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from sympy.sandbox.indexed_integrals import IndexedIntegral
from sympy.core.symbol import symbols
from sympy.functions.elementary.trigonometric import (cos, sin)
from sympy.tensor.indexed import (Idx, IndexedBase)
def test_indexed_integrals():
A = IndexedBase('A')
i, j = symbols('i j', integer=True)
a1, a2 = symbols('a1:3', cls=Idx)
assert isinstance(a1, Idx)
assert IndexedIntegral(1, A[i]).doit() == A[i]
assert IndexedIntegral(A[i], A[i]).doit() == A[i] ** 2 / 2
assert IndexedIntegral(A[j], A[i]).doit() == A[i] * A[j]
assert IndexedIntegral(A[i] * A[j], A[i]).doit() == A[i] ** 2 * A[j] / 2
assert IndexedIntegral(sin(A[i]), A[i]).doit() == -cos(A[i])
assert IndexedIntegral(sin(A[j]), A[i]).doit() == sin(A[j]) * A[i]
assert IndexedIntegral(1, A[a1]).doit() == A[a1]
assert IndexedIntegral(A[a1], A[a1]).doit() == A[a1] ** 2 / 2
assert IndexedIntegral(A[a2], A[a1]).doit() == A[a1] * A[a2]
assert IndexedIntegral(A[a1] * A[a2], A[a1]).doit() == A[a1] ** 2 * A[a2] / 2
assert IndexedIntegral(sin(A[a1]), A[a1]).doit() == -cos(A[a1])
assert IndexedIntegral(sin(A[a2]), A[a1]).doit() == sin(A[a2]) * A[a1]
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