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The following is a table of derivatives of some basic functions: f(x) f (x) x is the variable of integration. To verify. ∫ xexdx = xex − ex + C, Implicit Differentiation and Related Rates Indefinite Integrals and Substitutions There are two more basic ways to change a function. apparent that the function you wish to integrate is a derivative in some straightforward way. For example, faced with. ∫ x10 dx. Limit is a fundamental concept in calculus. It is used when we consider differentiation (to define derivatives) and integration (to define definite integrals). Differentiation Formulas d dx k = 0. (1) d dx. [f(x) ± g(x)] = f (x) ± g (x) Integration Formulas. ∫ dx = x + C. (1). ∫ xn dx = xn+1. Common Derivatives and Integrals. Visit tutorial.math.lamar.edu for a complete set of Calculus I Derivatives. Basic Properties/Formulas/Rules. For both Differentiation and Integration these are usually 3 of the 12 students elected to take Differentiation basic ideas of calculus. Mathematics Learning Centre. Introduction to Integration. Part 1: Anti-Differentiation. Mary Barnes c@1999. University of Sydney