der_wachtmeister at freenet.de> Is this a problem of Maxima
Yes. The integrator of Maxima 5.9.2 is fairly weak.
The answer to your integral
integrate(%e^(-%i*w*t)/(t^2+2), t,-1,1)
is
1/4*%i*SQRT(2)*(-%e^(SQRT(8)*w)*ei(1,-%i*w+SQRT(2)*w)+
ei(1,-%i*w-SQRT(2)*w)+%e^(SQRT(8)*w)*ei(1,%i*w+SQRT(2)*w)
-ei(1,%i*w-SQRT(2)*w))*%e^(-SQRT(2)*w)
where ei is a special function named the exponential integral
http://mathworld.wolfram.com/ExponentialIntegral.html
which can be defined as integrate(exp(-t*z)*t^(-a),t,1,inf).
Best wishes,
Vladimir Bondarenko
VM and GEMM architect
Co-founder, CEO, Mathematical Director
Cyber Tester, LLC
http://www.cybertester.com/http://maple.bug-list.org/http://www.CAS-testing.org/
----- Original Message -----
From: <der_wachtmeister at freenet.de>
To: <maxima at math.utexas.edu>
Sent: Thursday, January 05, 2006 1:48 PM
Subject: Why do some integrations not work?
> Why can Maxima solve this:
>
> (%i3) integrate ( %e ^ ( -%i * w * t ), t, -1, 1 );
>
> and this not:
>
> (%i5) integrate ( %e ^ ( -%i * w * t ) / ( t ^ 2 + 2 ), t, -1, 1 );
>
> ? Is this a problem of Maxima (i.e. could Mathematica or Maple solve it)
> or of CAS in general?
>
> Phil
>
>
>
_______________________________________________
Maxima mailing list
Maxima at math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima