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Just wanted to say that this bug is not present in maxima 5.10.0. In fact, it returns (sqrt(2)*atan(sqrt(2)*tan(8)))/2, which is correct.
integrate(1/(sin(x)^2+1),x,0,8) returns
sqrt(2)/2*atan(sqrt(2)*tan(8)) + %pi/sqrt(2)
This is not right.
But integrate(1/(sin(x)^2+1),x,0,5*%pi/2) returns 5*sqrt(2)*%pi/4, which is probably correct according to quad_qags.
This latter integral works because intsc1 notices that the interval length is a rational multiple of %pi and breaks up the integral.
However, for the former integral, intsc1 gives up because the interval length is not a multiple of %pi.
Since we now have a floor function that works well, we should try to extend intsc1 to accept all numeric limits.
This issue affects all integrals of trig functions that are handled by intsc1.
See also the related bug 1552789.
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Just wanted to say that this bug is not present in maxima 5.10.0. In fact, it returns (sqrt(2)*atan(sqrt(2)*tan(8)))/2, which is correct.
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Fixed in cvs using pretty-good-floor-or-ceiling.
(%i25) integrate(1/(sin(x)^2+1),x,0,8);
(%o25) sqrt(2)*atan(sqrt(2)*sin(8)/cos(8))/2+sqrt(2)*%pi+%pi/sqrt(2)
(Note: Expressions such as
integrate(1/(sin(x-8)^2+1),x,0,8);
still give the wrong answer.)
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