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  2. 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."

  3. Change of variables - Wikipedia

    en.wikipedia.org/wiki/Change_of_variables

    In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.

  4. Substitution (logic) - Wikipedia

    en.wikipedia.org/wiki/Substitution_(logic)

    The identity substitution, which maps every variable to itself, is the neutral element of substitution composition. A substitution σ is called idempotent if σσ = σ, and hence tσσ = tσ for every term t. When x i ≠t i for all i, the substitution { x 1 ↦ t 1, …, x k ↦ t k} is idempotent if and only if none of the variables x i ...

  5. Euler substitution - Wikipedia

    en.wikipedia.org/wiki/Euler_substitution

    Euler substitution is a method for evaluating integrals of the form (, + +), where is a rational function of and + +. In such cases, the integrand can be changed to a rational function by using the substitutions of Euler.

  6. 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 .

  7. Could changes be coming to Medicare, Medicaid with Dr. Oz ...

    www.aol.com/could-changes-coming-medicare...

    With President-elect Donald Trump's recent announcement of former surgeon-turned-TV host Dr. Mehmet Oz to lead the Centers for Medicare and Medicaid Services (CMS), questions are swirling about ...

  8. Change of variables (PDE) - Wikipedia

    en.wikipedia.org/wiki/Change_of_variables_(PDE)

    Often, theory can establish the existence of a change of variables, although the formula itself cannot be explicitly stated. For an integrable Hamiltonian system of dimension n {\displaystyle n} , with x ˙ i = ∂ H / ∂ p j {\displaystyle {\dot {x}}_{i}=\partial H/\partial p_{j}} and p ˙ j = − ∂ H / ∂ x j {\displaystyle {\dot {p}}_{j ...

  9. Dying To Be Free - The Huffington Post

    projects.huffingtonpost.com/dying-to-be-free...

    Founded in the late 1940s on a farm, the clinic brought order and professionalism to the 12-step method. Hazelden’s recent merger with the Betty Ford Center has made it an even more powerful force. Administrators made headlines in early 2013 when they integrated buprenorphine into their treatment of opioid addicts.