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I have been systematically working through the wonderful book Quantum mechanics and path integrals by Feynman and Hibbs and have come to realize that it has a shockingly large number of typos. I have been trying to derive eqn 5-13 on Pg 103 starting from eqn 3-42 Pg. 57 by using Fourier transforms on the variables x and t. I can get the same expression except the integral over t1 which later leads to a delta function in energy for the free particle kernel. Can anyone guide me as to whether it is just another typos or am I really missing something?

Thanks