Integrate sin x cos 2x

By Angle-Addition, cos(2x) = 2cos(x)^2-1

So, sin(x)cos(2x) = [2cos(x)^2-1]sin(x) = 2sin(x)cos(x)^2 - sin(x)

Int[2sin(x)cos(x)^2 - sin(x)] = (-2/3)cos(x)^3 + cos(x) +K