Evaluate the integrals in Exercises 39–54.
∫ 1 / (x√x + 9) dx

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

∫₋∞^∞ (x dx) / (x² + 4)^(3/2)

Evaluate the integrals in Exercises 1–14.

∫ (2 dx) / (x³ √(x² - 1)), where x > 1

Evaluate the integrals in Exercises 39–54.

∫ (e⁴t + 2e²t - e^t) / (e²t + 1) dt

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 1–44 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

Evaluate the integrals in Exercises 33–52.

∫ 8 cot⁴(t) dt