7. Antiderivatives & Indefinite Integrals

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

Evaluate ∫ sec θ dθ by:

a. Multiplying by (sec θ + tan θ) / (sec θ + tan θ) and then using a u-substitution.

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ sin(2x) cos(3x) dx

Exercises 59–64 require the use of various trigonometric identities before you evaluate the integrals.

∫ cos²(2θ) sin(θ) dθ

Exercises 59–64 require the use of various trigonometric identities before you evaluate the integrals.

∫ sin³(θ) cos(2θ) dθ

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.

∫ (dθ / cos θ - 1)

Use the substitution u = tan x to evaluate the integral

∫ dx / (1 + sin² x).