A drivetrain having an active torsional vibration damping and a method for carrying out the active torsional vibration damping, having an internal combustion engine being affected by torsional vibrations and having a crankshaft, a torsional vibration damper that is operatively connected to the crankshaft and has at least one operating point of low vibration isolation of the torsional vibrations and has a primary inertial mass associated with the crankshaft and an inertial mass associated with a gear input shaft of a gearbox, the inertial mass being rotatable relatively and limitedly with respect to the primary inertial mass against the action of a spring device. The drivetrain also includes an electric motor having a rotating mass operatively connected to the gearbox input shaft, and a control unit, the spring device being formed by linear springs, the rotating mass of the electric motor being designed as a secondary inertial mass.