We know that,cos 3x = 4 cos3x - 3 cos x⇒cos3x = cos 3x + 3 cos x4Now, I = ∫cos3x dx=14∫cos 3x + 3 cos x dx=14sin 3x3 + 3 sin x + C

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Integral of cos^3(x)

We know that, \cos 3 x = 4 \cos^{3} x - 3 \cos x \Rightarrow \cos^{3} x = \frac{\cos 3 x + 3 \cos x}{4} Now, I = \int \cos^{3} x dx = \frac{1}{4} \int [\cos 3 x + 3 \cos x] dx = \frac{1}{4} [\frac{\sin 3 x}{3} + 3 \sin x] + C

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