## #1227 integrate(1/(sin(x)^2+1),x,0,8) wrong

closed
nobody
5
2007-08-13
2007-06-22
Raymond Toy
No

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.

## Discussion

• Julien B. O. - 2007-07-12

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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.

• Dan Gildea - 2007-07-29
• status: open --> pending

• Dan Gildea - 2007-07-29

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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);

• SourceForge Robot - 2007-08-13

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This Tracker item was closed automatically by the system. It was
previously set to a Pending status, and the original submitter
did not respond within 14 days (the time period specified by

• SourceForge Robot - 2007-08-13
• status: pending --> closed