Scrabble?! NONELEMENTARY

Definitions of NONELEMENTARY in various dictionaries:

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: 1 − x 4 {\displaystyle {\sqrt {1-x^{4}}}} (see Elliptic integral) ln ⁡ ( ln ⁡ x ) {\displaystyle \ln(\ln x)\,} 1 ln ⁡ x {\displaystyle {\frac {1}{\ln x}}} (see Logarithmic integral) e x x {\displaystyle {\frac {e^{x}}{x}}} (see Exponential integral) e e x {\displaystyle e^{e^{x}}\,} e − x 2 2 {\displaystyle e^{-{\frac {x^{2}}{2}}}\,} (see Error function and Gaussian integral) sin ⁡ ( x 2 ) {\displaystyle \sin(x^{2})} and cos ⁡ ( x 2 ) {\displaystyle \cos(x^{2})} (see Fresnel integral) sin ⁡ ( x ) x = sinc ⁡ ( x ) {\displaystyle {\frac {\sin(x)}{x}}=\operatorname {sinc} (x)} (see Sine integral and Dirichlet integral)The evaluation of nonelementary antiderivatives can o...