Factoring out the 1/5 doesn't change the answer. It just makes it easier to understand.
Not sure what you're getting hung up on...Maybe try these two websites and throw some integrals/derivatives into the calculator. It will try and break down each step for you.
http://www.integral-calculator.com/http://www.derivative-calculator.net/Think about this: ln(5x) = ln(5) + ln(x). ln(5) is a constant. When you take an integral you're not going to add in a constant as well as doing the "+ C". The ln(5) portion that you're trying to throw in there is already included in the "+C".
Yes, but that still doesn't change the answer.
derivative (ln(5x)) = 1/(5x) * derivative(5x) = 1/(5x) * 5 = 1/x
idk why i keep thinking of ln "w/e is in denominator" is the integral of dy/"constant"*y