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It was first discovered simultaneously by Isaac newton and another mathematician named Gottfried Leibniz. (see related link). However, the notation that we use today is for the most part that of Leibniz. As far as development, it is still an actively researched field of mathematics with thousands of contributors.

Also, integral calculus is often attributed to Archimedes of Syracuse (c. 250 BC), having been largely ignored after him.

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