We know, you're expecting us to begin this section by telling you what equals. But that's not really what's important here. If you really must know, it equals , but few professors expect you to remember that (although it can be worked out using integration by parts, a section coming up shortly, and there, it makes a good problem.)
No, in this section we would just like to reverse the formula
There are a couple of things to notice here. First, by integrating a function 1/x that appears to have nothing whatsoever to do with e , wouldn't recognize e if e bit it on the nose, we get the log base e. Just another way of saying,``e, you're mighty special."
Second, you will notice that somehow, the x in the solution picked up absolute value signs. That's because the natural log function is only defined for positive values of x, so if x were negative and we didn't have the absolute value signs, it would make no sense. Should you worry about the absolute value signs? If you're going for the A+, YES, otherwise forget about them.
Now, was that as good for you as it was for us?