Re: Re: Integral confusion

• To: mathgroup at smc.vnet.net
• Subject: [mg107316] Re: [mg107297] Re: Integral confusion
• From: "Nasser M. Abbasi" <nma at 12000.org>
• Date: Tue, 9 Feb 2010 02:44:02 -0500 (EST)
• References: <hkm7d8\$os0\$1@smc.vnet.net> <201002080836.DAA29853@smc.vnet.net> <op.u7tlcde4tgfoz2@bobbys-imac.local>
• Reply-to: "Nasser M. Abbasi" <nma at 12000.org>

```The "weird" thing is not what specific constant of integration it returned,
but the fact that it did return one at all.

Integrate[x^2, x] gives x^3/2. not x^3/2+Pi*Sqrt[-1]  or x^3/2+99 even
though both are correct.

> I don't know Integrate's steps in obtaining the result, but I'm sure it
> didn't add extraneous constants deliberately.

Ofcourse. I am sure of that too. But the final result is NOT what one would
normally see in a textbook or expect or do when solving by hand, even though
as I said, it is correct. It is just not "normal" looking.

I am sorry, I did not mean to say anything bad about Mathematica when I said
this result was "weird" even though it is correct.

--Nasser

----- Original Message -----
From: "DrMajorBob" <btreat1 at austin.rr.com>
To: "Nasser M. Abbasi" <nma at 12000.org>; <mathgroup at smc.vnet.net>
Sent: Monday, February 08, 2010 9:54 AM
Subject: [mg107316] Re: [mg107297] Re: Integral confusion

>> But Mathematica does (normally?) return results for indefinite integrals
>> without an explicit constant of integration.
>
> What's "explicit" or weird about the constants of integration in this
> problem?
>
> I don't know Integrate's steps in obtaining the result, but I'm sure it
> didn't add extraneous constants deliberately.
>
> Bobby
>
> On Mon, 08 Feb 2010 02:36:16 -0600, Nasser M. Abbasi <nma at 12000.org>
> wrote:
>
>>
>> "Jon Joseph" <josco.jon at gmail.com> wrote in message
>> news:hkm7d8\$os0\$1 at smc.vnet.net...
>>> All: Is this integral wrong? If not could someone explain the minus sign
>>> inside the log?
>>>
>>> Integrate[1/(x + 1) - 1/(x + 6), x] // Simplify
>>>
>>> log(-2 (x + 1)) - log(2 (x + 6))
>>>
>>> Thanks, Jon.=
>>>
>>
>> Well, lets see:
>>
>> log(-2 (x + 1)) - log(2 (x + 6))
>>           = log(-2)+log(1+x) -log(2)-log(x+6)
>>           = log(-1)+log(2)+log(1+x)-log(2)-log(x+6)
>>           = log(-1)+ log(1+x) - log(x+6)
>>
>> but log(-1) = Sqrt[-1]*Pi
>>
>> so result is
>>
>>          Sqrt[-1]*Pi + log(1+x) - log(x+6)
>>
>> But we all know that the result should be
>>
>>          log(1+x) - log(x+6)
>>
>> So, an extra term, Sqrt[-1]*Pi term pops up. But this term is a
>> constant, so
>> its derivative is zero, i.e. a constant of integration.
>>
>> Since
>>
>> D[log(-2 (x + 1)) - log(2 (x + 6)),x] will give back
>>
>>                1/(x + 1) - 1/(x + 6)
>>
>> So, in theory, the answer given by Mathematica is NOT wrong.
>>
>> But Mathematica does (normally?) return results for indefinite integrals
>> without an explicit constant of integration. So I am not sure why it
>> does in
>> this case, and if it it does, why did not pick this constant? Why not
>> C[1]
>> as it does for DSolve[]?
>>
>> So, if I have to guess, I'd say this result is at least very weired, but
>> mathematically it is not wrong?
>>
>> --Nasser
>>
>>
>>
>
>
> --
> DrMajorBob at yahoo.com

```

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