  We study motivic Donaldson-Thomas invariants for a class of quivers with
potentials using the strategy of Behrend, Bryan, and Szendroi. This class
includes quivers with potentials arising from consistent brane tilings and
quivers with zero potential. Our construction is an alternative to the
constructions of Kontsevich and Soibelman. We construct an integration map from
the equivariant Hall algebra to the quantum torus and show that our motivic
Donaldson-Thomas invariants are images of the natural elements in the
equivariant Hall algebra. We show that the inegration map is an algebra
homomorphism and use this fact to prove the Harder-Narasimhan relation for the
motivic Donaldson-Thomas invariants.
