Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 6 - Applications of Integration - 6.10 Hyperbolic Functions - 6.10 Exercises: 35

Answer

$$\tanh x + x + C$$

Work Step by Step

$$\eqalign{ & \int {{{\tanh }^2}xdx} \cr & {\text{hyperbolic identity 1}} - {\tanh ^2}x = {\operatorname{sech} ^2}x \cr & = \int {\left( {{{\operatorname{sech} }^2}x + 1} \right)} dx \cr & {\text{split the integrand}} \cr & = \int {{{\operatorname{sech} }^2}x} dx + \int {dx} \cr & {\text{find the antiderivative}} \cr & = \tanh x + x + C \cr} $$
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