Evaluate the integrals in Exercises 33–54.
∫(from ln4 to ln9)e^(x/2)dx

In Exercises 59–86, find the derivative of y with respect to the given independent variable.

71. y = log₂(5θ)

Evaluate the integrals in Exercises 39–56.

55. ∫dx/(2√x + 2x)

41. Cooling soup Suppose that a cup of soup cooled from 90°C to 60°C after 10 min in a room where the temperature was 20°C. Use Newton’s Law of Cooling to answer the following questions.

a. How much longer would it take the soup to cool to 35°C?

In Exercises 59–86, find the derivative of y with respect to the given independent variable.

85. y = log₂(8t^(ln 2))

7. Order the following functions from slowest growing to fastest growing as x→∞.

a. e^x

b. x^x

c. (ln x)^x

d. e^(x/2)

In Exercises 59–86, find the derivative of y with respect to the given independent variable.

73. y = log₄ x + log₄ x²