Compute the indefinite integral ∫ cos x dx.

Find ∫ cos(3x) dx.

A product's demand function (units per month) is modeled by v(t) = 4 cos t - 3 sin t. Compute the displacement (net change in units) from t = 0 to t = π/2 by integrating v(t).

An object's acceleration is a(t) = sec^2 t (m/s^2). If its velocity at t=0 is v(0)=1 m/s, what is its velocity at t=π/4? (Integrate acceleration.)

Compute ∫ (2 sec x tan x + 3 csc x cot x - 5 sin x) dx and present the simplified antiderivative.