∫xcos(x/2)dx

问题描述:

∫xcos(x/2)dx

用分部积分
∫xcos(x/2)dx
=2∫xcos(x/2)d(x/2)
=2∫xdsin(x/2)
=2xsin(x/2)-2∫sin(x/2)dx
=2xsin(x/2)-4∫sin(x/2)d(x/2)
=2xsin(x/2)+4cos(x/2)+C