Learn how to solve problems step by step online. Find the integral int((6x^2-2x+-1)/(x^3+x^2-2x))dx. Rewrite the expression \frac{6x^2-2x-1}{x^3+x^2-2x} inside the integral in factored form. Rewrite the fraction \frac{6x^2-2x-1}{x\left(x+2\right)\left(x-1\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{2x}+\frac{9}{2\left(x+2\right)}+\frac{1}{x-1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{2x}dx results in: \frac{1}{2}\ln\left(x\right).

Find the integral int((6x^2-2x+-1)/(x^3+x^2-2x))dx