To me, this is a tough problem. I don’t think I would have solved it, the final solution and answer, with infinite time and resources.
I do provide a solution that I figured out from the hints from the solutions manual. I included the solution below.
 Harding, Chris. (2018, Feb. 11). Solution: Tough Vector Calculus Problem. I would need infinite time and resources to solve this problem in my opinion. Retrieved (2018, Feb. 11). scribd[com]. Available from: https://www.scribd.com/document/371287480/Tough-Vector-Calculus-Problem ; Google URL: https://goo.gl/RKRa84