Learn how to solve limits by direct substitution problems step by step online. Find the integral int((x+1)/(x^3+x^2-6x))dx. Rewrite the expression \frac{x+1}{x^3+x^2-6x} inside the integral in factored form. Rewrite the fraction \frac{x+1}{x\left(x+3\right)\left(x-2\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-1}{6x}+\frac{-2}{15\left(x+3\right)}+\frac{3}{10\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}{6x}dx results in: -\frac{1}{6}\ln\left(x\right).

Find the integral int((x+1)/(x^3+x^2-6x))dx