Here is what I get using Maple 10
> integrate(1/(sin(x)^2+1),x=0..z);
>
Warning, unable to determine if Pi*_Z3+1/2*Pi is between 0 and z; try
to use assumptions or set _EnvAllSolutions to true
z
/
| 1
| ----------- dx
| 2
/ sin(x) + 1
0
> integrate(1/(sin(x)^2+1),x);
>
1/2 1/2
1/2 2 arctan(tan(x) 2 )
> _EnvAllSolutions := true:
> integrate(1/(sin(x)^2+1),x=0..z);
>
{
{ 1/2 / 1/2 -Pi + 2 z \ Pi
{ 1/2 2 |arctan(tan(z) 2 ) + ceil(---------) Pi| , z < - ----
{ \ 2 Pi / 2
1/2
Pi 2 Pi
- ------- , z = - ----
4 2
1/2 1/2 Pi
1/2 arctan(tan(z) 2 ) 2 , z < ----
2
1/2
Pi 2 Pi
------- , z = ----
4 2
1/2 / 1/2 -Pi + 2 z \
1/2 2 |arctan(tan(z) 2 ) + Pi floor(---------) + Pi| ,
\ 2 Pi /
Pi
---- < z
2
Barton
-----maxima-bounces at math.utexas.edu wrote: -----
>To: Maxima List <maxima at math.utexas.edu>
>From: Raymond Toy <raymond.toy at ericsson.com>
>Sent by: maxima-bounces at math.utexas.edu
>Date: 06/27/2007 10:51AM
>Subject: integrate(1/(sin(x)^2+1),x,a,b)?
>
>Bug 1741705
>>=4933&atid=104933>
>
>says the integral from 0 to 8 is wrong. I have a fix for this that
>depends on floor(x/%pi) working correctly when x is a number, or
>expression possibly including %pi. I believe floor is working
>correctly, and the changes I've made are also working correctly.
>
>However, what should maxima do for the integral from 0 to z, say?
>Currently, it returns
>
>sqrt(2)/2*atan(sqrt(2)*sin(z)/cos(z)) + %pi/sqrt(2)
>
>This isn't quite right, unless you carefully select the correct branch
>for atan. This is, howveer, the correct answer if z < 2*%pi.
>
>What should maxima do here? What do Macsyma, Maple, and/or
>Mathematica return for this integral?
>
>Ray
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