Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be integrated on a computer. However, that method treats integration as equivalent to natural language translation and does not reflect mathematical information. In this study, we adjusted the learning model to take mathematical information into account and developed a wide range of learning models that learn the order of numerical operations more robustly. In this way, we achieved a 98.80% correct answer rate with symbolic integration, a higher rate than that of any existing method. We judged the correctness of the integration based on whether the derivative of the primitive function was consistent with the integrand. By building an integrated model based on this strategy, we achieved a 99.79% rate of correct answers with symbolic integration.

中文翻译：

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通过整合具有不同优点和缺点的学习模型进行符号集成

积分是必不可少的，不仅在数学上，而且在其他许多领域也是如此。最近开发了一种深度学习方法，该方法表明它能够集成以前无法在计算机上集成的数学函数。但是，该方法将集成视为等同于自然语言翻译，并且不反映数学信息。在本研究中，我们调整了学习模型以考虑数学信息，并开发了范围更广的学习模型，可以更可靠地学习数字运算的顺序。这样，我们通过符号集成获得了98.80％的正确答案率，这比任何现有方法都更高。我们根据原始函数的导数是否与被积分数一致来判断积分的正确性。通过基于此策略构建集成模型，我们通过符号集成获得了正确答案的99.79％的正确率。