Combinations of powers, exponentials, and logarithms
Victor H. Moll · 2014
The uninitiated reader of the table of integrals by I. S. Gradshteyn and I. M. Ryzhik [40] will surely be puzzled by choice of integrands. In this note we provide an elementary proof of the evaluation 4.353.3∫ 1 (ax+ n+ 1)xneax lnx dx = ea n∑ (−1)k−1 n! (n− k)!ak+1 + (−1) n n!