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This is a tricky domain because, unlike simple arithmetic, to solve a calculus problem - and in particular to perform integration - you have to be smart about which integration technique should be used: integration by partial fractions, integration by parts, and so on. ↗
If you just have a single problem to solve, then fine, go ahead and use a neural network. But if you want to do science and understand how to choose architectures, or how to go to a new problem, you have to understand what different architectures can and cannot do. ↗