Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((5x-18)/(x(x^2-5x+6)))dx. Rewrite the expression \frac{5x-18}{x\left(x^2-5x+6\right)} inside the integral in factored form. Rewrite the fraction \frac{5x-18}{x\left(x-2\right)\left(x-3\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-3}{x}+\frac{4}{x-2}+\frac{-1}{x-3}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-3}{x}dx results in: -3\ln\left(x\right).

Find the integral int((5x-18)/(x(x^2-5x+6)))dx