Evaluate the integrals in Exercises 39–54.
∫ 1 / (cos θ + sin 2θ) dθ

Evaluate the integrals in Exercises 51–56 by making a substitution (possibly trigonometric) and then applying a reduction formula.

∫ (from 0 to 1/√3) dt / (t² + 1)^(7/2)

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ √(x - x²) / x dx

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ x (7x + 5)^(3/2) dx

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

∫ arcsin(y) dy

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

∫₀^∞ (16 tan⁻¹x dx) / (1 + x²)

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

∫₋₈¹ dx / x^(1/3)