Evaluate the integrals in Exercises 1–24 using integration by parts.
∫ e^(-y) cos(y) dy

Evaluate the integrals in Exercises 33–52.

∫ sec³(x) tan³(x) dx

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

∫₀¹ (−ln(x)) dx

Evaluate the integrals in Exercises 33–52.

∫ sec⁶(x) dx

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

∫₁^∞ (1 / (x² + 3x)) dx

Use the substitution u = tan x to evaluate the integral

∫ dx / (1 + sin² x).

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

(t⁴ + 9) / (t⁴ + 9t²)