Learn how to solve problems step by step online. Find the integral int((4x^2+2x+-1)/(x^4-2x^2+-8))dx. Rewrite the expression \frac{4x^2+2x-1}{x^4-2x^2-8} inside the integral in factored form. Rewrite the fraction \frac{4x^2+2x-1}{\left(x^{2}+2\right)\left(x+2\right)\left(x-2\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-\frac{1}{3}x+\frac{3}{2}}{x^{2}+2}+\frac{-11}{24\left(x+2\right)}+\frac{19}{24\left(x-2\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-\frac{1}{3}x+\frac{3}{2}}{x^{2}+2}dx results in: \frac{1}{3}\ln\left(\frac{\sqrt{2}}{\sqrt{x^{2}+2}}\right)+\frac{3\arctan\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{\left(2\right)^{3}}}.

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