Multiple symbolic array integration

Hi all,

I am struggling to find both a structure and the right tools to handle my problem. Let's say I have a function f1(x,r1,r2,...,rk) where k is a random variable and all the variables of the function are symbolic.

I first need to integrate w.r.t. the variable x but, in general, all the integrals' bounds within my question are the same (let's call a and b respectively the lower and upper bound).

In second place, I then need to perform multiple integrations w.r.t. the variables of the array of symbols R=[r1,r1,...,rk].

The general structure of the problem is the following

and, in the end, I need to perform a numerical integration(in that picture, variable R is a length, nothing in common with the previous R=[r1,r1,...,rk]).

I checked a previous example in which a non-array symbolic variable is considered ( %3Chttps://it.mathworks.com/matlabcentral/answers/174009-symbolic-integration-vs-numerical-integration%3E ), a similar situation where a non-randomic size of the symbolic array R is implemented.

Moreover

1. f1 has a complicated form such as int() can't find a closed-form solution to it.
2. Within f1, variables can't be separated (expand() has already been used)

Any help is very welcome. After some days on it I feel I don't have experience enough to face with it.

This is a previous job I need to complete before use fmincon in such a way its result is not conditioned by the randomness brought by K random variables R=[r1,...,rk].

Thanks a lot in advance