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# sympy.integrals.risch.integrate_primitive

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```"""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_primitive():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)],
'Tfuncs': [log]})
assert integrate_primitive(Poly(t, t), Poly(1, t), DE) == (x*log(x), -1, True)
# (x*log(x) - x, True)
assert integrate_primitive(Poly(x, t), Poly(t, t), DE) == (0, NonElementaryIntegral(x/log(x), x), False)

DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x + 1), t2)],
'Tfuncs': [log, Lambda(i, log(i + 1))]})
assert integrate_primitive(Poly(t1, t2), Poly(t2, t2), DE) == \
```
```    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x*t1), t2)],
'Tfuncs': [log, Lambda(i, log(log(i)))]})
assert integrate_primitive(Poly(t2, t2), Poly(t1, t2), DE) == \
(0, NonElementaryIntegral(log(log(x))/log(x), x), False)

```

```"""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_primitive():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)],
'Tfuncs': [log]})
assert integrate_primitive(Poly(t, t), Poly(1, t), DE) == (x*log(x), -1, True)
# (x*log(x) - x, True)
assert integrate_primitive(Poly(x, t), Poly(t, t), DE) == (0, NonElementaryIntegral(x/log(x), x), False)

DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x + 1), t2)],
'Tfuncs': [log, Lambda(i, log(i + 1))]})
assert integrate_primitive(Poly(t1, t2), Poly(t2, t2), DE) == \
```
```    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x*t1), t2)],
'Tfuncs': [log, Lambda(i, log(log(i)))]})
assert integrate_primitive(Poly(t2, t2), Poly(t1, t2), DE) == \
(0, NonElementaryIntegral(log(log(x))/log(x), x), False)

```