Evaluate the integrals in Exercises 23–32.
∫₋π^π (1 - cos²(t))^(3/2) dt

The integrals in Exercises 1–34 converge. Evaluate the integrals without using tables.

∫₀¹ dr / r^0.999

In Exercises 21–32, express the integrand as a sum of partial fractions and evaluate the integrals.

∫ (x² + x) / (x⁴ - 3x² - 4) 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 / (4 - x²)^(3/2) from 0 to 1

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

Exercises 59–64 require the use of various trigonometric identities before you evaluate the integrals.

∫ cos²(2θ) sin(θ) dθ