How to solve this ODE system which involves these integrals?

Hi, I'm trying to solve the following (simplified) ODE system (see attached file).

Where X1 and X2 are my functions, z is the integration variable and f1,g1,f2,g2 are 4 different functions of X1 and X2.

My biggest problem is that the integrals depend on the integration variable itself.

I tried to consider z as a symbolic variable in this way:

syms z
integral(f(X1,X2), [0,z])

but I got an error.

Thank you!

[Jan]

syms r? Why "r"?

[Elia Paini]

Sorry, was z

Answer 1

[Jan]

What about using two further variables?

function dx = fcn(z, x)
dx = [f1(x(1), x(2)) / x(3); ...
      f2(x(1), x(2)) / x(4); ...
      g1(x(1), x(2)); ...
      g2(x(1), x(2))];
end

This does calculate the integral from 0 to the current z over g1(x1,x2) already.

[Elia Paini]

You're a genius, thank you!