In-Field Integration: derivative of an element in k(t)

Determines if a given function f in k(t) there exists u in k(t)
such that Du = f. Returns q such that i = f - Dq; v, c such that
i = Dv + cDt where v, c are in k; Output -> tuple (q, v, c) if there
exists a derivative for given function in k(t) else returns None