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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. 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. Change of variables - Wikipedia

    en.wikipedia.org/wiki/Change_of_variables

    The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem. Change of variables is an operation that is related to substitution. However these are different operations, as can be seen when considering differentiation or integration (integration by substitution).

  5. Euler substitution - Wikipedia

    en.wikipedia.org/wiki/Euler_substitution

    The substitutions of Euler can be generalized by allowing the use of imaginary numbers. For example, in the integral +, the substitution + = + can be used. Extensions to the complex numbers allows us to use every type of Euler substitution regardless of the coefficients on the quadratic.

  6. Integration using Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Integration_using_Euler's...

    Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely and and then integrated. This technique is often simpler and faster than using trigonometric identities or integration by parts , and is sufficiently powerful to integrate any rational expression involving trigonometric functions.

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  8. Trigonometric substitution - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_substitution

    For a definite integral, the bounds change once the substitution is performed and are determined using the equation = ⁡, with values in the range < <. Alternatively, apply the boundary terms directly to the formula for the antiderivative.

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    www.aol.com/news/deadliest-plane-accidents-see...

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