Integral sin³x itu berapa?

integral trigonometri

sin³ x = sin² x . sin x = (1/2 - 1/2 cos 2x)(sin x)
∫ sin³ x dx = ∫ (1/2  - 1/2 cos 2x)(sin x) dx
= 1/2∫ (1 - cos 2x)(sin x) dx
= 1/2 ∫ sin x - cos 2x sin x dx
= 1/2 ∫ sin x dx - 1/2 ∫ 1/2 (2 cos 2x sin x) dx
= 1/2 ∫ sin x dx - 1/4 ∫ sin 1/2(2x+x) - sin 1/2 (2x - x)
= 1/2 ∫ sin x dx - 1/4 ∫ sin 3/2 x - sin 1/2 x dx
= -1/2 cos x - 1/4 [(2/3) (-cos 3/2 x -  2 ( - cos 2x) ] + c
= -1/2 cos x  + 1/4 [ - 2/3  cos 3/2 x  + 2 cos 2x ] + c
= -1/2 cos x - 1/6 cos 3/2 x + 1/2 cos 2x + c
= -1/6 { 3 cos x + cos 3/2x + 3 cos 2x ] + c