Does anyone know how to do laplace transforms? . I keep trying it, and I keep getting different results. Here are my attempts:

NOTE: I will denote L to be the laplace operator symbol as I don't know how to do a curly L, and [ and ] will denote { and }, respectively.

Use partial fractions:

And then not sure how to get this to piecewise func, but I don't think this is right any way. Please help!