∫xcos²xdx=∫x(1+cos2x)/2dx=1/2(∫xdx+∫xcos2xdx)=1/2(1/2x²+∫xcos2xdx)=1/2(1/2x²+1/2∫xdsin2x)=1/2(1/2x²+1/2(xsin2x-∫sin2xdx))=1/2(1/2x²+1/2xsin2x+1/4cos2x)+C
