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nonele

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There are 6 letters in NONELE ( E1L1N1O1 )

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Definitions of nonele in various dictionaries:

NONELE - In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative that is, itself, not an elementary function (i.e. ...

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Nonele might refer to
In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential, and logarithmic functions using field operations). A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. This theorem also provides a basis for the Risch algorithm for determining (with difficulty) which elementary functions have elementary antiderivatives. It can be shown that, if one is given a function of any complexity, the probability that it will have an elementary antiderivative is very low.Some examples of such functions are:*
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* 1
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* 4
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* {\displaystyle {\sqrt {1-x^{4}}}}
* (see Elliptic integral)
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* ln
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* ln
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* x
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* {\displaystyle \ln(\ln x)\,}
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* 1
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* ln
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* x
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* {\displaystyle {\frac {1}{\ln x}}}
* (see Logarithmic integral)
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* e
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* x
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* x
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* {\displaystyle {\frac {e^{x}}{x}}}
* (see Exponential integral)
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* e
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* {\displaystyle e^{e^{x}}\,}
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* 2
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* {\displaystyle e^{-{\frac {x^{2}}{2}}}\,}
* (see Error function and Gaussian integral)
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* sin
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* {\displaystyle \sin(x^{2})}
* and
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* cos
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* {\displaystyle \cos(x^{2})}
* (see Fresnel integral)
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* {\displaystyle {\frac {\sin(x)}{x}}=\operatorname {sinc} (x)}
* (see Sine integral and Dirichlet integral)The evaluation of nonelementary antiderivatives can o...
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