Chapter 5 - Section 5.4 - Indefinite Integrals and the Net Change Theorem - 5.4 Exercises - Page 415: 17

${e^x} + \ln \left| x \right| + C$

$$\eqalign{ & \int {\left( {{e^x} + \frac{1}{x}} \right)} dx \cr & {\text{Use the sum rule for integration}} \cr & = \int {{e^x}} dx + \int {\frac{1}{x}} dx \cr & {\text{Apply the formulas: }}\int {{e^x}dx = {e^x} + C,\int {\frac{1}{x}dx = \ln \left| x \right| + C} } \cr & = {e^x} + \ln \left| x \right| + C \cr} $$