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  2. List of integrals of inverse trigonometric functions - Wikipedia

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

    There are three common notations for inverse trigonometric functions. The arcsine function, for instance, could be written as sin −1, asin, or, as is used on this page, arcsin. For each inverse trigonometric integration formula below there is a corresponding formula in the list of integrals of inverse hyperbolic functions.

  3. 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.

  4. 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.

  5. 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 .

  6. Inverse trigonometric functions - Wikipedia

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

    Trigonometric functions of inverse trigonometric functions are tabulated below. A quick way to derive them is by considering the geometry of a right-angled triangle, with one side of length 1 and another side of length x , {\displaystyle x,} then applying the Pythagorean theorem and definitions of the trigonometric ratios.

  7. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    In particular, this explains use of integration by parts to integrate logarithm and inverse trigonometric functions. In fact, if f {\displaystyle f} is a differentiable one-to-one function on an interval, then integration by parts can be used to derive a formula for the integral of f − 1 {\displaystyle f^{-1}} in terms of the integral of f ...

  8. Tangent half-angle substitution - Wikipedia

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

    The tangent half-angle substitution relates an angle to the slope of a line. Introducing a new variable = ⁡, sines and cosines can be expressed as rational functions of , and can be expressed as the product of and a rational function of , as follows: ⁡ = +, ⁡ = +, = +.

  9. Integral of inverse functions - Wikipedia

    en.wikipedia.org/wiki/Integral_of_inverse_functions

    His second proof was geometric. If () = and () =, the theorem can be written: + =.The figure on the right is a proof without words of this formula. Laisant does not discuss the hypotheses necessary to make this proof rigorous, but this can be proved if is just assumed to be strictly monotone (but not necessarily continuous, let alone differentiable).

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