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 expression $\frac{1}{x^3+x}$ inside the integral in factored form
$\int\frac{1}{x\left(x^2+1\right)}dx$
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$\int\frac{1}{x\left(x^2+1\right)}dx$
Learn how to solve problems step by step online. Find the integral int(1/(x^3+x))dx. Rewrite the expression \frac{1}{x^3+x} inside the integral in factored form. 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).
Final answer to the problem
$\ln\left|x\right|-\frac{1}{2}\ln\left|x^2+1\right|+C_0$
