The integrals in Exercises 1–34 converge. Evaluate the integrals without using tables.
∫₀² (s + 1) / √(4 − s²) ds

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

∫ x^2 √(2x - x^2) dx

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

∫₋∞⁴ [x / (x² + 9)^(2/5)] dx

Exercises 59–64 require the use of various trigonometric identities before you evaluate the integrals.

∫ sin³(θ) cos(2θ) dθ

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

∫ x^2 / √(x^2 - 4x + 5) dx

Evaluate the integrals in Exercises 1–14.

∫ dx / (8 + 2x²) from 0 to 2

Arc length:

Find the length of the curve y = x², 0 ≤ x ≤ √3/2.