6. $\int \sin(2x)\cos(7x)\sin(12x)dx$
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The product-to-sum formula states that sin(a)cos(b) = 1/2[sin(a+b) + sin(a-b)]. Applying this formula to the integrand sin(2x)cos(7x), we get: sin(2x)cos(7x) = 1/2[sin(2x+7x) + sin(2x-7x)] = 1/2[sin(9x) + sin(-5x)] = 1/2[sin(9x) - sin(5x)] Show more…
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