integral 4sin 5x sin x dx

Integral of Trigonometry Function.

sin α sin β = 1/2 [cos (α - β) - cos (α + β)]
∫ 4 sin 5x sin x dx
= ∫ 2 [cos (5x - x) - cos (5x + x)] dx
= 2 ∫ (cos 4x - cos 6x) dx
= 2 (1/4 sin 4x - 1/6 sin 6x) + C
= 1/2 sin 4x - 1/3 sin 6x + C