def ratint_ratpart(f, g, x):
    from sympy import solve

    f = Poly(f, x)
    g = Poly(g, x)

    u, v, _ = g.cofactors(g.diff())

    n = u.degree()
    m = v.degree()

    A_coeffs = [ Dummy('a' + str(n - i)) for i in range(0, n) ]
    B_coeffs = [ Dummy('b' + str(m - i)) for i in range(0, m) ]

    C_coeffs = A_coeffs + B_coeffs

    A = Poly(A_coeffs, x, domain=ZZ[C_coeffs])
    B = Poly(B_coeffs, x, domain=ZZ[C_coeffs])

    H = f - A.diff()*v + A*(u.diff()*v).quo(u) - B*u

    result = solve(H.coeffs(), C_coeffs)

    A = A.as_expr().subs(result)
    B = B.as_expr().subs(result)

    rat_part = cancel(A/u.as_expr(), x)
    log_part = cancel(B/v.as_expr(), x)

    return rat_part, log_part
Horowitz-Ostrogradsky algorithm.
dataset/ETHPy150Open sympy/sympy/sympy/integrals/rationaltools.py/ratint_ratpart