Evaluate the integrals in Exercises 29–32 (b) using a trigonometric substitution.
∫ [t / √(4t² − 1)] dt

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

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

∫ [y / √(16 − y²)] dy

Use any method to evaluate the integrals in Exercises 55–66.

∫ x² √(1 - x²) dx

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ dy / (y² − 2y + 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.

∫ dx / (1 + x²)

Evaluate the integrals in Exercises 33–36.

∫ [1 / √(9 - x²)] dx