This work aims at the evaluation of a univariate integral based on one node fluctuation free integration and by using exponential weight function. This is the companion of a paper presenting fundamental aspects of one node integration. In contrast to companion paper, this paper deals with more than one conditions. We construct weight function generating subspace which has three parts: (1) Eigenpolynomials, (2) Principle polynomials, (3) Unaffecting polynomials. The exponential weight function is used as the most important agent to this end. An extension to multinode case is also given.