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  2. List of integrals of inverse trigonometric functions - Wikipedia

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

    The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions.For a complete list of integral formulas, see lists of integrals.

  3. 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]

  4. List of integrals of trigonometric functions - Wikipedia

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

    Generally, if the function ⁡ is any trigonometric function, and ⁡ is its derivative, ∫ a cos ⁡ n x d x = a n sin ⁡ n x + C {\displaystyle \int a\cos nx\,dx={\frac {a}{n}}\sin nx+C} In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration .

  5. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_trigonometric...

    The points labelled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point. Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin.

  6. Antiderivative - Wikipedia

    en.wikipedia.org/wiki/Antiderivative

    The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.

  7. Differentiation of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Differentiation_of...

    The following derivatives are found by setting a variable y equal to the inverse trigonometric function that we wish to take the derivative of. Using implicit differentiation and then solving for dy/dx, the derivative of the inverse function is found in terms of y.

  8. NYT ‘Connections’ Hints and Answers Today, Wednesday, January 15

    www.aol.com/nyt-connections-hints-answers-today...

    Today's NYT Connections puzzle for Wednesday, January 15, 2025The New York Times

  9. Integral of secant cubed - Wikipedia

    en.wikipedia.org/wiki/Integral_of_secant_cubed

    where is the inverse Gudermannian function, the integral of the secant function. There are a number of reasons why this particular antiderivative is worthy of special attention: The technique used for reducing integrals of higher odd powers of secant to lower ones is fully present in this, the simplest case. The other cases are done in the same ...