Chapter 7: Transcendental Functions - Section 7.3 - Exponential Functions - Exercises 7.3 - Page 391: 83

$$\frac{{{5^x}}}{{\ln 5}} + C $$

$$\eqalign{ & \int {{5^x}} dx \cr & {\text{Integrate using }}\int {{a^u}} du = \frac{{{a^u}}}{{\ln a}} + C;{\text{ For this exercise}}{\text{, set }}u = x{\text{ and }}a = 5 \cr & {\text{Then}} \cr & \int {{5^x}} dx = \frac{{{5^x}}}{{\ln 5}} + C \cr} $$