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- Integrate by partial fractions
- Integrate by substitution
- 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
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We can factor the polynomial $2x^3+9x^2+14x+8$ 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 $8$
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$1, 2, 4, 8$
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((2x^3+9x^214x+8)/(x(x+2)(x^2+2)))dx. We can factor the polynomial 2x^3+9x^2+14x+8 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 8. Next, list all divisors of the leading coefficient a_n, which equals 2. The possible roots \pm\frac{p}{q} of the polynomial 2x^3+9x^2+14x+8 will then be. Trying all possible roots, we found that -2 is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.
