Thank you for the note.
You claim: "For \int_{1/3}^1 fra(1/x) dx Maple returns ln 3 - 1/3".
I can't reproduce this on Maple 13 on linux,
here is a session:
> fra1:=x->1/2+I/(2*Pi)*log(-exp(-2*Pi*I*x)):
> ii:=int(fra1(1/x),x=1/3..1);
ii := - 5/6 + ln(3)
>
What about this:
> i2:=int(cos(x)*fra1(1/x),x=1 .. infinity);
i2 := -Ci(1)
Wolfram Alpha (and possibly Mathematice) return the same:
http://www.wolframalpha.com/input/?i=integral+from+1+to+infinity+of+cos%28x%29*frac%281%2Fx%29
> i3:=int(sin(x)*fra1(1/x),x=1 .. infinity);
i3 := -1/2 I Ei(1, -I) + 1/2 I Ei(1, I)
On Mon, Aug 26, 2013 at 09:56:41PM +0100, James Davenport wrote:
> On Sun, 25 Aug 2013, Georgi Guninski wrote:
>
> >Well, after full simplification fra1() no longer equals {x}:
> Like Maple's simplify(,symbolic).
> See attached for some thoughts.
> >
> James Davenport
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