# [Maxima] integrate(1/(sin(x)^2+1),x,a,b)?

Raymond Toy raymond.toy at ericsson.com
Wed Jun 27 14:29:13 CDT 2007

```>>>>> "Barton" == Barton Willis <willisb at unk.edu> writes:

Barton> Here is what I get using Maple 10
[snip]
>> integrate(1/(sin(x)^2+1),x);
>>

Barton>                           1/2                1/2
Barton>                      1/2 2    arctan(tan(x) 2   )

>> _EnvAllSolutions := true:
>> integrate(1/(sin(x)^2+1),x=0..z);
>>

Barton>   {
Barton>   {      1/2 /               1/2         -Pi + 2 z    \          Pi
Barton>   { 1/2 2    |arctan(tan(z) 2   ) + ceil(---------) Pi| , z < - ----
Barton>   {          \                             2 Pi       /          2

Barton>               1/2
Barton>           Pi 2             Pi
Barton>         - ------- , z = - ----
Barton>              4             2

Barton>                            1/2   1/2        Pi
Barton>         1/2 arctan(tan(z) 2   ) 2    , z < ----
Barton>                                             2

Barton>             1/2
Barton>         Pi 2           Pi
Barton>         ------- , z = ----
Barton>            4           2

Barton>              1/2 /               1/2             -Pi + 2 z      \
Barton>         1/2 2    |arctan(tan(z) 2   ) + Pi floor(---------) + Pi| ,
Barton>                  \                                 2 Pi         /

Barton>          Pi
Barton>         ---- < z
Barton>          2

I'm sorry, I can't understand what this is trying to tell me.  I see
there are 3 possible answers?  But what are those z things?

Ray
```