Question

Интеграл dx/x^2-2x+1

Answer 1

$\int \frac{dx}{x^2-2x+1} =\int \frac{dx}{(x-1)^2}=\Big [\, t=x-1\; ,\; dt=dx\, \Big ]=\\\\=\int \frac{dt}{t^2}=\int t^{-2}\, dt=\frac{t^{-1}}{-1}+C=-\frac{1}{t}+C=- \frac{1}{x-1}+C$