Learn how to solve problems step by step online. Find the integral int((x^3-x+1)/((x+2)^2(x-1)^2))dx. Rewrite the fraction \frac{x^3-x+1}{\left(x+2\right)^2\left(x-1\right)^2} in 4 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-5}{9\left(x+2\right)^2}+\frac{1}{9\left(x-1\right)^2}+\frac{23}{27\left(x+2\right)}+\frac{4}{27\left(x-1\right)}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-5}{9\left(x+2\right)^2}dx results in: \frac{5}{9\left(x+2\right)}. The integral \int\frac{1}{9\left(x-1\right)^2}dx results in: \frac{-1}{9\left(x-1\right)}.

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