Your sentence has a different meaning: I claim it in order to hear (yes that is an odd sentence in Dutch as well).
The more common location to add om in this kind of sentences is: Ik beweer om het te horen, doesn't work here, I'm not sure why.
I said "I claim I can hear it" but it wasn't accepted. The accepted answer could mean "I (make a) claim (in order) to hear it" which is unlikely but might make sense with other verbs.
"Ik denk het te weten" accepts "I think I know it" and "I think to know it" is a strange sentence! Something like "I think it would be a good idea to learn it".
Translations are often not word for word. Can you explain what "I claim to hear it" means in English? Or "Ik beweer het te horen"?