NEC-LIST: Quick method on Complex Exponential Integration

Hi,

My study region is Wire Surface Junction problems in
electromagnetics. I have a question to ask you.

There is a Complex Exponential Integration written in language
MATHMATICS 3.0. It is as following,

    Integrate[Exp[-I k u]/u,{u,u1,u2}] (1)

where u1,u2 are complex variables.

Equation (1) also can be,

    Integrate[(Exp[-I k u]-1)/u,{u,u1,u2}]+Log[u2/u1] (2)

Singularity may be occurred in (1) is abandoned in (2).

However, to calculate (2) is too slowly. I know from reference in the
following that equation (1) must have a quick method to calculate. It
is a subroutine named 'EXPJ'. Would anyone who are kind enough tell me
about the idea on the quick method please?

Reference

J.H.Richmond and N.H.Geary "Mutual Impedance of Nonplanar -Skew
Sinusoidal Dipoles", IEEE Trans. on AP. Vol.23 No.3 May 1975 pp.412

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