7. Antiderivatives & Indefinite Integrals

Evaluate the integrals in Exercises 1–22.

∫ sin⁴(2x) cos(2x) dx

Evaluate the integrals in Exercises 1–22.

∫ cos³(4x) dx

Evaluate the integrals in Exercises 1–22.

∫ cos³(2x) sin⁵(2x) dx

Evaluate the integrals in Exercises 1–22.

∫ 7cos⁷(t) dt

Evaluate the integrals in Exercises 33–52.

∫ sec(x) tan²(x) dx

Evaluate the integrals in Exercises 33–52.

∫ sec³(x) tan³(x) dx

Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.

∫ x² sin(x³) dx

Evaluate the integrals in Exercises 33–52.

∫ sec⁴(x) tan²(x) dx

Evaluate the integrals in Exercises 33–52.

∫ eˣ sec³(eˣ) dx

Evaluate the integrals in Exercises 33–52.

∫ tan⁴(x) sec³(x) dx

Evaluate the integrals in Exercises 33–52.

∫ sec⁶(x) dx

Use any method to evaluate the integrals in Exercises 65–70.

∫ sin³(x) / cos⁴(x) dx

Use any method to evaluate the integrals in Exercises 65–70.

∫ cot(x) / cos²(x) dx

Evaluate the integrals in Exercises 53–58.

∫ sin(2x) cos(3x) dx

The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫ (tan θ + 3 / sin θ) dθ