Fitst of all, you should specify --nothing can be done with an arbtrary function. Then, you can try to calculate the integrals analytically using the call function "int" in the Symbolic Math Toolbox, but there is no guarantee that an analytical solution exists at all. To find the numerical solution you should compute the integrals numerically at every x, y, i of interest; use the call function "inegral" for this purpose. There are special cases where the computetion can be simplifyed, e.g., in a case you mean the Fourier transfer (you are expressed in terms of complex exponents or sin/cos functions), the call function "fourier" (symbolic) or "fft" and "ifft" (numerical) can be used. The new non-uniform Fourier transform functions "nufft" and "nufftn" are announced to be introduced in Matlab 2020a.