Evaluate the integrals in Exercises 1–14.
∫ dx / (8 + 2x²) from 0 to 2

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

∫₀² (s + 1) / √(4 − s²) ds

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

Arc length:

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

Evaluate the integrals in Exercises 1–24 using integration by parts.

∫ 4x sec²(2x) dx

Evaluate the integrals in Exercises 1–24 using integration by parts.

∫(from 1 to e) x³ ln(x) dx