"mind engaging" is correct and usable in written English.
You can use it to describe something that is intellectually stimulating and thought-provoking. For example: "The professor's lectures were always mind engaging."
Paul didn't mind engaging.
His creative mind, engaging personality and boundless energy will be deeply missed.
In contrast to other creatures, an individual regarded as having mind, engaging with others in social acts, can respond to his own gestures as others respond to them thus taking on social roles and becoming an "other" in respect to himself.
"The undulating glass-and-steel structure was the largest building in the land, 40 meters tall and 400 long, the size of four football pitches, and yet the whole conveyed a sense of continuous lightness and ease, like an intelligent mind engaging effortlessly with complexity," he writes.
After 33 years of solitary confinement - 23 hours a day in a 6' by 9' jail cell with an hour a week outside - Herman was sharp in mind, engaging with questions, and deeply committed to ideologies of black liberation and freedom.
She was energetic and vibrant and kept her keen mind engaged until the end.
He never smoked, never drank, maintained a normal weight (though without vigorous exercise), kept his mind engaged.
Without it, we could not do the weekly shopping – never mind engage in a correspondence such as this.
With my senses covered and my mind engaged elsewhere, I couldn't help but think how I would feel about playing it for long stretches alone.
He sees that Shakespeare discovered how he might use analogy and metaphor as the acutest representation possible of a mind engaged in thought.
And although these moments are intermittent, they are persuasive enough to keep the eye and mind engaged in Ms. Uchizono's mysterious universe.
