Use any method to evaluate the integrals in Exercises 65–70.
∫ x cos³(x) dx

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))

Find the value of the constant c so that the given function is a probability density function for a random variable X over the specified interval.

f(x) = c * x * √(25 - x²) over [0, 5]

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ √(x - x²) / x dx

Evaluate the integrals in Exercises 1–22.

∫₀^(π/6) 3cos⁵(3x) 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