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.?

Use any method to evaluate the integrals in Exercises 15–38. Most will require trigonometric substitutions, but some can be evaluated by other methods.

∫ dx / (x² √(x² + 1))

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

∫ √(x - 2) / √(x - 1) dx

Evaluate the integrals in Exercises 39–54.

∫ 1 / ((x¹/³ - 1)√x) dx

(Hint: Let x = u⁶.)

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

∫ 2 / (x(ln x - 2)³) dx

Evaluate the integrals in Exercises 1–24 using integration by parts.

∫x e^(3x) dx

In Exercises 67–73, use integration by parts to establish the reduction formula.

∫ x^n sin(x) dx = -x^n cos(x) + n ∫ x^(n-1) cos(x) dx