Chapter 6 - Applications of Integration - 6.8 Logarithmic and Exponential - 6.8 Exercises - Page 480: 3

$$\frac{{{4^x}}}{{\ln 4}} + C$$

$$\eqalign{ & \int {{4^x}} dx \cr & {\text{We know that }}\frac{d}{{dx}}\left[ {{a^x}} \right] = {a^x}\ln a,{\text{ then }}\int {{a^x}dx} = \frac{{{a^x}}}{{\ln a}} + C \cr & {\text{Therefore}} \cr & \underbrace {\int {{4^x}} dx}_{\int {{a^x}dx} } = \underbrace {\frac{{{4^x}}}{{\ln 4}} + C}_{\frac{{{a^x}}}{{\ln a}} + C} \cr & {\text{ }} = \frac{{{4^x}}}{{\ln 4}} + C \cr} $$