Evaluate the integrals in Exercises 33–52.
∫ cot³(t) csc⁴(t) dt

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

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))