Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions - Exercises - Page 415: 5


$$\frac{-1}{2}\tanh (1-2x)+C$$

Work Step by Step

Given $$\int \operatorname{sech}^{2}(1-2 x) d x$$ Let $$ u=1-2x \ \ \ \to du =-2dx$$ Then \begin{aligned} \int \operatorname{sech}^{2}(1-2 x) d x&=-\frac{1}{2} \int \operatorname{sech}^{2}(u) d u\\ &=\frac{-1}{2}\tanh u+C\\ &=\frac{-1}{2}\tanh (1-2x)+C \end{aligned}
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