To do sth/into

To do sth/into
 

Is this correct?

-This thing had provoked him to (not into here) rethink his life.

If not, and if you think into doing sth should be used with provoke, then why can we say?:

-The president suggested that something must have provoked the girl to carry out the attack.

The first sentence sounds downright wrong to me, but the second sounds OK.

The first sentence is correct. An alternative and more natural way of writing it is, this thing had provoked him into rethinking his life.

provoke someone + to + infinitive : to rethink
provoke someone + into + gerund : into rethinking

Both the full infinitive (to rethink) and the prepositional phrase (into rethinking) can be used.
I prefer using the full infinitive. It sounds very natural to me.

Excellent answers. Thank you.