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Compute Sophisticated Holonomic Integrals
The integral of a holonomic function is always holonomic.
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DifferentialRootReduce[Exp[1/(x^3 + 1)], x]
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DifferentialRootReduce[Exp[1/(x^3 + 1)], x];

Integrate[%, x]
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DifferentialRootReduce[Exp[1/(x^3 + 1)], x];

Integrate[%, x];

D[%, x] == Exp[1/(x^3 + 1)] // FullSimplify
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