A verb that follows pleje always uses the infinitive (kind of like "I love to swim" in English). In Danish "pleje" is a verb (like in past tense plejede at translates to used to but in Danish this form is also used in present tense) and not being a modal verb, the second verb usually needs to change for it to sound right (in this case the "at-infinitive"). Sorry if that was a bit confusing, but basically "pleje" is a verb and so, in this case, the secondary verb that follows it uses the at-infinitve
You can say "He is used to swimming" in English, but that's slightly different.
English simply doesn't have a common construction that matches the use of "at pleje" well, but you might find a way if you translate pleje: it means "to take care of" or "to tend to". And there you go: you could say "He tends to swim." A bit old-fashioned, but it's an okay translation.