Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((-2x+1)/(x^3+6x^212x+8))dx. Rewrite the expression \frac{-2x+1}{x^3+6x^2+12x+8} inside the integral in factored form. Rewrite the fraction \frac{-2x+1}{\left(x+2\right)^{3}} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-2}{\left(x+2\right)^{2}}+\frac{5}{\left(x+2\right)^{3}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-2}{\left(x+2\right)^{2}}dx results in: \frac{2}{x+2}.

Find the integral int((-2x+1)/(x^3+6x^212x+8))dx