  We construct a relationship between integral and differential representation
of second-order Jordan chains. Conditions to obtain regular potentials through
the confluent supersymmetry algorithm when working with the differential
representation are obtained using this relationship. Furthermore, it is used to
find normalization constants of wave functions of quantum systems that feature
energy-dependent potentials. Additionally, this relationship is used to express
certain integrals involving functions that are solution of Schrodinger
equations through derivatives.
