Eugene Volokh points to a post on Language Log discussing an egregious example of an unsplit infinitive:
How wirelessly to hack ?? Unbelievable. (You can find the article online with a Google search on "how wirelessly to hack". As I write, it is the only hit: no one has ever written that misbegotten four-word sequence in the prior history of the world.
The Language Log post goes on to point out that “how” can be used to modify an adjective or adverb phrase, giving the example of “how gratefully to acknowledge the gift.” That phrase asks how grateful your acknowledgment should be, not how to make your acknowledgment grateful.
Sometimes splitting an infinitive offends the ear. Sometimes not doing so offends the ear or alters the meaning of the sentence. It’s a question of judgment. Cultivate your judgment.