Learn how to solve problems step by step online. Find the integral int((4x)/(x^3-x^2x+-1))dx. Rewrite the expression \frac{4x}{x^3-x^2+x-1} inside the integral in factored form. Take out the constant 4 from the integral. Rewrite the fraction \frac{x}{\left(x^{2}+1\right)\left(x-1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-\frac{1}{2}x+\frac{1}{2}}{x^{2}+1}+\frac{1}{2\left(x-1\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.

Find the integral int((4x)/(x^3-x^2x+-1))dx