Indefinite Integration of sin x

Indefinite Integration of sin x

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

Formula

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

∫ sin x dx = -cos x + C

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

Derivative of cos x

Example

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

Square of a sum

sin2 (x/2) + cos2 (x/2) = 1

Pythagorean identities

2 sin (x/2) cos (x/2) = sin x

sin 2A (Double-angle formula)

∫ sin x dx = -cos x

So (given) = x - cos x + C.