Compute the indefinite integral ∫ sin x dx.

Compute ∫ cos(2x) dx.

A seasonal demand model is D(t)=100+20 sin(π t/6) (units per month). Compute the total extra demand above the baseline (the integral of 20 sin(π t/6)) over one year from t=0 to t=12.

Compute the integral I = ∫_{0}^{π/2} sin^2 x dx.

Evaluate the definite integral ∫_{π/4}^{π/3} tan x dx and provide the exact value.

Compute ∫ tan^2 x sec^4 x dx by choosing u = tan x and expanding appropriately.