Evaluate the integrals in Exercises 33–52.
∫ eˣ sec³(eˣ) 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

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.

∫₀^π sin⁵(x/2) dx

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

∫ (x² - 2x + 1) e^(2x) dx

In Exercises 33–38, perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral.

∫ 2y⁴ / (y³ - y² + y - 1) dy