ABSTRACT
The classical table of integrals by I. Gradshteyn and I. M. Ryzhik [40] contains many entries from the family∫ 1
R(x) lnx dx (12.1.1)
where R is a rational function. For instance, the elementary integral 4.231.1∫ 1 0
lnx dx
1 + x = −π
12 , (12.1.2)
is evaluated simply by expanding the integrand in a power series. In [2], the first author and collaborators have presented a systematic study of integrals of the form
hn,1(b) =
ln t dt
(1 + t)n+1 , (12.1.3)
as well as the case in which the integrand has a single purely imaginary pole
hn,2(a, b) =
ln t dt
(t2 + a2)n+1 . (12.1.4)
The work presented here deals with integrals where the rational part of the integrand is allowed to have arbitrary complex poles.
