Как найти определённый интеграл от функции (x–1)/(x^2–2)/(x^2–2x+2) на промежутке от 0 до 1?

Find the definite integral of the function (x–1)/(x^2–2)/(x^2–2x+2) over the interval from 0 to 1. It turns out that the problem can be solved even without factoring the integrand into simple fractions or using the Newton-Leibniz formula. Simply use a few substitutions, including a trigonometric one, and then express the integral in terms of itself. Video on the @Hmath channel:    • Число Пи: вывод формулы Бэйли-Боруэйна-Плаффа