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- Integrate by substitution
- Integrate by partial fractions
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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$\int\frac{3x^4-9x^3-32x^2+11x-5}{x-5}dx$
Learn how to solve problems step by step online. Integrate the function (3x^4-9x^3-32x^211x+-5)/(x-5). Find the integral. We can factor the polynomial 3x^4-9x^3-32x^2+11x-5 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 -5. Next, list all divisors of the leading coefficient a_n, which equals 3. The possible roots \pm\frac{p}{q} of the polynomial 3x^4-9x^3-32x^2+11x-5 will then be.