integrate((x^2+1)/(x^4+1),x,0,1) can't be simplified
Subject: integrate((x^2+1)/(x^4+1),x,0,1) can't be simplified
From: Juan Pablo Romero Bernal
Date: Mon, 28 Apr 2008 01:50:13 -0500
Hi,
2008/4/27 cunzhang <apzc2529 at gmail.com>:
> hi,sorry for my unclear expression. I mean
>
>
> (%i1) integrate((x^2+1)/(x^4+1),x,0,1);
> sqrt(2) + 2 2 - sqrt(2)
> atan(-----------) atan(-----------)
> sqrt(2) sqrt(2)
> ----------------- + -----------------
> sqrt(2) sqrt(2)
> should be simplified to sqrt(2)/4*%pi, say,
>
> sqrt(2) + 2 2 - sqrt(2)
> atan(-----------) atan(-----------)
> sqrt(2) sqrt(2) %pi
> ----------------- + ----------------- = ----
> sqrt(2) sqrt(2) 3/2
> 2
>
> is exact.
> So how can Maxima do it?
>
Yes. With the package atrig1, you can to apply several simplification
rules to inverse trigonometric functions. In this case, i've added two
rules to the Maxima simplifier:
(%i1) tellsimpafter(atan(sqrt(2)-1),3*%pi/8)$
(%i2) tellsimpafter(atan(sqrt(2)+1),%pi/8)$
(%i3) integrate((x^2+1)/(x^4+1),x,0,1)$
(%i4) expand(%);
%pi
(%o4) ---------
2 sqrt(2)
If you want, you can to add this rules into the atrig1, package, in the file:
$MAXIMA_INSTALLATION_DIR/share/trigonometry/atrig1.mac
Bye,
--
Juan Pablo Romero Bernal
Grupo Linux Universidad Distrital
Blog: http://jpromerobx.blogspot.com/
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