Beverly Goulet loves a challenge. Good thing for American Airlines.

Goulet was named chief integration officer at Fort Worth-based American in March 2013, a promotion from her previous position of vice president of corporate development and treasurer. In her current role, Goulet, an executive vice president, is tasked with overseeing the massively complex integration of American Airlines and US Airways.

The airlines officially merged in December 2013, with the merger providing American an exit…