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  2. Integration by substitution - Wikipedia

    en.wikipedia.org/wiki/Integration_by_substitution

    Calculus. In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, [ 1] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards."

  3. Antiderivative - Wikipedia

    en.wikipedia.org/wiki/Antiderivative

    The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a function f is a differentiable function F whose derivative is equal to the original function f.

  4. Nonelementary integral - Wikipedia

    en.wikipedia.org/wiki/Nonelementary_Integral

    Nonelementary integral. In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential, trigonometric, and logarithmic functions using field ...

  5. List of integrals of exponential functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    (Note that the value of the expression is independent of the value of n, which is why it does not appear in the integral.) ∫ x x ⋅ ⋅ x ⏟ m d x = ∑ n = 0 m ( − 1 ) n ( n + 1 ) n − 1 n !

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  8. Morera's theorem - Wikipedia

    en.wikipedia.org/wiki/Morera's_theorem

    Morera's theorem states that a continuous, complex -valued function f defined on an open set D in the complex plane that satisfies for every closed piecewise C1 curve in D must be holomorphic on D . The assumption of Morera's theorem is equivalent to f locally having an antiderivative on D . The converse of the theorem is not true in general.

  9. Nvidia, ASML, and TSMC stocks got hammered — here's why - AOL

    www.aol.com/finance/nvidia-asml-tsmc-stocks...

    Nvidia sales to China decreased as a percentage of total data center revenue from 19% in fiscal year 2023 to 14% in fiscal year 2024. ASML stock saw the steepest decline on Wednesday, falling more ...