I've learned [not to] [to not] trust them.

[Marika33]

Which of the two should I say (if I had to)?

I've learned not to trust them.
I've learned to not trust them.

 

[jutfrank]

It depends on what emphasis you want.

The first places the emphasis on the awareness of their untrustworthiness as the result of your learning. 'Don't trust them' is what you've learned.

The second places the emphasis on what you've learned, as if trusting them is something you've actively learned to refrain from doing.

 

[Rover_KE]

#1 (if you had helpfully numbered them, Marika33) is the only one used by those who (mistakenly) believe you mustn't split an infinitive.