Re: Understanding the Output

• To: mathgroup at smc.vnet.net
• Subject: [mg32825] Re: Understanding the Output
• From: adam.smith at hillsdale.edu (Adam Smith)
• Date: Thu, 14 Feb 2002 01:43:48 -0500 (EST)
• References: <a4au3v\$bs9\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Steven,

The results you get and mathematica are essentially the same.  This
can be seen below:

In[25]:=
thing = Integrate[(x - 1)^(1/2), x]

Out[25]=
(-(2/3) + (2*x)/3)*Sqrt[-1 + x]

In[27]:=
FullSimplify[thing]

Out[27]=
(2/3)*(-1 + x)^(3/2)

In[28]:=
other = Integrate[x^3*(1 - x^4)^5, x]

Out[28]=
x^4/4 - (5*x^8)/8 + (5*x^12)/6 - (5*x^16)/8 + x^20/4 -
x^24/24

In[30]:=
Expand[(-24^(-1))*(1 - x^4)^6]

Out[30]=
-(1/24) + x^4/4 - (5*x^8)/8 + (5*x^12)/6 - (5*x^16)/8 +
x^20/4 - x^24/24

For the "(x - 1)^(1/2), I don't know why your FullSimplify did not
work.

For the "x^3*(1 - x^4)^5" integral, the two differ only by the
constant term:
-1/24.  This is not really a difference because indefinite integrals
always have an undetermined additive constant.

"Steven Spear" <smitsky at mindspring.com> wrote in message news:<a4au3v\$bs9\$1 at smc.vnet.net>...
> 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

```

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