The word "absentmindedly" is correct and usable in written English.
You can use it to describe an action that was done without due attention or care. For example, "She absentmindedly dropped the bowl and it shattered on the ground."
I can't even get through an episode of Better Call Saul without absentmindedly checking my emails.
She cocks it absentmindedly between verses, with the expression of a love-struck school girl (and that voice, like glass).
During a medal ceremony, law-enforcement officers gaze absentmindedly at the French Prime Minister.
She wrote back: I have a precise memory of sitting in a hotel room in December of 2007 at Charles De Gaulle, absentmindedly drawing notes in on GarageBand via my laptop.
Their legs are forever carrying on like a pair of compasses which someone is absentmindedly twiddling.
My father took it absentmindedly, read it absentmindedly, and returned it to me absentmindedly, saying: "Where did you copy this from?" Then he went on talking to my mother in a lowered voice about his important and remote affairs.
She breathed on one of her two 24k.-gold glue-on fingernails and polished it absentmindedly.
Even my cats have gotten into the spirit of the season, stuffing themselves with as much cat food as I can absentmindedly give them.
The alternative comedian Maria Bamford's new Web series "Ask My Mom!" is a fake-advice show in which Bamford poses viewer-submitted questions to her seventy-year-old mother, Marilyn — about sex, or religion, or raising kids — and then impersonates her mom absentmindedly responding as she goes about her household routines.
The writer begins with a story about an otherwise harmonious couple who separated violently when the wife absentmindedly gave a Greek coin - her husband's lucky drachma - along with some ordinary coins that were lying around, to a beggar.
The Washington Post reported on the time he "went for a swim, then searched for his clothes and realized that he had absentmindedly undressed in the ladies' bathhouse".
