\( \int \sin ^{3} x d x \)

1.	\( \int \sin ^{3} x d x \)
Answer» ∫sin³x dx = ∫\(\frac{3sin\,x-sin\,3x}{4}dx\) (∵ sin 3θ = 3 sin θ - 4 sin³θ ⇒ sin³θ \(=\frac{3sin\,\theta-sin\,3\theta}{4}\)) = 1/4 (-3cos x + \(\frac{cos3x}3\)) + c (∵ ∫sin ax dx \(= \frac{-cos\,ax}{a})\) = -3/4 cos x + 1/12 cos 3x + c

Answer»

∫sin³x dx

= ∫\(\frac{3sin\,x-sin\,3x}{4}dx\) (∵ sin 3θ = 3 sin θ - 4 sin³θ ⇒ sin³θ \(=\frac{3sin\,\theta-sin\,3\theta}{4}\))

= 1/4 (-3cos x + \(\frac{cos3x}3\)) + c (∵ ∫sin ax dx \(= \frac{-cos\,ax}{a})\)

= -3/4 cos x + 1/12 cos 3x + c

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\( \int \sin ^{3} x d x \)

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