Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.3 Derivatives Of Inverse Functions; Derivatives And Integrals Involving Exponential Functions - Exercises Set 6.3 - Page 433: 75

$$5\left( {{e^3} - 2} \right)$$

$$\eqalign{ & \int_{\ln 2}^3 {5{e^x}} dx \cr & {\text{Drop out the constant}} \cr & = 5\int_{\ln 2}^3 {{e^x}} dx \cr & {\text{integrating}} \cr & = 5\left[ {{e^x}} \right]_{\ln 2}^3 \cr & {\text{evaluating the limits}} \cr & = 5\left( {{e^3} - {e^{\ln 2}}} \right) \cr & {\text{simplify}} \cr & = 5\left( {{e^3} - 2} \right) \cr} $$