I'm not sure if my title makes any sense... sorry, it has been a while since I've done cal.
I'm taking a Probability course and I'm reading one of my profs solutions that involves finding the moment-generating function of a continuous random variable. During the integration steps I got lost. Can someone please help understand how he gets from one step to another (I'll just include the part that confuses me):
Q1: why is it necessary to introduce in the second line?
Q2: How does he get from the second line to the third? What method is that? Would it not be possible to simply take out all the constants from the integral and just have
Q3: Is there any quicker way to write the equations? It took me an hour to type this up using the code...