By equating coefficients, we get A = 0 A=0, B = 4 B=4, and C = 4 C=4. Thus: \[ \int \frac{4}{x^2(2+x)} , dx = \int \left(\frac{4}{x^2} - \frac{4}{2+x} ight) , dx = -\frac{4}{x} - 4\ln|2+x| C_4 \]