If ∫ cos 4 x + 1 cot x - tan x = k cos 4 x + c , then " k " is equal to

Step-by-step solution

∫ cos 4 x + 1 cot x - tan x = ∫ cos 4 x + 1 cos 2 x - sin 2 x cos x sin x Use:   cos 2 x = 2 cos 2 x - 1 = 1 - 2 sin 2 x = ∫ 2 cos 2 2 x cos 2 x × sin x cos x d x = 1 2 ∫ 2 cos 2 x sin 2 x d x = 1 2 ∫ sin 4 x d x = 1 2 × - cos 4 x 4 + c = - 1 8 cos 4 x + c ⇒   k = - 1 8