Exercise 22, § 1

Let $f$ and $g$ be two relatively prime polynomials (with complex coefficients), the degree of $f$ being strictly less than that of $g$. Let K be a subfield of $\mathbf{C}$ containing the coefficients of $f$ and $g$, and such that $g$ is irreducible over K. For there to be a primitive of $f/g$ of the form $\sum_i a_i \log u_i$, where the $a_i$ are constants belonging to K and the $u_i$ are irreducible polynomials over K, it is necessary and sufficient that $f = c g'$, where $c$ is a constant in K.