The integral of 1/x is ln(x). Where does that come from? That always puzzled me. We can continue to take derivatives through x^0 and into the negative integers, and just use the plain old power rule to get the answers. We can do the same for the integral of x all the way from negative exponents through positive exponents with the exception of x^-1. If we try to take the integral here, we get x^0/0, which is 1/0, and is undefined. OK, I get that, but how do we get a natural logarithm out of this undefined expression?