Evaluate ∫ x³ √(1 - x²) dx using:
c. A trigonometric substitution.

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

∫ (1 - x²)^(1/2) / x⁴ 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

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

∫ (1 - r²)^(5/2) / r⁸ dr

For Exercises 49–52, complete the square before using an appropriate trigonometric substitution.

∫ 1 / √(x² - 2x + 5) 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.

∫ (dθ / √(2θ - θ²))

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.

∫ (6 dy / √y(1 + y))

Evaluate the integrals in Exercises 29–32 (b) using a trigonometric substitution.

∫ [x / √(4 − x²)] dx

Evaluate the integrals in Exercises 29–32 (b) using a trigonometric substitution.

∫ [x / √(4 + x²)] dx