How would I integrate the form du/(a^2 * u)?

[Q_Q]

Hi guys, I'm new here, but I'm hoping someone will be able to give me a hand:

How would I integrate the form du/(a^2 * u)?

I've been straining for hours to put this one together, but I'm having trouble with some big concepts (and, as it's well-known, math is a cumulative science), so I'm very far behind at this point. I'm getting two different answers from Mathmatica and my TI-89, which might very well be equivalent, but if someone could work through this one for me, or at least give me a nudge in the right direction, I'd really appreciate it.

Thanks!

 

[pka]

Which is it \(\displaystyle \L\int {\frac{{du}}{{a^2 u}}\quad \mbox{or}\quad \int {\frac{{du}}{{a^{2u} }}} } ?\)

 

[Q_Q]

sorry, it's the first one

 

[pka]

\(\displaystyle \L
\int {\frac{{du}}{{a^2 u}} = \frac{1}{{a^2 }}\ln |u|}\)

 

[Q_Q]

would you mind filling me in just a bit on how you managed that?

 

[pka]

Well, that is the most basic of all logarithmic integral forms.
\(\displaystyle \int {\frac{{du}}{u} = \ln |u|}.\)

Because \(\displaystyle \frac{d}{{du}}\ln |u| = \frac{1}{u}.\)

 

[Q_Q]

okay, and the 1/a^2 just gets pushed out then?