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

Find the integral int((5x-4)/((x-1)^2(x+1)))dx