d. The Epdochal Camouflage of Ideas in Leibniz' Notation

The designation of antiderivatives as indefinite integrals and of derivatives as differential quotients has had two important consequences.

On the one hand, that notation camouflages the fundamental result of calculus and ( as will be seen in Chapter VIII) some difficult operations on derivatives as truisms. In past centuries, undoubtedly, this very camouflage secured the basic ideas of calculus acceptance by many who would have shunned a method obviously surpassing their understanding. Without the protection of a plausible appearance, those great ideas might not even have survived - just as some bright butterflies would perish if, with folded wings, they did not assume the appearance of inconspicuous leaves.

On the other hand, the traditional notation has made it difficult to understand calculus. The symbol $\int_a^b f(x) dx$, while objectionable on account of its dummy part, is at least reminiscent of the sums  of products as whose limit the integral is defined. The symbol $\int f(x) dx$, however, not only fails to remind one of the inverse of derivation - the operation he has to perform - but strongly suggests sums of products (the same sums of which the integral is reminiscent) with which the antiderivative concept has absolutely nothing to do.

The traditional symbols, introduced essentially by Leibniz, make it hard to distinguish definitions from theorems, technical difficulties from profound problems, and minor results from tremendous discoveries.

All in all, Leibniz' notation accounts for what, from a sociological point of view, are the two most striking facts in the history of calculus: that for centuries the use  of that great theory has been enormously wide, and that even today its use is often mechanical.''

Taken from Calculus.