What is the advantage of the blisk design in the new Trent XWB engine? What advantage does the "blisk" or "bladed disk" type rotor have over the usual rotor system?
Since the blades and rotor disc are a single piece, there are no additional fittings (bolts, screws etc) to attach the blades reducing complexity and weight.  The blade root joints are also a source of failure through manufacturing defects and fatigue cracks.

The disadvantage is that any damage to a blade requires the entire assembly to be replaced rather than a single blade.