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MathGroup Archive 1998

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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


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