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

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