Evaluate the integrals in Exercises 1–22.
∫₀^(π/2) sin²(2θ) cos³(2θ) dθ

Evaluate the integrals in Exercises 39–54.

∫ 1 / (x⁶(x⁵ + 4)) dx

In Exercises 69–80, determine whether the improper integral converges or diverges. If it converges, evaluate the integral.

∫₂^∞ (1 / (x√x)) dx

Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.

∫₀¹/√2 2x arcsin(x²) dx

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

∫ (x⁴ - 1) / (x⁵ - 5x + 1) dx

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

∫ e^(-2x) sin(2x) dx

In Exercises 17–20, express the integrand as a sum of partial fractions and evaluate the integrals.

∫ (x³ dx) / (x² - 2x + 1) from -1 to 0