Why does version 6.0.1 of Mathematica give a different answer than 5.2 for
Integrate[Tan[x] - Tan[x/2], x]
Version 5.2 on Windows Mathematica gives (which is what I also get by hand)
2 Log[Cos[x/2]] - Log[Cos[x]]
Version 6.0.1 on Mac OS X gives
The 6.0.1 result can be transformed into the 5.2 result but seems odd that this would be so much more complex in version 6.0.1. Have tried //Simplify and //FullSimplify but in makes no difference.
Another curious thing about version 6.0.1 is if you take the derivative of the just computed integral, you get something different than what you started out with (but this time I cannot transform Mathematica's answer to what should be an equivalent form - but the results plot the same so it would appear they are equivalent -- anyone see how to get one from the other??).
In fact while looking at this and trying to discover if the forms are equivalent I came across another problem having to do with plotting. I was trying to plot the function (Sin[x]+1)/2Cos[x] from -pi to pi. There should be discontinuities at pi/2 and -pi/2, but only the pi/2 one appears in the plot. What is going on??? Division by zero ought to be the same for positives and negatives, right???
Any ideas or comments about why or if there is something I can do to get Mathematica versions to agree or why they don't and why the plot does not appear as expected?? I have attached a simple notebook that will show the problems. I don't have version 5.2 on a Mac so can't compare to see if this is one issue, but 6.0.1 on the Mac and Windows do give the same result.
Attachment: m-problem.nb, URL: ,