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 -1 to 1 of (dθ / (θ² - 2θ))

Evaluate the integrals in Exercises 1–22.

∫ sin⁴(2x) cos(2x) dx

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

∫₀² dx / √|x − 1|

The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫₋₁¹ (√(1 + x²) sin x) dx

Evaluate the integrals in Exercises 33–52.

∫ eˣ sec³(eˣ) dx

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

∫ (x² - 2x + 1) e^(2x) dx

Evaluate the integrals in Exercises 1–14.

∫ √(1 - 9t²) dt