Indefinite IntegrationHard
Question
The value of ∫ 4 sin x cos 
cos 
dx is equal to
cos dx is equal to Options
A.cos x -
cos 2x + 
cos 3x + C
cos 2x + cos 3x + CB.cos x - cos 2x - cos 3x + C
cos 2x - cos 3x + CC.cos x + cos 2x + cos 3x + C
cos 2x + cos 3x + CD.cos x + cos 2x - cos 3x + C
cos 2x - cos 3x + CSolution
∫4sin x cos 
cos 
dx
= ∫2 sin x(cos 2x + cos x) dx
= ∫2sin x cos 2x dx + ∫sin 2x dx
= ∫(sin 3x - sinx + sin2x) dx
= cos x -
cos 2x - 
cos 3x + C
cos dx= ∫2 sin x(cos 2x + cos x) dx
= ∫2sin x cos 2x dx + ∫sin 2x dx
= ∫(sin 3x - sinx + sin2x) dx
= cos x -
cos 2x - cos 3x + C Create a free account to view solution
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