Select the mesh, choose polygon or element mode on the sidebar, then scroll down to Smoothing Groups. Make sure the polygons you want smoothed are all selected, then use Auto-smooth. The number to the right of the button is for the smoothing threshold angle. Any two adjacent faces are put in the same smoothing group if the angle between their normals is less than the threshold angle.
You might need to fiddle around somewhat with the angle to get a good effect, and there might be a few areas here and there that need hand smoothing for the best visuals.
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