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- Integrate by partial fractions
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Rewrite the fraction $\frac{-9x-9}{x\left(x^2-9\right)}$ in $2$ simpler fractions using partial fraction decomposition
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$\frac{1}{x}+\frac{-x-9}{x^2-9}$
Learn how to solve problems step by step online. Find the integral int((-9x-9)/(x(x^2-9)))dx. Rewrite the fraction \frac{-9x-9}{x\left(x^2-9\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{x}+\frac{-x-9}{x^2-9}\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-9}{x^2-9}dx results in: \ln\left(\frac{3}{\sqrt{x^2-9}}\right)+\frac{3}{2}\ln\left(x+3\right)-\frac{3}{2}\ln\left(x-3\right).
