be busy doing sth 其实也可以是 be busy (in) doing sth.意为忙于做某事.
例：I'm busy (in) doing my home work.
be busy to do sth.如果是 be too busy to do sth.
那就是too...to...结构了,可以这样用,太忙了以至于不能干什么.
但是如果没有那个too那就不能用to do只能用doing表示忙于做某事