Как решается интеграл: dx/x (1+x) ^2.

1/x (1+x) ^2 = A/x + B / (1+x) + C / (1+x) ^2

A * (1+x) ^2 + B*x * (1+x) + C*x = 1

Ax^2 + 2Ax + A + Bx^2 + Bx + Cx = 1

(^0) - - > A = 1

(^1) - > 2A + B + C = 0

(^2) - > A + B = 0

--> A = 1, B = - 1, C = - 1

1/x (1+x) ^2 = 1/x - 1 / (1+x) - 1 / (1+x) ^2

--> ∫ dx/x (1+x) ^2 = ∫ dx/x - ∫ dx / (1+x) - ∫ dx / (1+x) ^2 = ln|x| - ln|1+x| + 1 / (1+x) + C