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

Raymond Toy

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.


  • Julien B. O.

    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

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

    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
    still give the wrong answer.)

  • SourceForge Robot

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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
    the administrator of this Tracker).

  • SourceForge Robot

    • status: pending --> closed

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