Найти интерграл [tex] \int\limits^a_b {dx/ x (1 + ln^(2) x} [/tex]. Created by liksa456. matematika-ru

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Найти интерграл
[tex] \int\limits^a_b {dx/ x (1 + ln^(2) x} [/tex]

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ProGroomer

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$\int\limits^a_b {dx\over x(1+\ln^2 x)} =\{t=\ln x, dt={dx\over x}\}= \int\limits^a_b {dt\over 1+t^2} \, dx =(arctg(t))|^{^a}_{_b}=\\=arctg(\ln a)-arctg(\ln b)$

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