Learn how to solve problems step by step online. Find the integral int((x^2-4x+-8)/((x+1)(x^2-4)))dx. Rewrite the expression \frac{x^2-4x-8}{\left(x+1\right)\left(x^2-4\right)} inside the integral in factored form. Rewrite the fraction \frac{x^2-4x-8}{\left(x+1\right)\left(x+2\right)\left(x-2\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{x+1}+\frac{1}{x+2}+\frac{-1}{x-2}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{x+1}dx results in: \ln\left(x+1\right).

Find the integral int((x^2-4x+-8)/((x+1)(x^2-4)))dx