I am trying to learn probability theory through self study, so I have been working through the MIT open courseware problems. I am pretty stuck on the following one

How do we find the marginal pdf of $f_Y(y)$? I know we need to integrate the joint over $X$ but I don't see how to do it?

Source: https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/assignments/MIT6_041F10_assn05.pdf