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Keywords:
integration; primitive; rational function; Wronskian
integration; primitive; rational function; Wronskian
Summary:
Let $P$ and $Q$ be polynomials in one variable with complex coefficients and let $n$ be a natural number. Suppose that $Q$ is not constant and has only simple roots. Then there is a rational function $\varphi$ with $\varphi '=P/Q^{n+1}$ if and only if the Wronskian of the functions $Q',(Q^2)',\ldots,(Q^n)',P$ is divisible by $Q$.
References:
[1] G. H. Hardy: The integration of functions of a single variable. Second edition, Cambridge, 1928.
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