An "infinitive" in English is a verb preceded by the word to, as in to study. Many English verbs can be followed by a grammatical structure that contains an infinitive and is known as an "infinitive ...

In an um...zu... clause, the infinitive has to be at the end. But when using a separable verb, you 'separate' the prefix and the rest of the infinitive by inserting ...

There is no rule as such. All we can say is that the to-infinitive clause is used after certain abstract nouns to show what action they relate to. So we can say: ...