Final answer to the problem
$x-\frac{8}{81}\ln\left|x\right|+\frac{15x}{2\left(x^2+9\right)}-\frac{11}{2}\arctan\left(\frac{x}{3}\right)+\frac{23}{9\left(x^2+9\right)}+\frac{8}{81}\ln\left|\sqrt{x^2+9}\right|+C_1$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
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- Integrate using tabular integration
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- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Expand
$\int\frac{x^5-6x^3-6x^2-8}{x^{5}+18x^{3}+81x}dx$
Learn how to solve problems step by step online. Find the integral int((x^5-6x^3-6x^2+-8)/(x(x^2+9)^2))dx. Expand. Divide x^5-6x^3-6x^2-8 by x^{5}+18x^{3}+81x. Resulting polynomial. Simplify the expression.
Final answer to the problem
$x-\frac{8}{81}\ln\left|x\right|+\frac{15x}{2\left(x^2+9\right)}-\frac{11}{2}\arctan\left(\frac{x}{3}\right)+\frac{23}{9\left(x^2+9\right)}+\frac{8}{81}\ln\left|\sqrt{x^2+9}\right|+C_1$
