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2 Answers

I also don't know what you mean by the golden rule for an antiderivative. However, one of the most useful formulas when taking the antiderivative of a single term of the form xis

∫xndx = xn+1/(n+1).



By "golden rule" you may be thinking of the Fundamental Theorem of Calculus, which states that the derivative of the integral of a function is just equal to the original function (they cancel out). On the other hand, the integral of the derivative of a function is equal to the value of the function at the upward bound of the integral, minus the value of the function at the lower bound of the integral. For example, taking the integral from 0 to 1 of df(x)/dx gives you f(1) - f(0). Therefore, even though derivative and anti-derivative are reverse processes in a sense, taking the derivative of the integral gives you very different results from taking the integral of a derivative.