Multicenter integrals over noninteger n Slater type orbitals with integer and noninteger, values of indices u of screened Coulomb type potentials, f(u)(eta, r) = r(u-1) e(-etar), and their first and second derivatives with respect to Cartesian coordinates of the nuclei of a molecule are described. Using complete orthonormal sets of Psi(alpha) exponential type orbitals and rotation transformation of two-center overlap integrals, these integrals are expressed through the noncentral potential functions depending on the molecular auxiliary functions A(k) and B-k. The series expansion formulas derived for molecular integrals of screened Coulomb potentials and their derivatives are especially useful for the computation of multicenter electronic attraction, electric field, and electric field gradient integrals. The convergence of series is tested for arbitrary values of parameters of potentials and orbitals. (C) 2004 American Institute of Physics.