Abstract:
The non-elementary integrals Siβ,α=∫[sin(λxβ)/(λxα)]dx,β⩾1,α>β+1 and Ciβ,α=∫[cos(λxβ)/(λxα)]dx,β⩾1,α>2β+1, where {β,α}∈R, are evaluated in terms of the hypergeometric function 2F3. On the other hand, the exponential integral Eiβ,α=∫(eλxβ/xα)dx,β⩾1,α>β+1 is expressed in terms of 2F2. The method used to evaluate these integrals consists of expanding the integrand as a Taylor series and integrating the series term by term.
Keywords:
Non-elementary integrals, Sine integral, Cosine integral, Exponential integral, Logarithmic integral, Hyperbolic sine integral, Hyperbolic cosine integral, Hypergeometric functions.
Bibliographic databases:
Document Type:
Article
Language: English
Citation:
Victor Nijimbere, “Evaluation of some non-elementary integrals involving sine, cosine, exponential and logarithmic integrals: part II”, Ural Math. J., 4:1 (2018), 43–55