The integrals in Gradshteyn and Ryzhik. Part 3: Combinations of logarithms and exponentials

Abstract

We present the evaluation of a family of exponential-logarithmic integrals. These have integrands of the form \(P(e^{tx} \cdot \ln x)\) where \(P\) is a polynomial.
The examples presented here appear in sections 4.33, 4.34 and 4.35 in the classical table of integrals by I. Gradshteyn and I. Ryzhik.