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  2. 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.

  3. Tangent half-angle substitution - Wikipedia

    en.wikipedia.org/.../Tangent_half-angle_substitution

    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.

  4. Integration by substitution - Wikipedia

    en.wikipedia.org/wiki/Integration_by_substitution

    In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, [1] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation , and can loosely be thought of as using the chain rule "backwards."

  5. Change of variables - Wikipedia

    en.wikipedia.org/wiki/Change_of_variables

    Difficult integrals may also be solved by simplifying the integral using a change of variables given by the corresponding Jacobian matrix and determinant. [1] Using the Jacobian determinant and the corresponding change of variable that it gives is the basis of coordinate systems such as polar, cylindrical, and spherical coordinate systems.

  6. List of integrals of rational functions - Wikipedia

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

    The following is a list of integrals (antiderivative functions) of rational functions. Any rational function can be integrated by partial fraction decomposition of the function into a sum of functions of the form:

  7. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    Integration by parts is a heuristic rather than a purely mechanical process for solving integrals; given a single function to integrate, the typical strategy is to carefully separate this single function into a product of two functions u(x)v(x) such that the residual integral from the integration by parts formula is easier to evaluate than the ...

  8. 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]

  9. Integration by reduction formulae - Wikipedia

    en.wikipedia.org/wiki/Integration_by_reduction...

    In integral calculus, integration by reduction formulae is a method relying on recurrence relations. It is used when an expression containing an integer parameter , usually in the form of powers of elementary functions, or products of transcendental functions and polynomials of arbitrary degree , can't be integrated directly.

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