Learn how to solve problems step by step online. Find the integral int((2-x)/(x(9x^2-12x+4)))dx. Rewrite the expression \frac{2-x}{x\left(9x^2-12x+4\right)} inside the integral in factored form. Rewrite the fraction \frac{2-x}{x\left(3x-2\right)^{2}} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{2x}+\frac{2}{\left(3x-2\right)^{2}}+\frac{-3}{2\left(3x-2\right)}\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((2-x)/(x(9x^2-12x+4)))dx