def test_subterm(u, u_diff):
substituted = simplify(integrand / u_diff)
if symbol not in substituted.free_symbols:
# replaced everything already
return False
substituted_ = substituted.subs(u, u_var).cancel()
if symbol not in substituted_.free_symbols:
_, denom = integrand.as_numer_denom()
_, denom2 = substituted_.as_numer_denom()
denom2 = denom2.subs(u_var, u)
constant = denom/denom2
if symbol not in constant.free_symbols:
return (constant, substituted_ / constant)
if u.is_polynomial(symbol):
h = Poly(u, symbol)
if h.degree() == 1 and h.nth(0) != 0:
t = (u_var - h.nth(0)) / h.nth(1)
substituted_ = simplify(integrand.subs(symbol, t))
args = list(get_args(substituted_, u_var))
if symbol not in substituted_.free_symbols and len(args) == 1 and args[0] == u_var:
return (1/h.nth(1), substituted_)
return False
