A method of additively manufacturing a composite part is disclosed. The method comprises depositing a segment of a continuous flexible line along a print path. The continuous flexible line comprises a non-resin component and a thermosetting resin component that is not fully cured. The method further comprises, while advancing the continuous flexible line toward the print path, delivering a predetermined or actively determined amount of curing energy at least to a portion of the segment of the continuous flexible line at a controlled rate after the segment of the continuous flexible line is deposited along the print path to at least partially cure at least the portion of the segment of the continuous flexible line.