Evaluation ofSome Non-Elementary Integrals Involving Sine, Cosine, Exponential And Logarithmic Integrals: Part Ii

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.