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

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