evaluate integrand sin(3x)cos(4x)cos(7x)

I = sin3x.cos4x.cos7xdx

  =1/2 [sin3x(2cos4xcos7x)]dx                  (2cosacosb = cosa+b+ cosa-b )

  =1/2[sin3x(cos11x + cos3x)]dx

  =1/4[2sin3xcos11x +2sin3xcos3x]dx        (2sinacosb = sina+b + sina-b)

  =1/4[sin14x - sin8x + sin6x]dx

  =1/4 [-cos14x/14 + cos8x/8 - cos6x/6] + c