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Verified answer
InTegraLcos 3x cos x
= 1/2 (cos (3x+x) + cos (3x-x))
= 1/2 (cos 4x + cos 2x)
∫3 cos 3x cos x dx
= 3 . 1/2 ∫(cos 4x + cos 2x) dx
= 3/2 (1/4 ∫dsin 4x + 1/2 ∫dsin 2x)
= 3/8 sin 4x + 3/4 sin 2x + C ✔