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- Integrate by partial fractions
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Rewrite the fraction $\frac{4x^2+2x+8}{x\left(x^2+2\right)^2}$ in $3$ simpler fractions using partial fraction decomposition
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$\frac{2}{x}+\frac{2}{\left(x^2+2\right)^2}+\frac{-2x}{x^2+2}$
Learn how to solve quadratic equations problems step by step online. Find the integral int((4x^2+2x+8)/(x(x^2+2)^2))dx. Rewrite the fraction \frac{4x^2+2x+8}{x\left(x^2+2\right)^2} in 3 simpler fractions using partial fraction decomposition. Simplify the expression. The integral \int\frac{2}{x}dx results in: 2\ln\left|x\right|. The integral \int\frac{2}{\left(x^2+2\right)^2}dx results in: \frac{\sqrt{2}}{2}\left(\frac{1}{2}\arctan\left(\frac{x}{\sqrt{2}}\right)+\frac{\sqrt{2}x}{2\left(x^2+2\right)}\right).