Definiting the slope y/x as a new variable z, the variable transformation from (x, y) to (x, z) is presented. It is found that such a set of new variable (x,z) almost makes the singular integrals dependent on the distance reciprocal r in potential fields become non-singular. By using the new variable, analytical expressions concerning common singular integrals in potential fields are derived as well. Numerical results show that the numerical integration con verges very fast with the method.