Evaluate the integrals in Exercises 1–14.
∫ (2 dx) / (x³ √(x² - 1)), where x > 1

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

Evaluate the integrals in Exercises 39–54.

∫ (e⁴t + 2e²t - e^t) / (e²t + 1) dt

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

∫₀^∞ 2e^(−θ) sinθ dθ

Evaluate the integrals in Exercises 33–52.

∫ sec(x) tan²(x) 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