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Showing content from https://dlmf.nist.gov/4.10 below:

§4.10 Integrals ‣ Logarithm, Exponential, Powers ‣ Chapter 4 Elementary Functions

§4.10 Integrals Contents
  1. §4.10(i) Logarithms
  2. §4.10(ii) Exponentials
  3. §4.10(iii) Compendia
§4.10(i) Logarithms

The left-hand side of (4.10.7) is a Cauchy principal value (§1.4(v)). For li ⁡ ( x ) see §6.2(i).

§4.10(ii) Exponentials

For a , b ≠ 0 ,

4.10.11 ∫ − ∞ ∞ e − c ⁢ x2 ⁢ d x = π c , ℜ ⁡ c > 0 , §4.10(iii) Compendia

Extensive compendia of indefinite and definite integrals of logarithms and exponentials include Apelblat (1983, pp. 16–47), Bierens de Haan (1939), Gröbner and Hofreiter (1949, pp. 107–116), Gröbner and Hofreiter (1950, pp. 52–90), Gradshteyn and Ryzhik (2015, Chapters 2–4), and Prudnikov et al. (1986a, §§1.3, 1.6, 2.3, 2.6).

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