  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.
