The Logarithm and the Exponential Function
A good illustration of the power of the fundamental theorem (30.1.2) is shown by the theory of the logarithm. After fruitless attempts at finding a known function with derivative 1/ℐ, it was realized by mathematicians that an integral did exist (by the fundamental theorem), provided they widened the early point of view that a function had to be ‘an expression’; they then had to make a new function.
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