International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 2, Pages 405-408
doi:10.1155/S0161171294000566
Certain integrals involving logarithmic and exponential functions
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Received 20 September 1991; Revised 5 May 1993
Copyright © 1994 M. Aslam Chaudhry and M. Ahmad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper we have evaluated the integrals∫0∞xn−1lnxexp(−ax−bx−1)dxand∫0∞xn−2(ax2−b)(lnx)2exp(−ax−bx−1)dxfor all n=1,2,3,…. Some applications of the results are discussed and an open problem is posed.