Final answer to the problem
$\ln\left|x\right|-\frac{1}{2}\ln\left|x^2+1\right|+C_0$
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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 fraction $\frac{1}{x\left(x^2+1\right)}$ in $2$ simpler fractions using partial fraction decomposition
$\frac{1}{x}+\frac{-x}{x^2+1}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int(1/(x(x^2+1)))dx. Rewrite the fraction \frac{1}{x\left(x^2+1\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+1}dx results in: -\frac{1}{2}\ln\left(x^2+1\right).
Final answer to the problem
$\ln\left|x\right|-\frac{1}{2}\ln\left|x^2+1\right|+C_0$
