Question

найти интеграл:
dx/x^2-2x

Answer 1

$int {} , frac{dx}{x^2-2x}= int {} , frac{dx}{x^2-2x+1-1}=int {} , frac{dx}{(x-1)^2-1}= \ =int {} , frac{d(x-1)}{(x-1)^2-1}=-int {} , frac{d(x-1)}{1-(x-1)^2}=- frac{1}{2}ln| frac{1+x-1}{1-(x-1)} |+C= \ =- frac{1}{2}ln| frac{x}{2-x} |+C$