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: 12



Work Step by Step

Given $$\int \frac{\cosh x}{\sinh^2 x} d x $$ Let $$ u= \sin h x \ \ \ \to du = \cosh x dx$$ Then \begin{aligned} \int \frac{\cosh x}{\sinh ^{2} x} d x &=\int \frac{1}{u^{2}} d u \\ &=\int u^{-2} d u \\ &=-u^{-1}+C \\ &=-\frac{1}{\sinh x}+C \\ &=-\operatorname{csch}x+C \end{aligned}
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