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Rewrite the fraction $\frac{1}{x\left(x^2+x+1\right)}$ in $2$ simpler fractions using partial fraction decomposition
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$\frac{1}{x}+\frac{-x-1}{x^2+x+1}$
Learn how to solve problems step by step online. int(1/(x(x^2+x+1)))dx. Rewrite the fraction \frac{1}{x\left(x^2+x+1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{x}+\frac{-x-1}{x^2+x+1}\right)dx into 2 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-1}{x^2+x+1}dx results in: -\int\frac{x+1}{x^2+x+1}dx.