Answer
$$\ \int e^{-x} \sinh x dx =\frac{1}{2}(x-\frac{1}{2}e^{-2x})+c .$$
Work Step by Step
We have
$$\ \int e^{-x} \sinh x dx =\frac{1}{2}\int e^{-x}(e^{x}-e^{-x})dx\\
=\frac{1}{2}\int 1-e^{-2x} dx=\frac{1}{2}(x-\frac{1}{2}e^{-2x})+c .$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.9 Hyperbolic Functions - Exercises - Page 384: 45
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