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.
