Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - Chapter Review Exercises - Page 460: 61


$$t+\frac{1}{4} \operatorname{coth}(1-4 t)+C$$

Work Step by Step

We integrate as follows: \begin{aligned} \int \operatorname{coth}^{2}(1-4 t) d t &=\int\left(1+\operatorname{csch}^{2}(1-4 t)\right) d t \\ &=\int 1 \, d t+\int \operatorname{csch}^{2}(1-4 t) d t \\ &=t+\frac{1}{4} \operatorname{coth}(1-4 t)+C \end{aligned}
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