7. Antiderivatives & Indefinite Integrals

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).

Evaluate the integrals in Exercises 33–52.

∫ cot⁶(2x) dx

Evaluate the integrals in Exercises 33–52.

∫ 8 cot⁴(t) dt

Evaluate the integrals in Exercises 33–52.

∫ cot³(t) csc⁴(t) dt

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

∫ sin(θ) sin(2θ) sin(3θ) dθ

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

∫ sin(t / 3) sin(t / 6) dt

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

∫ cos(θ / 2) cos(7θ) dθ

In Exercises 27–40, use a substitution to change the integral into one you can find in the table. Then evaluate the integral.

∫ dt / (tan(t)√4 - sin^2(t))

Evaluate the integrals in Exercises 37–44.

∫ cos⁵(x) sin⁵(x) dx

Evaluate the integrals in Exercises 37–44.

∫ tan³(x) sec³(x) dx

Evaluate the integrals in Exercises 37–44.

∫ sec²(θ) sin³(θ) dθ