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