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  2. List of integrals of exponential functions - Wikipedia

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

    The following is a list of integrals of exponential functions. For a complete list of integral functions, please see the list of integrals . Indefinite integral

  3. Exponential integral - Wikipedia

    en.wikipedia.org/wiki/Exponential_integral

    In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument .

  4. Fractional calculus - Wikipedia

    en.wikipedia.org/wiki/Fractional_calculus

    Fractional calculus was introduced in one of Niels Henrik Abel's early papers [3] where all the elements can be found: the idea of fractional-order integration and differentiation, the mutually inverse relationship between them, the understanding that fractional-order differentiation and integration can be considered as the same generalized ...

  5. List of integrals of rational functions - Wikipedia

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

    The resulting integrands are of the same form as the original integrand, so these reduction formulas can be repeatedly applied to drive the exponents m, p and q toward 0. These reduction formulas can be used for integrands having integer and/or fractional exponents.

  6. Integral - Wikipedia

    en.wikipedia.org/wiki/Integral

    A line integral (sometimes called a path integral) is an integral where the function to be integrated is evaluated along a curve. [42] Various different line integrals are in use. In the case of a closed curve it is also called a contour integral. The function to be integrated may be a scalar field or a vector field.

  7. Common integrals in quantum field theory - Wikipedia

    en.wikipedia.org/wiki/Common_integrals_in...

    1.3 Integrals of exponents and even powers of x. 1.4 Integrals with a linear term in the argument of the exponent. ... As an example consider the integral [1]: ...

  8. Integral element - Wikipedia

    en.wikipedia.org/wiki/Integral_element

    In commutative algebra, an element b of a commutative ring B is said to be integral over a subring A of B if b is a root of some monic polynomial over A. [1]If A, B are fields, then the notions of "integral over" and of an "integral extension" are precisely "algebraic over" and "algebraic extensions" in field theory (since the root of any polynomial is the root of a monic polynomial).

  9. Integration using Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Integration_using_Euler's...

    In integral calculus, Euler's formula for complex numbers may be used to evaluate integrals involving trigonometric functions. Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely e i x {\displaystyle e^{ix}} and e − i x {\displaystyle e^{-ix}} and then integrated.

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