[Maxima-bugs] [ maxima-Bugs-1552789 ] integrate(1/(sin(x)^2+1), x, 1, 1+%pi) takes forever

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Bugs item #1552789, was opened at 2006-09-05 11:08
Message generated for change (Comment added) made by willisbl
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Category: Lisp Core - Integration
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: Raymond Toy (rtoy)
Assigned to: Nobody/Anonymous (nobody)
Summary: integrate(1/(sin(x)^2+1),x,1,1+%pi) takes forever

Initial Comment:
This is a follow-on to Bug [ 1044318 ]
defint(1/(sin(x)^2+1),x,0,3*%pi) wrong.

integrate(1/(sin(x)^2+1),x,1,1+%pi) seems to take
forever.  But if the limits are 0 and %pi, the integral
is evaluated instantly with the correct value.



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>Comment By: Barton Willis (willisbl)
Date: 2006-09-06 06:38

Message:
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ldefint gives a wrong answer (basically bug 1044318)

(%i10) ldefint(1/(sin(x)^2+1),x,1,1+%pi);
(%o10) 0

integrate gives an antiderivative that isn't continuous
at odd integer multiples of  %pi / 2

(%i11) integrate(1/(sin(x)^2+1),x);
(%o11) atan((2*tan(x))/sqrt(2))/sqrt(2)

The expression
 atan(2*tan(x)/sqrt(2))/sqrt(2)+sqrt(2)*%pi*floor(x/%pi-1/2)/2

might be a valid antiderivative on all of R provided the
first term is assumed left continuous at each odd integer
multiple of %pi/2, I think.

Barton

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