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- Integrate by partial fractions
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Rewrite the fraction $\frac{x^3+x^2-5x+15}{\left(x^2+5\right)\left(x^2+2x+3\right)}$ in $2$ simpler fractions using partial fraction decomposition
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$\frac{-5}{x^2+5}+\frac{x+6}{x^2+2x+3}$
Learn how to solve problems step by step online. Find the integral int((x^3+x^2-5x+15)/((x^2+5)(x^2+2x+3)))dx. Rewrite the fraction \frac{x^3+x^2-5x+15}{\left(x^2+5\right)\left(x^2+2x+3\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-5}{x^2+5}+\frac{x+6}{x^2+2x+3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-5}{x^2+5}dx results in: -5\cdot \left(\frac{1}{\sqrt{5}}\right)\arctan\left(\frac{x}{\sqrt{5}}\right). Gather the results of all integrals.
