Learn how to solve problems step by step online. Find the integral int((3x+2)/(x^2(x+1)))dx. Rewrite the fraction \frac{3x+2}{x^2\left(x+1\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{2}{x^2}+\frac{-1}{x+1}+\frac{1}{x}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{2}{x^2}dx results in: \frac{-2}{x}. The integral \int\frac{-1}{x+1}dx results in: -\ln\left(x+1\right).

Find the integral int((3x+2)/(x^2(x+1)))dx