7. Antiderivatives & Indefinite Integrals

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

∫ sin³(θ) cos(2θ) dθ

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.

∫ 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

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

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ (tan²x + sec²x) dx

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ sinx·cos²x dx

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ (2 − cosx + sinx) / sin²x dx

Use reduction formulas to evaluate the integrals in Exercises 41–50.

∫ 8 cos^4(2πt) dt