Evaluate the integrals in Exercises 1–24 using integration by parts.
∫ 4x sec²(2x) dx

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.

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

∫(from 1 to e) x³ ln(x) dx

Evaluate the integrals in Exercises 1–14.

∫ √(y² - 25) / y³ dy, where y > 5

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

∫₁^∞ (1 / (x² + 3x)) dx