Integrals involving exponential and logarithmic functions. These functions have unique properties that make them stand out. In this section, we explore integration involving exponential and logarithmic functions. Integrate functions involving the natural logarithmic function. Learning Objectives Write the definition of the natural logarithm as an integral. 6 Prove properties of logarithms and exponential Exponential and logarithmic functions are used to model population growth, cell growth, and financial growth, as well as depreciation, radioactive decay, and resource consumption, to name only a few applications. 5 Recognize the derivative and integral of the exponential function. Substitution is often used for more complex exponential integrals Exponential functions are common in real-life applications, especially in growth and decay scenarios Exponential and logarithmic functions are used to model population growth, cell growth, and financial growth, as well as depreciation, radioactive decay, and resource consumption, to name only a few applications. Substitution is often used to evaluate integrals involving exponential functions or logarithms. 7. They pop up in many real-world scenarios, from population growth to compound interest. lnast ya9od jrbu4m hzck 0paz4 yf2nm 1cb7em qlx 4nu rpure3