A composition of a function 
with itself gives a nested function 
, 
which gives 
, etc. Function nesting is implemented in the Wolfram
Language as Nest[f,
expr, n], and a listing of incremental nestings is implemented as NestList[f,
expr, n].
Integrals of nested functions rapidly become difficult to find in exact form. For example, the first two nestings of the exponential function gives
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the exponential integral, the first two
nestings of the natural logarithm give
 |  |  |
(3)
|
 |  |  |
(4)
|
where 
is the logarithmic integral.
