From: gerber@sirius.astro.uiuc.edu (Richard A. Gerber)
Subject: Re: Maple can diff(expr), but not int(diff(expr))?
Organization: University of Illinois at Urbana
Date: Tue, 14 Apr 1992 13:33:40 GMT

In <1992Apr13.155641.28344@ux1.cso.uiuc.edu> gerber@sirius.astro.uiuc.edu (Richard A. Gerber) writes:

>I can get Maple to differentiate a simple expression, but then I can't
>seem to get an answer if I ask it to calculate the indefinite integral
>of that expression. Here's the problem:

I wrote that Maple could not seem to solve:
int( diff(BesselJ(1,x),x), x);

I received a nice way to solve this:


    |\^/|      MAPLE V
._|\|   |/|_.  Copyright (c) 1981-1990 by the University of Waterloo.
 \  MAPLE  /   All rights reserved.  MAPLE is a registered trademark of
 <____ ____>   Waterloo Maple Software.
      |        Type ? for help.
                             Welcome to Amiga MapleV

                   Amiga 2000/68030/68882 @ 22 MHz w/ 6 MB RAM

--------------------------------------------------------------------------------
> diff(BesselJ(1,x),x);
                                          BesselJ(1, x)
                          BesselJ(0, x) - -------------
                                                x

--------------------------------------------------------------------------------
> int(",x=0..X);
                        X
                        /
                       |                  BesselJ(1, x)
                       |  BesselJ(0, x) - ------------- dx
                       |                        x
                      /
                      0

--------------------------------------------------------------------------------
> laplace(",X,Y);
                               1          2     1/2
                          ----------- - (Y  + 1)    + Y
                            2     1/2
                          (Y  + 1)
                          -----------------------------
                                        Y

--------------------------------------------------------------------------------
> normal(");
                                     2     1/2
                                 - (Y  + 1)    + Y
                               - -----------------
                                      2     1/2
                                    (Y  + 1)

--------------------------------------------------------------------------------
> invlaplace(",Y,x);
                                  BesselJ(1, x)

--------------------------------------------------------------------------------


I also wrote that even though a simple closed form solution exists,
I could not get Maple V to evaluate:

>int(BesselJ(1,x)*exp(-x),x=0..infinity);

I received responses stating that this was not as simple a problem as it
appeared. This is an example of a definite integral that has a closed
form solution, while the corresponding indefinite integral does not. 
I've been told that the people at Maple at actively working on these
type of integrals.

Thanks to all who responded,

--
-------------------------------------------------------------
Richard Gerber
Grad Student Physics
gerber@rigel.astro.uiuc.edu
University of Illinois @ Urbana-Champaign
------------------------------------------------------------- 
Newsgroups: sci.math.symbolic