The Exponential and Trigonometric Integrals

Integrals of e qmnential and trigonometric functions appear so frequently, they have become widely tabulated (Abramowitz and Stegun 1965). These functions also arise in the inversion process for Laplace transforms. The exponential, sine, and cosine integrals are defined according to the relations  

Only the sine integral remains finite at the origin, and this information is helpful in evaluating arbitrary constants of integration. It is also important to note that Ei x) is infinite at c - oo, hence Ei(—x) is also unbounded as X -oo. These boundary values are worth listing 

Useful recipes for calculating integral functions are available in Press et al. (1988). 

Abramowitz, A., and I. A. Stegun. Handbook of Mathematical Functions. Dover Publications, Inc., New York (1965). 

Friedman. Handbook of EU tic Integrals for Engineers and Physicists. Springer-Verlag, Berlin (1954). 

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