Accurate evaluation of integrals with kernel 1/rx has always been a crucial issue for the development of various numerical methods,especially for the singular integrals/nearly singular integrals arising in boundary element method(BEM).In most existing methods,the integration is usually carried out over a regular domain in local coordinate system,which is independent of element shape,and thus the distortion of elements is omitted unwarily.Consequently,the performance of current methods is highly sensitive to the shape of elements.In this paper,integrals with kernel 1/rx are concerned with the following three aspects: a).the near singularity caused by distorted element shape; b).the near singularity derived from the angular direction; c).the singularity/near singularity in the radial direction.