Final answer to the problem
$\ln\left|x\right|+\ln\left|\frac{2}{\sqrt{x^2+4}}\right|+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
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- Weierstrass Substitution
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1
Rewrite the fraction $\frac{4}{x\left(x^2+4\right)}$ in $2$ simpler fractions using partial fraction decomposition
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$\frac{1}{x}+\frac{-x}{x^2+4}$
Learn how to solve problems step by step online. Find the integral int(4/(x(x^2+4)))dx. Rewrite the fraction \frac{4}{x\left(x^2+4\right)} in 2 simpler fractions using partial fraction decomposition. Simplify the expression. The integral \int\frac{1}{x}dx results in: \ln\left(x\right). The integral -\int\frac{x}{x^2+4}dx results in: \ln\left(\frac{2}{\sqrt{x^2+4}}\right).
Final answer to the problem
$\ln\left|x\right|+\ln\left|\frac{2}{\sqrt{x^2+4}}\right|+C_0$
