Thermodynamic and kinetic aspects of crystalline (c-KTP) and amorphous (a-KTP) ketoprofen dissolution in water have been investigated by molecular dynamics simulation focusing on free energy properties. Absolute free energies of all relevant species and phases have been determined by thermodynamic integration on a novel path, first connecting the harmonic to the anharmonic system Hamiltonian at low T and then extending the result to the temperature of interest. The free energy required to transfer one ketoprofen molecule from the crystal to the solution is in fair agreement with the experimental value. The absolute free energy of the amorphous form is 19.58 kJ/mol higher than for the crystal, greatly enhancing the ketoprofen concentration in water, although as a metastable species in supersaturated solution. The kinetics of the dissolution process has been analyzed by computing the free energy profile along a reaction coordinate bringing one ketoprofen molecule from the crystal or amorphous phase to the solvated state. This computation confirms that, compared to the crystal form, the dissolution rate is nearly 7 orders of magnitude faster for the amorphous form, providing one further advantage to the latter in terms of bioavailability. The problem of drug solubility, of great practical importance, is used here as a test bed for a refined method to compute absolute free energies, which could be of great interest in biophysics and drug discovery in particular.