integral cos x . cos 4 x dx =

jawab

∫ cos x cos 4x  dx
∫ 1/2 ( 2 cos 4x cos 2x) dx
= 1/2 ∫  cos 6x + cos 2x)  dx
= 1/2 (1/6 sin 6x + 1/2 sin 2x) + c
= 1/12 sin 6x + 1/4 sin 2x + c
= 1/12 ( sin 6x + 3 sin 2x) + c

InTegraL

∫cos 4x cos x dx
= 1/2 ∫(cos (4x + x) + cos (4x - x)) dx
= 1/2 ∫(cos 5x + cos 3x) dx
= 1/2 (1/5 ∫dsin 5x + 1/3 ∫dcos 3x)
= 1/10 sin 5x + 1/6 cos 3x + C