Certain integrals involving logarithmic and exponential functions

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.

Keywords

• Macdonald functions
• logarithmic and exponential function
• statistical inference theory.