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