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 / (4 - x²)^(3/2) from 0 to 1

Evaluate the integrals in Exercises 1–14.

∫ 5 dx / √(25x² - 9), where x > 3/5

Evaluate the integrals in Exercises 39–54.

∫ sin(θ) dθ / (cos²θ + cos θ - 2)

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

∫ (ln x)^n dx = x (ln x)^n - n ∫ (ln x)^(n-1) dx

Evaluate the integrals in Exercises 33–52.

∫ tan⁴(x) sec³(x) dx

In Exercises 9–16, express the integrand as a sum of partial fractions and evaluate the integrals.

∫ (x + 3) / (2x³ - 8x) dx

Evaluate the integrals in Exercises 23–32.

∫₋π^π (1 - cos²(t))^(3/2) dt