Đáp án:

• \( \int \frac{1}{x^2(1+x)} \, dx = \int \frac{1 + x - x}{x^2(1+x)} \, dx \)

\( = \int \frac{1}{x^2} \, dx - \int \frac{1}{x(1+x)} \, dx \)

\( = -\frac{1}{x} - \int \left( \frac{1}{x} - \frac{1}{x+1} \right) \, dx \)

\( = -\frac{1}{x} - \ln \left| \frac{x}{x+1} \right| + C \)