Re: Understanding the Output

• To: mathgroup at smc.vnet.net
• Subject: [mg32808] Re: Understanding the Output
• From: Erk Jensen <Erk.Jensen at cern.ch>
• Date: Thu, 14 Feb 2002 01:43:22 -0500 (EST)
• Organization: CERN http://www.cern.ch
• References: <a4au3v\$bs9\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Steven Spear wrote:
>
> Hi. I'm having trouble understanding some output in Mathematica. If I enter
> Int [x-1] dx, the output I receive is ((-2/3) + (2x/3)) Sqrt(-1+x). If I do
> the calculation by hand, I get 2/3.(x-1)^3/2. If I perform:
> FullSimplify(((-2/3) + (2x/3)) Sqrt(-1+x)), I get the same answer
> (2/3.(x-1)^3/2).
>
> With trying to use u-substitution, and figuring more complex Integrals, it
> get harder to discern the output. For instance: I tried to evaluate the
> Integral Int [x^3 (1-x^4)^5] dx. I may not be correct, but by hand I got
> 1/24.(1-x^4)^6. Mathematica gave a very different output, and using
> FullSimplify didn't seem to help.
>
> Is there any way to get Mathematica to output these values a little
> differently? Am I incorrect on the second example? Any ideas will be
> appreciated. Thanks, Steve

Hi Steve,

I don't have a problem with the first output, since it is the same that you get.

In the second case, try
Simplify[Integrate[x^3 (1-x^4)^5,x]-1/24] and you'll be happy.

Remember that to the indefinite integral you can always add an arbitrary
constant, which happens to be different, und thus, simplification didn't work
the way you expected. The result is however correct

Cheers
-erk-
--
Dr.-Ing. Erk JENSEN                    mailto:Erk.Jensen at cern.ch
CERN  PS/RF  L19510                    http://cern.ch/Erk.Jensen
CH-1211 Geneva 23                      Tel.:     +41 22 76 74298
Switzerland                            Fax.:     +41 22 76 78510

```

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