Learn how to solve problems step by step online. Find the integral int(6/(x^3-5x^2-6x))dx. Rewrite the expression \frac{6}{x^3-5x^2-6x} inside the integral in factored form. Rewrite the fraction \frac{6}{x\left(x-6\right)\left(x+1\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-1}{x}+\frac{1}{7\left(x-6\right)}+\frac{6}{7\left(x+1\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-1}{x}dx results in: -\ln\left(x\right).

Find the integral int(6/(x^3-5x^2-6x))dx