Final answer to the problem
$\frac{1}{2}x^2+\frac{-19\sqrt{3}\arctan\left(\frac{-3+2x}{\sqrt{3}}\right)}{7}-\frac{25}{7}\ln\left|\sqrt{\left(x-\frac{3}{2}\right)^2+\frac{3}{4}}\right|+\frac{4}{7}\ln\left|x+1\right|+C_2$
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Step-by-step Solution
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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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1
Rewrite the expression $\frac{x^4-3x^2-x-2x^3+3}{x^3-2x^2+3}$ inside the integral in factored form
Learn how to solve problems step by step online.
$\int\frac{x^4-3x^2-x-2x^3+3}{\left(x^{2}-3x+3\right)\left(x+1\right)}dx$
Learn how to solve problems step by step online. Find the integral int((x^4-3x^2-x-2x^3+3)/(x^3-2x^2+3))dx. Rewrite the expression \frac{x^4-3x^2-x-2x^3+3}{x^3-2x^2+3} inside the integral in factored form. Expand. Divide x^4-3x^2-x-2x^3+3 by x^{3}-2x^2+3. Resulting polynomial.
Final answer to the problem
$\frac{1}{2}x^2+\frac{-19\sqrt{3}\arctan\left(\frac{-3+2x}{\sqrt{3}}\right)}{7}-\frac{25}{7}\ln\left|\sqrt{\left(x-\frac{3}{2}\right)^2+\frac{3}{4}}\right|+\frac{4}{7}\ln\left|x+1\right|+C_2$
