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  2. List of integrals of irrational functions - Wikipedia

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

    For a complete list of integral functions, see lists of integrals. Throughout this article the constant of integration is omitted for brevity. Integrals involving r = √ a 2 + x 2

  3. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    An even larger, multivolume table is the Integrals and Series by Prudnikov, Brychkov, and Marichev (with volumes 1–3 listing integrals and series of elementary and special functions, volume 4–5 are tables of Laplace transforms).

  4. Trigonometric substitution - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_substitution

    For a definite integral, the bounds change once the substitution is performed and are determined using the equation = ⁡, with values in the range < <. Alternatively, apply the boundary terms directly to the formula for the antiderivative.

  5. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    This visualization also explains why integration by parts may help find the integral of an inverse function f −1 (x) when the integral of the function f(x) is known. Indeed, the functions x(y) and y(x) are inverses, and the integral ∫ x dy may be calculated as above from knowing the integral ∫ y dx.

  6. List of integrals of trigonometric functions - Wikipedia

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

    For the special antiderivatives involving trigonometric functions, see Trigonometric integral. [ 1 ] Generally, if the function sin ⁡ x {\displaystyle \sin x} is any trigonometric function, and cos ⁡ x {\displaystyle \cos x} is its derivative,

  7. Multiple integral - Wikipedia

    en.wikipedia.org/wiki/Multiple_integral

    Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane which contains its domain. [1]

  8. List of integrals of rational functions - Wikipedia

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

    Integrands of the form (d + e x) m (a + b x + c x 2) p when b 2 − 4 a c = 0 [ edit ] 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 and p toward 0.

  9. Order of integration (calculus) - Wikipedia

    en.wikipedia.org/wiki/Order_of_integration...

    The integral can be reduced to a single integration by reversing the order of integration as shown in the right panel of the figure. To accomplish this interchange of variables, the strip of width dy is first integrated from the line x = y to the limit x = z , and then the result is integrated from y = a to y = z , resulting in: