It is notational convention. Whenever I do improper integrals with an infinite limit of integration I never do this, I just leave it as infinity. But it is up to your instructor to stipulate the notation he prefers.
Q1: why is it necessary to introduce in the second line?
No, you are using a non-existant rule of exponents. I bet if you look closely again you will see why. And the method is just substitution.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
Nope, sorry. You will eventually learn and get faster. And just think, for all the time you put into actually typing the code out the more likely people will respond.Q3: Is there any quicker way to write the equations? It took me an hour to type this up using the code...