Use the substitution u = tan x to evaluate the integral
∫ dx / (1 + sin² x).

Evaluate the integrals in Exercises 33–52.

∫ sec³(x) tan³(x) dx

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

∫ e^(-y) cos(y) dy

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

Expand the quotients in Exercises 1–8 by partial fractions.

(t⁴ + 9) / (t⁴ + 9t²)