#831 integrate(sin(x)/cos(x)^2,x,0,%pi/3);

[Anonymous]

Should return 1 but returns 0 if cos(x) is declared
positive.
Strange enough, if cos(x) is declared zero, maxima
returns the correct result.

poul.riis@skolekom.dk

[Raymond Toy]

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The hint that the result is correct if cos(x) is declared
zero is key.

It seems the problem is in sin-cos-intsubs1 in defint.lisp.
There's a clause there:

  \(\(not \(equal \($asksign denom\) '$zero\)\)
   0.\)

This seems bizarre. If the denom is not zero, why should it
return 0? My limited understanding is that sin-cos-intsubs1
is supposed to substitute the limits of the integral into
the indefinite integral. (Which, by the way is correctly
computed by antideriv.)

Changing it to read (equal ($asksign denom) '$zero)) makes
more sense, but I don't know about returning zero as the
result. Undefined or infinity seems better, if a choice
must be made.

[Raymond Toy]

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user_id=28849

Fixed as described, but we return '$undefined instead of 0,
for want of a better solution. Seems better than 0 anyway.