Indefinite Integration of cos x

Indefinite Integration of cos x

How to solve the indefinite integration of cos x problems: formula, example, and its solution.

Formula

(integral of cos x dx) = sin x + C

∫ cos x dx = sin x + C

This is true because
[sin x + C]' = cos x.

Derivative of sin x

Example

Find the given indefinite integral. The integral of (cos^2 x/2) dx

cos x/2 = ±√(1 + cos x)/2

So cos2 x/2 = (1 + cos x)/2.

cos A/2 (Half-angle formula)

Take 1/2 out from the integral.

∫ cos x dx = sin x

So (given) = (1/2)(x + sin x) + C.