be busy to do sth.
忙于做某事
be busy doing
忙于做某事
意思上没有区别
通常来说固定短语只有be busy (in) doing sth.或者be busy with sth
如：
He was busy (in) preparing for the exam.
He was busy with his work and didn't notice his mother come in.
be busy to do 是没有的，但是我们可以用be too busy to do sth，表示“太忙不能（去）做……”，如：
I'll be too busy to come to the party.
She was always too busy to listen.
be busy to do sth.忙于做什么事和be busy doing忙于正在做
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