Use any method to evaluate the integrals in Exercises 55–66.
∫ (x⁴ - 1) / (x⁵ - 5x + 1) dx

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

∫ sin(t / 3) sin(t / 6) dt

Use reduction formulas to evaluate the integrals in Exercises 41–50.

∫ 8 cos^4(2πt) dt

Evaluate the integrals in Exercises 1–22.

∫ cos³(2x) sin⁵(2x) dx

Evaluate the integrals in Exercises 39–54.

∫ 1 / (x⁶(x⁵ + 4)) dx

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