[Coda]

How did I not know this thread existed? >.>

To answer your question: 行く can be read as both いく and ゆく. The "yuku" pronunciation is an older one and is considered very poetic, while the "iku" pronunciation is the "official" one. So you'll often see music where the lyrics are listed as -te iku but the vocalist sings -te yuku. It's the same word.

Edit: Not to mention that "-te yuku" just flows better when singing; the "~e i~" sound just blends into a single "ey" sound (in fact in casual conversation "-te iku" VERY frequently gets contracted to "-teku") while "~e yu~" is distinctly two syllables. Perhaps this is WHY it's considered more poetic.