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