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
Copyright 1988-96 Wolfram Research, Inc.
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