  In this work we propose a novel approach to integrate the Lane-Emden
equations for relativistic anisotropic polytropes. We take advantage of the
fact that Gravitational Decoupling allows to decrease the number of degrees of
freedom once a well known solution of the Einstein field equations is provided
as a seed so after demanding the polytropic equation for the radial pressure
the system is automatically closed. The approach not only allows to extend both
isotropic or anisotropic known solutions but simplifies the computation of the
Tolman mass whenever the Minimal Geometric Deformation is considered given that
the $g_{tt}$ component of the metric remains unchanged. We illustrate how the
the method works by analyzing the solutions obtained from Tolman IV, Durgapal
IV and Wymann IIa isotropic systems as a seed for the integration.
