Inagotablemente translates to "inexhaustibly" or "unfathomably." It's a strong, descriptive adverb that isn't commonly found in everyday conversation or many song lyrics.
In "A Tu Lado," Amaia Montero uses this word to express the depth of her belief and trust, singing "Creo en ti, inagotablemente en ti" (I believe in you, inexhaustibly in you). It beautifully conveys an endless, unwavering faith, making it a memorable and impactful word choice.