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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

    This is one of several integrals usually done in a first-year calculus course in which the most natural way to proceed involves integrating by parts and returning to the same integral one started with (another is the integral of the product of an exponential function with a sine or cosine function; yet another the integral of a power of the ...

  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...

    The following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. For a complete list of antiderivative functions, see Lists of integrals.

  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. 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 .

  8. Bioche's rules - Wikipedia

    en.wikipedia.org/wiki/Bioche's_rules

    Bioche's rules, formulated by the French mathematician Charles Bioche (1859–1949), are rules to aid in the computation of certain indefinite integrals in which the integrand contains sines and cosines. In the following, () is a rational expression in ⁡ and ⁡.

  9. Trigonometric substitution - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_substitution

    Because integration above requires that / < < /, can only go from to / Neglecting this restriction, one might have picked θ {\displaystyle \theta } to go from π {\displaystyle \pi } to 5 π / 6 , {\displaystyle 5\pi /6,} which would have resulted in the negative of the actual value.