Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.11 - Hyperbolic Functions - 3.11 Exercises - Page 264: 25

Answer

$y=ln(x\sqrt {1+x^2})$

Work Step by Step

Let suppose $y=sinh^{-1}x$ $x=sinh$ $y$ The example 1(a) shows that $cosh^2$ $ y-sinh^2 $ $ y=1$ As we know from exercise $9$. $e^y=cosh$ $ y+sinh $ $ y$ $=x+\sqrt {1+x^2}$ $y=ln(x\sqrt {1+x^2})$
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