令a=sinx则原式=∫dsinx/(sin²a-6sina+12)=∫da/[(a-3)²+3]=1/3*∫da/[(a-3)²/3+1]=1/3*√3*∫d(a/√3-√3)/[(a/√3-√3)²+1]=√3/3*arctan(a/√3-√3)+C=√3/3*arctan(sinx/√3-√3)+C...