When I integrate this:

I get:

However, when I plug this into Wolfram Alpha, it spits out this:

I have no idea why this is happening. A footnote in Wolfram Alpha says it's equivalent, but when I use the answer I get with the rest of the problem, I get an erroneous result - whereas the reversed version works fine.

I thought I understood how to take an integral of a simple fraction like this, but clearly I don't.

What am I missing?