Please don't use frullani intergrals or Feynman trick, thank you

With the tools of double integration. you can now revisit some previously thought impossible single variable integrals and evaluate them. Consider the improper integral no 2.r_ 4;: 1:] ;dz 0 which you are told converges. In fact, I = 111(3). (a) Determine a function f(:t, y) such that I: f(:r:,y)dy = Fat"5'. Verify your result by directly showing the integration. (b) Use part (a) to rewrite the above single integral as a double integral. (c) Reverse the order of integration in part (b) and evaluate the double integral to obtain the desired result. Even though change of order has so far been restricted to bounded regions, you can assume the results holds for (strongly) convergent integrals over unbounded regions