# §6.7 Integral Representations

## §6.7(i) Exponential Integrals

6.7.1, ,
6.7.3, ,
6.7.4, .

Many integrals with exponentials and rational functions, for example, integrals of the type , where is an arbitrary rational function, can be represented in finite form in terms of the function and elementary functions; see Lebedev (1965, p. 42).

## §6.7(iii) Auxiliary Functions

The path of integration does not cross the negative real axis or pass through the origin.

The first integrals on the right-hand sides apply when ; the second ones when and (in the case of (6.7.14)) .

## §6.7(iv) Compendia

For collections of integral representations see Bierens de Haan (1939, pp. 56–59, 72–73, 82–84, 121, 133–136, 155, 179–181, 223, 225–227, 230, 259–260, 374, 377, 397–398, 408, 416, 424, 431, 438–439, 442–444, 488, 496–500, 567–571, 585, 602, 638, 675–677), Corrington (1961), Erdélyi et al. (1954a, vol. 1, pp. 267–270), Geller and Ng (1969), Nielsen (1906b), Oberhettinger (1974, pp. 244–246), Oberhettinger and Badii (1973, pp. 364–371), and Watrasiewicz (1967).