Learn how to solve problems step by step online. Find the integral int((x+3)/(x^3-5x^26x))dx. Rewrite the expression \frac{x+3}{x^3-5x^2+6x} inside the integral in factored form. Rewrite the fraction \frac{x+3}{x\left(x-3\right)\left(x-2\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{2x}+\frac{2}{x-3}+\frac{-5}{2\left(x-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((x+3)/(x^3-5x^26x))dx