Learn how to solve problems step by step online. Find the integral int((3x+1)/((x-1)^2(x+2)))dx. Rewrite the fraction \frac{3x+1}{\left(x-1\right)^2\left(x+2\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{4}{3\left(x-1\right)^2}+\frac{-5}{9\left(x+2\right)}+\frac{5}{9\left(x-1\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{4}{3\left(x-1\right)^2}dx results in: \frac{-4}{3\left(x-1\right)}. The integral \int\frac{-5}{9\left(x+2\right)}dx results in: -\frac{5}{9}\ln\left(x+2\right).

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