Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.
∫ (cos(√x))/(√x) dx

In Exercises 39–48, use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

∫ √(x - 2) / √(x - 1) dx

Use any method to evaluate the integrals in Exercises 55–66.

∫ (x + 2) / (x³ - 2x² - 3x) dx

Evaluate the integrals in Exercises 25–30 by using a substitution prior to integration by parts.

∫ z(ln z)² dz

Use any method to evaluate the integrals in Exercises 65–70.

∫ x cos³(x) dx

Evaluate the integrals in Exercises 1–22.

∫₀^(π/6) 3cos⁵(3x) dx

Annual rainfall The annual rainfall in inches for San Francisco, California, is approximately a normal random variable with mean 20.11 in. and standard deviation 4.7 in. What is the probability that next year’s rainfall will exceed 17 in.?