coding some nested integrals in matlab, C or C++

coding some nested integrals in matlab, C or C++

I there I need help coding some nested integrals in matlab, C or C++

I am flexible with the language but I need something that is fast and efficient. The code runs very slowly in mathematica. I have created a written document that outlines the code I need to be written please let me know if you can do this. Thank you!