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This integral has no antiderivative. But why sympy gives exception? It should just return the input as is
from sympy import *
x=symbols('x')
integrate( exp( x/ln(x) ),x)
gives
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/usr/lib/python3.11/site-packages/sympy/integrals/integrals.py", line 1567, in integrate
return integral.doit(**doit_flags)
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3.11/site-packages/sympy/integrals/integrals.py", line 612, in doit
antideriv = self._eval_integral(
^^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3.11/site-packages/sympy/integrals/integrals.py", line 955, in _eval_integral
result, i = risch_integrate(f, x, separate_integral=True,
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3.11/site-packages/sympy/integrals/risch.py", line 1829, in risch_integrate
ans, i, b = integrate_hyperexponential(fa, fd, DE, conds=conds)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3.11/site-packages/sympy/integrals/risch.py", line 1562, in integrate_hyperexponential
qa, qd, b = integrate_hyperexponential_polynomial(pp, DE, z)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3.11/site-packages/sympy/integrals/risch.py", line 1514, in integrate_hyperexponential_polynomial
va, vd = rischDE(iDta, iDtd, Poly(aa, DE.t), Poly(ad, DE.t), DE)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3.11/site-packages/sympy/integrals/rde.py", line 786, in rischDE
n = bound_degree(A, B, C, DE)
^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3.11/site-packages/sympy/integrals/rde.py", line 330, in bound_degree
n = max(n, m[0])
^^^^^^^^^^^^
TypeError: '>' not supported between instances of 'Poly' and 'int'
This integral has no antiderivative. But why sympy gives exception? It should just return the input as is
gives
Version info
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