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  2. Integral of the secant function - Wikipedia

    en.wikipedia.org/wiki/Integral_of_the_secant...

    A standard method of evaluating the secant integral presented in various references involves multiplying the numerator and denominator by sec θ + tan θ and then using the substitution u = sec θ + tan θ. This substitution can be obtained from the derivatives of secant and tangent added together, which have secant as a common factor. [6]

  3. Integral of secant cubed - Wikipedia

    en.wikipedia.org/wiki/Integral_of_secant_cubed

    Just as the integration by parts above reduced the integral of secant cubed to the integral of secant to the first power, so a similar process reduces the integral of higher odd powers of secant to lower ones. This is the secant reduction formula, which follows the syntax:

  4. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

  5. 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,

  6. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.

  7. List of integrals of exponential functions - Wikipedia

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

    For a complete list of integral functions, please see the list of integrals. Indefinite integral. Indefinite integrals are antiderivative functions.

  8. 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.

  9. Tangent half-angle substitution - Wikipedia

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

    The substitution is described in most integral calculus textbooks since the late 19th century, usually without any special name. [5] It is known in Russia as the universal trigonometric substitution , [ 6 ] and also known by variant names such as half-tangent substitution or half-angle substitution .