There are many English transitive verbs which, grammar books tell me, should have the form of the present participle as the form of the object if the object is an verb. Why? Are there any cases in which these transitive verbs could be followed by infinitives, such as "consider to change her job"? If there are, what do they mean? Or what are the differences between the ones with the present participle as the object and the ones with the infinitive as the object?

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There should be sample lists of each in your grammar book: ( 1 ) verbs which take only the to form as complement, ( 2 ) verbs which take only the -ing form, ( 3 ) verbs which take both and have the same meaning, and ( 4 ) verbs which take both and produce different meanings. As far as I know, the reasons are purely historical: some verbs do and some verbs don't.

Consider is in group #2.
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Thank you very much! Mister Micawber.

So there should be no cases in which a native speaker of English would have the to form (infinitives) as the complement of the verbs of group # 2. If there should be, it has no other special meaning but that the speaker has just made a grammatical mistake (he or she should change the to form into the -ing form). Am I right?

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(X) She considered to change her job.

In that form, yes. However:

She considered him to be a jerk
He was considered to be a jerk.

Here, I think 'consider to be' is idiomatic, or that 'be' is a unique case.
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