Chapter 7 - Principles Of Integral Evaluation - 7.1 An Overview Of Integration Methods - Exercises Set 7.1 - Page 490: 7

$$\cosh \left( {{e^x}} \right) + C$$

$$\eqalign{ & \int {{e^x}\sinh \left( {{e^x}} \right)} dx \cr & {\text{substitute }}u = {e^x},{\text{ }}du = {e^x}dx \cr & = \int {\sinh u} du \cr & {\text{find the antiderivative using the theorem 6}}{\text{.8}}{\text{.3 }}\left( {{\text{see page 476}}} \right) \cr & = \cosh u + C \cr & {\text{write in terms of }}x \cr & = \cosh \left( {{e^x}} \right) + C \cr} $$