Integral 6 sin 5x cos 3x dx

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2 sin 5x cos 3x = sin 8x + sin 2x

∫6 sin 5x cos 3x dx
= 3 ∫2 sin 5x cos 3x dx
= 3 ∫(sin 8x + sin 2x) dx
= 3 ( -1/8 ∫dcos 8x - 1/2 ∫dcos 2x)
= 3 (-1/8 cos 8x - 1/2 cos 2x) + C
= -3/8 cos 8x - 3/2 cos 2x + C