A result regarding monotonicity of the Gamma function

In this paper we analyze the monotony of the function ln Γ(x)ln (x2+τ)-ln (x+τ)${{{\rm{ln}}\,\Gamma ({\rm{x}})} \over {{\rm{ln}}\,({\rm{x}}^2 + \tau) - {\rm{ln}}\,({\rm{x}} + \tau)}}$ , for τ > 0. Such functions have been used from different authors to obtain inequalities concerning the gamma function.