UA-UMO 1997 Problem 101

Find the maximum value of the function:

$f(x)=\frac{x}{x^2+9}+\frac{1}{x^2-6x+21}+\cos {2 \pi x}, x>0.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.