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))
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
Evaluate the integrals in Exercises 1–24 using integration by parts.
∫ e^(-2x) sin(2x) dx
Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.
∫ √(x² - 4) / x dx
In Exercises 39–48, use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.
∫ (e^{t} dt) / ((1 + e^{2t})^{3/2}) from ln(3/4) to ln(4/3)
