integrate((1+tan(x)^2)/tan(x),x);

• Subject: integrate((1+tan(x)^2)/tan(x),x);
• From: Nikos Apostolakis
• Date: Wed, 23 Nov 2005 12:07:41 +0000

On Tue, Nov 22, 2005 at 09:48:42PM +0100, thus spake Gilles Schintgen:
> On Tuesday 22 November 2005 21:16, Boris Gaertner wrote:
> > With that derivative, the first stage of the Maxima integration
> > algorithm would be able to answer  log(tan(x))  as the integral
> > of the given problem.
> 
> Hi, I'm new here, so maybe I don't get the point of this discussion. Maxima 
> (5.9.1) _does_ answer LOG(TAN(X)).
> 

I get 

log(sin(x)) - ((log(sin^2(x) - 1))/2

both with maxima 5.9.2 and with 5.9.1 in an older machine.

Boris, I think that what the OP hinted at was not so much the fact
that maxima gives a wrong answer but that it gives an *absurd* answer.
sin^2(x)-1 is always negative or zero (for real x) and the log of a 
negative or zero number does not exist (or at least is not a real 
number).

Best regards,
Nikos

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