https://www.animelyrics.com/anime/gate/gate.htm
This is completely down to Tetrix's preferences to be honest, but while the Japanese (in the two instances it appears) reads "kaeteiku" with iku in hiragana, it's clearly sung "kaeteyuku" (youtube .com/watch?v=qVEVRTUAy0M the line's at 1:05)
either way it's no big loss
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