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$\int\frac{x^2}{x^3+3x+1+3x^2}dx$
Learn how to solve problems step by step online. Find the integral of (x^2)/(x^3+3x+13x^2). Find the integral. We can factor the polynomial x^3+3x+1+3x^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 1. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^3+3x+1+3x^2 will then be.