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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