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It is well known that the third-order Lorentz-Dirac equation admits runawaysolutions wherein the energy of the particle grows without limit, even whenthere is no external force. These solutions can be denied simply on physicalgrounds, and on the basis of careful analysis of the correspondence betweenclassical and quantum theory. Nonetheless, one would prefer an equation thatdid not admit unphysical behavior at the outset. Such an equation - anintegro-differential version of the Lorentz-Dirac equation - is currentlyavailable either in 1 dimension only, or in 3 dimensions only in thenon-relativistic limit.  It is shown herein how the Lorentz-Dirac equation may be integrated withoutapproximation, and is thereby converted to a second-order integro-differentialequation in 3D satisfying the above requirement. I.E., as a result, noadditional constraints on the solutions are required because runaway solutionsare intrinsically absent. The derivation is placed within the historicalcontext established by standard works on classical electrodynamics by Rohrlich,and by Jackson.Comment: (updated journal reference & email address

Relativistic integro-differential form of the Lorentz-Dirac equation in 3D without runaways