"contribute to investigating" or "contribute to investigate" [closed]
You're misanalysing your "sources".
Contribute normally takes "to" plus a noun phrase, or something which can act as a noun phrase; hence contribute to investigating. Contribute to investigate is not grammatical.
Similarly routes to investigating.
But More factors are analysed to investigate... is an entirely different construction. Analyse doesn't take a "to" phrase, so to investigate is something different. In fact, it is a "purpose" clause - infinitive with "to" often has the meaning "in order to ...".