Use any method to evaluate the integrals in Exercises 15–38. Most will require trigonometric substitutions, but some can be evaluated by other methods.
∫ dx / (4 - x²)^(3/2) from 0 to 1

Evaluate the integrals in Exercises 1–14.

∫ 5 dx / √(25x² - 9), where x > 3/5

Evaluate the integrals in Exercises 39–54.

∫ sin(θ) dθ / (cos²θ + cos θ - 2)

In Exercises 69–80, determine whether the improper integral converges or diverges. If it converges, evaluate the integral.

∫₁^∞ (1 / x^(1/5)) dx

Evaluate the integrals in Exercises 33–52.

∫ tan⁴(x) sec³(x) dx

In Exercises 27–40, use a substitution to change the integral into one you can find in the table. Then evaluate the integral.

∫ (√2 - x) / √x dx

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.

∫ (dt / t√(3 + t²)