  Active particles moving through fluids generate disturbance flows due to
their activity. For simplicity, the induced flow field is often modeled by the
leading terms in a far-field approximation of the Stokes equations, whose
coefficients are the force, torque and stresslet (zeroth and first-order force
moments) of the active particle. This level of approximation is quite useful,
but may also fail to predict more complex behaviors that are observed
experimentally. In this study, to provide a better approximation, we evaluate
the contribution of the second-order force moments to the flow field and, by
reciprocal theorem, present explicit formulas for the stresslet dipole, rotlet
dipole and potential dipole for an arbitrarily-shaped active particle. As
examples of this method, we derive modified Fax\'en laws for active spherical
particles and resolve higher-order moments for active rod-like particles.
