Learn how to solve problems step by step online. Find the integral int(x(3x^2+3x+1)/(x^3+2x^22x+1))dx. Multiplying the fraction by x. We can factor the polynomial x^3+2x^2+2x+1 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+2x^2+2x+1 will then be.

Find the integral int(x(3x^2+3x+1)/(x^3+2x^22x+1))dx