Question

Evaluate the ∫(1-1/x)² dx

Answer 1

Solution.

$$\int(1-\frac{1}{x})^2dx=$$ $$\int(1-\frac{2}{x}+\frac{1}{x^2})dx=$$ $$\int1dx-2\int\frac{1}{x}dx+\int\frac{1}{x^2}dx=$$ $$x-2\ln{|x|}+\frac{x^{-1}}{-1}+C=$$ $$x-2\ln{|x|}-\frac{1}{x}+C,$$

where $C$ is some constant.

Answer. $x-2\ln{|x|}-\frac{1}{x}+C.$