Re: [sage-support] Integral result differ from Wolfram|Alpha
On Mon, 13 Nov 2023 at 21:32, Bùi Gia Nghĩa wrote: > > Hi! > I have used Sage Cell Server to integrate the function (ln(x)^2 - 1) / (x * > ln(x)). It should resulted in (ln(x)^2) / 2 - |ln(ln(x))| + C, as noted by my > textbook and Wolfram|Alpha, but instead resulted in 1/2*log(x)^2 - > 1/2*log(log(x)^2). Your textbook assumes that you are only interested in real antiderivatives and so describes the antiderivative with abs that is not complex-differentiable (i.e. not valid for non-real values of x). The result from Sage is valid for e.g. x = 1+i whereas your textbook result would be incorrect in that case. -- Oscar -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAHVvXxTrpcPGrhTnfVfNkKvyf-dJBr-BCzT_NEqVonKRDEt8bQ%40mail.gmail.com.
Re: [sage-support] Re: Integral result differ from Wolfram|Alpha
Oh that's why! Thank you because that is exactly the problem!
On Tue, Nov 14, 2023, 4:54 AM John H Palmieri
wrote:
> Isn't log(log(x)^2) = 2 * log(log(x))? Is this your concern, or is it the
> absolute value?
>
> On Monday, November 13, 2023 at 1:32:11 PM UTC-8 Bùi Gia Nghĩa wrote:
>
>> Hi!
>> I have used Sage Cell Server to integrate the function (ln(x)^2 - 1) / (x
>> * ln(x)). It should resulted in (ln(x)^2) / 2 - |ln(ln(x))| + C, as noted
>> by my textbook and Wolfram|Alpha, but instead resulted in 1/2*log(x)^2 -
>> 1/2*log(log(x)^2).
>> (I do notice that SageMath use log(a) to denote natural logarithm, so
>> that's not the question here).
>> Anyone knows why it happen? I think that this is a bug from some system
>> SageMath use to calculate this, but I am new to SageMath so have zero
>> knowledge about the system.
>> Here is the exact code I input:
>> var("x")
>> f = (log(x)**2 - 1) / (x * log(x))
>> integral(f, x)
>>
>> Thanks in advance!
>>
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[sage-support] Re: Integral result differ from Wolfram|Alpha
Isn't log(log(x)^2) = 2 * log(log(x))? Is this your concern, or is it the
absolute value?
On Monday, November 13, 2023 at 1:32:11 PM UTC-8 Bùi Gia Nghĩa wrote:
> Hi!
> I have used Sage Cell Server to integrate the function (ln(x)^2 - 1) / (x
> * ln(x)). It should resulted in (ln(x)^2) / 2 - |ln(ln(x))| + C, as noted
> by my textbook and Wolfram|Alpha, but instead resulted in 1/2*log(x)^2 -
> 1/2*log(log(x)^2).
> (I do notice that SageMath use log(a) to denote natural logarithm, so
> that's not the question here).
> Anyone knows why it happen? I think that this is a bug from some system
> SageMath use to calculate this, but I am new to SageMath so have zero
> knowledge about the system.
> Here is the exact code I input:
> var("x")
> f = (log(x)**2 - 1) / (x * log(x))
> integral(f, x)
>
> Thanks in advance!
>
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[sage-support] Integral result differ from Wolfram|Alpha
Hi!
I have used Sage Cell Server to integrate the function (ln(x)^2 - 1) / (x *
ln(x)). It should resulted in (ln(x)^2) / 2 - |ln(ln(x))| + C, as noted by
my textbook and Wolfram|Alpha, but instead resulted in 1/2*log(x)^2 -
1/2*log(log(x)^2).
(I do notice that SageMath use log(a) to denote natural logarithm, so
that's not the question here).
Anyone knows why it happen? I think that this is a bug from some system
SageMath use to calculate this, but I am new to SageMath so have zero
knowledge about the system.
Here is the exact code I input:
var("x")
f = (log(x)**2 - 1) / (x * log(x))
integral(f, x)
Thanks in advance!
--
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