Re: Understanding the Output

• To: mathgroup at smc.vnet.net
• Subject: [mg32811] Re: [mg32792] Understanding the Output
• From: BobHanlon at aol.com
• Date: Thu, 14 Feb 2002 01:43:26 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 2/12/02 7:30:46 AM, smitsky at mindspring.com writes:

>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
>

Integrate[Sqrt[x-1],x]//Simplify

(2/3)*(x - 1)^(3/2)

Integrate[-x^3 (1-x^4)^5,x]//FullSimplify

(1/24)*x^4*(x^4 - 2)*(x^8 - 3*x^4 + 3)*(x^8 - x^4 + 1)

%-1/24(1-x^4)^6 // Simplify

-(1/24)

They differ by a constant so they are both the integral of the input;
however, you will not be able to Simplify one to the other since they are not
equal.

Bob Hanlon
Chantilly, VA  USA

```

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