for n integer and n>=0.
Maple finds it if I tell it this in the assumptions. But if I remove the assumption that n>=0 and just keep the assumption that n is integer, it hangs. (at least I waited 5 minutes and gave up).
Is this something to be expected? If I try the same thing in Mathematica, i.e. telling it n is an integer, but not that it is n>=0, it returns result immediately, with condition that the result is valid for n>=0.
int(x^n*exp(-x),x=0..infinity) assuming n::integer
seems to hang.
My question is if this behaviour of int hanging is to be expected, since it was not told than n>=0? Should it have returned result of n! like Mathematica, with the assumption given in the result as well?
Since for n<0 the integral does not converge, and maple knows this
May be this is just a design issue in int and it was stuck trying to evaluate the integral for negative integers, and could not determine if it converges or not?