[Maxima-bugs] [ maxima-Bugs-2827474 ] integrate(log(sec(x)), x) --> lisp error

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Bugs item #2827474, was opened at 2009-07-26 23:52
Message generated for change (Comment added) made by crategus
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Category: Lisp Core - Integration
Group: None
>Status: Closed
>Resolution: Works For Me
Priority: 5
Private: No
Submitted By: Barton Willis (willisbl)
Assigned to: Nobody/Anonymous (nobody)
Summary: integrate(log(sec(x)),x) --> lisp error

Initial Comment:
(%i4) integrate(log(sec(x)),x);
Maxima encountered a Lisp error:

(%i5) build_info();
Maxima version: 5.18.1
Maxima build date: 20:57 4/19/2009
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8
(%o5) 

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>Comment By: Dieter Kaiser (crategus)
Date: 2009-08-20 00:10

Message:
As reported in the last posting the integral of this bug report works. The
answer does not look nice but can be shown to be equivalent to the result


-(%i*li[2](-%e^(2*%i*x)))/2-(%i*x^2)/2+x*log(1+%e^(2*%i*x))+x*log(sec(x))

from wolfram alpha.

Closing this bug report as "works for me".

Remark: Related integrals with integrands like log(sin(x)) or log(cos(x))
give an answer too.

Dieter Kaiser



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Comment By: Dieter Kaiser (crategus)
Date: 2009-07-27 00:21

Message:
With the current CVS version and in a fresh Maxima this problem is not
present:

Maxima version: 5.18post
Maxima build date: 0:14 7/27/2009
host type: i686-pc-linux-gnu
lisp-implementation-type: CLISP
lisp-implementation-version: 2.44.1 (2008-02-23) (built 3436700604)
(memory 3457635278)

(%i4) integrate(log(sec(x)),x);
(%o4) (x*log(sin(2*x)^2+cos(2*x)^2+2*cos(2*x)+1)
       +2*%i*x*atan2(sin(2*x),cos(2*x)+1)-%i*li[2](-%e^(2*%i*x))-%i*x^2)
       /2
       +x*log(sec(x))

I have not checked the result.

Dieter Kaiser

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