On Mon, 13 Nov 2023 at 21:32, Bùi Gia Nghĩa <nghiatha...@gmail.com> 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.
