Another not so difficult Putnam problem
I found another easy problem from an old Putnam competition (in 1987). Again, it is the first problem in one of the sessions (afternoon in this case) so it is probably by design to be easy for participants to warm up their brain muscles.
For ambitious students, you can try to generalize the trick here and you will notice that there is no particular requirements for the function in the integrand. The square root of the natural logarithm is just to make it look complicated. The main conditions are within the lower and upper limits of the integral, and the two numbers (3 and 9) within the integrand. Once you figure out the relationship of these four numbers, you can put any functions within the integration (as long as the function is continuous and integrable between the lower and upper limits)