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  2. 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,

  3. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    Then | | = ⁡ (()) +, where sgn(x) is the sign function, which takes the values −1, 0, 1 when x is respectively negative, zero or positive. This can be proved by computing the derivative of the right-hand side of the formula, taking into account that the condition on g is here for insuring the continuity of the integral.

  4. Trigonometric integral - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_integral

    Si(x) (blue) and Ci(x) (green) shown on the same plot. Sine integral in the complex plane, plotted with a variant of domain coloring. Cosine integral in the complex plane. Note the branch cut along the negative real axis. In mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions.

  5. List of integrals of hyperbolic functions - Wikipedia

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

    3.1 Integrals of hyperbolic tangent, cotangent, secant, cosecant functions 3.2 Integrals involving hyperbolic sine and cosine functions 3.3 Integrals involving hyperbolic and trigonometric functions

  6. Integration using Euler's formula - Wikipedia

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

    At this point we can either integrate directly, or we can first change the integrand to 2 cos 6x − 4 cos 4x + 2 cos 2x and continue from there. Either method gives Either method gives ∫ sin 2x cos ⁡ 4 x d x = − 1 24 sin ⁡ 6 x + 1 8 sin ⁡ 4 x1 8 sin ⁡ 2 x + C . {\displaystyle \int \sin ^{2}x\cos 4x\,dx=-{\frac {1}{24 ...

  7. List of integrals of inverse hyperbolic functions - Wikipedia

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

    For a complete list of integral formulas, see lists of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration. For each inverse hyperbolic integration formula below there is a corresponding formula in the list of integrals of inverse trigonometric functions.

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    $220 at Amazon. See at Le Creuset. 2024 F&W Best New Chef Leina Horii of Kisser in Nashville thinks that a large, seasoned cast iron skillet makes for a fantastic (albeit, heavy) holiday gift ...

  9. Tangent half-angle substitution - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle...

    Leonhard Euler used it to evaluate the integral / (+ ⁡) in his 1768 integral calculus textbook, [3] and Adrien-Marie Legendre described the general method in 1817. [ 4 ] The substitution is described in most integral calculus textbooks since the late 19th century, usually without any special name. [ 5 ]