On Friday, February 28, 2014 11:33:56 PM UTC-5, Richard Fateman wrote: > I don't consider a solution that includes > Si, Ci, or hypergeometric functions as a solution > in closed form in terms of elementary functions. > > Unless there is no way of expressing the answer in > terms of elementary functions. > > After all, you could always decide that the > difficult integral in question deserves its own > name, say FooI, and then return the answer in terms > of FooI.
_Indefinite_ integral above can not be done using elementary functions. For such integral 'li' and 'Ei' play the same as logarithms. 'Ci' and 'Si' are similar to 'atan'. As long as CAS can compute needed limits at infinity computing indefinite integral in terms of special functions is valid method of computing definite integral. And it is much more general than methods based on residue theorem.