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