is exact if and only if A has an antiderivative (but not necessarily one in terms of elementary functions). If A has an antiderivative and let Q be an antiderivative of A so d Q d x = A , then A ( x ) d x obviously satisfies the condition for exactness. If A does not have an antiderivative, then we cannot write d Q = d Q d x d x with A = d Q d x for a differentiable function Q so A ( x ) d x is inexact.