∫xsin^2xdx
=1/2∫x(1-cos2x)dx
=1/4x^2-1/2∫xcos2xdx
=1/4x^2-1/4∫xdsin2x
=1/4x^2-1/4xsin2x+1/4∫sin2xdx
=1/4x^2-1/4xsin2x-1/8cos2x+C