integral of a real function is real ?

• To: mathgroup at smc.vnet.net
• Subject: [mg13840] integral of a real function is real ?
• From: pokornp at math.vscht.cz ()
• Date: Sat, 29 Aug 1998 04:41:17 -0400
• Organization: Prague Institute of Chemical Technology
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Mathematica friends,

how can one simplify the following result  to come to a real funcion ?

\$ math
Mathematica 3.0 for HP-UX PA-RISC

In[1]:= Integrate [ Sqrt [1 + x^2 + y^2], x, y]

3                 2    2
-x   x    x y Sqrt[1 + x  + y ]   ArcTan[x]
Out[1]= -- - -- + --------------------- + --------- +
3    18             3                 3

2                    2    2
y (3 + y ) Log[x + Sqrt[1 + x  + y ]]
>    ------------------------------------- +
6

2                    2    2
x (3 + x ) Log[y + Sqrt[1 + x  + y ]]
>    ------------------------------------- -
6

2                   2    2
I     12 (-I + x - I y )   12 I Sqrt[1 + x  + y ]
>    - Log[------------------ - ----------------------] +
6                  2             (-I + x) y
(-I + x) y

2                   2    2
I     12 (I + x + I y )   12 I Sqrt[1 + x  + y ]
>    - Log[----------------- + ----------------------]
6                 2             (I + x) y
(I + x) y

Pavel Pokorny
Math Dept, Prague Institute of Chemical Technology e-mail:
Pavel.Pokorny at vscht.cz
http://staff.vscht.cz/mat/Pavel.Pokorny

```

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