If ∫ d x cos 3 x 2 sin 2 x = tan x A + C tan x B + k , where k is a constant of integration, then A + B + C equals

Step-by-step solution

∫ d x cos 3 x 4 sin x cos x = ∫ d x 2 cos 4 x tan x Let, tan x = t 2 ⇒ sec 2 x = 1 + t 4 And sec 2 x d x = 2 t d t ∴ I =   ∫ sec 4 x d x 2 tan x =   ∫ sec 2 x . sec 2 x d x 2 tan x = ∫ 1 + t 4 2 t   d t 2 t = ∫ 1 + t 4 d t = t + t 5 5 + k , where k is a constant of integration. =   tan x + 1 5 tan 5 2 x + k Where, t =   tan x . A = 1 2 ,   B = 5 2 ,   C = 1 5 A + B + C = 16 5