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$\int\frac{x^2-x+1}{\left(x^2-1\right)\left(x-1\right)^3}dx$
Learn how to solve differential equations problems step by step online. Integrate the function (x^2-x+1)/((x^2-1)(x-1)^3). Find the integral. Factor the difference of squares \left(x^2-1\right) as the product of two conjugated binomials. When multiplying exponents with same base you can add the exponents: \left(x+1\right)\left(x-1\right)^3\left(x-1\right). Rewrite the fraction \frac{x^2-x+1}{\left(x+1\right)\left(x-1\right)^{4}} in 5 simpler fractions using partial fraction decomposition.