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- Integrate by partial fractions
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Rewrite the fraction $\frac{5x^2+5x-4}{\left(x+2\right)\left(x+1\right)\left(x^2+x+1\right)}$ in $3$ simpler fractions using partial fraction decomposition
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$\frac{-2}{x+2}+\frac{-4}{x+1}+\frac{6x+3}{x^2+x+1}$
Learn how to solve problems step by step online. Find the integral int((5x^2+5x+-4)/((x+2)(x+1)(x^2+x+1)))dx. Rewrite the fraction \frac{5x^2+5x-4}{\left(x+2\right)\left(x+1\right)\left(x^2+x+1\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-2}{x+2}+\frac{-4}{x+1}+\frac{6x+3}{x^2+x+1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-2}{x+2}dx results in: -2\ln\left(x+2\right). The integral \int\frac{-4}{x+1}dx results in: -4\ln\left(x+1\right).