# How do you integrate #(sinx)(cosx)(cos2x)dx#?

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To integrate ( (\sin{x})(\cos{x})(\cos{2x}) ) with respect to ( x ), you can use integration by parts. Let ( u = \sin{x} ) and ( dv = (\cos{x})(\cos{2x})dx ). Then, ( du = \cos{x}dx ) and ( v = \int (\cos{x})(\cos{2x})dx ).

Integrating ( v ) requires applying the angle addition formula: ( \cos{A}\cos{B} = \frac{1}{2}[\cos{(A-B)} + \cos{(A+B)}] ).

After integrating ( v ), you'll need to apply the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

This will give you the result of the integration.

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