The discussion revolves around the integral of arctg(x) divided by the square root of (1-x^2). Participants explore various methods for solving this integral, including substitution and series expansion, while expressing concerns about the appropriateness of certain techniques given the audience's background.
Participants express differing opinions on the methods to be used for solving the integral, with some advocating for series expansion and others insisting on traditional methods. There is no consensus on the best approach.
Some participants highlight the limitations of the audience's knowledge, specifically mentioning that they have not studied series yet, which affects the applicability of certain proposed methods.
Students and educators interested in integral calculus, particularly those exploring different methods of integration and the challenges of teaching complex topics without prior foundational knowledge.
leprofece said:integral of arctg(x)/sqrt(1-x^2)
maybe u = arctg x du = 1 /1+x^2
but x = tg u
maybe this is the way isn't it?
chisigma said:A possible approach is to use the MacLaurin expansion...
$\displaystyle \frac{\tan^{-1} x}{\sqrt{1-x^{2}}} = x + \frac{1}{6}\ x^{3} + \frac{49}{120}\ x^{5} + \frac{81}{560}\ x^{7} + \mathcal{O}\ (x^{9})\ (1)$
... and to integrate term by term...
Kind regards $\chi$ $\sigma$
leprofece said:Thank for your answer but you must solve it by normal or traditional methods students have not studied series yet
Could anybody do that way??