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# sympy.integrals.risch.integrate_hypertangent_polynomial

All Samples(6)  |  Call(4)  |  Derive(0)  |  Import(2)

```"""Most of these tests come from the examples in Bronstein's book."""
from sympy import (Poly, I, S, Function, log, symbols, exp, tan, sqrt,
Symbol, Lambda, sin, cos, Eq, Piecewise, factor)
from sympy.integrals.risch import (gcdex_diophantine, frac_in, as_poly_1t,
derivation, splitfactor, splitfactor_sqf, canonical_representation,
```
```def test_integrate_hypertangent_polynomial():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
assert integrate_hypertangent_polynomial(Poly(t**2 + x*t + 1, t), DE) == \
(Poly(t, t), Poly(x/2, t))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(a*(t**2 + 1), t)]})
assert integrate_hypertangent_polynomial(Poly(t**5, t), DE) == \
```

```"""Most of these tests come from the examples in Bronstein's book."""
from sympy import (Poly, I, S, Function, log, symbols, exp, tan, sqrt,
Symbol, Lambda, sin, cos, Eq, Piecewise, factor)
from sympy.integrals.risch import (gcdex_diophantine, frac_in, as_poly_1t,
derivation, splitfactor, splitfactor_sqf, canonical_representation,
```
```def test_integrate_hypertangent_polynomial():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
assert integrate_hypertangent_polynomial(Poly(t**2 + x*t + 1, t), DE) == \
(Poly(t, t), Poly(x/2, t))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(a*(t**2 + 1), t)]})
assert integrate_hypertangent_polynomial(Poly(t**5, t), DE) == \
```