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  2. 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.

  3. 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.

  4. Integral of the secant function - Wikipedia

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

    Twice the area of the purple triangle is the stereographic projection s = tan ⁠ 1 / 2 ⁠ ϕ = tanh ⁠ 1 / 2 ⁠ ψ. The blue point has coordinates (cosh ψ, sinh ψ). The red point has coordinates (cos ϕ, sin ϕ). The purple point has coordinates (0, s). The integral of the hyperbolic secant function defines the Gudermannian function:

  5. 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 ...

  6. Trigonometric integral - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_integral

    Integral sine in the complex plane, plotted with a variant of domain coloring. Integral cosine 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.

  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.

  8. 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 and and then integrated.

  9. 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.