Find: ^ 3 x d x - Vidyadip

Question

Find: $\int \sin ^{3} x d x$

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Answer

From the identity $\sin 3x = 3 \sin x - 4 \sin^3 x$, we find that
$\sin ^{3} x=\frac{3 \sin x-\sin 3 x}{4}$
Therefore, $\int \sin ^{3} x d x=\frac{3}{4} \int \sin x d x-\frac{1}{4} \int \sin 3 x d x$
Integral = $-\frac{3}{4} \cos x+\frac{1}{12} \cos 3 x+c$

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