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: 33


$$\frac{1}{2}\cot (3-2 x)+c$$

Work Step by Step

Given $$\int \csc ^{2}(3-2 x) d x$$ Let $$ u=3-2x\ \ \Rightarrow \ \ du=-2dx$$ Then \begin{align*} \int \csc ^{2}(3-2 x) d x&=\frac{1}{2} \int\left(-\csc ^{2} u\right) d u\\ &=\frac{1}{2}\cot u+c\\ &=\frac{1}{2}\cot (3-2 x)+c \end{align*}
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