Integral of sin^3 x cos^3 x in terms of cos 2x and cos 6x

The same question, asked 2 times: 12 May 2026 S2, 19 May 2026 S2. Every wording below, oldest first.

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Question 1
12 May 2026 S2
80 $\displaystyle\int\sin^3 x \cdot \cos^3 x\,dx = \dfrac{1}{32}\left[\dfrac{3}{2}f(x) + \dfrac{1}{6}g(x)\right] + C$
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Question 2
19 May 2026 S2
78 $\int \sin^3 x\cos^3 x\,dx = \ldots$
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