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I'm sorry, you had written infinitive (which, based on another comment in this post, I thought should have been indicative). Given the context you just provided, I can see that your textbook is correct. The example given is clearly one of doubt. This would certainly trigger the use of the subjunctive mood IF another clause is created (that's what it means by another subject). The person in that second clause could be the same person or another person. Either way, the subjunctive must be used.
Dudo poder venir. = I doubt I can come.
Dudo que pueda venir. = I doubt I can come.
Dudo que ella pueda venir. = I doubt she can come.
Thanks for the example from your textbook. It really helped to make this more clear for me.
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