DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly((t**2 + 1), t)], 'Tfuncs': [Lambda(x, tan(x))]})
integrate_hypertangent(Poly(-(t**2 - 1), t), Poly(t**2 + 1, t), DE) fails because 
p = (t**2 - 1)/ (t**2 + 1).as_poly(t) returns None 
I'll pass numerator and denominator of p separately to overcome this issue