求解 ∫sin(6x)^3*cos(6x)^8 dx=? 范围[pi/2,0]

原式=-1/6∫(0→π/2)sin^2(6x)cos^8(6x)d(cos(6x))=-1/6∫(0→π/2)(1-cos^2(6x))cos^8(6x)d(cos(6x))=-1/6∫(0→π/2)cos^8(6x)d(cos(6x))+1/6∫(0→π/2)cos^10(6x)d(cos(6x))=-1/54cos^9(6x)|(0→π/2)+1/66cos^11(6x)|(0→π/2)=1/54+1/54-1/66-1/66=1/27-1/33=2/297