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

Find the integral int((x^2-x+18)/(x^3+3x))dx