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$\int\frac{x^3-x^2-5x-3}{x^4+2x^3-x^2-4x-2}dx$
Learn how to solve equations problems step by step online. Integrate the function (x^3-x^2-5x+-3)/(x^4+2x^3-x^2-4x+-2). Find the integral. We can factor the polynomial x^4+2x^3-x^2-4x-2 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -2. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^4+2x^3-x^2-4x-2 will then be.