Are you 100% sure that p can always be written as a polynomial in t and 1/t? This seems to fail with

```py
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)
```