# [Maxima] integrate((x^2+1)/(x^4+1),x,0,1) can't be simplified

cunzhang apzc2529 at gmail.com
Sun Apr 27 22:09:42 CDT 2008

```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?

ÔÚ Mon, 28 Apr 2008 09:29:43 +0800£¬Juan Pablo Romero Bernal
<jromerobernal at gmail.com> Ð´µÀ:

> Hi,
>
>>  How to make Maxima simplify it?
>
> You can use:
>
> (%i7) numer:true;
> (%o7)                                true
> (%i8) integrate((x^2+1)/(x^4+1),x,0,1);
>
> (%o8)                          1.110720726114594
>
> or
>
> (%i15) ev(integrate((x^2+1)/(x^4+1),x,0,1),numer:true);
> (%o15)                         1.110720726114594
>
> By default, the numer variable is set to false.
>
> Bye,
>

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