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[Axiom-developer] [#198 integrate(sin(x**2),x) is not handled ]

From: kratt6
Subject: [Axiom-developer] [#198 integrate(sin(x**2),x) is not handled ]
Date: Sat, 20 Aug 2005 12:30:19 -0500

Although this does not really solve the original problem, I think I found a bug 
in 'INTPM'. Currently, there is an operation::

           pmComplexintegrate(f, x) ==
             (rc := splitConstant(f, x)).const ^= 1 =>
               (u := pmintegrate(rc.nconst, x)) case "failed" => "failed"
               rec := u::ANS
               [rc.const * rec.special, rc.const * rec.integrand]
             cse := (rec := matcherfei(f, x, true)).which
             cse = ERF  => [rec.coeff * erf(rec.exponent), 0]

It is pretty obvious that the third line should read::

               (u := pmComplexintegrate(rc.nconst, x)) case "failed" => "failed"

instead. If we perform this change, we get instead of

the correct answer, same for

For some reason, it still won't do 

Curiously, the pattern matcher is not even invoked in this case... Even if we 
enter the integral as
it fails, although in this case the pattern matcher is invoked. It would need 
to be invoked on each summand seperately, though.

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