Learn how to solve problems step by step online. Find the integral int((x-2)/((x^2+2x+2)(x-4)))dx. Rewrite the fraction \frac{x-2}{\left(x^2+2x+2\right)\left(x-4\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-\frac{1}{13}x+\frac{7}{13}}{x^2+2x+2}+\frac{1}{13\left(x-4\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{13\left(x-4\right)}dx results in: \frac{1}{13}\ln\left(x-4\right). Gather the results of all integrals.

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