  We present an efficient approach to evaluate two-center two-electron
integrals with exponential functions and with an arbitrary polynomial in
electron-nucleus and electron-electron distances. We show that the master
integral with the single negative power of all distances can be obtained from
the second order differential equation in $r$, the distance between nuclei. For
particular values of nonlinear parameters corresponding to the James-Coolidge
basis, we find a fully analytic expression. For integrals with arbitrary powers
of all distances, we construct recursion relations which starts from the master
integral. The presented approach opens a window for the high precision
calculations of relativistic effects in diatomic molecules.
