Question regarding integrating (int(1/u))

[Linday12]

Homework Statement

I'm confused about integrating something like \int\frac{1}{u}
Sometimes the answer seems to be ln|u| and sometimes just ln(u), and I wasn't sure why it is different from problem to problem. (after subbing u back in; I'm using the u-sub method)

It looks like the answer should be very straight forward as I can't find an explanation, so I'm not seeing something. My only guess would be that the absolute value symbols are used only if a negative value of x could give a negative value for u when subbing back in, making the ln(blah) undefined (for my course anyways). Is this about right? Thanks.

 

[ideasrule]

Don't worry about it. The integral should be ln(|u|) because deriving that gives you 1/u for both u>0 and u<0. Sometimes, writing ln(u) works because (1) it's convenient and (2) it often works out in the end even if u is negative and the absolute value sign is ignored.