Evaluate the integrals in Exercises 33–52.
∫ 8 cot⁴(t) dt

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

∫₋∞^∞ (x dx) / (x² + 4)^(3/2)

Evaluate the integrals in Exercises 39–54.

∫ 1 / (x√x + 9) dx

Use any method to evaluate the integrals in Exercises 15–38. Most will require trigonometric substitutions, but some can be evaluated by other methods.

∫ 6 dt / (9t² + 1)²

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

∫₁^∞ dx / [x√(x² − 1)]

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

∫ (from 0 to √3/2) dy / (1 - y²)^(5/2)

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.

∫ (2 ln(z³)) / (16z) dz