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

Find the integral int((-2x^2+8x+8)/((x^2+4)(x-2)^3))dx