In Exercises 35–68, use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.
∫ from 0 to ∞ of (dθ / (θ² - 1))
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 1–22.
∫₀^(π/2) sin²(2θ) cos³(2θ) dθ
Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.
∫₀¹/√2 2x arcsin(x²) 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
Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.
∫ √(x² - 4) / x dx
