csc x \end{align*} Then \begin{align*} \int x \csc x \cot x \, d x&= x\csc x +\int \csc xdx\\ &=-x \csc x-\ln |\csc x+\cot x|+C \end{align*}
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