Wrong result for definite integral of sin(x)*exp(I*x)

[Jeremie Knuesel]

Hi,

integrate(sin(x)*exp(I*x),x,-pi,0) returns 3/2*I*pi instead of 1/2*I*pi

Is this a known issue? I couldn't find it reported elsewhere.

Best regards,

Jeremie Knuesel

[Eric Gourgoulhon]

Hi,

Indeed, this seems a bug in Sage.
Note that both SymPy and Giac return the correct answer:

sage: integrate(sin(x)*exp(I*x), x, -pi, 0)
3/2*I*pi
sage: integrate(sin(x)*exp(I*x), x, -pi, 0, algorithm='sympy')
1/2*I*pi
sage: integrate(sin(x)*exp(I*x), x, -pi, 0, algorithm='giac')
1/2*I*pi

Eric.

[Ralf Stephan]

Not Sage, it's Maxima:

(%i2) integrate(sin(x)*exp(%i*x),x,-%pi,0);      
                               log(- 1)
(%o2)                          -------- + %i %pi
                                  2

[Martin R]

FriCAS also would get it right, except that there is a bug in the interface, see https://trac.sagemath.org/ticket/25174

If someone can give me a hint on how to send %i instead of I for the imaginary unit to fricas, I'll fix it...

(1) -> integrate(sin(x)*exp(%i*x),x=-%pi..0)

        %i %pi

   (1)  ------

           2

but

sage: integrate(sin(x)*exp(I*x),x,-pi,0,algorithm="fricas")

---------------------------------------------------------------------------

ZeroDivisionError                         Traceback (most recent call last)

because

sage: fricas.integrate(sin(x)*exp(I*x), x)

    I x                 I x

I %e   sin(x) - cos(x)%e

---------------------------

            2

           I  + 1

Martin

[rjf]

If Sage calls Maxima, then it is a bug in Sage also.

Interestingly, Maxima gets the INdefinite integral correct.