Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- 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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Find the integral
Learn how to solve differential equations problems step by step online.
$\int\frac{\frac{-1}{x^3+2x^2+x}}{x^3+x^2-x-1}dx$
Learn how to solve differential equations problems step by step online. Integrate the function (-1/(x^3+2x^2x))/(x^3+x^2-x+-1). Find the integral. Divide fractions \frac{\frac{-1}{x^3+2x^2+x}}{x^3+x^2-x-1} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. We can factor the polynomial \left(x^3+2x^2+x\right) 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 0. Next, list all divisors of the leading coefficient a_n, which equals 1.
