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$\int\frac{x^4-2x^3-3x^2-x+3}{\left(x^3-8x^2+16x\right)\left(x^2-9\right)}dx$
Learn how to solve integral calculus problems step by step online. Find the integral of (x^4-2x^3-3x^2-x+3)/((x^3-8x^216x)(x^2-9)). Find the integral. We can factor the polynomial x^4-2x^3-3x^2-x+3 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 3. 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^3-3x^2-x+3 will then be.