ABSTRACT

The table of integrals by I. S. Gradshteyn and I. M. Ryzhik [40] contains a large selection of definite integrals of the form

R(x) lnm x dx, (2.1.1)

where R(x) is a rational function, a, b ∈ R+ and m ∈ N. We call integrals of the form (2.1.1) elementary logarithmic integrals. The goal of this note is to present methods to evaluate them. We may assume that a = 0 using

R(x) lnm x dx =

R(x) lnm x dx− ∫ a 0

R(x) lnm x dx. (2.1.2)

Section 2.2 describes the situation when R is a polynomial. Section 2.3 presents the case in which the rational function has a single simple pole. Finally section 2.4 considers the case of multiple poles.