In looking for a compact way of writing down the partial fraction formula in general, with repeated factors, I noticed how the expansion of a determinant by its top or bottom row suggested a method. The following gives a formula perfectly easy to write down in any given case where the factors of the denominator of the fraction are known. Incidentally it gives, as a determinant, the integral of a rational fraction f(x)/Q(x) where f(x) and Q(x) are polynomials, Q(x) having higher order.