Evaluate the integrals in Exercises 33–54.
∫ 2t e^(-t²) dt

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))

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

83. y = 3^(log₂ t)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

23. y=arcsin(√2t)

Solve the differential equation in Exercises 9–22.

11. (dy/dx) = e^(x-y)