Final answer to the problem
$2x-5\arctan\left(\frac{x}{2}\right)+\frac{6x}{x^{2}+4}+\frac{5}{-2\left(x^{2}+4\right)}+C_0$
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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
Rewrite the expression $\frac{2x^5+5x^2+16x}{x^5+8x^3+16x}$ inside the integral in factored form
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$\int\frac{2x^{4}+5x+16}{\left(x^{2}+4\right)^{2}}dx$
Learn how to solve problems step by step online. Find the integral int((2x^5+5x^216x)/(x^5+8x^316x))dx. Rewrite the expression \frac{2x^5+5x^2+16x}{x^5+8x^3+16x} inside the integral in factored form. Expand. Divide 2x^{4}+5x+16 by x^{4}+8x^{2}+16. Resulting polynomial.
Final answer to the problem
$2x-5\arctan\left(\frac{x}{2}\right)+\frac{6x}{x^{2}+4}+\frac{5}{-2\left(x^{2}+4\right)}+C_0$
