Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Section 8.1 - Using Basic Integration Formulas - Exercises 8.1 - Page 448: 34

Answer

$${e^{{e^z}}} + C $$

Work Step by Step

$$\eqalign{ & \int {{e^{z + {e^z}}}} dz \cr & {\text{use the property }}{e^{m + n}} = {e^m}{e^n} \cr & = \int {{e^z}{e^{{e^z}}}} dz \cr & {\text{integrate by the substitution method}} \cr & {\text{set }}u = {e^z}{\text{ then }}du = {e^z}dz \cr & {\text{write the integrand in terms of }}u \cr & \int {{e^z}{e^{{e^z}}}} dz = \int {{e^u}} du \cr & {\text{integrating}}{\text{,}} \cr & = {e^u} + C \cr & {\text{replace }}{e^z}{\text{ for }}u \cr & = {e^{{e^z}}} + C \cr} $$
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