EVALUATION OF SOME NON-ELEMENTARY INTEGRALS INVOLVING SINE, COSINE, EXPONENTIAL AND LOGARITHMIC INTEGRALS: PART II

摘要

The non-elementary integrals (mbox{Si}_{eta,lpha}=int [sin{(lambda x^eta)}/(lambda x^lpha)] dx,)  (etage1,) (lpha>eta+1) and (mbox{Ci}_{eta,lpha}=int [cos{(lambda x^eta)}/(lambda x^lpha)] dx,)  (etage1,)  (lpha>2eta+1,) where ({eta,lpha}inmathbb{R},) are evaluated in terms of the hypergeometric function  (_{2}F_3). On the other hand, the exponential integral (mbox{Ei}_{eta,lpha}=int (e^{lambda x^eta}/x^lpha) dx,)  (etage1,)  (lpha>eta+1) is expressed in terms of (_{2}F_2). The method used to evaluate these integrals consists of expanding the integrand  as a Taylor series and integrating the series term by term.