  We present an algorithm to compute the annihilator of (i.e., the linear
differential equations for) the logarithm of a polynomial in the ring of
differential operators with polynomial coefficients. The algorithm consists of
differentiation with respect to the parameter s of the annihilator of f^s for a
polynomial f and quotient computation. More generally, the annihilator of
f^s(log f)^m for a complex number s and a positive integer m can be computed,
which constitutes what is called a holonomic system in D-module theory. This
enables us to compute a holonomic system for the integral of a function
involving the logarithm of a polynomial by using integration algorithm for
D-modules.
